Tire force estimation method based on in-utero sensing information and bayesian neural network

Abstract

The application discloses a tire force estimation method based on in-utero sensing information and a Bayesian neural network, builds an acceleration type intelligent tire finite element model based on finite element and coordinate system conversion theory; determines the optimal installation position of the acceleration sensor for the three-way tire force by using a Fourier amplitude sensitivity test (FAST); collects acceleration signal-tire force data sets under different test conditions, extracts the acceleration signal in the footprint area, and selects the optimal input features by using a linear discriminant analysis (LDA); processes the acceleration signal-tire force data set after optimal feature selection by using linear normalization theory; builds a tire force estimation algorithm based on a Bayesian neural network according to the characteristics of the training data and the test data, and finally outputs the predicted value and the prediction variance of the tire force. The application has high prediction accuracy, good stability and strong generalization performance, and provides a more reliable technical solution for tire force estimation.

Description

TECHNICAL FIELD

[0001] The present application relates to a tire force estimation method based on in-utero sensing information and a Bayesian neural network, and belongs to the technical field of vehicle control. BACKGROUND

[0002] Accurate and real-time acquisition of tire force is the key to vehicle dynamics control. However, due to cost and technical limitations, direct measurement of tire force under vehicle operating conditions is very costly. Therefore, many experts and scholars have developed various tire force estimation methods based on different technologies, including the well-known tire force estimation methods based on Kalman filter, recursive least squares, and sliding mode observer. These methods mostly require the use of simplified vehicle / tire models, although simplified models can handle most driving conditions, but they still face challenges in accurately representing the actual motion state of the vehicle under extreme driving conditions. Although using more complex vehicle / tire models can effectively improve this problem, it also increases the system calculation time, thereby reducing the operating efficiency and system performance of the vehicle control system.

[0003] With the development of sensor technology and electronic information technology, intelligent tire technology has emerged. This technology collects tire dynamic characteristic information through sensors installed inside the tire and combines machine learning or physical models to achieve real-time and accurate estimation of tire state. Compared with traditional tire force estimation methods, this method directly uses sensor signals inside the tire to estimate tire state parameters, significantly reducing the use of on-board sensors, and effectively avoiding the problem of decreased estimation accuracy caused by cumulative errors in multiple sensor signal acquisition. However, there are still some areas that can be optimized in the current tire force estimation methods based on intelligent tire technology. On the one hand, existing intelligent tire force estimation methods lack sufficient consideration of sensor installation location selection, making it difficult to ensure high-quality continuous acquisition of dynamic characteristic signals during tire operation. On the other hand, there is a lack of effective means to remove redundant information in the characteristic signals, which cannot guarantee the training effect of the tire force estimation model. In addition, in the current intelligent tire force estimation field, when constructing the signal feature-tire force mapping relationship, some data-driven techniques are often used in a general way without fully considering the matching between signal features and mapping methods, which also makes it difficult to guarantee the performance of the tire force estimation model trained. At the same time, the mapping relationship construction also lacks compatibility consideration with subsequent vehicle control system design. SUMMARY

[0004] Invention purposes: In view of the deficiencies in the prior art, the present application provides a tire force estimation method based on in-utero sensing information and Bayesian neural network. The present application considers the determination of the installation position of the accelerometer sensor inside the tire, and at the same time, uses fewer input characteristic values and combines the Bayesian neural network to build a tire estimation algorithm. The algorithm can output the uncertainty while outputting the force estimation value, which provides a basis for the optimization design of the vehicle control system.

[0005] Technical scheme: The tire force estimation method based on in-utero sensing information and Bayesian neural network comprises the following steps:

[0006] S1, a tire finite element model is established based on the finite element method, an acceleration sensor model is constructed using the coordinate system conversion theory, and on this basis, an acceleration type intelligent tire finite element model is built;

[0007] S2, a first-order sensitivity index calculation simulation scheme is designed, the characteristic values are determined, the first-order sensitivity index of the tire force and the accelerometer output signal is calculated, and the optimal installation position of the sensor is determined;

[0008] S3, acceleration-tire force data sets are collected, the optimal input features of the data sets are screened and processed using the LDA method, further normalized processing is performed on the data sets combined with the linear normalization theory, and the training set and the test set are divided;

[0009] S4, according to the tire force training set and test set obtained in step S3, a tire force estimation model based on Bayesian neural network is built;

[0010] S5, on the basis of the tire force estimation model obtained in step S4, the optimal acceleration characteristic is input, the tire force normalized prediction value and its variance are output, and then the tire force actual prediction value can be obtained through the inverse normalization.

[0011] Step S1 specifically comprises the following steps:

[0012] S1-1, analyze the tire structure, size and material parameters, and on this basis, build a tire finite element model;

[0013] S1-2, build an acceleration sensor model using the coordinate system conversion theory, and on this basis, form an acceleration type intelligent tire finite element model;

[0014] S1-3, build an intelligent tire real vehicle verification platform to verify the accuracy of the finite element model built in step S1-2.

