Method and system for predicting frictional wear performance of resin-based brake material based on PSO-FPA-BP

Abstract

The invention provides a PSO-FPA-BP-based friction and wear performance prediction method and system for a resin-based brake material, and the method and system carry out the preprocessing of a friction and wear performance data set of the brake material, and obtain a preprocessed sample data set; the initial weight and the initial threshold of the BP neural network are used as initial population positions of a PSO-FPA hybrid optimization algorithm for optimization, and the optimal weight and the optimal threshold of the BP neural network are obtained; using the preprocessed sample data set to train the brake material friction and wear performance prediction model formed by the BP neural network with the optimal initial threshold value and the optimal initial weight value, and using samples which do not participate in training to test the friction and wear performance prediction model which is trained to be qualified. According to the method, the friction wear performance of the brake material can be accurately predicted.

Description

Technical Field

[0001] This invention proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, which relates to the field of braking materials. Background Technology

[0002] The braking system is a critical factor in vehicle safety, and its importance is self-evident. Brake pads, as the actuators of the braking system, have a crucial impact on the entire system's tribological properties. Resin-based brake materials are currently the most widely used automotive brake pads. For a long time, copper has been a component of these friction materials, and its unique properties have played a vital role in enhancing the desired characteristics of brake pad composites. However, in recent years, it has been proven that copper residues from brake materials and brake discs, when directly released into the air, can harm the environment, especially aquatic life. Therefore, international conventions regarding copper limits in brake material formulations have emerged, and copper-free brake pads are receiving increasing attention.

[0003] The friction and wear properties of braking materials directly affect the safety, durability, and maintenance costs of vehicles. During use, friction and wear can lead to degradation of material surface properties, affecting braking performance and even causing accidents. Therefore, accurately predicting the friction and wear properties of braking materials is crucial for improving traffic safety and optimizing material design. Furthermore, the friction and wear properties of braking materials are influenced by a variety of factors, the most important of which include braking temperature, pressure, speed, friction surface characteristics, material composition, and load. These factors not only act independently but also interact in complex ways. Traditional physical models often derive friction and wear laws based on linear or simplified assumptions, which limits their effectiveness in complex real-world conditions. These models typically fail to comprehensively consider the combined effects of material properties, friction surface conditions, and changes in operating conditions, making it difficult to accurately predict the behavior and characteristics of friction and wear. Summary of the Invention

[0004] In view of this, in order to fill the gaps and deficiencies in the existing technology, this invention proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, which is used to make a more accurate prediction of the friction and wear performance of braking materials.

[0005] This invention proposes a method and system for predicting the tribological properties of resin-based braking materials based on PSO-FPA-BP, including the following:

[0006] A method for predicting the tribological properties of resin-based braking materials based on PSO-FPA-BP includes the following steps:

[0007] Step S1: Prepare resin-based braking material and collect experimental data, including the material composition, friction coefficient and wear rate of the braking material, through friction and wear experiments;

[0008] Step S2: Divide the dataset obtained from the friction and wear test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. Normalize the dataset to obtain the final friction and wear performance dataset of the braking material.

[0009] Step S3: Build a BP neural network and determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network;

[0010] Step S4: Use the initial weights and initial thresholds of each node of the BP neural network as the initial positions of the population in the particle swarm flower pollination hybrid optimization algorithm to find the optimal initial weights and optimal initial thresholds of the BP neural network.

[0011] Step S5: Extract the optimal initial weights and optimal initial thresholds to train the normalized training set of the friction and wear test data, and use the trained brake material friction and wear performance prediction model to verify it using the test set.

[0012] Further, step S2 includes the following:

[0013] Step S21: Divide the dataset obtained from the friction and wear test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%.

[0014] Step S22: Normalize the dataset using the mapminmax function. This function maps the dataset to the range (0, 1) for better model training and prediction. Normalization prevents the training process from being affected by excessively large or small values ​​of a particular variable. The formula for the mapminmax function is shown below:

[0015]

[0016] Among them, x norm This represents the normalized value, where x represents the original data. min and x max Let y represent the minimum and maximum values ​​of the feature in the current training data, respectively. max and y min These represent the maximum and minimum values ​​of the normalization target interval, respectively.

[0017] Further, step S3 includes the following:

[0018] Step S31: Determine the number of nodes in the input layer of the BP neural network; where the number of nodes in the input layer of the BP neural network is equal to the dimension of the input vector;

[0019] Step S32: Determine the number of output layer nodes of the BP neural network; wherein the number of output layer nodes is consistent with the number of prediction results, and the prediction results are the wear rate;

[0020] Step S33: Determine the number of hidden layer nodes in the BP neural network, where the number of hidden layer nodes includes the following:

[0021]

[0022] Where N is the number of neurons in the hidden layer; m is the number of neurons in the input layer; n is the number of neurons in the output layer; and a is a constant between 1 and 10.

[0023] Furthermore, step S3 also includes the following:

[0024] Step S34: Set the basic parameters of the BP neural network, using the sigmoid function as the activation function for the hidden layer and the purelin function as the activation function for the output layer. This is a linear transfer function, meaning the neuron's input value equals its output value. The formula for the sigmoid function is shown below:

[0025]

[0026] Where x represents the input value of the hidden layer neuron, and f(x) represents the output value of the hidden layer neuron.

