An aero-engine mixed-line pulsating assembly adaptive scheduling method and system

Abstract

The present application relates to the technical field of aero-engine assembly manufacturing, and more particularly to an aero-engine mixed-line pulsating assembly adaptive scheduling method and system.The method comprises: obtaining basic production data of an aero-engine mixed-line pulsating assembly production line, and constructing a directed acyclic assembly process topology network; constructing a mixed-line pulsating assembly scheduling optimization model; converting the scheduling optimization model into a Markov decision process, and solving the Markov decision process based on a deep Q network model to generate a prior robust pre-scheduling scheme; collecting real-time production states and updating the current scheduling system state, adopting a look-ahead search algorithm to perform in-process scheduling, and rolling updating the scheduling scheme of the remaining assembly process, and finally outputting an aero-engine mixed-line pulsating assembly scheduling scheme that meets preset conditions.The present application significantly reduces the total expected production cost, improves resource utilization efficiency, enhances the stability of the production system beat and the adaptability to random disturbances.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of aero-engine assembly manufacturing, production operation optimization and artificial intelligence, and more specifically, to an adaptive scheduling method and system for mixed-line pulse assembly of aero-engines oriented towards random time disturbances. Background Technology

[0002] The final assembly process of aero-engines is characterized by a wide variety of parts, deep assembly levels, strong process coupling, high requirements for quality traceability, and complex resource coordination constraints. As aero-engine research and production tasks gradually shift from single-model, small-batch to multi-model, batch, and cyclical development, the traditional fixed-station assembly organization method is difficult to meet the requirements of increased production capacity, stable delivery, and balanced resource utilization.

[0003] The mixed-line pulse assembly method for aero-engines refers to an assembly method where assembly processes for different models or batches of engines are allocated to various workstations on the same pulse assembly line for aero-engines. After completing fixed operations at each workstation, the products are uniformly transferred to the next workstation according to a preset pulse cycle. This method lies between fixed-station assembly and continuous moving assembly, characterized by the physical production principle of "products do not move during assembly, and products do not assemble when they move." In this process, aero-engine assembly is also constrained by inherent rules such as unit assembly sequence, sequential relationships between processes, multi-worker collaboration, workstation space limitations, quality inspection, and rework / repair. Therefore, assembly scheduling must simultaneously consider manufacturing process factors such as process topology, workstation flow, personnel collaboration, and random time disturbances.

[0004] However, in the mixed-line, pulsed assembly scheduling process of aero-engines, existing technologies still face the following problems: First, the production scheduling constraints are too simplistic, resulting in insufficient on-site executability. Engine assembly processes exhibit typical serial-parallel topologies, with strict predecessor and successor constraints between different unit components and accessories, and some processes requiring multiple workers to collaborate. If the production scheduling model only considers process sequence or workstation load without simultaneously considering workstation allocation, worker configuration, collaborative operations, and synchronous workflow relationships, the generated production scheduling plan is difficult to directly implement on-site.

[0005] Secondly, deterministic scheduling struggles to adapt to the randomness of work hours, resulting in poor cycle time stability. Aero-engine assembly time exhibits significant randomness; factors such as manual assembly deviations, material supply fluctuations, equipment condition fluctuations, rework, and quality re-inspections can all cause actual processing time to deviate from the nominal time. Traditional deterministic scheduling methods typically use average or empirical time as input, which fails to reflect the impact of random disturbances on fluctuating cycle times, easily leading to workstation overruns, cycle time blockages, and waiting times for subsequent processes.

[0006] Secondly, static scheduling lacks rolling adaptive capabilities, making it easy for plans to become disconnected from the actual production process. Existing intelligent scheduling methods mostly focus on offline optimization or single static solutions, lacking rolling adaptive capabilities oriented towards the production execution process. When process delays, changes in worker resource status, or risks of workstation cycle times exceeding the deadline occur on-site, if the scheduling plan for the remaining processes cannot be adjusted in a timely manner based on the real-time status, it will lead to a disconnect between the pre-planned plan and the actual situation on-site, reducing the stability and resilience of the mixed-line pulse assembly system.

[0007] Furthermore, existing algorithms struggle to balance decision-making accuracy with online computational efficiency. While deep reinforcement learning methods can learn the mapping relationship between complex states and scheduling actions from historical production data, relying solely on deep Q-networks for online decision-making lacks the ability to accurately anticipate local disturbances. On the other hand, traditional dynamic programming or rolling time-domain optimization, although possessing some foresight, suffers from high computational complexity and time-consuming solutions in high-dimensional state-space scenarios such as aero-engine assembly, making it difficult to meet the timeliness requirements of real-time scheduling during production.

[0008] Therefore, it is necessary to construct a production scheduling scheme that takes into account both pre-production global robustness and in-production local adaptability, so as to achieve multi-objective collaborative optimization of process allocation, worker configuration, workstation load, cycle stability and random disturbance adaptability during the mixed-line pulse assembly of aero-engines. Summary of the Invention

[0009] The purpose of this invention is to provide an adaptive scheduling method and system for mixed-line pulse assembly of aero-engines, which solves the problem that existing scheduling schemes are difficult to effectively adapt to random time disturbances and lack the ability to adaptively adjust scheduling in real time.

[0010] To achieve the above objectives, the present invention provides an adaptive scheduling method for mixed-line pulse assembly of aero-engines, comprising the following steps: Step S1: Obtain basic production data of the mixed-line pulsed assembly production line of aero-engines, and construct a directed acyclic assembly process topology network to characterize the relationship between processes based on the aero-engine assembly process flow. Step S2: Based on the basic production data and the directed acyclic assembly process topology network, construct a mixed-line pulsed assembly scheduling optimization model; Step S3: Transform the production scheduling optimization model into a Markov decision process, and perform offline training and solution on the Markov decision process based on a deep Q-network model to generate a robust pre-scheduling plan. Step S4: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time and the current production scheduling system status is updated. A look-ahead search algorithm based on an approximate dynamic programming framework is used for in-process production scheduling. The state value is estimated by combining the DQN (Deep Q Network) value network obtained by offline training. The production scheduling plan for the remaining assembly processes is updated in a rolling manner. Finally, the production scheduling plan for mixed-line pulse assembly of aero-engines that meets the preset conditions is output.

[0011] In some embodiments, step S1 includes: Step S11: Obtain the basic production data of the mixed-line pulsed assembly production line for aero-engines. The basic production data includes the assembly process set, workstation set, total number of available workers, maximum number of workers per workstation, pulsed cycle, minimum number of cooperating workers required for each assembly process, process preceding constraint relationship, process random processing time distribution parameters, labor cost per worker, and unit overdue penalty cost. Step S12: Based on the aero-engine assembly process, the aero-engine assembly object is divided into several assembly units and peripheral accessory systems according to its functional structure, assembly interface and process sequence. The assembly process of each assembly unit and peripheral accessory system is decomposed into several assembly steps. A directed acyclic assembly process topology network is constructed according to the process sequence between each assembly step. Step S13: Based on the aero-engine assembly process, and combined with the time disturbance characteristics of aero-engine assembly, construct a random processing time characterization model for the process, and use the overdue time of the workstation to characterize the impact of random disturbances on the pulsating cycle time.

[0012] In some embodiments, step S2 includes: Step S21: Construct a mixed-line pulse assembly scheduling optimization model that considers random processing time, multi-worker collaborative operation, process preceding constraints, fixed pulsation cycle, and synchronous flow between workstations. Step S22: Determine the optimization objective and set the corresponding production scheduling constraints. The production scheduling constraints are used to ensure that the generated production scheduling scheme meets the process rules, resource boundaries and cycle control requirements of the aero-engine pulse assembly site.

[0013] In some embodiments, step S3 includes: Step S31: Define the mixed-line pulse assembly scheduling optimization model as a Markov decision process, construct a deep Q-network model for pre-production robust scheduling, and define the system state space, action space, state transition mechanism and instant reward function. Step S32: The deep Q-network model is trained offline using historical production data. During the training process, Monte Carlo sampling is used to simulate the fluctuation of random processing time in the assembly process. The action value function is updated using experience replay, target network and ε-greedy strategy to obtain a converged DQN value network. Step S33: Generate a robust pre-scheduling plan based on the converged DQN value network. The robust pre-scheduling plan includes the workstation allocation results, workstation worker configuration results, workstation collaborative operation worker allocation results, planned start time of the workstation, planned completion time of the workstation, and workstation process sequencing results.

