Angular contact ball bearing protrusion prediction method based on particle swarm optimization BP neural network

Abstract

The invention discloses an angular contact ball bearing protrusion prediction method based on a particle swarm optimization BP neural network. The method comprises the steps of 1, creating a bearing parameter measurement data set; 2, determining influence factors of the protrusion amount through grey relational analysis; 3, constructing a basic protrusion prediction BP neural network; and 4, optimizing the BP neural network by using a particle swarm algorithm and an improved algorithm thereof: optimizing the initial weight and threshold value of the BP neural network by using the particle swarm algorithm so as to determine the optimal initial weight and threshold value. According to the method, the mapping relation between the part parameters and the protruding amount of the finished bearing is established, and the protruding amount of the combined finished bearing can be predicted only by obtaining the sizes of the parameters of the inner ring and the outer ring. The problem of low protruding amount measurement efficiency is solved, the end faces of the inner ring and the outer ring can be ground according to the prediction result, the bearing can be effectively prevented from being damaged in the disassembly and assembly process, and the pairing efficiency of the bearing is improved.

Description

Technical Field

[0001] The invention relates to a method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network. Background Art

[0002] Angular contact ball bearings are often used in pairs. Selecting two angular contact ball bearings with matching protrusions can simultaneously withstand axial and radial loads, increase bearing stiffness, improve rotation accuracy, reduce vibration and noise, and increase bearing service life. Protrusion is an important basis for the matching of angular contact ball bearings, which can greatly affect the matching efficiency, cost and quality.

[0003] In the current production process, when pairing angular contact ball bearings, a part of the rolling elements are pre-installed first, and the protrusion of the pre-installed bearings is detected using a protrusion measuring instrument. If the protrusions of the two bearings do not match, the pre-installed bearings can only be disassembled, and the end faces of the inner and outer rings of the disassembled bearings are ground according to the measurement results. After the grinding is completed, the inner and outer rings of the bearings, rolling elements and cages are put together to match the protrusions of the finished bearings.

[0004] This method has the following problems: when using a protrusion measuring instrument to detect the protrusion of a pre-assembled bearing, the detection efficiency is low; and the bearing is easily damaged during the disassembly and assembly process. At the same time, the disassembly and assembly process is time-consuming and complicated, which leads to low matching efficiency. Therefore, it is necessary to predict the protrusion of the bearing to avoid pre-assembly and disassembly and improve the assembly efficiency. Summary of the invention

[0005] The technical problem to be solved by the present invention is: in view of the problems of low detection efficiency and easy bearing damage when pairing angular contact ball bearings, a method for predicting the protrusion of angular contact ball bearings based on particle swarm optimization BP neural network is proposed.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network comprises the following steps:

[0008] Step 1: Create a bearing parameter measurement data set;

[0009] Step 2: Determine the influencing factors of protrusion through grey relational analysis;

[0010] Step 3: Construct a basic protrusion prediction BP neural network:

[0011] (1) Normalization of input data and output data;

[0012] (2) Denormalization of input and output data;

[0013] (3) Selection of transfer function and training function: The inner and outer ring widths, inner and outer ring groove positions, inner and outer ring groove curvature radii and inner and outer ring groove diameters of the angular contact ball bearing are used as input variables, and the measured value of the protrusion is used as the output variable. The excitation function from the input layer to the hidden layer adopts the logsig function, and the excitation function from the hidden layer to the output layer adopts the purelin function. A BP neural network prediction model for the protrusion of angular contact ball bearings is established, and the Levenberg-Marquardt optimization method is used as the training function to train the prediction model.

[0014] (4) Selection of the number of hidden layer nodes: When constructing the BP neural network angular contact ball bearing protrusion prediction model, a trial-based method is used to determine the most suitable number of hidden layer neurons;

[0015] (5) Determination of evaluation indicators: The root mean square error is used to evaluate the prediction accuracy of the model;

[0016] Step 4: Particle swarm and its improved algorithm optimize BP neural network: The particle swarm algorithm is used to optimize the initial weights and thresholds of the BP neural network, thereby determining the optimal initial weights and thresholds, and also determining the optimal BP neural network.

