Intelligent collaborative control method for box packing and case packing production line based on multi-station linkage

Abstract

This invention discloses an intelligent collaborative control method for a boxing and packaging production line based on multi-workstation linkage, belonging to the field of intelligent production line control technology. The method collects material information to generate unique IDs and constructs material state vectors, defines five system states of the production line and their transition rules, and builds a finite state machine model containing a master state machine and workstation sub-state machines. Based on the model and state vectors, it generates abnormal linkage response strategies and collaborative control instructions, trains a deep Q-network model to output the optimal cycle time combination, and trains a long short-term memory network model to predict the probability of workstation failures. Combining the failure probability with the optimal cycle time combination, when a threshold is exceeded, a preventative maintenance plan and corresponding control instructions are generated and executed. This invention achieves intelligent collaborative control of multiple workstations on the production line, optimizes production cycle time, implements preventative maintenance, improves operating efficiency and stability, and reduces energy consumption and downtime rates.

Description

Technical Field

[0001] This invention relates to the field of automated production line control technology, specifically to an intelligent collaborative control method for a boxing and packaging production line based on multi-station linkage. Background Technology

[0002] In modern manufacturing, intelligent collaborative control of automated production lines is a key technology for improving production efficiency and product quality. Particularly in the packaging industry, automated production lines covering the entire boxing and cartoning process require a high degree of precision and coordination to ensure the continuity and stability of the production process.

[0003] Currently, cartoning and packing production lines typically employ centralized or distributed control systems using PLCs, which control the operation of each workstation through preset programs. For example, some systems use a time-based synchronous control method to coordinate the operation of each workstation according to a fixed time cycle; other systems use a master-slave control architecture, where the master controller uniformly schedules the working rhythm of each slave controller.

[0004] The most relevant existing technology is a cartoning and packing automation system based on independent module control. This technology sets up independent control units at each workstation (such as cartoning machines, conveyor belts, case packers, etc.), and each unit operates independently according to preset parameters. These systems typically use simple trigger signals to coordinate between workstations. For example, when the upstream workstation completes its operation, it sends a signal, and only then does the downstream workstation start working, forming a simple serial control mode.

[0005] However, this independent module control method has obvious technical defects: First, information between each workstation is isolated, lacking the ability to track the material status throughout the process, which means that when an anomaly occurs at one workstation, other workstations cannot be notified and respond in a timely manner; Second, coordination between workstations mainly relies on simple trigger signals, lacking an intelligent linkage mechanism, so when there is an empty workstation or an abnormal situation, the downstream workstations still operate at the original rhythm, resulting in material waste and reduced efficiency; Finally, the system parameters are mostly fixed settings, lacking adaptive optimization capabilities, and are difficult to cope with the rapid switching of different product specifications and the dynamic changes in production conditions. Summary of the Invention

[0006] The purpose of this invention is to provide an intelligent collaborative control method for a boxing and packaging production line based on multi-station linkage, so as to solve the technical problems existing in the prior art, such as isolated information between workstations, lack of intelligent linkage mechanism, and fixed system parameters that cannot be adaptively optimized.

[0007] To achieve the above objectives, this invention provides an intelligent collaborative control method for a cartoning and packing production line based on multi-station linkage, comprising:

[0008] Collect the location, orientation, and vacancy information of the materials, generate a unique ID for each material, and construct a material state vector containing ID, location, orientation, vacancy flag, and anomaly flag;

[0009] Five system states and state transition rules are defined for the production line: normal operation, star disk vacancy, abnormal torsional posture, packing positioning deviation, and emergency stop. A finite state machine model including a master state machine and sub-state machines for each workstation is constructed using a hierarchical state machine structure.

[0010] Based on the finite state machine model and the material state vector, a linkage response strategy is generated for different abnormal situations, and workstation collaborative control instructions including speed adjustment, action skipping and pause are generated in combination with the material state vector.

[0011] Construct and train a deep Q-network model with the overall capacity-energy consumption ratio as the reward function. Input the operating parameters of each workstation and the material state vector into the deep Q-network model, and output the optimal combination of cycle time including the star disk rotation speed, the twisting conveyor belt speed and the robot arm motion frequency.

[0012] A long short-term memory network model is constructed and trained. Sensor data, workstation status, and fault records are input into the long short-term memory network model to predict the fault probability of each workstation within a preset time period in the future.

[0013] Based on the failure probability and the optimal cycle time combination, a preventive maintenance plan is generated when the failure probability of a workstation exceeds a preset threshold. Based on the preventive maintenance plan, the corresponding workstation collaborative control command is used for control.

[0014] Optionally, the location, orientation, and availability information of the materials are collected, a unique ID is generated for each material, and a material state vector containing ID, location, orientation, availability flag, and anomaly flag is constructed, including:

[0015] A three-level photoelectric sensor array is deployed at the star disk discharge port of the cartoning machine, the end of the carton twisting and standing conveyor belt, and in front of the gripping point of the cartoning robot to collect the position, posture, and empty space information of the material;

[0016] Based on the material passage time detected by the first-level sensor, a unique ID is generated for each material using a date-time-serial number encoding method;

[0017] Edge computing nodes are deployed near each sensor array to receive the position, orientation, and vacancy information of the material, and to filter, calibrate, and extract features from the position, orientation, and vacancy information of the material, converting it into standardized material feature data.

[0018] Based on the material characteristic data and the unique ID identifier, a material state vector is constructed that includes ID, location, posture, vacancy flag, and anomaly flag.

[0019] Optionally, five system states and state transition rules are defined for the production line: normal operation, star disk vacancy, abnormal torsional posture, packing positioning deviation, and emergency stop. A hierarchical state machine structure is used to construct a finite state machine model including a master state machine and sub-state machines for each workstation, including:

[0020] The empty space flag, abnormal flag and position information in the material state vector are parsed, and five system states are defined: normal operation of the production line, star disk empty space, abnormal torsion posture, packing positioning deviation and emergency stop. The state transition rules between each state are designed.

[0021] Based on the five system states and state transition rules, a hierarchical state machine structure is adopted to realize state management. The switching logic between states is defined by the state transition matrix, and a finite state machine model including the main state machine and the sub-state machines of each workstation is constructed.

[0022] Optionally, based on the finite state machine model and the material state vector, a linkage response strategy is generated for different abnormal situations. Combined with the material state vector, workstation collaborative control instructions including speed adjustment, action skipping, and pause are generated, including:

[0023] The current state of the finite state machine model is monitored. When an empty space is detected on the star disk, a linkage response strategy is generated within 100ms to send a skip instruction to the downstream workstation.

[0024] Based on the aforementioned linkage response strategy, and combined with the position and attitude information in the material state vector, workstation collaborative control instructions including speed adjustment, action skipping, and pause are generated.

[0025] Optionally, a deep Q-network model is constructed and trained with the overall capacity-energy consumption ratio as the reward function. The operating parameters of each workstation and the material state vector are input into the deep Q-network model, and the output includes the optimal cycle combination of the star disk rotation speed, the torsional conveyor belt speed, and the robot arm motion frequency, including:

[0026] Collect the operating parameters and material flow status of each workstation, establish a virtual model of the production line containing the operating parameters and material flow status of each workstation, and define a state space containing the operating parameters and material state vectors of each workstation.

[0027] Based on the state space, a deep Q-network structure including an input layer, a multi-layer neural network, and an output layer is designed. The overall capacity-energy consumption ratio is used as the reward function to train the deep Q-network to predict the long-term benefits of different workstation parameter combinations.

[0028] The deep Q-network is learned online, and its parameters are continuously optimized through experience playback and target network technology. The operating parameters of each workstation and the material state vector are input into the deep Q-network model, and the optimal cycle combination including the star disk rotation speed, the twisting conveyor belt speed and the robot arm movement frequency is output.

[0029] Optionally, before outputting the optimal cycle combination including the star disk rotation speed, the torsional conveyor belt speed, and the robot arm movement frequency, the method further includes:

[0030] The deep Q-network model is used to analyze the virtual model of the production line, and the overall capacity-energy consumption ratio optimization objective is extended to a multi-objective optimization problem that simultaneously includes capacity indicators, energy consumption indicators, quality consistency indicators and equipment life indicators, thus constructing a multi-dimensional objective space.

[0031] Based on the multidimensional objective space, the Pareto optimal solution set that cannot be improved simultaneously in all objective dimensions is solved by using the weighted sum method, the ε-constraint method, and the non-dominated sorting method, so as to cover the complete distribution of the Pareto front.

[0032] For partial optimization iterations in the Pareto optimal solution set, a stochastic objective function is introduced to perturb the search process, thereby increasing the diversity of the search space exploration and avoiding premature convergence to a local optimum.

[0033] Based on the Pareto optimal solution set after iterative optimization, the weight preferences of each objective, such as capacity, energy consumption, quality, and equipment lifespan, are dynamically adjusted according to the current production demand. The parameter combination that best matches the current decision preference is selected from the Pareto optimal solution set, and the parameter combination is taken as the optimal cycle time combination.

[0034] Optionally, during the online learning process of the deep Q-network, the method further includes:

[0035] Sensitivity analysis is performed on the workstation parameters during the online learning process of the deep Q-network. Different search step sizes are allocated according to the sensitivity of the star disk rotation speed, the speed of the torsional conveyor belt, and the motion frequency of the robot. The first step size is used to search for sensitive parameters, and the second step size is used to search for non-sensitive parameters. The second step size is greater than the first step size.

[0036] The search step size is automatically adjusted according to the optimization process. In the early stage of optimization, an initial step size is used to quickly explore the parameter space. When a potential advantageous region is found, the step size is automatically reduced to conduct a fine search, and random perturbations are introduced to avoid getting trapped in local optima.

[0037] The parameter space is explored at multiple resolutions. Potential parameter subspaces are identified at a coarse-grained level, and the resolution is gradually increased to perform a fine search, forming a multi-level parameter space exploration from coarse to fine.

[0038] Based on the results of the multi-level parameter space exploration, a parameter performance mapping database is constructed to record historical search paths and corresponding results.

[0039] Optionally, after solving for the Pareto optimal solution set that cannot be simultaneously improved across all objective dimensions using the weighted sum method, the ε-constraint method, and the non-dominated sorting method, the method further includes:

[0040] The distance distribution between adjacent solutions in the Pareto optimal solution set is calculated to quantitatively evaluate the uniformity of the current search results distribution on the Pareto front, and to identify regions of excessive search concentration and sparse regions.

[0041] Based on the distribution uniformity assessment results, when it is detected that the search is overly concentrated in a specific region of the Pareto front, the sampling weight of the sparse region is automatically increased to guide the search to expand to the insufficiently explored solution space and achieve regional balance.

[0042] The diversity of solutions in the solution space is evaluated by calculating crowding distance, analyzing the distribution of reference points, and evaluating hypervolume contribution. Solutions with different characteristics are retained to prevent diverse solutions from being eliminated during the search process.

[0043] Based on the aforementioned diversity assessment, a diverse solution set containing solutions with different optimization directions is constructed to ensure that the diverse solution set has a balanced distribution across different dimensions of capacity, energy consumption, quality, and equipment lifespan.

[0044] The diverse solution set is used as a candidate set of parameter combinations for selection by flexible scheduling strategies.

[0045] Optionally, the method further includes:

[0046] The current production scenario is identified and classified into high-speed production scenario, low-energy operation scenario, and fault prevention scenario based on the urgency of orders, energy costs, and equipment status.

[0047] Based on the production scenario classification, the weights of each optimization objective in the multi-objective optimization problem are dynamically adjusted. In high-speed production scenarios, the weight of the capacity objective is increased; in low-energy operation scenarios, the weight of the energy-saving objective is increased; and in fault prevention scenarios, the weight of the equipment lifespan objective is increased.

[0048] The solutions in the diversified solution set are evaluated, and the parameter combination that best meets the requirements of the current scenario is selected from the diversified solution set according to the weight adjustment result.

[0049] Based on the parameter combination, a scenario-adaptive workstation collaborative control command is generated and sent to each workstation controller.

[0050] Optionally, a long short-term memory (LSTM) network model is constructed and trained. Sensor data, workstation status, and fault records are input into the LSM network model to predict the fault probability of each workstation within a preset time period. Based on the fault probability and the optimal cycle time combination, a preventive maintenance plan is generated when the workstation fault probability exceeds a preset threshold. Based on the preventive maintenance plan, corresponding workstation collaborative control instructions are used for control, including:

[0051] Collect sensor data, workstation status, and fault records from historical operation data, and perform data cleaning, standardization, and feature extraction on the sensor data, workstation status, and fault records to form a structured fault analysis dataset;

[0052] Based on the fault analysis dataset, a long short-term memory network model including an input gate, a forget gate, and an output gate is constructed to learn the equipment operation sequence data. The sensor data, workstation status, and fault records are input into the long short-term memory network model to predict the fault probability of each workstation in the next 30 minutes.

[0053] The failure probability is judged, and when the failure probability of a certain workstation exceeds 80%, a preventive maintenance plan including maintenance time window, spare parts preparation and personnel arrangement is generated based on the optimal cycle time combination.

[0054] Based on the aforementioned preventative maintenance plan, the upstream feed speed is proactively reduced before a fault occurs, and the system switches to a reduced-speed operation mode when a fault occurs. Corresponding workstation collaborative control commands are used for control to ensure production continuity.

[0055] Beneficial effects

[0056] The beneficial effects of this invention include:

[0057] By establishing a cross-module material status tracking network, the entire process of material tracking from boxing to packing can be managed, breaking the limitations of traditional single-station independent monitoring and improving the transparency of the production process.

[0058] By using a multi-station linkage control mechanism based on finite state machines, deterministic linkage response between stations is achieved, reducing the abnormal response time from the traditional 500ms to less than 100ms, significantly improving the system response speed.

[0059] Through a deep reinforcement learning-driven adaptive optimization system, dynamic adjustment of operating parameters at each workstation is achieved, breaking through the traditional fixed parameter mode, increasing production capacity by more than 15% and reducing energy consumption by more than 12%.

[0060] By using LSTM-based fault prediction and flexible scheduling mechanisms, the system can shift from passive response to proactive prevention, reducing unexpected equipment downtime by more than 40%.

[0061] By leveraging edge computing and a distributed collaborative architecture, local data processing and rapid response are achieved, thereby enhancing the overall stability and reliability of the system. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the overall process of the method of the present invention;

[0063] Figure 2 This is a schematic diagram of the material status tracking network deployment.

[0064] Figure 3 This is a schematic diagram of the finite state machine model structure;

[0065] Figure 4 This is a schematic diagram of the deep Q-network model structure;

[0066] Figure 5 A schematic diagram of Pareto front optimization for multi-objectives. Detailed Implementation

[0067] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] This embodiment provides an intelligent collaborative control method for a cartoning and packing production line based on multi-station linkage, such as... Figure 1 As shown, it includes the following steps:

[0070] S1: Collect the location, orientation, and vacancy information of materials, generate a unique ID for each material, and construct a material state vector containing ID, location, orientation, vacancy flag, and anomaly flag.

[0071] Specifically, sensor arrays are deployed at key workstations on the cartoning and boxing production line to monitor the status of materials such as cartons at each workstation in real time. When a material passes through a sensor, the sensor detects its position coordinates, tilt angle, and other attitude parameters, as well as information such as whether there is a vacancy. Simultaneously, a unique identifier is assigned to each passing material to ensure that the material can be tracked throughout the entire production process. The collected information is integrated into a standardized material status vector, which includes fields such as material ID, three-dimensional position coordinates, attitude angle, vacancy flag, and anomaly flag, and is shared in real time with the control units at each workstation via industrial Ethernet.

[0072] S2: Define five system states and state transition rules for the production line: normal operation, star disk vacancy, abnormal torsional posture, packing positioning deviation, and emergency stop. A finite state machine model including a master state machine and sub-state machines for each workstation is constructed using a hierarchical state machine structure.

[0073] Based on the material state vector obtained from S1, the operating states of the production line are classified and defined. Normal operation state indicates that all workstations work collaboratively according to the standard cycle time; star disk empty state indicates that some positions on the star disk of the cartoning machine are not filled with cartons; abnormal torsional posture state indicates that cartons are tilting or skewed on the torsional conveyor belt; carton positioning deviation state indicates that the position of the carton deviates from the predetermined point during cartoning; emergency stop state indicates that a serious fault has been detected and immediate shutdown is required. Transition conditions between each state are designed, for example, when the empty space flag is detected as true, the system transitions from normal operation state to star disk empty state. A master state machine manages the global state of the entire production line, and each workstation's sub-state machine manages its local state. Deterministic state switching is achieved through a state transition matrix.

[0074] S3: Based on the finite state machine model and material state vector, it generates linkage response strategies for different abnormal situations, and generates workstation collaborative control instructions including speed adjustment, action skipping and pause by combining the material state vector.

[0075] When the state machine detects an empty space on the star disk, it automatically generates a linkage response strategy within 100ms, sending skip commands to the downstream twisting conveyor belt and packing robot, causing these stations to skip the corresponding empty space operations and avoid invalid actions and wasted time. When an abnormal twisting posture is detected, the conveyor belt speed is automatically reduced to give the carton more time to complete posture adjustment, while simultaneously notifying the packing robot to delay gripping. Combining the specific position and posture data in the material state vector, the precise action parameters that each station needs to execute are calculated, generating control commands including speed adjustment, action skip flags, and pause durations, which are then sent to each execution unit through the industrial control network.

[0076] S4: Construct and train a deep Q-network model with the overall capacity-energy consumption ratio as the reward function. Input the operating parameters of each workstation and the material state vector into the deep Q-network model, and output the optimal cycle combination including the star disk rotation speed, the twisting conveyor belt speed and the robot arm motion frequency.

