Cooperative scheduling method and system for cat litter production line equipment based on digital twinning

Abstract

The invention discloses a cooperative scheduling method and system for cat litter production line equipment based on digital twinning, and the method comprises the steps: S1, collecting operation sensor data of all equipment in a cat litter production line in real time, carrying out the preprocessing and feature fusion, and obtaining a real-time performance vector set of the equipment; s2, acquiring a scheduling effectiveness curve of the cat litter equipment based on a parameterized model of physical constraint, and outputting fuzzy operation spaces of different equipment at the t moment based on the real-time performance vector of the equipment in combination with the scheduling effectiveness curve; s3, based on the fuzzy operation spaces of all the devices, mapping the fuzzy operation spaces of all the devices into a game strategy, performing multi-target game simulation in digital twinning, converting the game strategy into a potential function maximization problem, and performing strategy solution based on distributed strategy learning with virtual regret value minimization to obtain an optimal regulation and control strategy; and S4, issuing the optimal scheduling strategy set to the corresponding physical equipment to execute cooperative scheduling of the cat litter production line equipment.

Description

Technical Field

[0001] This invention relates to the field of next-generation information technology, and in particular to a method and system for collaborative scheduling of cat litter production line equipment based on digital twins. Background Technology

[0002] In process manufacturing scenarios like cat litter production lines, early equipment scheduling primarily relied on static scheduling methods based on fixed rules, or offline optimization using linear programming and heuristic algorithms. While these methods improved the rationality of production plans to some extent, they could not adapt to the dynamic fluctuations in equipment performance and unexpected situations on the production floor.

[0003] In existing collaborative scheduling systems for cat litter production line equipment, key performance parameters of equipment are often preset static values ​​or based on long-term statistical averages. They fail to fully consider the instantaneous performance drift caused by factors such as wear and tear and changes in raw material characteristics during operation. This disconnect between static parameters and dynamic performance causes simulation optimization gaps to occur in the actual execution of the optimal scheduling scheme based on digital twins. Furthermore, existing methods typically treat production efficiency as a single objective during scheduling optimization, neglecting the balance between long-term equipment health and short-term output efficiency. When the scheduling system continuously keeps the equipment running near its limit parameters in pursuit of maximum output, it will accelerate equipment aging, increase the risk of failure, and ultimately affect the long-term stability and economy of production. To address the aforementioned issues, a collaborative scheduling method and system for cat litter production line equipment based on digital twins is proposed. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art and to achieve the above objectives, the present invention proposes the following technical solution: A collaborative scheduling method for cat litter production line equipment based on digital twins includes: S1. Real-time acquisition of operating sensor data from various devices in the cat litter production line, followed by preprocessing and feature fusion to obtain a real-time performance vector set of the devices; S2. Obtain the scheduling effectiveness curve of the cat litter device based on the parameterized model of physical constraints, and output the fuzzy running space of different devices at time t based on the device real-time performance vector and the scheduling effectiveness curve; S3. Based on the fuzzy operating space of all devices, the fuzzy operating space of all devices is mapped to the game strategy, and multi-objective game simulation is carried out in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. S4. Distribute the optimal scheduling strategy set to the corresponding physical devices to achieve collaborative scheduling of cat litter production line equipment.

[0005] The process of obtaining the device's real-time performance vector is as follows: Data from the operating sensors of each device in the cat litter production line is collected. The 3σ criterion is used to detect and process outliers in the sensor data. The mean μ and standard deviation σ of each sensor's data within the sampling time window are calculated. For any sensor reading at time t... If it meets the conditions If the value is not found, it is identified as an outlier and replaced with the arithmetic mean of the two adjacent normal data points. After outlier handling, all normal data are normalized using a min-max standardization method, mapping all sensor readings to the [0,1] interval to eliminate the influence of dimensions, thus obtaining the output at time t as the normalized real-time performance vector of the device. Furthermore, a feature-level fusion method is employed to concatenate these scalar values ​​into an n-dimensional column vector according to a fixed sensor order, thereby obtaining the device's real-time performance vector set. .