[0017] Bearing parameters include outer ring width, outer ring groove position, outer ring groove curvature, outer ring groove diameter, inner ring width, inner ring groove position, inner ring groove curvature and inner ring groove diameter.

[0018] The grey relational analysis in step 2 includes the following steps:

[0019] (1) Determine the sequence to be analyzed;

[0020] (2) Dimensionless transformation of original data;

[0021] (3) Calculate the absolute value of the difference, the maximum value of the difference, and the minimum value of the absolute value of the difference;

[0022] (4) Calculate the grey correlation coefficient;

[0023] (5) Calculate the grey relational degree;

[0024] (6) Sort the grey correlation degree.

[0025] In the construction process of the BP neural network in step 3, (3) the selection of transfer function and training function: the excitation function from the input layer to the hidden layer adopts the logsig function, and the excitation function from the hidden layer to the output layer adopts the purelin function, as shown in the following formula:

[0026]

[0027] purelin(x)=x (2)

[0028] The BP neural network prediction model of angular contact ball bearing protrusion is expressed as:

[0029]

[0030] The number of neurons in the hidden layer is 6. is the weight corresponding to the i-th input variable to the j-th hidden layer neuron, is the threshold value corresponding to the i-th hidden layer neuron, is the weight corresponding to the jth hidden layer neuron to the output layer, is the threshold of the output neuron, 1≤i≤8, 1≤j≤6;

[0031] The Levenberg-Marquardt optimization method is used as the training function, and the following weight correction formula is used to achieve fast optimization:

[0032] Δw=-(J T J+μI) -1 J T E (4)

[0033] Among them, Δw represents the correction amount of weights and thresholds, E is the prediction error, J represents the Jacobian matrix, that is, the first-order derivative matrix of the error function with respect to weights and thresholds, μ is an adjustment factor that controls the conversion of the search direction of the algorithm between gradient descent and Newton's method, and I is the identity matrix.

[0034] Determining the most appropriate number of hidden layer neurons consists of two stages:

[0035] ①. Estimate the theoretical range of the number of neurons in the hidden layer. The estimation formula is as follows:

[0036]

[0037] Where X is the estimated number of neurons in the hidden layer, m and n are the known numbers of neurons in the input layer and output layer, respectively, and a is a constant ranging from 1 to 10;

[0038] ② Within the estimated range, calculate each possible number of hidden layer neurons, apply it to the constructed neural network model, and determine the optimal number of hidden layer neurons through model fitting effect and performance testing.

[0039] In the construction process of the BP neural network in step 3, the calculation formula of (5) the root mean square error is as follows:

[0040]

[0041] In the formula, n represents the number of predicted data, x i represents the actual measured value of the protrusion of the i-th bearing, y i represents the predicted value of the protrusion of the i-th bearing.

[0042] In step 4, the entire construction steps of the particle swarm algorithm to optimize the BP neural network are as follows:

[0043] ① Construct the BP neural network structure: divide the measured data into input layer and output layer, set the initial weight and threshold range of the BP neural network, select the appropriate number of hidden layers, number of hidden layer nodes, transfer function, and determine the learning rate, maximum number of training times, and iteration termination accuracy of the BP neural network;

[0044] ② Establish the corresponding relationship between particles and the initial weights and thresholds of the neural network: In the particle swarm optimization algorithm, the dimension D of each particle corresponds to the sum of all weights and thresholds in the BP neural network;

[0045] ③ Initialize particle swarm parameters: determine the size of the population, initialize the speed and position of the particles, set the learning factor and inertia weight parameters;

[0046] ④ Particle swarm parameter update: particle update in the particle swarm, namely, update of initial weights and thresholds;

[0047] ⑤ Calculation of particle fitness: The root mean square error of the neural network test set is used as the fitness value. After determining the BP neural network structure, the BP neural network is trained according to the initial weights and thresholds represented by each particle in the particle swarm. After the training, the root mean square error of the model is calculated through the test set to obtain the particle fitness value.

