Tire three-way force prediction method based on piezoelectric intelligent tire technology and BKA-GPR

Abstract

The invention discloses a tire three-way force prediction method based on a piezoelectric type intelligent tire technology and a BKA-GPR. A finite element model of a tire and a PVDF (polyvinylidene fluoride) sensor is constructed, and a piezoelectric type intelligent tire model is established in combination with an Inp fusion method; through global sensitivity analysis, sensitivity of changes of a longitudinal force (Fx), a lateral force (Fy) and a vertical force (Fz) to voltage output of the PVDF sensor at different positions in the tire is evaluated, and the optimal installation position of the sensor is determined. A Sobol method is used for collecting a voltage-tire force data set, and extraction and normalization processing are carried out on signals of the ground mark area; the method comprises the following steps of: designing a tire force Gaussian process regression (GPR) model according to data characteristics, and optimizing hyper-parameters of the model through a black-wing kite algorithm (BKA); the optimal input features and the data scale are determined through a random forest (RF) algorithm, and a tire three-way force prediction model which is low in cost, high in precision and good in stability and generalization performance can be obtained by retraining the model.

Description

Technical Field

[0001] The present invention relates to the fields of vehicle control technology and machine learning, and in particular to a piezoelectric intelligent tire technology and a BKA-GPR tire triaxial force prediction method. Background Art

[0002] The control of vehicle motion is essentially the control of tire forces. Therefore, the tire forces, especially the three-dimensional forces (longitudinal force F x , lateral force F y and vertical force F z ) is the premise for keeping the actual motion state of the vehicle consistent with the ideal motion state at all times. The current cost of direct tire force measurement is very high, and it is difficult to carry out comprehensive commercial applications. Therefore, many experts and scholars have developed a variety of tire force estimation methods based on different technologies, among which the more famous ones are tire force prediction methods based on sliding mode observers, Kalman filters, and least squares methods. These methods will use vehicle / tire models to a greater or lesser extent, which will lead to a common problem that it is difficult to achieve a reasonable balance between tire force solution accuracy and solution efficiency. In other words, although the use of simplified vehicle / tire models can meet the tire force estimation requirements under most driving conditions, when the vehicle is in extreme driving conditions (such as high-speed large corners or wet and slippery road driving, etc.), the simplified vehicle / tire model is difficult to accurately represent the actual motion behavior of the vehicle, making it difficult to guarantee the performance of the tire force prediction methods built based on these models. Although the use of more complex vehicle / tire models can improve the prediction performance of these tire force prediction methods, this will also increase the complexity of the prediction system and increase the prediction time, making it difficult to meet the real-time requirements of the vehicle control system.

[0003] Smart tire technology is to install sensors inside the tire, directly measure the dynamic parameters of the tire during movement, and combine machine learning or theoretical models to estimate the key state of the tire. Compared with traditional tire state estimation methods, this technology can obtain more accurate and reliable tire states. Therefore, if the prediction of tire force can be achieved based on smart tire technology, the process of traditional tire force prediction methods can be simplified, and the estimation accuracy and reliability of tire force can be improved, especially the estimation accuracy and reliability of tire force under extreme driving conditions, so as to achieve the purpose of improving the overall performance of the vehicle control system. Although many scholars have proposed some tire force prediction methods based on smart tire technology, there are still some areas that can be optimized, mainly including the improvement of the signal acquisition quality of the smart tire system and the optimization of the mapping relationship between signal features and tire forces. In terms of signal acquisition, the current field of smart tire force prediction lacks sufficient theoretical support for the scientific selection of sensor installation positions, and it is difficult to ensure the continuous and high-quality acquisition of tire dynamic features during tire operation. In terms of mapping relationship construction, many links in the signal feature selection used in the current smart tire force prediction still rely on artificial experience methods, and it is impossible to ensure that the selected features are widely representative, thereby affecting the accuracy of the signal feature-tire force mapping relationship constructed based on these features. In addition, too much or too little training data size and incorrect selection of mapping methods can also lead to poor performance of the final tire force prediction model. Summary of the invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to provide a tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR in response to the above-mentioned deficiencies in the prior art, taking into account the selection of the optimal installation position of the PVDF sensor inside the tire, and using a wrapper method based on an intelligent algorithm to screen the optimal features, and training a GPR tire three-axis force prediction model based on BKA optimization with the optimal scale of training data.

[0005] Technical solution: A tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR, including the following steps:

[0006] S1. Establish finite element models of tire and PVDF sensor, and on this basis use Inp fusion method to construct finite element model of piezoelectric intelligent tire;

[0007] S2. Design a simulation scheme for calculating the first-order main effect index, select the calculation features, calculate the first-order main effect index of tire force and PVDF output voltage, and determine the optimal installation position of the sensor;

[0008] S3. Design a voltage-tire force data set simulation condition based on the Sobol method, collect PVDF output voltage and tire force data and perform data preprocessing to form a data set that can be used for training and testing;

[0009] S4. Based on the characteristics of the voltage-tire force data set, the mean function and covariance function type of the GPR model are selected to construct a general training process for the GPR tire force prediction model;

[0010] S5, using BKA to optimize the GPR model obtained in step S4 by a hyperparameter optimization method to obtain a BKA-GPR model;

[0011] S6. Based on the BKA-GPR model obtained in step S5, determine the optimal input features and the optimal training data set size, and retrain the tire force prediction model;

[0012] S7, input the optimal voltage feature into the tire force prediction model after retraining in step S6, output the normalized prediction value of the tire force and its variance, and then obtain the actual prediction value of the tire force through denormalization.

[0013] Step S1 specifically includes the following steps:

[0014] S1-1. Establish a tire finite element model, calibrate its accuracy through a stiffness test, and then output its Inp code;

[0015] S1-2, establish a finite element model of the PVDF sensor, calibrate its accuracy through a single cantilever beam experiment, and then output its Inp code;

[0016] S1-3, integrate the Inp code of the tire finite element model and the PVDF sensor finite element model, set boundary conditions and constraints to form a piezoelectric smart tire finite element model, and calibrate its accuracy through real vehicle experiments.