[0006] The process of obtaining the scheduling effectiveness curve of the cat litter device using the parameterized model based on physical constraints is as follows: Extract real-time performance vector sets of devices from historical databases. and scheduling effectiveness Construct key sample data and define a parameterized model framework. Through a parameterized model framework Mapping device real-time performance vector set To the scheduling effective index The predicted values ​​are obtained, and physical constraints are introduced to obtain a parametric model. ; Real-time performance vector of the device As training data, the model parameters θ of the parameterized model framework are adjusted using the conjugate gradient method optimization algorithm to improve the model prediction values. With scheduling efficiency index The optimal parameters obtained after fitting with minimal difference. , to the optimal parameters Substituting the parameters back into the parameterized model, the parameterized model directly outputs the scheduling effectiveness curve. .

[0007] The process of outputting the fuzzy running space of different devices at time t is as follows: Obtain the device's real-time performance vector at time t. ,Will Inputting these values ​​into a physically constrained parametric model yields physical scalar values. , ; The device real-time performance vector at time t Adjustable operating parameters Based on this, set both hard and soft safety constraints; The soft safety constraint condition is that when the equipment is operating under adjustable operating parameters... When constructing a new real-time performance vector for devices, its scheduling effectiveness It will not fall below the acceptable threshold, i.e. ; The hard safety constraints are adjustable operating parameters. The search is limited to the device's security limits. Within; Adjustable operating parameters obtained under the premise of satisfying the above-mentioned hard safety constraints and soft performance constraints. upper and lower fluctuation range This interval is the fuzzy running space C, denoted as... .

[0008] The process of mapping the fuzzy running space of all devices to a game strategy is as follows: Represent the fuzzy running space of the i-th device as... Transform it into a set of candidate strategies, and set a discretization precision parameter. Fuzzy operating space for each device From the lower limit Up to the limit Uniform sampling is performed to generate a series of discrete candidate parameter values, thus obtaining a set of game strategies. , where m is the total number of policy points sampled for the device, and i is the device index.

[0009] The process of transforming the game strategy into a potential function maximization problem is as follows: Define the entire cat litter production line as a non-cooperative game. ,in, It is a collection of equipment. It is a collection of policy spaces for each device. The payment function represents the device under a specific strategy. The revenue obtained includes revenue from production payments. and health payment benefits ; For a given strategy combination, using digital twin simulation as an initial setting, the complete production process within a future rolling time window T is simulated to obtain its payment function vector. ; The complex multi-objective non-cooperative game G is transformed into a single-objective weighted game, with a payoff function vector for each device. Introduce a dynamic weight vector And define a potential function for the transformed single-objective weighted game. The problem of maximizing the potential function is transformed into: ; in, Indicates payment based on equipment output. Dynamic weights for overall dimensional performance. Indicates that the device is in health payment The weighting of the overall performance across dimensions. The value is the potential function value.

[0010] The process of obtaining the optimal control strategy is as follows: based on the potential function maximization problem... Each device is treated as an intelligent agent, and online distributed learning is performed using a virtual regret value minimization algorithm. Each device maintains a policy selection probability distribution. And calculate the virtual regret value for each device: ; in, This represents the current iteration number. For device i in the first The actual strategies adopted in the round For the first The strategy combination for all other devices except device i in the round. For any other candidate strategy that was unilaterally adopted but not actually implemented, Indicates virtual income. Indicates actual returns. The symbol representing the revenue calculation for device i; updating the strategy selection probability distribution of the device based on the virtual regret value. After a preset number of iterations, the policy probability distribution of all devices is... After reaching equilibrium, from the converged probability distribution The strategy with the highest probability is selected to form the optimal scheduling strategy set. k is the index of the optimal scheduling strategy.

[0011] A digital twin-based collaborative scheduling system for cat litter production line equipment includes: S1. Real-time acquisition of operating sensor data from various devices in the cat litter production line, followed by preprocessing and feature fusion to obtain a set of real-time device performance vectors; S2. Obtaining the scheduling effectiveness curve of the cat litter equipment using a parameterized model based on physical constraints, and outputting the fuzzy operating space of different devices at time t based on the real-time device performance vectors combined with the scheduling effectiveness curves; S3. Based on the fuzzy operating space of all devices, the fuzzy operating space of all devices is mapped to the game strategy, and multi-objective game simulation is carried out in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. S4. Distribute the optimal scheduling strategy set to the corresponding physical devices to achieve collaborative scheduling of cat litter production line equipment.