[0027] Further, step S4 includes the following:

[0028] Step S41: Set the parameters of the particle swarm optimization algorithm, which include: learning factor, population size, and maximum number of iterations;

[0029] Step S42: Encode the initial weights between each layer in the BP neural network and the initial thresholds of the hidden and output layers into particles in the particle swarm optimization algorithm. The sum of the number of initial weights and initial thresholds is used as the dimension of particle motion.

[0030] Step S43: Import the training set from the dataset into the BP neural network for training, and then obtain the determination coefficient R of the predicted values ​​of the training set. 2 As an optimization objective, let the fitness function be denoted as (1-R). 2 The fitness function expression is as follows:

[0031]

[0032] in, y represents the predicted value from the training set. i Represents the true values ​​in the training set. This represents the average value of the true values ​​in the training set.

[0033] Furthermore, step S4 also includes the following:

[0034] Step S44: Initialize the lower and upper bounds of the search space, and initialize the initial velocity of each particle;

[0035] Step S45: Randomly initialize the positions of the particles in the particle swarm, where each position of the particles is a weight and threshold distribution of the neural network;

[0036] Step S46: Calculate the fitness function according to the formula in step S43, and use the fitness function obtained in step S43 as the fitness function of the particle swarm flower pollination hybrid optimization algorithm, and use this function as the optimization target.

[0037] Step S47: Particle swarm iteration stage;

[0038] The dataset, divided into training sets, is imported into the BP neural network model for training. During training, the particle velocity and position are updated based on the individual historical best solution and the global historical best solution. The formulas for updating particle velocity and position include the following:

[0039] v i+1 =ω×v i +c1×rand()×(gbest i -x i )+c2×rand()×(zbest i -x i )

[0040] x i+1 =x i +v i+1

[0041] Among them, v i v is the velocity of the particle in the i-th iteration. i+1 c1 is the velocity of the particle in the (i+1)th iteration; c1 is the individual learning factor, which represents the particle's self-improvement ability; rand() is a random number between [0,1]; gbest i Let c1 be the local optimum position in the i-th iteration, and c2 be the global learning factor, representing the degree to which the particle moves towards the swarm optimum; zbest i Let x be the globally optimal position in the i-th iteration. i It is the position of the particle in the i-th iteration, x i+1 ω is the position of the particle in the (i+1)th iteration, and ω is the inertia weight factor.

[0042] Furthermore, step S4 also includes the following content:

[0043] Step S48: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue the iteration; otherwise, stop the iteration.

[0044] Step S49: Extract the population position after the iteration of the particle swarm optimization algorithm, and use this population position as the initial position of the pollen population in the flower pollination algorithm. After the initialization is completed, perform the iteration of the flower pollination algorithm.

[0045] Furthermore, step S4 also includes the following content:

[0046] Step S410: Execute the iteration stage of the flower pollination algorithm, including the following content:

[0047] Step S4101: Simplify the flower pollination algorithm: Among them, cross-pollination of plants is considered that the pollination process follows Levy flight and performs a global search process. Self-pollination of plants is equivalent to a local search process. Self-pollination and cross-pollination are controlled by a conversion probability P. When rand() < P, cross-pollination is performed; otherwise, self-pollination is performed, where rand() is a random number uniformly distributed between [0, 1], and P ∈ [0, 1].

[0048] Furthermore, when rand() < P, cross-pollination is performed, and cross-pollination includes performing a global search. The update formula for cross-pollination is as follows:

[0049]

[0050] where, g * is the optimal pollen in the population, that is, the current global optimal solution, and represent the pollen individuals in the (t + 1)-th generation and the t-th generation respectively. The parameter L is an N-dimensional pollination intensity vector, and each dimension is a random number obeying the Levy distribution. The calculation formula is as follows:

[0051]

[0052] where, Γ(γ) is the standard gamma function, and s is the step size generated by the nonlinear transformation.

[0053] Furthermore, step S4 also includes the following content:

[0054] Step S4102: When rand() < P, self-pollination is performed, and self-pollination includes performing a local search. The update formula for self-pollination is as follows:

[0055]

[0056] in, and These represent pollen individuals from generation t+1 and generation t, respectively. and It is different from the population Two random pollen individuals, where ε is a random number uniformly distributed on [0,1].

[0057] Step S411: Update the fitness and determine whether the maximum number of iterations has been reached. If not, continue iterating; otherwise, stop iterating and output the optimal pollen individual, which is the optimal initial threshold and optimal initial weight of the BP neural network based on the particle swarm flower pollination hybrid optimization algorithm.

[0058] According to a second aspect of the present invention, a system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP is provided, comprising an electronic device, wherein the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements a method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP as described in any one of the present invention.

[0059] According to a third aspect of the present invention, a system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP is provided, comprising a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements a method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP as described in any one of the present invention.

[0060] The present invention has the following advantages:

[0061] This invention proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP. Since the Particle Swarm Optimization (PSO) algorithm is prone to getting trapped in local optima and exhibits low convergence accuracy in the later stages of iteration, its local search capability is poor. Therefore, the accuracy of the PSO-based BP neural network model for predicting friction and wear performance is generally limited. The flower pollination algorithm, however, has two iterative modes: cross-pollination and self-pollination. Cross-pollination corresponds to the global search stage, while self-pollination corresponds to the local search stage. Introducing the flower pollination algorithm can improve the probability of local search during iteration by controlling the transformation probability P, thus addressing the problem of poor local search capability and susceptibility to local optima in the PSO algorithm. Furthermore, using this hybrid optimization algorithm to construct a PSO-FPA-BP neural network for predicting the friction and wear performance of braking materials solves the problem of accurately selecting weights and thresholds in BP neural networks. This allows for more accurate prediction of the friction and wear performance of braking materials without the need for additional experiments to obtain the friction and wear performance data. Attached Figure Description

[0062] Figure 1 This is a flowchart of the BP neural network optimized by the particle swarm optimization algorithm for flower pollination of the present invention.

