Tire force estimation method based on in-tire sensing information and Bayesian neural network

Abstract

The invention discloses a tire force estimation method based on in-tire sensing information and a Bayesian neural network. An acceleration type intelligent tire finite element model is built based on a finite element and coordinate system conversion theory; the method comprises the following steps of: determining an optimal mounting position of an acceleration sensor aiming at the three-dimensional force of the tire by adopting a Fourier amplitude sensitivity test (FAST) method, and determining the optimal mounting position of the acceleration sensor aiming at the three-dimensional force of the tire; the method comprises the following steps of: acquiring acceleration signal-tire force data sets under different test working conditions, extracting acceleration signals of a grounding imprinting area, and screening out optimal input characteristics by adopting a linear discriminant analysis (LDA) method; processing the acceleration signal-tire force data set after optimal feature screening by adopting a linear normalization theory; according to the characteristics of training data and test data, a tire force estimation algorithm based on a Bayesian neural network is established, and finally a predicted value and a predicted variance of tire force are output. The method is high in prediction precision, good in stability and high in generalization performance, and a more reliable technical scheme is provided for tire force estimation.

Description

Technical Field

[0001] The invention relates to a tire force estimation method based on in-tire sensor information and a Bayesian neural network, and belongs to the technical field of vehicle control. Background Art

[0002] Accurate and real-time acquisition of tire forces is the key to vehicle dynamics control. However, due to cost and technical limitations, it is very expensive to directly measure tire forces under vehicle operation. Therefore, many experts and scholars have developed a variety of tire force estimation methods based on different technologies, among which the more famous ones include tire force estimation methods based on Kalman filters, recursive least squares methods, and sliding mode observers. Most of these methods require the use of simplified vehicle / tire models. Although simplified models are capable of handling most driving conditions, they still pose challenges for high-precision characterization of the actual motion state of the vehicle under extreme driving conditions. Although the use of more complex vehicle / tire models can effectively improve this problem, it will also lead to an increase in 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 feature information through sensors installed inside the tire, and combines machine learning or physical models to achieve real-time and accurate estimation of tire status. Compared with the traditional tire force estimation method, this method directly uses the sensor signal inside the tire to estimate the tire state parameters, significantly reducing the use of on-board sensors, and can effectively avoid the problem of reduced estimation accuracy caused by the cumulative error of multi-sensor signal acquisition. However, there are still some areas that can be optimized in the tire force estimation method based on intelligent tire technology. On the one hand, the existing intelligent tire force estimation method lacks sufficient consideration for the selection of sensor installation position, and it is difficult to ensure the high-quality continuous acquisition of dynamic feature signals during tire operation. On the other hand, there is a lack of effective means for removing redundant information in the feature signal, and the training effect of the tire force estimation model cannot be guaranteed. In addition, when constructing the signal feature-tire force mapping relationship in the field of intelligent tire force estimation, some data-driven technologies are often used in general, and the matching between signal features and mapping methods is not fully considered, which will also make the performance of the trained tire force estimation model difficult to guarantee. At the same time, when constructing the mapping relationship, there is also a lack of compatibility consideration with the subsequent vehicle control system design. Summary of the invention

[0004] Purpose of the invention: In view of the shortcomings of the prior art, the present invention provides a tire force estimation method based on in-tire sensor information and Bayesian neural network. The invention takes into account the determination of the installation position of the accelerometer sensor inside the tire, and uses fewer input feature values ​​and combines Bayesian neural network to build a tire estimation algorithm. The algorithm can output uncertainty while outputting the force estimation value, which provides a basis for the optimal design of the vehicle control system.

[0005] Technical solution: A tire force estimation method based on in-tire sensor information and Bayesian neural network includes the following steps:

[0006] S1. Establish a tire finite element model based on the finite element method, use the coordinate system transformation theory to build an acceleration sensor model, and build an acceleration-type intelligent tire finite element model on this basis;

[0007] S2. Design a simulation scheme for calculating the first-order sensitivity index, 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;

[0008] S3, collecting acceleration-tire force data sets, using LDA method to screen and process the optimal input features of the data sets, further combining linear normalization theory to normalize the data sets, and dividing them into training sets and test sets;

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

[0010] S5. Based on the tire force estimation model obtained in step S4, the optimal acceleration characteristics are input, and the normalized predicted value of the tire force and its variance are output, and then the actual predicted value of the tire force can be obtained by denormalization.

[0011] Step S1 specifically includes the following steps:

[0012] S1-1. Analyze tire structure, size and material parameters, and build a tire finite element model based on this;

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

[0014] S1-3. Build a smart tire real vehicle verification platform to verify the accuracy of the finite element model built in step S1-2.