[0014] In some embodiments, step S4 includes: Step S41: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time, and the current production scheduling system status is updated according to the on-site production status. Step S42: In-process production scheduling is performed using a look-ahead search algorithm based on an approximate dynamic programming framework. For each candidate production scheduling action that meets the constraints in the current state, a preset number of decision steps are derived. During the look-ahead derivation process, the random processing time distribution of the assembly process and Monte Carlo multi-scenario sampling are combined to calculate the state transition and immediate reward under different random disturbance scenarios. Step S43: When the prospective search reaches the boundary state corresponding to the preset number of steps, the DQN value network trained offline is called to estimate the future value of the boundary state. Based on the Bellman expectation backtracking mechanism, the boundary future value is backtracked to the current state layer by layer. The expected value of each candidate scheduling action is calculated, and the candidate scheduling action with the largest expected value is selected as the optimal scheduling action at the current decision moment. Step S44: The optimal production scheduling action at the current decision moment is sent to the production execution end. When a change in production execution status event is detected, steps S41 to S43 are repeated to continuously update the production scheduling plan for the remaining assembly processes. Finally, a mixed-line pulse assembly production scheduling plan for aero-engines that meets the preset conditions is output.

[0015] In some embodiments, in the directed acyclic assembly process topology network of step S12, each assembly operation is taken as a vertex and the preceding priority relationship between operations is taken as a directed edge, which is used to characterize the serial and parallel assembly relationship between different assembly unit bodies and peripheral accessory systems assembly processes.

[0016] In some embodiments, in the process random processing time characterization model of step S13, the actual processing time of a single process is composed of the nominal process time plus the time increment of multiple types of disturbances. The disturbance duration increment includes the duration increment caused by rework and repair, as well as the non-negative exogenous duration increment caused by manual assembly deviations, material supply fluctuations, and equipment status fluctuations.

[0017] In some embodiments, in step S21, the decision variables of the mixed-line pulse assembly scheduling optimization model include process station allocation variables, station personnel configuration variables, process worker allocation variables, process planned start time variables, and station overdue duration variables.

[0018] In some embodiments, in step S22, the optimization objective is to minimize the total expected production cost, which is the mathematical expectation of the sum of the total cycle labor cost and the overdue penalty cost. The total cycle labor cost is calculated based on the actual number of workers on the entire line and the labor cost per worker per cycle, and the overdue penalty cost is calculated based on the total overdue time on the entire line and the unit overdue penalty cost.

[0019] In some embodiments, the scheduling constraints in step S22 include unique workstation allocation constraints for processes, preceding and succeeding constraints for processes, workstation cycle time overdue constraints, minimum number of cooperating workers constraints for processes, worker and workstation affiliation constraints, constraints that the same worker cannot participate in multiple processes simultaneously, maximum number of workers per workstation constraints, and decision variable value constraints.

[0020] In some embodiments, in step S31, the state space of the Markov decision process includes the process completion status, the estimated completion time of the process in progress, the number of unscheduled processes, the number of remaining available workers, the completion time of the completed work at each workstation, the next available time for each worker, and the current partial production scheduling plan. The action space includes process scheduling actions and workstation switching actions. The process scheduling action is used to indicate the start of production of a process in the current workstation, and simultaneously determine the workstation allocation, the workers participating in the collaborative operation, and the planned start time for that process. The workstation switching action is used to indicate the switch to the next workstation after completing the current workstation scheduling, and determine the number of workers configured for the next workstation. The instant reward function is derived from the production cost of the production scheduling plan and is used to guide the deep Q-network model to converge iteratively toward the production scheduling optimization target, prioritizing the selection of production scheduling actions that match the optimization direction.

[0021] In some embodiments, in step S3, the deep Q-network model adopts a neural network structure that includes an input layer, at least one fully connected hidden layer, and an output layer; The input layer is used to receive the current system state, the hidden layer is used to extract the nonlinear relationship between the process completion state, workstation load state, worker availability state and remaining production scheduling space, and the output layer is used to output the action value of each candidate action in the current state.

[0022] In some embodiments, during step S32, when training the deep Q-network model, trajectory samples consisting of state, action, immediate reward and next state are stored in the experience replay pool, small batches of samples are randomly sampled from the experience replay pool to update network parameters, and target network parameters are periodically synchronized.

[0023] In some embodiments, in step S33, when generating a robust pre-production scheduling plan, the initial production scheduling state before the start of batch production is used as the input of the deep Q-network model. The optimal production scheduling action is selected step by step based on the greedy decision rule and the production scheduling state is updated until all assembly processes have completed the allocation of workstations, worker configuration and start-up time arrangement.

[0024] In some embodiments, the real-time collected on-site production status in step S41 includes the actual completion status of the assembly process, the actual progress of the assembly process in progress, the next available time for each worker, the current completion time of each workstation, the remaining unscheduled assembly processes, and the actual processing time of the processes.

[0025] In some embodiments, in step S44, the production execution status change events include actual completion of assembly process, extended process processing time, rework and repair, abnormal quality inspection, fluctuation in material supply, abnormal equipment or tooling status, risk of workstation cycle time exceeding the deadline, and changes in worker resource status. The final production scheduling plan includes the workstations of each assembly process, the set of workers assigned to each workstation, the set of workers cooperating with each assembly process, the planned start time of each assembly process, the planned completion time of each assembly process, the overdue production time of each workstation, the actual number of workers employed on the entire line, the total expected production cost of the entire line, and the production scheduling execution Gantt chart data.

[0026] To achieve the above objectives, the present invention provides an adaptive scheduling system for mixed-line pulsed assembly of aero-engines, comprising a processor and a memory: The memory stores computer programs; When the processor executes the computer program, it implements the aforementioned adaptive scheduling method for mixed-line pulse assembly of aero-engines.

[0027] This invention provides an adaptive scheduling method and system for mixed-line pulse assembly of aero-engines. By constructing a directed acyclic assembly process topology network and a stochastic processing time representation model, it integrates a deep Q-network pre-scheduling robust pre-scheduling mechanism with a lookahead search in-process adaptive pre-scheduling mechanism based on an approximate dynamic programming framework. This achieves full-dimensional collaborative optimization of process station allocation, multi-worker collaborative configuration, station load balancing, pulse cycle control, and response to stochastic time disturbances. It significantly reduces the total expected production cost, improves resource utilization efficiency, and enhances the cycle stability and adaptability to stochastic disturbances of the production system. Attached Figure Description

[0028] The above and other features, properties and advantages of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings and embodiments, in which the same reference numerals always denote the same features, wherein: Figure 1 A flowchart illustrating the steps of an adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to an embodiment of the present invention is disclosed. Figure 2 A flowchart of the DQN pre-robust pre-scheduling training process according to an embodiment of the present invention is disclosed; Figure 3 A schematic diagram of the synchronous flow of the aero-engine assembly process topology network and workstations according to an embodiment of the present invention is disclosed; Figure 4 A flowchart of Lookahead search and DQN boundary value estimation based on an approximate dynamic programming framework according to an embodiment of the present invention is disclosed. Figure 5 A Gantt chart showing the production scheduling results of mixed-line pulsed assembly of aero-engines according to an embodiment of the present invention is disclosed. Figure 6 The diagram shows a comparison of different algorithms for scheduling mixed-line pulsed assembly of aero-engines according to an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0030] To address the problems of insufficient robustness of mixed-line pulsed assembly scheduling for aero-engines, slow response to in-process disturbances, and low computational efficiency in high-dimensional states in existing technologies, this invention provides an adaptive scheduling method and system for mixed-line pulsed assembly of aero-engines oriented towards random time disturbances. Through four main stages—"basic data and process modeling, scheduling optimization model construction, pre-production robust scheduling, and in-process adaptive scheduling"—it achieves a synergistic balance between scheduling robustness under random time disturbances and dynamic adjustment capability under on-site disturbances.

[0031] Figure 1 A flowchart illustrating the steps of an adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to an embodiment of the present invention is shown, as follows: Figure 1 As shown, the present invention provides an adaptive scheduling method for mixed-line pulse assembly of aero-engines, comprising the following steps: Step S1: Obtain basic production data of the mixed-line pulsed assembly production line of aero-engines, and construct a directed acyclic assembly process topology network to characterize the relationship between processes based on the aero-engine assembly process flow. Step S2: Based on the basic production data and the directed acyclic assembly process topology network, construct a mixed-line pulsed assembly scheduling optimization model; Step S3: Transform the production scheduling optimization model into a Markov decision process, and perform offline training and solution on the Markov decision process based on a deep Q-network model to generate a robust pre-scheduling plan. Step S4: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time and the current production scheduling system status is updated. A look-ahead search algorithm based on an approximate dynamic programming framework is used for in-process production scheduling. The state value is estimated by combining the deep Q-network (DQN) value network obtained by offline training. The production scheduling plan for the remaining assembly processes is updated in a rolling manner, and finally the production scheduling plan for mixed-line pulse assembly of aero-engines that meets the preset conditions is output.

