A multi-objective robust optimization method for process parameters of lithium battery coating section drying process

Abstract

This invention discloses a multi-objective robust optimization method for process parameters in the drying process of lithium battery coating sections. Using conveyor belt speed, drying temperature, slurry surface density, and initial slurry temperature as decision variables, and energy consumption and drying efficiency as optimization objectives, a robust multi-objective Gaussian process (GP) model of the slurry drying process is first constructed. Then, a robust multi-objective evolutionary algorithm based on surrogate assistance is designed to solve the model. The optimization process is divided into two tasks: robust optimization and deterministic optimization. Effective knowledge is transferred between tasks, and task weights and knowledge transfer probabilities are updated in real time to achieve efficient allocation of computational resources. This invention avoids the drawbacks of constructing mechanistic models, can quickly and effectively find the robust optimal solution for the drying process, reduces expensive robustness calculations, meets the accuracy requirements of process parameters, improves the economics of drying, provides a guarantee for stable and efficient production in the drying process, and achieves energy saving and consumption reduction.

Description

Technical Field

[0001] This invention belongs to the field of lithium battery production technology, specifically relating to a multi-objective robust optimization method for process parameters of the drying process in the coating section of lithium batteries. Background Technology

[0002] The coating and drying of lithium-ion battery electrodes is a crucial process in battery manufacturing, directly determining the battery's performance, safety, and lifespan. This process involves uniformly coating positive and negative electrode slurries onto metal electrodes, then removing the solvent through energy transfer, ultimately forming a dry electrode coating with a specific porous structure. In the complete process chain of "mixing-coating-drying-rolling-slitting" in lithium-ion battery manufacturing, the drying process occupies a pivotal position, and its precise control has a decisive impact on battery safety. For example, excessively high drying temperatures can cause a film layer to form on the slurry surface, leading to coating wrinkling or cracking.

[0003] Currently, traditional drying technologies for lithium battery coating sections include far-infrared radiation drying, conventional convection hot air drying, and circulating hot air impact drying. With the continuous improvement of lithium battery performance requirements, emerging drying technologies such as double-sided air-blown floating drying, superheated steam drying, and microwave drying are gradually being introduced into the slurry drying field. While these emerging drying technologies offer the advantage of higher thermal efficiency, they also bring problems such as more complex equipment structures and more process parameters. Tuning these process parameters using traditional methods is time-consuming, labor-intensive, and inefficient.

[0004] Furthermore, the environment of lithium battery production lines is complex, with numerous unpredictable disturbances: on the one hand, the large number of equipment on the production line and the aging of the equipment can easily affect the coating stability, especially the wear of the active roller of the coating head, which can directly lead to fluctuations in electrode tension and slurry surface density uniformity; on the other hand, the large and frequently moving personnel on the production line can cause significant disturbances to the ambient temperature and humidity. Currently, most optimization methods for the drying process parameters do not consider these disturbances in their initial design, resulting in poor robustness of the optimization results and difficulty in adapting to the complex scenarios of actual production. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing a multi-objective robust optimization method for process parameters in the drying process of lithium battery coating. It solves the technical problems of parameter optimization in lithium battery coating drying process being affected by disturbances, the difficulty of traditional modeling, and the low efficiency and high computational cost of optimization methods. This method achieves robust optimization of process parameters in the drying process, thereby improving the economy and production stability of the drying process.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: A multi-objective robust optimization method for process parameters in the drying process of the coating section of lithium batteries includes the following steps: Step 1: Using belt speed, drying temperature, slurry surface density and initial slurry temperature as decision variables, and energy consumption and drying efficiency as optimization objectives, construct a robust multi-objective Gaussian process (GP) model for the slurry drying process. Step 2: Design a robust multi-objective evolutionary algorithm based on surrogate assistance, and use the GP model to replace the real optimization objective function for solving, so as to obtain the economically optimal drying process parameters with lower optimization cost.