[0015] Step S2 specifically includes the following steps:

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

[0017]

[0018] Among them, the simulation condition YX(ξ) i,j The value of (ξ=1,2,…n,i=1,2,3…,n,j=1,2,3…,n) can be calculated by the FAST value formula, which is written as:

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

[0020] Among them, 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, based on 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 corresponding tire force signals output by the accelerometers at all potential installation positions are extracted;

[0023] S2-2. According to the generation mechanism of tire force, the acceleration values ​​of q (q = 1, 2 ..., 16) specific positions on the acceleration signal curve are selected at intervals of б° (б>0) on both sides of the circumference of the tire-ground contact center as the FOSEI calculation characteristic values; at this time, the longitudinal, transverse and radial characteristic value vectors Acc_x of the acceleration curve collected by the acceleration sensor at the jth (j = 1, 2, ..., 66) sensor installation position are calculated. j 、Acc_y j and Acc_z j It can be expressed as:

[0024]

[0025] S2-3, the average value of all the calculated characteristic points FOSEI contained in the radial acceleration signal curve collected at the j-th sensor installation position is taken as the final FOSEI at this position, recorded as MFOSEI; at this time, the tire force F at the j-th installation position l(l = x / y / z, indicating the longitudinal, lateral and vertical directions of the tire) and the MFOSEI of the radial acceleration of the acceleration sensor can be expressed as:

[0026]

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

[0028]

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

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

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

[0032] Step S3 specifically includes the following steps:

[0033] S3-1, designing the 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 result between the acceleration signal and the tire force determined in step S2-4, extracting the acceleration signal and the tire force signal to form the acceleration-tire force data set; finally, using the contact patch area signal extraction method in step S2-3 to extract the contact patch 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 j)|j=1,2,3...,ψ}=(a,y)

[0035] in, is the acceleration signal matrix of ψ×(p*q) dimensions, a j is the jth (p*q)-dimensional acceleration signal vector in a, and y is the ψ-dimensional F x Numeric vector, y j is the longitudinal force value of the jth tire 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 dimension reduction principle of LDA method, calculate the inter-class scatter matrix S of a respectively. B and the intra-class scatter matrix S W , written as:

[0038]

[0039]

[0040] Among them, K represents the total number of classes, q represents the rth class sample, and N r represents the total number of samples in the rth class, ψ r represents the mean of the r-th class sample, C r represents the sample set of the rth class;

[0041] Furthermore, the formula S is transformed into B and S W The solution is transformed into the solution of the optimization problem, and the corresponding loss function can be written as:

[0042]

[0043] Among them, W is the projection vector; since the solution of the loss function is only related to the direction of W and has nothing to do with its size, let W T S W W = 1; at this time, the constrained form of the loss function can be written as:

[0044]

[0045] Furthermore, by combining the objective function and the constraints, the Lagrangian function is constructed, the partial derivative of W is calculated and set to zero, and maxJ(W) can be further written as:

[0046]

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

[0048]

[0049] Among them, λ l is the lth eigenvalue, P is the number of selected eigenvalues; on the basis of obtaining 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 the matrix W opt =[W1,W2,…,W 32 ], then the expression of a after optimal feature screening can be written as:

[0050] a o =aW opt

[0051] S3-3, using linear normalization theory to o and y are normalized, and the normalized expression is:

[0052]

[0053] Among them, a onor (h,p) is the normalized input feature a onor The data in the hth row and pth column, y nor (h,p) is the normalized longitudinal force output y nor The data in the hth row and pth column, a omin and a omax They are respectively o The minimum and maximum values ​​in a o (h,p) is a o The data of the hth row and pth column of y(h,p) is the data of the hth row and pth column of matrix y. min and max are the minimum and maximum values ​​in y respectively; finally, select the normalized data set D_F x _nor={(a onorj ,y norj )|j=1,2,3,…,ψ}=(a onor ,y nor ) are used as training set inputs, respectively. and output And the input of the test set 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 partitioning operations.

[0054] Step S4 specifically includes the following steps:

[0055] S4-1. Specifically, the training set divided in step S3 and test set Input into the Bayesian neural network prediction model, by learning the training set D_F x Output values ​​in _nor_train and input value The relationship between them is established into a mapping model, which can be written as:

[0056]

[0057] Among them, ω is the weight parameter;

[0058] S4-2. Further expand the prior distribution P(ω) of ω into:

[0059]

[0060] Among them, the normalization factor Z ω (α) and the expected E ω It can be further written as:

[0061]

[0062] Among them, α is a hyperparameter;

[0063] Furthermore, we define the noise to have a mean of 0 and a variance of σ 2 Gaussian distribution, then ε~N(0,σ 2 ); At this point, the likelihood function of the entire data set can be expressed as the product of all sample likelihoods, written as:

[0064]