[0012] The present invention has the following beneficial effects: 1. Improved the actual execution effect of the scheduling scheme: By establishing a dynamic mapping relationship between the real-time performance vector of the equipment and the scheduling effectiveness curve, the digital twin model can accurately reflect the instantaneous performance status of the equipment, solving the simulation optimization gap problem caused by model mismatch, making the scheduling scheme highly consistent with the actual operating status of the equipment, and reducing the waiting time between equipment and the imbalance of material flow.

[0013] 2. Achieved a balanced optimization of efficiency and health: By incorporating long-term equipment health losses into the scheduling target system, and seeking the optimal balance between equipment durability and multi-objective game simulation, this balanced optimization strategy not only ensures the efficient completion of current production tasks, but also extends equipment lifespan, reduces maintenance costs, and achieves a unity of short-term benefits and long-term sustainability. 3. Enhanced system adaptability and fault tolerance: The elastic scheduling mechanism based on fuzzy operating space provides a reasonable range of parameter fluctuations for each device, enabling the system to tolerate a certain degree of performance deviation. When individual devices experience performance fluctuations, the system can quickly generate alternative solutions through online rescheduling to avoid production interruptions and ensure the continuity and stability of the production process.

[0014] 4. Improved computational efficiency of large-scale collaborative scheduling: By transforming the complex multi-non-cooperative game into a potential function maximization problem and using a distributed virtual regret value minimization algorithm to solve it, the computational complexity is effectively reduced. This optimization strategy enables the system to handle complex scheduling problems involving multiple devices and multiple objectives within a reasonable time, meeting the high efficiency requirements of real-time scheduling. Attached Figure Description

[0015] Figure 1 This diagram illustrates the steps of the collaborative scheduling method and system for cat litter production line equipment based on digital twins proposed in this invention.

[0016] Figure 2 This is a system block diagram of the collaborative scheduling method and system for cat litter production line equipment based on digital twins proposed in this invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Example

[0018] like Figure 1 As shown, the collaborative scheduling method for cat litter production line equipment based on digital twins proposed in this invention includes: S1. Real-time acquisition of operating sensor data from various devices in the cat litter production line, followed by preprocessing and feature fusion to obtain a real-time performance vector set of the devices; The system synchronously collects operating sensor data from various equipment in the cat litter production line, such as mixers, granulators, screening machines, and packaging machines. The operating sensor data includes raw data streams such as current, spindle speed, vibration signals, and output pulse counts. The operating sensor data is then preprocessed and feature fusion is performed. First, the 3σ criterion is used to detect and process outliers in the operating sensor data. The raw data stream collected from the cat litter equipment is input, and the mean μ and standard deviation σ of each sensor's data within the sampling time window are calculated. For any sensor reading at time t... If it meets the conditions If the value is not found, it is considered an outlier and is replaced by the arithmetic mean of the two adjacent normal data points. After outlier handling, all normal data are normalized using a min-max standardization method, mapping all sensor readings to the [0,1] interval to eliminate the influence of dimensions, thus obtaining the normalized real-time performance vector of the device at time t. ; Then, feature fusion processing is performed, with the input being the standardized data scalar of the cat litter device at time t. Using a feature-level fusion method, these scalar values ​​are concatenated into an n-dimensional column vector according to a fixed sensor order. This column vector is the device's real-time performance vector set, represented as follows: .