[0007] Furthermore, the specific method for constructing the robust multi-objective GP model is as follows: Step 1.1: Data collection and preprocessing. Collect experimental data related to the slurry drying process, including key process parameters such as belt speed, drying temperature, slurry surface density and initial slurry temperature, as well as corresponding energy consumption and drying efficiency indicators; preprocess the collected experimental data, remove outliers and normalize them to ensure the validity and consistency of the data. Step 1.2: Select a suitable kernel function to match the parameter characteristics and data patterns of the drying process; Step 1.3: Use the method of maximizing the log marginal likelihood function to optimize the hyperparameters of the model and improve the fitting accuracy of the model; Step 1.4: Based on the preprocessed data, use the GP model to train and validate the data to determine the model's predictive ability; Step 1.5: Perform inverse normalization on the model's prediction results to restore the actual scale of the data, and calculate the model's error and performance indicators to preliminarily evaluate the model's effectiveness. Step 1.6: Calculate the confidence interval of the model prediction results and determine the error range of the model prediction; Step 1.7: Analyze the residuals of the model, further evaluate the performance and reliability of the model, and ensure that the model can be used for subsequent optimization solutions.

[0008] Furthermore, the Gaussian process model for the drying process consists of a constant mean function and a squared exponential (SE) covariance function, which is adapted to the nonlinear characteristics of the drying process in the lithium battery coating section, thereby improving the model's prediction accuracy for the drying process.

[0009] Furthermore, the process of using a GP model to replace the actual optimization objective function and solving it through a surrogate-assisted robust multi-objective evolutionary algorithm is divided into five stages, as follows: I. Task Construction and Selection Phase Step 2.1: Initialize two subpopulations to provide a population foundation for subsequent dual-task optimization; Step 2.2: Assign the two subpopulations to the robust optimization task and the deterministic optimization task, respectively. The robust optimization task is used to optimize the solution under the perturbation scenario, and the deterministic optimization task is used to find the perturbation-free Pareto solution. Step 2.3: Apply perturbation to the population corresponding to the robust optimization task to simulate uncertainties in actual production; Step 2.4: Select a task as the main task according to the task weight. In the early stage of evolution, the task weight is kept constant at 50% to avoid unreasonable weight allocation due to insufficient information, i.e., the cold start problem. During the evolution process, the main task is randomly selected by roulette. The probability of roulette is determined by the real-time updated weight of each task.

[0010] II. Agent-Assisted Evolution Stage Step 2.5: Build and update the GP model for the main task to ensure the model's fit with the population's evolutionary state; Step 2.6: The populations in the main task and the populations in the auxiliary task undergo differential evolution according to probability. The mutant individuals consist of three individuals. The base individuals are randomly selected from the populations of the two tasks according to migration probability. The two differential individuals are randomly selected only from the population of the main task. Step 2.7: Use the GP model to replace the real objective function to evaluate the post-evolutionary population, thereby reducing the computational cost of the real function; Step 2.8: Repeat steps 2.6 to 2.7 until the maximum number of iterations is reached to complete the evolution of the main task population.

[0011] III. Filling Sampling Phase Step 2.9: Use non-dominated sorting and crowding distance to filter out a small number of high-quality new solutions from the main task population. The filtering method is as follows: First, determine the non-dominated level of all solutions participating in the sorting through non-dominated sorting. Then, select solutions layer by layer starting from the first layer according to the required number of solutions. If the number of solutions in the first few layers does not meet the requirements, and the number of solutions exceeds the requirements after adding the current layer, then set the current layer as the critical layer. Calculate the crowding distance for the solutions in the critical layer, and select solutions one by one starting from the solution with the smallest distance until the required number of solutions is met. Step 2.10: Evaluate the selected high-quality new solutions using the actual optimization objective function to ensure the practical effectiveness of the high-quality new solutions; Step 2.11: Update the population using the non-dominated sorting and crowding distance methods described above to maintain the quality and size of the population.