[0065] in, For a given input data Under the condition of and weight parameter ω, the target value is The probability distribution of β is a hyperparameter;

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

[0067]

[0068] Among them, P(D_F x_nor) is the marginal likelihood, the normalized coefficient Z s (α,β)=∫e -S(ω) dω, regularized error function

[0069] Furthermore, the Laplace method is used to approximate S(ω) to the minimum point ω MP The second-order expansion at is written as:

[0070]

[0071] Among them, the function S(ω) is MP The matrix of the Hessian matrix at Then the normalization factor Z s The approximate calculated value of (α,β) is:

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

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

[0074]

[0075] S4-4. Based on the Monte Carlo method, the parameter ω is sampled multiple times, and the function value corresponding to each sampling point is calculated. On this basis, all calculated function values ​​are averaged to obtain the final normalized expected value. That is, the normalized longitudinal force estimate, and the variance It can be written as:

[0076]

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

[0078] Step S5 specifically includes the following steps:

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

[0080]

[0081] Similarly, actual estimated values ​​of the tire's lateral and radial force estimation models are obtained;

[0082] S5-2. Quantify the uncertainty of the longitudinal force estimate through a confidence interval (CI). Repeat the above steps to estimate the tire lateral and vertical forces and their uncertainty estimates.

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

[0084]

[0085] Among them, up_value is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, and lo_value is the lower limit vector of the confidence interval corresponding to the tire force prediction vector. o is the confidence interval coefficient; repeating the above steps can estimate the tire lateral and vertical forces and their uncertainty estimates.

[0086] Compared with the prior art, the present invention has the following significant beneficial effects:

[0087] The finite element model of the acceleration-type intelligent tire was established through finite element software, which can effectively reduce the time and financial costs required for the scientific selection of the installation position of the acceleration sensor in the tire and the extraction of tire force prediction algorithm training data;

[0088] The optimal installation position of the sensor was determined based on the FAST method, which effectively improved the accuracy and reliability of signal acquisition and provided a higher-quality data source for subsequent tire force prediction.

[0089] The LDA method is used to reduce the dimensionality of input features, effectively eliminating redundant information while retaining key features, which is beneficial to reducing model complexity and improving tire force estimation efficiency;

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

[0091] Figure 1The present invention is a flowchart of an embodiment of a tire force estimation method based on in-tire sensor information and Bayesian neural network in the present invention.

[0092] Figure 2 This is the finite element modeling process of the acceleration-type smart tire in the patent of this invention.

[0093] Figure 3 This is a diagram of the sensor installation position of the tire in the intelligent tire finite element model test in the patent of this invention.

[0094] Figure 4 This is a schematic diagram of the sensor installation position at the lining layer of the patent of this invention.

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

[0096] Figure 6 It is the calculation result of the first-order sensitivity index corresponding to the longitudinal, lateral and vertical forces of the tire.

[0097] Figure 7 Dimensionality reduction results for tire longitudinal, lateral and vertical force input features.

[0098] Figure 8 This is a diagram showing the estimation results of the tire force model under low adhesion and compound slip conditions.

[0099] Fig. 9 This is a diagram showing the estimation results of the tire force model under high adhesion and complex slip conditions. Specific implementation plan

[0100] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0101] like Figure 1 As shown, a tire force estimation method based on in-tire sensor information and Bayesian neural network includes the following steps:

[0102] S1. Establish a tire finite element model based on the finite element method, use the coordinate system transformation theory to build an acceleration sensor model, and build an acceleration-type intelligent tire finite element model on this basis;

[0103] Figure 2The modeling process of the finite element model of the acceleration-type smart tire in the present invention is demonstrated, 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 using Abaqus software, and the relevant materials are assigned and the grid is drawn. On this basis, the finite element model based on the accelerometer-type smart tire is built using the global-local coordinate system transformation theory. Then, the effectiveness of the model is verified through the smart tire test platform. Figure 3 As shown in the figure, during the test and simulation process, the acceleration sensors are installed at the center of the inner liner, the left and right shoulders, and the sidewalls of the tire, respectively named ACC-M, ACC-L1, ACC-R1, ACC-L2, and ACC-R2. Under the straight free rolling condition, if the acceleration curves collected by the accelerometer at the same position of the smart tire finite element model and the test tire are consistent, the model is saved. Otherwise, the smart tire finite element model is readjusted and generated according to the feedback.