[0048] ⑥ Update particle speed and position: If the fitness value after the individual position is updated is better than the current individual extreme value, then replace the current individual extreme value and update the speed and position; after all individuals in the population have completed the update, if the individual's optimal fitness value is better than the global extreme value of the current population, then update the global extreme value with the optimal fitness value;

[0049] ⑦ Output the optimal particle solution: After the iteration is completed, the initial weights and thresholds of the BP neural network optimized by the particle swarm algorithm can be obtained, and the optimal BP neural network can be output at the same time.

[0050] The inertia weight is an adaptive inertia weight:

[0051]

[0052] Among them, ω max is the maximum inertia weight, ω min is the minimum inertia weight, fitness IterFitness is the optimal fitness value of the population under the current number of iterations; Iter-1 is the optimal fitness value of the population within the previous iteration.

[0053] The present invention adopts the above technical solution to establish a mapping relationship between part parameters and the protrusion of the finished bearing. It is not necessary to fit the inner and outer rings together. Only by obtaining the sizes of some inner and outer ring parameters, the protrusion of the finished bearing after fitting can be predicted. It not only solves the problem of low efficiency in measuring the protrusion, but also can grind the end faces of the inner and outer rings according to the prediction results, and can also effectively avoid damage to the bearing during the disassembly and fitting process, thereby improving the matching efficiency of the bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is the grey relational analysis flow chart;

[0055] Figure 2 It is the technical roadmap of BP neural network;

[0056] Figure 3 It is the topological structure diagram of BP neural network;

[0057] Figure 4 This is the flow chart of particle swarm algorithm;

[0058] Figure 5 Optimize BP neural network flow chart for particle swarm algorithm. DETAILED DESCRIPTION

[0059] The present invention provides a method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network, comprising the following steps:

[0060] Step 1: Create a bearing parameter measurement data set;

[0061] Step 2: Determine the influencing factors of protrusion through grey relational analysis;

[0062] Step 3: Construct a basic protrusion prediction BP neural network;

[0063] Step 4: Particle swarm and its improved algorithm optimize BP neural network.

[0064] In step 1, when the preload and the size of the steel ball are determined, the protrusion of the angular contact ball bearing is determined by the size of the bearing parts and the geometric relationship between the parts. The main influencing factors include the outer ring width, outer ring groove position, outer ring groove curvature, outer ring groove diameter, inner ring width, inner ring groove position, inner ring groove curvature, and inner ring groove diameter. Therefore, it is necessary to measure the part parameters of a batch of bearing inner and outer rings, and then fit them together. After fitting, the protrusion of the finished bearing is measured and numbered to form a bearing parameter data set for the training and testing of the particle swarm optimization BP neural network. As shown in Table 1.

[0065] Table 1 - Bearing parameter data set

[0066]

[0067] n is the total number of groups of bearing data sets, which are divided into training sets and test sets. The training set is used for training the particle swarm optimization BP neural network, and the test set is used to verify the prediction accuracy of the network. For example, when n=200, 150 groups can be divided into training sets and 50 groups into test sets.

[0068] In step 2, grey relational analysis:

[0069] Firstly, the grey correlation analysis is used to select the factors that have a greater impact on the protrusion from the inner and outer circle parameters, which are used as the input variables of the subsequent BP neural network. The process of grey correlation analysis is shown in the attached figure. Figure 1 The specific steps are as follows:

[0070] (1) Determine the sequence to be analyzed. The dependent variable is the reference sequence X0, and the independent variable is the comparison sequence X. In the present invention, the dependent variable is the protrusion of the angular contact ball bearing, and the independent variable is the influencing factor of the protrusion. X0 and X are collectively referred to as the variable sequence, and X0 and X are as follows:

[0071] X0=(x 0,1 ,x 0,2 ,...,x 0,j ,...,x 0,n ) (6)

[0072]

[0073] In the formula, x 0,n is the protrusion of the nth workpiece; X i is the i-th impact factor sequence, x i,j is the measurement data of the i-th influencing factor of the j-th workpiece. There are 8 influencing factors of protrusion, so m=8, 1≤i≤8; 1≤j≤n, for example, n can be 200.