[0017] Step S2 specifically includes the following steps:

[0018] S2-1. Determine the influencing factors and value range of the output voltage of the PVDF sensor in the piezoelectric intelligent tire according to daily driving conditions, and design the voltage-tire force data set simulation matrix SC based on the definition form of the first-order main effect index calculation scheme based on the global sensitivity analysis theory optimized by the multiplication dimensionality reduction method, and write it as:

[0019]

[0020] in, It represents the median of each influencing factor within its value range. The specific values ​​of BL1, BL2, BL3, ..., BLn can be calculated by the five-node Gaussian value formula, written as:

[0021]

[0022] Where a and b are the upper and lower limits of the influencing factor BL(i), respectively. t (t=1,2,3,4,5) are the node values ​​of the five-node Gaussian value formula;

[0023] S2-2. According to the tire force generation mechanism, the voltage value at the q (q>0) specific position on the PVDF sensor output voltage curve is selected as the first-order main effect indicator (FMEI) to calculate the characteristic value; the selection logic of the specific position is: taking the tire-ground contact center point as a reference, select the q (q>0) voltage values ​​on the PVDF sensor output voltage curve along this point to both sides of the tire circumference at intervals of η° (η>0). At this time, the calculated characteristic value vector VC of the PVDF sensor voltage curve at the j (j=1,2,..,62)th sensor installation position is j It can be expressed as:

[0024]

[0025] in, and are the 1st, 2nd and qth calculated characteristic value points of the PVDF sensor voltage curve at the jth sensor installation position respectively;

[0026] S2-3, the average value of the FMEI of all the calculated characteristic points contained in the voltage signal curve collected at the j-th sensor installation position is taken as the final FMEI of the position, recorded as MFMEI; at this time, the MFMEI of the tire force and the output voltage of the PVDF sensor at the j-th installation position can be expressed as:

[0027]

[0028] When the superscript Δ of MFMEI is 1, 2 or 3, it represents the NFMEI of longitudinal, transverse and vertical forces. The calculation formula can be further written as:

[0029]

[0030] in, is the origin moment value corresponding to the jjth calculated eigenvalue of the voltage signal at the jth sensor installation position when the influencing factor is BL(i), k = 1 or 2, indicating the first-order or second-order origin moment, w t is the weight of the five-node Gaussian value formula, PVDF_IT FEM (·) is the solution equation for the output voltage of the PVDF sensor in the finite element model of the piezoelectric smart tire;

[0031] S2-4. After calculating the tire force and output voltage MFMEI corresponding to all potential installation positions of the PVDF sensor in the tire, a screening index is set, and the position greater than the set screening index is used as the sensor installation position. p (p>0) installation positions that meet the conditions are screened out to achieve the selection of the optimal installation position of the PVDF sensor, and the piezoelectric intelligent tire finite element model is reconstructed.

[0032] Step S3 specifically includes the following steps:

[0033] S3-1. Generate an m×n (m>0, n>0) dimensional sampling sequence matrix qs based on the Sobol method. Combined with the value range of each influencing factor set in step S2-1, calculate the specific value of each influencing factor in each dimension of the data set simulation matrix. The value formula is:

[0034] st λ =varmin+qs λ (varmax-varmin)

[0035] Among them, st λ is the λth (λ>0) n-dimensional simulation value vector, qs λ is the λth n-dimensional sampling vector in the sampling sequence matrix qs, varmax and varmin are two n-dimensional vectors composed of the upper and lower limits of the value range of each influencing factor; finally, the longitudinal force (F x ), lateral force (F y ) and vertical force (F z ) of three m×n dimensional voltage-tire force data set simulation matrices;

[0036] S3-2, using the piezoelectric smart tire finite element model reconstructed in step S2-4 to calculate the three m×n dimensional voltage-tire force data set simulation matrices obtained in step S3-1, and extract the PVDF sensor output voltage VT0 l and tire force data Data_F l , where l = x / y / z, representing the longitudinal, transverse and vertical directions of the tire respectively;

[0037] S3-3, using the feature extraction method in step S2-2 to extract VT0 l Perform feature extraction to obtain voltage data set VT1 l On this basis, the linear normalization theory is used to VT1 l and Data_F l Perform normalization to obtain the normalized data set VT1 norl and Data_F norl , the normalized expression is:

[0038]

[0039] Among them, VT1 norl (i,j) represents VT1 norl The data in row i and column j in VT1 l (i,j) is VT1 l The data in row i and column j in VT1 minl and VT1 maxl VT1 l The minimum and maximum values ​​in Data_F norl (i,j) is Data_F norl The data in row i and column j in Data_F l (i,j) is Data_F l The data in row i and column j in Data_F minl and Data_F maxl They are Data_F l The minimum and maximum values ​​in ;

[0040] S3-4, take VT1 norl and Data_F norl The first 85% of is used as the training set, defined as and Take the last 15% as the test set, defined as and

[0041] Step S4 specifically includes the following steps:

[0042] S4-1, according to VT1 norl and Data_F norl The data characteristics are combined with the empirical method to determine the form of the mean function and covariance function, written as:

[0043] m(x)=E[f(x)]

[0044]

[0045] Where f(x) is the latent function, which represents VT1 norl Input x corresponding to the tire force Data_F norl , E is the mathematical expectation, is the signal variance, M = diag(η 2 ), η is the variance scale, is the noise variance, δ ij is the Kronecker delta function; in this case, the hyperparameter set θ can be written as

[0046] S4-2, based on VT1 obtained in step S3-3 norl and Data_F norl , a general training method for tire force GPR prediction model is designed.

[0047] In step S4-2, the general training method of the tire force GPR prediction model is:

[0048] First, using VT1 obtained in step S3-4 norl and Data_F norl , the tire force prior distribution function is obtained as follows:

[0049]

[0050] Then, based on the principle of Gaussian process for joint prior distribution, combined with the established prior distribution function, the extracted data in step S3-4 are used to and The joint prior distribution can be obtained and written as:

[0051]

[0052] in, is the test set input With the input of the training set The n×1 order covariance matrix between is the covariance of the test set into and out of itself, I n is the n-dimensional identity matrix;

[0053] Furthermore, the predicted value can be calculated The posterior distribution of is:

[0054]

[0055] in, is the predicted mean, that is, the predicted value, is the variance corresponding to the predicted value, which can be further expressed as:

[0056]

[0057]

[0058] Furthermore, the value of the hyperparameter set θ can be obtained by maximizing the log-likelihood function, which is written as:

[0059]

[0060] in, After obtaining the value of θ, substitute it back into and The normalized tire force prediction value can be obtained and its variance

[0061] Finally, the tire force prediction value can be solved by linear denormalization theory: Written as:

[0062]

[0063] Step S5 specifically includes the following steps:

[0064] S5-1, initialize BKA parameters, including population size pop, maximum number of iterations T, dimension dim of feasible solution, and corresponding upper and lower limits ub and lb;

[0065] S5-2. Initialize the initial positions of the individuals in the black-winged kite population, i.e., the initial solution θ, and the fitness, i.e., the negative log-likelihood function value corresponding to the initial solution θ. The initial position P of the individuals is expressed as:

[0066] P=rd pop,dim ·(ub-lb)+lb

[0067] Among them, rd is a random number in [0,1]. After the initial position of the individual in the population is calculated, substitute it into the log-likelihood function to calculate its negative value as the individual fitness value. After the initial position and fitness of all individuals in the population are calculated, find the individual with the minimum fitness as the leader of the black-winged kite population to lead the flight direction of the entire population, that is, the search direction of the global optimal solution of θ.