[0015] Step S2 specifically comprises the following steps:

[0016] S2-1, determine the influencing factors and their value ranges of the acceleration sensor output acceleration in the acceleration type intelligent tire according to the daily driving working conditions, and refer to the definition form of the first order sensitivity index calculation scheme based on the FAST method, the first order sensitivity index simulation scheme of the tire force can be written as:

[0017]

[0018] wherein, the simulation working condition YX(ξ) i,j (ξ=1,2,……n,i=1,2,3…,n,j=1,2,3…,n) value can be calculated by the FAST value formula, written as:

[0019] YX(ξ) i，j =0.5(1+sin(ω ξ )t j )

[0020] wherein, ω ξ is the integral angular frequency of the influencing factor, when ξ=1,2,…,n, it represents the integral angular frequency of YX1,YX2,…,YXn, t is the sampling time point, the specific value is:

[0021] t j =π / 250+(j-1)π / 250

[0022] Further, on the basis of obtaining the first order sensitivity index calculation simulation scheme, the acceleration type intelligent tire finite element model established in step S1-2 is used for simulation calculation, and the acceleration signals and the corresponding tire force signals of all potential installation positions of the accelerometer are extracted;

[0023] S2-2, according to the generation mechanism of the tire force, along the circumferential two sides of the tire-ground contact center point, the acceleration values of q(q=1,2…,16) specific positions on the acceleration signal curve are selected as FOSEI calculation characteristic values with an interval of б°(б>0); At this time, the longitudinal, transverse and radial calculation characteristic value vectors Acc_x j , Acc_y j and Acc_z j of the acceleration curve collected by the j(j=1,2,..,66)th sensor installation position acceleration sensor can be represented as:

[0024]

[0025] S2-3, the average value of all calculation characteristic points FOSEI contained in the radial acceleration signal curve collected by the jth sensor installation position is taken as the final FOSEI of the position, denoted as MFOSEI; At this time, the tire force F lThe MFOSEI of the longitudinal acceleration signal of the jth sensor installation position and the acceleration sensor radial acceleration can be expressed as:

[0026]

[0027] wherein, is the average value of the first-order sensitivity index of the longitudinal acceleration signal of the jth sensor installation position and the influencing factor YX(ξ), var_ACC_x(j, e) is the variance of the mth (m > 0) sampling result of the e (e = 1, 2, …, q) calculation characteristic of the longitudinal acceleration curve of the jth installation position, A YX(ξ) (j, e) and B YX(ξ) (j, e) respectively represent the first-order Fourier coefficients A and B of the e (e = 1, 2, …, q) calculation characteristic value point of the longitudinal acceleration signal of the jth sensor installation position when the influencing factor is YX(ξ), which can be further written as:

[0028]

[0029] The MFOSEI between the longitudinal, lateral and radial acceleration signals of the acceleration sensor at different installation positions and the tire longitudinal force is obtained by repeating the above method;

[0030] Similarly, the first-order sensitivity index between the acceleration signals at different positions and the tire lateral force and the tire radial force is calculated.

[0031] S2-4, on the basis of calculating the tire force corresponding to all potential installation positions of the acceleration sensor in the tire and the MFOSEI of the output acceleration, a screening index is set, and the positions greater than the set screening index are selected as the sensor installation positions, and p (p > 0) installation positions with higher sensitivity are screened out to realize the selection of the optimal installation position of the acceleration sensor, and the finite element model of the acceleration type intelligent tire is reconstructed.

[0032] Step S3 specifically includes the following steps:

[0033] S3-1, a simulation calculation working condition of the acceleration-tire force data set is designed, the reconstructed finite element model of the acceleration type intelligent tire obtained in step S1-2 is used to calculate the data set, and the sensitivity analysis results between the acceleration signal and the tire force are combined to extract the acceleration signal and the tire force signal to form the acceleration-tire force data set. Finally, the footprint area signal extraction method in step S2-3 is used to extract the footprint area characteristic signal of the acceleration-tire force data set. The tire longitudinal force-acceleration data set can be expressed as:

[0034] D_F x = {(a j ,y jj = 1,2,3..., ψ} = (a,y)

[0035] wherein, is a ψ x (p*q) -dimensional acceleration signal matrix, a j is the jth (p*q) -dimensional acceleration signal vector in a, y is a ψ -dimensional F x numerical vector, y j is the jth tire longitudinal force value in y, F x is: tire longitudinal force; further, the acceleration signal matrix a can be expressed as:

[0036]

[0037] S3-2, based on the dimensionality reduction principle of LDA method, respectively calculate the between-class scatter matrix S B and the within-class scatter matrix S W , written as:

[0038]

[0039]

[0040] wherein, K represents the total number of classes, q represents the rth class sample, N r represents the total number of the rth class sample, ψ r represents the mean of the rth class sample, C r represents the sample set of the rth class;

[0041] Further, by Fisher linear discriminant, the solution of formula S B and S W is converted into the solution of an optimization problem, and the corresponding loss function can be written as:

[0042]

[0043] wherein, W is the projection vector; since the solution of the loss function is only related to the direction of W, and is irrelevant to its size, W T S W W = 1; at this time, the loss function with constraint can be written as:

[0044]

[0045] Further, combining the objective function and the constraint condition, a Lagrange function is constructed, the partial derivative of W is taken and set to zero, and max J(W) can be further written as:

[0046]

[0047] Further, the eigenvalues and eigenvectors of the above equation are solved, and the variance contribution rate (VC) and the accumulated variance contribution rate (AVC) of each eigenvalue are calculated, which can be written as:

[0048]

[0049] where λ l is the lth eigenvalue, and P is the number of selected eigenvalues; based on the obtained AVC, the threshold value of 95% of the accumulated variance contribution rate is selected, and the first b eigenvectors with the accumulated variance rate reaching 95% are screened out to form a matrix W opt = [W1, W2, …, W 32 ], and the expression of a after the optimal feature screening can be written as:

[0050] a o = aW opt

[0051] S3-3, the linear normalization theory is used to normalize a o and y, and the normalized expression is:

[0052]

[0053] where a onor (h, p) is the hth row and pth column data in the normalized input feature a onor , y nor (h, p) is the hth row and pth column data in the normalized longitudinal force output y nor , a omin and a omax are the minimum value and the maximum value in a o , respectively, a o (h, p) is the hth row and pth column data in a o , y(h, p) is the hth row and pth column data in the matrix y, y min and y max are the minimum value and the maximum value in y, respectively; finally, 70% and 30% of the normalized data set D_F x _nor = {(a onorj , y norj )|j = 1, 2, 3, …, ψ} = (a onor , y nor ) are selected as the training set input and output and the test set input and output Similarly, the data sets corresponding to the tire lateral force and vertical force are respectively subjected to optimal input feature screening, normalization and data division operations.

