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

Abstract

The application discloses a tire three-way force prediction method based on piezoelectric intelligent tire technology and BKA-GPR. A finite element model of a tire and a PVDF (polyvinylidene fluoride) sensor is constructed, and a piezoelectric intelligent tire model is established in combination with an Inp fusion method; through global sensitivity analysis, the sensitivity of the voltage output of the PVDF sensor at different positions in the tire to the changes of a longitudinal force (F x ), a lateral force (F y ) and a vertical force (F z ) is evaluated, and the optimal installation position of the sensor is determined; the Sobol method is used to collect a voltage-tire force data set, and signals in a ground footprint area are extracted and normalized; a tire force Gaussian process regression (GPR) model is designed according to data characteristics, and the hyperparameters of the model are optimized through a Black-winged kite algorithm (BKA); the Random forest (RF) algorithm is used to determine the optimal input features and data size, and a tire three-way force prediction model with low cost, high precision, stability and good generalization performance can be obtained through retraining of the model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle control and the field of machine learning, in particular to the technical field of piezoelectric intelligent tire and a tire three-direction force prediction method based on BKA-GPR. BACKGROUND

[0002] The control of vehicle motion is essentially the control of tire force, so the real-time and accurate acquisition of tire force, especially the tire three-direction force (longitudinal force F x , lateral force F y and vertical force F z ) is the prerequisite for keeping the actual motion state of the vehicle consistent with the ideal motion state at all times. The direct measurement of current tire force is very costly and difficult to be fully commercialized. Therefore, many experts and scholars have developed various tire force estimation methods based on different technologies, among which the most famous are tire force prediction methods based on sliding mode observer, Kalman filter and least square method. These methods more or less use vehicle / tire models, which will lead to a common problem, that is, it is difficult to achieve a reasonable balance between tire force calculation accuracy and calculation efficiency. In other words, using a simplified vehicle / tire model can meet the tire force estimation requirements of most driving conditions, but when the vehicle is in extreme driving conditions (such as high-speed large cornering or wet 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 method based on these models. Although using a more complex vehicle / tire model can improve the prediction performance of these tire force prediction methods, it will also increase the complexity of the prediction system, making the prediction time increase, thus making it difficult to meet the real-time requirements of the vehicle control system.

[0003] The intelligent tire technology is to install sensors inside the tire to directly measure dynamic parameters in the tire movement process, and to realize the estimation of the key state of the tire by combining machine learning or theoretical model. Compared with the traditional tire state estimation method, the technology can obtain more accurate and reliable tire state. Therefore, if the intelligent tire technology is used to realize the prediction of tire force, the process of the traditional tire force prediction method can be simplified, and the estimation accuracy and reliability of the tire force, especially in extreme driving conditions, can be improved, so as to improve the overall performance of the vehicle control system. Although some scholars have proposed some tire force prediction methods based on intelligent tire technology, there are still some places that can be optimized, mainly including the improvement of the signal collection quality of the intelligent tire system and the optimization of the mapping relationship between the signal characteristics and the tire force. In the aspect of signal collection, the current intelligent tire force prediction field lacks sufficient theoretical support for the scientific selection of the sensor installation position, and it is difficult to ensure the continuous and high-quality collection of tire dynamic characteristics during tire operation. In the aspect of mapping relationship construction, the selection of signal characteristics in the current intelligent tire force prediction still relies on the artificial experience method, which cannot guarantee that the selected characteristics have wide representativeness, thereby affecting the accuracy of the mapping relationship between the signal characteristics and the tire force constructed based on these characteristics. In addition, too much or too little training data size and incorrect selection of the mapping method will also lead to poor performance of the finally established tire force prediction model. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a tire three-way force prediction method based on piezoelectric intelligent tire technology and BKA-GPR, which considers the selection of the optimal installation position of the PVDF sensor inside the tire, uses the encapsulator method based on intelligent algorithm to select the optimal features, and trains the BKA-optimized GPR tire three-way force prediction model with the best size of training data.

[0005] The technical scheme of the present application is a tire three-way force prediction method based on piezoelectric intelligent tire technology and BKA-GPR, comprising the following steps:

[0006] S1, a tire and PVDF sensor finite element model is established, and on this basis, an Inp fusion method is used to construct a piezoelectric intelligent tire finite element model;

[0007] S2, a first-order main effect index calculation simulation scheme is designed, the calculation characteristics are selected, the first-order main effect index of the tire force and the PVDF output voltage is calculated, and the optimal installation position of the sensor is determined;

[0008] S3, a voltage-tire force data set simulation condition is designed based on the Sobol method, the PVDF output voltage and tire force data are collected and preprocessed, and a data set that can be used for training and testing is formed;

[0009] S4, selecting the GPR model mean function and covariance function type based on the voltage-tire force dataset characteristics, and constructing a general training process of the GPR tire force prediction model;

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

[0011] S6, on the basis of obtaining the BKA-GPR model in step S5, determining the optimal input feature and the best training dataset size, and retraining the tire force prediction model;

[0012] S7, inputting the optimal voltage feature into the tire force prediction model retrained in step S6, outputting the tire force normalized prediction value and its variance, and then obtaining the actual tire force prediction value through inverse normalization.

[0013] Step S1 specifically includes the following steps:

[0014] S1-1, establishing a tire finite element model, outputting its Inp code after calibrating its accuracy through stiffness experiment;

[0015] S1-2, establishing a PVDF sensor finite element model, outputting its Inp code after calibrating its accuracy through a single cantilever beam experiment;

[0016] S1-3, merging the Inp codes of the tire finite element model and the PVDF sensor finite element model, setting boundary conditions and constraints to form a piezoelectric intelligent tire finite element model, and calibrating its accuracy through real vehicle experiment.