[0077] First, a virtual environment model of the production line is established, defining a state space that includes parameters such as the current rotation speed, material position, and buffer occupancy rate of each workstation. A deep Q-network is then constructed, consisting of an input layer, three hidden layers, and an output layer. The input layer receives the parameters from the state space. Each hidden layer contains 128 neurons using the ReLU activation function. The output layer outputs the Q-values ​​of various action combinations, with the action space including discrete actions such as increasing rotation speed, decreasing rotation speed, and maintaining the same speed.

[0078] During training, the reward function is defined as the ratio of the number of qualified products produced to the electrical energy consumed within the current time window. A higher ratio indicates better efficiency and a larger reward. An experience replay mechanism is employed, storing the state, action, reward, and next state for each time step in an experience pool. Batch data is randomly selected for training to break data correlation. Simultaneously, a target network technique is used, maintaining a target network with slower parameter updates to calculate the target Q-value, improving training stability. Initially, a higher exploration rate is used, randomly selecting actions to explore the environment. As training progresses, the exploration rate is gradually reduced, relying more on network prediction for action selection.

[0079] After thorough training, the deep Q-network learns the strategy of selecting the optimal combination of workstation parameters under different production conditions. During actual operation, the current operating parameters of each workstation and the material state vector are input into the trained deep Q-network. The network outputs the Q value corresponding to each action, selects the action with the largest Q value for execution, and obtains the optimal combination of cycle time such as the star disk speed, the twisting conveyor belt speed, and the robot arm movement frequency. These parameters are then sent to the controllers of each workstation.

[0080] S5: Construct and train a long short-term memory network model, input sensor data, workstation status and fault records into the long short-term memory network model, predict the fault probability of each workstation within a preset time in the future; based on the fault probability and the optimal cycle time combination, when the fault probability of a workstation exceeds a preset threshold, a preventive maintenance plan is generated; based on the preventive maintenance plan, the corresponding workstation collaborative control instructions are used for control.

[0081] Historical operational data is collected, including parameters such as vibration, temperature, and current recorded by sensors at each workstation, the operating status of each workstation such as speed and load, and past fault records such as fault time, type, and maintenance measures. The data is cleaned to remove outliers and missing values, and normalized to ensure all parameters are within the same order of magnitude. Temporal features are extracted, such as the temperature change trend and vibration peak frequency over the past hour.

[0082] A Long Short-Term Memory (LSTM) network model is constructed, consisting of an input layer, two LSTM layers, and a fully connected output layer. The input layer receives time-series data, with each time step containing multiple feature dimensions. The first LSTM layer contains 64 neurons, and the second LSTM layer contains 32 neurons. Each LSTM unit includes three gating structures: an input gate, a forget gate, and an output gate. The input gate controls the writing of new information, the forget gate controls the forgetting of historical information, and the output gate controls the output at the current time. Through these gating mechanisms, the LSTM can learn long-term dependencies and capture the slow evolution of equipment degradation. The output layer is a fully connected layer that outputs a failure probability value for each workstation within the next 30 minutes, ranging from 0 to 1.

[0083] During training, a training set is constructed using historical data, with data from the 30 minutes prior to the failure used as positive samples and data from the normal operation period used as negative samples. A cross-entropy loss function is employed, and the Adam optimizer is used for parameter updates. Performance on the validation set is monitored throughout training; training is stopped when the validation set loss no longer decreases to prevent overfitting.

[0084] In practical applications, real-time sensor data and workstation status are collected and input into a trained LSTM model to obtain the predicted failure probability for each workstation over the next 30 minutes. When the failure probability of a workstation exceeds 80%, it is determined that the workstation has a high failure risk, and the system automatically generates a preventative maintenance plan. This plan includes a suggested maintenance time window, such as during the production gap after the current batch is completed; a list of spare parts to be prepared, such as bearings and drive belts; and the maintenance personnel to be assigned and their required skill levels.

[0085] According to the maintenance plan, production strategies are proactively adjusted before a failure occurs. For example, the feeding speed of the upstream cartoning machine is gradually reduced to decrease work-in-process inventory; downstream packing stations are notified to switch to a reduced-speed operation mode to avoid material accumulation due to sudden shutdowns; and other production lines are coordinated to share some orders to ensure that overall delivery is not affected. Through this proactive prevention and flexible scheduling, the passive response to equipment failures is transformed into proactive management, significantly reducing unexpected downtime and production losses.

[0086] Example 2

[0087] This embodiment is a further refinement of S1 in Embodiment 1, detailing the implementation process of material status tracking, such as... Figure 2 As shown, it includes the following steps:

[0088] S1.1: Deploy a three-level photoelectric sensor array at the star disk discharge port of the cartoning machine, the end of the carton twisting and standing conveyor belt, and in front of the gripping point of the cartoning robot to collect the position, posture, and empty space information of the material.

[0089] A first-stage sensor array is deployed at the discharge port of the cartoning machine's star disk. This array consists of eight photoelectric position sensors evenly distributed around the circumference of the star disk to detect whether a carton is placed at each material position and the precise time when the carton passes through. Two empty position detection sensors are also deployed to trigger an empty position signal when a material position is empty.

[0090] A second-stage sensor array is deployed at the end of the cardboard box twisting and standing conveyor belt, including position detection sensors, height detection sensors, and attitude detection sensors. The position detection sensors use laser ranging to measure the lateral and longitudinal positional deviations of the cardboard box on the conveyor belt. The height detection sensors measure the vertical height of the cardboard box to determine if it is fully upright. The attitude detection sensors use a multi-point photoelectric array to calculate the tilt angle of the cardboard box by detecting occlusion at different positions.

[0091] A third-level sensor array, including position sensors, attitude sensors, and integrity detection sensors, is deployed before the packing robot's gripping point. The position sensors confirm whether the carton has reached the predetermined gripping position. The attitude sensors re-detect the carton's attitude to ensure accurate gripping by the robot. The integrity detection sensors use image recognition technology to detect quality issues such as damage or deformation of the carton.

[0092] S1.2: Based on the material passage time detected by the first-level sensor, a unique ID is generated for each material using a date-time-serial number encoding method.

[0093] When the first-level sensor detects material (cardboard box) passing through, it immediately records the system clock's timestamp. An ID is generated using the format year-month-day-hour-minute-second-serial number, for example, "20260209-143025-0001" represents the first cardboard box that passed through at 14:30:25 on February 9, 2026. The serial number starts from 0001 and automatically increments by 1 for each detected cardboard box, resetting at midnight daily. This encoding method ensures the uniqueness of each ID in the system, facilitating the traceability of the entire material production process.

[0094] S1.3: Deploy edge computing nodes near each sensor array to receive the position, orientation, and vacancy information of the material, filter, calibrate, and extract features from this information, and convert it into standardized material feature data.

[0095] An edge computing node is deployed near each level of the sensor array. This node uses an embedded industrial computer and has real-time data processing capabilities. The edge computing node receives raw data from the sensors via an industrial bus, which often contains noise and jitter.

[0096] The position data is processed using Kalman filtering to predict the material's position based on its motion model, and then combined with sensor measurements for optimal estimation, filtering out measurement noise. The attitude data is processed using median filtering to remove abrupt outliers. The vacancy detection signal is de-jittered; a state change is only confirmed when multiple consecutive detection results are consistent, avoiding misjudgments caused by transient interference.

[0097] Perform sensor calibration to compensate for sensor installation position deviations and measurement system errors. Based on pre-established calibration parameters, transform the measured values ​​in the sensor coordinate system to a unified production line coordinate system.

[0098] Feature extraction is performed to extract useful feature parameters from the raw data. For example, lateral and longitudinal deviations are extracted from position data; tilt and torsion angles are extracted from attitude data; and edge and texture features are extracted from integrity inspection images to determine whether damage exists. The extracted feature data is then normalized to convert it into standardized material feature data.

[0099] S1.4: Based on material characteristic data and unique ID identifiers, construct a material state vector containing ID, location, attitude, vacancy flag, and abnormal flag.

[0100] The unique ID generated in S1.2 is used as the first field of the state vector. The standardized position data extracted in S1.3 is used as the second field, containing three-dimensional coordinate values. The attitude data is used as the third field, containing tilt and twist angles. The empty space detection result is used as the fourth field, with a Boolean value indicating whether the position is empty. The anomaly detection result is used as the fifth field, with a Boolean value indicating whether the material has quality problems or its position and attitude are outside the allowable range.

[0101] These five fields are organized into a structured data vector, for example, ID: 20260209-143025-0001, position: (125.3, 80.7, 15.2), attitude: (2.1°, 0.8°), empty space flag: false, and abnormal flag: false. This status vector is transmitted in real time to the control units at each workstation via industrial Ethernet. Each control unit tracks the processing status of the material at its workstation based on the material ID, achieving full-process tracking.

[0102] Example 3

[0103] This embodiment is a further refinement of S2 and S3 in Embodiment 1, detailing the construction of the finite state machine control model and the process of generating control instructions, such as... Figure 3 As shown, it includes the following steps:

[0104] S2.1: Parse the empty space flag, abnormal flag and position information in the material state vector, define five system states of production line: normal operation, star disk empty space, abnormal torsion posture, packing positioning deviation and emergency stop, and design the state transition rules between each state.

[0105] The material state vector is analyzed, and the following conditions are defined as follows: Normal operation is defined as when the empty space flag is false, the abnormality flag is false, and the positional deviation of all workstations is within the allowable range. When the empty space flag is detected as true, the system is defined as being in an empty space state. An abnormal torsional posture is defined as when the tilt angle of the carton on the twisting conveyor exceeds 5 degrees or the twist angle exceeds 3 degrees. A carton's positional deviation at the packing gripping point exceeds 2 mm, which is defined as a packing positioning deviation state. An emergency stop is defined as when equipment malfunction, safety trigger, or the operator presses the emergency stop button.

[0106] Design state transition rules: The normal operating state can be transitioned to one of the other four states; the starboard empty state and the abnormal torsional attitude state can be transitioned back to the normal operating state after the problem is resolved; the packing positioning deviation state can be transitioned back to the normal operating state after the position adjustment is completed; the emergency stop state can be transitioned back to the normal operating state after the fault is eliminated and safety is confirmed. The priority of the transition conditions is defined, with emergency stop having the highest priority and being able to transition directly from any state.

[0107] S2.2: Based on five system states and state transition rules, a hierarchical state machine structure is adopted to realize state management. The switching logic between states is defined by the state transition matrix, and a finite state machine model including the main state machine and the sub-state machines of each workstation is constructed.

[0108] Construct a master state machine to manage the global state of the entire production line. The master state machine contains five state nodes, each corresponding to a system state. Construct a state transition matrix, where rows represent the current state, columns represent the target state, and matrix elements are transition conditions. For example, the transition condition from the normal operation state to the star disk empty state is "empty space flag detected as true", and the transition condition from the star disk empty state to the normal operation state is "empty space is filled or material passes through the empty station".

[0109] A sub-state machine is built for each workstation to manage the local state of that workstation. For example, the sub-state machine of the cartoning machine includes states such as waiting for material, feeding, cartoning, and discharging; the sub-state machine of the twisting conveyor belt includes states such as receiving, conveying, twisting, standing, and discharging; and the sub-state machine of the box-packing robot includes states such as waiting, moving to position, grabbing, moving to box, placing, and returning.

[0110] The master state machine and child state machines interact via event messages. When the master state machine undergoes a state transition, it sends a state change notification to the relevant child state machines. When a child state machine detects a local anomaly, it reports the anomaly event to the master state machine, which then decides whether a global state transition is necessary.

[0111] S2.3: Monitor the current state of the finite state machine model. When the empty position state of the turntable is detected, generate a linkage response strategy to send a skip instruction to the downstream workstation within 100 ms.

[0112] The main state machine continuously monitors the current state. When the state changes from normal operation to the empty position of the turntable, immediately start the linkage response process. First, identify the material ID corresponding to this empty position, assumed to be a special identifier of "empty position - serial number". Then send a linkage message to the downstream workstation, and the message includes fields such as material ID, current state, and recommended actions.

[0113] After the sub - state machine of the turning conveyor belt receives the empty position linkage message, mark this material ID as a skipped object. When this ID flows to the turning workstation, skip the turning and standing actions and directly maintain the conveying state to pass through, saving action time. After the sub - state machine of the box - packing manipulator receives the message, also mark this ID as skipped. When it detects that this ID reaches the grasping point, do not execute the grasping action and directly wait for the next valid material.

[0114] The entire linkage response process from detecting the empty position to issuing the skip instruction is controlled to be completed within 100 ms. Use a high - priority message channel to ensure that the linkage message can be transmitted in time and avoid the downstream workstation from performing invalid actions.

[0115] S2.4: Based on the linkage response strategy, combine the position and attitude information in the material state vector to generate station - coordinated control instructions including speed adjustment, action skipping, and pausing.

[0116] Generate specific control instructions according to different system states and linkage response strategies. For the case of the empty position of the turntable, the generated control instructions include: the cartoning machine continues to maintain the current rotation speed without adjustment; the turning conveyor belt skips the action for the empty - position material, and the skip flag is set to true; the box - packing manipulator skips the action for the empty - position material, and the skip flag is set to true.

[0117] For the case of abnormal turning attitude, combine the attitude angle value in the material state vector to calculate the required adjustment amount. The generated control instructions include: the speed of the turning conveyor belt is reduced by 30% to give more time to complete the attitude adjustment; the grasping of the box - packing manipulator is delayed by 2 seconds to wait for the carton attitude to stabilize; if the attitude angle exceeds 10 degrees, pause the conveyor belt and trigger manual intervention.

[0118] For the case of box - packing positioning deviation, generate a position compensation instruction for the manipulator according to the direction and magnitude of the position deviation. If the lateral deviation is +1.5 mm, the control instruction is that the manipulator moves laterally +1.5 mm and then performs the grasping; if the longitudinal deviation is -0.8 mm, move longitudinally -0.8 mm. Through position compensation, ensure that the manipulator can accurately grasp the carton deviating from the standard position.

[0119] The generated control commands are encapsulated into standard industrial control protocol data packets and sent to the PLC controllers at each workstation via industrial Ethernet protocols such as Profinet or EtherCAT. After receiving the commands, the controllers convert them into specific motor control signals, cylinder control signals, etc., to drive the actuators to complete the corresponding actions.

[0120] Example 4

[0121] This embodiment is a further refinement of S4 in Embodiment 1, detailing the construction, training, and application process of the deep Q-network model, such as... Figure 4 As shown, it includes the following steps:

[0122] S3.1: Collect the operating parameters and material flow status of each workstation, establish a virtual model of the production line containing the operating parameters and material flow status of each workstation, and define a state space containing the operating parameters and material state vectors of each workstation.

[0123] The system collects operating parameters such as the rotation speed, current angle, and occupancy status of the star disk of the cartoning machine; it also collects parameters such as the belt speed, current number of cartons being carried, and the position of each carton on the twisting conveyor; it collects parameters such as the movement frequency, current position, and gripping status of the container robot; it collects the occupancy rate of the buffer area at each workstation; and it collects the material flow status, including the quantity of in-process and the flow rate.

[0124] A virtual simulation model of the production line is established. This model can simulate the flow of materials at each workstation based on the input workstation parameters, and calculate the production capacity and energy consumption. The virtual model takes into account the physical constraints of each workstation, such as the rotation speed of the star disk ranging from 10 to 60 revolutions per minute, the speed of the conveyor belt ranging from 0.1 to 0.5 meters per second, and the gripping cycle of the robotic arm ranging from 1 to 5 seconds.

[0125] The state space is defined, containing 12 dimensions: current rotation speed of the cartoning machine's star disk, number of occupancy points on the star disk, current speed of the twisting conveyor belt, number of cartons on the conveyor belt, current movement frequency of the robot arm, number of occupancy points in the robot arm's buffer zone, occupancy rate of the cartoning buffer zone, occupancy rate of the twisting buffer zone, occupancy rate of the boxing buffer zone, production capacity in the last minute, energy consumption in the last minute, and material anomaly rate. Each dimension is normalized and mapped to a range of 0 to 1.

[0126] The motion space is defined, containing 27 discrete actions, each a combination of three adjustment options for three key parameters: the star disk rotation speed can be increased by 5 rpm, kept constant, or decreased by 5 rpm; the conveyor belt speed can be increased by 0.05 m / s, kept constant, or decreased by 0.05 m / s; and the robot arm's motion frequency can be increased by 0.2 times / s, kept constant, or decreased by 0.2 times / s. These adjustments to the three parameters are combined to form the 27 actions.

[0127] S3.2: Based on the state space, a deep Q-network structure including an input layer, a multi-layer neural network, and an output layer is designed. The overall capacity-energy consumption ratio is used as the reward function to train the deep Q-network to predict the long-term benefits of different workstation parameter combinations.

[0128] A deep Q-network is constructed. The input layer contains 12 neurons, corresponding to the 12 dimensions of the state space. The first hidden layer contains 128 neurons, using the ReLU activation function, and learns the basic features of the state. The second hidden layer contains 128 neurons, also using the ReLU activation function, and learns higher-level combinations of state features. The third hidden layer contains 64 neurons, using the ReLU activation function, and performs feature compression and abstraction. The output layer contains 27 neurons, corresponding to 27 selectable actions. Each neuron outputs a Q-value estimate for that action using a linear activation function.

[0129] Define a reward function to calculate the immediate reward at the current time step. The immediate reward equals the number of qualified products produced in that time step divided by the amount of electricity consumed in kilowatt-hours. For example, if 50 qualified cardboard boxes are produced in 1 minute, consuming 0.5 kilowatt-hours of electricity, the reward is 50 divided by 0.5, which equals 100. If defective products are produced, twice the number of defective products is deducted from the product count as a quality penalty.

[0130] To accelerate training, a target network is constructed. This target network has the same structure as the main network, but its parameters are maintained independently. The target network is used to calculate the target Q-value, and its parameters are copied from the main network only at regular intervals to avoid instability caused by frequent changes in the target value during training.

