CN113353085B - Road surface unevenness identification method based on Kalman filtering theory - Google Patents

Abstract

The invention discloses a road surface roughness recognition method based on Kalman filter theory, which belongs to the technical field of vehicle road roughness recognition in vehicle engineering; firstly, the road contour recognition is defined as an inverse problem of a semi-vehicle model in a state space, and the calibration Collect the vertical acceleration signals of the vehicle body, front wheels and rear wheels on the road as the measurement data of the present invention; then input the collected data into the established road surface roughness recognition algorithm to obtain the dynamic response of the vehicle to reverse the road surface roughness information; wherein, the road surface roughness recognition algorithm is established based on the Kalman filter theory. The present invention only needs to collect a kind of measurement data such as acceleration signal, the arrangement of acceleration sensor is simple, the cost of hardware is low, and the operability is strong; Response for a given vehicle speed.

Description

A road surface roughness identification method based on Kalman filter theory

technical field

The invention belongs to the technical field of vehicle road roughness recognition in vehicle engineering, and in particular relates to a road surface roughness recognition method based on Kalman filter theory.

Background technique

Road surface roughness is an important input affecting vehicle dynamics, especially for some special vehicles, it may lead to fatigue failure of components or decrease of ride comfort. Road surface information is essential for road quality assessment, road roughness index calculation, vehicle dynamics analysis, suspension design, and control system development. However, for technical and economical reasons these signals cannot be measured in standard vehicles and must therefore be identified using special methods. Identifying the excitation acting on the system from the given response of the system is a so-called inverse problem, which is usually an ill-posed problem.

In order to facilitate road maintenance and measurement, some scholars have developed a longitudinal profile (LPA) profiler, which is an instrument used to generate digital sequences related to real road profiles (Piasco, Legeay, 1997; 2005). However, due to the high price, the application of the profiler in ordinary vehicles is limited. (Kim, 2002) studied profilometry based on visual inspection, but this method is limited in rainy weather. With the development of artificial intelligence methods, some scholars have used neural network models to identify road unevenness, but neural network methods require a long calculation time due to the complexity of the model (Mahdi et al., 2010; et al., 2012; Ngwangwa et al., 2010). (Kim et al., 2002; Imine et al., 2006) proposed a model-based sliding mode observer approach, which leads to long computation time for complex models. Meanwhile, the final reconstruction results largely depend on the quality of the model.

It is a typical inverse problem to deduce the road excitation of the vehicle according to the dynamic response of the vehicle structure on the ground, and related methods in this field can be referred to. In recent years, some methods combining determinism and randomness have been developed. These methods treat noise as a stochastic process and assume that noise exists not only on measured values but also on state variables. Steven Gillijns and Bart De Moor (2007a, 2007b) developed a recursive filter to identify system inputs and states from system outputs. E. Lourens (2012) developed an enhanced Kalman filter for force identification in structural dynamics, where unknown forces are included in the state vector and identified together with the state. To obtain a cost-effective and easy-to-implement approach, the proposed input force recognition method is based on acceleration measurements. However, methods based on acceleration measurements are inherently unstable, so F. Naets et al. (2015) proposed virtual measurements of positions in order to stabilize the results. Furthermore, since it is a formulation based on a spatial state, it can easily incorporate information from different sensors on the vehicle.

The theory of Kalman filter was put forward in early 1961. By using the recursive algorithm in the time domain to filter the random signal, the state prediction close to the actual state can be obtained. In simple terms, the Kalman filter is a recursive linear minimum variance estimator, which acts as an optimal linear filter and is thus applied to identify the excitations acting on the system.

Contents of the invention

Technical problem to be solved:

In order to avoid the deficiencies of the prior art, the present invention proposes a road surface roughness recognition method based on Kalman filter theory. First, the road contour recognition is defined as a half-vehicle model inverse problem in the state space. On the calibrated road surface Collect the vertical acceleration signals of the vehicle body, front wheels and rear wheels as the measurement data of the present invention; then input the collected data into the established road surface roughness recognition algorithm to obtain the dynamic response of the vehicle to reversely push the road surface roughness information; Wherein, the road surface roughness recognition algorithm is established based on the Kalman filter theory.

