A two-dimensional pump damping groove multi-objective optimization method based on GA-BP neural network

Abstract

A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network includes the following steps: S1, establishing design variable parameters in the two-dimensional pump damping groove structure; S2, constructing a simulation model of a two-dimensional piston pump and using this model to simulate and obtain the performance parameters of the hydraulic pump; S3, constructing a GA-BP surrogate model, the process of which is as follows: S31, generating a sample dataset with good parameter space filling performance using Latin hypersquare sampling based on the design variable parameters; S32, establishing a BP neural network model and using a genetic algorithm to optimize and train the model based on the sample dataset, finally obtaining a BP neural network model optimized by the genetic algorithm; S4, using the GA-BP neural network surrogate model as the fitness function, performing multi-objective optimization of the damping groove structure parameter space using a fast non-dominated sorting genetic algorithm to obtain the optimal parameter solution set. This invention significantly improves the comprehensive fluid performance of two-dimensional pumps.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic pump optimization design, specifically relating to a multi-objective optimization method for the structural parameters of the damping groove of the flow distribution window in a two-dimensional pump. Background Technology

[0002] As the core power source of hydraulic systems, the performance of hydraulic pumps directly affects the energy efficiency and reliability of equipment in many fields. However, axial piston pumps have long been constrained by problems stemming from three sets of sliding friction pairs, such as cavitation, component tilting motion, and thermal imbalance. At high speeds, friction losses intensify, and the risk of oil film rupture becomes prominent. To address this bottleneck, the team led by Ruan Jian at Zhejiang University of Technology innovatively designed a two-dimensional hydraulic pump. By using two degrees of freedom motion, the friction pairs are reduced to one, significantly reducing mechanical friction while achieving high integration. Although the structural innovation of the two-dimensional hydraulic pump effectively solves the problem of excessive sliding friction pairs, the periodic backflow generated by the reciprocating motion of the piston reduces volumetric efficiency and causes pressure pulsation during actual operation. To suppress backflow and pressure pulsation in two-dimensional pumps, two common techniques are used: setting staggered angles or adding damping grooves to the distribution plate.

[0003] However, existing methods for designing and optimizing damping groove parameters have significant limitations and cannot meet the requirements for high-performance development of two-dimensional hydraulic pumps. Specifically, these limitations are manifested in the following aspects: 1. Low level of intelligence in the optimization process, relying on human experience and high-cost simulation: Traditional optimization approaches are essentially manual trial-and-error modes. This process heavily relies on the designer's experience to adjust parameters and requires frequent calls to computationally expensive simulation models for verification, resulting in long optimization cycles, high costs, and difficulty in achieving effective global automatic optimization in complex multi-parameter coupled spaces, leading to low overall efficiency.

[0004] 2. Insufficient model accuracy, making it difficult to adapt to the special flow field of a two-dimensional pump: Existing technologies have two typical defects in model building: Limited accuracy due to reliance on simplified theoretical models: Existing technologies (CN111456923A, "An Optimization Design Method for the Distribution Plate of an Axial Piston Pump") are mainly based on simplified theoretical mathematical formulas, deriving flow pulsation by calculating the flow area and leakage under ideal conditions. This method ignores the compressibility of the oil under high-pressure conditions and transient backflow impact, and relies on manual observation of curve smoothness for qualitative optimization, failing to accurately capture the complex fluid dynamic characteristics of a two-dimensional pump during high-speed reversal.

[0005] General-purpose intelligent algorithms have poor adaptability to specific objects: Although optimization attempts based on surrogate models have emerged in fields such as centrifugal pumps (Sichuan University of Science and Engineering. An optimization method for centrifugal pumps: CN202411056695.5[P]. 2024-08-30.), these methods mostly focus on continuous indicators such as "head" and "efficiency," and their direct application to the field of two-dimensional pumps faces challenges. The unique two-degree-of-freedom guide rail drive mechanism of two-dimensional pumps results in severe periodic backflow and pressure pulsation during their distribution process. Conventional neural networks, without the integration of genetic algorithms (GA) for initial weight optimization, are prone to getting trapped in local minima, leading to a significant decrease in the accuracy of sensitive prediction of small structural parameters of the damping groove (such as depth angle and cross angle).