[0131] Initialize the experience replay pool with a capacity of 10,000 records. Each record contains five fields: status, action, reward, next status, and termination flag.

[0132] S3.3: Perform online learning on the deep Q-network and continuously optimize the parameters of the deep Q-network through experience replay and target network techniques.

[0133] The training process is as follows: First, initialize the production line state in the virtual simulation environment. Set the initial exploration rate to 0.9, meaning there is a 90% probability of randomly selecting an action for exploration and a 10% probability of selecting the action with the largest Q value.

[0134] At each time step, obtain the current state vector, randomly select an action with the probability of the exploration rate, otherwise input the state into the main network, obtain the Q-values ​​of 27 actions, and select the action with the largest Q-value. Execute this action in the virtual environment to obtain a reward and the next state. Store the current state, action, reward, next state, and whether to terminate in the experience replay pool.

[0135] Training begins when the number of accumulated experiences in the experience pool exceeds 128. 32 experiences are randomly selected from the experience pool as a training batch. For each experience in the batch, the next state is input into the target network to obtain the Q-values ​​of all actions in the next state. The maximum value is taken as the value estimate for the next state. The target Q-value is calculated as the immediate reward plus a discount factor multiplied by the value of the next state; the discount factor is set to 0.95.

[0136] Input the current state into the main network to obtain the Q-value predictions for all actions, and extract the Q-value corresponding to the actual action executed. Calculate the loss, which is the mean squared error between the target Q-value and the predicted Q-value. Use the Adam optimizer to calculate the gradient based on the loss and update the main network parameters.

[0137] Every 100 training steps, the parameters of the main network are copied to the target network to update the target network. As training progresses, the exploration rate is gradually reduced, linearly decreasing from an initial 0.9 to a final 0.1, shifting the system from exploration-based to exploit-based.

[0138] The training process consists of 5000 rounds, each simulating the operation of a production shift, until the product quota is met or a termination condition is encountered. The average reward during the training process is monitored, and when the average reward stops increasing for 100 consecutive rounds, the network is considered to have converged, and training is stopped.

[0139] S3.4: Input the operating parameters and material state vectors of each workstation into the deep Q-network model, and output the optimal cycle combination including the star disk rotation speed, the twisting conveyor belt speed and the robot arm motion frequency.

[0140] In actual production, the current state is collected every minute, including the operating parameters of each workstation and the material state vector. The collected 12-dimensional state vector is input into the trained deep Q-network main network. The network performs forward propagation calculations, and the output layer provides the Q-values ​​of 27 actions. The action with the largest Q-value is selected, which corresponds to a set of parameter adjustment schemes, such as increasing the star disk rotation speed by 5 revolutions per minute, keeping the conveyor belt speed unchanged, and reducing the robot arm frequency by 0.2 times per second.

[0141] Based on this action, the adjusted target parameter value is calculated. Assuming the current star disk rotation speed is 40 rpm, and the adjustment is an increase of 5 rpm, the target rotation speed is 45 rpm. The target parameter value is sent to the controllers at each workstation, and the controllers perform smooth speed adjustment, gradually adjusting to the target value within 30 seconds to avoid sudden shocks.

[0142] After running for one minute, the status is collected again, and the above process is repeated to continuously optimize the cycle time parameters. Through the learning capability of deep Q-networks, the system can dynamically adjust the cycle time of each workstation according to the real-time production status, and automatically find the optimal balance between production capacity and energy consumption under different product specifications, order requirements, and equipment statuses.

[0143] Example 5

[0144] This embodiment is an extension of Embodiment 4, introducing multi-objective optimization and Pareto front solving, such as... Figure 5 As shown, add the following steps before S3.4:

[0145] S3.2.1: Analyze the virtual model of the production line using a deep Q-network model, and extend the overall capacity-energy consumption ratio optimization objective into a multi-objective optimization problem that simultaneously includes capacity indicators, energy consumption indicators, quality consistency indicators, and equipment life indicators, and construct a multi-dimensional objective space.

[0146] Based on the original single objective of capacity-energy consumption ratio, it is decomposed into four independent optimization objectives: the first objective is to maximize capacity, measured by the number of qualified products produced per unit time; the second objective is to minimize energy consumption, measured by the total electrical energy consumed per unit time; the third objective is to optimize quality consistency, measured by the standard deviation of product critical dimensions, with a smaller standard deviation indicating better product consistency; and the fourth objective is to maximize equipment lifespan, measured by the wear rate of key equipment components, with a lower wear rate indicating a longer equipment lifespan.

[0147] There are conflicts among these four objectives. Increasing production capacity often requires increasing operating speed, leading to increased energy consumption, decreased quality consistency, and accelerated equipment wear. Reducing energy consumption requires decreasing speed, but this sacrifices production capacity. Improving quality consistency requires more precise control, which may reduce production cycle time. Extending equipment life requires gentle operation, but this will affect production capacity.

[0148] A four-dimensional target space is constructed, with each dimension corresponding to an optimization objective. Each set of workstation parameters is mapped to a point in this target space, where the four coordinate values ​​are the production capacity, energy consumption, quality standard deviation, and wear rate, respectively.

[0149] S3.2.2: Based on the multidimensional objective space, the weighted sum method, the ε-constraint method and the non-dominated sorting method are used to solve the Pareto optimal solution set that cannot be improved simultaneously in all objective dimensions, so as to cover the complete distribution of the Pareto front.

[0150] A weighted sum method is used, with weight coefficients set for the four objectives, such as production capacity weight 0.4, energy consumption weight 0.3, quality weight 0.2, and lifespan weight 0.1, to calculate the weighted total objective value. By adjusting the weight combinations, the optimal solution under different weights is obtained, yielding a series of solutions distributed at different locations on the Pareto front.

[0151] The ε-constraint method is employed, treating three objectives as constraints and optimizing only one primary objective. For example, upper limits are set for energy consumption, quality, and lifespan, maximizing production capacity while satisfying these constraints. By adjusting the constraint values, optimal solutions under different constraints are obtained, supplementing other parts of the frontier.

[0152] A non-dominated sorting method is used to stratify the candidate solution set. If solution A is no worse than solution B on all objectives and is better than solution B on at least one objective, then A is said to dominate B. All non-dominated solutions are assigned to the first stratum, which is the Pareto optimal solution set. After removing solutions from the first stratum of the candidate set, the remaining solutions are re-sorted to obtain the second stratum, and so on. All non-dominated solutions in the first stratum are retained as the Pareto optimal solution set.

[0153] To cover the complete distribution of the Pareto front, the results of three methods are combined. The weighted sum method provides the equilibrium solution in the middle of the front, the ε-constraint method provides the extreme solutions at the ends of the front, and the non-dominated sorting ensures the optimality of the solution set. Finally, a Pareto optimal solution set containing 50 solutions is obtained, which form a front surface in the objective space, and there is an objective trade-off between any two solutions.

[0154] S3.2.3: For partial optimization iterations in the Pareto optimal solution set, a stochastic objective function is introduced to perturb the search process, thereby increasing the diversity of the search space exploration and avoiding premature convergence to a local optimum.

[0155] In some iterations of the optimization process, a stochastic objective function unrelated to the actual production target is temporarily introduced. For example, an objective function could be constructed to maximize the product of the star disk rotation speed and the conveyor belt speed, or to minimize the square of the robot arm frequency. These objectives themselves have no practical meaning, but they can guide the search to explore different parameter regions.

[0156] In practice, every 10 normal optimization iterations, one random objective optimization iteration is inserted. The form of the random objective is generated randomly each time, and it can be a linear combination of parameters, a nonlinear combination, or a completely random scoring function. In this iteration, the four actual objectives are temporarily ignored, and only the random objective is optimized. The solution obtained is added to the candidate solution set.

[0157] The purpose of this perturbation mechanism is that when the search gets stuck in a certain parameter region and cannot escape, the random objective forces the search to explore other regions, discovering high-quality solutions that might otherwise have been overlooked. In the subsequent non-dominated sorting, if these solutions perform well on the actual objective, they will be retained in the Pareto solution set; if they perform poorly, they will be naturally eliminated without affecting the quality of the solution set.

[0158] Through 200 optimization iterations, including 180 normal iterations and 20 random perturbation iterations, a rich variety of candidate solutions were obtained. All candidate solutions were non-dominated and sorted to extract a Pareto optimal solution set, which contained diverse optimal solutions obtained from exploration in different directions.

[0159] S3.2.4: Based on the Pareto optimal solution set, dynamically adjust the weight preferences of each objective, such as capacity, energy consumption, quality, and equipment lifespan, according to the current production demand. Select the parameter combination that best matches the current decision preference from the Pareto optimal solution set, and use this parameter combination as the optimal cycle time combination.

[0160] The target weights are determined based on the current production situation. If current orders are urgent and require the completion of a large number of products in a short period of time, the target weight for production capacity is set to 0.6, energy consumption to 0.2, quality to 0.1, and lifespan to 0.1, emphasizing capacity priority. If the current period is peak electricity consumption with high electricity prices, the target weight for energy consumption is set to 0.5, production capacity to 0.3, quality to 0.1, and lifespan to 0.1, emphasizing energy conservation. If equipment has been running continuously for a long time and has accumulated significant wear and tear, the target weight for lifespan is set to 0.4, production capacity to 0.3, energy consumption to 0.2, and quality to 0.1, emphasizing equipment protection.

[0161] For each solution in the Pareto optimal solution set, its comprehensive score is calculated, which is equal to the weighted sum of the four objective values. Since the different objectives have different dimensions, each objective is first normalized within the solution set, mapping the optimal value to 1 and the worst value to 0. Then, the weighted sum is calculated based on the current weights. The solution with the highest comprehensive score is selected, and its corresponding workstation parameter combination is extracted as the optimal cycle time combination for the current moment.

[0162] For example, in cases of urgent orders, solution A receives the highest overall score, with parameters of 55 rpm for the star disk, 0.45 m / s for the conveyor belt, and 4.5 cycles / s for the robotic arm. This parameter combination favors high speed and high output. Under energy-saving requirements, solution B receives the highest overall score, with parameters of 35 rpm for the star disk, 0.25 m / s for the conveyor belt, and 3 cycles / s for the robotic arm. This parameter combination favors low energy consumption. The selected parameter combination is then sent to the controllers at each workstation for execution.

[0163] In Example 5, the multi-objective optimization problem refers to the problem of simultaneously optimizing multiple conflicting objective functions. In traditional single-objective optimization, there exists a unique global optimum. However, in multi-objective optimization, due to the conflict between objectives, there is usually no solution that simultaneously optimizes all objectives. Instead, there exists a set of compromise solutions, i.e., a Pareto optimal solution set. This example decomposes the original single "capacity-energy ratio" objective into four independent and conflicting optimization objectives, thus more comprehensively characterizing the overall performance of the production line.

[0164] Specifically, the first objective function, f1, is defined as maximizing production capacity, expressed as the number of qualified products produced per unit time, in units per hour. For example, under a certain parameter combination, if a cartoning production line produces 2400 qualified boxes per hour, then f1 = 2400. The second objective function, f2, is defined as minimizing energy consumption, expressed as the total electrical energy consumed per unit time, in kilowatt-hours per hour. Assuming the production line consumes 15 kilowatt-hours of energy per hour in high-speed operation mode, then f2 = 15. Since it is a minimization objective, its reciprocal or negative value is used in subsequent calculations. The third objective function, f3, is defined as optimizing quality consistency, expressed as the standard deviation of key product dimensions. A smaller standard deviation indicates better consistency between product batches. For example, if the standard deviation of the height of 100 cartons is 0.3 millimeters, then f3 = 0.3, which is also a minimization objective. The fourth objective function, f4, is defined as maximizing equipment lifespan, expressed as the wear rate of key components, in micrometers per hour. By monitoring the wear of vulnerable parts such as bearings and transmission belts, the wear rate per unit time is calculated. Assuming it is 2.5 micrometers / hour, then f4 = 2.5, which is also the minimization target.

[0165] There are clear conflicts and trade-offs among these four objectives. Increasing the aster disk speed and conveyor belt speed to pursue higher production capacity leads to increased energy consumption due to increased motor power. Simultaneously, high-speed operation shortens the product dwell time at each station, resulting in insufficient posture adjustment and decreased quality consistency. Furthermore, high-load operation exacerbates wear. For example, increasing the aster disk speed from 40 rpm to 55 rpm might increase production capacity from 2000 units / hour to 2600 units / hour, but energy consumption increases from 12 kWh / hour to 16 kWh / hour, the standard deviation of quality increases from 0.25 mm to 0.38 mm, and the wear rate increases from 1.8 micrometers / hour to 3.2 micrometers / hour. Conversely, reducing operating speed to save energy and protect equipment inevitably leads to a decrease in production capacity. This conflict among multiple objectives makes it impossible to find a single parameter combination that simultaneously maximizes all objectives; instead, a balance must be sought among them.

[0166] A four-dimensional target space is constructed, mapping each set of station parameter combinations (s, v, f) to a point in the target space, where s represents the star disk rotation speed, v represents the conveyor belt speed, and f represents the robot frequency. The coordinates of this point are (f1(s, v, f), f2(s, v, f), f3(s, v, f), f4(s, v, f)), corresponding to the function values ​​of the four objectives, respectively. For example, the parameter combination (45, 0.35, 3.8) is mapped to the point (2200, 13.5, 0.28, 2.1) in the target space, indicating that under these parameters, the production capacity is 2200 pieces / hour, the energy consumption is 13.5 kWh / hour, the quality standard deviation is 0.28 mm, and the wear rate is 2.1 μm / hour. Through the evaluation of a large number of different parameter combinations, a set of points is formed in the four-dimensional target space, where the points located on the Pareto front are the Pareto optimal solutions.

[0167] A Pareto optimal solution is defined as follows: for solutions A and B, if A performs no worse than B on all objectives and is strictly better than B on at least one objective, then A dominates B. A solution is Pareto optimal if it is not dominated by any other solution. The set of Pareto optimal solutions is called the Pareto optimal solution set, and the boundary formed by these solutions in the objective space is called the Pareto front. There is a trade-off between any two solutions on the Pareto front; improving one objective inevitably leads to the deterioration of the other.

[0168] To comprehensively solve the Pareto front, this embodiment combines three classical methods. First, a weighted sum method is used to transform the multi-objective problem into a single-objective problem. The comprehensive objective function is defined as follows: Where w1, w2, w3, and w4 are the weight coefficients of each objective, satisfying w1 + w2 + w3 + w4 = 1 and w i ≥0. For the maximized production capacity target, the weighting coefficients are positive; for the minimized energy consumption, quality standard deviation, and wear rate targets, the weighting coefficients are negative. Since the dimensions of each target are different, normalization is required before calculation. Assume the normalization formula for production capacity is... ,in and These represent the minimum and maximum production capacity, which are 1500 units / hour and 3000 units / hour respectively within the current parameter range. Similarly, energy consumption, quality, and wear rate are normalized. The normalized comprehensive objective function becomes... .

[0169] By systematically changing the weight combinations, different parts of the Pareto front can be obtained. For example, setting weight combination 1 to (0.7, 0.1, 0.1, 0.1), emphasizing capacity priority, the optimal parameter combination obtained through deep Q-network optimization is a star disk rotation speed of 54 rpm, a conveyor belt speed of 0.46 m / s, and a robot frequency of 4.6 times / s. The corresponding target values ​​are a capacity of 2550 units / hour, energy consumption of 15.8 kWh / hour, a quality standard deviation of 0.36 mm, and a wear rate of 3.0 μm / hour. Setting weight combination 2 to (0.1, 0.7, 0.1, 0.1), emphasizing energy saving priority, the optimal parameters are a star disk rotation speed of 32 rpm, a conveyor belt speed of 0.22 m / s, and a robot frequency of 2.8 times / s. The corresponding target values ​​are a capacity of 1680 units / hour, energy consumption of 9.5 kWh / hour, a quality standard deviation of 0.22 mm, and a wear rate of 1.5 μm / hour. By using 20 different weight combinations, 20 solutions are obtained that are distributed at different locations on the Pareto front.

[0170] Secondly, the ε-constraint method is employed. This method transforms all objectives except the primary objective into constraints. Assuming that production capacity f1 is chosen as the primary objective for maximization, and energy consumption, quality, and wear rate are used as constraints, the optimization problem is formulated as: maximizing f1, with the constraint f2 ≤ 2, f3≤ 3, f4≤ 4, of which 2, 3, 4 represents the upper limit of the constraint. For example, setting an energy consumption constraint. 2 = 12 kWh / hour, mass constraint 3 = 0.30 mm, wear constraint Given a speed of 4 = 2.2 micrometers / hour, the optimal parameter combination for maximizing production capacity was sought. The solver determined the optimal parameters to be: star disk rotation speed 43 rpm, conveyor belt speed 0.34 m / s, and robot arm frequency 3.7 cycles / s, corresponding to a production capacity of 2180 pieces / hour. This perfectly satisfies the constraints of energy consumption 11.9 kWh / hour, mass 0.29 mm, and wear rate 2.1 micrometers / hour. The upper limit of these constraints was adjusted. For example, relaxing the energy consumption constraint to 14 kWh / h can yield solutions with higher productivity. Using 10 different constraint settings, another 10 solutions on the Pareto front are obtained. These solutions are mainly distributed in the end region of the front, supplementing the extreme cases that the weighted sum method cannot fully cover.

[0171] Third, a non-dominated sorting method is employed, which directly stratifies the solution set based on Pareto dominance. First, an initial solution set containing 500 candidate solutions is generated, obtained through random sampling or grid sampling in the parameter space. For any two solutions A and B in the solution set, their performance on four objectives is compared. If A's productivity is no lower than B's, its energy consumption is no higher than B's, its quality is no worse than B's, and its wear is no higher than B's, and at least one aspect is strictly superior to B, then A dominates B. For example, if the objective value of solution A is (2300, 13.0, 0.27, 2.0) and the objective value of solution B is (2200, 13.5, 0.28, 2.1), the comparison reveals that A has higher productivity, lower energy consumption, better quality, and less wear, outperforming B in all four dimensions; therefore, A dominates B. All solution pairs are iterated through, and the number of times each solution is dominated and the number of other solutions it dominates are counted.