The technical scheme of the present invention is: a kind of road surface roughness recognition method based on Kalman filter theory, it is characterized in that concrete steps are as follows:

Step 1: Acquiring actual data to be identified, the actual data to be identified is to collect the vertical acceleration of the vehicle body, front wheels and rear wheels on the calibration road surface;

Step 2: Input the data collected in Step 1 into the established road surface roughness recognition algorithm to obtain road surface roughness information;

The road surface roughness identification algorithm is established based on the Kalman filter theory, specifically:

a) Establish a half-vehicle two-dimensional model considering the vehicle and the objects it carries, and the motion equation of the half-vehicle model excited by the road surface is expressed as:

和Y分别表示结构的加速度、速度和位移；S_p是与F(t)对应的荷载分布矩阵,F(t)表示外力向量；where M, C and K represent the mass, damping and stiffness matrices of the structure, respectively;

and Y represent the acceleration, velocity and displacement of the structure, respectively; S _p is the load distribution matrix corresponding to F(t), and F(t) represents the external force vector;

b) Select the displacement and velocity as the state quantity on the calibrated road surface, select the acceleration sensor as the observation quantity, introduce the state vector X(t) and the measured response vector Z(t) into the motion equation of the semi-vehicle model, and then deduce respectively The state equation and observation equation of the system are:

X _k+1 ＝A _c X _k +B _c F _k +w _k (11)

Z _k ＝GX _k +JF _k +v _k (12)

where w _k and v _k represent system uncertainty and measurement noise, respectively;

响应向量为Z＝[y₁,y₂,y₃,y₄,θ]^T；输出影响矩阵和直接传输矩阵定义为：G＝[S_d-S_aM^-1K S_v-S_aM^-1C],J＝[S_aM^-1S_p]；X _k ＝X(kDt), F _k ＝F(kDt), Z _k ＝Z(kDt), k＝1,...,N), A _c ＝exp(AΔt), B _c ＝[A _c - I]A ^{- 1} B; the state variable is set to

The response vector is Z=[y ₁ ,y ₂ ,y ₃ ,y ₄ ,θ] ^T ; the output influence matrix and direct transmission matrix are defined as: G=[S _d -S _a M ^-1 KS _v -S _a M ^{- 1} C], J＝[S _a M ^-1 S _p ];

得到增广的状态方程和观测方程分别为：c) According to the state equation and observation equation obtained in step b), introduce the augmented state vector

The augmented state equation and observation equation are obtained as follows:

G_a＝[G J]，

in,

G _a =[GJ],

d) Based on the Kalman filter theory, the recursive prediction scheme is applied to the augmented observation equation. Through time update and measurement update, the estimate is updated by the observed variable, and the measurement estimate is calculated according to the vehicle parameter conditions, that is, the body under the given state vector, Vertical acceleration response of front and rear wheels;

Time update process:

where, denote the prior estimates of the state vector and error covariance, respectively,

Status update process:

The error covariance matrix of the estimated value and the true value is updated as follows:

P _k|k ＝P _k|k-1 -L _k G _a P _k|k-1 (19)

Among them, the Kalman gain formula is:

Through the vehicle dynamic response obtained through the above process, reverse the road surface excitation u ₁ (t) and u ₂ (t) to identify road surface roughness information, u ₁ (t) and u ₂ (t) represent the front wheel and rear wheel respectively The road excitation of the wheels; assuming that the front and rear wheels of the vehicle are running on the same straight line, so the road excitation u ₁ (t) and u ₂ (t) are the same, and the excitation time is different, therefore, u ₁ (t) and u ₂ The relationship between (t) in the time domain is expressed as:

A further technical solution of the present invention is: in the first step, the method for obtaining the data to be identified is to install acceleration sensors at the bottom of the vehicle body, the centers of the front wheels and the rear wheels in advance, and collect the wheel sag when the vehicle is running on the calibrated road. to the acceleration signal.