[0012] IV. Task Weight and Migration Probability Update Phase Step 2.12: Calculate the dominance relationship between the superior new solution and the replaced solutions in the old population and denote it as Rp, where the replaced solutions are the equal number of solutions that were removed from the original population due to the addition of the superior new solution in order to maintain a constant population size; Step 2.13: Calculate the proportion of knowledge transferred from auxiliary tasks in high-quality new solutions and denote it as Rc. This proportion is the ratio of the number of base individuals from auxiliary tasks to the total number of high-quality new solutions when differential evolution generates high-quality new solutions. It is used to increase the task weight of auxiliary tasks when they help the evolution of the main task. Step 2.14: Update the task weights using the calculation results of Rp and Rc to allocate computing resources to more efficient tasks; Step 2.15: Calculate the dominance relation of the high-quality new solution in the updated population and denote it as Rd; Step 2.16: Update the knowledge transfer probability using the calculation results of Rd to improve the effectiveness of knowledge transfer between tasks.

[0013] V. Termination Determination and Solution Selection Stage Step 2.17: Repeat steps 2.3 to 2.16 until the termination condition is met. In a population of a certain size and with non-dominant members, select the most suitable robust optimal solution according to the actual production process requirements and economic needs.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention constructs a robust multi-objective GP model to predict the economic efficiency of the drying process of lithium battery coating section, avoiding the problems of high difficulty in constructing traditional mechanism models and complex calculations. At the same time, it is adapted to the actual scenario of limited experimental data and uncertainty in the production process, which is more in line with the actual needs of drying process modeling, and improves the practicality and prediction accuracy of the model.

[0015] 2. This invention divides the optimization process into robust optimization tasks and deterministic optimization tasks, and transfers effective knowledge between tasks, which effectively accelerates the convergence of robust solutions and reduces unnecessary waste of computing resources; real-time updates of task weights and knowledge transfer probabilities enable efficient allocation of computing resources and reduce optimization costs.

[0016] 3. The robust multi-objective evolutionary algorithm based on surrogate assistance designed in this invention uses the GP model to replace the real objective function for most of the evaluation calculations, and only uses the real objective function to verify a small number of high-quality new solutions, which greatly reduces the expensive robustness calculations and ensures the effectiveness of the optimized solutions.

[0017] 4. The optimization method of the present invention can quickly and effectively find the robust optimal solution of the drying process, meet the accuracy requirements of the slurry drying process parameters, adapt to various disturbance factors in actual production, provide a guarantee for the stable and efficient production of the drying process, and help improve the economy of the drying process and achieve the production needs of energy saving and consumption reduction. Attached Figure Description

[0018] Figure 1This is a flowchart of a multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, according to the present invention. Detailed Implementation

[0019] The following detailed description of the implementation of the present invention is provided in conjunction with the technical solution of the present invention. The scope of protection of the present invention is not limited to the following embodiments.

[0020] This invention discloses a multi-objective robust optimization method for process parameters in the drying process of lithium battery coating stages, belonging to the field of lithium battery production technology. It solves the technical problems of parameter optimization in lithium battery coating drying processes being affected by disturbances, and the low efficiency and high modeling difficulty of traditional methods. This method uses conveyor belt speed, drying temperature, slurry surface density, and initial slurry temperature as decision variables, and energy consumption and drying efficiency as optimization objectives. First, a robust multi-objective Gaussian process (GP) model of the slurry drying process is constructed. Then, a robust multi-objective evolutionary algorithm based on surrogate assistance is designed to solve the model. The optimization process is divided into two tasks: robust optimization and deterministic optimization. Effective knowledge is transferred between tasks, and task weights and knowledge transfer probabilities are updated in real time to achieve efficient allocation of computational resources. This invention avoids the drawbacks of mechanistic model construction, can quickly and effectively find the robust optimal solution for the drying process, reduces expensive robustness calculations, meets the accuracy requirements of process parameters, improves the economic efficiency of drying, provides a guarantee for stable and efficient production in the drying process, and achieves energy saving and consumption reduction.

[0021] like Figure 1 As shown, a multi-objective robust optimization method for process parameters in the drying process of the coating section of a lithium battery is described, and the specific implementation steps are as follows: Step 1: Construct a robust multi-objective GP model for the slurry drying process.