[0172] Solutions not dominated by any other solution are grouped into the first layer, i.e., the Pareto optimal solution set. Of the 500 candidate solutions, 48 ​​are assumed to be undominated, forming the first layer. After removing these 48 solutions from the candidate set, the remaining 452 solutions are re-sorted for non-dominated solutions, resulting in 55 undominated solutions in the second layer. This process is repeated to obtain multiple layers. The 48 solutions from the first layer are retained as the final Pareto optimal solution set. These solutions are relatively evenly distributed in the target space, covering various equilibrium points from high productivity and high energy consumption to low productivity and low energy consumption, and from high quality and low speed to low quality and high speed.

[0173] Combining the results of the three methods, some solutions were found to be duplicated among the 20 solutions obtained by the weighted sum method, the 10 solutions obtained by the ε-constraint method, and the 48 solutions obtained by the non-dominated sorting method. After removing duplicate solutions, a Pareto optimal solution set containing 52 unique solutions was formed. To verify the completeness of this solution set, these 52 points were plotted in the target space to observe whether they were continuously distributed to form a clear leading edge surface. The spacing between adjacent solutions was calculated, and the standard deviation of the spacing was found to be 0.18, and the coefficient of variation was 0.24, both below the threshold of 0.3, indicating a relatively uniform distribution. This Pareto optimal solution set provides a wealth of choices for subsequent decision-making, allowing production managers to select the parameter combination that best suits the current situation based on different production needs.

[0174] Example 6

[0175] This embodiment is a further extension of S3.3 in Embodiment 4, introducing an adaptive variable search step size mechanism, and adding the following steps to the online learning process in S3.3:

[0176] S3.3.1: Sensitivity analysis is performed on the station parameters during the online learning process of the deep Q network. Different search step sizes are allocated according to the sensitivity of the star disk rotation speed, the speed of the torsional conveyor belt, and the motion frequency of the robot. The first step size is used for searching sensitive parameters, and the second step size is used for searching non-sensitive parameters. The second step size is greater than the first step size.

[0177] Sensitivity analysis was conducted using a virtual simulation model, with fine-tuning of three parameters to observe the changes in the capacity-energy consumption ratio. Increasing the star disk rotation speed by 1 rpm resulted in a 0.8% change in the capacity-energy consumption ratio; increasing the conveyor belt speed by 0.01 m / s resulted in a 1.5% change; and increasing the robot arm frequency by 0.1 times / s resulted in a 0.5% change. The analysis results show that the conveyor belt speed is the most sensitive, followed by the star disk rotation speed, while the robot arm frequency is the least sensitive.

[0178] The search step size was allocated based on the sensitivity analysis results. The conveyor belt speed was defined as a sensitive parameter, with an initial step size of 0.02 m / s, meaning each adjustment was ±0.02 m / s. The astrolabe rotation speed was defined as a medium-sensitive parameter, with a medium step size of 3 rpm. The robot arm frequency was defined as a non-sensitive parameter, with a second step size of 0.3 cycles / second, the second step size being a multiple of the first step size.

[0179] Using a smaller step size to search for sensitive parameters allows for fine-tuning within sensitive regions, avoiding missing optimal values ​​or causing oscillations due to excessively large step sizes. Using a larger step size to search for insensitive parameters allows for rapid traversal of regions with minimal impact on the target, improving search efficiency and avoiding wasting computational resources on minor parameters.

[0180] S3.3.2: The search step size is automatically adjusted according to the optimization process. In the early stage of optimization, an initial step size is used to quickly explore the parameter space. When a potential advantageous region is found, the step size is automatically reduced to conduct a fine search, and random perturbations are introduced to avoid getting trapped in local optima.

[0181] A step size adjustment strategy was set, using a larger initial step size for coarse searching in the initial optimization phase. The initial step size for the conveyor belt speed was set to 0.05 m / s, the initial step size for the star disk rotation speed was set to 8 rpm, and the initial step size for the robot arm frequency was set to 0.5 cycles / s. In the first 500 training rounds, the initial step size was used for extensive exploration to quickly identify potential regions in the parameter space.

[0182] The system monitors reward changes during the exploration process. When the average reward remains within a certain range for 50 consecutive rounds, with a change of less than 5%, a potential advantageous area is identified. At this point, the search step size is automatically reduced: the conveyor belt speed step size is reduced to 0.02 m / s, the star disk rotation speed step size is reduced to 3 rpm, and the robot arm frequency step size is reduced to 0.3 times / s, equivalent to 40% of the original step size.

[0183] During the fine-grained search phase, random perturbations are introduced at regular intervals. Specifically, every 20 normal search steps, a perturbation step is inserted, in which a random offset following a normal distribution is applied to the parameters. The standard deviation of the offset is set to 50% of the current step size, and the direction is random. For example, a random offset with a standard deviation of 0.01 m / s is applied to the conveyor belt speed. These random perturbations allow the search to escape possible local optima and explore other feasible solutions in the vicinity.

[0184] If a better solution is found after introducing a perturbation, the search continues with that solution as the center; if the quality of the solution decreases after the perturbation, the search returns to the position before the perturbation. By combining dynamic step size adjustment and random perturbation, the search process takes into account both the breadth and depth of exploration, enabling rapid location of advantageous regions, fine-tuning of local areas, and avoiding premature convergence.

[0185] Specifically, the search step size determines the magnitude of parameter adjustments and is a key factor affecting optimization efficiency and accuracy. An excessively large step size leads to a leapfrog search, potentially skipping the optimal solution without precise localization; an excessively small step size results in a slow search, requiring numerous iterations to approach the optimal region, leading to inefficiency. Dynamic step size adjustment strategies adaptively change the step size according to different stages of the optimization process, achieving a balance between exploration speed and convergence accuracy.

[0186] In the initial optimization phase, with limited understanding of the global characteristics of the parameter space, rapid exploration is needed to identify potential regions. A large initial step size is used for coarse searching at this stage. Assuming the conveyor belt speed parameter range is 0.1 to 0.5 m / s, the initial step size is set to 0.08 m / s, equivalent to 20% of the parameter range. Starting from an initial point of 0.3 m / s, the first iteration attempts speeds of 0.38 m / s and 0.22 m / s in two directions to quickly explore different regions of the parameter space. For the star disk rotation speed, the parameter range is 10 to 60 rpm, with an initial step size of 10 rpm. Starting from an initial point of 40 rpm, speeds of 50 rpm and 30 rpm are attempted. For the robot arm frequency, the parameter range is 1 to 5 cycles / second, with an initial step size of 0.8 cycles / second, starting the exploration from 3 cycles / second.

[0187] In the first 100 iterations, an extensive exploration was conducted using the initial step size to evaluate the production-energy ratio under various parameter combinations. The objective function value was recorded for each iteration, and the optimization curve was plotted. It was observed that in the first 50 iterations, the objective function value rapidly increased from the initial 166 to 192, indicating that the search was approaching the dominant region. From iterations 50 to 100, the objective function value fluctuated between 188 and 195, with the fluctuation range gradually narrowing, indicating that it had entered a potential dominant region.

[0188] When optimization is detected to have entered a stable phase, a step size reduction mechanism is triggered. The criterion is that the average objective function value over 30 consecutive iterations must have a change rate of less than 3% compared to the average of the previous 30 iterations. Assuming the average value from iterations 80 to 110 is 191.5 and the average value from iterations 50 to 80 is 186.2, the change rate is (191.5 - 186.2) / 186.2 = 2.85%, which is less than the 3% threshold, thus satisfying the step size reduction condition. A fixed reduction factor of 0.4 is used for the step size reduction. The conveyor belt speed step size is reduced from 0.08 m / s to 0.08 × 0.4 = 0.032 m / s, the star disk rotation speed step size is reduced from 10 rpm to 4 rpm, and the robot arm frequency step size is reduced from 0.8 times / s to 0.32 times / s.

[0189] After entering the fine-grained search phase, a smaller step size is used to conduct a more detailed exploration near the discovered advantageous region. Assume the current optimal parameters are a star disk rotation speed of 46 rpm, a conveyor belt speed of 0.37 m / s, and a robot arm frequency of 3.9 times / s, with an objective function value of 194. Centering on this point, various combinations of star disk rotation speeds of 42, 46, and 50 rpm (step size 4), conveyor belt speeds of 0.338, 0.37, and 0.402 m / s (step size 0.032), and robot arm frequencies of 3.58, 3.9, and 4.22 times / s (step size 0.32) are attempted. Through fine-grained search, it is found that the objective function value of the parameter combination (46, 0.402, 3.9) reaches 196, which is better than the current optimal solution. Therefore, this point is updated as the optimal solution.

[0190] To avoid getting trapped in local optima, random perturbations are introduced periodically during the fine-grained search process. The perturbation strategy involves inserting one perturbation step every 15 normal search steps. The perturbation amount follows a normal distribution with a mean of 0 and a standard deviation of 50% of the current step size. For example, for the conveyor belt speed parameter, with a current step size of 0.032 m / s, the standard deviation of the perturbation is 0.032 × 0.5 = 0.016 m / s. The perturbation is triggered at the 150th iteration. The current speed is 0.402 m / s, and a random number following an N(0, 0.0162) distribution is generated, assumed to be 0.023. Therefore, the perturbed speed is 0.402 + 0.023 = 0.425 m / s. Similar random perturbations are applied to the astrolabe rotation speed and the robot arm frequency, resulting in the perturbed parameter combination (48, 0.425, 4.05).

[0191] The parameter combination after perturbation is evaluated, assuming its objective function value is 193, lower than the unperturbed value of 196. According to the Metropolis criterion, a poorer solution is accepted with a certain probability to prevent the search from prematurely fixing in a local optimum. The acceptance probability is calculated as follows:

[0192]

[0193] Where f current The current optimal value is 196, f new The value after perturbation is 193, and T is the temperature parameter, initially set to 5, decreasing with the number of iterations. The calculation yields... Generate a random number between 0 and 1, say 0.42, which is less than the acceptance probability of 0.549. Therefore, accept the perturbation and move the current search point to (48, 0.425, 4.05). Although this point is currently performing poorly, it may create an opportunity to escape the local optimum later.

[0194] The search continued from the new point. After several iterations, on the 175th iteration, the objective function value of the parameter combination (47, 0.415, 4.1) was found to be 197, exceeding the previous optimal value of 196. This indicates that the random perturbation successfully helped the search escape the local optimum and find a better solution. Without the perturbation mechanism, the search might have stalled near (46, 0.402, 3.9), failing to find the better (47, 0.415, 4.1). By combining dynamic step size adjustment and random perturbation, the optimization process balanced global exploration and local development, enabling it to quickly approach the optimal region, accurately converge to the optimal solution, and avoid falling into local optimum traps.

[0195] Furthermore, the multi-resolution exploration strategy draws on the concept of multi-scale analysis in image processing. By progressively refining the search range at different precision levels, it avoids blindly performing high-precision searches across the entire parameter space, significantly reducing computational load. The core idea of ​​this strategy is to first quickly scan the entire parameter space with a coarse grid to identify sub-regions with higher objective function values, and then perform a secondary search within these sub-regions using a denser grid, iterating in this way until the desired precision is achieved.

[0196] The first stage is a coarse-grained global scan. The star disk rotation speed range of 10-60 rpm is divided into 5 intervals: [10, 20), [20, 30), [30, 40), [40, 50), [50, 60], with the midpoint of each interval taken as 15, 25, 35, 45, and 55 rpm. The conveyor belt speed range of 0.1-0.5 m / s is divided into 4 intervals: [0.1, 0.2), [0.2, 0.3), [0.3, 0.4), [0.4, 0.5], with representative points of 0.15, 0.25, 0.35, and 0.45 m / s. The robot arm frequency range of 1-5 times / s is divided into 4 intervals: [1, 2), [2, 3), [3, 4), [4, 5], with representative points of 1.5, 2.5, 3.5, and 4.5 times / s. The combination of the three parameters forms 5×4×4=80 grid nodes.

[0197] A virtual simulation model of the production line is run for each grid node, simulating a production process of approximately 10 minutes over 100 time steps. Average capacity and energy consumption are recorded, and the capacity-energy consumption ratio is calculated as the objective function value. For example, node (15, 0.15, 1.5) corresponds to the low-speed operation mode, with a simulated capacity of 1320 units / hour and energy consumption of 7.8 kWh / hour, resulting in a capacity-energy consumption ratio of 1320 / 7.8 = 169. Node (45, 0.35, 3.5) corresponds to the medium-high speed mode, with a simulated capacity of 2280 units / hour and energy consumption of 13.2 kWh / hour, resulting in a capacity-energy consumption ratio of 2280 / 13.2 = 173. Node (55, 0.45, 4.5) corresponds to the high-speed mode, with a simulated capacity of 2720 units / hour and energy consumption of 16.5 kWh / hour, resulting in a capacity-energy consumption ratio of 2720 / 16.5 = 165.

[0198] The objective function values ​​of the 80 nodes were sorted, and the top 20%, or the top 16 nodes, were selected, all of which had objective function values ​​higher than 170. Analysis of the parameter distribution of these 16 nodes revealed that they were mainly concentrated in the region where the star disk rotation speed was 40-50 rpm, the conveyor belt speed was 0.30-0.40 m / s, and the robot arm frequency was 3-4 times / s. This region was identified as a potential parameter subspace and will be explored in more detail in the second phase.

[0199] The second stage involves medium-grained local refinement. A denser search is performed only within the identified subspace [40, 50] × [0.30, 0.40] × [3, 4]. The star disk rotation speed of 40-50 rpm is divided into 5 smaller intervals, spaced 2 rpm apart, with representative points at 41, 43, 45, 47, and 49 rpm. The conveyor belt speed of 0.30-0.40 m / s is divided into 5 intervals, spaced 0.02 m / s apart, with representative points at 0.31, 0.33, 0.35, 0.37, and 0.39 m / s. The robotic arm frequency of 3-4 times / s is divided into 5 intervals, spaced 0.2 times / s apart, with representative points at 3.1, 3.3, 3.5, 3.7, and 3.9 times / s. This results in 5 × 5 × 5 = 125 new grid nodes.

[0200] Simulations were performed on these 125 nodes, with each node running for 150 time steps (approximately 15 minutes) to obtain a more accurate evaluation. For example, the objective function value for node (43, 0.33, 3.5) was 174, for node (47, 0.37, 3.7) it was 176, and for node (45, 0.35, 3.9) it was 175. The top 20%, or the top 25 nodes, were then selected, and their objective function values ​​were all higher than 175. Analysis of the distribution of these 25 nodes revealed a further concentration in a smaller region with a star disk rotation speed of 44-48 rpm, a conveyor belt speed of 0.34-0.38 m / s, and a robot arm frequency of 3.6-3.9 times / s.

[0201] The third stage is fine-grained continuous optimization. Within the second-refined subspace [44, 48] × [0.34, 0.38] × [3.6, 3.9], the aforementioned adaptive step-size continuous optimization method is used for searching. The initial point is chosen as the node with the highest objective function value in the second stage (47, 0.37, 3.7). The initial step size is set to 1 revolution / minute for the star disk rotation, 0.01 m / s for the conveyor belt speed, and 0.1 cycles / s for the robot arm frequency, and gradient search begins. In each iteration, multiple candidate points near the current point are evaluated, and the direction that provides the greatest improvement in the objective function value is selected for movement. After 50 iterations, the search gradually converges to the parameter combination (46.8, 0.375, 3.82), and the objective function value reaches 177.5, an improvement of 1.5 compared to the optimal value of 176 in the second stage.

[0202] Through three stages of progressive refinement, the search range is narrowed from the initial full space of 50 × 0.4 × 450 units to 10 × 0.1 × 110 units after the first stage, and then to 4 × 0.04 × 0.34 units after the second stage, finally converging within a fine-grained region of 0.48 units. If a fine-grained search were performed directly across the full space, the number of nodes to be evaluated would reach tens of thousands. In contrast, the multi-resolution strategy only requires evaluating 80 + 125 + 50 = 255 nodes, reducing computational cost by over 99%, while still finding a near-global optimum. This strategy is particularly suitable for optimization problems in high-dimensional parameter spaces; the computational advantages of the multi-resolution strategy become even more pronounced as the parameter dimension increases.

[0203] The memory-enhanced search mechanism enables the optimization system to learn from historical experience, avoiding repeated calculations of the same or similar parameter combinations. When encountering similar production conditions, it can quickly call upon historical optimal solutions as initial points, significantly accelerating the convergence process. This mechanism relies on a structured parameter performance mapping database, which records all previously evaluated parameter combinations and their corresponding performance metrics.

[0204] The database data structure is designed as a key-value pair. The key is a coded string representing the parameter combination, in the form of a triple: "S{Starboard Rotation Speed}-V{Conveyor Belt Speed}-F{Robot Frequency}". For example, "S45-V0.35-F3.8" represents a starboard rotation speed of 45 rpm, a conveyor belt speed of 0.35 m / s, and a robot frequency of 3.8 times / s. The value is a performance record structure containing multiple fields, including: evaluation timestamp (marking when the parameter combination was evaluated); production capacity (units / hour); energy consumption (unit kilowatt-hours / hour); quality standard deviation (unit millimeters); wear rate (unit micrometers / hour); production capacity-energy ratio; production condition label (recording product specifications, ambient temperature, and other external conditions at the time of evaluation); access count (recording the frequency of querying or using the parameter combination); and last access time (used to implement the elimination strategy).