The further technical scheme of the present invention is: in described step 2, the establishment of semi-vehicle two-dimensional model is specifically as follows:

Firstly, it is set that the transportation equipment is placed on the center line symmetrical with the longitudinal direction of the vehicle, and the swaying vibration of the vehicle is ignored;

Then, the model is simplified to a two-dimensional planar model;

There are 6 degrees of freedom in the model, respectively representing the movement of the suspension, body and equipment in the x and y directions; the coordinate system is established on the moving vehicle, which involves the stiffness kt of the tire, the tire stiffness and the road surface displacement u( t) and assuming that the damping of the tires is negligible; the parameters on each axis of the two suspension systems of the actual vehicle are combined to obtain the following six-degree-of-freedom differential equation of motion:

忽略后求解；在研究车辆和设备的振动时，考虑以方程(2)-(5)的求解和计算；其中，L₁为车辆重心到后轮的距离，L₂为车辆重心到前轮的距离，e为车辆质量偏心，m₁为车辆设备重量，m₂为车辆车身重量，m₃,m₄为车辆轮胎重量，I为车辆惯性矩，k₁,k₂为车辆横向刚度，k₃为车辆垂直刚度，k₄为车辆悬架刚度，k₅为车辆轮胎刚度，c₁,c₂为车辆横向阻尼，c₃为车辆垂直阻尼，c₄为车辆悬架阻尼；Equations (1)-(6) are six-degree-of-freedom nonlinear coupled dynamical differential equation systems; in equation (1), θ ² (t) and

Solve after ignoring; when studying the vibration of vehicles and equipment, consider solving and calculating equations (2)-(5); where L ₁ is the distance from the center of gravity of the vehicle to the rear wheels, and L ₂ is the distance from the center of gravity of the vehicle to the front wheels distance, e is the eccentricity of vehicle mass, m ₁ is the weight of vehicle equipment, m ₂ is the weight of vehicle body, m ₃ and m ₄ are the weight of vehicle tires, I is the moment of inertia of the vehicle, k ₁ and k ₂ are the lateral stiffness of the vehicle, k ₃ is the vehicle vertical stiffness, k ₄ is the vehicle suspension stiffness, k ₅ is the vehicle tire stiffness, c ₁ and c ₂ are the vehicle lateral damping, c ₃ is the vehicle vertical damping, and c ₄ is the vehicle suspension damping;

Write equations (1)-(6) in the form of a matrix such as formula (7), where:

和

and

u ₁ (t) and u ₂ (t) represent the road excitations of the front and rear wheels respectively, assuming that the front and rear wheels of the vehicle are running on the same straight line, so the road excitations u ₁ (t) and u ₂ (t ) are the same, but the timing of the incentive is different. Therefore, the relationship between u ₁ (t) and u ₂ (t) in the time domain can be expressed as:

Beneficial effect

The beneficial effect of the present invention is: the present invention proposes a kind of road surface roughness recognition method based on Kalman filtering theory, 1) the present invention only needs to gather a kind of measurement data such as acceleration signal, and acceleration sensor layout is simple, and hardware cost is low, can Strong operability; 2) Use the Kalman filter theory to filter the acceleration signal in the time domain with a recursive algorithm, and establish a formula on the space state, which can easily incorporate information from different sensors on the vehicle, thus obtaining The state prediction close to the actual state has a small amount of real-time calculation, which improves the recognition rate of road roughness; 3) The excitation acting on the system through the white noise filter random analog input reflects the actual road conditions of the vehicle, highlighting its solution under the random framework ability to problem. At the same time, the accuracy of identification in actual use is improved by comparing the measured data with the simulation results; 4) This method can not only be used to predict the road excitation of the vehicle in the early stage of vehicle design, but also calculate the response of the vehicle to any given speed .

Description of drawings

Fig. 1 is the vehicle dynamics model figure of the embodiment of the present invention;

Fig. 2 is the power spectrum figure of the E grade road surface of the embodiment of the present invention;

Fig. 3 is the dynamic response figure of the vehicle of the example of the present invention under 10m/s;

Fig. 4 is the comparison diagram of the recognized road surface and the real road surface of the example of the present invention;

Detailed ways

The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

1.1. Step 1. Collect the vertical acceleration of the vehicle body, front wheels and rear wheels on the calibration road surface;

Specifically, in order to measure the unevenness of the road surface, it is necessary to obtain some actual data to be identified. Acceleration sensors are installed at the bottom of the vehicle body, the center of the front and rear wheels in advance, and the vertical acceleration signals of the wheels are collected during the driving process of the vehicle.