[0032] This invention establishes a mixed-line pulsed assembly scheduling optimization model (considering random processing time, multi-worker collaborative operations, process precedence constraints, fixed pulse cycles, and synchronous workstation rotation), combines it with offline training of a deep Q-network to generate a robust pre-scheduling plan, and employs a Lookahead search algorithm based on an approximate dynamic programming framework during production execution. It also calls upon an offline-trained DQN value network to estimate the future value of the lookahead boundary states, continuously updating the scheduling plan for the remaining assembly processes. Therefore, this invention can generate an initial scheduling plan robust to random working hours before batch production begins, and perform in-process scheduling based on the actual on-site conditions during assembly execution. This effectively reduces total cycle time labor costs and overdue penalty costs, comprehensively improving the stability of the pulse cycle, the feasibility of worker collaboration, and the production system's resilience.

[0033] Figure 2 A flowchart of the DQN pre-robust pre-scheduling training process according to an embodiment of the present invention is disclosed below, which will be combined with Figure 1 and Figure 2 These steps are described in detail. It should be understood that, within the scope of this invention, the above-described technical features of this invention and the technical features specifically described below (such as in the embodiments) can be combined and related to each other to form preferred technical solutions.

[0034] Step S1: Obtain basic production data of the mixed-line pulsed assembly production line of aero-engines, and construct a directed acyclic assembly process topology network to characterize the relationship between processes based on the aero-engine assembly process flow.

[0035] This step involves analyzing production line resources and process constraints to prepare basic data for production scheduling and to model the process, providing input for the subsequent construction of optimization models. Step S1 specifically includes three sub-steps: S11 to S13.

[0036] Step S11: Obtain basic production data for the mixed-line pulse assembly production line of aero-engines.

[0037] The basic production data includes the assembly process set, workstation set, total number of available workers, maximum number of workers per workstation, pulse cycle, minimum number of cooperating workers required for each assembly process, process prerequisite constraints, process random processing time distribution parameters, labor cost per worker, and unit overdue penalty cost.

[0038] In some embodiments, the basic set and parameters of the mixed-line pulse assembly scheduling problem for aero-engines are symbolically defined to facilitate subsequent model construction: Define the assembly process set as: ; in, Represents a set of assembly processes. Indicates the total number of assembly processes; Define the workstation set as: ; in, Represents a set of workstations. Indicates the total number of workstations; Define the worker set as: ; in, Indicates the assembly of workers. Indicates the total number of workers available on the production line; definition For a single pulse cycle with a fixed duration, The maximum number of workers that can be configured for a single workstation. For process Minimum number of collaborating workers required For process The set of all preceding processes, The cost of labor per worker per cycle. Penalty cost per unit of overdue period.

[0039] Step S12: Based on the aero-engine assembly process, the aero-engine assembly object is divided into several assembly units and peripheral accessory systems according to its functional structure, assembly interface and process sequence. The assembly process of each assembly unit and peripheral accessory system is decomposed into several assembly steps. A directed acyclic assembly process topology network is constructed according to the process sequence relationship between each assembly step.

[0040] The assembly process set is obtained by decoupling the aero-engine final assembly process path into units. For a typical aero-engine final assembly scenario, the final assembly unit and peripheral accessory system may include a fan / booster stage unit, a high-pressure compressor unit, a combustion chamber unit, a high-pressure turbine unit, a low-pressure turbine unit, and peripheral accessory systems. The structural decomposition of complex assembly processes is achieved through unit decoupling.

[0041] In some embodiments, the directed acyclic assembly process topology network uses each assembly operation as a vertex and the preceding priority relationship between operations as directed edges to characterize the serial and parallel assembly relationships between different assembly unit bodies and peripheral accessory systems.

[0042] Figure 3 A schematic diagram of the topology network and synchronous flow of workstations in the aero-engine assembly process according to an embodiment of the present invention is disclosed, such as... Figure 3 As shown, the topology network uses 61 assembly operations as vertices, with directed edges representing the precedence relationships between operations. The nodes are arranged from left to right according to the assembly process flow, and the directed arrows indicate the constraint direction from the preceding operation to the subsequent operation, intuitively presenting the sequential dependencies between the operations.

[0043] Figure 3 Different colors or regions are used to identify the sets of process nodes corresponding to each assembly unit and peripheral accessory system. The assembly processes of the fan / booster stage unit, high-pressure compressor unit, combustion chamber unit, high-pressure turbine unit, low-pressure turbine unit, and peripheral accessory systems are located in different functional areas of the topology network. Process nodes within the same area are connected by directed edges to represent their internal serial / parallel relationships, while directed edges between different areas represent the assembly sequence and interface matching relationships between units and accessories. Furthermore, Figure 3 The process execution areas of each workstation are divided by background color, and arrows indicate that the product flows synchronously between each workstation according to a preset pulse cycle, reflecting the pulse assembly production characteristics of "the product does not move during assembly and the product does not assemble when it moves".

[0044] The directed acyclic assembly process topology network is formally represented by graph theory as follows: ; in, Represents the set of assembly operation nodes. This represents the set of directed preceding constraint edges between assembly operations; For any directed edge , indicating process For process The immediate preceding process, process The planned start time should meet hard constraints: ; in, For process The planned start date For process The planned start date, For process The actual random processing time. This constraint reflects the most basic process logic in assembly operations, namely that a certain operation can only begin after all its preceding operations have been completed.

[0045] By constructing the above-mentioned directed acyclic assembly process topology network, we can accurately characterize the serial and parallel relationships and immediate predecessor and successor constraints between assembly processes of different unit bodies and peripheral accessory systems, thus avoiding the problem of infeasible scheduling schemes caused by traditional scheduling models that only consider the process sequence and ignore the process topology.

[0046] Step S13: Based on the aero-engine assembly process, and combined with the time disturbance characteristics of aero-engine assembly, construct a random processing time characterization model for the process, and use the overdue time of the workstation to characterize the impact of random disturbances on the pulsating cycle time.

[0047] In some embodiments, in the random processing time characterization model of a process, the actual processing time of a single process is composed of the nominal process time plus the time increment of multiple types of disturbances. The disturbance duration increment includes the duration increment caused by rework and repair, as well as the non-negative exogenous duration increment caused by manual assembly deviations, material supply fluctuations, and equipment status fluctuations.

[0048] The specific model for representing the random processing time of the process is as follows: ; in, For process The actual processing time, For the first j The nominal process time of each step The increased time due to rework and repairs, These represent the non-negative exogenous duration increments caused by manual assembly deviations, material supply fluctuations, and equipment status fluctuations, respectively.

[0049] Optionally, the non-negative exogenous time increment refers to the additional operation time caused by factors such as manual assembly deviation, material supply fluctuation and equipment status fluctuation. Its value is not less than 0. It is used to characterize the characteristic that various disturbance factors cause the actual processing time of the process to increase or remain unchanged relative to the nominal process time. It can also be called "non-negative external disturbance time increment".

[0050] The increase in rework and repair time The mathematical expectation can be derived from the first The first-pass yield and average rework time of each process are calculated and determined.

[0051] By constructing the above-mentioned random processing time characterization model, the overtime of workstations caused by random processing time can be included in the expected production cost for quantitative evaluation, thereby providing a data basis for the robust design of random working hours in the subsequent production scheduling optimization model.

[0052] Step S2: Based on the basic production data and the directed acyclic assembly process topology network, construct a mixed-line pulsed assembly scheduling optimization model.

[0053] This step takes basic production data and process topology network as input, and integrates assembly process constraints, human resource constraints, and pulse cycle constraints into a quantitative optimization framework, providing a model foundation for subsequent pre-production scheduling and in-process dynamic scheduling. Step S2 specifically includes two sub-steps, S21 and S22.

[0054] Step S21: Construct a mixed-line pulse assembly scheduling optimization model that considers random processing time, multi-worker collaborative operation, process preceding constraints, fixed pulsation cycle, and synchronous flow between workstations. In some embodiments, the decision variables of the mixed-line pulsed assembly scheduling optimization model include process station allocation variables, station personnel configuration variables, process worker allocation variables, process planned start time variables, and station overdue duration variables. The variables are defined as follows: The workstation allocation variable Defined as: ; The workstation personnel configuration variables Defined as: ; Worker assignment variables in the process Defined as: ; Step S22: Determine the optimization objective and set the corresponding production scheduling constraints. The production scheduling constraints are used to ensure that the generated production scheduling scheme meets the process rules, resource boundaries and cycle control requirements of the aero-engine pulse assembly site.

[0055] Specifically, based on the decision variables in step S21, the set of workstation processes, the overdue time of workstations, and the total number of workers on the entire production line can be further derived: The workstation process set Defined as: ; The workstation Production overdue time Defined as: ; The total overdue time of the entire line Defined as: ; The actual number of employees across the entire line Defined as: ; In this embodiment, the mixed-line pulse assembly scheduling optimization model aims to minimize the total expected production cost, which is the mathematical expectation of the sum of the total cycle labor cost and the overdue penalty cost. The total cycle labor cost is calculated based on the actual number of workers on the entire line and the labor cost per worker per cycle, while the overdue penalty cost is calculated based on the total overdue time of the entire line and the unit overdue penalty cost.