[0104] S2. Design a simulation scheme for calculating the first-order sensitivity index, 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, the factors that may affect the output of the accelerometer acceleration signal should be considered as much as possible when designing the simulation calculation scheme of the first-order sensitivity index. x 、F y and F z The estimation model is based on the slip rate, slip angle, load, tire pressure, speed and adhesion coefficient, which are recorded as YX1, YX2, YX3, YX4, YX5 and YX6 respectively. At the same time, the value range of each influencing factor is determined according to the daily vehicle driving conditions, and the value range is shown in Table 1. Figure 4 As shown in FIG. 1 , a single tire pitch will repeatedly pass through the contact patch area when the tire rolls, so it is only necessary to determine the sensor installation position in the lateral direction of the single tire pitch. For the convenience of calculation, the present invention uses a lateral grid to quantify all potential sensor installation positions in the lateral direction of a single tire and labels them (see FIG. 1 ). Figure 4 ), there are a total of 66 potential sensor installation locations. At this point, the problem is to select the locations that are more sensitive to changes in the longitudinal, lateral and vertical forces of the tire from these 66 installation locations.

[0106] Table 1: Range of influencing factors

[0107]

[0108] Design of simulation scheme for calculation of first-order sensitivity index: The present invention sets the total number of samples of the simulation scheme for calculation of first-order sensitivity index to 500 groups. At this time, combined with the definition of the first-order sensitivity index calculation matrix by the FAST method, the simulation scheme can be formally written as:

[0109]

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

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

[0112] Among them, ω ξ is the integral angular frequency of the influencing factors. When ξ=1 / 2 / 3 / 4 / 5 / 6, it represents the integral angular frequencies of YX1, YX2, YX3, YX4, YX5 and YX6. The integral angular frequencies of these influencing factors are 5, 7, 9, 11, 13 and 15 respectively. t is the sampling time point. The specific values ​​are:

[0113] t j =π / 250+(j-1)π / 250 (3)

[0114] Furthermore, based on 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 and corresponding tire force signals output by the accelerometers at 66 installation positions are extracted.

[0115] Selection of calculation characteristic values: During the rolling process of the tire, the acceleration signal collected by the acceleration sensor is a time series signal, that is, it is composed of countless acceleration value points and cannot be directly used to calculate FOSEI. Therefore, it is necessary to extract several specific acceleration values ​​on a single acceleration curve in order to calculate FOSEI. In view of the fact that the purpose of the present invention is to predict tire forces, and tire forces are mainly generated by the relative sliding between the tire-ground contact surface, the acceleration value points of the acceleration curve located in the contact footprint are mainly selected as calculation characteristic values. Figure 5The radial and lateral acceleration signal curves collected by ACC-M when the tire rolls one circle are shown, where points B and D are the points where the tire enters and leaves the contact patch, that is, the two end points of the longitudinal length of the tire contact patch. It can be seen from the figure that the angle interval between the two peak values ​​of the ACC-M radial acceleration is very close to the tire contact angle occupied by the tire contact patch, so the signal of the contact patch area in the ACC-M acceleration full circle signal can be extracted through this feature. Similarly, the acceleration signal of the acceleration sensor located in the contact patch area at other installation positions can also be extracted through this feature. In order to eliminate the influence of vehicle speed change on the total amount of acceleration signal sampling, the present invention calculates the acceleration value of a specific tire angle position in the contact patch as a calculated characteristic value based on the acceleration signal in the contact patch area obtained by the online interpolation method. When extracting a specific acceleration value point, the center of the contact patch (that is, the tire angle position C corresponding to the peak value of the ACC-M acceleration curve) is set as 0°, and 8 acceleration value points are extracted at intervals of 3.5° on both sides by the interpolation method as calculated characteristic values, totaling 16 calculated characteristic values. At this time, the longitudinal, transverse and radial calculated eigenvalue vectors Acc_x of the acceleration curve of the acceleration sensor at the jth sensor installation position j 、Acc_y j and Acc_z j It 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 their calculation feature points is exactly the same, which can be seen from formula (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 j-th sensor installation position and the tire force is described below. It is worth mentioning that the present invention uses the average value of all the calculated feature points FOSEI contained in the radial acceleration signal curve collected at the j-th sensor installation position as the final FOSEI of the position, denoted as MFOSEI. In addition, whether in reality or in simulation, it is impossible to implement F x 、F y and F z Direct control of the tire requires indirect control through tire slip rate, side slip angle and vertical load. At this time, the tire force F at the jth installation position is l (l = x / y / z, representing the longitudinal, transverse and vertical directions of the tire, corresponding to the influencing factors YX1, YX2 and YX3 and the MFOSEI of the radial acceleration of the acceleration sensor 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 and the influencing factor YX(ξ), var_ACC_x(j,e) is the variance of the 500 sampling results of the eth calculation feature of the longitudinal acceleration curve of the jth installation position, A YX(ξ) (j,e) and B YX(ξ) (j, e) represent the first-order Fourier coefficients A and B of the e-th calculated eigenvalue point of the longitudinal acceleration signal at the j-th 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. By repeatedly calculating formulas (4) and (5), the first-order sensitivity index between the longitudinal, lateral and radial acceleration signals of the acceleration sensor and the tire force at different installation positions can be obtained.