[0068] S5-3. Simulate the attack behavior of black-winged kites to calculate the individual position. The formula is:

[0069]

[0070] in, and denote the position of the bjth dimension of the bith black-winged kite in the tth and (t+1th) iterations, respectively. p is a constant with a value of 0.9. t is the number of iterations completed so far. The coefficient After the individual position is updated, it is necessary to use [ub, lb] to constrain the value range of the hyperparameter θ, and then use the θ value after the range constraint to calculate the negative log-likelihood function value and compare it with the function value of the current individual. If it is less than, update the individual position and function value, otherwise do not update;

[0071] S5-4. Calculate the individual position by imitating the migration behavior of black-winged kites. The formula is:

[0072]

[0073] in, represents the fitness of the bj-th dimensional black-winged kite leader at the t-th iteration so far, that is, the optimal solution of the current population, C(0,1) represents the Cauchy mutation, and the coefficient After the individual position is updated, it is necessary to use [ub, lb] to constrain the range of θ values, and then use the constrained θ value to calculate the negative log-likelihood function value and compare it with the function value of the current individual. If it is less than, update the individual position and function value, otherwise do not update;

[0074] S5-5, population optimal fitness and position update; when one iteration of the population is completed, if the optimal fitness of the population in this iteration is better than the optimal fitness of the population searched so far, it is replaced with the optimal fitness of the population in this iteration, and the corresponding optimal position of the population is updated; the optimal position of the population is the optimal θ of the GPR model;

[0075] S5-6, loop calculation; return to step 3, loop calculation until the convergence condition is met or the maximum number of iterations is reached; finally, substitute the optimal θ solution searched by BKA back into the GPR model to obtain the BKA-GPR tire force prediction model.

[0076] Step S6 specifically includes the following steps:

[0077] S6-1. Define the set DS = {(x u ,y u )|u=1,2,3,…,m}=(VT1 norl ,Data_F norl ), where: x u ∈R n is the n-dimensional input vector, i.e., the voltage value of the PVDF sensor, y u ∈R is the value corresponding to x u The output scalar, i.e., tire force, the m×n dimensional input matrix can be expressed as X=[x1,x2,…,x m ];

[0078] S6-2. Use the bootstrap method to repeatedly extract b (b>0) sub-sample sets from the original training data set with replacement, thereby constructing b regression trees, where the ψth feature (ψ>0) in the b sub-sample set can be defined as X ψ On this basis, the prediction performance of the model is evaluated by the prediction accuracy of out-of-bag data to form an error matrix, which is written as:

[0079]

[0080] S6-3, based on the error matrix obtained in step S6-2, calculate all the features X ψThe average reduction in error is the importance score, and they are arranged in descending order; the calculation formula is:

[0081]

[0082] S6-4, using the sequence forward search strategy to add the features with the highest importance score in the current input feature set one by one, pass them to the optimized GPR tire force prediction model obtained in step S5-5 for training, and test to obtain the prediction error of the current input feature set until all input features are traversed; finally, the input feature set with the smallest prediction error is used as the optimal input feature set, and the data set is and Perform optimal feature screening to obtain and

[0083] S6-5, based on the training set after the optimal feature extraction processing obtained in step S6-4, extract the training data set in 5% increments and submit it to step S5-5 to optimize the GPR tire model for training, and use the test set for testing until all the data in the training data set are extracted as the training data set, and record each test error; finally, the training data scale with the smallest prediction error is used as the optimal training data scale;

[0084] S6-6. Based on the obtained training data set with optimal input features and optimal data size, the general training method of the designed BKA-GPR tire force prediction model is combined to retrain F x 、F y and F z Predictive models.

[0085] Step S7 specifically includes the following steps:

[0086] S7-1, based on the retrained BKA-GPR tire three-axis force prediction model obtained in step S6-6, use As the input of the BKA-GPR tire force prediction model, the normalized tire force prediction value is output and its variance On this basis, the actual predicted value of tire force can be obtained by denormalization.

[0087] S7-2. Calculate the confidence interval of the tire force prediction value to quantify the uncertainty of the tire force prediction value.

[0088] It is characterized in that, in step S7-2, the confidence interval calculation formula is:

[0089]

[0090] Wherein, upper is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, lower is the lower limit vector of the confidence interval corresponding to the tire force prediction vector, and t o is the confidence interval coefficient.

[0091] Beneficial effects: The finite element model of the piezoelectric intelligent tire was established through finite element software, which greatly reduced the time and financial costs required for the scientific selection of the PVDF sensor installation position in the tire and the extraction of training data for the tire three-axis force prediction algorithm;

[0092] Based on the global sensitivity analysis theory, the sensitivity of the longitudinal, lateral and vertical force changes of the tire during operation to the output voltage of the PVDF sensor is measured, and the optimal installation position of the sensor is determined based on this, which can improve the signal acquisition quality of the intelligent tire system.

[0093] A wrapper method based on the RF algorithm is designed to screen input features, which effectively avoids the influence of human subjective factors in the feature screening process and is beneficial to screening out more representative signal features;

[0094] Based on the Sobol method, a uniformly distributed voltage-tire force data set was collected, and the optimal tire force prediction model training data set size was determined by combining the step-by-step increase method of the training set, which helps to improve the prediction model training effect;

[0095] A GPR tire force prediction model training process based on BKA optimization was designed to enhance the global and local search capabilities for the optimal solution of hyperparameters during GPR model training, which is beneficial to improving the prediction performance of the tire force GPR prediction model.

[0096] Compared with the traditional tire force prediction method, the tire force estimation algorithm proposed in the present invention has low cost, simple estimation process, high prediction accuracy, good stability and good generalization. In addition, the tire force prediction model can well complete the prediction of test data by relying on only a small data set, and can not only output the tire force prediction value, but also quantify the uncertainty of the output prediction value, which can better serve the optimization design of the subsequent vehicle control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 This is a flow chart of an embodiment of the piezoelectric intelligent tire technology and the BKA-GPR tire three-axis force prediction method in the patent of this invention.

[0098] Figure 2 This is the modeling process of the piezoelectric smart tire finite element model in the patent of this invention.

[0099] Figure 3 This is a schematic diagram of the installation position of the PVDF sensor during the verification of the finite element model of the smart tire in the patent of this invention.

[0100] Figure 4 The PVDF-M voltage curve and ground pressure curve when the tire rolls one circle.

[0101] Figure 5 This is a schematic diagram of the tire inner liner sensor installation location.

[0102] Figure 6 Calculation results of the first-order main effect index for different sensor installation positions when the longitudinal force changes.

[0103] Figure 7 Calculation results of the first-order main effect index for different sensor installation positions when the lateral force changes.

[0104] Figure 8 Calculation results of the first-order main effect index for different sensor installation positions when the vertical force changes.

[0105] Fig. 9 Screening results of optimal voltage feature set for longitudinal force prediction model.

[0106] Fig.10 Screening results of optimal voltage feature set for lateral force prediction model.

[0107] Fig.11 Screening results of the optimal voltage feature set for the vertical force prediction model.

[0108] Fig.12 Results were determined for the optimal training data size for the longitudinal, lateral, and vertical force prediction models.

[0109] Fig.13 High-adhesion-high-speed prediction results of the longitudinal, lateral and vertical force prediction models under double lane-shifting conditions.