[0056] Based on the above definition, the objective function of the mixed-line pulse assembly scheduling optimization model is in the following form: ; When expanded, it appears as follows: ; in, The cost of labor per worker per cycle. Penalty cost per unit of overdue period.

[0057] The first term of the objective function is used to characterize the total cycle labor cost, and the second term is used to characterize the penalty cost for exceeding the cycle time due to random processing time. By taking the expected value of the total production cost, the model can generate a robust production scheduling plan under random processing time fluctuations.

[0058] Furthermore, to ensure the on-site requirements of the production scheduling plan are met, multi-dimensional production scheduling constraints are set. These constraints include unique workstation allocation constraints for each process, preceding and succeeding process constraints, workstation cycle time exceeding constraints, minimum number of cooperating workers constraints for each process, worker and workstation affiliation constraints, constraints that the same worker cannot participate in multiple processes simultaneously, maximum number of workers per workstation constraints, and constraints on the values ​​of decision variables.

[0059] In some embodiments, the specific forms and meanings of the constraints are as follows: (1) Unique workstation allocation constraint for each process: ; This constraint means that any assembly process can only be assigned to one workstation and cannot be split across workstations, thus ensuring the integrity of process execution.

[0060] (2) Pre-process and post-process constraints: ; This constraint is consistent with the constraint of the process topology network in step S12, indicating that any assembly process can only start after all its preceding processes are completed, which meets the rigid requirements of the assembly process.

[0061] (3) Workstation cycle time overdue constraint: ; in, For sufficiently large positive numbers; when When =1, the above formula indicates allocation to workstations. process The completion time must not exceed the pulsation cycle. The sum of the overdue time of the workstations allows for quantitative control of the pulse rhythm.

[0062] (4) Minimum number of cooperating workers constraint for each process: ; This constraint represents the process. At least The work is completed collaboratively by multiple workers to meet the actual needs of multi-worker collaborative operations in the aero-engine assembly process.

[0063] (5) Worker-workstation affiliation constraints: ; When the process Assigned to work station When the above equation degenerates into: ; This constraint indicates the participation process. Workers must belong to the work process. The workstation location ensures consistency between staffing and workstation allocation.

[0064] (6) The constraint that the same worker cannot participate in multiple processes simultaneously is: ; ; ; in, For workers In the process With process The order of tasks is an auxiliary variable. This constraint is used to ensure that the same worker can only participate in one assembly process at a time, thus avoiding human resource conflicts.

[0065] (7) The maximum number of workers per workstation is constrained as follows: ; This constraint stipulates that the total number of workers configured at a single workstation must not exceed a preset maximum worker count threshold. K Matching the space capacity and work organization capabilities of the workstations.

[0066] (8) The constraints on the values ​​of the decision variables are: ; ; This constraint clarifies the discrete value attributes of the 0-1 decision variables, as well as the non-negative attributes of start time and overdue duration.

[0067] Through the above constraints, the production scheduling model can simultaneously ensure assembly process sequence, workstation load balance, worker collaboration, cycle time stability, and on-site resource feasibility.

[0068] Step S2 incorporates the requirements for workstation allocation, worker configuration, multi-worker collaborative operation, and synchronous workstation flow into the optimization framework through the above-mentioned production scheduling optimization model and constraints. Combined with the directed acyclic assembly process topology network constructed in step S12, the generated production scheduling scheme can meet the requirements of process sequence, resource coordination, and execution feasibility of the mixed-line pulsed assembly site of aero-engines.

[0069] Step S3: Transform the production scheduling optimization model into a Markov decision process, and perform offline training and solution on the Markov decision process based on a deep Q-network model to generate a robust pre-scheduling plan.

[0070] This step, based on the mixed-line pulsed assembly scheduling optimization model constructed in step S2, formalizes the scheduling problem under constraints into a Markov decision process. A deep Q-network is used for offline training and value fitting to obtain a pre-scheduling plan that balances robustness to stochastic working hours and on-site feasibility, providing a benchmark for subsequent production execution and in-process scheduling. Step S3 specifically includes three sub-steps: S31 to S33.

[0071] Step S31: Define the mixed-line pulse assembly scheduling optimization model as a Markov decision process, construct a deep Q-network model for pre-scheduling robustness, define the system state space, action space, state transition mechanism and instant reward function, so that the deep Q-network model can output the action value of each candidate scheduling action according to the current scheduling state. In this embodiment, the mixed-line pulsed assembly scheduling model is defined as a Markov decision process, which can be represented as a quintuple: ; in, For state space, For the action space, Let be the state transition probability. For instant reward function, This is the discount factor.

[0072] The state transition matrix is ​​used to describe the current production scheduling state. Next, execute candidate production scheduling actions Then, the system moves to the next production schedule. The probability distribution of is denoted as: ; Since the processing time of a step is random, the state transition process can be achieved through a state transition function. Combined with random processing time vector representation: ; in, This is the state transition function. It is a random processing time vector composed of the random processing times of each assembly process; The state transition probability is approximated using Monte Carlo sampling: ; in Number of samples for Monte Carlo For the first The random processing time vector obtained from the second sampling. The indicator function is defined as follows: ; The specific update rules for state transition are as follows for the two different types of scheduling actions: If candidate scheduling action For process scheduling actions, that is, at the current workstation Internal start-up process And if the workers participating in the collaborative operation are determined, then the state transition function is... According to the process Planned start time and random processing time Update process Workstation allocation variables Worker allocation variables in each process Expected completion time workstation The completed time of filled tasks, the next available time for relevant workers, the number of remaining unscheduled processes, and the current partial production scheduling plan.

[0073] If candidate scheduling action For a workstation switching action, which involves completing the scheduling of the current workstation and switching to the next workstation, while simultaneously determining the number of workers to be assigned to the next workstation, the state transition function is as follows: Synchronize and update workstation personnel configuration variables The remaining number of available workers, the current workstation status, and the current partial production scheduling plan.

[0074] Furthermore, the core components of the Markov decision-making process will be explained one by one: At the moment of decision The state vector is composed of the process execution state, resource occupancy state, and production scheduling state.

[0075] In this embodiment, the state space of the Markov decision process includes the process completion status, the estimated completion time of the processes in progress, the number of unscheduled processes, the number of remaining available workers, the completion time of the completed tasks at each workstation, the next available time for each worker, and the current partial production scheduling plan, which can be specifically represented as follows: ; in, This represents the process completion state vector. If the process... Assembly and inspection have been completed. ,otherwise ; This represents the estimated completion time vector for the currently processing step; This indicates the number of processes that have not yet been scheduled; This indicates the number of remaining available workers who have not yet been assigned to production. This represents the completion time vector of the tasks that have been filled at each workstation; This represents the next available time vector for each worker; This indicates the partial production scheduling plan that has already been finalized; In this embodiment, the action space includes two categories: process scheduling actions and workstation switching actions, covering all decision-making behaviors in the scheduling process.

[0076] The process scheduling action is used to indicate the start of production of a process at the current workstation, and simultaneously determine the workstation allocation, the workers participating in the collaborative operation, and the planned start time for that process.

[0077] The process scheduling action is represented as follows: ; in, This indicates that the process will be started at the current workstation. Production, and simultaneously determine the process. Workstation allocation, workers participating in collaborative operations, and planned start times.

[0078] The workstation switching action is used to indicate that after completing the current workstation scheduling, the workstation will switch to the next workstation and determine the number of workers to be configured for the next workstation.

[0079] The workstation switching action is represented as follows: ; in, This indicates that the scheduling of the current workstation has been completed, the process has been switched to the next workstation, and the configuration of the next workstation has been confirmed. A worker.

[0080] Therefore, the complete action space of a deep Q-network can be represented as: ; In any state Next, based on the current process topology constraints, worker collaboration constraints, number of workstations constraints, and worker time conflict constraints, legal actions are selected to obtain the possible action space: ; The immediate reward function is derived from the production cost of the scheduling plan and is used to guide the deep Q-network model to iteratively converge towards the scheduling optimization objective, prioritizing scheduling actions that match the optimization direction. More specifically, the immediate reward function guides the deep Q-network model to prioritize scheduling actions that can reduce labor costs, reduce overdue penalties, and maintain a balanced workload at workstations.

[0081] The specific form of the instant reward function is as follows: ; in, It is a sufficiently large positive number, and its value needs to cover the sum of the maximum labor cost over the entire cycle and the conservatively estimated maximum overdue penalty cost, in order to ensure that the immediate reward value is always non-negative; In the state Next action The production schedule obtained after the update; The expected production cost corresponding to the production scheduling plan is consistent with the objective function definition in step S22.

[0082] The production cost of the aforementioned production scheduling plan is: ; in, Indicates production scheduling plan The corresponding actual number of employees, Indicates production scheduling plan The corresponding total overdue period; ; in, For the number of samples taken in Monte Carlo, For the first l The random processing time vector obtained from the sampling.