[0122] Determination of the optimal installation position of the sensor: 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 under different sensor installation positions, where A1, A2 and A3 represent the longitudinal, lateral and radial accelerations, respectively. It is worth mentioning that these three figures only show the calculation results of the first 20 positions when the first-order sensitivity index is arranged in descending order, and these positions are adjusted so that they are arranged symmetrically about the installation position of the longitudinal center position of the tire. The results show that for the longitudinal force, the radial acceleration signals at positions 12 and 55 show high sensitivity. For the lateral force, the lateral acceleration signals at positions 18 and 49 show high sensitivity. For the radial force, the radial acceleration signals at positions 9, 10, 20, 47, 57 and 58 all show high sensitivity. Finally, the present invention selects the positions corresponding to these position numbers as the optimal sensor installation positions for the longitudinal, lateral and vertical forces. On this basis, the finite element model of the acceleration-type intelligent tire is reconstructed using the modeling method of step S1 to adjust the installation position of the acceleration sensor.

[0123] S3, collecting the acceleration-tire force data set, using the LDA method to screen and process the optimal input features of the data set, further combining the linear normalization theory to normalize the data set, and dividing it into a training set and a test set;

[0124] On the basis of the value range of each influencing factor determined in step S2, their values ​​are further refined (see Table 2), and a 5000×6-dimensional acceleration-tire force data set simulation calculation condition can be obtained by combining the permutation and combination method. On this basis, the reconstructed acceleration-type intelligent tire finite element model obtained in step S2 is used to calculate the data set, and the acceleration signal and tire force signal are extracted to form the acceleration-tire force data set in combination with the sensitivity analysis results between the acceleration signal and the tire force determined in step S2. Finally, the contact patch area signal extraction method in step S2 is used to extract the characteristic signal of the contact patch area of ​​the acceleration-tire force data set. In fact, for F x 、F y and F z The optimal feature screening, normalization, and data set partitioning operations of F are completely consistent, so in order to simplify the description, we will only use F x The tire longitudinal force-acceleration dataset 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 5000×32-dimensional acceleration signal matrix, a j is the jth 32-dimensional acceleration signal vector in a, and y is the 5000-dimensional F x Numeric vector, y j is the longitudinal force value of the jth tire in y.

[0127] Table 2: Specific values ​​of various influencing factors under test conditions

[0128]

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

[0130]

[0131] Based on the dimension reduction principle of LDA method, calculate the inter-class scatter matrix S of a respectively B and the intra-class scatter matrix S W , written as:

[0132]

[0133]

[0134] Among them, K represents the total number of classes, q represents the rth class sample, and N rrepresents the total number of samples in the rth class, ψ r represents the mean of the r-th class sample, C r Represents the sample set of the rth class.

[0135] Furthermore, the solutions of equations (9) and (10) are transformed into solutions of optimization problems through Fisher linear discriminant, and the corresponding loss function can be written as:

[0136]

[0137] Where W is the projection vector. Since the solution of the loss function is only related to the direction of W and has nothing to do with its size, let W T S W W = 1. At this time, the constrained form of the loss function can be written as:

[0138]

[0139] Furthermore, by combining the objective function and the constraints, the Lagrangian function is constructed, the partial derivative of W is calculated and set to zero, and equation (11) can be further written as:

[0140]

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

[0142]

[0143] Among them, λ l is the lth eigenvalue, and P is the number of selected eigenvalues. Based on the AVC, the cumulative variance contribution rate of 95% is selected as the threshold, and 21 eigenvectors are selected to form the matrix W opt =[W1,W2,…,W 32 ], then the expression of a after optimal feature screening can be written as:

[0144] a o =aW opt (15)

[0145] Furthermore, the linear normalization theory is used to o and y are normalized, and the normalized expression is:

[0146]

[0147] Among them, a onor (h,p) is the normalized input feature a onor The data in the hth row and pth column, y nor (h,p) is the normalized longitudinal force output ynor The data in the hth row and pth column, a omin and a omax They are respectively o The minimum and maximum values ​​in a o (h,p) is a o The data of the hth row and pth column of y(h,p) is the data of the hth row and pth column of matrix y. min and max are the minimum and maximum values ​​in y, respectively.

[0148] Finally, select the normalized data set D_F x _nor={(a onorj ,y norj )|j=1,2,3,…,5000}=(a onor ,y nor ) are used as training set inputs, respectively. and output And the input of the test set and output writing:

[0149]

[0150]

[0151]

[0152]

[0153] The above method is repeatedly used to perform optimal input feature screening, normalization and data partitioning operations on the data sets corresponding to the tire lateral force and vertical force. Figure 7 The optimal input feature screening results of these three forces are shown. It is worth mentioning that in order to make the display effect clearer, the figure only describes the calculation results of the first 10 features when AVC reaches 95%. In the end, the number of optimal input features after screening for longitudinal, transverse and vertical forces is 21, 17 and 16 respectively.