[0205] During each optimization process, whenever a new combination of parameters is evaluated through simulation or actual operation, the combination and its performance results are stored in the database. For example, in one optimization, the parameter combination (46, 0.37, 3.9) was evaluated, and the simulation yielded a production capacity of 2350 units / hour, energy consumption of 13.8 kWh / hour, a quality standard deviation of 0.28 mm, a wear rate of 2.3 μm / hour, and a production capacity-energy consumption ratio of 170. This record is stored in the database with the key "S46-V0.37-F3.9", the initial access count is set to 1, and the last access time is set to the current timestamp 2026-02-09 14:30:00.

[0206] The database uses a Least Recently Used (LRU) eviction policy to control its size. The database capacity is set to a maximum of 5000 records. When the number of stored records exceeds 5000, records are sorted by last access time, and the least recently accessed record is deleted. Each time a new record is inserted, the capacity is checked; if the limit is exceeded, the oldest 10% of records (500 records) are evicted. This ensures that the database retains only recently evaluated or frequently used parameter combinations, guaranteeing both information timeliness and control over storage space.

[0207] When a new round of optimization needs to begin, such as switching production from product specification A to specification B, or from day shift to night shift, the system first queries the database for historical records under similar conditions. Similarity judgment is based on matching production condition labels and parameter ranges. For example, if product specification A corresponds to a cardboard box with dimensions of 20 cm (length) × 15 cm (width) × 10 cm (height), and product specification B has dimensions of 22 cm (length) × 15 cm (width) × 10 cm (height), these dimensions are close and defined as similar specifications. Searching the database for all historical records tagged with specification A yields 320 relevant records.

[0208] From these 320 records, the best-performing records were selected, with the top 32 records chosen based on their production capacity-to-energy consumption ratio. The parameter combinations corresponding to these 32 records are mainly distributed in the range of 43-48 rpm for the star disk rotation speed, 0.33-0.39 m / s for the conveyor belt speed, and 3.6-4.0 cycles / s for the robot arm frequency. The centroid of these 32 parameter combinations was calculated as the initial search point for specification B optimization. The centroid was calculated as a weighted average of the parameters, with the weights being the corresponding production capacity-to-energy consumption ratios. Assuming the calculated centroid parameters are 45.6 rpm for the star disk rotation speed, 0.362 m / s for the conveyor belt speed, and 3.78 cycles / s for the robot arm frequency.

[0209] In addition to the initial point, a step size strategy was extracted from historical records. The average step size used during the final convergence phase of specification A optimization was statistically analyzed, revealing that the effective step size for the star disk rotation speed was 1.2 rpm, the conveyor belt speed was 0.015 m / s, and the robot arm frequency was 0.12 times / s. These step sizes were used as the initial step sizes for specification B optimization, avoiding trial and error starting with excessively large or small step sizes.

[0210] Starting with the centroid parameters and historical step size, specification B was optimized. Since the initial point was already near the advantage region, the optimization process converged quickly. After only 30 iterations, the optimal parameters for specification B were found to be: a star disk rotation speed of 46.2 rpm, a conveyor belt speed of 0.368 m / s, a robot arm frequency of 3.85 times / s, and a production capacity-energy consumption ratio of 168. The entire optimization and debugging process took approximately 3 minutes. Without the memory enhancement mechanism, optimization starting from a random initial point typically takes 8-12 minutes to converge; memory enhancement reduced the debugging time by more than 70%.

[0211] The optimization results for specification B are also stored in the database, forming a positive feedback loop. As the production line processes an increasing number of product specifications, the database accumulates more experience and becomes more adaptable to new specifications. For example, after processing six specifications from A to F, the initial point hit rate for the seventh specification G reaches 95%, meaning there is a 95% probability that the initial point is already within the neighborhood of the optimal solution, further reducing the debugging time to less than one minute. The memory-enhanced search mechanism enables the optimization system to evolve from single-time optimization to continuous learning, giving the production line the ability to quickly adapt to multi-variety, small-batch production.

[0212] S3.3.3: Multi-resolution exploration of the parameter space is carried out. Potential parameter subspaces are identified at the coarse-grained level, and the resolution is gradually increased to carry out fine search, forming a multi-level parameter space exploration from coarse to fine.

[0213] The first phase involved coarse-grained exploration, dividing the parameter space into large grids. The star disk rotation speed range of 10-60 rpm was divided into 5 intervals, each spanning 10 rpm; the conveyor belt speed range of 0.1-0.5 m / s was divided into 4 intervals, each spanning 0.1 m / s; and the robot arm frequency range of 1-5 cycles / s was divided into 4 intervals, each spanning 1 cycle / s. Eighty nodes in a 5×4×4 grid were evaluated, with each node running a virtual simulation for 100 time steps, and the average reward recorded.

[0214] Identify the top 20% of grid nodes in terms of reward; the regions containing these nodes are considered potential parameter subspaces. Assume that regions with a star disk rotation speed of 40-50 rpm, a conveyor belt speed of 0.3-0.4 m / s, and a robot arm frequency of 3-4 times / s are identified as advantageous regions.

[0215] The second phase involves a medium-granularity exploration, conducting a more intensive search only within the identified dominant subspaces. The star disk rotation speed of 40-50 rpm is divided into 5 smaller intervals, each spanning 2 rpm; the conveyor belt speed of 0.3-0.4 m / s is divided into 5 intervals, each spanning 0.02 m / s; and the robot arm frequency of 3-4 cycles / s is divided into 5 intervals, each spanning 0.2 cycles / s. A total of 125 nodes (5×5×5) are evaluated.

[0216] Re-identify the top 20% of nodes in the medium-grained region, assuming a further narrowing down to the region with a star disk rotation speed of 44-48 rpm, a conveyor belt speed of 0.34-0.38 m / s, and a robot frequency of 3.4-3.8 times / s.

[0217] The third stage involves fine-grained exploration, employing the aforementioned adaptive step size for continuous optimization search within the subspace of the secondary optimization until convergence to a local optimum. This multi-level exploration, from coarse to fine, avoids blind fine-grained searching across the entire parameter space, significantly reducing computational cost while ensuring that advantageous regions are not overlooked.

[0218] S3.3.4: Constructing Memory-Enhanced Search

[0219] Based on the results of multi-level parameter space exploration, a parameter performance mapping database is constructed to record historical search paths and corresponding results.

[0220] A parameter performance mapping database is established, using a key-value pair storage structure. The key represents the parameter combination, encoded as a string; for example, "S45-V0.35-F3.6" indicates a star disk rotation speed of 45 rpm, a conveyor belt speed of 0.35 m / s, and a robotic arm frequency of 3.6 times / s. The value represents the performance index corresponding to that parameter combination, including the specific values ​​of four targets: production capacity, energy consumption, quality, and lifespan, as well as the comprehensive reward value.

[0221] During each optimization process, whenever a new combination of parameters is evaluated, that combination and its performance results are stored in the database. The database employs a least recently used eviction policy; when the capacity exceeds 5000 records, the least recently accessed record is evicted to keep the database size manageable.

[0222] When a new round of optimization needs to begin, such as switching to a new product specification or new production conditions, the database is first queried to see if there are historical records under similar conditions. Similarity is measured by calculating the Euclidean distance between the condition vectors; if the distance is less than a threshold, the records are considered similar. If a similar record is found, its optimal parameter combination is extracted as the initial search point, and the step size strategy used at that time is extracted as the initial step size.

[0223] Searching based on historical experience can significantly accelerate convergence. For example, when switching from production specification A to a similar specification B, the optimal parameters of specification A can be used directly as the starting point, requiring only minor adjustments, reducing debugging time from 10 minutes to 2 minutes. Memory-enhanced search enables the accumulation and reuse of optimization experience, giving the system the ability to learn and evolve.

[0224] Example 7

[0225] This embodiment is a further extension of Embodiment 5, introducing Pareto front homogeneity assessment and diversity preservation mechanisms, and adding the following steps after S3.2.2:

[0226] A1: Calculate the distance distribution between adjacent solutions in the Pareto optimal solution set, quantitatively evaluate the uniformity of the current search results distribution on the Pareto front, and identify regions of excessive search concentration and sparse regions.

[0227] For the 50 solutions in the Pareto optimal solution set, the distance from each solution to its nearest neighbor solution is calculated in the four-dimensional objective space. Using the Euclidean distance metric, for solutions i and j, the square root of the sum of the squares of the differences in productivity, energy consumption, quality, and lifetime is taken to obtain the distance value. To eliminate the influence of dimensions, the four objectives are first normalized so that each objective falls within the range of 0 to 1.

[0228] For each solution, find its nearest neighbor and record the minimum distance. Calculate the minimum distance distribution for all solutions, and then calculate the mean minimum distance and standard deviation. A large standard deviation indicates an uneven distribution of solutions, with both dense and sparse regions. If the minimum distance of some solutions is much smaller than the mean, these solutions are too densely clustered; if the minimum distance of some solutions is much larger than the mean, these solutions are too isolated and surrounded by sparse regions.

[0229] The uniformity index is calculated using the coefficient of variation of the minimum distance, which is equal to the standard deviation divided by the mean. The smaller the coefficient of variation, the more uniform the distribution. A uniformity threshold of 0.3 is set; if the coefficient of variation exceeds 0.3, the current solution set is considered unevenly distributed and regional balancing adjustments are required.

[0230] A2: Based on the distribution uniformity assessment results, when it is detected that the search is overly concentrated in a specific region of the Pareto front, the sampling weight of the sparse region is automatically increased to guide the search to expand to the solution space that has not been fully explored, thereby achieving regional balance.

[0231] Dense and sparse regions are identified. Solutions with a minimum distance less than half the average are marked as dense regions, while solutions with a minimum distance greater than twice the average are marked as sparse regions. It is assumed that solutions are clustered in the high-capacity, low-energy-consumption quadrant, while solutions are sparser in the medium-capacity, high-quality quadrant.

[0232] The search sampling strategy was adjusted by increasing the sampling weight of sparse regions in subsequent optimization iterations. Specifically, when selecting the starting point for optimization, solutions located near sparse regions were given a higher probability of being selected. The solutions in the solution set were divided into three levels according to their density: solutions in dense regions had a sampling weight of 0.2, solutions in medium-density regions had a weight of 0.3, and solutions in sparse regions had a weight of 0.5.

[0233] More candidate solutions are generated and evaluated around sparse regions. For example, in a sparse region with medium capacity and high quality, the optimization algorithm is guided to search this region by reducing the weight of the capacity objective and increasing the weight of the quality objective. The ε-constraint method is used to set a lower limit constraint on capacity and an upper limit objective on quality, generating candidate solutions for this region.

[0234] After 100 rounds of equilibrium search, sparse regions are gradually filled, and the solution density in dense regions decreases relatively. The homogeneity index is recalculated, and when the coefficient of variation decreases to below 0.3, regional equilibrium is considered to have been achieved, and the Pareto front coverage is relatively complete and uniform.

[0235] A3: To evaluate the diversity of solutions in the solution space, solutions with different characteristics are retained by calculating crowding distance, analyzing the distribution of reference points, and evaluating hypervolume contribution, thus preventing diverse solutions from being eliminated during the search process.

[0236] Calculate the crowding distance for each solution to measure the crowding level around that solution. For solution i, in each target dimension, find the two solutions adjacent to solution i in that dimension, and calculate the difference between their coordinates in that dimension as the crowding distance for that dimension. Sum the crowding distances of the four dimensions to obtain the total crowding distance of solution i. A solution with a large crowding distance indicates that its surroundings are relatively open and it is a relatively unique solution; a solution with a small crowding distance indicates that the surrounding solutions are more densely packed.

[0237] During the solution selection phase of the optimization process, when choosing which solutions to retain from the candidate solutions, not only the merits of the objective value are considered, but also the crowding distance. For multiple solutions with similar objective values, solutions with larger crowding distances are prioritized for retention, while solutions with smaller crowding distances are eliminated, thereby maintaining solution diversity.

[0238] A reference point distribution is established by pre-setting a set of uniformly distributed reference points in the target space. For example, 81 reference points can be set in four-dimensional space to cover various combinations of targets. For each reference point, the solution closest to that reference point in the solution set is calculated and used as the representative solution for that reference point. This ensures that each reference point has a representative solution, covering different regions of the target space and achieving solution diversity.

[0239] Evaluate the contribution of each solution to the Pareto front hypervolume. Hypervolume is a comprehensive indicator of the quality of the solution set, representing the volume dominated by the solution set in the target space. Calculate the hypervolume increment contributed individually by each solution. Solutions with large contributions are key solutions supporting the front and should be retained even if their target value may not be an extremum in a certain dimension. Solutions with small contributions may be dominated by other solutions or highly overlap with other solutions and can be considered for elimination.

[0240] By employing a triple mechanism of crowding distance, reference point, and hypervolume, we ensure that the retained solution set not only covers the complete distribution of the Pareto front but also maintains the differences between solutions, providing a wealth of options for subsequent decision-making.

[0241] A4: Based on diversity assessment, construct a diverse set of solutions containing solutions with different optimization directions to ensure that the diverse set of solutions has a balanced distribution across different dimensions of capacity, energy consumption, quality, and equipment lifespan; use the diverse set of solutions as a candidate set of parameter combinations for selection by flexible scheduling strategies.

[0242] Cluster analysis was performed on the Pareto optimal solution set, dividing it into multiple clusters based on the solution's position in the target space. The K-means clustering algorithm was used, with 10 clusters assigned to each of the 50 solutions. Each cluster represents a class of solutions with similar characteristics; for example, one cluster represents high-capacity, high-energy-consumption solutions, another low-capacity, low-energy-consumption solutions, and yet another high-quality, medium-capacity solutions.

[0243] Representative solutions are selected from each cluster, prioritizing those closest to the cluster center and with a large crowding distance. This yields 10 representative solutions, covering various equilibrium points from extremely high productivity to extremely energy efficiency, and from quality-first to lifetime-first priorities.

[0244] Ten representative solutions are labeled based on their performance on each objective. Labels could include "maximum capacity type," "balanced type," "energy-saving priority type," "high-quality type," and "equipment protection type." These solutions and their labels are stored as a diverse solution set, serving as a candidate set for parameter combinations in flexible scheduling.

[0245] In actual production, solutions with corresponding labels are directly selected from a diverse set of solutions based on the current production scenario and needs. For example, when orders are urgent, the "maximum capacity" solution is selected; when electricity prices are at their peak, the "energy saving priority" solution is selected; and when equipment has been running for a long time, the "equipment protection" solution is selected. When switching scenarios, only different solutions need to be selected from the candidate set, without the need for complex optimization calculations, thus achieving rapid response.

[0246] Specifically, the uniformity of the Pareto front is an important indicator for measuring the quality of multi-objective optimization. A uniformly distributed Pareto front provides decision-makers with a complete selection space of various equilibrium solutions, while an unevenly distributed front can lead to a lack of alternatives for certain objective trade-offs. This embodiment quantitatively evaluates the uniformity of the front by calculating the distance distribution between adjacent solutions in the solution set, providing a basis for subsequent regional equilibrium searches.

[0247] In Example 5, the obtained Pareto optimal solution set contains 52 solutions, each corresponding to a point in the four-dimensional target space, with coordinates representing the values ​​of four objectives: production capacity, energy consumption, quality standard deviation, and wear rate. To calculate the distance between adjacent solutions, the four objectives are first normalized to eliminate the influence of different dimensions; specifically, the production capacity ranges from 1500 to 3000 units / hour, the energy consumption ranges from 8 to 18 kWh / hour, the quality standard deviation ranges from 0.2 to 0.45 mm, and the wear rate ranges from 1.2 to 3.5 micrometers / hour. The normalization process uses the extreme value method, which subtracts the minimum value from each target value and then divides it by the difference between the maximum and minimum values, so that all target values ​​are normalized to the range of 0 to 1. For example, the normalized value of production capacity of 2300 units / hour is (2300-1500) / (3000-1500) = 0.533, and the normalized value of energy consumption of 13 kWh / hour is (13-8) / (18-8) = 0.5.

[0248] For each solution in the solution set, calculate its Euclidean distance to all other solutions and find its nearest neighbor. Take solution A as an example; its normalized objective values ​​are: capacity 0.533, energy consumption 0.5, quality 0.4, and wear 0.481. Calculate the distance from solution A to solution B, whose normalized objective values ​​are: capacity 0.6, energy consumption 0.6, quality 0.5, and wear 0.556. The distance is calculated by taking the square root of the sum of the squares of the capacity difference, energy consumption difference, quality difference, and wear difference, i.e., the square of 0.067 plus the square of 0.1 plus the square of 0.075, totaling 0.019825. Taking the square root yields 0.141. Similarly, calculate the distances from solution A to the other 50 solutions, finding the minimum distance of 0.089, whose nearest neighbor is solution C. Record the minimum neighbor distance of solution A as 0.089.

[0249] The minimum neighbor distances of the 52 solutions were calculated, resulting in 52 distance values. The distribution of these distance values ​​reflects the density of solutions on the Pareto front. The average of these 52 distance values ​​is 0.095, and the standard deviation is 0.038. A larger standard deviation indicates that some solutions are very close together, forming dense regions, while others are very far apart, forming sparse regions. Further analysis revealed that 12 solutions have minimum neighbor distances less than 0.06, indicating that these solutions are clustered too tightly; 8 solutions have minimum neighbor distances greater than 0.15, indicating that these solutions are relatively isolated, surrounded by large unexplored areas.

[0250] The uniformity index is calculated using the coefficient of variation, which is the standard deviation divided by the mean. In this example, the coefficient of variation is 0.038 divided by 0.095, equaling 0.4, exceeding the preset uniformity threshold of 0.3. This indicates that the current solution set is not uniformly distributed and needs adjustment. Visual analysis is used to project the 52 points into a four-dimensional target space. Using capacity and energy consumption as the horizontal and vertical axes, a two-dimensional projection is drawn. It is observed that in the high-capacity, high-energy-consumption quadrant, 18 points cluster in a small area with very small distances between them; the distance between the three densest points is less than 0.05. In contrast, the medium-capacity, low-energy-consumption quadrant has only 3 points, with distances exceeding 0.2, indicating a significant gap. This uneven distribution means that if decision-makers wish to choose a balanced solution with medium capacity and low energy consumption, the available parameter combinations are very limited, while the high-capacity, high-energy-consumption quadrant offers too many redundant options.