[0017] Step S2 specifically includes the following steps:

[0018] S2-1, determining the influencing factors of the piezoelectric intelligent tire in-tire PVDF sensor output voltage and their value range according to the daily driving conditions, designing the voltage-tire force dataset simulation matrix SC based on the definition form of the first-order main effect index calculation scheme of the global sensitivity analysis theory of multiplicative dimension reduction method optimization, written as:

[0019]

[0020] wherein, represent the median of each influencing factor within its value range, and the specific values of BL1, BL2, BL3, …, BLn can be calculated by the five-node Gaussian value formula, written as:

[0021]

[0022] where a, b are the upper and lower limits of the impact factor BL(i) values, respectively, z t (t = 1, 2, 3, 4, 5) are the node values of the five-node Gauss value formula;

[0023] S2-2, according to the tire force generation mechanism, the voltage values of q (q > 0) specific positions on the PVDF sensor output voltage curve are 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 the reference, respectively along the point to the tire circumferential two sides with η ° (η > 0) as the interval, q (q > 0) Voltage values on the PVDF sensor output voltage curve are selected, at this time, the calculation characteristic value vector VC j can be expressed as:

[0024]

[0025] wherein, and are the first, second and qth calculation characteristic value points of the PVDF sensor voltage curve at the jth sensor installation position;

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

[0027]

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

[0029]

[0030] wherein, is the zeroth moment value corresponding to the jth calculation characteristic value of the voltage signal at the jth sensor installation position when the impact factor is BL(i), k = 1 or 2, indicating the first or second zeroth moment, w t is the weight of the five-node Gauss value formula, PVDF_IT FEM (·) is the solving equation of the PVDF sensor output voltage in the piezoelectric intelligent tire finite element model;

[0031] S2-4, on the basis of calculating the tire force corresponding to all potential installation positions of the PVDF sensor in the tire and the output voltage MFMEI, setting a screening index, and selecting the positions greater than the screening index as the sensor installation positions, screening p (p>0) installation positions meeting the conditions, and realizing the selection of the optimal installation position of the PVDF sensor, and reconstructing the piezoelectric intelligent tire finite element model.

[0032] Step S3 specifically comprises the following steps:

[0033] S3-1, generating an m*n (m>0, n>0) dimensional sampling sequence matrix qs based on the Sobol method, combining the value range of each influencing factor set in step S2-1, and calculating the specific value of each influencing factor in each dimension of the data set simulation matrix, and the value formula is:

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

[0035] wherein, 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, three m*n-dimensional voltage-tire force data set simulation matrices representing the longitudinal force (F x ), lateral force (F y ) and vertical force (F z ) can be obtained respectively;

[0036] S3-2, using the piezoelectric intelligent 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 extracting the PVDF sensor output voltage VT0 l and the tire force data Data_F l , wherein l=x / y / z respectively represent the longitudinal, lateral and vertical directions of the tire;

[0037] S3-3, using the feature extraction method in step S2-2 to perform feature extraction operation on VT0 l respectively, and then obtaining the voltage data set VT1 l ; on this basis, using linear normalization theory to normalize VT1 l and Data_F l to obtain the normalized data sets VT1 norl and Data_F norl , and the normalization expression is:

[0038]

[0039] where VT1 norl (i,j) represents the data in the i-th row and j-th column of VT1 norl , VT1 l (i,j) is the data in the i-th row and j-th column of VT1 l , VT1 minl and VT1 maxl are the minimum and maximum values in VT1 l , respectively, Data_F norl (i,j) represents the data in the i-th row and j-th column of Data_F norl , Data_F l (i,j) is the data in the i-th row and j-th column of Data_F l , Data_F minl (i,j) represents the data in the i-th row and j-th column of Data_F maxl , Data_F l and Data_F norl are the minimum and maximum values in Data_F norl , respectively;

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

[0041] Step S4 specifically comprises the following steps:

[0042] S4-1, determine the form of the mean function and the covariance function according to the data characteristics of VT1 norl and Data_F norl , and combine empirical methods, written as:

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

[0044]

[0045] where f(x) is the latent function, representing the tire force Data_F norl corresponding to the input x of VT1 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; at this time, the hyperparameter set θ can be written as

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

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

[0048] First, using the 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, using the extracted and in step S3-4, the joint prior distribution can be obtained, written as:

[0051]

[0052] wherein, is the test set input and the input of the training set n×1 order covariance matrix, is the covariance of the test set input itself, I n is the n-dimensional unit matrix;

[0053] Further, the posterior distribution of the predicted value can be calculated as:

[0054]

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

[0056]

[0057]

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

[0059]

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

[0061] Finally, the tire force prediction value can be solved by linear reverse normalization theory is written as

[0062]

[0063] Step S5 specifically includes the following steps:

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

[0065] S5-2, initialize the initial position of the black kite population individual, i.e. the initial solution θ, and the fitness, i.e. the negative log-likelihood function value corresponding to the initial solution θ, the expression of the initial position P of the individual is:

[0066] P = rd pop,dim ·(ub-lb)+lb

[0067] Wherein, rd is a random number in [0, 1]; after the initial position of the population individual is calculated, the negative value of the log-likelihood function is calculated as the fitness value of the individual; after the initial positions and fitness of all individuals in the population are calculated, the individual corresponding to the minimum fitness is found as the leader of the black kite population, leading the flight direction of the whole population, i.e. the search direction of the global optimal solution θ;

[0068] S5-3, simulate the attack behavior of the black kite to calculate the individual position, the formula is:

[0069]

[0070] Wherein, and respectively represent the position of the bi-th black kite in the t-th and (t+1)-th iteration, p is a constant with a value of 0.9, t is the number of iterations completed so far, and the coefficient After the individual position is updated, the value range of the hyperparameter θ needs to be constrained using [ub, lb], and then the negative log-likelihood function value is calculated using the range-constrained θ value, and compared with the current individual function value. If it is smaller, update the individual position and function value, otherwise do not update;

[0071] S5-4, simulate the migration behavior of the black kite to calculate the individual position, the formula is:

[0072]

[0073] wherein, C(bj-1,t) represents the fitness of the bj-1 dimensional black-winged kite leader at the t th iteration so far, i.e. the current population optimum, C(0,1) represents the Cauchy mutation, and the coefficient After the individual position is updated, the range of the value of θ is constrained using [ub, lb], and then the value of the negative log-likelihood function is calculated using the constrained value of θ, and compared with the function value of the current individual. If it is smaller, the individual position and function value are updated, otherwise they are not updated.