[0006] 3. Insufficient ability to handle multi-objective conflicts, making it difficult to achieve performance balance: The core of optimizing two-dimensional pumps lies in resolving the conflicting physical mechanisms of suppressing backflow and reducing pressure pulsation. Existing technologies often lack a systematic multi-objective trade-off framework: either they adjust parameters only for a single indicator (such as only looking at leakage), directly sacrificing pressure stability; or they use unsuitable optimization algorithms, resulting in a scattered distribution of the generated Pareto solution set, making it impossible to find the optimal balance between "flow field stability" and "pressure smoothness," forcing engineers to compromise between performance. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network. First, Latin hypercube sampling technology is used to ensure the completeness of the sample space in the high-dimensional parameters of the damping groove. Second, a genetic algorithm is used to optimize the initial weights and thresholds of the BP neural network, constructing a high-precision surrogate model that can accurately reproduce the nonlinear flow field characteristics of the two-dimensional pump. This method effectively overcomes the problems of coarse calculations in traditional theoretical formulas and the tendency of conventional BP neural networks to get trapped in local convergence. Finally, the NSGA-II multi-objective algorithm is combined for global automatic optimization, outputting an optimal set of structural parameters that balances low backflow and low pulsation without manual intervention, thereby significantly improving the overall fluid performance of the two-dimensional pump.

[0008] The technical solution adopted by this invention to solve its technical problem is: A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network includes the following steps: S1. Establish the design variable parameters in the two-dimensional pump damping groove structure; S2. Construct a two-dimensional piston pump simulation model and use the model to simulate and obtain the performance parameters of the hydraulic pump; S3. Based on the GA-BP proxy model, the construction process is as follows: S31. Based on the design variable parameters, use the Latin hypersquare sampling method to generate a sample dataset with good parameter space filling performance; S32. Establish a BP neural network model and use a genetic algorithm (GA) to optimize and train the model based on the sample dataset to finally obtain a BP neural network model optimized by the genetic algorithm. S4. Using the GA-BP neural network surrogate model as the fitness function, the fast non-dominated sorting genetic algorithm (NSGA-II) is used to perform multi-objective optimization on the parameter space of the damping groove structure to obtain the optimal parameter solution set.

[0009] Furthermore, in S1, the design variable parameters are damping groove structural parameters, including width angle, depth angle, damping groove length, and stagger angle.

[0010] Furthermore, in S2, the simulation model of the hydraulic pump is an AMEsim simulation model, and the hydraulic performance includes the peak value of backflow and the chamber pressure pulsation value.

[0011] Furthermore, step S31 includes the following sub-steps: S311. Set the upper and lower limits of the structural parameters of the damping groove, including the width angle, depth angle, damping groove length, and staggered angle. S312. Based on the result parameter space, a set of sample points is generated using the Latin hypercube sampling method, where each sample point represents a specific combination of damping groove structural parameters; for each sample point, a corresponding simulation model is constructed. S313. Perform simulation calculations for each AMEsim model, extract the backflow rate and pressure fluctuation values ​​from the simulation results, integrate each set of parameter combinations and its simulation output into a data sample, and collect all training samples to form a sample dataset for subsequent model training.

[0012] S32 includes the following sub-steps: S321. Define the BP neural network architecture, specifying the number of nodes in its input layer, the configuration of its hidden layers, and the number of nodes in its output layer. S322. Encode all connection weights and neuron thresholds of the BP neural network into binary and randomly initialize them to generate the first generation parent population. S323. Perform fitness assessment on individuals in the population: decode each individual in the population to obtain the weight and threshold combination of its representation; assign the weight and threshold to a newly created BP neural network with the architecture described in S321; train the network using the sample dataset; calculate the fitness value of the network on the sample dataset. S324: Genetic operations: Based on the individual fitness value, parent individuals are selected using a roulette wheel or tournament selection mechanism; crossover and mutation operations are performed on the selected parent individuals to generate the offspring population; S325: Offspring evaluation and population update: For each individual in the offspring population, perform the fitness evaluation described in step S323; merge the parent population and the offspring population, and select individuals with high fitness based on fitness values ​​to form a new generation population; S326: Iteration Termination and Model Generation: Repeat steps S324 and S325 until the preset maximum number of generations is reached; decode the individual with the highest fitness in the final generation population to obtain the optimal weight matrix and threshold vector; use the optimal weights and thresholds to initialize and fix a BP neural network with the architecture described in S321 to form the final GA-BP model.