[0019] S2. Obtain the scheduling effectiveness curve of the cat litter device based on the parameterized model of physical constraints, and output the fuzzy running space of different devices at time t based on the device real-time performance vector and the scheduling effectiveness curve; The process of constructing a parameterized model based on physical constraints is as follows: From the historical database, retrieve all production batch records of equipment that successfully completed scheduling instructions. For each sample batch, extract two key data points to form a key sample data set, including: The real-time performance vector set of the equipment in this batch And the scheduling effectiveness of this batch of equipment. ; Specifically, scheduling effectiveness The calculation is based on the actual production data of the batch, defined as the ratio of the actual output to the planned output of the batch, multiplied by a coefficient reflecting production stability, such as 1 minus the ratio of the standard deviation of the rotational speed per unit time to the rated rotational speed. Its mathematical expression is as follows: in, Indicates the actual output of the batch. Indicates the planned production volume for the batch. Indicates the rated speed. Indicates the standard deviation of rotational speed; Define a parameterized model framework Through a parameterized model framework Mapping device real-time performance vector set To the scheduling effective index The predicted value is obtained by using a function whose structure reflects the physical constraints of equipment operation, including the positive correlation between output capacity and rotational speed within a certain range, and the fact that overload leads to performance degradation. A parametric model is obtained by introducing physical constraints, and the parametric model based on these physical constraints is expressed as follows: in, For overload losses, r is the speed component. θ is a known constant representing the typical operating speed, and θ is a model parameter; Then, a parameterized model is trained to obtain the scheduling effectiveness curve of the cat litter device: Real-time performance vector set of the device As training data, the model parameters θ of the parameterized model framework are adjusted using the conjugate gradient method optimization algorithm to improve the model prediction values. With scheduling efficiency index The optimal parameters obtained after fitting with minimal difference. ; Optimal parameters Substituting the parameters back into the parameterized model, the parameterized model directly outputs the scheduling effectiveness curve. ; Specifically, scheduling efficiency curve Able to predict when the device is running under the device's real-time performance vector When describing the state, the expected level of scheduling effectiveness is; The process of outputting the fuzzy running space of different devices at time t is as follows: Obtain the device's real-time performance vector at time t. ,Will Inputting these values ​​into a physically constrained parametric model yields physical scalar values. ; Specifically, physical scalar values It maps the current operating state of the equipment to a single metric that can quantify its scheduling performance, while the scheduling effectiveness curve... It is a parameterized form obtained through training on historical data, in which... It is the optimal parameter set obtained through optimization algorithm fitting. This curve can accurately reflect the scheduling effectiveness level of the equipment under different combinations of operating parameters. By vectorizing the real-time performance of the equipment... Substituting this curve, the system can predict the expected performance of the equipment in completing the scheduling task under the current operating conditions; then, using the real-time performance vector of the equipment at time t... Adjustable operating parameters Centered on the data, a dynamic fluctuation range is calculated. Specifically, adjustable operating parameters These are the core control variables around which the fuzzy processing model performs dynamic range calculations. Physically, they refer to key operating parameters that can be directly or indirectly adjusted by the scheduling system during equipment operation and have a significant impact on equipment performance. In actual cat litter production line equipment, adjustable operating parameters... Other key adjustable parameters can be configured according to the specific equipment type, for example: Mixer: the rotational speed of the agitator; Granulator: screw feed speed or spindle speed; Dryer: The frequency or speed of the hot air fan; Packaging machine: speed of conveyor belt or metering screw; What they have in common is that adjusting this parameter directly changes the device's processing speed, energy consumption, and status. Then, adjustable operating parameters are set to simultaneously satisfy both hard and soft safety constraints. upper and lower fluctuation range Specifically: The soft safety constraint is: when the equipment is operating under adjustable operating parameters When constructing a new real-time performance vector for devices, its scheduling effectiveness It will not fall below the acceptable threshold, i.e. ; The hard safety constraint is: adjustable operating parameters. The search is limited to the device's security limits. Within; adjustable operating parameters obtained under the premise of satisfying the above-mentioned hard safety constraints and soft performance constraints. upper and lower fluctuation range This interval is the fuzzy runtime space C, denoted as... It quantifies the range within which key equipment parameters can be flexibly adjusted under the current conditions, while ensuring safe equipment operation and maintaining scheduling efficiency at an acceptable level.