[0054] Step S4 specifically includes the following steps:

[0055] S4-1, specifically, the training set D_F and the test set D_F input into the Bayesian neural network prediction model, and the mapping model is established by learning the relationship between the output values in the training set D_F x _nor_train and the input values and the input values , written as:

[0056]

[0057] where ω is the weight parameter;

[0058] S4-2, the prior distribution P(ω) of ω is further expanded as:

[0059]

[0060] where the normalization factor Z ω (α) and the expectation E ω can be further written as:

[0061]

[0062] where α is a hyperparameter;

[0063] Further, define that the noise obeys a Gaussian distribution with mean 0 and variance σ 2 , then ε ~ N(0, σ 2 ); At this time, the likelihood function of the entire data set can be expressed as the product of the likelihood of all samples, written as:

[0064]

[0065] where, is the probability distribution of the target value being under the condition of given input data and weight parameter ω, the normalization factor β is a hyperparameter;

[0066] Further, based on the Bayesian principle, the posterior probability can be written as:

[0067]

[0068] where P(D_F x _nor_test | D_F _nor_train, ω) is the likelihood function of the test set D_F _nor_testnor) is the marginal likelihood, the normalization factor Z s (α,β) = ∫e -S(ω) dω, the regular error function

[0069] Further, the S(ω) is approximated to be equal to the second order expansion at the minimum point ω MP , which is written as:

[0070]

[0071] where the Hessian matrix of the function S(ω) at ω MP is the matrix Then the normalization factor Z s (α,β) is approximated to be:

[0072] Z s (α,β) = (2π) s / 2 |A|exp(-S(ω MP ))

[0073] S4-3, the ω MP value is solved by the update iteration method, and the hyperparameters α and β are calculated; on this basis, the distribution of the normalized prediction output corresponding to the test set input is calculated according to the Bayesian network principle, which is written as:

[0074]

[0075] S4-4, the parameter ω is sampled multiple times based on the Monte Carlo method, and the function value corresponding to each sampling point is calculated On this basis, the average of all calculated function values is taken, and then the final normalized expected value , i.e. the normalized longitudinal force estimation value, and the variance can be written as:

[0076]

[0077] Similarly, based on the tire lateral and vertical tire force data set obtained in step S3-3, a tire lateral and vertical force estimation model is built.

[0078] Step S5 specifically includes the following steps:

[0079] S5-1, on the basis of the tire longitudinal force estimation model obtained in step S4-4, use as the input of the tire force budget model, and output the tire normalized value and the variance On this basis, the actual estimated value of the longitudinal force can be obtained by inverse normalization Write:

[0080]

[0081] Similarly, the actual estimated value of the lateral and radial force estimation model of the tire is obtained;

[0082] S5-2, the uncertainty of the longitudinal force estimation value is quantified by the confidence interval (CI); the above steps can be repeated to estimate the tire lateral and vertical force and its uncertainty estimation.

[0083] In the step S5-2, the confidence interval calculation formula is:

[0084]

[0085] Where, up_value is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, lo_value is the lower limit vector of the confidence interval corresponding to the tire force prediction vector t o The confidence interval coefficient is repeated; the above steps can be repeated to estimate the tire lateral and vertical force and its uncertainty estimation.

[0086] Compared with the prior art, the present application has the following remarkable beneficial effects:

[0087] By establishing an acceleration type intelligent tire finite element model through a finite element software, the time and cost required for scientific selection of the in-tire installation position of the acceleration sensor and extraction of training data for the tire force prediction algorithm can be effectively reduced;

[0088] The optimal installation position of the sensor is determined based on the FAST method, which effectively improves the accuracy and reliability of signal acquisition, and provides a higher quality data source for subsequent tire force prediction;

[0089] The input features are processed by LDA method for dimension reduction, which effectively eliminates redundant information while retaining key features, which is beneficial to reduce the model complexity and improve the tire force estimation efficiency;

[0090] Compared with the traditional tire force estimation algorithm, the tire force estimation model proposed by the present application has the advantages of low cost, simple structure and high prediction accuracy. Even in the case of small sample training data, the model can still maintain high prediction accuracy. In addition, the prediction model can output the uncertainty of the tire force estimation value, which is beneficial to the optimization design of the vehicle control system based on the estimation technology. BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1An embodiment flowchart of the patent application for the tire force estimation method based on in-utero sensing information and Bayesian neural network.

[0092] Figure 2 An acceleration type intelligent tire finite element modeling flowchart in the patent application.

[0093] Figure 3 A sensor installation position map of the test tire of the intelligent tire finite element model in the patent application.

[0094] Figure 4 A sensor installation position map of the inner liner in the patent application.

[0095] Figure 5 Radial and lateral acceleration signal curves collected by ACC-M.

[0096] Figure 6 First-order sensitivity index calculation results corresponding to the longitudinal, lateral, and vertical forces of the tire.

[0097] Figure 7 Dimensionality reduction results map of the longitudinal, lateral, and vertical force input characteristics of the tire.

[0098] Figure 8 Tire force model estimation results map under low adhesion and complex slip conditions.