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

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

[0076] Step S6 specifically comprises the following steps:

[0077] S6-1, define a set DS={(x u ,y u )|u=1,2,3,…,m}=(VT1 norl ,Data_F norl ), wherein: x u ∈R n is an n-dimensional input vector, i.e. the PVDF sensor voltage value, y u ∈R is an output scalar corresponding to x u , i.e. the tire force, and 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 with replacement from the original training data set, thereby constructing b regression trees, wherein the ψ (ψ>0) features in the b sub-sample sets can be defined as X ψ On this basis, the prediction performance of the model is evaluated by out-of-bag data prediction accuracy, and an error matrix is formed, written as:

[0079]

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

[0081]

[0082] S6-4, using the sequence forward search strategy to add the feature with the highest importance score in the current input feature set one by one, and passing the optimized GPR tire force prediction model obtained in step S5-5 to training, and testing 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 taken as the optimal input feature set, and the data set and is subjected to optimal feature screening operation to obtain and

[0083] S6-5, on the basis of the training set obtained after optimal feature extraction processing in step S6-4, extracting the training data set in turn with an increment of 5%, submitting the training data set to the optimized GPR tire model in step S5-5 for training, and using the test set for testing until all data in the training data set are extracted as the training data set, and recording the test error each time; finally, the training data size with the smallest prediction error is taken as the best training data size;

[0084] S6-6, on the basis of the training data set obtained with optimal input features and the best data size, combining the general training method of the designed BKA-GPR tire force prediction model, retraining the F x , F y and F z prediction model.

[0085] Step S7 specifically includes the following steps:

[0086] S7-1, on the basis of the BKA-GPR tire three-way force prediction model retrained in step S6-6, using as the input of the BKA-GPR tire force prediction model, outputting the tire force normalized prediction value and the variance of the tire force normalized prediction value, and on this basis, performing reverse normalization to obtain the actual tire force prediction value

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

[0088] The feature lies 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, t o is a confidence interval coefficient.

[0091] Beneficial effects: the finite element software is used to establish the finite element model of the piezoelectric intelligent tire, and the time and cost required for scientific selection of the PVDF sensor installation position in the tire and extraction of training data of the tire three-way force prediction algorithm are greatly reduced.

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

[0093] The encapsulator method based on the RF algorithm is designed to select the input features, which effectively avoids the influence of human subjective factors in the feature selection process, and is beneficial to selecting more representative signal features.

[0094] Based on the Sobol method, the uniformly distributed voltage-tire force data set is collected, and the optimal tire force prediction model training data set size is determined by combining the incremental method of the training set, which is helpful to improve the training effect of the prediction model.

[0095] The GPR tire force prediction model training process based on BKA optimization is designed, which enhances the global and local search ability of the optimal solution of the hyperparameters in the GPR model training process, and is beneficial to improve 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 application 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 the test data only by relying on a small data set, not only can output the tire force prediction value, but also can quantitatively output the uncertainty of the prediction value, which can better serve the optimization design of the subsequent vehicle control system. BRIEF DESCRIPTION OF DRAWINGS

[0097] Figure 1 It is an embodiment process schematic diagram of the piezoelectric intelligent tire technology and the BKA-GPR tire three-way force prediction method in the application.

[0098] Figure 2 It is a modeling process of the piezoelectric intelligent tire finite element model in the application.

[0099] Figure 3 It is an installation position schematic diagram of the PVDF sensor in the verification process of the intelligent tire finite element model in the application.

[0100] Figure 4 PVDF-M voltage curve and ground pressure curve for one circle of tire rolling.

[0101] Figure 5 Tire inner liner sensor installation position schematic diagram.

[0102] Figure 6 First-order main effect index calculation results of different sensor installation positions when longitudinal force changes.

[0103] Figure 7 First-order main effect index calculation results of different sensor installation positions when lateral force changes.

[0104] Figure 8 First-order main effect index calculation results of different sensor installation positions when vertical force changes.

[0105] Figure 9 Optimal voltage feature set screening results of longitudinal force prediction model.

[0106] Figure 10 Optimal voltage feature set screening results of lateral force prediction model.

[0107] Figure 11 Optimal voltage feature set screening results of vertical force prediction model.

[0108] Figure 12 Best training data size determination results of longitudinal, lateral and vertical force prediction models.

[0109] Figure 13 High-attachment-high-speed prediction results of longitudinal, lateral and vertical force prediction models under double-shift-line working conditions.

[0110] Figure 14 Low-attachment-medium-speed prediction results of longitudinal, lateral and vertical force prediction models under double-shift-line working conditions. DETAILED DESCRIPTION

[0111] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0112] As shown in Figure 1 A tire three-way force prediction method based on piezoelectric intelligent tire technology and BKA-GPR, comprising the following steps:

[0113] S1, a finite element model of a tire and a PVDF sensor is established, and on this basis, an Inp fusion method is used to construct a piezoelectric intelligent tire finite element model;

[0114] Figure 2 The process of establishing the piezoelectric intelligent tire finite element model of the application is shown, including independent finite element modeling of the tire and the PVDF sensor and generating the Inp code of the piezoelectric intelligent tire finite element model by fusing the two. First, the three-dimensional model of the tire and the PVDF sensor is drawn by structure analysis, and the material parameters are extracted by material property analysis. Then, the three-dimensional structure model of the two is meshed, and the material is given, etc. to construct their finite element models. Then, the accuracy of the two finite element models is verified by tire stiffness experiment and piezoelectric material cantilever beam experiment respectively, and when the average absolute percentage error is less than 10%, the Inp code is generated, otherwise the finite element model is reconstructed to calibrate it. Finally, on the basis of obtaining the Inp of the tire and the Inp of the PVDF sensor, the piezoelectric intelligent tire finite element model is generated by the Inp fusion method. At the same time, the accuracy of the model is verified by real vehicle test. As shown in Figure 3 , in the verification process, the experimental equipment and the PVDF sensor in the finite element model are respectively installed at the longitudinal symmetry center line, the symmetrical shoulder on both sides and the symmetrical side on both sides of the tire, and are respectively named PVDF-M, PVDF-L1, PVDF-L2, PVDF-R1 and PVDF-R2. When the average absolute percentage error of the output voltage of the piezoelectric intelligent tire finite element model and the real vehicle test platform under the straight line free rolling condition is less than 10%, the model is saved, otherwise the piezoelectric intelligent tire finite element model is regenerated and calibrated.