[0110] Fig.14 These are the low-adhesion and medium-speed prediction results of the longitudinal, lateral and vertical force prediction models under double lane-shifting conditions. DETAILED DESCRIPTION

[0111] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0112] like Figure 1 As shown, a tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR includes the following steps:

[0113] S1. Establish finite element models of tire and PVDF sensor, and on this basis use Inp fusion method to construct finite element model of piezoelectric intelligent tire;

[0114] Figure 2 The process of establishing a piezoelectric smart tire finite element model of the present invention is demonstrated, including independent finite element modeling of tires and PVDF sensors and fusion of the Inp code of the two to generate a piezoelectric smart tire finite element model. First, a structural analysis is performed on the tire and PVDF sensor to draw their three-dimensional models, and a material property analysis is performed to extract material parameters. Then, the three-dimensional structural models of the two are respectively meshed, and materials are assigned, etc. to construct their finite element models. Next, the accuracy of the two finite element models is verified by tire stiffness experiments and piezoelectric material cantilever beam experiments, respectively. When their average absolute percentage errors are less than 10%, their Inp codes are generated, otherwise their finite element models are reconstructed and calibrated. Finally, based on the tire Inp and PVDF sensor Inp, a piezoelectric smart tire finite element model is generated by the Inp fusion method. At the same time, the accuracy of the model is verified by actual vehicle tests. Figure 3 As shown in the figure, during the verification process, the PVDF sensors in the experimental equipment and finite element model were installed at the longitudinal symmetrical center line of the tire, the bilaterally symmetrical shoulders and the bilaterally symmetrical sidewalls, and were named PVDF-M, PVDF-L1, PVDF-L2, PVDF-R1 and PVDF-R2 respectively. When the average absolute percentage error of the PVDF output voltage of the piezoelectric smart tire finite element model and the actual vehicle test platform under the straight free rolling condition is less than 10%, the model is saved, otherwise the piezoelectric smart tire finite element model is regenerated and calibrated.

[0115] S2. Design a simulation scheme for calculating the first-order main effect index, select the calculation features, calculate the first-order main effect index of tire force and PVDF output voltage, and determine the optimal installation position of the sensor;

[0116] In order to make the final selected PVDF sensor installation position have better adaptability to working conditions, it is necessary to consider as many factors as possible that may affect the output voltage of the PVDF sensor during actual vehicle driving when designing the first-order main effect index calculation simulation scheme. x 、F y and F z Prediction model, therefore, the influencing factors considered include tire slip rate, sideslip angle, vertical load, road adhesion coefficient, vehicle speed and tire pressure, and the value range of each influencing factor as shown in Table 1 is determined according to the daily vehicle driving state.

[0117] Table 1: Value ranges of various influencing factors

[0118]

[0119] At this time, referring to the definition of the first-order main effect index calculation scheme based on the global sensitivity analysis theory optimized by the multiplication dimensionality reduction method, the tire force first-order main effect index simulation scheme SC can be written as:

[0120]

[0121] Among them, BL1, BL2, BL3, BL4, BL5 and BL6 are tire slip rate, side slip angle, vertical load, road adhesion coefficient, vehicle speed and tire pressure respectively. and They represent the median of the above-mentioned influencing factors within their value ranges. The specific values ​​of BL1, BL2, BL3, BL4, BL5 and BL6 can be calculated by the five-node Gaussian value formula, written as:

[0122]

[0123] Where a and b are the upper and lower limits of the influencing factor BL(i), respectively. t (t = 1, 2, 3, 4, 5) are the node values ​​of the five-node Gaussian value formula. The specific values ​​can be seen in Table 2. Finally, by combining equations (1) and (2) and Tables 1 and 2, a 30 × 6 dimensional first-order main effect index calculation simulation numerical matrix can be obtained.

[0124] Table 2: Five-node Gauss-Langerangian Gauss integral table

[0125]

[0126] Selection of calculated characteristic values: During the rolling process of the tire, the voltage signal collected by the PVDF sensor is a time series signal, that is, it is composed of countless voltage value points and cannot be directly used to calculate the first-order main effect index (FMEI). Therefore, it is necessary to extract several specific voltage values ​​on a single voltage curve in order to calculate the FMEI. In view of the fact that the purpose of the present invention is to predict tire force, and tire force is mainly generated by the relative sliding between the tire-ground contact surface, the voltage value points of the voltage curve located in the contact footprint are mainly selected as the calculated characteristic values. Figure 4The voltage curve collected by PVDF-M when the tire rolls one circle is shown. The interval L3 between the two peak values ​​of the second-order derivative of the signal is closest to the interval between the trough values ​​on both sides of the Cpress curve (i.e., the tire angle interval occupied by the tire contact patch area), which means that the voltage curve can be identified in the contact patch based on this feature. Similarly, the voltage curve collected by sensors at other installation positions can also be used to identify the signal of the contact patch part according to this feature. In order to eliminate the influence of vehicle speed changes on the total amount of voltage signal sampling, the present invention calculates the voltage value of a specific tire angle position in the contact patch as a calculated characteristic value based on the voltage curve of the contact patch area obtained by the online interpolation method. When extracting specific voltage value points, the center of the contact patch (i.e., the tire angle position corresponding to the peak value of the PVDF-M voltage curve) is specified as 0°, and 15 voltage value points are extracted on both sides at intervals of 1.5° by interpolation as calculated characteristic values, for a total of 31 calculated characteristic values. In addition, by Figure 5 It can be seen that a single tire pitch will repeatedly pass through the contact area when the tire rolls, so it is only necessary to calculate the FMEI of all potential sensor installation positions in the lateral direction of a single pitch. In order to simplify subsequent calculations, the present invention quantifies and names all possible installation positions of PVDF sensors on a single tire pitch through a grid (see Figure 5 ). At this time, the calculated eigenvalue vector VC of the PVDF sensor voltage curve at the jth sensor installation position j It can be expressed as:

[0127]

[0128] in, are the 31 calculated eigenvalues ​​of the PVDF sensor voltage curve at the jth sensor installation position.

[0129] Calculation of the first-order main effect index: The average value of the FMEI of all the calculated characteristic points contained in the voltage signal curve collected at the j-th sensor installation position is taken as the final FMEI of the position, recorded as MFMEI. At this time, the MFMEI of the tire force and the output voltage of the PVDF sensor at the j-th installation position can be expressed as:

[0130]

[0131] When the superscript Δ of MFMEI is 1, 2 or 3, it represents the NFMEI of longitudinal, transverse and vertical forces. The calculation formula can be further written as:

[0132]

[0133] in, is the origin moment value corresponding to the jjth calculated eigenvalue of the voltage signal at the jth sensor installation position when the influencing factor is BL(i), k = 1 or 2, indicating the first-order or second-order origin moment, w t is the weight of the five-node Gaussian value formula, which can be obtained from Table 2, PVDF_IT FEM (·) is the solution equation for the output voltage of the PVDF sensor in the finite element model of the piezoelectric smart tire.

[0134] PVDF sensor installation location selection: Figure 6 , 7 Figures 1 and 2 respectively show the numbers of the first 10 positions of the MFMEI corresponding to all installation positions of a single tire pitch corresponding to the longitudinal, lateral and vertical forces of the tire when arranged in descending order. In this example, the positions corresponding to the first four lateral numbers of the tire three-axis force NFMEI calculation results are selected as the optimal installation positions of the PVDF sensor. The lateral numbers of the optimal installation positions corresponding to the longitudinal force are 2, 59, 51 and 10, the lateral numbers of the optimal installation positions corresponding to the lateral force are 10, 51, 49 and 12, and the lateral numbers of the optimal installation positions corresponding to the vertical force are 24, 37, 44 and 17. On the basis of obtaining the optimal installation position of PVDF, the finite element modeling method in step S1 is used to reconstruct the piezoelectric smart tire finite element model to readjust the installation position of the sensor.