[0013] S4 includes the following sub-steps: S41. Select "flow backflow peak value" and "chamber pressure fluctuation value" as optimization targets, and set the structural parameters of the triangular damping groove as design variables; S42. Using the BP neural network trained in S3 with optimal weights and thresholds, establish a proxy model that can quickly and accurately predict the target performance. S43. Genetic operations such as crossover and mutation are used to generate offspring individuals. The above-mentioned GA-BP surrogate model is used to calculate the peak flow backflow and chamber pressure fluctuation of each offspring individual in parallel. S44. Merge the parent and offspring populations, and select a new generation of parent populations based on non-dominated sorting and crowding distance. S45. Determine if the optimization process meets the convergence condition. If it converges, output the optimal solution; otherwise, return to step S43 to continue iteration. S46. After obtaining the optimized Pareto front, the optimal damping groove structure parameters are obtained by screening.

[0014] The mathematical model of the fast non-dominated sorting genetic algorithm is as follows: ; in, and Let represent the objective functions, and min indicates that the optimization aims to minimize these two objective functions. Represents the peak value of the backflow. Representing chamber pressure fluctuations, design variables include the angle of the crossover angle. Length of damping groove Angle of depth and the angle of width And the upper and lower limits of each variable.

[0015] This invention uses the GA-BP proxy model and proposes a BP algorithm optimization method based on genetic algorithm (GA) to accelerate the training speed of BP and overcome the shortcomings of BP being easily stuck in local minima and having poor convergence rate. Furthermore, it combines the NSGA-II multi-objective optimization algorithm to simultaneously solve the Pareto optimal solution set of "minimum flow pulsation value" and "minimum chamber pressure fluctuation value", thereby achieving efficient and accurate design of damping groove parameters.

[0016] The main beneficial effects of this invention are: significantly improving the overall fluid performance of the two-dimensional pump. Attached Figure Description

[0017] Figure 1 This is a two-dimensional cross-sectional view of a pump used in the application of the present invention.

[0018] Figure 2 This is a structural diagram of a two-dimensional pump damping groove.

[0019] Figure 3 This is a flowchart of the hydraulic pump damping groove optimization based on the GA-BP proxy model.

[0020] Figure 4 This is a comparison chart showing the predicted and actual values ​​of backflow for the GA-BP neural network model and the BP neural network.

[0021] Figure 5 This is a comparison chart of the error rates of flow backflow between the GA-BP neural network model and the BP neural network.

[0022] Figure 6 This is a comparison chart showing the predicted and actual values ​​of chamber pressure fluctuations using the GA-BP neural network model and the BP neural network.

[0023] Figure 7 This is a comparison chart showing the error rates of the GA-BP neural network model and the BP neural network for chamber pressure fluctuation values.

[0024] Figure 8 This is a global Pareto front distribution map.

[0025] Figure 9 To optimize the comparison chart of backflow flow before and after.

[0026] Figure 10 To optimize the comparison of pressure fluctuation values ​​before and after chambering.

[0027] Explanation of reference numerals in the attached diagram: 1. Cam 2. Roller 3. Flow channel 4. Right chamber 5. Piston shaft 6. Left chamber 7. Roller carrier. Detailed Implementation

[0028] The present invention will now be further described with reference to the accompanying drawings.

[0029] Reference Figures 1-10 A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network includes the following steps: S1. Establish the design variable parameters in the two-dimensional pump damping groove structure; First, the two-dimensional pump damping groove structure is as follows: Figure 2 As shown, the angle of the staggered angle in the two-dimensional pump damping groove structure is determined. Length of damping groove Angle of depth Angle of width Four structural parameters are design variables; the flow area of ​​the damping groove. S It is expressed as follows: ; in, For the angle of rotation, The length of the damping groove, The angle of the staggered angle, The angle is the depth angle. Where is the width angle, and D is the width of the distribution window.

[0030] S2. Construct a simulation model of the hydraulic pump and analyze its performance; A parametric simulation model of a two-dimensional pump was established using AMESim software. By adjusting the structural parameters of the damping groove and setting the rated operating parameters of the pump, transient simulation was performed to obtain the backflow of pump flow and the fluctuation of chamber pressure as evaluation indicators of the hydraulic pump performance.

[0031] S3, built based on the GA-BP proxy model; First, determine the upper and lower limits of each variable in the damping groove structure. Table 1 shows the design variables and their value ranges for the damping groove.

[0032] After determining the geometric variables and their range of values ​​(as shown in Table 1), the Latin hypercube sampling method was adopted. Through stratification, sampling and randomization operations, the samples were ensured to be uniformly distributed in the parameter space, effectively avoiding data clustering and generating 100 sets of sample points.