[0115] S2, a first-order main effect index calculation simulation scheme is designed, a characteristic is selected, a first-order main effect index of tire force and PVDF output voltage is calculated, and an optimal sensor installation position is determined;

[0116] In order to make the finally selected PVDF sensor installation position have good working condition adaptability, it is necessary to consider as many influencing factors as possible that may affect the output voltage of the PVDF sensor when the vehicle is driving when designing the first-order main effect index calculation simulation scheme. Since the purpose of the application is to construct the F x , F y and F z prediction model, the influencing factors considered include tire slip ratio, side slip angle, vertical load, road adhesion coefficient, vehicle speed and tire pressure, and the value range of each influencing factor is determined according to the daily vehicle driving state as shown in Table 1.

[0117] Table 1: Value range of each influencing factor

[0118]

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

[0120]

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

[0122]

[0123] wherein a and b are the upper and lower limit values of the influencing factor BL(i), and z t (t = 1, 2, 3, 4, 5) are the node values of the five-node Gaussian value formula, and the specific values can be seen in Table 2. Finally, in combination with formula (1) and (2) and Table 1 and 2, a 30x6-dimensional first-order main effect index calculation simulation value matrix can be obtained.

[0124] Table 2: Five-node Gaussian-Lagrange type Gaussian integral table

[0125]

[0126] Characteristic value selection: During the tire rolling process, the voltage signal collected by the PVDF sensor is a time series signal composed of countless voltage value points, which cannot be directly used to calculate the first-order main effect index (FMEI). Therefore, several specific voltage values on a single voltage curve need to be extracted for the calculation of FMEI. Since the purpose of the present application is to predict the tire force, and the tire force is mainly generated by the relative sliding between the tire-ground contact surface, therefore, the voltage value points on the voltage curve located in the footprint are mainly selected as the characteristic values for calculation. Figure 4The voltage curve collected by the PVDF-M when the tire rolls one circle is shown, the interval L3 between the two peaks of the second derivative of the signal is most close to the interval between the two wave troughs of the Cpress curve (i.e. the interval of the tire angle occupied by the tire footprint area), which means that the identification of the voltage curve in the footprint area can be realized based on this feature. Similarly, the voltage curves collected by the sensors in other installation positions can also be identified in the signal of the footprint area based on this feature. In order to eliminate the influence of the vehicle speed change on the total amount of voltage signal sampling, the voltage value of a specific tire angle position in the footprint area is calculated as a characteristic value by an online interpolation method based on the obtained voltage curve of the footprint area. When extracting the specific voltage value point, the center point of the footprint (i.e. the tire angle position corresponding to the peak value of the PVDF-M voltage curve) is defined as 0°, and 15 voltage value points are extracted as the calculation characteristic values by the interpolation method with an interval of 1.5° to both sides, totaling 31 calculation characteristic values. In addition, the FMEI of the tire force in the longitudinal direction of the tire pitch is calculated based on the 31 calculation characteristic values of the voltage curve of the PVDF sensor at the jth sensor installation position. Figure 5 It can be seen that a single tire pitch will repeatedly pass through the footprint area when the tire rolls, so it is only necessary to calculate the FMEI of all potential sensor installation positions in the longitudinal direction of the single tire pitch. In order to simplify the subsequent calculation, the present application quantizes and names all possible installation positions of the PVDF sensor on the single tire pitch (see Figure 5 ) at this time. The calculation characteristic value vector V j Cj of the PVDF sensor voltage curve at the jth sensor installation position can be expressed as:

[0127]

[0128] wherein, is the 31 calculation characteristic values of the PVDF sensor voltage curve at the jth sensor installation position.

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

[0130]

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

[0132]

[0133] wherein, The origin moment value corresponding to the j-th calculated eigenvalue of the voltage signal of the j-th sensor installation position when the influencing factor is BL(i), k = 1 or 2, represents 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 solving equation of the output voltage of the PVDF sensor in the finite element model of the piezoelectric intelligent tire.

[0134] Selection of PVDF sensor installation position: Figure 6 、 7 and 8 respectively show the labels of the top 10 positions in descending order of MFMEI corresponding to all installation positions of a single tire pitch corresponding to the longitudinal, lateral and vertical forces of the tire. In this example, the positions corresponding to the top four lateral labels in the NFMEI calculation results of the three forces of the tire are selected as the optimal installation positions of the PVDF sensor. Then the optimal installation positions of the longitudinal force are the lateral labels 2, 59, 51 and 10, the optimal installation positions of the lateral force are the lateral labels 10, 51, 49 and 12, and the optimal installation positions of the vertical force are the lateral labels 24, 37, 44 and 17. On the basis of obtaining the optimal installation position of the PVDF, the finite element modeling method in step S1 is used to rebuild the finite element model of the piezoelectric intelligent tire to adjust the installation position of the sensor.

[0135] S3, based on Sobol method, design voltage-tire force data set simulation working condition, collect PVDF output voltage and tire force data and carry out data pretreatment, form data set which can be used for training and testing;

[0136] Firstly, based on Sobol method, 3000x6 dimensional sampling sequence matrix qs is generated, wherein 3000 is the total amount of data of the voltage-tire force data set, and 6 is the total number of PVDF output voltage influencing factors. 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 by combining the Sobol sampling value formula, and the value formula is:

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

[0138] Wherein, st λ is the λ-th 6-dimensional simulation value vector, qs λ is the λ-th 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, the representative F x , F y and F zthree 3000 x 6-dimensional voltage-tire force dataset simulation matrices. On this basis, the piezoelectric intelligent tire finite element model reconstructed in step S2 is used to calculate these dataset simulation matrices, and the PVDF sensor output voltage VT0 l (l = x / y / z, respectively representing the longitudinal, lateral and vertical directions of the tire) and tire force data Data_F l .