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

[0155] Considering that the process of building the tire longitudinal, lateral and vertical force estimation models is completely the same, the following description will only take the longitudinal force estimation model building as an example. and test set Input into the Bayesian neural network prediction model, by learning the training set D_Fx Output values ​​in _nor_train and input value The relationship between them is established into a mapping model, which can be written as:

[0156]

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

[0158]

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

[0160]

[0161] Among them, α is a hyperparameter.

[0162] Furthermore, we define the noise to have a mean of 0 and a variance of σ 2 Gaussian distribution, then ε~N(0,σ 2 ). At this point, the likelihood function of the entire data set can be expressed as the product of all sample likelihoods, written as:

[0163]

[0164] in, For a given input data Under the condition of and weight parameter ω, the target value is The probability distribution of β is a hyperparameter.

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

[0166]

[0167] Among them, P(D_F x _nor) is the marginal likelihood, the normalized coefficient Z s (α,β)=∫e -S(ω) dω, regularized error function

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

[0169]

[0170] Among them, the function S(ω) isMP The matrix of the Hessian matrix at Then the normalization factor Z s The approximate calculated value of (α,β) is:

[0171] Z s (α,β)=(2π) s / 2 |A|exp(-S(ω MP )) (27)

[0172] Furthermore, we use the update iteration method to find ω in equation (27): MP value, and calculate the hyperparameters α and β. On this basis, the test set input is calculated according to the Bayesian network principle The corresponding normalized prediction output The distribution of is written as:

[0173]

[0174] Finally, 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, all calculated function values ​​are averaged to obtain the final normalized expected value. (i.e., the normalized longitudinal force estimate) and the variance It can be written as:

[0175]

[0176]

[0177] Based on the tire lateral and vertical tire force data sets obtained in step S3, a tire lateral and vertical force estimation model is built in combination with the above model building method.

[0178] S5. Based on the tire three-axis force estimation model obtained in step S4, the optimal acceleration characteristics are input, the normalized predicted value of the tire force and its variance are output, and then the actual predicted value of the tire force can be obtained by denormalization.

[0179] Considering that the estimation process of the tire longitudinal, lateral and vertical force estimation models is similar, the following description will only take the longitudinal force as an example. As the input of the tire force budget model, the tire normalized value is output and variance On this basis, the actual estimated value of the longitudinal force can be obtained by reverse normalization. writing:

[0180]

[0181] Furthermore, the uncertainty of the longitudinal force estimate is quantified by the 95% CI, with the upper and lower bounds up_value and lo_value as follows:

[0182]

[0183]

[0184] Figure 8 and 9 The test results of the double lane-shifting condition of the three-axis tire force estimation method proposed in the present invention when driving at high and medium speeds on high-adhesion (adhesion coefficient is 0.8) and low-adhesion (adhesion coefficient is 0.3) roads. In general, the true curves and estimated curves of the three tire forces have a high degree of overlap. The ranges of the longitudinal, lateral and vertical forces under the high-adhesion road test conditions are -4.16N~7.93N, -22.23N~20.62N and -26.56N~16.05N, respectively. Under the low-adhesion road test conditions, the absolute error fluctuation ranges of the longitudinal, lateral and vertical forces are -10N~2.06N, -22.97N~24.83N and -6.43N~4.49N, respectively. In general, whether it is a high-adhesion road or a low-adhesion road test condition, the tire longitudinal, lateral and radial force estimation algorithms show high estimation accuracy and good estimation stability. Although as the road adhesion coefficient decreases, the unstable tire-ground contact will cause the confidence intervals of the three tire force estimation prediction results to increase, they are still within an acceptable range, indicating that the tire longitudinal, lateral and vertical force estimation models also show good estimation stability.

[0185] In summary, the estimation method based on intra-fetal sensors and Bayesian neural network proposed in the present invention has high estimation accuracy and good estimation stability, and can also effectively quantify the uncertainty of estimation, providing more reliable technical support for related fields.

[0186] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A tire force estimation method based on in-tire sensor information and Bayesian neural network, characterized in that: The following steps are involved: S1. Establish a tire finite element model based on the finite element method, use the coordinate system transformation theory to build an acceleration sensor model, and build an acceleration-type intelligent tire finite element model on this basis; S2. Design a simulation scheme for calculating the first-order sensitivity index, 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; S3, collecting acceleration-tire force data sets, using LDA method to screen and process the optimal input features of the data sets, further combining linear normalization theory to normalize the data sets, and dividing them into training sets and test sets; S4, building a tire force estimation model based on a Bayesian neural network according to the tire force training set and test set obtained in step S3; S5. Based on the tire force estimation model obtained in step S4, the optimal acceleration characteristics are input, and the normalized predicted value of the tire force and its variance are output, and then the actual predicted value of the tire force can be obtained by denormalization.

2. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 1, characterized in that: Step S1 specifically includes the following steps: S1-1. Analyze tire structure, size and material parameters, and build a tire finite element model based on this; S1-2. Use the coordinate system transformation theory to build an acceleration sensor model, and on this basis form an acceleration-type intelligent tire finite element model; S1-3. Build a smart tire real vehicle verification platform to verify the accuracy of the finite element model built in step S1-2.

3. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 2, characterized in that: Step S2 specifically includes the following steps: S2-1. Determine the influencing factors and value range of the output acceleration of the acceleration sensor in the acceleration-type intelligent tire according to daily driving conditions, and refer to the definition form of the first-order sensitivity index calculation scheme based on the FAST method. The simulation scheme of the first-order sensitivity index of the tire force can be written as: Among them, the simulation condition YX(ξ) i,j The value of (ξ=1,2,…n,i=1,2,3…,n,j=1,2,3…,n) can be calculated by the FAST value formula, which is written as: YX(ξ) i，j =0.5(1+sin(ω) ξ )t j ) Among them, 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: t j =π / 250+(j-1)π / 250 Further, based on 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 corresponding tire force signals output by the accelerometers at all potential installation positions are extracted; S2-2. According to the generation mechanism of tire force, the acceleration values ​​of q (q = 1, 2 ..., 16) specific positions on the acceleration signal curve are selected at intervals of б° (б>0) on both sides of the circumference of the tire-ground contact center as the FOSEI calculation characteristic values; at this time, the longitudinal, transverse and radial characteristic value vectors Acc_x of the acceleration curve collected by the acceleration sensor at the jth (j = 1, 2, ..., 66) sensor installation position are calculated. j 、Acc_y j and Acc_z j It can be expressed as: S2-3, the average value of all the calculated characteristic points FOSEI contained in the radial acceleration signal curve collected at the j-th sensor installation position is taken as the final FOSEI at this position, recorded as MFOSEI; at this time, the tire force F at the j-th installation position l (l = x / y / z, indicating the longitudinal, lateral and vertical directions of the tire) and the MFOSEI of the radial acceleration of the acceleration sensor can be expressed as: Where MFOSEI j YX(ξ) is the average value of the first-order sensitivity index of the longitudinal acceleration signal of the j-th sensor installation position and the influencing factor YX(ξ), var_ACC_x(j,e) is the variance of the sampling result of the e-th (e=1,2,…,q) calculation feature m (m>0) of the longitudinal acceleration curve of the j-th installation position, A YX(ξ) (j,e) and B YX(ξ) (j, e) represent the first-order Fourier coefficients A and B of the e-th calculated eigenvalue point of the longitudinal acceleration signal at the j-th sensor installation 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 and the longitudinal force of the tire at different installation positions is obtained; Similarly, the first-order sensitivity index between the acceleration signal and the tire lateral force and radial force at different positions is calculated; S2-4. After calculating the tire force and output acceleration MFOSEI corresponding to all potential installation positions of acceleration sensors in the tire, a screening index is set, and positions greater than the set screening index are used as sensor installation positions. p (p>0) installation positions with higher sensitivity that meet the conditions are screened out to achieve the selection of the optimal installation position of the acceleration sensor, and reconstruct the finite element model of the acceleration-type intelligent tire.

4. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 3, characterized in that: Step S3 specifically includes the following steps: S3-1, designing the 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 result between the acceleration signal and the tire force determined in step S2-4, extracting the acceleration signal and the tire force signal to form the acceleration-tire force data set; finally, using the contact patch area signal extraction method in step S2-3 to extract the contact patch area characteristic signal of the acceleration-tire force data set; the tire longitudinal force-acceleration data set can be expressed as: D_F x ={(a j ,y j )|j=1,2,3...,ψ}=(a,y) Where a∈R p*q is the acceleration signal matrix of ψ×(p*q) dimensions, a j is the jth (p*q)-dimensional acceleration signal vector in a, and y is the ψ-dimensional F x Numeric vector, y j is the longitudinal force value of the jth tire in y, F x is: tire longitudinal force; further, the acceleration signal matrix a can be expressed as: S3-2. Based on the dimension reduction principle of LDA method, calculate the inter-class scatter matrix S of a respectively. B and the intra-class scatter matrix S W , written as: Among them, K represents the total number of classes, q represents the rth class sample, and N r represents the total number of samples in the rth class, ψ r represents the mean of the r-th class sample, C r represents the sample set of the rth class; Furthermore, the formula S is transformed into B and S W The solution is transformed into the solution of the optimization problem, and the corresponding loss function can be written as: Among them, W is the projection vector; since the solution of the loss function is only related to the direction of W and has nothing to do with its size, let W T S W W = 1; at this time, the constrained form of the loss function can be written as: Furthermore, by combining the objective function and the constraints, the Lagrangian function is constructed, the partial derivative of W is calculated and set to zero, and maxJ(W) can be further written as: Furthermore, the eigenvalues ​​and eigenvectors of the above formula are solved, and the variance contribution (VC) and accumulated variance contribution (AVC) of each eigenvalue are calculated, which can be written as: Among them, λ l is the lth eigenvalue, P is the number of selected eigenvalues; on the basis of obtaining 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 the matrix W opt =[W1,W2,…,W 32 ], then the expression of a after optimal feature screening can be written as: yes o =aW opt S3-3, using linear normalization theory to o and y are normalized, and the normalized expression is: Among them, a onor (h,p) is the normalized input feature a onor The data in the hth row and pth column, y nor (h,p) is the normalized longitudinal force output y nor The data in the hth row and pth column, a omin and a omax They are respectively o The minimum and maximum values ​​in a o (h,p) is a o The data of the hth row and pth column of y(h,p) is the data of the hth row and pth column of matrix y. min and max are the minimum and maximum values ​​in y respectively; finally, select the normalized data set D_F x _nor={(a onorj ,y norj )|j=1,2,3,…,ψ}=(a onor ,y nor ) are used as training set inputs, respectively. and output And the input of the test set 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 partitioning operations.

5. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 4, characterized in that: Step S4 specifically includes the following steps: S4-1. Specifically, the training set divided in step S3 and test set Input into the Bayesian neural network prediction model, by learning the training set D_F x Output values ​​in _nor_train and input value The relationship between them is established into a mapping model, which can be written as: Among them, ω is the weight parameter; S4-2. Further expand the prior distribution P(ω) of ω into: Among them, the normalization factor Z ω (α) and the expected E ω It can be further written as: Among them, α is a hyperparameter; Furthermore, we define the noise to have a mean of 0 and a variance of σ 2 Gaussian distribution, then ε~N(0,σ 2 ); At this point, the likelihood function of the entire data set can be expressed as the product of all sample likelihoods, written as: in, For a given input data Under the condition of and weight parameter ω, the target value is The probability distribution of β is a hyperparameter; Furthermore, based on the Bayesian principle, the posterior probability can be written as: Among them, P(D_F x _nor) is the marginal likelihood, the normalized coefficient Z s (α,β)=∫e -S(ω) dω, regularized error function Furthermore, the Laplace method is used to approximate S(ω) to the minimum point ω MP The second-order expansion at is written as: Among them, the function S(ω) is MP The matrix of the Hessian matrix at Then the normalization factor Z s The approximate calculated value of (α,β) is: Z s (a,b)=(2π) s / 2 |A|exp(-S(ω MP )) S4-3. Solving ω by updating iterative method MP value, and calculate the hyperparameters α and β; on this basis, calculate the test set input according to the Bayesian network principle The corresponding normalized prediction output The distribution of is written as: S4-4. Based on the Monte Carlo method, the parameter ω is sampled multiple times, and the function value corresponding to each sampling point is calculated. On this basis, all calculated function values ​​are averaged to obtain the final normalized expected value. That is, the normalized longitudinal force estimate, and the variance It can be written as: Similarly, a tire lateral and vertical force estimation model is built based on the tire lateral and vertical tire force data sets obtained in step S3-3.

6. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 5, characterized in that: Step S5 specifically includes the following steps: S5-1, based on the tire longitudinal force estimation model obtained in step S4-4, use As the input of the tire force budget model, the tire normalized value is output and variance On this basis, the actual estimated value of the longitudinal force can be obtained by reverse normalization. writing: Similarly, actual estimated values ​​of the tire's lateral and radial force estimation models are obtained; S5-2. Quantify the uncertainty of the longitudinal force estimate through a confidence interval (CI). Repeat the above steps to estimate the tire lateral and vertical forces and their uncertainty estimates.

7. The tire force estimation method based on in-tire sensor information and Bayesian neural network according to claim 6, characterized in that: In step S5-2, the confidence interval calculation formula is: Among them, up_value is the upper limit vector of the confidence interval corresponding to the tire force prediction vector, and lo_value is the lower limit vector of the confidence interval corresponding to the tire force prediction vector. o is the confidence interval coefficient; repeating the above steps can estimate the tire lateral and vertical forces and their uncertainty estimates.

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