[0063] Figure 2 This is a comparison chart of prediction errors for different numbers of neurons in the hidden layer according to the present invention.

[0064] Figure 3 This is a comparison chart of the friction coefficient prediction results of the unoptimized BP neural network of the present invention and the actual values.

[0065] Figure 4 This is a comparison chart of the wear rate prediction results of the unoptimized BP neural network of the present invention and the actual values.

[0066] Figure 5 This is a comparison chart of the friction coefficient prediction results and the actual values ​​of the BP neural network optimized by the particle swarm optimization algorithm of this invention.

[0067] Figure 6 This is a comparison chart of the wear rate prediction results of the BP neural network optimized by the particle swarm optimization algorithm of this invention and the actual values.

[0068] Figure 7 This is a comparison chart of the predicted friction coefficient of the BP neural network optimized by the flower pollination algorithm of this invention with the actual value.

[0069] Figure 8 This is a comparison chart of the wear rate prediction results and the actual values ​​of the BP neural network optimized by the flower pollination algorithm of this invention.

[0070] Figure 9This is a comparison chart of the predicted friction coefficient of the BP neural network optimized by the particle swarm pollination mixing optimization algorithm of this invention with the actual value.

[0071] Figure 10 This is a comparison chart of the wear rate prediction results of the BP neural network optimized by the particle swarm flower pollination hybrid optimization algorithm of the present invention and the actual values.

[0072] Figure 11 This is a comparison chart of the prediction residuals of the various friction coefficient prediction models of this invention.

[0073] Figure 12 This is a comparison chart of the prediction residuals of the various wear rate prediction models of this invention.

[0074] Figure 13 These are the fitness function value change curves of the various friction coefficient prediction models of this invention during the iterative process.

[0075] Figure 14 These are the fitness function value change curves of the various wear rate prediction models of this invention during the iterative process. Detailed Implementation

[0076] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0077] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0078] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0079] The flowchart of the BP neural network optimized by the particle swarm optimization algorithm for flower pollination in this invention is as follows: Figure 1 As shown, this invention proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, including the following embodiments:

[0080] Regarding the coefficient of friction, the present invention proposes Example 1.

[0081] Specifically, regarding the wear rate, this invention proposes Example 2.

[0082] Furthermore, Example 1 includes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, and its application in predicting the friction coefficient of resin-based braking materials.

[0083] Furthermore, Example 2 includes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, and its application in predicting the wear rate of resin-based braking materials.

[0084] Furthermore, Example 1 includes the following:

[0085] Step S1: Prepare resin-based braking material and collect experimental data including the material composition, friction coefficient and wear rate of the braking material through friction coefficient experiments;

[0086] Step S2: Divide the dataset obtained from the friction coefficient test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. Normalize the dataset to obtain the final friction coefficient performance dataset of the braking material.

[0087] Step S3: Build a BP neural network and determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network;

[0088] Step S4: Use the initial weights and initial thresholds of each node of the BP neural network as the initial positions of the population in the particle swarm flower pollination hybrid optimization algorithm to find the optimal initial weights and optimal initial thresholds of the BP neural network.

[0089] Step S5: Extract the optimal initial weights and optimal initial thresholds to train the normalized training set of the friction coefficient test dataset, and use the trained brake material friction coefficient performance prediction model to verify it using the test set.

[0090] Further, step S2 includes the following:

[0091] Step S21: The friction and wear performance dataset contains a total of 162 sets of experimental data. The dataset is divided into a training set and a test set, with 130 sets of data in the training set (accounting for 80% of the dataset) and 32 sets of data in the test set (accounting for 20% of the dataset).

[0092] Step S22: Normalize the dataset using the mapminmax function. This function maps the dataset to the range (0, 1) for better model training and prediction. Normalization prevents the training process from being affected by excessively large or small values ​​of a particular variable. The formula for the mapminmax function is shown below:

[0093]

[0094] Among them, x norm This represents the normalized value, where x represents the original data. min and x max Let y represent the minimum and maximum values ​​of the feature in the current training data, respectively. max and y min These represent the maximum and minimum values ​​of the normalization target interval, respectively.

[0095] Further, step S3 includes the following:

[0096] Step S31: Determine the number of nodes in the input layer of the BP neural network. During the construction process, the number of nodes in the input layer of the BP neural network is equal to the dimension of the input vector. In this invention, the dimension of the input vector is the dimension of the friction coefficient dataset variables, which include six variables: foundry waste sand, cashew nut shell oil-modified phenolic resin, bamboo fiber, alumina, barium sulfate, and temperature. The units for the components are mass fractions, and the unit for temperature is degrees Celsius. Therefore, the number of nodes in the input layer of the BP neural network is 6.

[0097] Step S32: Determine the number of output layer nodes of the BP neural network; the number of output layer nodes is consistent with the number of prediction results, and the prediction result is the wear rate, so the number of output layer nodes is 1;

[0098] Step S33: Determine the number of hidden layer nodes in the BP neural network, where the number of hidden layer nodes includes the following:

[0099]

[0100] Where N is the number of neurons in the hidden layer; m is the number of neurons in the input layer; n is the number of neurons in the output layer; and a is a constant between 1 and 10. Figure 2 Analysis shows that the number of hidden layer nodes in this invention is determined to be 13.