[0083] The deep Q-network used in step S31 can approximate the action value function through a neural network, and is suitable for solving complex sequential decision problems in high-dimensional state spaces. However, the pre-production scheduling method of this method needs to take into account factors such as process topology, workstation load, worker collaboration, pulse cycle and random processing time. The state information has a high dimension and the candidate action combination is complex. Therefore, the technical characteristics of deep Q-network outputting candidate action value according to state are highly matched with the solution requirements of this scenario.

[0084] Step S32: The deep Q-network model is trained offline using historical production data. During the training process, Monte Carlo sampling is used to simulate the fluctuation of random processing time in the assembly process. The action value function is updated using experience replay, target network and ε-greedy strategy to obtain a converged DQN value network. The deep Q-network model adopts a neural network structure containing an input layer, at least one fully connected hidden layer, and an output layer. The mapping relationship between the function of each layer and the production scheduling scenario is as follows: The input layer is used to receive the current system state. The hidden layer is used to extract the nonlinear correlation between process completion status, workstation load status, worker availability status, and remaining scheduling space, realizing feature abstraction of high-dimensional state information. The output layer is used to output each candidate scheduling action in the current state. The corresponding action value provides a quantitative basis for action decision-making.

[0085] This step uses historical production data as a foundation, combined with Monte Carlo sampling to simulate random time fluctuations, and iteratively optimizes the network parameters. Monte Carlo sampling is a numerical calculation method based on random sampling using a known probability distribution. In this step, based on the historical statistical distribution of processing time for each assembly process (such as normal distribution, log-normal distribution, etc.), a large number of processing time samples are randomly extracted to generate multiple sets of different random time scenarios to simulate various fluctuations in processing time during actual production. By generating training samples covering different levels of fluctuation through multiple Monte Carlo samplings, the deep Q-network can fully engage with various random disturbance scenarios during the training phase, improving the robustness of the value network to uncertainty after training.

[0086] In this embodiment, during the training of the deep Q-network model, trajectory samples consisting of state, action, immediate reward and next state are stored in the experience replay pool. Small batches of samples are randomly sampled from the experience replay pool to update the network parameters, and the target network parameters are periodically synchronized to ensure the stability and convergence efficiency of the training process.

[0087] The action value function of a deep Q-network can be expressed as: ; in, These are the trainable parameters for a deep Q-network. The system state at the moment of decision-making. These are candidate production scheduling actions to be evaluated.

[0088] The trajectory sample, consisting of state, action, reward, and next state, is stored in the experience replay pool: ; in, For the first t Trajectory samples (empirical samples) generated through step-by-step interaction. The current state of the system at the moment of decision-making. Select the scheduling action to execute in the current state. The immediate reward obtained after performing this action. This represents the system state at the next moment after the state transition.

[0089] Training involves randomly sampling small batches of samples from the experience replay pool to break the temporal correlation between samples, avoid oscillations during training, and improve the stability of network convergence.

[0090] During training, an ε-greedy strategy is used to select production actions, balancing the weights of exploration and utilization to prevent the network from getting trapped in local optima.

[0091] The action selection rule of the ε-greedy strategy is as follows:

[0092] in, , which is a random number that follows a uniform distribution of 0-1; ε This is a preset exploration probability threshold. When the random number is less than this threshold, a scheduling action is randomly selected from the action space corresponding to the current state to explore the unknown action space; when the random number is greater than or equal to this threshold, the scheduling action with the highest action value output by the current network is selected to utilize existing experience.

[0093] For the For each training sample, the target action value is calculated using the following formula: ; in, For the target network parameters, For the first i The target action value of each sample For the first i Actions are performed in each sample. The instant reward obtained afterward For the first i The state at the next time step after the state transition in each sample. These are candidate actions for the next state. This is a discount factor, consistent with the definition of the Markov decision process in step S31.

[0094] The mean squared error between the current action value and the target action value is used as the loss function. The format is: ; in, For small batch sample size, For the first i The value of the target action for each sample For the first i The state corresponding to each sample For the first i The execution action of each sample These are the trainable parameters for a deep Q-network.

[0095] The “mini-batch” here refers to the conventional sampling method in deep neural network training, which means the number of samples randomly sampled from the experience replay pool. It is usually a positive integer such as 32, 64 or 128, which is much smaller than the total capacity of the experience replay pool. It is used to calculate the loss and update the network parameters on the current batch.

[0096] This loss function is used to quantify the deviation between the action value of the current network output and the target value, providing a clear direction for parameter updates.

[0097] The trainable parameters of the current deep Q-network are iteratively updated using the gradient descent algorithm. : ; in, The learning rate is used to control the step size for parameter updates. The target network parameters are periodically updated during training. ; By synchronizing the target network parameters at fixed intervals, training oscillations caused by frequent fluctuations in target value during training are avoided, thus ensuring the stability of target value calculation.

[0098] In this step, during the offline training of the Deep Q-Network, Monte Carlo sampling is used to simulate the fluctuations in random processing time of the assembly process. This enables the DQN value network to fully learn the state-action value mapping relationship under random time perturbations, providing support for the subsequent generation of pre-scheduling plans with robustness to random time perturbations.

[0099] Repeat the above action interaction, sample sampling, and parameter update process until the network loss converges, ultimately obtaining the converged optimal DQN value network. It is used for generating robust pre-production scheduling plans in advance, and for estimating the boundary state value of in-process look-ahead search.

[0100] Step S33: Generate a robust pre-scheduling plan based on the converged DQN value network. The robust pre-scheduling plan includes the workstation allocation results, workstation worker configuration results, workstation collaborative operation worker allocation results, planned start time of the workstation, planned completion time of the workstation, and workstation process sequencing results.

[0101] Based on convergent DQN value network When generating a robust pre-production scheduling plan, the initial production scheduling state before the start of batch production is used. As input to the deep Q-network model, the optimal production scheduling action is selected step by step based on the greedy decision rule and the production scheduling status is updated until all assembly processes complete the workstation allocation, worker configuration and start-up time arrangement.

[0102] Specifically, at any decision-making moment t Based on the set of possible actions in the current state The following greedy decision rule is used to progressively select scheduling actions, that is, the action with the highest action value is taken as the current optimal scheduling action, and the corresponding expression is: ; in, For decision-making moments t The optimal scheduling action output by the DQN value network. For decision-making moments t The current production schedule a These are the candidate production scheduling actions to be evaluated under the current conditions.

[0103] According to the optimal scheduling action Update the current production scheduling status using the state transition function: ; in, This is the state transition function. This is a random processing time vector composed of the random processing times of each assembly process, consistent with the definition in step S31. For decision-making moments t The current production schedule For decision-making moments t The optimal production scheduling action output. The system scheduling status at the next decision moment is updated after the optimal scheduling action is executed.

[0104] Repeat the above action selection and status update process until all assembly processes have completed workstation allocation, worker configuration, and start-up time scheduling to obtain a robust pre-production scheduling plan.

[0105] The aforementioned robust pre-scheduling plan can be symbolically represented as: ; in, This is the pre-production scheduling stage. j The workstation allocation results For workers k At workstation m The configuration results For workers k Whether to participate in the process j Collaborative work, For process j The planned start date, For process j The planned completion time, For workstation m The expected overdue period.

[0106] Process j Planned completion time By planning the start time Processing time of superimposed processes The mathematical expectation is obtained, and the corresponding expression is: ; The total expected production cost of the robust pre-production scheduling plan is: ; in, For workers k At workstation m The configuration results For workstation m The expected overdue period, The cost of labor per worker per cycle. Penalty cost per unit of overdue period For workstation collection, To assemble the workers.

[0107] The robust pre-scheduling plan in step S3 is used to determine the workstation allocation, workstation personnel configuration, workstation coordinator allocation, planned start time, planned completion time, and workstation sequence results in the mixed-line pulse assembly process of aero-engines before the start of batch production, thereby providing an initial baseline plan for subsequent in-process scheduling.

[0108] Step S4: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time and the current production scheduling system status is updated. A look-ahead search algorithm based on an approximate dynamic programming framework is used for in-process production scheduling. The state value is estimated by combining the DQN (Deep Q Network) value network obtained by offline training. The production scheduling plan for the remaining assembly processes is updated in a rolling manner. Finally, the production scheduling plan for mixed-line pulse assembly of aero-engines that meets the preset conditions is output.

[0109] Based on the robust pre-scheduling plan formed in step S3, step S4, during the actual execution of the mixed-line pulse assembly of aero-engines, collects the on-site production status in real time and updates the current scheduling system status. It then uses Lookahead search and DQN boundary value estimation based on an approximate dynamic programming framework to schedule the remaining assembly processes in real time. The scheduling plan for the remaining assembly processes is updated continuously, thereby correcting the planning deviations caused by random time disturbances such as workstation overdue risks and process delays in a timely manner. This ensures that the scheduling plan can continuously maintain its responsiveness to the actual on-site status during the production execution process.