[0135] S3. Design a voltage-tire force data set simulation condition based on the Sobol method, collect PVDF output voltage and tire force data and perform data preprocessing to form a data set that can be used for training and testing;

[0136] First, a 3000×6-dimensional sampling sequence matrix qs is generated based on the Sobol method, where 3000 is the total amount of data in the voltage-tire force data set, and 6 is the total number of factors affecting the PVDF output voltage. Then, based on the value range of each influencing factor in Table 1, the specific value of each influencing factor in each dimension of the data set is calculated in combination with the Sobol sampling value formula. The value formula is:

[0137] st λ =varmin+qs λ (varmax-varmin) (6)

[0138] Among them, st λ is the λth 6-dimensional simulation value vector, qs λ is the λth 6-dimensional sampling vector in the sampling sequence matrix qs, varmax and varmin are two 6-dimensional vectors composed of the upper and lower limits of the value range of each influencing factor. Finally, we can get the values ​​representing F x 、F y and F zOn this basis, the piezoelectric smart tire finite element model reconstructed in step S2 is used to calculate the simulation matrices of these data sets and extract the PVDF sensor output voltage VT0 l (l = x / y / z, representing the longitudinal, transverse and vertical directions of the tire respectively) and tire force data Data_F l .

[0139] Further, the computational feature extraction method in step S2 is used to extract VT0 l Perform feature extraction to obtain voltage data set VT1 l On this basis, the linear normalization theory is used to calculate VT1 l and Data_F l Perform normalization to obtain the normalized data set VT1 norl and Data_F norl , in order to improve the accuracy of the tire force prediction model trained based on this data set. The normalized expression is:

[0140]

[0141] Among them, VT1 norl (i,j) represents VT1 norl The data in row i and column j in VT1 l (i,j) is VT1 l The data in row i and column j in VT1 minl and VT1 maxl VT1 l The minimum and maximum values ​​in Data_F norl (i,j) is Data_F norl The data in row i and column j in Data_F l (i,j) is Data_F l The data in row i and column j in Data_F minl and Data_F maxl They are Data_F l The minimum and maximum values ​​in .

[0142] Finally, take VT1 norl and Data_F norl The first 85% of is used as the training set, defined as and Take the last 15% as the test set, defined as and

[0143] S4. Based on the characteristics of the voltage-tire force data set, the mean function and covariance function type of the GPR model are selected to construct a general training process for the GPR tire force prediction model;

[0144] According to VT1 norl and Data_F norl The data characteristics are combined with the manual experience method to determine the form of the mean function m(x) and the covariance function k(x,x'), written as:

[0145] m(x)=E[f(x)] (8)

[0146]

[0147] Where f(x) is the latent function, which represents VT1 norl Input x corresponding to the tire force Data_F norl , E is the mathematical expectation, is the signal variance, M = diag(η 2 ), η is the variance scale, is the noise variance, δ ij is the Kronecker delta function, where the hyperparameter set θ can be written as For the convenience of subsequent calculations, this example preprocesses the data to make its mean function equal to 0.

[0148] Design of a general training method for tire force GPR prediction model: First, use the VT1 obtained in step S3 norl and Data_F norl , the tire force prior distribution function is obtained as follows:

[0149]

[0150] Then, based on the principle of Gaussian process for joint prior distribution, combined with the established prior distribution function, the extracted in step S3 is used to and The joint prior distribution can be obtained and written as:

[0151]

[0152] in, is the test set input With the input of the training set The n×1 order covariance matrix between is the covariance of the test set into and out of itself, I n is the n-dimensional identity matrix.

[0153] Furthermore, the predicted value can be calculated The posterior distribution of is:

[0154]

[0155] in, is the tire force prediction mean, that is, the tire force prediction value, is the variance corresponding to the predicted value, which can be further expressed as:

[0156]

[0157] Furthermore, the value of the hyperparameter set θ can be obtained by maximizing the log-likelihood function, which is written as:

[0158]

[0159] in, After obtaining the value of θ, substitute it back into equations (13) and (14) to obtain the normalized tire force prediction value: and its variance

[0160] Finally, the tire force prediction value can be solved by linear denormalization theory: Written as:

[0161]

[0162] S5, using BKA to optimize the GPR model obtained in step S4 by a hyperparameter optimization method to obtain a BKA-GPR model;

[0163] Based on the general training process of the tire force GPR prediction model constructed in step S4, BKA is used to search for the minimum value of the negative log-likelihood function, indirectly achieving the purpose of maximizing the likelihood function, thereby determining the optimal hyperparameter θ value to obtain the optimal tire force GPR prediction model, that is, the BKA-GPR tire force prediction model. The process of searching for the optimal value of θ based on BKA includes the following steps:

[0164] Step 1: Initialize BKA parameters, set the population size pop to 30, the maximum number of iterations T to 50, the dimension dim of the feasible solution to 5, and the corresponding upper and lower limits ub and lb to 5 and -5 respectively;

[0165] Step 2: Initialize the initial position of the black-winged kite population (i.e., the initial solution of θ) and the fitness (i.e., the negative log-likelihood function value corresponding to the initial solution of θ). The initial position P of the individual is expressed as:

[0166] P=rd pop, dim ·(ub-lb)+lb (17)

[0167] Where rd is a random number in [0,1]. After the initial position of the individuals in the population is calculated, substitute the log-likelihood function to calculate its negative value as the individual fitness value. After the initial position and fitness of all individuals in the population are calculated, find the individual with the minimum fitness as the leader of the black-winged kite population to lead the flight direction of the entire population, which is the search direction of the global optimal solution of θ.

[0168] Step 3: Simulate the biological behavior of black-winged kites searching for prey in the air and circling to adjust their attack posture, dynamically adjust the positions of individuals in the population, and enhance the search ability for the local optimal solution of θ. The calculation formula for the individual position under attack behavior is:

[0169]

[0170] in, and denote the position of the bjth dimension of the bith black-winged kite in the tth and (t+1th) iterations, respectively. p is a constant with a value of 0.9. t is the number of iterations completed so far. The coefficient After the individual position is updated, it needs to be constrained using [-5,5], and then used to calculate the negative log-likelihood function value and compare it with the function value of the current individual. If it is less than, the individual position and function value are updated, otherwise they are not updated.

[0171] Step 4: Imitate the migration behavior of birds in search of better living conditions and resources. The migration direction of the group is determined by the leader bird mentioned in step 2. The leader bird changes dynamically during the migration process. Its notable feature is that its fitness value is the minimum value of the group to ensure the success of the migration of the group, that is, to enhance the search ability of the global optimal solution of θ. The calculation formula for the individual position under migration behavior is:

[0172]

[0173] in, represents the fitness of the bj-th dimension black-winged kite leader at the t-th iteration so far (the optimal solution of the current population), C(0,1) represents the Cauchy mutation, and the coefficient Similar to step 2, after the individual position is updated, position constraints, individual fitness calculations and update operations are required.