[0101] Step S34: Set the basic parameters of the BP neural network: a maximum of 200 training iterations, a learning rate of 0.01, and a target error of 0.001. Use the sigmoid function as the activation function for the hidden layers and the purelin function as the activation function for the output layers. The purelin function is a linear transfer function, meaning the neuron's input value equals its output value.

[0102] The formula for the Sigmoid function is shown below:

[0103]

[0104] Where x represents the input value of the hidden layer neuron, and f(x) represents the output value of the hidden layer neuron.

[0105] Further, step S4 includes the following:

[0106] Step S41: Set the parameters of the particle swarm optimization algorithm, which include: learning factor, population size, and maximum number of iterations;

[0107] Step S42: Encode the initial weights between each layer in the BP neural network and the initial thresholds of the hidden and output layers into particles in the particle swarm optimization algorithm. The sum of the number of initial weights and initial thresholds is used as the dimension of particle motion.

[0108] Step S43: Import the training set from the dataset into the BP neural network for training, and then obtain the determination coefficient R of the predicted values ​​of the training set. 2 As an optimization objective, let the fitness function be denoted as (1-R). 2 The fitness function expression is as follows:

[0109]

[0110] in, y represents the predicted value from the training set. i Represents the true values ​​in the training set. This represents the average value of the true values ​​in the training set.

[0111] Furthermore, step S4 also includes the following:

[0112] Step S44: Initialize the lower and upper bounds of the search space, and initialize the initial velocity of each particle;

[0113] Step S45: Randomly initialize the positions of the particles in the particle swarm, where each position of the particles is a weight and threshold distribution of the neural network;

[0114] Step S46: Calculate the fitness function according to the formula in step S43, and use the fitness function obtained in step S43 as the fitness function of the particle swarm flower pollination hybrid optimization algorithm, and use this function as the optimization target.

[0115] Step S47: Particle swarm iteration stage;

[0116] The dataset, divided into training sets, is imported into the BP neural network model for training. During training, the particle velocity and position are updated based on the individual historical best solution and the global historical best solution. The formulas for updating particle velocity and position include the following:

[0117] v i+1 =ω×v i +c1×rand()×(gbest i -x i) + c2 × rand() × (zbest i - x i )

[0118] x i+1 = x i + v i+1

[0119] where v i is the velocity of the particle at the i-th iteration, and v i+1 is the velocity of the particle at the (i + 1)-th iteration; c1 is the individual learning factor, and c1 represents the self-improving ability of the particle; rand() is a random number between [0, 1]; gbest i is the local optimal position at the i-th iteration, c2 is the global learning factor, and c2 represents the degree to which the particle moves towards the global optimum; zbest i is the global optimal position at the i-th iteration, x i is the position of the particle at the i-th iteration, and x i+1 is the position of the particle at the (i + 1)-th iteration, and ω is the inertia weight factor.

[0120] Furthermore, step S4 further includes the following content:

[0121] Step S48: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue the iteration; otherwise, stop the iteration;

[0122] Step S49: Extract the population position after the iteration of the particle swarm optimization algorithm, and use this population position as the initial position of the pollen population in the flower pollination algorithm. After initialization, perform the iteration of the flower pollination algorithm.

[0123] Furthermore, step S4 further includes the following content:

[0124] Step S410: Execute the iteration stage of the flower pollination algorithm, including the following content:

[0125] Step S4101: Simplify the flower pollination algorithm: Among them, it is considered that the pollination process of cross-pollination of plants follows Levy flight and performs a global search process, and self-pollination of plants is equivalent to a local search process. Self-pollination and cross-pollination are controlled by a conversion probability P. When rand() < P, cross-pollination is performed, otherwise self-pollination is performed, where rand() is a random number uniformly distributed between [0, 1], and P ∈ [0, 1];

[0126] Furthermore, when rand() < P, cross-pollination is performed, and cross-pollination includes performing a global search. The update formula for cross-pollination is as follows:

[0127]

[0128] Among them, g * is the optimal pollen in the population, that is, the current global optimal solution, and represent the pollen individuals in the (t + 1)-th generation and the t-th generation respectively. The parameter L is an N-dimensional pollination intensity vector, and each dimension of which is a random number obeying the Levy distribution. The calculation formula is as follows:

[0129]

[0130] Among them, Γ(γ) is the standard gamma function, and s is the step size generated by non-linear transformation.

[0131] Furthermore, step S4 further includes the following content:

[0132] Step S4102: When rand() < P, self-pollination is performed, and self-pollination includes performing local search. The update formula for self-pollination is shown as follows:

[0133]

[0134] Among them,, and represent the pollen individuals in the (t + 1)-th generation and the t-th generation respectively; and are two random pollen individuals different from in the population, and ε is a random number uniformly distributed on [0, 1];

[0135] Step S411: Update the fitness and judge whether the maximum number of iterations is reached. If not, continue the iteration; otherwise, stop the iteration and output the optimal pollen individual, which is the optimal initial threshold and the optimal initial weight of the BP neural network optimized by the particle swarm flower pollination hybrid optimization algorithm.

[0136] In Embodiment 1, the present invention proposes a method and system for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP in a system for predicting the friction coefficient of resin-based brake materials, including an electronic device. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. It is characterized in that when the processor executes the computer program, it realizes the application of the method for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP in predicting the friction coefficient of resin-based brake materials as described in any one of the present invention.