[0033] By simulating the corresponding damping groove parameters for each group using the AMESIM simulation model of the hydraulic pump, the peak flow backflow and chamber pressure fluctuation values ​​can be obtained. Using the corresponding structural parameters and their corresponding peak flow backflow and chamber pressure fluctuation values ​​as training samples, simulations are performed on each set of sample points to obtain the training set. A partial training set is shown in Table 2, which contains partial damping groove parameter samples and corresponding simulation results.

[0034] The structure of the BP neural network is determined as follows: the input layer contains 4 neurons, corresponding to the damping groove design parameters, including the stagger angle, damping groove length, depth angle, and width angle; the hidden layer consists of 9 neurons, using radial basis functions as activation functions to achieve nonlinear mapping; the output layer has 2 neurons, which are used to predict flow backflow and pressure chamber fluctuation values, respectively.

[0035] All values ​​and thresholds of the BP neural network are binary encoded, and an initial population of 50 is randomly generated. The number of iterations is set to 100, and the crossover probability is 0.85. After decoding each individual, its parameters are assigned to the newly built BP network, and the network is trained using sample data. The mean squared error (MSE) between the network's predictions and the actual values ​​is calculated. ; The fitness was then calculated again, and individuals with high fitness were selected as parents. ; Strategies such as roulette wheel selection are applied to select parent individuals for crossover, exchanging some gene segments to generate new offspring. Mutation operations are then performed, flipping or altering gene loci in the offspring according to preset probabilities to enhance diversity. After decoding and retraining the BP neural network, the fitness of the offspring individuals is calculated, and the population is updated accordingly: low-fitness individuals are replaced. This process is repeated until a preset number of generations is reached or the fitness threshold is met, ultimately obtaining the optimal weights and thresholds. Using these optimal weights and thresholds, the BP neural network is trained to form the final GA-BP model.

[0036] like Figure 3 , Figure 4 As shown, by comparing the prediction performance on the test set, it was found that the traditional BP model exhibited average biases of 8.08% and 5.66% in flow backflow prediction and chamber pressure fluctuation, respectively. In contrast, the GA-BP model optimized by the genetic algorithm showed biases of 2.72% and 2.99% in flow backflow prediction and chamber pressure fluctuation, respectively. This demonstrates that the GA-BP model, through the optimization of initial weights and thresholds using a genetic algorithm, effectively avoids the problem of the traditional BP model getting trapped in local minima, thus maintaining its robustness even in the highly nonlinear parameter boundary region.

[0037] S4. Use the NSGA-II algorithm to perform global optimization on the GA-BP neural network model; With the goal of minimizing the peak backflow and chamber pressure fluctuation, the NSGA-II algorithm is used to globally optimize the GA-BP neural network model to determine the optimal structural parameters of the triangular damping groove and their variation range. ; The constructed BP neural network surrogate model is used as a prediction tool for target performance, which can quickly estimate the peak backflow and chamber pressure fluctuation under different combinations of design variables, replacing the actual complex simulation calculations and improving optimization efficiency.

[0038] The population size is set to 100, and the maximum number of iterations is 50. After initializing the population, new individuals are generated through genetic operations such as crossover and mutation. The fitness of the new individuals is predicted using a surrogate model. Individuals are selected based on fitness and crowding distance to form a new generation of parent population, and this iterative optimization process is repeated.

[0039] Repeat the above optimization process until convergence, and finally obtain... Figure 6 The diagram shows a uniformly distributed Pareto optimal solution set. A set of triangular damping groove structural parameters with a good trade-off between the two optimization objectives of backflow flow peak and chamber pressure fluctuation is selected on the Pareto front, thereby optimizing the damping groove of the hydraulic pump.

[0040] Table 3 shows the damping groove structure parameters obtained after NSGA-II optimization;

[0041] Before and after multi-objective optimization, the chamber pressure fluctuation decreased from 1.68 Bar to 0.81 Bar, a reduction of 51.8%. Flow backflow decreased from 11.50 L / min to 10.56 L / min, a reduction of 8.2%. It is evident that during operation, the chamber pressure pulsation of the two-dimensional pump can be significantly reduced, achieving optimal matching of multiple structural parameters to suppress flow backflow and pressure pulsation.