[0251] To quantitatively describe dense and sparse regions, classification criteria were established. Solutions with a minimum adjacent distance less than half the average (less than 0.0475) were labeled as dense region solutions, totaling 15. Solutions with a minimum adjacent distance greater than twice the average (greater than 0.19) were labeled as sparse region solutions, totaling 6. The remaining 31 solutions were classified as medium-density solutions. The 15 solutions in the dense region are mainly distributed in two corners of the target space: one corner corresponds to an extreme high-speed scheme with high productivity, high energy consumption, low quality, and high wear, containing 9 solutions; the other corner corresponds to an extreme energy-saving scheme with low productivity, low energy consumption, high quality, and low wear, containing 6 solutions. The 6 solutions in the sparse region are scattered in the middle of the target space, corresponding to various compromise balance schemes, such as a balanced scheme with medium-high productivity, medium energy consumption, high quality, and medium wear.

[0252] The uniformity assessment results indicate that the current search strategy focuses excessively on exploring extreme solutions while neglecting compromise solutions. This bias may stem from the inherent characteristics of optimization algorithms; some algorithms tend to first find extreme points on the boundary of the target space and then gradually fill in the intermediate regions. However, if the number of search iterations is insufficient, the intermediate regions may not be fully explored. Another reason might be that the weighted sum method favors extreme weight combinations, such as a 0.8 to 0.2 combination, while using fewer combinations with moderate weights, such as 0.5 to 0.5. Having identified these issues, subsequent region balancing searches will specifically increase the search intensity for sparse regions and reduce repeated searches for dense regions, gradually adjusting the solution set to a more uniform distribution.

[0253] The goal of regional balanced search is to gradually bring solutions that are initially unevenly distributed on the Pareto front to a more uniform distribution by adjusting the allocation of search resources. The core idea of ​​this strategy is to prioritize allocating limited computational resources to regions with sparser solutions, while reducing the search in regions where solutions are already dense, thereby achieving overall distribution balance.

[0254] Based on the dense and sparse regions identified in the previous step, the sampling strategy for the search is first adjusted. In traditional multi-objective optimization, new candidate solutions are usually generated by randomly selecting a solution from the current solution set as a starting point for mutation or crossover. In the regional equilibrium search, the selection mechanism is modified to assign different selection probabilities to solutions in regions of different densities. The sampling weight of the 15 solutions in the dense region is set to 0.15, meaning that when generating new candidate solutions, the probability of each solution in the dense region being selected as a starting point is 0.15 divided by 15, which equals 0.01. The sampling weight of the 31 solutions in the medium-density region is set to 0.35, meaning the probability of each medium-density solution being selected is 0.35 divided by 31, which is approximately 0.011. The sampling weight of the 6 solutions in the sparse region is set to 0.5, meaning the probability of each solution in the sparse region being selected is 0.5 divided by 6, which is approximately 0.083. Through this weight allocation, the probability of solutions in the sparse region being selected is more than 8 times that of solutions in the dense region, causing the search resources to be significantly tilted towards the sparse region.

[0255] In the subsequent 100 iterations of optimization, a starting point is selected in each round according to the new sampling weights. Assuming that in the first iteration, the random number generator produces a value of 0.62, which falls within the weight range of the sparse region according to the cumulative probability distribution, a sparse region solution is selected as the starting point. The parameters corresponding to this sparse region solution are: a star disk rotation speed of 42 revolutions per minute, a conveyor belt speed of 0.32 meters per second, and a robot arm frequency of 3.4 times per second. The target values ​​are: a production capacity of 2050 pieces per hour, an energy consumption of 11.2 kilowatt-hours per hour, a quality standard deviation of 0.24 millimeters, and a wear rate of 1.8 micrometers per hour. Starting from this point, a mutation operator is applied to generate neighborhood candidate solutions. The mutation operator applies small-amplitude random perturbations to the three parameters, with the perturbation range set to ±5% of the current value. The generated candidate solutions are: a star disk rotation speed of 43.5 revolutions per minute, a conveyor belt speed of 0.335 meters per second, and a robot arm frequency of 3.3 times per second.

[0256] The objective function value of the candidate solution was evaluated. Simulation yielded a production capacity of 2110 units per hour, energy consumption of 11.5 kWh per hour, a quality standard deviation of 0.25 mm, and a wear rate of 1.85 μm per hour. The candidate solution was then checked to see if it was dominated by any solutions in the existing solution set. Comparison revealed that no solution in the existing set was superior to or equal to the candidate solution in all four objectives; therefore, the candidate solution was considered non-dominated. The candidate solution was added to the solution set, and it was further checked whether it dominated any solutions in the existing set. Comparison showed that it dominated an existing dense region solution with objective values ​​of 2020 units per hour, 11.8 kWh per hour, a quality standard deviation of 0.27 mm, and a wear rate of 1.95 μm per hour. This existing solution was inferior to the new candidate solution in all objectives, and therefore removed from the solution set. The updated solution set contained 52 solutions.

[0257] The regional balancing search continued from the second to the 100th round. Due to the high sampling weight of the sparse region solutions, approximately 50 rounds in the 100 iterations started with sparse region solutions, 35 rounds with medium-density solutions, and 15 rounds with dense region solutions. This is basically consistent with the weight allocation ratio of 0.5:0.35:0.15. Through the dense sparse region search, eight new non-dominated solutions were discovered in the medium-capacity, low-energy-consumption region, filling the original gaps in this region. For example, one newly discovered solution has the following parameters: a star disk rotation speed of 40 revolutions per minute, a conveyor belt speed of 0.30 meters per second, and a robot arm frequency of 3.2 times per second. The target values ​​are a capacity of 1950 pieces per hour, an energy consumption of 10.8 kilowatt-hours per hour, a quality standard deviation of 0.23 millimeters, and a wear rate of 1.7 micrometers per hour. This solution is located at the center of the original sparse region, with a distance of 0.11 from the nearest surrounding solution, significantly smaller than the original 0.22, indicating that the sparse region is being filled.

[0258] Meanwhile, in another sparse region, corresponding to a medium-to-high capacity, low-energy consumption, and high-quality direction, six new non-dominated solutions were discovered. These solutions are characterized by maintaining high capacity while reducing energy consumption through optimized workstation coordination and improving quality consistency through refined control. For example, one new solution has parameters of 44 revolutions per minute for the star disk, 0.34 meters per second for the conveyor belt speed, and 3.65 cycles per second for the robotic arm frequency. This is a finely tuned combination of parameters, unlike the coarse combinations of rounded parameters found in the dense region. The target values ​​for this solution are a capacity of 2200 pieces per hour, energy consumption of 12.2 kilowatt-hours per hour, a quality standard deviation of 0.235 millimeters, and a wear rate of 2.0 micrometers per hour, achieving a good balance between capacity and quality.

[0259] After 100 rounds of balancing search, 14 new non-dominated solutions were added, while 9 redundant solutions dominated by the new solutions were eliminated from the original solution set, ultimately expanding the solution set to 57. The minimum neighbor distances of these 57 solutions were recalculated, with an average of 0.082, a standard deviation of 0.025, and a coefficient of variation of 0.025 divided by 0.082, approximately 0.305, which is close to the uniformity threshold of 0.3. Compared to before the balancing search, the average neighbor distance decreased from 0.095 to 0.082, indicating an overall increase in solution density, as the newly added solutions primarily filled the previously sparse regions. More importantly, the standard deviation decreased from 0.038 to 0.025, a 34% reduction, indicating a significant decrease in the fluctuation of distances between solutions and a more uniform distribution. The number of dense solutions with a minimum neighbor distance less than 0.06 decreased from 15 to 7, while the number of sparse solutions with a minimum neighbor distance greater than 0.15 decreased from 6 to 2, significantly improving both extreme dense and sparse conditions.

[0260] On the two-dimensional projection of the target space, the 18 points that were previously clustered in the high-productivity, high-energy-consumption quadrant have been reduced to 12, as 6 redundant similar solutions have been replaced by new, better solutions. In the medium-productivity, low-energy-consumption quadrant, the area that previously had only 3 points has increased to 9 points, significantly improving the solution richness in this region. The entire Pareto front exhibits a more continuous and smooth distribution, without obvious clustering or discontinuities, providing decision-makers with a more complete and balanced selection space. The regional equilibrium search successfully corrected the biases of the initial search, achieving comprehensive coverage of the Pareto front.

[0261] In the iterative process of multi-objective optimization, there is an inherent contradiction: on the one hand, it is necessary to continuously improve the quality of solutions and eliminate dominated inferior solutions; on the other hand, it is necessary to maintain the diversity of solutions and avoid all solutions being concentrated in a narrow region. The diversity preservation mechanism introduces evaluation indicators other than the objective value, and considers the uniqueness and representativeness of solutions when eliminating inferior solutions, ensuring that the retained solutions are not only of high quality but also widely distributed, covering different optimization directions.

[0262] The first diversity metric is crowding distance, which measures the degree of crowding around a solution. A solution with a large crowding distance indicates that its surroundings are relatively open and it is a relatively unique solution; a solution with a small crowding distance indicates that there are many similar solutions around it and it is relatively less important. The crowding distance is calculated by examining the neighboring solutions of the solution in each target dimension. Taking solution A as an example, in the capacity target dimension, all solutions in the solution set are sorted according to their capacity values ​​to determine the preceding and following neighboring solutions of solution A in the sorted sequence; assuming that the capacity of solution A is 2200 units / hour, its preceding neighboring solution has a capacity of 2150 units / hour, and its following neighboring solution has a capacity of 2280 units / hour, then the crowding distance of solution A in the capacity dimension is 2280-2150=130 units / hour. Similarly, in the energy consumption target dimension, the energy consumption of solution A is 12 kWh / hour, and the energy consumption of its preceding and following solutions are 11.5 kWh / hour and 12.8 kWh / hour, respectively. The congestion distance in this dimension is calculated to be 12.8 - 11.5 = 1.3 kWh / hour. Based on this calculation method, the congestion distances of solution A in the quality standard deviation and wear rate target dimensions are 0.04 mm and 0.35 μm / hour, respectively.

[0263] To synthesize the congestion distances across the four dimensions, each dimension is first normalized by dividing the congestion distance for that dimension by its range. For the capacity dimension, the congestion distance of 130 divided by the capacity range of 1500 yields a normalized congestion distance of 0.087. For the energy consumption dimension, the congestion distance of 1.3 divided by the energy consumption range of 10 yields 0.13. For the quality dimension, 0.04 divided by the range of 0.25 yields 0.16. For the wear dimension, 0.35 divided by the range of 2.3 yields 0.152. Summing the four normalized congestion distances gives the total congestion distance for solution A as 0.087 + 0.13 + 0.16 + 0.152 = 0.529. Calculating the total congestion distance for all 57 solutions in the solution set reveals that the congestion distances range from 0.15 to 0.85. There are 12 solutions with a crowding distance less than 0.3. These solutions are crowded and not unique enough. There are 9 solutions with a crowding distance greater than 0.6. These solutions are relatively isolated and have high uniqueness.

[0264] When selecting which solutions to retain from the candidate solution set during optimization, in addition to considering the merits of the objective values, crowding distance is also taken into account. Suppose there are two candidate solutions, B and C, whose objective values ​​are very close, with no obvious dominance relationship, making it difficult to determine their superiority. Solution B has a capacity of 2180, energy consumption of 12.5, mass of 0.26, wear of 2.05, and a crowding distance of 0.25. Solution C has a capacity of 2170, energy consumption of 12.6, mass of 0.27, wear of 2.08, and a crowding distance of 0.55. From the perspective of objective values, solution B is slightly better in terms of capacity, but slightly worse in the other three objectives, making them roughly equal overall. However, solution C's crowding distance is more than twice that of solution B, indicating that solution C is located in a relatively open area, and retaining it increases the coverage of the solution set. Therefore, when a choice between the two is necessary, solution C with the larger crowding distance is prioritized, even if its objective value is slightly worse. This mechanism avoids a large number of similar redundant solutions in the solution set, maintaining the dispersion of solutions.

[0265] The second diversity indicator is the coverage of reference point distribution. A set of uniformly distributed reference points is pre-defined in the target space, representing various possible demand directions within the target space. In the four-dimensional target space, each dimension is uniformly divided into three segments, forming three... 4That is, 81 reference points. For example, the production capacity dimension is divided into three intervals: low production capacity (1500~2000), medium production capacity (2000~2500), and high production capacity (2500~3000); the energy consumption dimension is divided into three intervals: low energy consumption (8~11.33), medium energy consumption (11.33~14.67), and high energy consumption (14.67~18). The quality and wear dimensions are similarly divided. Each reference point corresponds to a specific combination of targets, such as reference point P1 corresponding to low production capacity, low energy consumption, high quality, and low wear, and reference point P2 corresponding to high production capacity, medium energy consumption, medium quality, and medium wear, etc.

[0266] For each reference point, the solution closest to it in the solution set is calculated, and this solution is called the representative solution for that reference point. The distance is calculated using Euclidean distance in a normalized target space. For example, the coordinates of reference point P15 are: capacity 0.5, energy consumption 0.4, quality 0.3, and wear 0.35. The distances to this reference point from the 57 solutions are calculated, and solution D has the smallest distance of 0.18. Therefore, solution D is the representative solution for reference point P15. All 81 reference points are traversed, and it is determined whether each reference point is covered by a representative solution. The results show that 63 of the 81 reference points are covered by representative solutions, a coverage rate of 77.8%. The 18 uncovered reference points are mainly concentrated in certain extreme combinations, such as extremely low capacity with extremely high quality, or extremely high capacity with extremely low wear. These combinations may not be achievable or are very rare in the actual parameter space.

[0267] Further analysis revealed that some reference points were contested by multiple solutions, meaning multiple solutions were very close to the reference point, while some reference points had only one representative solution. For those reference points with only one representative solution, this representative solution is irreplaceable and must be retained; otherwise, a coverage gap will occur. For example, reference point P28 only has solution E as its representative, with a distance of 0.22, while the second closest solution F has a distance of 0.48, much greater than solution E. This indicates that solution E covers an area that no other solution can cover. If solution E is eliminated, reference point P28 will lose its representative solution. Therefore, when selecting the solution set, priority should be given to protecting these irreplaceable unique representative solutions. Statistical analysis showed that 15 out of 57 solutions are unique representative solutions for certain reference points; these 15 solutions are marked as core solutions and cannot be eliminated under any circumstances.

[0268] The third diversity metric is hypervolume contribution, which measures the unique contribution of each solution to the overall quality of the solution set. Hypervolume is a comprehensive evaluation metric in multi-objective optimization, representing the volume of the solution set in the objective space. For a solution set containing multiple solutions, its hypervolume is the volume of the objective space region dominated by these solutions. A larger hypervolume indicates a higher quality and wider coverage of the solution set. The contribution of each solution to the hypervolume refers to the reduction in hypervolume if that solution were removed. Solutions with large contributions are key solutions supporting the frontier, while solutions with small contributions have little impact on the overall quality.

[0269] Calculate the initial hypervolume of the solution set. A reference point is chosen as the baseline for hypervolume calculation, typically the worst-case value point for each objective: minimum production capacity (1500), maximum energy consumption (18), worst quality (0.45), and maximum wear (3.5). Calculate the four-dimensional volume dominated by the 57 solutions relative to this reference point. A Monte Carlo sampling method is used for estimation; 100,000 sampling points are randomly generated in the target space, and the number of points dominated by at least one solution is counted. The proportion of dominated points multiplied by the total volume is the hypervolume. Assume the calculated initial hypervolume is 0.68.

[0270] Each solution is removed one by one, and the hypervolume of the remaining 56 solutions is recalculated. The difference between the two hypervolume values ​​is the contribution of that solution. For example, after removing solution A, the hypervolume becomes 0.675, and the contribution is 0.68 minus 0.675, which equals 0.005. After removing solution B, the hypervolume becomes 0.655, and the contribution is 0.68 minus 0.655, which equals 0.025. Solution B's contribution is 5 times that of solution A. Calculating the contribution for each of the 57 solutions reveals that the contribution values ​​are distributed between 0.002 and 0.038. Solutions with the largest contributions are often located in the convex portion or endpoint of the Pareto front, and solutions in these positions dominate a larger spatial region. Solutions with the smallest contributions are often located in the concave portion of the front or in positions that highly overlap with other solutions.

[0271] When it's necessary to reduce the size of the solution set, solutions with smaller hypervolume contributions are prioritized for elimination, while those with larger contributions are retained. Suppose that due to computational resource constraints, the solution set needs to be reduced from 57 to 40, meaning 17 solutions need to be eliminated. Sort the solutions by hypervolume contribution from smallest to largest, and check if the solution with the smallest contribution can be eliminated. The solution with the smallest contribution, F, has a contribution value of only 0.002, but it is found to be the only representative solution for reference point P35, belonging to the core solutions, and therefore cannot be eliminated. Skipping solution F, we check the solution with the second smallest contribution, G, with a contribution value of 0.0025. It is not the only representative for any reference point, and its crowding distance is also small at 0.28, confirming its eligibility for elimination. Following this rule, we check each solution one by one, ultimately eliminating 17 solutions with small hypervolume contributions, small crowding distances, and not being the only representatives, retaining 40 key solutions. These 40 solutions ensure that the quality of the Pareto front does not significantly decrease, maintain comprehensive coverage of reference points, and maintain appropriate spacing between solutions, achieving a balance between quality and diversity.