[0137] In Example 1, the present invention also proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP. The system for predicting the friction coefficient of resin-based braking materials includes a computer-readable storage medium storing a computer program. The computer program is characterized in that, when executed by a processor, it implements the method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP as described in any one of the present invention for predicting the friction coefficient of resin-based braking materials.

[0138] Furthermore, Example 2 includes the following:

[0139] Step S1: Prepare resin-based braking material and collect experimental data including the material composition, wear rate, and wear rate through wear rate experiments;

[0140] Step S2: Divide the dataset obtained from the wear rate test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. Normalize the dataset to obtain the final brake material wear rate performance dataset.

[0141] Step S3: Build a BP neural network and determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network;

[0142] Step S4: Use the initial weights and initial thresholds of each node of the BP neural network as the initial positions of the population in the particle swarm flower pollination hybrid optimization algorithm to find the optimal initial weights and optimal initial thresholds of the BP neural network.

[0143] Step S5: Extract the optimal initial weights and optimal initial thresholds to train the normalized training set of the wear rate test dataset, and use the trained brake material wear rate performance prediction model to verify it using the test set.

[0144] Further, step S2 includes the following:

[0145] Step S21: The friction and wear performance dataset contains a total of 162 sets of experimental data. The dataset is divided into a training set and a test set, with 130 sets of data in the training set (accounting for 80% of the dataset) and 32 sets of data in the test set (accounting for 20% of the dataset).

[0146] Step S22: Normalize the dataset using the mapminmax function. This function maps the dataset to the range (0, 1) for better model training and prediction. Normalization prevents the training process from being affected by excessively large or small values ​​of a particular variable. The formula for the mapminmax function is shown below:

[0147]

[0148] Among them, x norm This represents the normalized value, where x represents the original data. min and x max Let y represent the minimum and maximum values ​​of the feature in the current training data, respectively. max and y min These represent the maximum and minimum values ​​of the normalization target interval, respectively.

[0149] Further, step S3 includes the following:

[0150] Step S31: Determine the number of nodes in the input layer of the BP neural network. During the construction process, the number of nodes in the input layer of the BP neural network is equal to the dimension of the input vector. In this invention, the dimension of the input vector is the dimension of the wear rate dataset variables, which include six variables: foundry waste sand, cashew nut shell oil-modified phenolic resin, bamboo fiber, alumina, barium sulfate, and temperature. The units for the components are mass fractions, and the unit for temperature is degrees Celsius. Therefore, the number of nodes in the input layer of the BP neural network is 6.

[0151] Step S32: Determine the number of output layer nodes of the BP neural network; the number of output layer nodes is consistent with the number of prediction results, and the prediction result is the wear rate, so the number of output layer nodes is 1;

[0152] Step S33: Determine the number of hidden layer nodes in the BP neural network, where the number of hidden layer nodes includes the following:

[0153]

[0154] Where N is the number of neurons in the hidden layer; m is the number of neurons in the input layer; n is the number of neurons in the output layer; and a is a constant between 1 and 10. Figure 2 Analysis shows that the number of hidden layer nodes in this invention is determined to be 13.

[0155] Step S34: Set the basic parameters of the BP neural network: a maximum of 200 training iterations, a learning rate of 0.01, and a target error of 0.001. Use the sigmoid function as the activation function for the hidden layers and the purelin function as the activation function for the output layers. The purelin function is a linear transfer function, meaning the neuron's input value equals its output value.

[0156] The formula for the Sigmoid function is shown below:

[0157]

[0158] Where x represents the input value of the hidden layer neuron, and f(x) represents the output value of the hidden layer neuron.

[0159] Further, step S4 includes the following:

[0160] Step S41: Set the parameters of the particle swarm optimization algorithm, which include: learning factor, population size, and maximum number of iterations;

[0161] Step S42: Encode the initial weights between each layer in the BP neural network and the initial thresholds of the hidden and output layers into particles in the particle swarm optimization algorithm. The sum of the number of initial weights and initial thresholds is used as the dimension of particle motion.

[0162] Step S43: Import the training set from the dataset into the BP neural network for training, and then obtain the determination coefficient R of the predicted values ​​of the training set. 2 As an optimization objective, let the fitness function be denoted as (1-R). 2 The fitness function expression is as follows:

[0163]

[0164] in, y represents the predicted value from the training set. i Represents the true values ​​in the training set. This represents the average value of the true values ​​in the training set.

[0165] Furthermore, step S4 also includes the following:

[0166] Step S44: Initialize the lower and upper bounds of the search space, and initialize the initial velocity of each particle;

[0167] Step S45: Randomly initialize the positions of the particles in the particle swarm, where each position of the particles is a weight and threshold distribution of the neural network;

[0168] Step S46: Calculate the fitness function according to the formula in step S43, and use the fitness function obtained in step S43 as the fitness function of the particle swarm flower pollination hybrid optimization algorithm, and use this function as the optimization target.