[0074] (2) Dimensionless transformation of original data. In this analysis, the mean change method is used to transform all data into dimensionless data. The processed variable sequence is denoted as X'0 and X'. The formula used in the processing is as follows:

[0075]

[0076] In the formula, is the average value of the protrusion and the eight influencing factors, y i,j It is the working condition data after normalization.

[0077] (3) Find the absolute value of the difference, the maximum value of the difference, and the minimum value of the difference. The absolute value of the difference refers to the absolute value of a certain observation object Δ i,j The absolute value of the difference between X'0 and X', that is

[0078] Δ i,j =|X' 0,j -X i ' ,j | (9)

[0079] The maximum absolute value of the difference:

[0080]

[0081] Minimum absolute value of the difference:

[0082]

[0083] (4) Calculate the grey correlation coefficient ξ i,j The correlation coefficient between the working condition data of the i-th influencing factor of the j-th workpiece and the protrusion of the angular contact ball bearing is calculated by the following formula:

[0084]

[0085] In the formula, ρ is the resolution coefficient, ρ∈(0,1), which is determined according to different background requirements, and is usually taken as ρ=0.5. i,j is a positive number less than 1, which reflects the i-th influencing factor X i and protrusion X 0,j The degree of association at the jth artifact.

[0086] (5) Calculate the grey relational degree γ i The correlation degree can be obtained by taking the average value of the correlation coefficient of each influencing factor in the comparison sequence, as shown in formula (8):

[0087]

[0088] In the formula, i = 1, 2, ..., 8, j = 1, 2, ..., n, generally speaking, γ i If it is greater than 0.5, it can be used as the input variable of the BP neural network protrusion prediction model.

[0089] (6) Sort the grey relational degree. i Sort from large to small, and judge the correlation between different influencing factors and the protrusion amount based on the sorting results. The higher the ranking, the stronger the correlation between the influencing factor and the protrusion amount, and vice versa.

[0090] Step 3: Construct a basic protrusion prediction BP neural network:

[0091] In the angular contact ball bearing protrusion prediction model, the BP neural network belongs to the subsequent data processing part, and its technical route is as shown in the attached Figure 2 As shown. Combining the trained network with the experimental data obtained from field measurements can realize the prediction of the protrusion of angular contact ball bearings. The establishment process of this model is to determine the network's training samples, test samples, input and output vectors, transfer functions, and training functions after experimental and theoretical analysis. After completing the network training, the test samples are used to test the prediction effect of the BP neural network model, and finally the prediction performance of the BP neural network is evaluated based on the test results. The construction process of the BP neural network is as follows:

[0092] (1) Normalization of input and output data

[0093] Data normalization is a process that normalizes input and output data with different magnitudes to the range of [0,1] through specific mathematical transformations. This process is mainly to optimize data processing efficiency and ensure the stability of algorithm performance. In the present invention, the range of input data and output data is normalized to the range of [0,1], using the Min-Max normalization method. The formula is:

[0094]

[0095] where y i is the normalized data, x i is the experimental data before processing. max 、x min are the maximum and minimum values ​​of the experimental data, respectively.

[0096] (2) Denormalization of input and output data

[0097] Since the data set is normalized before neural network training, in order to ensure the practicality of the network output and compatibility with actual production, these output data must be denormalized. This step is the key to restore the data to its original scale for effective use in actual application scenarios. The specific formula for denormalization is:

[0098] x i =y i (x max -x min )+x min (15)

[0099] where y i is the output data of the network, x i is the data after denormalization. max 、x min are the maximum and minimum values ​​of the experimental data, respectively.

[0100] (3) Selection of transfer function and training function

[0101] In the present invention, the inner and outer ring widths, inner and outer ring groove positions, inner and outer ring groove curvature radii and inner and outer ring groove diameters of the angular contact ball bearing are used as input variables, the measured value of the protrusion is used as the output variable, and the number of hidden layers is selected as 1. The excitation function from the input layer to the hidden layer adopts the logsig function, and the excitation function from the hidden layer to the output layer adopts the purelin function, as shown in the following formula:

[0102]

[0103] purelin(x)=x (17)

[0104] The BP neural network prediction model of angular contact ball bearing protrusion is expressed as:

[0105]

[0106] The number of neurons in the hidden layer is 6. is the weight corresponding to the i-th input variable to the j-th hidden layer neuron, is the threshold value corresponding to the i-th hidden layer neuron, is the weight corresponding to the jth hidden layer neuron to the output layer, is the threshold of the output neuron, 1≤i≤8, 1≤j≤6.