[0110] Figure 4 A flowchart of Lookahead search and DQN boundary value estimation based on an approximate dynamic programming framework according to an embodiment of the present invention is disclosed, as follows: Figure 4 As shown, this process takes the current production state as input, and gradually derives an accurate immediate reward through precise dynamic programming within the look-ahead window. At the boundary of the look-ahead search, an offline-trained DQN method is used to output an action value function to approximate the long-term future reward, achieving an organic combination of accurate local decision-making and global value approximation. Step S4 specifically includes four sub-steps S41 to S44.

[0111] Step S41: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time, and the current production scheduling system status is updated based on the on-site production status.

[0112] More specifically, during the pulsed assembly production of aero-engines, the on-site production status is collected in real time. This on-site production status includes the actual progress of completed assembly processes, ongoing assembly processes, the next available time for each worker, the current completion time for each workstation, remaining unscheduled assembly processes, and the actual processing time for each process. The current production scheduling system is updated based on this on-site production status, eliminating discrepancies between pre-scheduling assumptions and the actual execution status through real-time synchronization of on-site production data.

[0113] Step S42: The Lookahead search algorithm based on an approximate dynamic programming framework is used for in-process production scheduling. For each candidate scheduling action that meets the constraints in the current state, the decision steps of the preset number of steps are accurately derived forward. In the process of forward derivation, the random processing time distribution of the assembly process and Monte Carlo multi-scenario sampling are combined to calculate the state transition and immediate reward under different random disturbance scenarios. The decision accuracy under local disturbance scenarios is improved by precise forward look-ahead in a finite number of steps.

[0114] The in-process scheduling method requires rapid correction of the remaining processes based on the real-time status of the site, and the scheduling state space has a high dimension. The Lookahead search algorithm has the characteristics of finite-step look-ahead, rolling decision-making, and the ability to combine random scenario sampling, which can adapt to the requirements of the in-process scheduling method of "rapid response to local disturbances and dynamic correction of the remaining process scheduling in a high-dimensional state space", thereby ensuring the rationality of decision-making while controlling the amount of computation.

[0115] In this embodiment, the Lookahead search algorithm based on an approximate dynamic programming framework is used to perform rolling optimization of the remaining assembly processes according to the real-time status during production execution. The current decision moment is defined as... The current real-time status is The lookahead search step size is For any candidate action ,in front Within each decision step, precise dynamic programming is used to recursively calculate the immediate reward generated by different candidate actions within the local look-ahead window.

[0116] Candidate Action The forward-looking expected value is: ; in, For the first In the nth random scenario, the th The system state corresponding to each look-ahead step For the corresponding candidate production scheduling actions, Let the function be the future value estimation function for the forward boundary state. L For the number of samples taken in Monte Carlo, γThis is the discount factor.

[0117] Current prospective search reaches the first At the next decision step, stop fully expanding the state space and call the offline-trained DQN value network to estimate the future value of the boundary state: ; in, This is the approximate optimal action value function for DQN trained offline. Forward-looking boundary moments τ +P The set of executable scheduling actions corresponding to the system state. To achieve the first P The boundary system state at each decision step, i.e., the mixed-line pulsating assembly production state at the end of the local look-ahead window. Forward boundary state Candidate scheduling actions in the set of actionable actions.

[0118] Step S43: When the forward search reaches the boundary state corresponding to the preset number of steps, the DQN value network trained offline is invoked to estimate the future value of the boundary state. Based on the Bellman expectation backtracking mechanism, the future value of the boundary is backtracked to the current state layer by layer. The expected value of each candidate scheduling action is calculated, and the candidate scheduling action with the largest expected value is selected as the optimal scheduling action at the current decision moment.

[0119] This step calls upon the offline-trained DQN value network at the boundary of the Lookahead search to estimate future value, thereby evaluating the long-term scheduling effect of the remaining assembly processes after the P-th decision step without further fully expanding the high-dimensional state space, taking into account both accurate decision-making under local perturbations and computational efficiency of in-process scheduling.

[0120] When the lookahead search reaches the boundary state of the P-th decision step, the expansion of the subsequent high-dimensional state space is stopped. The DQN value network trained and converged offline in step S32 is invoked to estimate the optimal future value of the boundary state. This approximates the long-term production scheduling effect of the remaining assembly processes after the P-th decision step, significantly reducing the online computation while ensuring the globality of the decision. The calculation method for the future value of the boundary state is consistent with the definition in step S42.

[0121] Based on the Bellman expectation backtracking mechanism, the immediate rewards and long-term values ​​of the boundary states of each decision step within the look-ahead window are recursively backtracked to the current decision moment according to the discount factor γ, and then combined to obtain the overall look-ahead expected value of each candidate production scheduling action.

[0122] Finally, the candidate action with the highest expected value is selected as the optimal scheduling action at the current decision time τ, and the corresponding expression is as follows: ; in, Provides space for actions in the current real-time state. These are the candidate production scheduling actions to be evaluated under the current conditions. For the current decision-making moment τ The optimal production scheduling action, ( ) is the forward expected value function of the candidate production scheduling action, and its calculation method is consistent with the definition in step S42.

[0123] The Bellman expectation backtracking mechanism used in step S43 is a standard value recursion method in reinforcement learning. Its core function is to make the production scheduling in the process take into account both the immediate cost impact of local disturbances and the long-term scheduling effect of the remaining process. At the same time, it avoids the computational explosion problem caused by fully unfolding the high-dimensional state space, thus balancing decision accuracy and online computing efficiency.

[0124] Step S44: The optimal production scheduling action at the current decision moment is sent to the production execution end. When a change in production execution status event is detected, steps S41 to S43 are repeated to continuously update the production scheduling plan for the remaining assembly processes. Finally, a mixed-line pulse assembly production scheduling plan for aero-engines that meets the preset conditions is output.

[0125] In this embodiment, the production execution status change events include actual completion of assembly process, extended process processing time, rework and repair, abnormal quality inspection, fluctuation in material supply, abnormal equipment or tooling status, risk of workstation cycle time exceeding the deadline, and changes in worker resource status.

[0126] The preset conditions include pulse rhythm stability, worker collaboration constraints, and random disturbance adaptability.

[0127] It should be noted that the above-mentioned production execution status change events are not an exhaustive list, but rather typical on-site events that trigger in-process production scheduling during the mixed-line pulse assembly of aero-engines. These events cover all dynamic disturbances that cause deviations between the pre-planned production schedule and the actual on-site state, requiring updates to the system status and rolling production scheduling. All such events will lead to deviations between the pre-planned production schedule and the actual on-site state, necessitating in-process production scheduling and rolling updates to the scheduling of the remaining assembly processes.

[0128] When a change in production execution status is detected on-site, the current real-time status of the production site is obtained, and the system status is updated. : ; in, This represents the actual production status obtained from real-time production data on-site. Based on the updated real state, the action space is re-extracted: ; Perform Lookahead search again to obtain the current optimal scheduling action: ; The current optimal action is then sent to the production execution end to adjust the workstation allocation, worker configuration, process start time, or workstation switching strategy for the remaining processes, thereby achieving rolling dynamic optimization.

[0129] The final output of the mixed-line pulse assembly production schedule for aero-engines includes the workstations to which each assembly process belongs, the set of workers assigned to each workstation, the set of workers cooperating with each assembly process, the planned start time of each assembly process, the planned completion time of each assembly process, the overdue production time of each workstation, the actual number of workers employed on the entire line, the total expected production cost of the entire line, and the production schedule execution Gantt chart data.

[0130] Each core indicator can be calculated in the following ways: The workstations for each assembly process are indicated as follows: ; The set of workers assigned to each workstation is represented as follows: ; The set of workers cooperating in each process is represented as: ; The actual number of workers employed across the entire line is expressed as follows: ; The total expected production cost for the entire line is expressed as: ; in, The cost of labor per worker per cycle. Penalty cost per unit of overdue period For workstation collection, Gathering the workers For workstation m The actual overdue period This represents the actual number of workers employed across the entire line.

[0131] The above output results enable the coordinated optimization of process allocation, worker configuration, workstation load, cycle stability, and random disturbance adaptability during the mixed-line pulse assembly of aero-engines.

[0132] Figure 5A Gantt chart showing the mixed-line pulse assembly scheduling results of an aero-engine according to an embodiment of the present invention is disclosed, such as... Figure 5 As shown, the vertical axis of this Gantt chart represents each workstation (Server 1 to Server 12), and the horizontal axis represents time. Each color block represents an assembly process assigned to that workstation. The starting position and length of the color block on the horizontal axis represent the planned start and planned completion times of that assembly process, respectively. The numbers within the color blocks correspond to... Figure 3 The process node numbers in the directed acyclic assembly process topology network. By using color blocks with different process numbers, the planned start time, planned completion time, collaborating workers, and workstation cycle time overdue status of each assembly process are intuitively displayed. This clearly reflects the workstation cycle time execution status and production resource allocation, and intuitively presents the work arrangement of the production scheduling plan, providing a visual basis for on-site production execution.