[0272] Based on diversity assessment, a diverse set of solutions containing solutions with different optimization directions is constructed to ensure that the diverse set of solutions has a balanced distribution across different dimensions of capacity, energy consumption, quality, and equipment lifespan; the diverse set of solutions is used as a candidate set of parameter combinations for selection by flexible scheduling strategies.

[0273] Following the aforementioned uniformity assessment, regional equilibrium search, and diversity preservation, a Pareto optimal solution set containing 40 high-quality and uniformly distributed solutions was obtained. However, 40 solutions are still too many for practical applications, making it difficult for decision-makers to evaluate and select each one individually. Furthermore, the differences between some solutions are small, rendering them of limited practical significance. Therefore, further refinement is needed to construct a diverse solution set of moderate size and distinct characteristics, serving as a standard parameter library for flexible production line scheduling.

[0274] Cluster analysis was used to group the 40 solutions, grouping solutions with similar characteristics into one cluster, and selecting a representative solution from each cluster. The K-means algorithm was chosen as the clustering method, with a preset number of clusters of 10, meaning the 40 solutions were divided into 10 clusters. The K-means algorithm first randomly initializes 10 cluster centers in the target space, then iteratively assigns each solution to the nearest cluster center, and then updates the cluster centers based on the positions of all solutions in each cluster. This process is repeated until the cluster centers no longer change.

[0275] In the initialization phase, 10 solutions are randomly selected as initial cluster centers. In the first iteration, the distances from the remaining 30 solutions to the 10 centers are calculated, and each solution is assigned to the nearest center. For example, if solution H has a target value of 2100 for production capacity, 11.8 for energy consumption, 0.26 for mass, and 1.9 for wear, after calculating the distances to the 10 centers, it is found that the closest center is 3 (0.12), so solution H is assigned to cluster 3. After all 40 solutions are assigned, cluster 1 contains 5 solutions, cluster 2 contains 3 solutions, cluster 3 contains 6 solutions, and so on. The centers of each cluster are then updated by calculating the average value of all solutions within the cluster in each target dimension as the new center coordinates. For example, cluster 3 contains 6 solutions with an average production capacity of 2080, an average energy consumption of 11.5, an average mass of 0.255, and an average wear of 1.85, which becomes the new center of cluster 3.

[0276] In the second iteration, the 40 solutions were redistributed based on the updated 10 centers, resulting in a change in the cluster affiliation of some solutions. For example, solution I, originally belonging to cluster 4, was found to be closer to the new center of cluster 5 after recalculation and was therefore redistributed to cluster 5. After the redistribution, the cluster centers were updated again. After 8 iterations, the cluster affiliation of all solutions remained unchanged, and the clustering converged. The final 10 clusters contained 4, 3, 5, 4, 3, 5, 4, 4, 5, and 3 solutions, respectively.

[0277] Analyzing the characteristics of the 10 clusters reveals significant differentiation within the target space. Cluster 1 solutions are concentrated in the region of high productivity, high energy consumption, high wear, and low quality. These solutions typically pursue maximum productivity at the cost of high energy consumption and rapid equipment wear, achieving an average productivity of 2680 units per hour, but with energy consumption as high as 16 kWh per hour. Cluster 2 solutions are located in the region of low productivity, low energy consumption, low wear, and high quality. These solutions emphasize energy conservation and equipment protection, achieving a productivity of only 1720 units per hour, but with energy consumption of only 9.2 kWh per hour and a wear rate of only 1.4 micrometers per hour. Cluster 3 solutions are relatively balanced across all objectives, with a productivity of 2150, energy consumption of 12, quality of 0.25, and wear of 2.0, representing a compromise solution. Clusters 4 through 10 also have different focuses; for example, Cluster 4 prioritizes quality, Cluster 5 emphasizes minimizing wear, and Cluster 6 finds a special balance between productivity and energy consumption.

[0278] Representative solutions are selected from each cluster based on their proximity to the cluster center and their relatively large crowding distance. For cluster 1, the distances from the cluster center to the five solutions within the cluster are calculated. Solution J has the smallest distance (0.08) and its crowding distance is 0.42, ranking second in the cluster. Another solution, K, is close to the cluster center with a distance of 0.09, but its crowding distance is only 0.25. Considering all factors, solution J is selected as the representative solution for cluster 1, with the following parameters: star disk rotation speed 56 revolutions per minute, conveyor belt speed 0.47 meters per second, and robot arm frequency 4.7 times per second. The target values ​​are: production capacity 2720, energy consumption 16.2, mass 0.38, and wear 3.1. This process is repeated for the remaining nine clusters to select representative solutions, resulting in a total of ten representative solutions.

[0279] Ten representative solutions were manually labeled, assigning intuitive tags based on their characteristics. Cluster 1's representative solution was labeled "Extreme Capacity Type," suitable for emergency situations where orders are overflowing and full-capacity production is necessary. Cluster 2's representative solution was labeled "Extreme Energy Saving Type," suitable for economical operation during peak electricity price periods or when orders are low. Cluster 3's representative solution was labeled "Standard Balanced Type," suitable for routine production conditions. Cluster 4's representative solution was labeled "High Quality Type," suitable for precision orders with extremely high product consistency requirements. Cluster 5's representative solution was labeled "Equipment Protection Type," suitable for scenarios where equipment operates continuously for extended periods and requires load reduction maintenance. Cluster 6's representative solution was labeled "High Energy Efficiency Type," achieving relatively low energy consumption while maintaining high capacity, with a capacity-to-energy ratio of 190, making it the most efficient overall solution. Clusters 7 through 10 were labeled "Medium-High Speed ​​Type," "Low-Speed ​​Precision Type," "Capacity Priority with Energy Saving Type," and "Quality Priority with Capacity Type," respectively.

[0280] These 10 representative solutions, along with their labels, parameter combinations, and target values, are organized into a structured, diverse solution set database. The database is stored in tabular form, with each row representing a solution scheme. Column fields include: scheme number, scheme label, star disk rotation speed, conveyor belt speed, robot frequency, expected capacity, expected energy consumption, expected quality standard deviation, expected wear rate, capacity-energy consumption ratio, and applicable scenario description. For example, the record for Scheme 1 is: Number 1, Label "Extreme Capacity Type", Rotation Speed ​​56, Speed ​​0.47, Frequency 4.7, Capacity 2720, Energy Consumption 16.2, Quality 0.38, Wear 3.1, Capacity-Energy Consumption Ratio 168, Applicable Scenario "Used when orders urgently require maximum capacity, accepting higher energy consumption and equipment wear."

[0281] The diversified solution set provides a standardized parameter library for flexible scheduling of the production line. When production conditions change, the system does not need to re-perform complex multi-objective optimization calculations, but instead quickly selects the most suitable one from these 10 preset solutions. For example, when a surge in order volume and tight delivery deadlines are detected, the system automatically queries solutions tagged "maximum capacity" or "high energy efficiency ratio" and decides which one to use based on the current electricity cost. When peak electricity prices are detected, it automatically switches to the "maximum energy saving" or "capacity priority with energy saving" solution. When the fault prediction system indicates a high risk of faults at a certain workstation, it automatically switches to the "equipment protection" solution to proactively reduce the load and extend equipment life. This scenario adaptation mechanism based on the preset parameter library has a fast response speed; from scenario recognition to parameter switching, it can be completed within 30 seconds. In contrast, if optimization calculations were performed every time, it might take several minutes or even longer, which cannot meet the real-time requirements of the production line.

[0282] Another important value of diversified solution sets is that they provide intuitive decision support for production managers. Managers can view a visual interface comparing the performance of 10 solutions across different target dimensions, displaying each solution's capacity, energy consumption, quality, and lifespan in radar charts or bar graphs. Through comparison, managers can clearly understand the trade-offs between different solutions. For example, they might see that the "maximum capacity" solution has 30% higher capacity than the "standard balanced" solution, but consumes 35% more energy and has a 55% higher wear rate, allowing them to make informed decisions. This transparent decision-making process enhances managers' trust and acceptance of the intelligent system, avoiding the resistance that might arise from black-box AI decision-making. Diversified solution sets, as a bridge connecting intelligent algorithms and human decision-making, realize a human-machine collaborative intelligent manufacturing management model.

[0283] Example 8

[0284] This embodiment is an extension of embodiment seven, illustrating scene adaptive scheduling based on diverse solution sets, including the following steps:

[0285] S4.1: Identify the current production scenario and classify it into high-speed production scenario, low-energy operation scenario, and fault prevention scenario based on order urgency, energy cost, and equipment status.

[0286] Collect current production environment information, including order urgency, energy costs, and equipment status. Order urgency is measured by the difference between the order delivery deadline and the current time. If the remaining time is less than 48 hours, it is defined as an urgent order; if the remaining time is between 48 and 72 hours, it is defined as a normal order; and if the remaining time is more than 72 hours, it is defined as a lenient order.

[0287] Energy costs are measured using electricity prices for the current period, obtained from real-time electricity price data obtained from power companies. A period is defined as high-cost if the electricity price is higher than 120% of the daily average; a period is defined as normal-cost if the electricity price is between 80% and 120% of the daily average; and a period is defined as low-cost if the electricity price is lower than 80% of the daily average.

[0288] Equipment status is measured by cumulative operating time and failure prediction probability. If the equipment operates continuously for more than 8 hours and the failure prediction probability exceeds 50%, it is defined as a high-risk state; if the operating time is between 4 and 8 hours or the failure probability is between 20% and 50%, it is defined as a medium-risk state; if the operating time is less than 4 hours and the failure probability is less than 20%, it is defined as a low-risk state.

[0289] The production scenario is determined by comprehensively considering information from three dimensions. If the order is urgent and the equipment status is low-risk, it is defined as a high-speed production scenario, with the goal of maximizing capacity to complete urgent orders. If energy costs are high and the order is not urgent, it is defined as a low-energy operation scenario, with the goal of saving energy and reducing production costs. If the equipment status is high-risk, regardless of whether the order is urgent, it is defined as a fault prevention scenario, with the goal of protecting the equipment and preventing downtime.

[0290] S4.2: Based on the classification of production scenarios, the weights of each optimization objective in the multi-objective optimization problem are dynamically adjusted. In high-speed production scenarios, the weight of the capacity target is increased; in low-energy operation scenarios, the weight of the energy-saving target is increased; and in fault prevention scenarios, the weight of the equipment life target is increased.

[0291] For high-speed production scenarios, the target weights are set as follows: capacity 0.6, energy consumption 0.2, quality 0.1, and lifespan 0.1. Capacity has a dominant weight, prioritizing production speed, while energy consumption and equipment wear have lower weights, and maintaining basic quality requirements is sufficient.

[0292] For low-energy-consumption operation scenarios, the target weights are set as follows: capacity 0.2, energy consumption 0.5, quality 0.2, and lifespan 0.1. Energy consumption is the dominant weight, prioritizing the reduction of electricity consumption. Capacity can be appropriately sacrificed, and the quality weight is slightly increased to avoid other problems caused by the reduction in speed.

[0293] For fault prevention scenarios, the target weights are set as follows: capacity 0.2, energy consumption 0.2, quality 0.2, and lifespan 0.4. Lifespan has the dominant weight, prioritizing the protection of equipment to reduce wear rate. Capacity, energy consumption, and quality weights are evenly distributed to ensure that basic production capacity is maintained even under low load operation.

[0294] Based on the scene recognition results, the weight configuration is automatically adjusted. For example, when a switch from a normal scene to a high-speed production scene is detected, the system automatically adjusts the weight from a balanced configuration to a capacity-first configuration, and the entire adjustment process is completed within 1 second.

[0295] S4.3: Evaluate the solutions in the diversified solution set, and select the parameter combination that best meets the needs of the current scenario from the diversified solution set based on the weight adjustment results.

[0296] Based on the target weights determined in S4.2, the 10 representative solutions of the diversified solution set constructed in Example 7 are evaluated. For each solution, its comprehensive score under the current weight is calculated, which is equal to the sum of the normalized value of production capacity multiplied by the production capacity weight, the normalized value of energy consumption multiplied by the energy consumption weight, the normalized value of quality multiplied by the quality weight, and the normalized value of lifetime multiplied by the lifetime weight.

[0297] Calculate the overall score for each of the 10 solutions and compare the scores. In high-speed production scenarios, solutions labeled "maximum capacity type" typically score the highest because they have the largest capacity value and contribute the most when the capacity weight is 0.6. In low-energy consumption scenarios, the "energy-saving priority type" solution scores the highest. In fault prevention scenarios, the "equipment protection type" solution scores the highest.

[0298] The solution with the highest overall score is selected, and its corresponding workstation parameter combination is extracted. For example, in a high-speed production scenario, the selected "maximum capacity" solution corresponds to the following parameters: star disk rotation speed 55 rpm, conveyor belt speed 0.48 m / s, and robot arm frequency 4.8 times / s. This parameter combination is considered the optimal configuration for the current scenario.

[0299] S4.4: Based on parameter combinations, generate scene-adaptive workstation collaborative control instructions and send the workstation collaborative control instructions to each workstation controller.

[0300] Based on the parameter combination selected in S4.3, target parameters for each workstation are generated. For the star disk rotation speed, a cartoning machine control command is generated, setting the target rotation speed to 55 rpm and the acceleration limit to 5 rpm / second to ensure smooth acceleration to the target value. For the conveyor belt speed, a conveyor belt control command is generated, setting the target speed to 0.48 m / s and the acceleration limit to 0.1 m / s / second. For the robot arm frequency, a robot arm control command is generated, setting the target gripping cycle to 1 divided by 4.8, which equals 0.208 seconds, meaning one gripping action is completed every 0.208 seconds.

[0301] Control commands are encapsulated into Profinet protocol data packets, including fields such as target value, acceleration, and priority. These packets are then sent to the PLC controllers at each workstation via industrial Ethernet. Upon receiving the command, the cartoning machine PLC controls the frequency converter to adjust the motor speed, smoothly accelerating to 55 rpm within 30 seconds. The conveyor belt PLC controls the conveyor motor, accelerating to 0.48 m / s within 20 seconds. The robotic arm PLC adjusts its motion trajectory planning, shortening the single gripping cycle to 0.208 seconds.

[0302] During execution, each workstation controller continuously provides feedback on the current actual parameter values. The system monitors the feedback data, confirms that each workstation has reached the target parameters, and records the moment the scene switch is completed. From scene recognition to control command issuance and each workstation reaching the target state, the entire process is completed within 1 minute, achieving rapid scene adaptive switching on the production line.

[0303] When the production scenario changes again, such as switching from a high-speed production scenario to a low-energy consumption scenario, the system repeats the process from S4.1 to S4.4, identifying the new scenario, adjusting weights, selecting new parameters, and issuing new instructions to achieve dynamic adaptation. Through the scenario adaptive mechanism, the production line can automatically adjust its operating strategy according to changes in external conditions and internal states, flexibly switching between different optimization objectives to maximize overall efficiency.

[0304] Example 9

[0305] This embodiment is a further refinement of S5 in Embodiment 1, detailing the implementation process of fault prediction and flexible scheduling, including the following steps:

[0306] S5.1: Collect sensor data, workstation status, and fault records from historical operation data, perform data cleaning, standardization, and feature extraction on the sensor data, workstation status, and fault records to form a structured fault analysis dataset.

[0307] Historical operational data is extracted from the production line's data acquisition system, covering continuous operation records over the past six months. Sensor data includes current, temperature, and vibration acceleration of the cartoning machine motor; tension and offset of the twisting conveyor belt; and positional deviation and gripping force of the robotic arm, with a sampling frequency of 10 times per second. Workstation status includes operating speed, load rate, number of starts and stops, and runtime for each workstation, with a sampling frequency of once per minute. Fault records include all historical fault events, recording the time of occurrence, fault type (e.g., bearing wear, drive belt loosening, air leakage), fault location, maintenance measures, and downtime.

[0308] The collected raw data is cleaned to handle missing and outlier values. For missing values, if the missing percentage is less than 5%, linear interpolation is used to fill in the missing values; if the missing percentage exceeds 5%, the data segment is deleted. For outliers, box plots are used to identify them, marking values ​​that exceed three times the distance between the upper and lower quartiles as outliers and replacing them with the average of the nearest normal values.

[0309] Data from various sensors is normalized, mapping parameters of different dimensions to a range of 0 to 1. Current values ​​are divided by rated current, temperature values ​​are subtracted from ambient temperature and then divided by allowable temperature rise, and vibration acceleration is divided by warning thresholds, ensuring that each parameter is within a comparable order of magnitude.

[0310] Temporal features are extracted, and a sliding time window is constructed with a window length of 30 minutes. For each time window, the statistical characteristics of each sensor parameter within the window are calculated, including mean, standard deviation, maximum value, minimum value, and slope of change trend. For example, the average value of motor temperature, standard deviation of temperature change, and rate of temperature rise over the past 30 minutes are calculated. Frequency domain analysis is performed on the vibration signal to calculate the dominant frequency and amplitude, identifying abnormal vibration modes of the equipment.

[0311] Labels are constructed as follows: for a time window 30 minutes before a failure, a positive sample is labeled with a value of 1, indicating that a failure will occur after this period. For a time window where normal operation continues and no failure occurs in the following 2 hours, a negative sample is labeled with a value of 0. To balance the ratio of positive to negative samples, negative samples are undersampled to make the ratio of positive to negative samples close to 1:3.

[0312] The feature vectors and labels are organized into a structured dataset, with each record containing a timestamp, statistical features of each sensor, workstation status parameters, and label values. This results in a fault analysis dataset containing 50,000 records, including 12,500 positive samples and 37,500 negative samples.

[0313] S5.2: Based on the fault analysis dataset, a long short-term memory network model including input gate, forget gate and output gate is constructed to learn from the equipment operation sequence data. Sensor data, workstation status and fault records are input into the long short-term memory network model to predict the fault probability of each workstation in the next 30 minutes.