[0042] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network, characterized in that, The method includes the following steps: S1. Establish the design variable parameters in the two-dimensional pump damping groove structure; S2. Construct a two-dimensional piston pump simulation model and use the model to simulate and obtain the performance parameters of the hydraulic pump; S3. Based on the GA-BP proxy model, the construction process is as follows: S31. Based on the design variable parameters, use the Latin hypersquare sampling method to generate a sample dataset with good parameter space filling performance; S32. Establish a BP neural network model and use a genetic algorithm to optimize and train the model based on a sample dataset to finally obtain a BP neural network model optimized by the genetic algorithm. S4. Using the GA-BP neural network surrogate model as the fitness function, the fast non-dominated sorting genetic algorithm is used to perform multi-objective optimization on the parameter space of the damping groove structure to obtain the optimal parameter solution set.

2. The multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1, characterized in that, In S1, the design variable parameters are damping groove structural parameters, including width angle, depth angle, damping groove length, and stagger angle.

3. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1 or 2, characterized in that, In S2, the simulation model of the hydraulic pump is the AMEsim simulation model, and the hydraulic performance includes the peak value of backflow and the chamber pressure pulsation value.

4. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1 or 2, characterized in that, S31 includes the following sub-steps: S311. Set the upper and lower limits of the structural parameters of the damping groove, including the width angle, depth angle, damping groove length, and staggered angle. S312. Based on the result parameter space, a set of sample points is generated using the Latin hypercube sampling method, where each sample point represents a specific combination of damping groove structural parameters; for each sample point, a corresponding simulation model is constructed. S313. Perform simulation calculations for each AMEsim model, extract the backflow rate and pressure fluctuation values ​​from the simulation results, integrate each set of parameter combinations and its simulation output into a data sample, and collect all training samples to form a sample dataset for subsequent model training.

5. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1 or 2, characterized in that, S32 includes the following sub-steps: S321. Define the BP neural network architecture, specifying the number of nodes in its input layer, the configuration of its hidden layers, and the number of nodes in its output layer. S322. Encode all connection weights and neuron thresholds of the BP neural network into binary and randomly initialize them to generate the first generation parent population. S323. Perform fitness assessment on individuals in the population: decode each individual in the population and obtain the weight and threshold combination of its representation; The weights and thresholds are assigned to a newly created BP neural network with the architecture described in S321; The network is trained using the sample dataset; the fitness value of the network on the sample dataset is calculated. S324: Genetic operations: Based on the individual fitness value, parent individuals are selected using a roulette wheel or tournament selection mechanism; crossover and mutation operations are performed on the selected parent individuals to generate the offspring population; S325: Offspring evaluation and population update: For each individual in the offspring population, perform the fitness evaluation described in step S323; merge the parent population and the offspring population, and select individuals with high fitness based on fitness values ​​to form a new generation population; S326: Iteration Termination and Model Generation: Repeat steps S324 and S325 until the preset maximum number of generations is reached; decode the individual with the highest fitness in the final generation population to obtain the optimal weight matrix and threshold vector; use the optimal weights and thresholds to initialize and fix a BP neural network with the architecture described in S321 to form the final GA-BP model.

6. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1 or 2, characterized in that, S4 includes the following sub-steps: S41. Select "flow backflow peak value" and "chamber pressure fluctuation value" as optimization targets, and set the structural parameters of the triangular damping groove as design variables; S42. Using the BP neural network trained in S3 with optimal weights and thresholds, establish a proxy model that can quickly and accurately predict the target performance. S43. Genetic operations such as crossover and mutation are used to generate offspring individuals. The above-mentioned GA-BP surrogate model is used to calculate the peak flow backflow and chamber pressure fluctuation of each offspring individual in parallel. S44. Merge the parent and offspring populations, and select a new generation of parent populations based on non-dominated sorting and crowding distance. S45. Determine whether the optimization process meets the convergence condition. If it converges, output the optimal solution. Otherwise, return to step S43 and continue the iteration; S46. After obtaining the optimized Pareto front, the optimal damping groove structure parameters are obtained by screening.

7. A multi-objective optimization method for a two-dimensional pump damping groove based on a GA-BP neural network as described in claim 1 or 2, characterized in that, The mathematical model of the fast non-dominated sorting genetic algorithm is as follows: ； in, and Let represent the objective functions, and min indicates that the optimization aims to minimize these two objective functions. Represents the peak value of the backflow. Representing chamber pressure fluctuations, design variables include the angle of the crossover angle. Length of damping groove Angle of depth and the angle of width And the upper and lower limits of each variable.

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