1.2. Step 2: Input the collected data into the established road surface roughness recognition algorithm to obtain the road surface roughness information. Wherein, the road surface roughness recognition algorithm is established based on the Kalman filter theory;

Specifically, the establishment steps of the road surface roughness recognition algorithm are as follows:

a) Establish a semi-vehicle two-dimensional model considering the vehicle and the loaded objects, and write out the differential equation of motion considering the movement of the suspension, body and equipment in the x and y directions and transform it into a matrix form to obtain the motion equation of the semi-vehicle model;

When transporting a certain equipment, the vehicle will be placed on the longitudinal symmetrical center line of the vehicle. Since the vibration of the vehicle is generally small, the model can be simplified to a two-dimensional plane model.

There are 6 degrees of freedom in the model, representing the motion of the suspension, body, and equipment in the x and y directions, respectively. The coordinate system is established on the moving vehicle, which involves the tire stiffness kt, which is related to the road surface displacement u(t), and it is assumed that the damping of the tire is negligible. Generally there are two suspension systems in a real vehicle, but for ease of calculation, we combine the parameters on each axle. Thus, the following differential equations of motion with six degrees of freedom are obtained:

由于车身长度约为10米，实际驾驶试验中车身俯仰运动远小于车身垂直振动，因而将θ²(t)和

忽略掉。由于第一个方程没有与下面的五个方程耦合，所以第一个方程可以单独求解。在研究车辆和设备的振动时，可以考虑以下五个方程的求解和计算。车辆和设备模型的参数和物理意义如表1所示：Equations (1)-(6) are the six-degree-of-freedom nonlinear coupled dynamical differential equation system. In the first equation, there are nonlinear coupling terms θ ² (t) with respect to the vehicle pitch motion θ and

Since the length of the body is about 10 meters, the pitching motion of the body in the actual driving test is much smaller than the vertical vibration of the body, so θ ² (t) and

ignore it. Since the first equation is not coupled with the following five equations, the first equation can be solved independently. When studying the vibration of vehicles and equipment, the solution and calculation of the following five equations can be considered. The parameters and physical meanings of the vehicle and equipment models are shown in Table 1:

Table 1 Model parameters

The motion equation of the semi-vehicle model excited by the road surface can be expressed by the following formula:

和Y分别表示结构的加速度、速度和位移。S_p是与F(t)对应的荷载分布矩阵,F(t)表示外力向量。where M, C and K denote the mass, damping and stiffness matrices of the structure, respectively.

and Y denote the acceleration, velocity and displacement of the structure, respectively. S _p is the load distribution matrix corresponding to F(t), and F(t) represents the external force vector.

Above-mentioned equation (1)-(6) can be written as the matrix form of formula (7), wherein:

和

and

u ₁ (t) and u ₂ (t) represent the road excitations of the front and rear wheels respectively, assuming that the front and rear wheels of the vehicle are running on the same straight line, so the road excitations u ₁ (t) and u ₂ (t ) are the same, but the timing of the incentive is different. Therefore, the relationship between u ₁ (t) and u ₂ (t) in the time domain can be expressed as:

u ₁ (t)=u ₂ (t-Δt),

b) Select the displacement and velocity as the state quantity on the calibrated road surface, select the acceleration sensor as the observation quantity, introduce the state vector X(t) and the measured response vector Z(t) into the motion equation of the semi-vehicle model, and then deduce respectively The state equation and observation equation of the system;

式(7)可以表示为式(8)的形式:By introducing the state vector

Formula (7) can be expressed in the form of formula (8):

where A and B are:

Considering the measurement response vector Z(t), expressed as a linear combination of displacement, velocity and acceleration vectors as follows:

Among them, S _a , S _v and S _d are the selection matrices of acceleration, velocity and displacement, respectively. Formula (8) can be expressed as:

Z(t)=GX(t)+JF(t) (10)

where the output influence matrix and direct transfer matrix are defined as:

G＝[S _d -S _a M ^-1 KS _v -S _a M ^-1 C], J＝[S _a M ^-1 S _p ]

The state equation and observation equation of the system can be deduced as:

X _k+1 ＝A _c X _k +B _c F _k +w _k (11)

Z _k ＝GX _k +JF _k +v _k (12)

Where w _k and v _k represent system uncertainty and measurement noise, respectively.