[0020] S3. Based on the fuzzy operating space of all devices, the fuzzy operating space of all devices is mapped to the game strategy, and multi-objective game simulation is carried out in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. The process of mapping the fuzzy runtime space of all devices to a game strategy is as follows: Based on the fuzzy runtime space of all devices The fuzzy operating space of the i-th device is represented as: Then, the fuzzy running space of the i-th device is represented as The process of transforming this into a finite, enumerable set of candidate strategies is as follows: Set a discretization precision parameter Discretization accuracy parameters The smaller the step size, the denser the sampling points, and the higher the approximation of the original continuous space. However, this will exponentially increase the computational load for subsequent game simulation and solution. The larger the step size, the higher the computational efficiency. (This relates to the fuzzy operating space of each device.) From the lower limit Up to the limit Uniform sampling is performed to generate a series of discrete candidate parameter values: Where m is the total number of policy points sampled for the device, and i is the device index, representing the i-th device. The set of all these candidate parameter values ​​is defined as the set of game policies in subsequent games. Specifically, the set of candidate parameter values ​​is defined as the set of strategies in the subsequent game. Each device is precisely mapped from a continuous parameter range representing operational resilience to a clear, discretized strategy decision library, in preparation for constructing a formal game. Then based on the policy set In multi-objective game simulation using digital twins, the game strategy is transformed into a potential function maximization problem. The process is as follows: Define the entire cat litter production line as a non-cooperative game. ,in, It is a collection of devices (i.e., game participants). It is a collection of policy spaces for each device. The payment function represents the device under a specific strategy. The gains obtained; Furthermore, payment functions It is a two-dimensional vector containing two targets. Production payment The output contributed by the equipment in the simulation; Health Payment The estimated health loss of the equipment in the simulation; For a given strategy combination, digital twin simulation is used as an initial setting to quickly simulate the complete production process within a fixed rolling time window T. The digital twin simulation will simulate dynamic processes such as material flow, equipment interaction, and queue formation. After the simulation, the payoff function vector for each device is calculated. in, Represents the vector of payment functions , Indicates payment based on equipment output. The overall performance of dimensions Indicates that the device is in health payment A comprehensive representation of dimensions; The complex multi-objective non-cooperative game G is transformed into an easily solvable single-objective weighted game, with a payoff function vector for each device. Introduce a dynamic weight vector Subsequently, a potential function is defined for the transformed single-objective weighted game. The transformation of the potential function maximization problem is expressed as: in, Indicates payment based on equipment output. Dynamic weights for overall dimensional performance. Indicates that the device is in health payment The weighting of the overall performance across dimensions. The value is the potential function value; Specifically, the key characteristic of this potential function Φ is that when any device unilaterally changes its strategy, the change in its own weighted payoff is equal to the change in the potential function. This transformation makes the Nash equilibrium of the original game equivalent to the local optimum of this potential function. Therefore, solving the equilibrium problem of the original game is transformed into a more manageable potential function maximization problem. The process of solving the policy based on distributed policy learning that minimizes the virtual regret value is as follows: Based on the aforementioned potential function maximization problem, the potential function... Instead of performing a direct global optimization search, each device is treated as an intelligent agent, and an online distributed learning algorithm is used to minimize the virtual regret value. Each device maintains a policy selection probability distribution. In each iteration: The current device is based on the current probability distribution. From its strategy set Choose one strategy The digital twin system receives policies from all devices and forms new policy combinations. Perform rapid simulation and use potential function values Conduct an assessment; Calculate the virtual regret value for each device This represents the difference between the payoff of choosing the current strategy and the virtual best payoff of choosing other possible strategies. This difference is measured based on the global value of the potential function, and the process is as follows: set up This represents the current iteration number. For device i in the first The actual strategies adopted in the round For the strategy combination of all devices except device i in round t, For any other candidate strategy that was unilaterally adopted but not actually adopted; In round t, if device i unilaterally adopts hypothetical strategy a while other devices still adopt the same strategy... At that time, the virtual benefit that device i can obtain is represented as , represented as Represents the reference constant. This indicates that device i unilaterally adopts the assumed strategy a, while the strategies of other devices remain unchanged. The global situation function value, The symbol representing the revenue calculation for device i; The final virtual regret value Represented as ; in, This represents the actual benefit, i.e., the benefit of device i executing its actual policy. Subsequently, the actual benefits are obtained through actual sensor measurements or verification using twin models. The symbol representing the revenue calculation for device i; The device is based on the virtual regret value. Update its policy selection probability distribution The probability of a strategy with a virtual regret value being selected in the next round decreases. After a preset number of iterations, the strategy probability distribution for all devices... Converging to an equilibrium, in this potential game, the relevant equilibrium point also makes the potential function... Reaching a local optimum, ultimately, from the converged probability distribution... The strategy with the highest probability is selected to form the optimal scheduling strategy set. k is the index of the optimal scheduling strategy; Specifically, the optimal scheduling strategy set Make the global potential function of the system At the current position, a local optimum is reached. The potential function integrates the total output of the entire production line and the total health loss of the equipment. Therefore, the optimal scheduling strategy set is... This ensures that the cat litter production line can operate stably at a Pareto front that balances efficiency and equipment sustainability under this equilibrium state.