[0169] Step S47: Particle swarm iteration stage;

[0170] The dataset, divided into training sets, is imported into the BP neural network model for training. During training, the particle velocity and position are updated based on the individual historical best solution and the global historical best solution. The formulas for updating particle velocity and position include the following:

[0171] v i+1 =ω×v i +c1×rand()×(gbest i-x i ) + c2 × rand() × (zbest i -x i )

[0172] x i+1 = x i + v i+1

[0173] where v i is the velocity of the particle at the i-th iteration, v i+1 is the velocity of the particle at the (i + 1)-th iteration; c1 is the individual learning factor, and c1 represents the self-improving ability of the particle; rand() is a random number between [0, 1]; gbest i is the local optimal position at the i-th iteration, c2 is the global learning factor, and c2 represents the degree to which the particle moves towards the global optimum; zbest i is the global optimal position at the i-th iteration, x i is the position of the particle at the i-th iteration, x i+1 is the position of the particle at the (i + 1)-th iteration, and ω is the inertia weight factor.

[0174] Furthermore, step S4 further includes the following content:

[0175] Step S48: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue the iteration; otherwise, stop the iteration;

[0176] Step S49: Extract the population position after the iteration of the particle swarm optimization algorithm, and use this population position as the initial position of the pollen population in the flower pollination algorithm. After initialization, perform the iteration of the flower pollination algorithm.

[0177] Furthermore, step S4 further includes the following content:

[0178] Step S410: Execute the iteration stage of the flower pollination algorithm, including the following content:

[0179] Step S4101: Simplify the flower pollination algorithm: Among them, cross-pollination of plants is considered that the pollination process follows Levy flight and performs a global search process, and self-pollination of plants is equivalent to a local search process. Self-pollination and cross-pollination are controlled by a transition probability P. When rand() < P, cross-pollination is performed, otherwise self-pollination is performed, where rand() is a random number uniformly distributed between [0, 1], and P ∈ [0, 1];

[0180] Furthermore, when rand() < P, cross-pollination is performed, and cross-pollination includes performing a global search. The update formula for cross-pollination is as follows:

[0181]

[0182] Among them, g * is the optimal pollen in the population, that is, the current global optimal solution, and represent the pollen individuals in the (t + 1)-th generation and the t-th generation respectively. The parameter L is an N-dimensional pollination intensity vector, and each dimension thereof is a random number subject to the Levy distribution. The calculation formula is as follows:

[0183]

[0184] Among them, Γ(γ) is the standard gamma function, and s is the step size generated by the non-linear transformation.

[0185] Furthermore, step S4 further includes the following content:

[0186] Step S4102: When rand() < P, self-pollination is performed, and self-pollination includes performing local search. The update formula for self-pollination is shown as follows:

[0187]

[0188] Among them,, and represent the pollen individuals in the (t + 1)-th generation and the t-th generation respectively; and are two random pollen individuals different from in the population, and ε is a random number uniformly distributed on [0, 1];

[0189] Step S411: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue the iteration; otherwise, stop the iteration and output the optimal pollen individual, which is the optimal initial threshold and the optimal initial weight of the BP neural network optimized by the particle swarm flower pollination hybrid optimization algorithm.

[0190] In Embodiment 2, the present invention proposes a method and system for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP in a system for predicting the wear rate of resin-based brake materials, including an electronic device. The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. It is characterized in that when the processor executes the computer program, it implements the application of a method and system for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP in a method for predicting the wear rate of resin-based brake materials as described in any one of the present invention.

[0191] In Example 2, the present invention also proposes a method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP. The system for predicting the wear rate of resin-based braking materials includes a computer-readable storage medium storing a computer program. The computer program is characterized in that, when executed by a processor, it implements the application of the method and system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP as described in any one of the present invention in the method for predicting the wear rate of resin-based braking materials.

[0192] In addition to the above, the present invention also includes the following embodiments:

[0193] This invention proposes a method and system for predicting the tribological properties of resin-based braking materials based on PSO-FPA-BP, wherein PSO-FPA-BP has the following meanings:

[0194] A BP neural network model optimized using a particle swarm optimization algorithm for flower pollination.

[0195] The prediction performance of the PSO-FPA-BP neural network models established in Examples 1 and 2 was compared with that of the unoptimized BP neural network model, the BP neural network model optimized by the particle swarm optimization algorithm (PSO-BP), and the BP neural network model optimized by the flower pollination algorithm (FPA-BP). Evaluation metrics for each model were calculated, including mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). 2 The friction coefficient prediction model is an optimized BP neural network (PSO-FPA-BP) model based on the particle swarm optimization algorithm for flower pollination. The friction coefficient prediction model established in Example 1 is compared with other prediction models, and the evaluation indicators of each model are shown in Table 1.

[0196]

[0197] Table 1 Evaluation Indicators of Prediction Models for Different Friction Coefficients

[0198] Table 1 shows the coefficient of determination (R²) for Example 1 during the testing phase. 2 The coefficient of determination for Example 1 is 0.88, which is closer to 1 than that of the PSO-BP and FPA-BP models. Furthermore, the mean absolute error (MAE) and root mean square error (RMSE) of Example 1 are 0.013 and 0.016, respectively. These values ​​are lower than those of the PSO-BP, FPA-BP, and unoptimized BP models. Figure 5 , Figure 7 , Figure 9 , Figure 11Analysis shows that, compared to the PSO-BP model, FPA-BP model, and the unoptimized BP model, the friction coefficient prediction model established in Example 1 provides prediction results closer to the actual curve. Therefore, the prediction accuracy of the friction coefficient prediction model established in Example 1 is higher than that of the PSO-BP model, FPA-BP model, and the unoptimized BP model. Furthermore, to verify and illustrate the effectiveness of the proposed hybrid optimized BP neural network model (PSO-FPA-BP), the training iteration processes of each friction and wear performance prediction model are compared and analyzed. Figure 13 It can be seen that when the number of iterations of the PSO-BP friction coefficient prediction model reaches 120, the fitness function of the model converges to the optimal solution of 0.1822; when the number of iterations of the FPA-BP friction coefficient prediction model reaches 140, the fitness function of the model converges to the optimal solution of 0.1863; while the fitness function of the PSO-FPA-BP friction coefficient prediction model only converges to the optimal solution of 0.1215 when the number of iterations reaches 193, and when the number of iterations reaches 142, the fitness function value of this model is lower than that of other models.