[0099] Figure 9 Tire force model estimation results map under high adhesion and complex slip conditions. DETAILED DESCRIPTION

[0100] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying 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 of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0101] As shown in Figure 1 A tire force estimation method based on in-utero sensing information and Bayesian neural network, comprising the following steps:

[0102] S1, a tire finite element model is established based on the finite element method, an acceleration sensor model is constructed using coordinate system conversion theory, and an acceleration type intelligent tire finite element model is built on this basis;

[0103] Figure 2The modeling process of the acceleration type intelligent tire finite element model in the application is shown, including the establishment of the tire finite element model and the construction of the acceleration sensor model. First, by analyzing the material parameters and structure of the tire, the tire structure diagram is drawn by using Abaqus software, and the related materials are assigned and the grid is drawn. On this basis, the finite element model of the accelerometer type intelligent tire is built by using the global-local coordinate system transformation theory. Then, the effectiveness of the model is verified by the intelligent tire test platform. As shown in Figure 3 , during the test process and the simulation process, the acceleration sensors are installed at the center of the inner liner of the tire, the left and right tire shoulders, and the tire side, respectively, and are named ACC-M, ACC-L1, ACC-R1, ACC-L2 and ACC-R2. Under the condition of straight line free rolling, if the acceleration curves collected by the accelerometers at the same position of the intelligent tire finite element model and the test tire are consistent, the model is saved. Otherwise, the intelligent tire finite element model is regenerated according to the feedback and adjusted.

[0104] S2, design a first order sensitivity index calculation simulation scheme to determine the calculation characteristic value, calculate the first order sensitivity index of the tire force and the accelerometer output signal, and determine the optimal installation position of the sensor;

[0105] In order to select the optimal installation position of the accelerometer, as many factors as possible that will affect the acceleration signal output of the accelerometer should be considered in the simulation calculation scheme of the design of the first order sensitivity index. Since the purpose of the application is to construct the F x , F y and F z estimation model, the main factors to be considered include slip ratio, side slip angle, load, tire pressure, speed and adhesion coefficient, which are denoted as YX1, YX2, YX3, YX4, YX5 and YX6 respectively. At the same time, according to the daily vehicle driving conditions, the value range of each influencing factor is determined, as shown in Table 1. As shown in Figure 4 , when the tire is rolling, the single tire pitch will repeatedly pass through the ground print area, so only the sensor installation position in the transverse direction of the single tire pitch needs to be determined. In order to facilitate calculation, the application uses transverse grid to quantify all potential sensor installation positions in the transverse direction of the single tire, and labels them (see Figure 4 ), a total of 66 potential sensor installation positions. At this time, the problem is transformed into selecting the positions with higher sensitivity to the changes of longitudinal, lateral and vertical forces of the tire from the 66 installation positions.

[0106] Table 1: Value range of influencing factors

[0107]

[0108] First order sensitivity index calculation simulation scheme design: the total number of samples of the first order sensitivity index calculation simulation scheme is set to 500 groups, at this time, the definition of the first order sensitivity index calculation matrix is combined with the FAST method, and the simulation scheme can be written in form as:

[0109]

[0110] The value of YX(ξ) i,j can be calculated by the FAST value formula, which is written as:

[0111] YX(ξ) i，j = 0.5(1+sin(ω ξ )t j ) (2)

[0112] Where ω ξ is the integral angular frequency of the influencing factor, when ξ=1 / 2 / 3 / 4 / 5 / 6, it represents the integral angular frequency of YX1, YX2, YX3, YX4, YX5 and YX6, the integral angular frequency of these influencing factors is respectively 5, 7, 9, 11, 13 and 15, t is the sampling time point, and the specific value is:

[0113] t j = π / 250+(j-1)π / 250 (3)

[0114] Further, on the basis of obtaining the FOSEI calculation simulation scheme, the acceleration type intelligent tire finite element model established in step S1 is used for simulation calculation, and the acceleration signals of 66 installed accelerometers and the corresponding tire force signals are extracted.

[0115] Characteristic value selection: during the tire rolling process, the acceleration signal collected by the acceleration sensor is a time sequence signal, that is, composed of countless acceleration value points, which cannot be directly used to calculate FOSEI. Therefore, several specific acceleration values on a single acceleration curve need to be extracted in order to calculate FOSEI. 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 acceleration value points on the acceleration curve located in the footprint are mainly selected as the characteristic values for calculation. Figure 5The radial and lateral acceleration signal curves collected by ACC-M in one tire rolling circle are shown, in which points B and D are the points where the tire enters and leaves the footprint, i.e. the two end points of the tire footprint longitudinal length. As can be seen from the figure, the angular interval between the two peak values of the ACC-M radial acceleration is very close to the tire footprint angle occupied by the tire footprint, so the signal in the footprint area in the ACC-M acceleration whole circle signal can be extracted by this feature. Similarly, the acceleration signals of the acceleration sensors at other installation positions located in the footprint area can also be extracted by this feature. In order to eliminate the influence of vehicle speed change on the total amount of acceleration signal sampling, the acceleration values at specific tire angle positions in the footprint are calculated as the calculation characteristic values by the online interpolation method based on the obtained acceleration signals in the footprint area. When extracting specific acceleration value points, the center point of the footprint (i.e. the tire angle position C corresponding to the peak value of the ACC-M acceleration curve) is defined as 0°, and 8 acceleration value points are extracted as calculation characteristic values at intervals of 3.5° on both sides by the interpolation method, totaling 16 calculation characteristic values. At this time, the longitudinal, lateral and radial calculation characteristic value vectors of the acceleration curve of the acceleration sensor at the jth sensor installation position Acc_x j , Acc_y j and Acc_z j can be expressed as:

[0116]

[0117] First-order sensitivity index calculation: In fact, the process of calculating the first-order sensitivity index between the longitudinal, lateral and radial acceleration signals collected by the acceleration sensor at the same installation position and the tire force is exactly the same, because the number of calculation characteristic points is exactly the same, which can be seen from equation (3). Therefore, in order to simplify the description of the subsequent index calculation process, only the index calculation process between the longitudinal acceleration signal collected at the jth sensor installation position and the tire force will be described. It is worth mentioning that the average value of all calculation characteristic points FOSEI contained in the radial acceleration signal curve collected at the jth sensor installation position is taken as the final FOSEI of this position, denoted as MFOSEI. In addition, direct control of F x , F y and F z cannot be realized in reality or simulation, and indirect control of them needs to be realized through tire slip ratio, side slip angle and vertical load. At this time, the tire force F l (l=x / y / z, representing the longitudinal, lateral and vertical directions of the tire, corresponding to the influencing factors YX1, YX2 and YX3) at the jth installation position can be expressed as:

[0118]

[0119] In the formula, is the average value of the first order sensitivity index of the longitudinal acceleration signal of the jth sensor installation position to the influencing factor YX(ξ), var_ACC_x(j,e) is the variance of the e th calculation characteristic of the jth installation position longitudinal acceleration curve for 500 sampling results, A YX(ξ) (j,e) and B YX(ξ) (j,e) respectively represent the first order Fourier coefficients A and B of the e th calculation characteristic value point of the longitudinal acceleration signal at the jth sensor installation position when the influencing factor is YX(ξ), which can be further written as:

[0120]

[0121] where ii is a variable with a value of 1 to m, and by repeatedly calculating formulas (4) and (5), the first order sensitivity index between the longitudinal, lateral and radial acceleration signals of the acceleration sensor at different installation positions and the tire force can be obtained.

[0122] Sensor optimal installation position determination: Figure 6 (a), 6(b) and 6(c) are respectively the calculation results of the first order sensitivity index between the longitudinal, lateral and radial acceleration signals and the tire force at different sensor installation positions, wherein A1, A2 and A3 respectively represent the longitudinal, lateral and radial acceleration. It is worth mentioning that these three figures only show the calculation results of the top 20 positions in descending order of the first order sensitivity index, and these positions are adjusted to be symmetrically arranged about the longitudinal center position of the tire. The results show that for the longitudinal force, the radial acceleration signals at positions numbered 12 and 55 show high sensitivity. For the lateral force, the lateral acceleration signals at positions numbered 18 and 49 show high sensitivity. For the radial force, the radial acceleration signals at positions numbered 9, 10, 20, 47, 57 and 58 all show high sensitivity. Finally, the positions corresponding to these position numbers are selected as the optimal sensor installation positions for the longitudinal, lateral and vertical forces. On this basis, the modeling method of step S1 is used to reconstruct the finite element model of the acceleration type intelligent tire to adjust the installation position of the acceleration sensor.

[0123] S3, collect the acceleration-tire force data set, use the LDA method to screen the optimal input features of the data set, further combine the linear normalization theory to implement normalization processing on the data set, and divide the training set and the test set;

[0124] On the basis of determining the value range of each influencing factor in step S2, further refine their values (see Table 2), combined with the permutation and combination method can obtain a 5000x6 dimension acceleration-tire force data set simulation calculation conditions. On this basis, the reconstructed acceleration type intelligent tire finite element model obtained in step S2 is used to calculate the data set, and combined with the sensitivity analysis results between the acceleration signal and the tire force determined in step S2, the acceleration signal and the tire force signal are extracted to form the acceleration-tire force data set. Finally, the footprint area signal extraction method in step S2 is used to extract the footprint area characteristic signal of the acceleration-tire force data set. In fact, the optimal feature screening, normalization and data set division operations of F x , F y and F z are completely consistent, so in order to simplify the description, the following will only take F x data set as an example to introduce the operation details. The tire longitudinal force-acceleration data set can be expressed as:

[0125] D_F x ={(a j ,y j )|j=1,2,3...,5000}=(a,y) (7)

[0126] Where a∈R 32 is a 5000x32 dimension acceleration signal matrix, a j is the jth 32 dimension acceleration signal vector in a, y is a 5000 dimension F x value vector, y j is the jth tire longitudinal force value in y.

[0127] Table 2: Specific values of each influencing factor in test conditions

[0128]

[0129] Further, the acceleration signal matrix a can be expressed as:

[0130]

[0131] Based on the dimensionality reduction principle of LDA method, the between-class scatter matrix S B and the within-class scatter matrix S W of a are calculated, written as:

[0132]

[0133]

[0134] Where K represents the total number of classes, q represents the rth class sample, N rdenotes the total number of samples of the rth class, ψ r denotes the mean of the rth class, C r denotes the sample set of the rth class.