[0139] Further, the feature extraction method in step S2 is used to perform feature extraction operations on VT0 l respectively, and then voltage datasets VT1 l are obtained. On this basis, linear normalization theory is used to normalize VT1 l and Data_F l to obtain normalized datasets VT1 norl and Data_F norl , so as to improve the accuracy of the tire force prediction model trained based on the datasets subsequently. The normalization expression is:

[0140]

[0141] wherein VT1 norl (i,j) represents the i-th row and j-th column data in VT1 norl , VT1 l (i,j) is the i-th row and j-th column data in VT1 l , VT1 minl and VT1 maxl are the minimum value and maximum value in VT1 l respectively, Data_F norl (i,j) is the i-th row and j-th column data in Data_F norl , Data_F l (i,j) is the i-th row and j-th column data in Data_F l , Data_F minl and Data_F maxl are the minimum value and maximum value in Data_F l respectively.

[0142] Finally, the first 85% of VT1 norl and Data_F norl are taken as the training set, defined as and , and the last 15% is taken as the test set, defined as and

[0143] S4. Selecting the mean function and covariance function type of GPR model based on the characteristics of the voltage-tire force dataset, and constructing the general training process of GPR tire force prediction model;

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

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

[0146]

[0147] wherein f(x) is the latent function, representing the tire force Data_F norl corresponding to the input x 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, wherein the hyperparameter set θ can be written as For the convenience of subsequent calculation, the mean function is equal to 0 by data preprocessing in this example.

[0148] General training method design of tire force GPR prediction model: first, using VT1 norl and Data_F norl obtained in step S3, the tire force prior distribution function is as follows:

[0149]

[0150] Then, based on the principle of joint prior distribution of Gaussian process, combining the established prior distribution function, using the extracted and in step S3, the joint prior distribution can be obtained, written as:

[0151]

[0152] wherein, is the n×1 order covariance matrix between the test set input and the input of the training set, is the covariance of the test set input itself, I n is the n-dimensional unit matrix.

[0153] Further, the posterior distribution of the predicted value can be calculated as:

[0154]

[0155] where, is the mean of the tire force prediction, i.e., the tire force prediction, is the variance of the prediction, which can be further expressed as:

[0156]

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

[0158]

[0159] where, After obtaining the value of θ, it is substituted back into equations (13) and (14) to solve the normalized tire force prediction and its variance

[0160] Finally, the tire force prediction value can be obtained by linear de-normalization theory which is written as:

[0161]

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

[0163] Based on the general training process of the tire force GPR prediction model constructed in step S4, the minimum value of the negative log-likelihood function is searched using BKA, which indirectly achieves the purpose of maximizing the likelihood function, thereby determining the optimal hyperparameter θ value to obtain the optimal tire force GPR prediction model, i.e., 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] First step: initialize the BKA parameters, set the population size pop to 30, the maximum number of iterations T to 50, the dimension of the feasible solution dim to 5, and the corresponding upper and lower limits ub and lb to 5 and -5, respectively;

[0165] Second step: 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), and the initial position P 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 population individual is calculated, the negative value of the log-likelihood function is calculated as the individual fitness value. After the initial position and fitness of all individuals in the population are calculated, the individual with the minimum fitness is found as the leader of the black kite population, leading the flight direction of the entire population, i.e. the search direction of the global optimal solution of θ.

[0168] Step 3: The biological behavior of the black kite searching for prey in the air and adjusting the attack posture is simulated, the position of the population individual is dynamically adjusted, and the search ability of the local optimal solution of θ is enhanced. The calculation formula of the individual position under the attack behavior is:

[0169]

[0170] wherein, and respectively represent the position of the bi-th black kite in the t-th and (t+1)-th iteration, p is a constant with a value of 0.9, t is the number of iterations completed so far, and 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 compared with the current individual function value. If it is smaller, the individual position and function value are updated, otherwise they are not updated.

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

[0172]

[0173] wherein, represents the fitness of the leader of the bj-th dimension black kite in the t-th iteration so far (the current population optimal solution), C(0, 1) represents Cauchy mutation, and the coefficient Similarly to step 2, after the individual position is updated, the position constraint, individual fitness calculation and updating operation are needed.

[0174] Step 5: Population optimal fitness and position updating. When a population iteration is completed, if the population optimal fitness of this iteration is better than the population optimal fitness searched so far, the population optimal fitness of this iteration is replaced and the corresponding population optimal position is updated. The population optimal position is the optimal θ of the GPR model.

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

[0176] Finally, the optimal θ solution found by BKA is substituted back into equations (13) and (14) to obtain the BKA-GPR tire force prediction model.

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

[0178] On the basis of obtaining VT1 norl and Data_F norl in step S3, define the set DS={(x u ,y u )|u=1,2,3,…,m}=(VT1 norl ,Data_F norl ), wherein: x u ∈R n is an n-dimensional input vector, i.e., the PVDF sensor voltage value, y u ∈R is an output scalar corresponding to x u , i.e., the tire force, and the m*n-dimensional input matrix can be expressed as X=[x1,x2,…,x m ].

[0179] Further, b sub-sample sets are repeatedly extracted from the original training data set with replacement using the bootstrap method, thereby constructing b regression trees; when the b u th subset is extracted, the unselected observations constitute out-of-bag data; when the b u th regression tree is constructed, 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 minimum variance is used as the branch goodness criterion to select the split variable, written as:

[0180]

[0181] wherein L y is the optimal split variable, X ψ is the ψth voltage feature in the voltage feature vector, and is the mean value of the ψth feature in the input feature. Each regression tree adopts a no-pruning strategy to recursively branch from the root node top-down, and the minimum leaf node size is set as the regression tree growth termination condition. After the growth of the b regression trees is completed, the complete RF regression model can be constructed. Finally, the root mean square error (RMSE) is used to evaluate the prediction performance of the model through the out-of-bag data, i.e.,

[0182]

[0183] where n OOB is the number of out-of-bag data samples, y js is the true tire force, is the RF model tire force estimation. The RF model evaluates the degree of influence of each input feature on the tire force with feature importance score, and the importance score of each input feature is measured by the prediction RMSE and sorted. The b regression trees are tested using out-of-bag data, and the root mean square errors are RMSE1, RMSE2, …, RMSE b . The variable X ψ is replaced using the random disturbance method in the b out-of-bag data sets to form a new out-of-bag test set. The b regression trees are retested using the new out-of-bag data to form the random replacement RMSE matrix, written as:

[0184]

[0185] Further, the importance score of the ψth input variable can be expressed as: RMSE1, RMSE2, …, RMSE b is subtracted from the ψth row of the root mean square error matrix, and the average value of the b regression trees is taken, and finally divided by the standard error S E of the b regression trees, to obtain the average reduction of the root mean square error of the variable X ψ . Thus, the importance score formula of each input feature is obtained as:

[0186]

[0187] Finally, on the basis of obtaining the importance ranking of all input features, the importance scores are arranged in descending order according to the size, and the sequence forward search strategy is used to add the feature with the highest importance score in the current input feature set one by one, which is passed to step S5 to obtain the BKA-GPR tire force prediction model for training, and and are used for testing to obtain the current input feature set RMSE, 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. Figure 9 、 10 and 11 respectively show the traversal results of 10 voltage features near the voltage feature corresponding to the minimum RMSE of the longitudinal, lateral and vertical tire forces, wherein the bar chart is the feature importance score (arranged in descending order), and the line chart is the test set RMSE of the prediction model trained by the feature set composed of the current feature number searched by the sequence forward search. The first digit of the horizontal coordinate voltage feature number indicates which sensor the feature value point comes from (i.e. Figure 5The first number is the longitudinal number of the voltage feature, and the second number is the number of the voltage feature in the sensor (the voltage feature point number of the tire closest to the ground mark entry point is defined as 1). These figures show that the RMSE of the prediction model trained when the longitudinal, lateral and vertical force features traverse to 51-14, 51-5 and 37-5, respectively, is the smallest when predicting the test set, so the voltage feature value combination corresponding to all feature numbers before the cutoff point is extracted as the optimal input feature set of the tire three-way force prediction model. Based on the determination of the optimal input features, the optimal feature selection operation is performed on the data set and and Finally, the optimal feature set corresponding to the tire longitudinal, lateral and vertical force in this example contains 64, 51 and 36 voltage features, respectively.

[0188] The size of the training data is also a key factor affecting the estimation accuracy and speed of the model. Since the Sobol method is used in step S3 of the present application to collect the voltage-tire force data set, as long as the data in the data set is extracted in order, it can be ensured that the extracted data is uniformly covered in the sampling interval. Based on the obtained and , the initial data set is 5% of and the corresponding , and the training data set is extracted in increments of 5% and sequentially submitted to the optimized GPR tire model for training, and the test set composed of and is used for testing until all and data are extracted as training data sets, and the RMSE of each test set is recorded. Finally, the training data size corresponding to the minimum RMSE is selected as the best training data size. Figure 12 (a), 12(b) and 12(c) respectively show the test results of the models trained using different training data sizes for the longitudinal, lateral and vertical forces of the tire in this example. The results show that the longitudinal, lateral and vertical force prediction models achieve the best test results when the training data size is 80% (i.e. 2040 groups), 70% (i.e. 1785 groups) and 50% (i.e. 1275 groups), respectively, and the corresponding RMSE is 4.03N, 2.64N and 2.37N, respectively. Therefore, the training data sizes of 2040 groups, 1785 groups and 1275 groups are selected as the best training data sizes for training the longitudinal, lateral and vertical force BKA-GPR prediction models of the tire.

[0189] Finally, the optimal feature set for the longitudinal, lateral and vertical forces of the tire is obtained and ​and the best data scale of the training data set, the general training method of the BKA-GPR tire force prediction model established in steps S4 and S5 is used to retrain F x 、 y and F z prediction model.

[0190] S7, the tire force prediction model retrained in step S6 is inputted with the optimal voltage feature, and the tire force normalized prediction value and its variance are outputted, and the tire force actual prediction value can be obtained by inverse normalization.

[0191] On the basis of the retrained BKA-GPR tire three-direction force prediction model obtained in step S6, the input of the BKA-GPR tire force prediction model is used , and the output is the tire force normalized prediction value and its variance On this basis, the tire force actual prediction value can be obtained by inverse normalization is written as:

[0192]

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

[0194]

[0195]

[0196] Figure 13 and 14 The tire three-direction force prediction method proposed in the present application is tested under the double shift line working condition of high adhesion (adhesion coefficient is 0.8) and low adhesion (adhesion coefficient is 0.3) road surface at high speed and medium speed, wherein SWA is the steering wheel angle, V x is the vehicle speed. The results show that any one of the tire force prediction curves and the true value curves shown in the two figures has a high coincidence degree. In the high-speed high-adhesion test, the maximum absolute value of the absolute error of the F x , F y and F z prediction model is 21.31N, 22.44N and 14.33N respectively, which shows good estimation accuracy. Similarly, the prediction model also shows satisfactory performance in the medium-speed low-adhesion test, the maximum absolute value of the absolute error of the F x , F y and F zThe maximum absolute values of absolute errors of the prediction models are 12.64 N, 24.88 N and 4.09 N, respectively. Overall, the F x , F y and F z prediction models all show high estimation accuracy, whether the tire is in high-speed high-attachment or in medium-speed low-attachment. Although the confidence intervals of the three tire force estimation prediction results increase due to unstable tire-ground contact as the road adhesion coefficient decreases, the increase is still within an acceptable range, which indicates that the F x , F y and F z prediction models also show good prediction stability.

[0197] In summary, the tire three-way force prediction method based on the piezoelectric intelligent tire technology and the BKA-GPR provided by the present application has high F x , F y and F z prediction accuracy and good robustness, and can provide uncertainty quantification for the prediction results, i.e., 95% confidence interval, so as to better serve the optimization design of the subsequent vehicle control system.

[0198] The above content only illustrates the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical solution falls within the protection scope of the claims of the present application.