[0021] S4. The optimal scheduling strategy set is sent to the corresponding physical devices to implement collaborative scheduling of cat litter production line equipment; The generated optimal scheduling strategy set First, it is received by the central scheduling server, which then processes it according to standard industrial communication protocols such as OPCUA, MQTT, and Profinet. Encapsulation is performed, and during encapsulation, each optimal scheduling strategy is... The structured instructions are bound to unique identifiers of the target device, such as device ID and IP address. Subsequently, these instructions are sent to the programmable logic controllers (PLCs) of the corresponding equipment on the production line via industrial Ethernet or 5G networks. The local PLCs or edge controllers of each litter box device receive the instruction messages from the central server. The controllers parse the messages, verify the target device ID and the integrity of the instructions, and after confirming that there are no errors, extract the optimal scheduling strategy for their own specific needs. It is then stored in a dedicated instruction cache for control. While making adjustments, the device controller continuously collects its own real-time device performance vectors through sensors, packages the data, and feeds it back to the digital twin system in real time via the network, so that the virtual device state of the digital twin remains synchronized with the physical device state.

[0022] Example 2 like Figure 2 As shown, the digital twin-based cat litter production line equipment collaborative scheduling system includes: Status acquisition module: Real-time acquisition of operating sensor data of various equipment in the cat litter production line, and preprocessing and feature fusion to obtain real-time performance vector sets of the equipment; Intelligent processing module: Based on the parameterized model of physical constraints, the scheduling effectiveness curve of the cat litter device is obtained, and based on the real-time performance vector of the device and the scheduling effectiveness curve, the fuzzy operating space of different devices at time t is output. Scheduling optimization module: Based on the fuzzy running space of all devices, the fuzzy running space of all devices is mapped to a game strategy, and multi-objective game simulation is performed in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. Collaborative scheduling module: Distributes the best scheduling strategy set to the corresponding physical devices to achieve collaborative scheduling of cat litter production line equipment.

[0023] In the application, several formulas are calculated by removing dimensions and taking their numerical values. The formulas are established by collecting a large amount of data and simulating the most recent real situation. Some coefficients or weights in the formulas are set by those skilled in the art according to the actual situation, so they will not be elaborated here.

[0024] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0025] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A collaborative scheduling method for cat litter production line equipment based on digital twins, characterized in that, include: S1. Real-time acquisition of operating sensor data from various devices in the cat litter production line, followed by preprocessing and feature fusion to obtain a real-time performance vector set of the devices; S2. Obtain the scheduling effectiveness curve of the cat litter device based on the parameterized model of physical constraints, and output the fuzzy running space of different devices at time t based on the device real-time performance vector and the scheduling effectiveness curve; S3. Based on the fuzzy operating space of all devices, the fuzzy operating space of all devices is mapped to the game strategy, and multi-objective game simulation is carried out in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. S4. Distribute the optimal scheduling strategy set to the corresponding physical devices to achieve collaborative scheduling of cat litter production line equipment.

2. The method for collaborative scheduling of cat litter production line equipment based on digital twins according to claim 1, characterized in that, The process of obtaining the device's real-time performance vector is as follows: Data from the operating sensors of each device in the cat litter production line is collected. The 3σ criterion is used to detect and process outliers in the sensor data. The mean μ and standard deviation σ of each sensor's data within the sampling time window are calculated. For any sensor reading at time t... If it meets the conditions If the value is not found, it is identified as an outlier and replaced with the arithmetic mean of the two adjacent normal data points. After outlier handling, all normal data are normalized using a min-max standardization method, mapping all sensor readings to the [0,1] interval to eliminate the influence of dimensions, thus obtaining the output at time t as the normalized real-time performance vector of the device. Furthermore, a feature-level fusion method is employed to concatenate these scalar values ​​into an n-dimensional column vector according to a fixed sensor order, thereby obtaining the device's real-time performance vector set. .

3. The collaborative scheduling method for cat litter production line equipment based on digital twins according to claim 2, characterized in that, The process of obtaining the scheduling effectiveness curve of the cat litter device using the parameterized model based on physical constraints is as follows: Extract real-time performance vector sets of devices from historical databases. and scheduling effectiveness Construct key sample data and define a parameterized model framework. Through a parameterized model framework Mapping device real-time performance vector set To the scheduling effective index The predicted values ​​are obtained, and physical constraints are introduced to obtain a parametric model. ; Real-time performance vector of the device As training data, the model parameters θ of the parameterized model framework are adjusted using the conjugate gradient method optimization algorithm to improve the model prediction values. With scheduling efficiency index The optimal parameters obtained after fitting with minimal difference. , to the optimal parameters Substituting the parameters back into the parameterized model, the parameterized model directly outputs the scheduling effectiveness curve. .