[0022] Step 1.1 Collect experimental data on the drying process of the lithium battery coating section, including four key process parameters: belt speed, drying temperature, slurry surface density, and initial slurry temperature, as well as the corresponding energy consumption and drying efficiency. Preprocess the data, remove outliers using the 3σ principle, and then use the min-max normalization method to map the data to the [0,1] interval to ensure the validity and consistency of the data.

[0023] Step 1.2 Select the kernel function and determine that the Gaussian process model for the drying process consists of a constant mean function and a squared exponential (SE) covariance function to suit the nonlinear characteristics of the drying process.

[0024] (1) (2) Where c is the constant mean, indicating that the prior expectation is a constant; It is the signal variance, which controls the overall fluctuation range of the function; It is a feature length scale that controls the rate at which correlation decays; It is the observation noise variance, representing the model error; It's Kronecker A function used to add noise terms.

[0025] Step 1.3 Optimize the model hyperparameters by maximizing the logarithmic marginal likelihood function. Solve for the maximum value of the logarithmic marginal likelihood function using the gradient descent method to determine the optimal combination of hyperparameters.

[0026] Step 1.4 Divide the preprocessed data into a training set and a validation set in a 7:3 ratio. Use the training set to train the GP model and the validation set to validate the model and determine its predictive ability.

[0027] Step 1.5 Perform inverse normalization on the model's prediction results to restore them to the original scale of the data; calculate the root mean square error (RMSE) and coefficient of determination (R²) of the model to evaluate the model's fitting accuracy.

[0028] Step 1.6 Based on the probabilistic characteristics of the GP model, calculate the 95% confidence interval of the prediction results and clarify the prediction error range of the model.

[0029] Step 1.7 Analyze the residual distribution during model training and validation. If the residuals are randomly normally distributed, it indicates that the model fits well and can be used for subsequent optimization. If the residual distribution is abnormal, return to step 1.2 to reselect the kernel function and optimize the hyperparameters.

[0030] Step 2: Solve for the robust optimal solution using a proxy-assisted robust multi-objective evolutionary algorithm.

[0031] I. Task Construction and Selection Phase Step 2.1 Initialize two subpopulations. Each individual in the population is a combination of four decision variables: conveyor speed, drying temperature, slurry surface density, and initial slurry temperature. The variable values ​​are within the allowable boundary range of the process.

[0032] The two subpopulations refer to one subpopulation assigned to each task. Initially, both subpopulations form a single large population. For example, if the subpopulation size is 100, the large population size is 200. 200 points are randomly sampled using Latin hypercube sampling, and the fitness function is used to evaluate these 200 points to obtain the target value for each point, forming the large population. This large population is then randomly divided into two equal subpopulations, each with a size of 100.

[0033] Step 2.2 Assign the two subpopulations to the robust optimization task and the deterministic optimization task, respectively.

[0034] Step 2.3 Apply perturbations to the population of the robust optimization task. The types of perturbations include common perturbations in actual production, such as heat transfer loss and slurry surface density fluctuations. The perturbation amplitude is set according to the fluctuation range of actual production.

[0035] Step 2.4 The first 10 generations of evolution are the early stage, with a constant task weight of 50%, and one task is randomly selected as the main task; after 10 generations, the main task is selected according to the real-time updated task weight using a roulette wheel method.

[0036] II. Agent-Assisted Evolution Stage Step 2.5 Based on the current population data of the main task, establish and update the GP model to ensure that the model matches the population evolutionary state.

[0037] Before each iteration, one of the two tasks—the robust optimization task and the deterministic optimization task—is randomly selected to participate in the iteration. For ease of description, the selected task will be referred to as the main task.

[0038] Step 2.6 The populations of the main task and auxiliary task are subjected to differential evolution according to probability. The mutant individuals consist of 3 individuals. The base individuals are randomly selected from the two task populations according to the migration probability. The two differential individuals are selected only from the main task population. The crossover probability of differential evolution is set to 0.8 and the mutation factor is set to 0.5.