[0107] The present invention adopts the Levenberg-Marquardt (LM) optimization method as the training function. The LM algorithm does not need to calculate the Hessian matrix when adjusting the weights, which significantly accelerates the convergence speed of the BP neural network. The algorithm achieves rapid optimization through the following weight correction formula:

[0108] Δw=-(J T J+μI) -1 J T E (19)

[0109] Among them, Δw represents the correction amount of weights and thresholds, E is the prediction error, J represents the Jacobian matrix, that is, the first-order derivative (partial derivative) matrix of the error function with respect to weights and thresholds, μ is an adjustment factor that controls the conversion of the search direction of the algorithm between gradient descent and Newton's method, and I is the unit matrix.

[0110] (4) Selection of the number of hidden layer nodes

[0111] When constructing the BP neural network angular contact ball bearing protrusion prediction model, a trial-based method is used to determine the most suitable number of hidden layer neurons. This method is divided into two stages:

[0112] ①. Estimate the theoretical range of the number of neurons in the hidden layer. The estimation formula is as follows:

[0113]

[0114] Where X is the estimated number of neurons in the hidden layer, m and n are the known numbers of neurons in the input layer and output layer respectively, and a is a constant whose value ranges from 1 to 10.

[0115] ②. Within the estimated range, calculate the number of neurons in each possible hidden layer, apply it to the constructed neural network model, and determine the optimal number of neurons in the hidden layer through the model's fitting effect and performance test. For example, the final number of neurons in the hidden layer is selected as 6.

[0116] (5) Determination of evaluation indicators

[0117] The present invention uses Root Mean Square Error (RSME) to evaluate the prediction accuracy of the model.

[0118] The root mean square error (RMSE) is the square root of the average of the sum of the squares of the deviations between the predicted value and the true value, which is used to measure the deviation between the predicted value and the measured value. The calculation formula is as follows:

[0119]

[0120] In the formula, n represents the number of predicted data, x i represents the actual measured value of the protrusion of the i-th bearing, y i represents the predicted value of the protrusion of the i-th bearing.

[0121] For example, among 200 sets of data sets, 150 sets are selected as training sets for neural network training. After the training is completed, the other 50 sets are used as test sets, and the prediction accuracy of the neural network is evaluated by the RMSE of the test set.

[0122] Through the above process, the various parameters of the BP neural network are determined, and the final BP neural network topology is as shown in the attached figure. Figure 3 shown.

[0123] Step 4: Particle swarm and its improved algorithm optimize BP neural network:

[0124] The present invention uses a particle swarm algorithm to optimize the initial weights and thresholds of the BP neural network on the basis of constructing the BP neural network, thereby determining the optimal initial weights and thresholds, and also determining the optimal BP neural network. This method solves the problem that the BP network is prone to fall into a local optimal solution, and improves the prediction accuracy and prediction stability of the protrusion prediction model.

[0125] (1) Basic steps of particle swarm algorithm

[0126] The particle swarm algorithm (PSO) solves optimization problems in a multi-dimensional search space with its unique search strategy. The algorithm simulates the foraging behavior of a flock of birds, where each bird (particle) represents a potential solution. In the D-dimensional search space, the particle swarm consists of N particles, and the flight trajectory of each particle is determined by its velocity vector, and its performance is evaluated by the fitness function. During the iteration process, the particles adjust their flight direction and speed according to individual and group experience, and continuously approach the best position found by the individual (individual extreme value, pbest) and the best position in the group (global extreme value, gbest). This process continues, and the particles continuously iterate to find the global optimal solution, combining individual information and collective wisdom, effectively exploring the solution space, and finally reaching the optimal solution to the problem.