4. The collaborative scheduling method for cat litter production line equipment based on digital twins according to claim 3, characterized in that, The process of outputting the fuzzy operating space of different devices at time t is as follows: obtaining the real-time performance vector of the device at the current time t. ,Will Inputting these values ​​into a physically constrained parametric model yields physical scalar values. , ; The device real-time performance vector at time t Adjustable operating parameters Centered on this, hard safety constraints and soft safety constraints are set; the soft safety constraints are those that apply when the equipment is operating under adjustable operating parameters. When constructing a new real-time performance vector for devices, its scheduling effectiveness It will not fall below the acceptable threshold, i.e. ; The hard safety constraints are adjustable operating parameters. The search is limited to the device's security limits. Within; Adjustable operating parameters obtained under the premise of satisfying the above-mentioned hard safety constraints and soft performance constraints. upper and lower fluctuation range This interval is the fuzzy running space C, denoted as... .

5. The collaborative scheduling method for cat litter production line equipment based on digital twins according to claim 4, characterized in that, The process of mapping the fuzzy operating space of all devices to a game strategy is as follows: Let the fuzzy running space of the i-th device be represented as... Transform it into a set of candidate strategies, and set a discretization precision parameter. Fuzzy operating space for each device From the lower limit Up to the limit Uniform sampling is performed to generate a series of discrete candidate parameter values, thus obtaining a set of game strategies. , where m is the total number of policy points sampled for the device, and i is the device index.

6. The collaborative scheduling method for cat litter production line equipment based on digital twins according to claim 5, characterized in that, The process of transforming the game strategy into a potential function maximization problem is as follows: the entire cat litter production line is defined as a non-cooperative game. ,in, It is a collection of equipment. It is a collection of policy spaces for each device. The payment function represents the device under a specific strategy. The revenue obtained includes revenue from production payments. and health payment benefits ; For a given strategy combination, using digital twin simulation as an initial setting, the complete production process within a future rolling time window T is simulated to obtain its payment function vector. ; The complex multi-objective non-cooperative game G is transformed into a single-objective weighted game, with a payoff function vector for each device. Introduce a dynamic weight vector And define a potential function for the transformed single-objective weighted game. The problem of maximizing the potential function is transformed into: ; in, Indicates that the device is in health payment The weighting of the overall performance across dimensions. The value is the potential function value.

7. The collaborative scheduling method for cat litter production line equipment based on digital twins according to claim 4, characterized in that, The process of obtaining the optimal control strategy is as follows: Potential function based on the problem of maximizing potential function Each device is treated as an intelligent agent, and online distributed learning is performed using a virtual regret value minimization algorithm. Each device maintains a policy selection probability distribution. And calculate the virtual regret value for each device: ; in, This represents the current iteration number. For device i in the first The actual strategies adopted in the round For the first The strategy combination for all other devices except device i in the round. For any other candidate strategy that was unilaterally adopted but not actually adopted, Indicates virtual income, Indicates actual returns. The symbol representing the revenue calculation for device i; Probability distribution of strategy selection for updating devices based on virtual regret value After a preset number of iterations, the policy probability distribution of all devices is... After reaching equilibrium, from the converged probability distribution The strategy with the highest probability is selected to form the optimal scheduling strategy set. k is the index of the optimal scheduling strategy.

8. A collaborative scheduling system for cat litter production line equipment based on digital twins, implemented according to the method described in any one of claims 1-7, characterized in that, include: Status acquisition module: Real-time acquisition of operating sensor data of various equipment in the cat litter production line, and preprocessing and feature fusion to obtain real-time performance vector sets of the equipment; Intelligent processing module: Based on the parameterized model of physical constraints, the scheduling effectiveness curve of the cat litter device is obtained, and based on the real-time performance vector of the device and the scheduling effectiveness curve, the fuzzy operating space of different devices at time t is output. Scheduling optimization module: Based on the fuzzy running space of all devices, the fuzzy running space of all devices is mapped to a game strategy, and multi-objective game simulation is performed in the digital twin. The game strategy is transformed into a potential function maximization problem, and the strategy is solved based on distributed strategy learning that minimizes virtual regret value to obtain the optimal control strategy. Collaborative scheduling module: Distributes the best scheduling strategy set to the corresponding physical devices to achieve collaborative scheduling of cat litter production line equipment.

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