[0039] Step 2.7 Use the updated GP model to replace the real objective function to evaluate the energy consumption and drying efficiency of the evolved population individuals.

[0040] Step 2.8 Repeat steps 2.6 to 2.7 until the number of iterations reaches 50, completing a single evolution of the main task population.

[0041] The process boundaries of the GP model are as follows: The range of belt speed is: ; The drying temperature range is: ; The range of slurry surface density is: ; The initial temperature range of the slurry is: .

[0042] III. Filling Sampling Phase Step 2.9 Using the non-dominated sorting and crowding distance method, 20 high-quality new solutions are selected from the population after the main task evolution. During the selection, the non-dominated level is selected first, and the critical level is selected according to the crowding distance from small to large.

[0043] Step 2.10 Use the actual energy consumption and drying efficiency calculation model to evaluate the 20 selected high-quality new solutions and obtain the actual objective function value.

[0044] Step 2.11 Add 20 high-quality new solutions to the original main task population, remove 20 poor solutions using non-dominated sorting and crowding distance methods, update the population and keep the population size at 100.

[0045] IV. Task Weight and Migration Probability Update Phase Step 2.12 Calculate the dominance relationship Rp between the 20 high-quality new solutions and the 20 old solutions that were removed, and count the percentage of old solutions dominated by the high-quality new solutions.

[0046] Step 2.13 Calculate the proportion of base individuals in high-quality new solutions that come from auxiliary tasks, denoted as Rc. If Rc is high, it means that the auxiliary tasks are of great help to the evolution of the main task.

[0047] Step 2.14 Combine the calculation results of Rp and Rc to update the weights of the robust optimization task and the deterministic optimization task, and tilt the weights toward the task that is more effective for evolution.

[0048] Step 2.15 Calculate the dominance relationship Rd of all solutions in the main task population after the update, and count the dominance level of the high-quality new solutions in the population.

[0049] Step 2.16 Update the knowledge transfer probability using the calculation results of Rd. If the knowledge transfer effect of the high-quality new solution is good, then increase the knowledge transfer probability.

[0050] V. Termination Determination and Solution Selection Stage Step 2.17 Repeat steps 2.3 to 2.16 until the total number of iterations reaches 200, satisfying the termination condition; in the final main task population, select mutually non-dominated solutions to form a Pareto solution set. Based on the core requirements of "low energy consumption and high drying efficiency" in actual production, select the robust optimal solution from the Pareto solution set, which is the optimal combination of process parameters for the drying process of the lithium battery coating section.

[0051] This embodiment compares the above algorithm with the NSGA-II-DTI, CNSDE-DVC and RMOEA-DVA algorithms. The experimental results show that the solution obtained by the algorithm proposed in this invention has the best comprehensive performance in terms of robustness, energy consumption and drying efficiency. It can effectively adapt to the disturbance scenarios of actual production and improve the economy of the drying process.

[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, characterized in that, Includes the following steps: Step 1: Using belt speed, drying temperature, slurry surface density and initial slurry temperature as decision variables, and energy consumption and drying efficiency as objectives, construct a robust multi-objective Gaussian process (GP) model for the slurry drying process. Step 2: Design a robust multi-objective evolutionary algorithm based on surrogate assistance, and use the GP model to solve it to obtain the economically optimal drying process parameters.

2. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 1, is characterized in that... The method for constructing the robust multi-objective GP model is as follows: Step 1.1: Data collection and preprocessing. Collect experimental data on the process parameters of slurry drying, such as belt speed, drying temperature, slurry surface density, initial slurry temperature, and corresponding energy consumption and drying efficiency. Remove outliers from the data and normalize them. Step 1.2: Select a suitable kernel function; Step 1.3: Optimize the hyperparameters of the model by maximizing the log-marginal likelihood function; Step 1.4: Based on the processed data, train and validate the GP model; Step 1.5: Denormalize the prediction results and calculate the model error and performance indicators; Step 1.6: Calculate the confidence interval of the model prediction results; Step 1.7: Analyze the model residuals and evaluate the model's performance and reliability.

3. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 2, is characterized in that... The Gaussian process model for the drying process consists of a constant mean function and a squared exponential SE covariance function.

4. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 1, is characterized in that... The process of using a GP model to replace the real optimization objective function and solving it through a surrogate-assisted robust multi-objective evolutionary algorithm is divided into five stages: task construction and selection, surrogate-assisted evolution, filling and sampling, task weight and transition probability update, termination determination and solution selection, as detailed below: I. Task Construction and Selection Phase Step 2.1: Initialize two subpopulations; Step 2.2: Assign the two subpopulations to the robust optimization task and the deterministic optimization task, respectively; Step 2.3: Apply perturbation to the population corresponding to the robust optimization task; Step 2.4: Select a task as the primary task based on its weight; II. Agent-Assisted Evolution Stage Step 2.5: Build and update the GP model of the main task; Step 2.6: The populations within the main task and the populations within the auxiliary task undergo differential evolution based on probability; Step 2.7: Evaluate the post-evolutionary population by replacing the true objective function with a GP model; Step 2.8: Repeat steps 2.6 to 2.7 until the maximum number of iterations is reached; III. Filling Sampling Phase Step 2.9: Use non-dominated sorting and crowding distance to filter out a small number of high-quality new solutions in the main task population; Step 2.10: Evaluate the selected high-quality new solutions using the actual optimization objective function; Step 2.11: Update the population using non-dominated sorting and crowding distance; IV. Task Weight and Migration Probability Update Phase Step 2.12: Calculate the dominance relationship between the superior new solution and the replaced solution in the old population; Step 2.13: Calculate the proportion of knowledge transferred from auxiliary tasks in high-quality new solutions; Step 2.14: Update the task weights using the calculation results from steps 2.12 and 2.13; Step 2.15: Calculate the dominance of the superior new solution in the updated population; Step 2.16: Update the knowledge transfer probability using the calculation results from Step 2.15; V. Termination Determination and Solution Selection Stage Step 2.17: Repeat steps 2.3 to 2.16 until the termination condition is met, and output the robust optimal solution.

5. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... In step 2.4, the task weight in the early stage of evolution is kept constant at 50% to avoid unreasonable task weight allocation due to insufficient information in the early stage of evolution; during the evolution process, tasks are randomly selected by roulette, and the probability of roulette is determined by the real-time updated task weights.

6. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... In step 2.6, the mutant individuals of differential evolution consist of three individuals: the base individual is randomly selected from the populations of the robust optimization task and the deterministic optimization task according to the migration probability, and the two differential individuals are randomly selected only from the population of the main task.

7. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... The screening method in steps 2.9 and 2.11 is as follows: First, determine the non-dominated levels of all solutions involved in the sorting through non-dominated sorting, and select solutions layer by layer starting from the first level according to the required number of solutions; if the number of solutions in the first few levels does not meet the requirements, and the number of solutions exceeds the requirements after adding the current level, then set the current level as the critical level, calculate the crowding distance for the solutions in the critical level, and select solutions one by one starting from the solution with the smallest distance until the required number of solutions is met.

8. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... In step 2.12, the replaced solutions in the old population are the same number of solutions that were added due to the addition of high-quality new solutions and removed from the original population to maintain a constant population size. The dominance relationship between the high-quality new solutions and the replaced solutions is denoted as Rp.

9. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... In step 2.13, the proportion of base individuals generated by differential evolution from auxiliary tasks to the total number of high-quality new solutions is denoted as Rc. This proportion is used to increase the task weight of auxiliary tasks when they help the evolution of the main task.

10. The multi-objective robust optimization method for process parameters of the drying process in the coating section of a lithium battery, as described in claim 4, is characterized in that... In step 2.15, the dominance relationship between all solutions after the main task population is updated is denoted as Rd; in step 2.17, in a population of a certain size and which are mutually non-dominant, the most suitable robust optimal solution is selected according to actual production needs.

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