[0133] Figure 6 The diagram shows a comparison of different algorithms for scheduling mixed-line pulsed assembly of aero-engines according to an embodiment of the present invention, such as... Figure 6 As shown in the figure, the comparison chart presents the comprehensive comparison results of the proposed method (DQN+Lookahead) with genetic algorithm (GA), particle swarm optimization algorithm (PSO), simulated annealing algorithm (SA), rolling time domain optimization algorithm (RHO), and factory manual experience scheduling method in terms of total expected production cost, maximum cycle time overdue, decision time, and production line balance rate in the form of a bar chart.

[0134] Regarding the total expected production cost, the method of this invention is 120.00, which is lower than that of the genetic algorithm (140.01), particle swarm optimization algorithm (150.00), simulated annealing algorithm (131.52), rolling time domain optimization algorithm (142.26), and factory manual experience scheduling (185.22). This indicates that the method can effectively reduce the sum of labor costs and overdue penalty costs under random working hour disturbances.

[0135] In terms of the maximum cycle time overdue, the method of this invention is 0.00h, which is lower than that of the genetic algorithm (0.002h), simulated annealing algorithm (0.3h), rolling time domain optimization algorithm (0.457h), and factory manual experience scheduling (7.04h). This shows that the method can effectively control the risk of pulsating cycle time overdue and improve the cycle time stability of the assembly process.

[0136] In terms of decision-making time, the method of this invention is 28.01s, which is lower than that of genetic algorithm (55.11s), particle swarm optimization algorithm (58.25s), simulated annealing algorithm (71.97s) and rolling time domain optimization algorithm (36.92s), indicating that this method can meet the real-time requirements of in-process scheduling while ensuring the scheduling effect.

[0137] In terms of production line balance rate, the method of this invention is 86.12%, which is higher than that of genetic algorithm (72.14%), particle swarm optimization algorithm (62.30%), simulated annealing algorithm (77.45%), rolling time domain optimization algorithm (72.15%) and factory manual experience scheduling (62.30%). This indicates that the method can allocate processes and worker resources more reasonably and improve the problem of uneven load between workstations.

[0138] In summary, addressing the technical challenges of significant random time disturbances, complex process topology constraints, stringent multi-worker collaboration requirements, and dynamically changing on-site production conditions during mixed-line pulsed assembly of aero-engines, this invention proposes an adaptive scheduling method for mixed-line pulsed assembly of aero-engines. This method employs a two-layer optimization architecture combining deep Q-networks and approximate dynamic programming look-ahead search to achieve collaborative management of robust pre-scheduling and adaptive scheduling during the process. Figure 6 The illustrated embodiments demonstrate that this method, by forming a pre-scheduling plan with robustness to random working hours in the pre-stage and rolling correction of the remaining process scheduling plan based on on-site disturbances in the in-process stage, can effectively improve the cycle stability, resource utilization efficiency, and adaptability to random disturbances of the aero-engine pulse assembly production system.

[0139] Although the methods described above are illustrated and depicted as a series of actions for the sake of simplicity, it should be understood and appreciated that these methods are not limited by the order of the actions, as some actions may occur in a different order and / or concurrently with other actions from the illustrations and descriptions herein or not illustrated and described herein but which may be understood by those skilled in the art, according to one or more embodiments.

[0140] Based on the above-mentioned adaptive scheduling method for mixed-line pulse assembly of aero-engines, the present invention also provides an adaptive scheduling system for mixed-line pulse assembly of aero-engines.

[0141] This invention provides an adaptive scheduling system for mixed-line pulse assembly of aero-engines, comprising a memory and a processor: The memory is used to store computer programs; The processor is configured to execute the adaptive scheduling method for mixed-line pulse assembly of aero-engines provided in any of the above embodiments when the computer program is invoked.

[0142] Specifically, the memory may be an industrial-grade hard disk, random access memory (RAM), read-only memory (ROM), or other types of storage media, used to store program code, basic production data, DQN network model parameters, and historical scheduling schemes and other related data for implementing the adaptive scheduling method for mixed-line pulse assembly of aero-engines of the present invention.

[0143] The processor can be a central processing unit (CPU), an embedded industrial control processor, or other computing unit, used to execute program code in memory and complete the entire process of calculations such as process topology modeling, production scheduling optimization model construction, DQN offline training, Lookahead look-ahead search, and rolling production scheduling.

[0144] In addition, the system may include input / output interfaces for receiving basic production data from the production line and real-time production status data from the site, and outputting the final production scheduling plan, production execution Gantt chart, and core performance index data. Through the collaborative work of the memory and processor, this system can efficiently complete pre-production robust pre-scheduling and in-process adaptive scheduling for mixed-line pulsed assembly of aero-engines, effectively improving the cycle stability, resource utilization efficiency, and adaptability to random disturbances of the pulsed assembly line.

[0145] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the adaptive scheduling method for mixed-line pulse assembly of aero-engines provided in any of the above embodiments.

[0146] The readable storage medium may include, but is not limited to: portable storage disk, hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0147] This invention also provides a computer program product, including a computer program that, when executed by a processor, implements the adaptive scheduling method for mixed-line pulse assembly of aero-engines as described above.

[0148] The program code for executing the computer program product of the present invention can be written in any combination of one or more programming languages. The program code can be executed entirely on the user device, partially on the user device, as a standalone software package, partially on the user device and partially on a remote device, or entirely on a remote device.

[0149] The present invention provides an adaptive scheduling method and system for mixed-line pulsed assembly of aero-engines, which can achieve coordinated optimization of process allocation, worker configuration, workstation load, cycle stability and random disturbance adaptability during mixed-line pulsed assembly of aero-engines, reduce the actual number of workers and total expected production cost of the entire line, and improve the executability of assembly production plan and on-site adjustment capability.

[0150] The present invention provides an adaptive scheduling method and system for mixed-line pulse assembly of aero-engines, which has the following beneficial effects: 1) A production scheduling optimization framework that takes into account the constraints of aero-engine assembly process, resource coordination, pulse cycle time, and adaptability to random disturbances is established. By decomposing the engine assembly process into a directed acyclic assembly process topology network, it can accurately describe the serial and parallel process relationships between the fan / booster stage unit, high-pressure compressor unit, combustion chamber unit, high-pressure turbine unit, low-pressure turbine unit, and peripheral accessory systems, providing a basis for executable production scheduling of complex assembly processes. 2) By establishing a mixed-line pulse assembly scheduling model that considers random processing time, multi-worker collaborative operation and workstation synchronous flow, labor costs and overdue penalty costs are uniformly incorporated into the expected production cost target. This can effectively reflect the impact of random time disturbances on the stability of pulse cycle time and avoid workstation overdue and resource conflicts caused by the deterministic scheduling method ignoring time fluctuations. 3) Robust pre-scheduling is achieved through DQN value network, which can learn the mapping relationship between complex scheduling status and candidate actions from historical production data and random time sampling scenarios, so as to form a better work station allocation, worker configuration and process sequencing scheme before batch production begins. 4) In-process production scheduling is achieved by using the Lookahead search algorithm based on an approximate dynamic programming framework. When the on-site state changes, the current actionable actions are accurately anticipated in multiple steps, and the DQN value network is called at the lookahead boundary to estimate the long-term value. This avoids the computational burden caused by fully unfolding the high-dimensional state space and improves the online rescheduling response to local disturbances.

[0151] As illustrated in this invention, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0152] Those skilled in the art will understand that information, signals, and data can be represented using any of a variety of different techniques and skills. For example, the data, instructions, commands, information, signals, bits, symbols, and chips described throughout the above description can be represented by voltage, current, electromagnetic waves, magnetic fields or magnetic particles, light fields or optical particles, or any combination thereof.

[0153] Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of both. To clearly illustrate this interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps are described above in a generalized manner in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in different ways for each specific application, but such implementation decisions should not be construed as departing from the scope of the invention.

[0154] The various illustrative logic modules and circuits described in conjunction with the embodiments disclosed herein may be implemented or performed using a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The general-purpose processor may be a microprocessor, but in alternatives, it may be any conventional processor, controller, microcontroller, or state machine. The processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors cooperating with a DSP core, or any other such configuration.

[0155] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of both. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to a processor such that the processor can read and write information to / from the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and storage medium may reside as discrete components in the user terminal.

[0156] The above embodiments are provided for those skilled in the art to implement or use the present invention. Those skilled in the art can make various modifications or changes to the above embodiments without departing from the inventive concept of the present invention. Therefore, the protection scope of the present invention is not limited to the above embodiments, but should be the maximum scope that conforms to the innovative features mentioned in the present invention.