[0199] The wear rate prediction model established in Example 2 was compared with other prediction models. The evaluation indicators of each model are as follows:

[0200] As shown in Table 2:

[0201]

[0202]

[0203] Table 2 Evaluation Indicators of Different Wear Rate Prediction Models

[0204] Table 2 shows the coefficient of determination (R²) for Example 2 during the testing phase. 2 The coefficient of determination for Example 2 is 0.98, which is closer to 1 than that of the PSO-BP and FPA-BP models. Furthermore, the mean absolute error (MAE) and root mean square error (RMSE) of Example 2 are 0.059 and 0.080, respectively. These values ​​are lower than those of the PSO-BP, FPA-BP, and unoptimized BP models. Figure 6 , Figure 8 , Figure 10 , Figure 12 Analysis shows that, compared to the PSO-BP model, FPA-BP model, and the unoptimized BP model, the wear rate prediction model established in Example 2 provides prediction results closer to the actual curve. Therefore, the prediction accuracy of the wear rate prediction model established in Example 2 is higher than that of the PSO-BP model, FPA-BP model, and the unoptimized BP model. Figure 14It can be seen that when the number of iterations of the PSO-FPA-BP wear rate prediction model reaches 121, the fitness function of the model converges to the optimal solution of 0.02111; when the number of iterations of the PSO-BP wear rate prediction model reaches 23, the fitness function of the model converges to the local optimum of 0.1061; although the fitness function of the FPA-BP wear rate prediction model only converges to the local optimum when the number of iterations reaches 180, its convergence accuracy is lower than that of the PSO-FPA-BP wear rate prediction model, with the optimal solution being 0.08181.

[0205] Based on the above conclusions, the BP neural network (PSO-FPA-BP) prediction model for the friction and wear performance of resin-based braking materials, which is based on the particle swarm optimization algorithm for flower pollination and optimization, established in Examples 1 and 2, has higher accuracy than the PSO-BP neural network model, the FPA-BP neural network model, and the unoptimized BP neural network model. This solves the problem of low training accuracy caused by the random initialization of initial weights and initial thresholds in the BP neural network when predicting friction and wear performance.

[0206] Furthermore, a comparison chart of the friction coefficient prediction results from the unoptimized BP neural network with the actual values ​​is shown below. Figure 3 As shown, the comparison between the friction coefficient prediction results based on the PSO-FPA-BP model proposed in this invention and the actual values ​​is not as effective. The comparison between the unoptimized BP neural network wear rate prediction results and the actual values ​​is shown in the figure below. Figure 4 As shown, the comparison between the wear rate prediction results based on the PSO-FPA-BP model proposed in this invention and the actual values ​​is not as effective.

[0207] From the perspective of convergence accuracy, although the number of iterations required to reach the optimal fitness function value is slightly more than some single optimization models, its final convergence result is significantly better, reflecting higher prediction accuracy and stronger generalization ability. Therefore, it can be concluded that the PSO-FPA-BP tribological performance prediction model outperforms other models. The development of the PSO-FPA-BP tribological performance prediction model has greatly shortened the time for material research and development and performance evaluation, and improved the efficiency of research and engineering practice.

[0208] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions and effects do not exceed the scope of the technical solution of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting the tribological properties of resin-based braking materials based on PSO-FPA-BP, characterized in that, The following steps are involved: Step S1: Prepare resin-based braking material and collect experimental data, including the material composition, friction coefficient and wear rate of the braking material, through friction and wear experiments; Step S2: Divide the dataset obtained from the friction and wear test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. Normalize the dataset to obtain the final friction and wear performance dataset of the braking material. Step S3: Build a BP neural network and determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network; Step S4: Use the initial weights and initial thresholds of each node of the BP neural network as the initial positions of the population in the particle swarm flower pollination hybrid optimization algorithm to find the optimal initial weights and optimal initial thresholds of the BP neural network. Step S5: Extract the optimal initial weights and optimal initial thresholds to train the normalized training set of the friction and wear test data, and use the trained brake material friction and wear performance prediction model to verify it using the test set.

2. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 1, characterized in that, Step S2 includes the following: Step S21: Divide the dataset obtained from the friction and wear test into a training set and a test set, with the training set accounting for 80% and the test set accounting for 20%. Step S22: Normalize the dataset using the mapminmax function. This function maps the dataset to the range (0, 1) for better model training and prediction. Normalization prevents the training process from being affected by excessively large or small values ​​of a particular variable. The formula for the mapminmax function is shown below: Among them, x norm This represents the normalized value, where x represents the original data. min and x max Let y represent the minimum and maximum values ​​of the feature in the current training data, respectively. max and y min These represent the maximum and minimum values ​​of the normalization target interval, respectively.

3. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 1, characterized in that, Step S3 includes the following: Step S31: Determine the number of nodes in the input layer of the BP neural network; In a BP neural network, the number of nodes in the input layer is equal to the dimension of the input vector. Step S32: Determine the number of output layer nodes of the BP neural network; wherein the number of output layer nodes is consistent with the number of prediction results, and the prediction results are the wear rate; Step S33: Determine the number of hidden layer nodes in the BP neural network, where the number of hidden layer nodes includes the following: Where N is the number of neurons in the hidden layer; m is the number of neurons in the input layer; n is the number of neurons in the output layer; and a is a constant between 1 and 10. Step S34: Set the basic parameters of the BP neural network, using the sigmoid function as the activation function for the hidden layer and the purelin function as the activation function for the output layer. This is a linear transfer function, meaning the neuron's input value equals its output value. The formula for the sigmoid function is shown below: Where x represents the input value of the hidden layer neuron, and f(x) represents the output value of the hidden layer neuron.

4. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 1, characterized in that, Step S4 includes the following: Step S41: Set the parameters of the particle swarm optimization algorithm, which include: learning factor, population size, and maximum number of iterations; Step S42: Encode the initial weights between each layer in the BP neural network and the initial thresholds of the hidden and output layers into particles in the particle swarm optimization algorithm. The sum of the number of initial weights and initial thresholds is used as the dimension of particle motion. Step S43: Import the training set from the dataset into the BP neural network for training, and then obtain the determination coefficient R of the predicted values ​​of the training set. 2 As an optimization objective, let the fitness function be denoted as (1-R). 2 The fitness function expression is as follows: in, y represents the predicted value from the training set. i Represents the true values ​​in the training set. This represents the average value of the true values ​​in the training set.

5. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 4, characterized in that, Step S4 also includes the following: Step S44: Initialize the lower and upper bounds of the search space and initialize the initial velocity of each particle; Step S45: Randomly initialize the positions of the particles in the particle swarm, where each position in the particle is a distribution of weights and thresholds of the neural network; Step S46: Calculate the fitness function according to the formula in Step S43, and use the fitness function obtained by the calculation in S43 as the fitness function of the particle swarm flower pollination hybrid optimization algorithm, and use this function as the optimization objective; Step S47: The iteration stage of the particles in the particle swarm; Import the data set divided into the training set into the BP neural network model for training, and then update the velocity and position of the particles according to the individual historical optimal solution and the global historical optimal solution during the training. The particle velocity and position update formulas include the following content. v i+1 =ω×v i +c1×rand()×(gbest i -x i )+c2×rand()×(zbest i -x i ) x i+1 =x i +v i+1 Among them, v i v is the velocity of the particle in the i-th iteration. i+1 c1 is the velocity of the particle in the (i+1)th iteration; c1 is the individual learning factor, which represents the particle's self-improvement ability; rand() is a random number between [0,1]; gbest i Let c1 be the local optimum position in the i-th iteration, and c2 be the global learning factor, representing the degree to which the particle moves towards the swarm optimum; zbest i Let x be the globally optimal position in the i-th iteration. i It is the position of the particle in the i-th iteration, x i+1 ω is the position of the particle in the (i+1)th iteration, and ω is the inertia weight factor.

6. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 5, characterized in that, Step S4 also includes the following content: Step S48: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue to iterate; otherwise, stop iterating; Step S49: Extract the population position after the iteration of the particle swarm optimization algorithm, and use this population position as the initial position of the pollen population in the flower pollination algorithm. After the initialization is completed, perform the iteration of the flower pollination algorithm.

7. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 6, characterized in that, Step S4 also includes the following content: Step S410: Execute the iteration stage of the flower pollination algorithm, including the following content: Step S4101: Simplify the flower pollination algorithm: Among them, it is considered that the pollination process of cross-pollination of plants follows Levy flight and conducts a global search process. Self-pollination of plants is equivalent to a local search process. Self-pollination and cross-pollination are controlled by a conversion probability P. When rand() < P, cross-pollination is performed, otherwise self-pollination is performed, where rand() is a random number uniformly distributed between [0,1], and P ∈ [0,1]; Furthermore, when rand() < P, cross-pollination is performed, and the cross-pollination includes performing a global search. The update formula for cross-pollination is as follows: Among them, g * The optimal pollen in the population, i.e., the current globally optimal solution. and Let represent pollen individuals of generation t+1 and generation t, respectively. The parameter L is an N-dimensional pollination intensity vector, where each dimension is a random number following a Levy distribution. The calculation formula is as follows: Among them, Γ(γ) is the standard gamma function, and s is the step size generated by the nonlinear transformation.

8. The method for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP according to claim 7, characterized in that, Step S4 also includes the following content: Step S4102: When rand() < P, self-pollination is performed, and the self-pollination includes performing a local search. The update formula for self-pollination is as follows: in, and These represent pollen individuals from generation t+1 and generation t, respectively. and It is different from the population Two random pollen individuals, where ε is a random number uniformly distributed on [0,1]. Step S411: Update the fitness and determine whether the maximum number of iterations is reached. If not, continue to iterate; otherwise, stop iterating and output the optimal pollen individual, which is the optimal initial threshold and optimal initial weight of the BP neural network optimized by the particle swarm flower pollination hybrid optimization algorithm.

9. A system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, comprising an electronic device, wherein the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a method for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP as described in any one of claims 1 to 8.

10. A system for predicting the friction and wear performance of resin-based braking materials based on PSO-FPA-BP, comprising a computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a method for predicting the friction and wear performance of resin-based brake materials based on PSO-FPA-BP as described in any one of claims 1 to 8.

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