[0127] Assume that in a D-dimensional target search space, there are N particles forming a population, where the i-th particle is represented as a D-dimensional vector:

[0128] X i =(x i1 ,x i2 ,…,x iD ),i=1,2,…,N

[0129] The flying speed of the i-th particle is also a D-dimensional vector, recorded as:

[0130] V i =(v i1 ,v i2 ,…,v iD ),i=1,2,…,N

[0131] The optimal position searched by the i-th particle is called the individual extreme value, which is recorded as:

[0132] pbest=(p i1 ,p i2 ,…,p iD ),i=1,2,…,N

[0133] The global optimal position searched by the particle swarm is the global extreme value, which is recorded as:

[0134] gbest=(p g1 ,p g2 ,…,p gD )

[0135] After finding these two optimal values, the particle updates its velocity and position according to the following formulas (17) and (18):

[0136] v i+1=ω*v i +c1r1(pbest i -x i )+c2r2(gbest-x i ) (17)

[0137] x i+1 =x i +v i+1 (18)

[0138] Among them, ω is the inertia weight factor, c1 and c2 are learning factors, also known as acceleration constants, and their values ​​are all random numbers between (0, 2); r1 and r2 are uniform random numbers in the range of (0, 1); v i is the velocity vector of the particle, v i ∈[-v max ,v max ],v max is a constant, set according to the problem to be solved, used to limit the speed of the particle; pbest i is the current optimal position of the particle, i.e., the individual extreme value, gbest i is the current optimal position of the particle swarm, i.e. the global extreme value.

[0139] The basic particle swarm algorithm process is as follows Figure 4 As shown, the specific steps are as follows:

[0140] ① Initialize the particle swarm. Initialize the population size N, the speed, position and individual extreme value pbest of the particle swarm according to the problem to be solved. i and the global extreme value gbest i .

[0141] ② Calculate the fitness value of the particles. Select a suitable fitness function according to the objective function of the problem to be solved, and calculate the fitness value of the particles in the initial population.

[0142] ③ Update individual extreme value pbest i Compare the individual fitness value calculated in step ② with the individual extreme value pbest i If the new individual fitness value is better than the current individual extreme value, the individual extreme value is updated to the current position of the individual; otherwise, the existing individual extreme value is kept unchanged until a better individual fitness value is found.

[0143] ④Update the global extreme value gbest i . Compare individual extreme values ​​pbest i and the global extreme value gbest i, if the fitness of an individual extreme value is better than the current global extreme value, the optimal position of the individual is updated to the new global extreme value; otherwise, the current global extreme value is maintained until a better individual extreme value appears.

[0144] ⑤ Update the particle's speed and position. Update the particle's speed v according to the particle swarm algorithm speed and position update formulas (17) and (18) i and position x i .

[0145] ⑥ Determine whether the iteration is terminated. Determine whether the algorithm needs to terminate the iteration based on the set end condition. If the condition is not met, return to step ②, otherwise execute step ⑦.

[0146] ⑦ Output gbest. gbest is the global optimal solution obtained by searching with the PSO algorithm.

[0147] (2) Improvement of inertia weight of particle swarm algorithm

[0148] In the particle swarm optimization algorithm, the setting of the inertia weight ω is crucial, as it determines the inertia of the particles to maintain their current motion. In the standard velocity update formula of the particle swarm optimization algorithm, the inertia weight ω is often set as a fixed constant. However, this setting often fails to achieve the desired effect in practical applications, mainly because it does not effectively use the feedback information generated during the search process to dynamically adjust the algorithm parameters. Studies have shown that a larger inertia weight helps the algorithm to escape from the local optimal solution, while a smaller inertia weight is conducive to the local optimization of the algorithm.

[0149] In order to effectively use the feedback information obtained during the search process to correct the inertia weight, the present invention proposes an adaptive inertia weight adjustment formula:

[0150]

[0151] Among them, ω max is the maximum inertia weight, ω min is the minimum inertia weight, generally taken as ω max =0.9,ω min =0.4; fitness Iter Fitness is the optimal fitness value of the population under the current number of iterations; Iter-1 is the optimal fitness value of the population within the previous iteration.