[0174] Step 5: Update the optimal fitness and position of the population. When an iteration of the population is completed, if the optimal fitness of the population in this iteration is better than the optimal fitness of the population searched so far, it will be replaced with the optimal fitness of the population in this iteration, and the corresponding optimal position of the population will be updated. The optimal position of the population is the optimal θ of the GPR model.

[0175] Step 6: Loop calculation. Return to step 3 and loop calculation until the maximum number of iterations is met.

[0176] Finally, the BKA-GPR tire force prediction model can be obtained by substituting the optimal θ solution searched by BKA into equations (13) and (14).

[0177] S6. Based on the BKA-GPR model obtained in step S5, determine the optimal input features and the optimal training data set size, and retrain the tire force prediction model;

[0178] In step S3, VT1 is obtained. norl and Data_F norl Based on this, we define the set DS = {(x u ,y u )|u=1,2,3,…,m}=(VT1 norl ,Data_F norl ), where: x u ∈R n is the n-dimensional input vector, i.e., the voltage value of the PVDF sensor, y u ∈R is the value corresponding to x u The output scalar, i.e., tire force, the m×n dimensional input matrix can be expressed as X=[x1,x2,…,x m ].

[0179] Furthermore, the bootstrap method is used to repeatedly extract b subsample sets from the original training data set with replacement, thereby constructing b regression trees; extracting the bth u When there are subsets, the unselected observations constitute the out-of-bag data; construct the bth u When a regression tree is built, a fixed number of 10 input feature sets are randomly selected from the 31-dimensional input variables as the feature space of the regression tree. For regression problems, the splitting process uses the minimum variance as the branch goodness criterion to select the splitting variables, written as:

[0180]

[0181] Among them, L y For this optimal splitting variable, X ψ is the ψth voltage feature in the voltage feature vector, is the mean of the ψth feature in the input feature. Each regression tree uses a no-pruning strategy to recursively branch from the root node from top to bottom, and sets the minimum size of the leaf node as the termination condition for the growth of the regression tree. After the growth of b regression trees is completed, the complete RF regression model can be constructed. Finally, the prediction performance of the model is evaluated by the root mean square error (RMSE) of the out-of-bag data prediction, that is:

[0182]

[0183] Among them, n OOB is the number of out-of-bag data samples, y js is the real tire force, is the tire force estimation value of the RF model. The RF model evaluates the influence of each input feature on the tire force by feature importance score, and measures and ranks the importance scores of each input feature by predicting RMSE. The b regression trees are tested using out-of-bag data, and the root mean square errors are RMSE1, RMSE2, …, RMSE b .VARIABLE X ψ Use random perturbation to permute the b out-of-bag data sets to form a new out-of-bag test set. Use the new out-of-bag data to retest the b regression trees to form the RMSE matrix after random permutation, written as:

[0184]

[0185] Furthermore, the importance score of the ψth input variable can be expressed as: Substituting RMSE1, RMSE2, …, RMSE b Subtract the corresponding row of the root mean square error matrix and take the average of b regression trees, and finally divide it by the standard error S of b regression trees E , get the variable X ψ The average reduction in the root mean square error of . The importance scoring formula for each input feature is obtained as follows:

[0186]

[0187] Finally, based on the importance ranking of all input features, they are arranged in descending order according to the importance scores, and the features with the highest importance scores are added to the current input feature set one by one using the sequence forward search strategy, and passed to step S5 to obtain the BKA-GPR tire force prediction model for training, and used and The test is performed to obtain the RMSE of the current input feature set until all input features are traversed, and finally the input feature set corresponding to the minimum RMSE is taken as the optimal input feature set. Fig. 9 , 10 Figures 1 and 11 show the traversal results of the 10 voltage features near the voltage feature corresponding to the minimum RMSE of the tire longitudinal, lateral and vertical forces, respectively. The bar graph is the feature importance score (arranged in descending order), and the line graph is the test set RMSE of the prediction model trained by the feature set combined when the sequence forward search is searched to the current feature number. The first digit of the voltage feature number on the horizontal axis indicates which sensor the feature value point comes from (i.e. Figure 5The first number is the lateral number shown in the figure), and the second number is the number of the voltage feature in the sensor (the voltage feature point closest to the tire contact patch entry point is numbered 1). These figures show that when the longitudinal, lateral and vertical force features are traversed to 51-14, 51-5 and 37-5 respectively, the RMSE of the prediction model trained for the test set prediction is the smallest. Therefore, this example uses these feature numbers as the cutoff points to extract the voltage feature value combination corresponding to all previous feature numbers as the optimal input feature set for the tire three-axis force prediction model. Based on the determination of the optimal input features, the data set is trained. and Perform optimal feature screening to obtain and Finally, the optimal feature sets corresponding to the longitudinal, lateral and vertical forces of the tire in this example include 64, 51 and 36 voltage features, respectively.

[0188] The scale of training data is also a key factor affecting the accuracy and speed of model estimation. Since the present invention uses the Sobol method in step S3 to collect the voltage-tire force data set, as long as the data in the data set are extracted in sequence, it can be ensured that the extracted data always evenly covers the sampling interval. and Based on 5% and its corresponding The data is used as the initial data set, and the training data set is extracted in increments of 5% and submitted to the optimized GPR tire model for training. and The test set composed of and The data is used as the training data set, and the RMSE of each test set is recorded. Finally, the training data scale corresponding to the minimum RMSE is used as the optimal training data scale. Fig.12 (a), 12(b) and 12(c) respectively show the model test results of the tire longitudinal, lateral and vertical forces in this example using training data of different training data scales. The results show that the longitudinal, lateral and vertical force prediction models achieve the best test results when the training data scale is 80% (i.e. 2040 groups), 70% (i.e. 1785 groups) and 50% (i.e. 1275 groups), respectively, and the corresponding RMSEs are 4.03N, 2.64N and 2.37N, respectively. Therefore, this example selects 2040 groups, 1785 groups and 1275 groups of training data scales as the optimal training data scales for training the tire longitudinal, lateral and vertical force BKA-GPR prediction model.

[0189] Finally, in obtaining and Based on the training data set with the optimal data size, the general training method of the BKA-GPR tire force prediction model established in steps S4 and S5 is combined to retrain F x 、F y and F z Predictive models.

[0190] S7, input the optimal voltage feature into the tire force prediction model after retraining in step S6, output the normalized prediction value of the tire force and its variance, and then obtain the actual prediction value of the tire force through denormalization.