Claims

1. A tire three-way force prediction method based on piezoelectric type smart tire technology and BKA-GPR, characterized by, The method comprises the following steps: S1, a tire and PVDF sensor finite element model is established, and on this basis, an Inp fusion method is used to construct a piezoelectric intelligent tire finite element model; S2, a first-order main effect index calculation simulation scheme is designed, a calculation feature is selected, a first-order main effect index of tire force and PVDF output voltage is calculated, and an optimal installation position of the sensor is determined; S3, a voltage-tire force data set simulation working condition is designed based on the Sobol method, PVDF output voltage and tire force data are collected and preprocessed, and a data set that can be used for training and testing is formed; S4, based on the characteristics of the voltage-tire force data set, the mean function and the covariance function type of the GPR model are selected, and a general training process of the GPR tire force prediction model is constructed; S5, the GPR model obtained in step S4 is optimized by using the BKA hyperparameter optimization method, and a BKA-GPR model is obtained; S6, based on the BKA-GPR model obtained in step S5, the optimal input feature and the best training data set size are determined, and the tire force prediction model is retrained; Step S6 specifically comprises the following steps: S6-1, define a set DS = {(x u , y u ) | u = 1, 2, 3, …, m} = (VT1 norl , Data_F norl ), wherein: x u ∈R n is an n-dimensional input vector, that is, a PVDF sensor voltage value, y u ∈R is an output scalar corresponding to x u , that is, a tire force, and an m*n-dimensional input matrix can be expressed as X = [x1, x2, …, x m ]; S6-2, repeatedly draw b (b > 0) sub-sample sets from the original training data set with replacement by using the bootstrap method, thereby b regression trees can be constructed, wherein the ψ (ψ > 0) features in the b sub-sample sets can be defined as X ψ On this basis, the prediction performance of the model is evaluated by the out-of-bag data prediction accuracy, and an error matrix is formed, written as: ； S6-3, based on the error matrix obtained in step S6-2, calculate all features X ψ The error average reduction of each feature X is the importance score, and is arranged in descending order; the calculation formula is: ； S6-4, using the sequence forward search strategy, the feature with the highest importance score is added to the current input feature set one by one, the optimized GPR tire force prediction model obtained in step S5-5 is trained, and the prediction error of the current input feature set is tested until all input features are traversed; finally, the input feature set with the minimum prediction error is taken as the optimal input feature set, and the data set and is subjected to optimal feature screening operation to obtain and ; S6-5, based on the training set after optimal feature extraction in step S6-4, the training data set is extracted in increments of 5%, and is sequentially submitted to step S5-5 to optimize the GPR tire model for training, and is tested using the test set until all the data in the training data set are extracted as the training data set, and the test error of each time is recorded; finally, the training data size with the minimum prediction error is taken as the best training data size; S6-6, on the basis of the obtained training data set with optimal input characteristics and optimal data size, combined with the general training method of the designed BKA-GPR tire force prediction model, retrain F x , F y and F z prediction model; S7, the tire force prediction model retrained in step S6 is inputted with the optimal voltage feature, and outputs the tire force normalized prediction value and its variance, and the actual tire force prediction value can be obtained through inverse normalization.

2. The piezoelectric type smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 1, characterized in that, Step S1 specifically comprises the following steps: S1-1, a tire finite element model is established, and its Inp code is outputted after its accuracy is calibrated through a stiffness experiment; S1-2, a PVDF sensor finite element model is established, and its Inp code is outputted after its accuracy is calibrated through a single cantilever beam experiment; S1-3, the Inp codes of the tire finite element model and the PVDF sensor finite element model are fused, boundary conditions and constraints are set to form a piezoelectric intelligent tire finite element model, and the accuracy thereof is calibrated through a real vehicle experiment.

3. The piezoelectric type smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 2, characterized in that, Step S2 specifically comprises the following steps: S2-1, the influencing factors of the voltage output by the PVDF sensor in the piezoelectric intelligent tire and the value range thereof are determined according to daily driving conditions, a voltage-tire force data set simulation matrix SC is designed based on the definition form of the first-order main effect index calculation scheme according to the global sensitivity analysis theory of the multiplicative dimension reduction method, and is written as: ； wherein , , …, represent 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, b are the upper and lower limits of the values of the influencing factor BL(i), z t (t = 1, 2, 3, 4, 5) are the node values of the five-node Gaussian value formula; S2-2, according to the generation mechanism of tire force, the voltage values of q (q>0) specific positions on the PVDF sensor output voltage curve are selected as the first-order main effect indicator (FMEI) to calculate the characteristic value; the selection logic of the specific positions is: taking the tire-ground contact center point as the reference, q (q>0) voltage values on the PVDF sensor output voltage curve are selected at intervals of η° (η>0) along the two sides of the point in the tire circumferential direction, at this time, the calculation characteristic value vector VC of the PVDF sensor voltage curve at the j (j=1, 2,.., 62) sensor installation position is VC j may be represented as: ； wherein, , and are the 1st, 2nd, and qth calculated characteristic value points of the PVDF sensor voltage curve at the jth sensor mounting location, respectively. S2-3, the average value of the FMEI of all calculation feature points contained in the voltage signal curve collected at the jth sensor installation position is taken as the final FMEI of the position, and is denoted as MFMEI; at this time, the MFMEI of the tire force and the PVDF sensor output voltage at the jth installation position can be expressed as: ； where the superscript of MFMEI = 1 or 2 or 3 represents the longitudinal, lateral and vertical forces NFMEI, The calculation formula of MFMEI can be further written as: ； wherein, is the value of the origin moment corresponding to the jth calculated eigenvalue of the voltage signal of the jth sensor installation position when the influencing factor is BL(i), k = 1 or 2, indicating the first or second order origin moment, w t is the weight of the five-node Gauss value formula, PVDF_IT FEM (·) is the solving equation of the output voltage of the PVDF sensor in the finite element model of the piezoelectric intelligent tire; S2-4, on the basis of calculating the tire force corresponding to all potential installation positions of the PVDF sensor in the tire and the output voltage MFMEI, a screening index is set, and positions greater than the screening index are selected as the installation positions of the sensor, p (p>0) installation positions meeting the conditions are screened out, the optimal installation position of the PVDF sensor is selected, and a piezoelectric intelligent tire finite element model is reconstructed.