Claims

1. An adaptive scheduling method for mixed-line pulse assembly of aero-engines, characterized in that, Includes the following steps: Step S1: Obtain basic production data of the mixed-line pulsed assembly production line of aero-engines, and construct a directed acyclic assembly process topology network to characterize the relationship between processes based on the aero-engine assembly process flow. Step S2: Based on the basic production data and the directed acyclic assembly process topology network, construct a mixed-line pulsed assembly scheduling optimization model; Step S3: Transform the production scheduling optimization model into a Markov decision process, and perform offline training and solution on the Markov decision process based on a deep Q-network model to generate a robust pre-scheduling plan. Step S4: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time and the current production scheduling system status is updated. A look-ahead search algorithm based on an approximate dynamic programming framework is used for in-process production scheduling. The state value is estimated by combining the DQN value network obtained from offline training. The production scheduling plan for the remaining assembly processes is updated in a rolling manner. Finally, a mixed-line pulse assembly production scheduling plan for aero-engines that meets the preset conditions is output.

2. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 1, characterized in that, Step S1 includes: Step S11: Obtain the basic production data of the mixed-line pulsed assembly production line for aero-engines. The basic production data includes the assembly process set, workstation set, total number of available workers, maximum number of workers per workstation, pulsed cycle, minimum number of cooperating workers required for each assembly process, process preceding constraint relationship, process random processing time distribution parameters, labor cost per worker, and unit overdue penalty cost. Step S12: Based on the aero-engine assembly process, the aero-engine assembly object is divided into several assembly units and peripheral accessory systems according to its functional structure, assembly interface and process sequence. The assembly process of each assembly unit and peripheral accessory system is decomposed into several assembly steps. A directed acyclic assembly process topology network is constructed according to the process sequence between each assembly step. Step S13: Based on the aero-engine assembly process, and combined with the time disturbance characteristics of aero-engine assembly, construct a random processing time characterization model for the process, and use the overdue time of the workstation to characterize the impact of random disturbances on the pulsating cycle time.

3. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 1, characterized in that, Step S2 includes: Step S21: Construct a mixed-line pulse assembly scheduling optimization model that considers random processing time, multi-worker collaborative operation, process preceding constraints, fixed pulsation cycle, and synchronous flow between workstations. Step S22: Determine the optimization objective and set the corresponding production scheduling constraints. The production scheduling constraints are used to ensure that the generated production scheduling scheme meets the process rules, resource boundaries and cycle control requirements of the aero-engine pulse assembly site.

4. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 1, characterized in that, Step S3 includes: Step S31: Define the mixed-line pulse assembly scheduling optimization model as a Markov decision process, construct a deep Q-network model for pre-production robust scheduling, and define the system state space, action space, state transition mechanism and instant reward function. Step S32: The deep Q-network model is trained offline using historical production data. During the training process, Monte Carlo sampling is used to simulate the fluctuation of random processing time in the assembly process. The action value function is updated using experience replay, target network and ε-greedy strategy to obtain a converged DQN value network. Step S33: Generate a robust pre-scheduling plan based on the converged DQN value network. The robust pre-scheduling plan includes the workstation allocation results, workstation worker configuration results, workstation collaborative operation worker allocation results, planned start time of the workstation, planned completion time of the workstation, and workstation process sequencing results.

5. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 1, characterized in that, Step S4 includes: Step S41: During the mixed-line pulse assembly of aero-engines, the on-site production status is collected in real time, and the current production scheduling system status is updated according to the on-site production status. Step S42: In-process production scheduling is performed using a look-ahead search algorithm based on an approximate dynamic programming framework. For each candidate production scheduling action that meets the constraints in the current state, a preset number of decision steps are derived. During the look-ahead derivation process, the random processing time distribution of the assembly process and Monte Carlo multi-scenario sampling are combined to calculate the state transition and immediate reward under different random disturbance scenarios. Step S43: When the prospective search reaches the boundary state corresponding to the preset number of steps, the DQN value network trained offline is called to estimate the future value of the boundary state. Based on the Bellman expectation backtracking mechanism, the boundary future value is backtracked to the current state layer by layer. The expected value of each candidate scheduling action is calculated, and the candidate scheduling action with the largest expected value is selected as the optimal scheduling action at the current decision moment. Step S44: The optimal production scheduling action at the current decision moment is sent to the production execution end. When a change in production execution status event is detected, steps S41 to S43 are repeated to continuously update the production scheduling plan for the remaining assembly processes. Finally, a mixed-line pulse assembly production scheduling plan for aero-engines that meets the preset conditions is output.

6. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 2, characterized in that, In the directed acyclic assembly process topology network of step S12, each assembly operation is taken as a vertex and the preceding priority relationship between operations is taken as a directed edge, which is used to characterize the serial and parallel assembly relationship between different assembly unit bodies and peripheral accessory systems.

7. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 2, characterized in that, In the process random processing time characterization model of step S13, the actual processing time of a single process is composed of the nominal process time plus the time increment of multiple types of disturbances. The disturbance duration increment includes the duration increment caused by rework and repair, as well as the non-negative exogenous duration increment caused by manual assembly deviations, material supply fluctuations, and equipment status fluctuations.

8. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 3, characterized in that, In step S21, the decision variables of the mixed-line pulse assembly scheduling optimization model include process station allocation variables, station personnel configuration variables, process worker allocation variables, process planned start time variables, and station overdue duration variables.

9. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 3, characterized in that, In step S22, the optimization objective is to minimize the total expected production cost, which is the mathematical expectation of the sum of the total cycle labor cost and the overdue penalty cost. The total cycle labor cost is calculated based on the actual number of workers on the entire line and the labor cost per worker per cycle, while the overdue penalty cost is calculated based on the total overdue time on the entire line and the unit overdue penalty cost.

10. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 3, characterized in that, In step S22, the production scheduling constraints include unique workstation allocation constraints for processes, preceding and succeeding constraints for processes, workstation cycle time overdue constraints, minimum number of cooperating workers constraints for processes, worker and workstation affiliation constraints, constraints that the same worker cannot participate in multiple processes simultaneously, maximum number of workers per workstation constraints, and decision variable value constraints.

11. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 4, characterized in that, In step S31, the state space of the Markov decision process includes the process completion status, the estimated completion time of the process in progress, the number of unscheduled processes, the number of remaining available workers, the completion time of the completed work at each workstation, the next available time for each worker, and the current partial production scheduling plan. The action space includes process scheduling actions and workstation switching actions. The process scheduling action is used to indicate the start of production of a process in the current workstation, and simultaneously determine the workstation allocation, the workers participating in the collaborative operation, and the planned start time for that process. The workstation switching action is used to indicate the switch to the next workstation after completing the current workstation scheduling, and determine the number of workers configured for the next workstation. The instant reward function is derived from the production cost of the production scheduling plan and is used to guide the deep Q-network model to converge iteratively toward the production scheduling optimization target, prioritizing the selection of production scheduling actions that match the optimization direction.

12. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 4, characterized in that, In step S3, the deep Q-network model adopts a neural network structure that includes an input layer, at least one fully connected hidden layer, and an output layer. The input layer is used to receive the current system state, the hidden layer is used to extract the nonlinear relationship between the process completion state, workstation load state, worker availability state and remaining production scheduling space, and the output layer is used to output the action value of each candidate action in the current state.

13. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 12, characterized in that, In step S32, during the training of the deep Q-network model, the trajectory samples consisting of state, action, immediate reward and next state are stored in the experience replay pool. Small batches of samples are randomly sampled from the experience replay pool to update the network parameters, and the target network parameters are periodically synchronized.

14. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 12, characterized in that, In step S33, when generating a robust pre-production scheduling plan, the initial production scheduling state before the start of batch production is used as the input of the deep Q-network model. Based on the greedy decision rule, the optimal production scheduling action is selected step by step and the production scheduling state is updated until all assembly processes complete the allocation of workstations, worker configuration and start-up time arrangement.

15. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 5, characterized in that, In step S41, the real-time collected on-site production status includes the actual completion status of the assembly process, the actual progress of the assembly process in progress, the next available time for each worker, the current completion time of each workstation, the remaining unscheduled assembly processes, and the actual processing time of the processes.

16. The adaptive scheduling method for mixed-line pulsed assembly of aero-engines according to claim 5, characterized in that, In step S44, the production execution status change events include actual completion of assembly process, extended process processing time, rework and repair, abnormal quality inspection, material supply fluctuation, abnormal equipment or tooling status, risk of workstation cycle time exceeding the deadline, and changes in worker resource status. The final production scheduling plan includes the workstations of each assembly process, the set of workers assigned to each workstation, the set of workers cooperating with each assembly process, the planned start time of each assembly process, the planned completion time of each assembly process, the overdue production time of each workstation, the actual number of workers employed on the entire line, the total expected production cost of the entire line, and the production scheduling execution Gantt chart data.

17. An adaptive scheduling system for mixed-line pulsed assembly of aero-engines, characterized in that, Including the processor and memory: The memory stores computer programs; When the processor executes the computer program, it implements the adaptive scheduling method for mixed-line pulse assembly of aero-engines as described in any one of claims 1 to 16.

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