[0191] Based on the retrained BKA-GPR tire three-axis force prediction model obtained in step S6, use As the input of the BKA-GPR tire force prediction model, the normalized tire force prediction value is output and its variance On this basis, the actual predicted value of tire force can be obtained by denormalization. writing:

[0192]

[0193] Furthermore, the uncertainty of the tire force prediction value is quantified by a 95% confidence interval (CI), whose upper limit vector upper and lower limit vector lower are:

[0194]

[0195]

[0196] Fig.13 and 14 The results of the double lane change test of the tire triaxial force prediction method proposed in the present invention when driving at high and medium speeds on high-adhesion (adhesion coefficient is 0.8) and low-adhesion (adhesion coefficient is 0.3) roads, where SWA is the steering wheel angle, V x is the vehicle speed. The results show that any tire force prediction curve and the true value curve shown in these two figures have a high degree of overlap. x 、F y and F z The maximum absolute values ​​of the absolute errors of the prediction model are 21.31N, 22.44N, and 14.33N, respectively, showing good estimation accuracy. Similarly, the prediction model also showed satisfactory performance in the medium-speed and low-adhesion test. x 、F y and F zThe maximum absolute values ​​of the absolute errors of the prediction models are 12.64 N, 24.88 N, and 4.09 N, respectively. In general, whether it is high-speed high-adhesion or medium-speed low-adhesion, F x 、F y and F z The prediction models all showed high estimation accuracy. Although the confidence intervals of the three tire force estimation results increased due to the decrease of the road adhesion coefficient and the unstable tire-ground contact, they were still within an acceptable range, indicating that F x 、F y and F z The prediction models also showed good prediction stability.

[0197] In summary, the present invention provides a tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR. x 、F y and F z The prediction accuracy is high, the robustness is good, and it can provide uncertainty quantification for the prediction results, namely a 95% confidence interval, which can better serve the optimization design of the subsequent vehicle control system.

[0198] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR, characterized in that: The following steps are involved: S1. Establish finite element models of tire and PVDF sensor, and on this basis use Inp fusion method to construct finite element model of piezoelectric intelligent tire; S2. Design a simulation scheme for calculating the first-order main effect index, select the calculation features, calculate the first-order main effect index of tire force and PVDF output voltage, and determine the optimal installation position of the sensor; S3. Design a voltage-tire force data set simulation condition based on the Sobol method, collect PVDF output voltage and tire force data and perform data preprocessing to form a data set that can be used for training and testing; S4. Based on the characteristics of the voltage-tire force data set, the mean function and covariance function type of the GPR model are selected to construct a general training process for the GPR tire force prediction model; S5, using BKA to optimize the GPR model obtained in step S4 by a hyperparameter optimization method to obtain a BKA-GPR model; S6. Based on the BKA-GPR model obtained in step S5, determine the optimal input features and the optimal training data set size, and retrain the tire force prediction model; S7, input the optimal voltage feature into the tire force prediction model after retraining in step S6, output the normalized prediction value of the tire force and its variance, and then obtain the actual prediction value of the tire force through denormalization.

2. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S1-1. Establish a tire finite element model, calibrate its accuracy through a stiffness test, and then output its Inp code; S1-2, establish a finite element model of the PVDF sensor, calibrate its accuracy through a single cantilever beam experiment, and then output its Inp code; S1-3, integrate the Inp code of the tire finite element model and the PVDF sensor finite element model, set boundary conditions and constraints to form a piezoelectric smart tire finite element model, and calibrate its accuracy through real vehicle experiments.

3. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 2 is characterized in that: Step S2 specifically includes the following steps: S2-1. Determine the influencing factors and value range of the output voltage of the PVDF sensor in the piezoelectric intelligent tire according to daily driving conditions, and design the voltage-tire force data set simulation matrix SC based on the definition form of the first-order main effect index calculation scheme based on the global sensitivity analysis theory optimized by the multiplication dimensionality reduction method, and write it as: in, It represents the median of each influencing factor within its value range. The specific values ​​of BL1, BL2, BL3, ..., BLn can be calculated by the five-node Gaussian value formula, written as: Where a and b are the upper and lower limits of the influencing factor BL(i), respectively. t (t=1,2,3,4,5) are the node values ​​of the five-node Gaussian value formula; S2-2. According to the tire force generation mechanism, the voltage value at the q (q>0) specific position on the PVDF sensor output voltage curve is selected as the first-order main effect indicator (FMEI) to calculate the characteristic value; the selection logic of the specific position is: taking the tire-ground contact center point as a reference, select the q (q>0) voltage values ​​on the PVDF sensor output voltage curve along this point to both sides of the tire circumference at intervals of η° (η>0). At this time, the calculated characteristic value vector VC of the PVDF sensor voltage curve at the j (j=1,2,..,62)th sensor installation position is j It can be expressed as: in, and are the 1st, 2nd and qth calculated characteristic value points of the PVDF sensor voltage curve at the jth sensor installation position respectively; S2-3, the average value of the FMEI of all the calculated characteristic points contained in the voltage signal curve collected at the j-th sensor installation position is taken as the final FMEI of the position, recorded as MFMEI; at this time, the MFMEI of the tire force and the output voltage of the PVDF sensor at the j-th installation position can be expressed as: When the superscript Δ of MFMEI is 1, 2 or 3, it represents the NFMEI of longitudinal, transverse and vertical forces. The calculation formula can be further written as: in, is the origin moment value corresponding to the jjth calculated eigenvalue of the voltage signal at the jth sensor installation position when the influencing factor is BL(i), k = 1 or 2, indicating the first-order or second-order origin moment, w t is the weight of the five-node Gaussian value formula, PVDF_IT FEM (·) is the solution equation for the output voltage of the PVDF sensor in the finite element model of the piezoelectric smart tire; S2-4. After calculating the tire force and output voltage MFMEI corresponding to all potential installation positions of the PVDF sensor in the tire, a screening index is set, and the position greater than the set screening index is used as the sensor installation position. p (p>0) installation positions that meet the conditions are screened out to achieve the selection of the optimal installation position of the PVDF sensor, and the piezoelectric intelligent tire finite element model is reconstructed.

4. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 3 is characterized in that: Step S3 specifically includes the following steps: S3-1. Generate an m×n (m>0, n>0) dimensional sampling sequence matrix qs based on the Sobol method. Combined with the value range of each influencing factor set in step S2-1, calculate the specific value of each influencing factor in each dimension of the data set simulation matrix. The value formula is: st λ =sure+qs λ (varmax-varmin) Among them, st λ is the λth (λ>0) n-dimensional simulation value vector, qs λ is the λth n-dimensional sampling vector in the sampling sequence matrix qs, varmax and varmin are two n-dimensional vectors composed of the upper and lower limits of the value range of each influencing factor; finally, the longitudinal force (F x ), lateral force (F y ) and vertical force (F z ) of three m×n dimensional voltage-tire force data set simulation matrices; S3-2, using the piezoelectric smart tire finite element model reconstructed in step S2-4 to calculate the three m×n dimensional voltage-tire force data set simulation matrices obtained in step S3-1, and extract the PVDF sensor output voltage VT0 l and tire force data Data_F l , where l = x / y / z, representing the longitudinal, transverse and vertical directions of the tire respectively; S3-3, using the feature extraction method in step S2-2 to extract VT0 l Perform feature extraction to obtain voltage data set VT1 l On this basis, the linear normalization theory is used to VT1 l and Data_F l Perform normalization to obtain the normalized data set VT1 norl and Data_F norl , the normalized expression is: Among them, VT1 norl (i,j) represents VT1 norl The data in row i and column j in VT1 l (i,j) is VT1 l The data in row i and column j in VT1 minl and VT1 maxl VT1 l The minimum and maximum values ​​in Data_F norl (i,j) is Data_F norl The data in row i and column j in Data_F l (i,j) is Data_F l The data in row i and column j in Data_F minl and Data_F maxl They are Data_F l The minimum and maximum values ​​in ; S3-4, take VT1 norl and Data_F norl The first 85% of is used as the training set, defined as and Take the last 15% as the test set, defined as and 5. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 4 is characterized in that: Step S4 specifically includes the following steps: S4-1, according to VT1 norl and Data_F norl The data characteristics are combined with the empirical method to determine the form of the mean function and covariance function, written as: m(x)=E[f(x)] Where f(x) is the latent function, which represents VT1 norl Input x corresponding to the tire force Data_F norl , E is the mathematical expectation, is the signal variance, M = diag(η 2 ), η is the variance scale, is the noise variance, δ ij is the Kronecker delta function; in this case, the hyperparameter set θ can be written as S4-2, based on VT1 obtained in step S3-3 norl and Data_F norl , a general training method for tire force GPR prediction model is designed.

6. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 5 is characterized in that: In step S4-2, the general training method of the tire force GPR prediction model is: First, using VT1 obtained in step S3-4 norl and Data_F norl , the tire force prior distribution function is obtained as follows: Then, based on the principle of Gaussian process for joint prior distribution, combined with the established prior distribution function, the extracted data in step S3-4 are used to and The joint prior distribution can be obtained and written as: in, is the test set input With the input of the training set The n×1 order covariance matrix between is the covariance of the test set into and out of itself, I n is the n-dimensional identity matrix; Furthermore, the predicted value can be calculated The posterior distribution of is: in, is the predicted mean, that is, the predicted value, is the variance corresponding to the predicted value, which can be further expressed as: Furthermore, the value of the hyperparameter set θ can be obtained by maximizing the log-likelihood function, which is written as: in, After obtaining the value of θ, substitute it back into and The normalized tire force prediction value can be obtained and its variance Finally, the tire force prediction value can be solved by linear denormalization theory: Written as:

7. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 6 is characterized in that: Step S5 specifically includes the following steps: S5-1, initialize BKA parameters, including population size pop, maximum number of iterations T, dimension dim of feasible solution, and corresponding upper and lower limits ub and lb; S5-2. Initialize the initial positions of the individuals in the black-winged kite population, i.e., the initial solution θ, and the fitness, i.e., the negative log-likelihood function value corresponding to the initial solution θ. The initial position P of the individuals is expressed as: P=rd pop,dim ·(ub-lb)+lb Among them, rd is a random number in [0,1]. After the initial position of the individual in the population is calculated, substitute it into the log-likelihood function to calculate its negative value as the individual fitness value. After the initial position and fitness of all individuals in the population are calculated, find the individual with the minimum fitness as the leader of the black-winged kite population to lead the flight direction of the entire population, that is, the search direction of the global optimal solution of θ. S5-3. Simulate the attack behavior of black-winged kites to calculate the individual position. The formula is: in, and denote the position of the bjth dimension of the bith black-winged kite in the tth and (t+1th) iterations, respectively. p is a constant with a value of 0.

9. t is the number of iterations completed so far. The coefficient After the individual position is updated, it is necessary to use [ub, lb] to constrain the value range of the hyperparameter θ, and then use the θ value after the range constraint to calculate the negative log-likelihood function value and compare it with the function value of the current individual. If it is less than, update the individual position and function value, otherwise do not update; S5-4. Calculate the individual position by imitating the migration behavior of black-winged kites. The formula is: in, represents the fitness of the bj-th dimensional black-winged kite leader at the t-th iteration so far, that is, the optimal solution of the current population, C(0,1) represents the Cauchy mutation, and the coefficient After the individual position is updated, it is necessary to use [ub, lb] to constrain the range of θ values, and then use the constrained θ value to calculate the negative log-likelihood function value and compare it with the function value of the current individual. If it is less than, update the individual position and function value, otherwise do not update; S5-5, population optimal fitness and position update; when one iteration of the population is completed, if the optimal fitness of the population in this iteration is better than the optimal fitness of the population searched so far, it is replaced with the optimal fitness of the population in this iteration, and the corresponding optimal position of the population is updated; the optimal position of the population is the optimal θ of the GPR model; S5-6, loop calculation; return to step 3, loop calculation until the convergence condition is met or the maximum number of iterations is reached; finally, substitute the optimal θ solution searched by BKA back into the GPR model to obtain the BKA-GPR tire force prediction model.

8. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 7 is characterized in that: Step S6 specifically includes the following steps: S6-1. Define the set DS = {(x u ,y u )|u=1,2,3,…,m}=(VT1 norl ,Data_F norl ), where: x u ∈R n is the n-dimensional input vector, i.e., the voltage value of the PVDF sensor, y u ∈R is the value corresponding to x u The output scalar, i.e., tire force, the m×n dimensional input matrix can be expressed as X=[x1,x2,…,x m ]; S6-2. Use the bootstrap method to repeatedly extract b (b>0) sub-sample sets from the original training data set with replacement, thereby constructing b regression trees, where the ψth feature (ψ>0) in the b sub-sample set can be defined as X ψ On this basis, the prediction performance of the model is evaluated by the prediction accuracy of out-of-bag data to form an error matrix, which is written as: S6-3, based on the error matrix obtained in step S6-2, calculate all the features X ψ The average reduction in error is the importance score, and they are arranged in descending order; the calculation formula is: S6-4, using the sequence forward search strategy to add the features with the highest importance score in the current input feature set one by one, pass them to the optimized GPR tire force prediction model obtained in step S5-5 for training, and test to obtain the prediction error of the current input feature set until all input features are traversed; finally, the input feature set with the smallest prediction error is used as the optimal input feature set, and the data set is and Perform optimal feature screening to obtain and S6-5, based on the training set after the optimal feature extraction processing obtained in step S6-4, extract the training data set in 5% increments and submit it to step S5-5 to optimize the GPR tire model for training, and use the test set for testing until all the data in the training data set are extracted as the training data set, and record each test error; finally, the training data scale with the smallest prediction error is used as the optimal training data scale; S6-6. Based on the obtained training data set with optimal input features and optimal data size, the general training method of the designed BKA-GPR tire force prediction model is combined to retrain F x 、F y and F z Predictive models.

9. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 8 is characterized in that: Step S7 specifically includes the following steps: S7-1, based on the retrained BKA-GPR tire three-axis force prediction model obtained in step S6-6, use As the input of the BKA-GPR tire force prediction model, the normalized tire force prediction value is output and its variance On this basis, the actual predicted value of tire force can be obtained by denormalization. S7-2. Calculate the confidence interval of the tire force prediction value to quantify the uncertainty of the tire force prediction value.

10. The tire three-axis force prediction method based on piezoelectric intelligent tire technology and BKA-GPR according to claim 9 is characterized in that: In step S7-2, the confidence interval calculation formula is: Wherein, upper is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, lower is the lower limit vector of the confidence interval corresponding to the tire force prediction vector, and t o is the confidence interval coefficient.

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