[0135] Further, by Fisher linear discriminant, the solution of formula (9) and (10) is converted into the solution of optimization problem, and the corresponding loss function can be written as:

[0136]

[0137] wherein, W is the projection vector. Since the solution of the loss function is only related to the direction of W, and is irrelevant to its size, let W T S W W=1. At this time, the loss function with constraint can be written as:

[0138]

[0139] Further, combined with the objective function and the constraint condition, the Lagrange function is constructed, the partial derivative of W is taken and is set to zero, and formula (11) can be further written as:

[0140]

[0141] Finally, the eigenvalues and eigenvectors of formula (13) are solved, and the VC and cumulative AVC of each eigenvalue are calculated, which can be written as:

[0142]

[0143] wherein, λ l is the lth eigenvalue, and P is the number of selected eigenvalues. On the basis of obtaining the AVC, the cumulative variance contribution rate of 95% is selected as the threshold, and 21 eigenvectors are screened to form the matrix W opt =[W1,W2,…,W 32 ]. At this time, the expression of a after optimal feature screening can be written as:

[0144] a o =aW opt (15)

[0145] Further, linear normalization theory is used to normalize a o and y, and the normalized expression is:

[0146]

[0147] wherein, a onor (h,p) is the hth row and pth column data in the normalized input feature a onor , and y nor (h,p) is the normalized vertical force output ynor the (h, p)th data in a omin and a omax are the minimum and maximum values in a o o the (h, p)th data in a o the (h, p)th data in a min and y max are the minimum and maximum values in a

[0148] Finally, the normalized dataset D_F x _nor = {(a onorj , y norj )|j = 1, 2, 3, …, 5000} = (a onor , y nor ) is divided into 70% and 30% as the input and output of the training set and the input and output of the test set, respectively, and is written as:

[0149]

[0150]

[0151]

[0152]

[0153] The above method is repeated to select the optimal input features, normalize and divide the data sets corresponding to the tire lateral force and vertical force. Figure 7 The optimal input feature selection results of the three forces are shown. It is worth mentioning that in order to make the display effect clearer, this figure only describes the calculation results of the top 10 features when AVC reaches 95%. Finally, the number of optimal input features after screening is 21, 17 and 16 for longitudinal, lateral and vertical forces, respectively.

[0154] S4, according to the tire force training set and test set obtained in step S3, a tire force estimation model based on Bayesian neural network is built;

[0155] Considering that the tire longitudinal, lateral and vertical force estimation model building process is completely consistent, the subsequent description will still take the longitudinal force estimation model building as an example. Specifically, the training set and test set are input into the Bayesian neural network prediction model, and the training set D_F​x output values in _nor_train and input values establishes a mapping model, written as:

[0156]

[0157] where ω is a weight parameter. Further, the prior distribution P(ω) of ω can be written as:

[0158]

[0159] where Z ω (α) and E ω are normalization factors, which can be further written as:

[0160]

[0161] where α is a hyperparameter.

[0162] Further, define that the noise ε obeys a Gaussian distribution with mean 0 and variance σ 2 , i.e., ε ~ N(0, σ 2 ). At this time, the likelihood function of the entire data set can be expressed as the product of the likelihoods of all samples, written as:

[0163]

[0164] where, is the probability distribution of the target value given the input data and the weight parameter ω, and the normalization factor β is a hyperparameter.

[0165] Further, based on the Bayesian principle, the posterior probability can be written as:

[0166]

[0167] where P(D_F x _nor) is the marginal likelihood, and the normalization coefficient Z s (α, β) = ∫e -S(ω) dω, and the regular error function

[0168] Further, the Laplace method is used to approximate S(ω) to be equal to the second-order expansion at the minimum point ω MP , written as:

[0169]

[0170] where the function S(ω) at ωMP matrix of the Heaviside matrix the normalization factor Z s The approximate value of (a, b) is:

[0171] Z s (a, b) = (2p) s / 2 |A|exp(-S(w MP )) (27)

[0172] Further, the value of w MP in equation (27) is obtained by the update iteration method, and the hyperparameters a and b are calculated. On this basis, the distribution of the normalized prediction output of the test set input is calculated according to the Bayesian network principle, and is written as:

[0173]

[0174] Finally, the parameter w is sampled multiple times based on the Monte Carlo method, and the function value corresponding to each sampling point is calculated On this basis, the average of all calculated function values is taken, and then the final normalized expected value (namely, the normalized longitudinal force estimation value) and the variance can be obtained, which can be written as:

[0175]

[0176]

[0177] Based on the tire lateral and vertical force data set obtained in step S3, a tire lateral and vertical force estimation model is built by combining the above model construction method.

[0178] S5, on the basis of obtaining the tire three-way force estimation model in step S4, input the optimal acceleration feature, output the tire force normalized prediction value and its variance, and then obtain the actual tire force prediction value through denormalization.

[0179] Considering that the estimation process of the tire longitudinal, lateral and vertical force estimation model is similar, only the longitudinal force is described as an example in the following. On the basis of obtaining the tire longitudinal force estimation model in step S4, use as the input of the tire force budget model, output the tire normalized value and the variance On this basis, the actual longitudinal force estimation value is obtained by denormalization, which is written as:

[0180]

[0181] Further, the uncertainty of the longitudinal force estimate is quantified by 95% CI, and the upper limit vector up_value and the lower limit vector lo_value are:

[0182]

[0183]

[0184] Figure 8 and 9 The test results of the three-direction force estimation method of the tire proposed in the application under the double-migration 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. Overall, the true curve and the estimated curve of the three tire forces have high coincidence. In the high adhesion road test working condition, the range of longitudinal, lateral and vertical forces is-4.16N-7.93N, -22.23N-20.62N and-26.56N-16.05N respectively. In the low adhesion road test working condition, the absolute error fluctuation range of longitudinal, lateral and vertical forces is-10N-2.06N, -22.97N-24.83N and-6.43N-4.49N respectively. Overall, whether it is high adhesion road test working condition or low adhesion road test working condition, the tire longitudinal, lateral and radial force estimation algorithm shows high estimation accuracy and good estimation stability. Although with the decrease of road adhesion coefficient, the tire-ground contact instability will lead to the increase of the confidence interval of the estimation prediction result of the three tire forces, but it is still within an acceptable range, which shows that the tire longitudinal, lateral and vertical force estimation model also shows good estimation stability.