4. The piezoelectric type smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 3, characterized in that, Step S3 specifically includes the following steps: S3-1, based on the Sobol method, an m*n (m>0, n>0) dimensional sampling sequence matrix qs is generated, and the specific values of each influencing factor in each dimension in the data set simulation matrix are calculated in combination with the value range of each influencing factor set in step S2-1, and the value formula is: ； where st λ is the λth (λ>0) n-dimensional simulation value vector of qs λ is the λth n-dimensional sample vector of the sample 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, respectively; finally, three m x n-dimensional voltage-tire force dataset simulation matrices representing the longitudinal force (F x ), lateral force (F y ), and vertical force (F z ) can be obtained, respectively. S3-2, using the piezoelectric intelligent tire finite element model reconstructed in step S2-4, calculate the simulation matrix of the three m x n dimension voltage-tire force data sets 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 respectively represent the longitudinal, lateral and vertical directions of the tire; S3-3, using the feature extraction method in step S2-2 to respectively extract features of VT0 l , and then obtain the voltage data set VT1 l ; on this basis, linear normalization theory is used to normalize VT1 l and Data_F l to obtain the normalized data set VT1 norl and Data_F norl , and the normalization expression is: ； wherein VT1 norl (i, j) represents the data in the ith row and jth column of VT1 norl (i, j) represents the data in the ith row and jth column of VT1 l (i, j) is the data in the ith row and jth column of VT1 l (i, j) represents the data in the ith row and jth column of VT1 minl and VT1 maxl are the minimum and maximum values in VT1 l respectively, Data_F norl (i, j) is Data_F norl (i, j) represents the data in the ith row and jth column of Data_F l (i, j) is Data_F l (i, j) represents the data in the ith row and jth column of Data_F minl and Data_F maxl are the minimum and maximum values in Data_F l respectively; S3-4, take VT1 norl and Data_F norl The first 85% as training set, defined as and The last 15% as test set, defined as and .

5. The piezoelectric smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 4, characterized in that, Step S4 specifically includes the following steps: S4-1, according to VT1 norl and Data_F norl The form of the mean function and the covariance function are determined from the data characteristics of VT1 and Data_F and from experience, written as: ； ； wherein, is a latent function, representing VT1 norl Data_F corresponding to the input x 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 the 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 piezoelectric type smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 5, characterized in that, In step S4-2, the general training method of the tire force GPR prediction model is: First, the VT1 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 、 、 and The joint prior distribution can be derived, written as: ； in, The test set input Input to the training set The n×1 covariance matrix between them The covariance of the test set itself. for 3D identity matrix; Further, a prediction value can be calculated The posterior distribution of the parameters is ； wherein, is the predicted mean, i.e. the predicted value, is the variance corresponding to the predicted value, which can be further expressed as: ； ； Further, the value of the hyperparameter set θ can be obtained by maximizing the log-likelihood function, and the log-likelihood function is written as: ； where ; after obtaining the value of θ, substitute it back and then the normalized tire force prediction value and its variance ; Finally, the predicted value of tire force can be obtained by linear de-normalization theory and is written as: 。 7. The piezoelectric smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 6, wherein, Step S5 specifically includes the following steps: S5-1, initialize the BKA parameters, including the population size pop, the maximum number of iterations T, the dimension of the feasible solution dim, and the corresponding upper and lower limits ub and lb; S5-2, initialize the initial position of the black kite population individual, that is, the initial solution θ, and the fitness, that is, the negative log-likelihood function value corresponding to the initial solution θ of the individual, and the expression of the initial position P of the individual is: ； Wherein, rd is a random number in [0, 1]; after the initial position of the population individual is calculated, the negative value of the log-likelihood function is calculated as the fitness value of the individual; after the initial position and fitness of all individuals in the population are calculated, the individual corresponding to the minimum fitness is found as the leader of the black kite population, which leads the flight direction of the whole population, that is, the search direction of the global optimal solution θ; S5-3, simulate the attack behavior of the black kite to calculate the individual position, and the formula is: ； wherein, and respectively represent the position of the bi black-winged kite in the tth and (t+1)th iteration in bj dimensions, p is a constant with a value of 0.9, t is the number of iterations completed so far, the coefficient is 0.05e ^ (-2tT -1 ) 2 After the individual position is updated, the value range of the hyperparameter θ is constrained using [ub, lb], and then the negative log-likelihood function value is calculated using the θ value after the range constraint processing, and compared with the function value of the current individual. If it is smaller, the individual position and function value are updated, otherwise they are not updated. S5-4, simulate the migration behavior of the black kite to calculate the individual position, and the formula is: ； wherein, C(bj, t) represents the fitness of the bj-dimensional black-winged kite leader representing the tth iteration so far, i.e. the current population optimal solution, C(0, 1) represents the Cauchy mutation, the coefficient h = 2sin(r + Π / 2); after the individual position is updated, the range of the value of theta is constrained using [ub, lb], then the value of the negative log-likelihood function is calculated using the constrained theta value, and compared with the function value of the current individual, if smaller, the individual position and function value are updated, otherwise not updated; S5-5, update the optimal fitness and position of the population; after 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, the optimal fitness of the population in this iteration is replaced and the corresponding optimal position of the population is updated; wherein the optimal position of the population is the optimal θ of the GPR model; S5-6, loop calculation; return to step three, loop calculation, until the convergence condition is met or the maximum number of iterations is reached; finally, the optimal θ solution searched by the BKA is substituted back into the GPR model to obtain the BKA-GPR tire force prediction model.

8. The piezoelectric type smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 7, characterized in that, Step S7 specifically includes the following steps: S7-1, on the basis of the retrained BKA-GPR tire three-direction force prediction model obtained in step S6-6, using as the input of the BKA-GPR tire force prediction model, the tire force normalized prediction value and the variance thereof , on the basis of which the actual tire force prediction value is obtained by performing reverse normalization. S7-2, calculate the confidence interval of the tire force prediction value to quantify the uncertainty of the tire force prediction value.

9. The piezoelectric smart tire technology and BKA-GPR based tire three-way force prediction method according to claim 8, wherein, In step S7-2, the confidence interval calculation formula is: ； ； wherein upper is an upper limit vector of the confidence interval corresponding to the tire force prediction vector, lower is a lower limit vector of the confidence interval corresponding to the tire force prediction vector, t o is a confidence interval coefficient.

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