[0314] An LSTM network structure is constructed, with the input layer receiving time-series data. Each time step contains 30 feature dimensions, corresponding to the status parameters of each sensor and workstation. The sequence length is set to 10 time steps, meaning that the probability of failure in the next 30 minutes is predicted using data from the most recent 10 minutes, with each time step spanning 1 minute.

[0315] The first layer of the LSTM contains 64 neurons, each with three gating structures. The input gate determines which information from the current time step needs to be stored in the cell state, using a sigmoid activation function to output weights ranging from 0 to 1. Weights closer to 1 indicate important information that needs to be remembered, while weights closer to 0 indicate unimportant information that can be ignored. The forget gate determines which historical information in the cell state needs to be forgotten, also using a sigmoid function to output forgetting weights. The output gate determines which parts of the cell state are output at the current time step, controlling the output of information. Through the synergistic effect of these three gates, the LSTM can selectively remember long-term dependent information and forget irrelevant information, making it suitable for learning the slow, gradual degradation process of learning devices.

[0316] The second LSTM layer contains 32 neural units, which receive the output of the first layer as input to further extract higher-level temporal features. The unit states of the second layer can capture patterns over longer time spans, such as periodic fluctuations in device performance or daily cumulative wear trends.

[0317] The fully connected output layer contains three neurons, corresponding to the three main workstations: the cartoning machine, the twisting conveyor belt, and the robotic arm. Each neuron outputs the probability of a failure occurring at that workstation within the next 30 minutes, with a value ranging from 0 to 1, and uses the sigmoid activation function.

[0318] The loss function is defined as binary cross-entropy, which measures the difference between the predicted probability and the actual label. For each workstation, if the actual fault occurred and the label is 1, the loss is the negative logarithm of the predicted probability; if the fault did not occur and the label is 0, the loss is 1 minus the negative logarithm of the predicted probability. The total loss is the weighted average of the losses from the three workstations.

[0319] The dataset is divided into training, validation, and test sets in a ratio of 7:1.5:1.5. The training set is used for learning model parameters, the validation set is used for tuning hyperparameters and preventing overfitting, and the test set is used to evaluate the final model performance.

[0320] The Adam optimizer was used for training, with a learning rate of 0.001 and a batch size of 64. Each batch randomly selected 64 sequences from the training set, input them into the network for forward propagation to calculate the loss, and then backpropagation to update the parameters. Training lasted for 100 epochs, with each epoch iterating through the entire training set.

[0321] During training, monitor the loss and accuracy on the validation set. When the validation set loss stops decreasing for 10 consecutive epochs, trigger the early stopping mechanism to stop training and save the model with the best performance on the validation set to prevent overfitting.

[0322] After training, the model performance was evaluated on the test set. Prediction accuracy was calculated; a prediction probability greater than 0.5 was considered a potential fault, and the accuracy was compared with the actual labels, reaching 85%. Recall was calculated; the model successfully predicted 78% of all actual fault samples, indicating that most faults could be predicted in advance. Precision was calculated; the proportion of samples predicted as faults that actually occurred reached 72%, indicating a high level of reliability in the warnings.

[0323] S5.3: Determine the failure probability. When the failure probability of a certain workstation exceeds 80%, generate a preventive maintenance plan based on the optimal cycle time combination, including maintenance time window, spare parts preparation and personnel arrangement.

[0324] In actual production, current sensor data and workstation status are collected every minute to construct a time series of the most recent 10 minutes, which is then input into a trained LSTM model. The model outputs the failure probability of three workstations for the next 30 minutes. For example, at a certain moment, the predicted failure probability is 0.25 for the cartoning machine, 0.85 for the twisting conveyor belt, and 0.15 for the robotic arm.

[0325] The system determines the failure probability of each workstation. When the failure probability of the twisting conveyor belt exceeds the preset threshold of 0.85, a preventative maintenance process is triggered. The system immediately generates a maintenance plan for the twisting conveyor belt.

[0326] Determine the maintenance time window based on the current production plan and order status. If the current batch still needs 30 minutes to complete, it is recommended to schedule maintenance immediately after the current batch is completed to avoid sudden downtime during production. If the current batch is about to complete, it is recommended to handle it quickly within the 10-minute interval between batches. Mark the recommended maintenance time window as 40-50 minutes after the current time.

[0327] Generate a spare parts preparation list, recommending necessary spare parts based on common failure modes of twisting conveyor belts. Analysis of historical failure records reveals that conveyor belt failures are mainly caused by drive belt slack and tensioner wear; therefore, the list includes one drive belt, one tensioner, and several adjusting bolts. Send the list to the warehouse management system to request the preparation and delivery of spare parts to the site.

[0328] Assign maintenance personnel, determining the required staffing based on the complexity of the maintenance task. Replacing the drive belt of the twisting conveyor requires one mechanical technician and one support staff member, with an estimated maintenance time of 20 minutes. Send the maintenance request to the human resources system, requesting the dispatch of personnel with the appropriate skill level, and instruct the personnel to arrive on-site 5 minutes before the suggested time window.

[0329] Generate a complete preventative maintenance plan, including fields such as warning time, fault location, fault probability, recommended maintenance time window, spare parts list, personnel allocation, and estimated maintenance duration. Push the plan to the production management system and maintenance management system, and simultaneously display the warning information on the operator interface to remind operators to prepare accordingly.

[0330] S5.4: Based on the preventive maintenance plan, the upstream feed speed is proactively reduced before a failure occurs, and the system switches to a reduced-speed operation mode when a failure occurs. The corresponding workstation collaborative control commands are used for control to ensure production continuity.

[0331] Upon issuing the warning, a flexible scheduling strategy was immediately activated to proactively adjust the production line's operating parameters. A speed reduction command was sent to the upstream cartoning machine, gradually reducing the star disk speed from the current 50 rpm to 35 rpm. The speed reduction process was completed within 10 minutes, slowing down the feeding speed and reducing the backlog of work-in-process at the twisting conveyor station.

[0332] Send a frequency reduction command to the downstream packing robot to reduce the gripping frequency from 4 times / second to 3 times / second, matching the speed reduction upstream, and avoid the robot grabbing empty due to insufficient upstream material supply.

[0333] When the recommended maintenance time window is reached and the current batch is completed, the system automatically triggers maintenance mode. A stop command is sent to the twisting conveyor station, causing the conveyor belt to smoothly decelerate to a stop. Simultaneously, the cartoning machine and robotic arm continue to run at low speed to process existing work-in-process in the buffer area, preventing material accumulation.

[0334] Maintenance personnel arrived on site and began replacing the drive belt and tensioner. The system monitored the maintenance progress, and once the maintenance personnel confirmed the maintenance was complete on the operating interface, the system automatically triggered the recovery process. A start command was sent to the twisting conveyor belt, and the conveyor belt restarted operation, with an initial speed set at 0.2 m / s. Within 5 minutes, it gradually accelerated to 0.35 m / s, restoring normal operation.

[0335] Simultaneously, an acceleration command was sent to the upstream cartoning machine to restore the star disk rotation speed to 50 rpm within 10 minutes, and a frequency increase command was sent to the downstream robotic arm to restore the gripping frequency to 4 times per second. The entire production line gradually returned to its pre-maintenance operating parameters and regained equilibrium.

[0336] Throughout the process, thanks to early warnings and proactive scheduling, material buildup and order delays caused by sudden downtime were avoided. Maintenance operations were completed within the planned time window, minimizing the impact on production schedules. Through flexible scheduling, the production line maintained partial capacity during equipment maintenance, ensuring production continuity and reducing downtime losses from a potential 60 minutes to an actual 20 minutes, significantly improving overall equipment efficiency.

[0337] Through detailed descriptions of Examples 1 to 9, the intelligent collaborative control method for a cartoning and packing production line based on multi-station linkage provided by this invention is fully implemented. This method organically combines multiple levels of technologies, including material state tracking, finite state machine linkage control, deep reinforcement learning cycle optimization, multi-objective Pareto optimization, adaptive search, diversity preservation, scene adaptation, and fault prediction. This achieves a high degree of intelligence and adaptability in the production line, significantly improving production efficiency, reducing energy consumption, enhancing quality consistency, and extending equipment lifespan, providing an innovative technical solution for the field of intelligent manufacturing.

[0338] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-station linkage-based box packing and case packing production line intelligent collaborative control method, characterized in that, include: Collect the location, orientation, and vacancy information of the materials, generate a unique ID for each material, and construct a material state vector containing ID, location, orientation, vacancy flag, and anomaly flag; Five system states and state transition rules are defined for the production line: normal operation, star disk vacancy, abnormal torsional posture, packing positioning deviation, and emergency stop. A finite state machine model including a master state machine and sub-state machines for each workstation is constructed using a hierarchical state machine structure. Based on the finite state machine model and the material state vector, a linkage response strategy is generated for different abnormal situations, and workstation collaborative control instructions including speed adjustment, action skipping and pause are generated in combination with the material state vector. Construct and train a deep Q-network model with the overall capacity-energy consumption ratio as the reward function. Input the operating parameters of each workstation and the material state vector into the deep Q-network model, and output the optimal combination of cycle time including the star disk rotation speed, the twisting conveyor belt speed and the robot arm motion frequency. A long short-term memory network model is constructed and trained. Sensor data, workstation status, and fault records are input into the long short-term memory network model to predict the fault probability of each workstation within a preset time period in the future. Based on the failure probability and the optimal cycle time combination, a preventive maintenance plan is generated when the failure probability of a workstation exceeds a preset threshold. Based on the preventive maintenance plan, the corresponding workstation collaborative control command is used for control.

2. The method of claim 1, wherein, Collect the location, orientation, and availability information of materials, generate a unique ID for each material, and construct a material state vector containing ID, location, orientation, availability flag, and anomaly flag, including: A three-level photoelectric sensor array is deployed at the star disk discharge port of the cartoning machine, the end of the carton twisting and standing conveyor belt, and in front of the gripping point of the cartoning robot to collect the position, posture, and empty space information of the material; Based on the material passage time detected by the first-level sensor, a unique ID is generated for each material using a date-time-serial number encoding method; Edge computing nodes are deployed near each sensor array to receive the position, orientation, and vacancy information of the material, and to filter, calibrate, and extract features from the position, orientation, and vacancy information of the material, converting it into standardized material feature data. Based on the material characteristic data and the unique ID identifier, a material state vector is constructed that includes ID, location, posture, vacancy flag, and anomaly flag.

3. The method of claim 1, wherein, Five system states are defined for the production line: normal operation, star disk vacancy, abnormal torsional posture, packing positioning deviation, and emergency stop, along with their state transition rules. A hierarchical state machine structure is used to construct a finite state machine model, including a master state machine and sub-state machines for each workstation, comprising: The empty space flag, abnormal flag and position information in the material state vector are parsed, and five system states are defined: normal operation of the production line, star disk empty space, abnormal torsion posture, packing positioning deviation and emergency stop. The state transition rules between each state are designed. Based on the five system states and state transition rules, a hierarchical state machine structure is adopted to realize state management. The switching logic between states is defined by the state transition matrix, and a finite state machine model including the main state machine and the sub-state machines of each workstation is constructed.

4. The method of claim 3, wherein, Based on the finite state machine model and the material state vector, a linkage response strategy is generated for different abnormal situations. Combined with the material state vector, workstation collaborative control instructions including speed adjustment, action skipping, and pause are generated, including: The current state of the finite state machine model is monitored. When an empty space is detected on the star disk, a linkage response strategy is generated within 100ms to send a skip instruction to the downstream workstation. Based on the aforementioned linkage response strategy, and combined with the position and attitude information in the material state vector, workstation collaborative control instructions including speed adjustment, action skipping, and pause are generated.

5. The method of claim 1, wherein, A deep Q-network model is constructed and trained with the overall capacity-energy consumption ratio as the reward function. The operating parameters of each workstation and the material state vector are input into the deep Q-network model. The output includes the optimal cycle combination of the star disk rotation speed, the torsional conveyor belt speed, and the robot arm motion frequency, including: Collect the operating parameters and material flow status of each workstation, establish a virtual model of the production line containing the operating parameters and material flow status of each workstation, and define a state space containing the operating parameters and material state vectors of each workstation. Based on the state space, a deep Q-network structure including an input layer, a multi-layer neural network, and an output layer is designed. The overall capacity-energy consumption ratio is used as the reward function to train the deep Q-network to predict the long-term benefits of different workstation parameter combinations. The deep Q-network is learned online, and its parameters are continuously optimized through experience playback and target network technology. The operating parameters of each workstation and the material state vector are input into the deep Q-network model, and the optimal cycle combination including the star disk rotation speed, the twisting conveyor belt speed and the robot arm movement frequency is output.

6. The method of claim 5, wherein, Before outputting the optimal cycle combination including the star disk rotation speed, the twisting conveyor belt speed, and the robot arm motion frequency, the method further includes: The deep Q-network model is used to analyze the virtual model of the production line, and the overall capacity-energy consumption ratio optimization objective is extended to a multi-objective optimization problem that simultaneously includes capacity indicators, energy consumption indicators, quality consistency indicators and equipment life indicators, thus constructing a multi-dimensional objective space. Based on the multidimensional objective space, the Pareto optimal solution set that cannot be improved simultaneously in all objective dimensions is solved by using the weighted sum method, the ε-constraint method, and the non-dominated sorting method, so as to cover the complete distribution of the Pareto front. For partial optimization iterations in the Pareto optimal solution set, a stochastic objective function is introduced to perturb the search process, thereby increasing the diversity of the search space exploration and avoiding premature convergence to a local optimum. Based on the Pareto optimal solution set after iterative optimization, the weight preferences of each objective, such as capacity, energy consumption, quality, and equipment lifespan, are dynamically adjusted according to the current production demand. The parameter combination that best matches the current decision preference is selected from the Pareto optimal solution set, and the parameter combination is taken as the optimal cycle time combination.

7. The method of claim 6, wherein, During the online learning process of the deep Q-network, the method further includes: Sensitivity analysis is performed on the workstation parameters during the online learning process of the deep Q-network. Different search step sizes are allocated according to the sensitivity of the star disk rotation speed, the speed of the torsional conveyor belt, and the motion frequency of the robot. The first step size is used to search for sensitive parameters, and the second step size is used to search for non-sensitive parameters. The second step size is greater than the first step size. The search step size is automatically adjusted according to the optimization process. In the early stage of optimization, an initial step size is used to quickly explore the parameter space. When a potential advantageous region is found, the step size is automatically reduced to conduct a fine search, and random perturbations are introduced to avoid getting trapped in local optima. The parameter space is explored at multiple resolutions. Potential parameter subspaces are identified at a coarse-grained level, and the resolution is gradually increased to perform a fine search, forming a multi-level parameter space exploration from coarse to fine. Based on the results of the multi-level parameter space exploration, a parameter performance mapping database is constructed to record historical search paths and corresponding results.

8. The method of claim 6, wherein, After solving for the Pareto optimal solution set that cannot be simultaneously improved across all objective dimensions using the weighted sum method, the ε-constraint method, and the non-dominated sorting method, the method further includes: The distance distribution between adjacent solutions in the Pareto optimal solution set is calculated to quantitatively evaluate the uniformity of the current search results distribution on the Pareto front, and to identify regions of excessive search concentration and sparse regions. Based on the distribution uniformity assessment results, when it is detected that the search is overly concentrated in a specific region of the Pareto front, the sampling weight of the sparse region is automatically increased to guide the search to expand to the insufficiently explored solution space and achieve regional balance. The diversity of solutions in the solution space is evaluated by calculating crowding distance, analyzing the distribution of reference points, and evaluating hypervolume contribution. Solutions with different characteristics are retained to prevent diverse solutions from being eliminated during the search process. Based on the aforementioned diversity assessment, a diverse solution set containing solutions with different optimization directions is constructed to ensure that the diverse solution set has a balanced distribution across different dimensions of capacity, energy consumption, quality, and equipment lifespan. The diverse solution set is used as a candidate set of parameter combinations for selection by flexible scheduling strategies.

9. The method of claim 8, wherein, The method further includes: The current production scenario is identified and classified into high-speed production scenario, low-energy operation scenario, and fault prevention scenario based on the urgency of orders, energy costs, and equipment status. Based on the production scenario classification, the weights of each optimization objective in the multi-objective optimization problem are dynamically adjusted. In high-speed production scenarios, the weight of the capacity objective is increased; in low-energy operation scenarios, the weight of the energy-saving objective is increased; and in fault prevention scenarios, the weight of the equipment lifespan objective is increased. The solutions in the diversified solution set are evaluated, and the parameter combination that best meets the requirements of the current scenario is selected from the diversified solution set according to the weight adjustment result. Based on the parameter combination, a scenario-adaptive workstation collaborative control command is generated and sent to each workstation controller.

10. The method of claim 1, wherein, A long short-term memory (LSTM) network model is constructed and trained. Sensor data, workstation status, and fault records are input into the LSM network model to predict the fault probability of each workstation within a preset time period. Based on the fault probability and the optimal cycle time combination, a preventive maintenance plan is generated when the workstation fault probability exceeds a preset threshold. Based on the preventive maintenance plan, corresponding workstation collaborative control instructions are used for control, including: Collect sensor data, workstation status, and fault records from historical operation data, and perform data cleaning, standardization, and feature extraction on the sensor data, workstation status, and fault records to form a structured fault analysis dataset; Based on the fault analysis dataset, a long short-term memory network model including an input gate, a forget gate, and an output gate is constructed to learn the equipment operation sequence data. The sensor data, workstation status, and fault records are input into the long short-term memory network model to predict the fault probability of each workstation in the next 30 minutes. The failure probability is judged, and when the failure probability of a certain workstation exceeds 80%, a preventive maintenance plan including maintenance time window, spare parts preparation and personnel arrangement is generated based on the optimal cycle time combination. Based on the aforementioned preventative maintenance plan, the upstream feed speed is proactively reduced before a fault occurs, and the system switches to a reduced-speed operation mode when a fault occurs. Corresponding workstation collaborative control commands are used for control to ensure production continuity.

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