[0152] The advantage of formula (19) is that the inertia weight can be adaptively adjusted by comparing the current optimal fitness value with the previous optimal fitness value. For smaller particles whose fitness values ​​are close to the global optimal solution, a smaller inertia weight is assigned to them, which promotes the particles to perform more refined local searches during their update process; for particles with larger fitness values ​​during the iteration process, a larger inertia weight is assigned to them, which increases their search range and helps the particles to jump out of the local minimum.

[0153] (3) Particle Swarm Optimization BP Neural Network

[0154] The whole construction process of particle swarm algorithm optimization BP neural network is shown in the attached figure. Figure 5 As shown, the specific steps are as follows:

[0155] ① Construct the BP neural network structure. Divide the measured data into input layer and output layer, set the initial weight and threshold range of the BP neural network, select the appropriate number of hidden layers, number of hidden layer nodes, and transfer function, and determine the learning rate, maximum number of training times, and iteration termination accuracy of the BP neural network.

[0156] ② Establish the corresponding relationship between particles and the initial weights and thresholds of the neural network. In the particle swarm optimization algorithm, the dimension D of each particle corresponds to the sum of all weights and thresholds in the BP neural network.

[0157] ③ Initialize the particle swarm parameters. Determine the size of the swarm, initialize the speed and position of the particles, and set parameters such as learning factor and inertia weight.

[0158] ④ Particle swarm parameter update: The particle update in the particle swarm is the update of initial weights and thresholds.

[0159] ⑤ Calculation of particle fitness. The present invention uses the root mean square error of the neural network test set as the fitness value. After determining the BP neural network structure, the BP neural network training is performed according to the initial weights and thresholds represented by each particle in the particle swarm. After the training is completed, the root mean square error of the model is calculated through the test set to obtain the particle fitness value.

[0160] ⑥ Update particle speed and position. If the fitness value after the individual position update is better than the current individual extreme value, replace the current individual extreme value and update the speed and position. After all individuals in the population have completed the update, if the individual's optimal fitness value is better than the global extreme value of the current population, the global extreme value will be updated with the optimal fitness value.

[0161] ⑦ Output the optimal particle solution. After the iteration is completed, the initial weights and thresholds of the BP neural network optimized by the particle swarm algorithm can be obtained, and the optimal BP neural network can be output at the same time.

Claims

1. A method for predicting the protrusion of angular contact ball bearings based on particle swarm optimization BP neural network, characterized in that: The steps include: Step 1: Create a bearing parameter measurement data set; Step 2: Determine the influencing factors of protrusion through grey relational analysis; Step 3: Construct a basic protrusion prediction BP neural network: (1) Normalization of input data and output data; (2) Denormalization of input and output data; (3) Selection of transfer function and training function: The inner and outer ring widths, inner and outer ring groove positions, inner and outer ring groove curvature radii and inner and outer ring groove diameters of the angular contact ball bearing are used as input variables, and the measured value of the protrusion is used as the output variable. The excitation function from the input layer to the hidden layer adopts the logsig function, and the excitation function from the hidden layer to the output layer adopts the purelin function. A BP neural network prediction model for the protrusion of angular contact ball bearings is established, and the Levenberg-Marquardt optimization method is used as the training function to train the prediction model. (4) Selection of the number of hidden layer nodes: When constructing the BP neural network angular contact ball bearing protrusion prediction model, a trial-based method is used to determine the most suitable number of hidden layer neurons; (5) Determination of evaluation indicators: The root mean square error is used to evaluate the prediction accuracy of the model; Step 4: Particle swarm and its improved algorithm optimize BP neural network: The particle swarm algorithm is used to optimize the initial weights and thresholds of the BP neural network, thereby determining the optimal initial weights and thresholds, and also determining the optimal BP neural network.

2. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: Bearing parameters include outer ring width, outer ring groove position, outer ring groove curvature, outer ring groove diameter, inner ring width, inner ring groove position, inner ring groove curvature and inner ring groove diameter.

3. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: The grey relational analysis in step 2 includes the following steps: (1) Determine the sequence to be analyzed; (2) Dimensionless transformation of original data; (3) Calculate the absolute value of the difference, the maximum value of the difference, and the minimum value of the absolute value of the difference; (4) Calculate the grey correlation coefficient; (5) Calculate the grey relational degree; (6) Sort the grey correlation degree.

4. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: In the construction process of the BP neural network in step 3, (3) the selection of transfer function and training function: the excitation function from the input layer to the hidden layer adopts the logsig function, and the excitation function from the hidden layer to the output layer adopts the purelin function, as shown in the following formula: purelin(x)=x (2) The BP neural network prediction model of angular contact ball bearing protrusion is expressed as: The number of neurons in the hidden layer is 6. is the weight corresponding to the i-th input variable to the j-th hidden layer neuron, is the threshold value corresponding to the i-th hidden layer neuron, is the weight corresponding to the jth hidden layer neuron to the output layer, is the threshold of the output neuron, 1≤i≤8, 1≤j≤6; The Levenberg-Marquardt optimization method is used as the training function, and the following weight correction formula is used to achieve fast optimization: Δw=-(J T J+μI) -1 J T E (4) Among them, Δw represents the correction amount of weights and thresholds, E is the prediction error, J represents the Jacobian matrix, that is, the first-order derivative matrix of the error function with respect to weights and thresholds, μ is an adjustment factor that controls the conversion of the search direction of the algorithm between gradient descent and Newton's method, and I is the identity matrix.

5. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: Determining the most appropriate number of hidden layer neurons consists of two stages: ①. Estimate the theoretical range of the number of neurons in the hidden layer. The estimation formula is as follows: Where X is the estimated number of neurons in the hidden layer, m and n are the known numbers of neurons in the input layer and output layer, respectively, and a is a constant ranging from 1 to 10; ② Within the estimated range, calculate each possible number of hidden layer neurons, apply it to the constructed neural network model, and determine the optimal number of hidden layer neurons through model fitting effect and performance testing.

6. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: In the construction process of the BP neural network in step 3, the calculation formula of (5) the root mean square error is as follows: In the formula, n represents the number of predicted data, x i represents the actual measured value of the protrusion of the i-th bearing, y i represents the predicted value of the protrusion of the i-th bearing.

7. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 1, characterized in that: In step 4, the entire construction steps of the particle swarm algorithm to optimize the BP neural network are as follows: ① Construct the BP neural network structure: divide the measured data into input layer and output layer, set the initial weight and threshold range of the BP neural network, select the appropriate number of hidden layers, number of hidden layer nodes, transfer function, and determine the learning rate, maximum number of training times, and iteration termination accuracy of the BP neural network; ② Establish the corresponding relationship between particles and the initial weights and thresholds of the neural network: In the particle swarm optimization algorithm, the dimension D of each particle corresponds to the sum of all weights and thresholds in the BP neural network; ③ Initialize particle swarm parameters: determine the size of the population, initialize the speed and position of the particles, set the learning factor and inertia weight parameters; ④ Particle swarm parameter update: particle update in the particle swarm, namely, update of initial weights and thresholds; ⑤ Calculation of particle fitness: The root mean square error of the neural network test set is used as the fitness value. After determining the BP neural network structure, the BP neural network is trained according to the initial weights and thresholds represented by each particle in the particle swarm. After the training, the root mean square error of the model is calculated through the test set to obtain the particle fitness value. ⑥ Update particle speed and position: If the fitness value after the individual position is updated is better than the current individual extreme value, then replace the current individual extreme value and update the speed and position; after all individuals in the population have completed the update, if the individual's optimal fitness value is better than the global extreme value of the current population, then update the global extreme value with the optimal fitness value; ⑦ Output the optimal particle solution: After the iteration is completed, the initial weights and thresholds of the BP neural network optimized by the particle swarm algorithm can be obtained, and the optimal BP neural network can be output at the same time.

8. The method for predicting the protrusion of an angular contact ball bearing based on a particle swarm optimization BP neural network according to claim 7, characterized in that: The inertia weight is an adaptive inertia weight: Among them, ω max is the maximum inertia weight, ω min is the minimum inertia weight, fitness Iter Fitness is the optimal fitness value of the population under the current number of iterations; Iter-1 is the optimal fitness value of the population within the previous iteration.

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