[0185] In summary, the tire estimation method based on the in-tire sensor and the Bayesian neural network proposed in the application has high estimation accuracy and good estimation stability, and can effectively quantify the estimation uncertainty, providing more reliable technical support for related fields.

[0186] The above content only illustrates the technical idea of the application, and cannot limit the protection scope of the application. Any modification made according to the technical idea of the application on the basis of the technical scheme falls within the protection scope of the claims of the application.

Claims

1. A tire force estimation method based on in-utero sensing information and a Bayesian neural network, characterized by, The method comprises the following steps: S1, based on the finite element method, a tire finite element model is established, an acceleration sensor model is constructed using coordinate system conversion theory, and an acceleration type intelligent tire finite element model is built on this basis; S2, a first-order sensitivity index calculation simulation scheme is designed, the characteristic value is determined, the first-order sensitivity index of the tire force and the accelerometer output signal is calculated, and the optimal installation position of the sensor is determined; S3, the acceleration-tire force data set is collected, the optimal input features of the data set are screened and processed using the LDA method, further combined with the linear normalization theory, the data set is normalized, and the training set and the test set are divided; S4, according to the tire force training set and test set obtained in step S3, a tire force estimation model based on a Bayesian neural network is built; S5, on the basis of the tire force estimation model obtained in step S4, the optimal acceleration features are input, the tire force normalized prediction value and its variance are output, and then the tire force actual prediction value can be obtained through the inverse normalization; Step S1 specifically comprises the following steps: S1-1, analyze the tire structure, size and material parameters, and build a tire finite element model on this basis; S1-2, build an acceleration sensor model using the coordinate system conversion theory, and form an acceleration type intelligent tire finite element model on this basis; S1-3, build an intelligent tire real vehicle verification platform to verify the accuracy of the finite element model built in step S1-2; Step S2 specifically comprises the following steps: S2-1, according to the daily driving conditions, determine the influencing factors of the acceleration sensor output acceleration in the acceleration type intelligent tire and its value range, and refer to the definition form of the first-order sensitivity index calculation scheme based on the FAST method, the first-order sensitivity index simulation scheme of the tire force can be written as: ； Wherein, the simulation working condition YX(ξ) i, j The values of (ξ=1, 2, … n, i=1, 2, 3…, n, j=1, 2, 3…, n) can be calculated by the FAST value formula, written as: ； where ω ξ is the integral angular frequency of the influencing factor, and when ξ = 1, 2, …, n, represents the integral angular frequency of YX1, YX2, …, YXn, and t is a sampling time point, and the specific value is: ； On the basis of obtaining the first-order sensitivity index calculation simulation scheme, the acceleration type intelligent tire finite element model established in step S1-2 is used for simulation calculation, and the acceleration signals of the accelerometers at all potential installation positions and the corresponding tire force signals are extracted; S2-2, according to the generation mechanism of tire force, along the circumferential direction of the tire-ground contact center point, select the acceleration values of q (q = 1, 2…, 16) specific positions on the acceleration signal curve as FOSEI calculation characteristic values with interval b ° (b > 0); At this time, the longitudinal, lateral and radial calculation characteristic value vectors Acc_x j , Acc_y j and Acc_z j of the acceleration curve collected by the acceleration sensor at the j (j = 1, 2,.., 66) sensor installation position can be represented as: ； S2-3, the average of all calculated feature points FOSEI contained in the radial acceleration signal curve collected at the jth sensor mounting position is taken as the final FOSEI of the position, denoted as MFOSEI; at this time, the tire force F l The MFOSEI of the longitudinal, lateral and vertical (l=x / y / z) tire forces and the radial acceleration of the acceleration sensor can be expressed as: ； wherein, is the average value of the first order sensitivity index of the longitudinal acceleration signal at the jth sensor mounting position to the influencing factor YX(ξ), var_ACC_x(j, e) is the variance of the mth (m > 0) sampling result of the e (e = 1, 2, …, q) calculation characteristic value of the longitudinal acceleration curve at the jth mounting position, and respectively represent the first order Fourier coefficients A and B of the e (e = 1, 2, …, q) calculation characteristic value point of the longitudinal acceleration signal at the jth sensor mounting position when the influencing factor is YX(ξ), which can be further written as: ； By repeating the above method, the MFOSEI between the longitudinal, lateral and radial acceleration signals of the acceleration sensor at different installation positions and the tire longitudinal force is obtained; Similarly, the first-order sensitivity index between the acceleration signals at different positions and the tire lateral force and radial force is calculated; S2-4, on the basis of calculating the tire force and output acceleration MFOSEI corresponding to all potential installation positions of the acceleration sensor in the tire, a screening index is set, the positions greater than the set screening index are used as the sensor installation position, p(p>0) installation positions with higher sensitivity that meet the conditions are screened out, the optimal installation position of the acceleration sensor is selected, and the acceleration type intelligent tire finite element model is reconstructed.

2. The tire force estimation method based on in-utero sensing information and a Bayesian neural network according to claim 1, characterized by, Step S3 specifically comprises the following steps: S3-1, design acceleration-tire force data set simulation calculation working condition, using the reconstructed acceleration type intelligent tire finite element model obtained in step S1-2 to calculate the data set, and combining the sensitivity analysis results of the acceleration signal and the tire force determined in step S2-4, the acceleration signal and the tire force signal are extracted to form the acceleration-tire force data set; finally, the footprint area signal extraction method in step S2-3 is used to extract the footprint area characteristic signal of the acceleration-tire force data set; the tire longitudinal force-acceleration data set can be expressed as: ； where a e R p*q is a ψ x (p * q) -dimensional acceleration signal matrix, a j is the jth (p * q) -dimensional acceleration signal vector in a, y is a ψ -dimensional F x numerical vector, y j is the jth tire longitudinal force value in y, F x is: tire longitudinal force; the acceleration signal matrix a can be expressed as: ； S3-2, based on the principle of LDA dimension reduction, respectively, the class scatter matrix S of a B and the within-class scatter matrix S W , written as: ； ； where K represents the total number of classes, q represents the rth class sample, N r represents the total number of the rth class sample, ψ r represents the mean of the rth class sample, C r represents the sample set of the rth class; By Fisher linear discriminant, the solution of the equation S B and S W is transformed into the solution of an optimization problem, and the corresponding loss function can be written as: ； where, is the projection vector; since the solution of the loss function only depends on the direction of W, not its magnitude, let ; in this case, the constrained form of the loss function can be written as: ； Combined with the objective function and the constraint condition, the Lagrange function is constructed, the partial derivative of W is taken and it is zero, and maxJ(W) can be further written as: ； Solve the eigenvalue and eigenvector of the above formula, and calculate the variance contribution rate VC and the cumulative variance contribution rate AVC of each eigenvalue, which can be written as: ； wherein λ l is the lth eigenvalue, and P is the number of eigenvalues selected; based on the AVC, the cumulative variance contribution rate of 95% is selected as the threshold, and the first b eigenvectors with a cumulative variance rate of 95% are screened out to form a matrix W opt = [W1, W2,…, W 32 ], and the expression of a after the optimal feature screening can be written as: ； S3-3, the linear normalization theory is adopted to a o and y are normalized, and the normalized expression is: ； Among them, a onor (h, p) represents the normalized input features a onor The data in the h-th row and p-th column, y nor (h, p) represents the normalized longitudinal force output y. nor The data in row h and column p, a omin and a omax a o The minimum and maximum values ​​in, a o (h,p) represents a o Let y(h, p) be the data in the h-th row and p-th column of matrix y. min and y max Let be the minimum and maximum values ​​of y, respectively; finally, select the normalized dataset D_F. x _nor={(a onorj , y norj ) | j=1, 2, 3, …,ψ}=(a onor , y nor 70% and 30% of the data were used as input to the training set, respectively. and output and the input of the test set and output Similarly, the optimal input feature selection, normalization, and data partitioning operations are performed on the datasets corresponding to the tire lateral force and vertical force, respectively.

3. The tire force estimation method based on in-utero sensing information and a Bayesian neural network according to claim 2, characterized in that, Step S4 specifically includes the following steps: S4-1. Specifically, the training set D_F divided in step S3... x _nor_train={( , ) | j=1, 2,3, …, ψ1}=( , ) and test set D_F x _nor_test={( , ) | j=1, 2, 3, …, ψ2}=( , The input is fed into the Bayesian neural network prediction model, and the model learns from the training set D_F. x Output values ​​in _nor_train and input values Establish a mapping model for the relationships between them, written as: ； Wherein, ω is a weight parameter; S4-2, the prior distribution P(ω) of ω is further expanded as: ； where the normalization factor Z ω (α) and the expectation E ω may be further written as: ； Wherein, α is a hyperparameter; The noise is defined to follow a Gaussian distribution with mean 0 and variance , i.e., ε ~ N(0, ); in this case, the likelihood function of the entire dataset can be expressed as the product of the likelihoods of all samples, written as: ； wherein, is the probability distribution of the target value under the condition of given input data and weight parameter ω, the normalization factor , is a hyperparameter; Based on the Bayesian principle, the posterior probability can be written as: ； P(D_F|nor) = P(D_F|nor) / P(D_F) (1) x where P(D_F|nor) is the marginal likelihood, the normalization coefficient , the regularized error function ; Using the Laplace method, we have approximately equal to the second order expansion at the minimum point which can be written as ； where the function At the matrix of the Hadamard matrix at The normalized factor is approximated by ； S4-3, solving by update iteration method the values of the parameters and compute the hyperparameters a and b; on this basis, the distribution of the normalized predicted output corresponding to the input of the test set is computed according to the principle of Bayesian networks is written as: ； S4-4, based on the Monte Carlo method, multiple sampling of the parameter ω, and calculating the function value corresponding to each sampling point ; on this basis, the average of all the calculated function values, and then the final normalized expected value That is, the normalized longitudinal force estimate, and the variance , can be written as: ； ； Similarly, based on the tire lateral and vertical tire force data set obtained in step S3-3, the tire lateral and vertical force estimation model is built.

4. The tire force estimation method based on in-utero sensing information and a Bayesian neural network according to claim 3, characterized by, Step S5 specifically includes the following steps: S5-1, on the basis of the tire longitudinal force estimation model obtained at step S4-4, using as input to the tire force budget model, output tire normalized values and variances on the basis of which the inverse normalization gives the longitudinal force actual estimation value written as: ； Similarly, the actual estimation value of the tire lateral and radial force estimation model is obtained; S5-2, the uncertainty of the longitudinal force estimation value is quantified by the confidence interval CI; repeating the above steps can estimate the tire lateral and vertical force and its uncertainty.

5. The tire force estimation method based on in-utero sensing information and a Bayesian neural network according to claim 4, characterized in that, In step S5-2, the confidence interval calculation formula is: ； ； wherein up_value is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, lo_value is the lower limit vector of the confidence interval corresponding to the tire force prediction vector t o is the confidence interval coefficient; repeating the above steps allows to estimate the tire lateral and vertical forces and their uncertainty estimates.

Images