响应向量为Z＝[y₁,y₂,y₃,y₄,θ]^T。X _k ＝X(kDt), F _k ＝F(kDt), Z _k ＝Z(kDt), k＝1,...,N), A _c ＝exp(AΔt), B _c ＝[A _c - I] A ^{- 1} B, state variable is set to in the present invention

The response vector is Z=[y ₁ ,y ₂ ,y ₃ ,y ₄ ,θ] ^T .

得到增广的状态方程和观测方程；c) According to the state equation and observation equation obtained in b), the augmented state vector is introduced

Get the augmented state equation and observation equation;

F _k+1 can be regarded as F _k plus a disturbance η _k ,

F _k+1 = F _k +η _k (13)

By introducing the augmented state vector X ^a

The augmented state equation and observation equation can be obtained as follows:

G_a＝[G J],

in

G _a =[GJ],

d) Based on the Kalman filter theory, the recursive prediction scheme is applied to the augmented observation equation. Through time update (prediction) and measurement update (correction), the estimation is updated from the observed variables, and the quantity can be calculated according to the parameter conditions given in Table 1. The estimated measurement is the vertical acceleration response of the body, front wheels and rear wheels under a given state vector;

噪声矩阵

和

一般的卡尔曼滤波器可以定义为一个递归线性状态估计器，在最小方差意义下为最优，利用递推的方式对每一时刻的测量值和预测值求出其最小均方误差,得出更为精确的最优估计。在这种情况下，可以将递归预测方案应用于Z_k。假设初始值

存在，通过以下步骤进行计算：The change of the known acceleration within the sampling period can be simulated by Gaussian white noise w with zero mean, and its variance is

noise matrix

and

The general Kalman filter can be defined as a recursive linear state estimator, which is optimal in the sense of minimum variance, and uses the recursive method to find the minimum mean square error for the measured value and predicted value at each moment, and obtains A more precise best estimate. In this case, a recursive prediction scheme can be applied to Z _k . Assumed initial value

exists, the calculation is performed by the following steps:

Time update (prediction) process:

where, denote the prior estimates of the state vector and error covariance, respectively,

Status update (correction) process:

The Kalman gain formula is:

The Kalman gain is the proportion of the predicted minimum mean square error error of the state at k time to the error at k time by k-1 time prediction. The larger the proportion, the greater the probability that the real value is close to the predicted value.

By updating the estimation of the observed variable Z _k , the posterior estimator of the state vector at time k can be obtained, which is the latest state estimator, the measurement estimator sought by the present invention, and the prior state estimator for the next prediction. The status update formula is as follows:

The error covariance matrix of the estimated value and the true value is updated as follows:

P _k|k ＝P _k|k-1 -L _k G _a P _k|k-1 (19)

The vehicle dynamic response obtained through the above process can invert the road surface excitation u ₁ (t) and u ₂ (t) to identify road surface roughness information;

Example:

Referring to Figure 1, in this example, the vehicle will be placed on the center line symmetrical to the longitudinal direction of the vehicle. Generally, the vibration of the vehicle is small, so the model can be simplified to a two-dimensional plane model, as shown in Figure 1. There are 6 degrees of freedom in the model, representing the suspension, body and equipment motion respectively. The coordinate system is established on the moving vehicle, which involves the tire stiffness kt, which is related to the road surface displacement u(t), and it is assumed that the damping of the tire is negligible.

The following is a specific embodiment using the method proposed above, wherein the data used are generated by simulation. Considering that the road roughness is a smooth, Gaussian random process with zero mean and an ergodic random process, the random input can reflect the actual road conditions of the vehicle. Therefore, white noise filtering is used to generate a large number of different road roughness signals. Referring to ISO8608, the power spectral density of road surface roughness can be fitted as:

Wherein, n represents the spatial frequency, which represents the cycle number of waves per meter, and its unit is m ⁻¹ . n ₀ =0.1m ⁻¹ represents the spatial reference frequency. G _q (n ₀ ) is the power spectral density of the road surface roughness at the reference spatial frequency. The power spectral density is related to the road surface level, and is also called the road surface roughness coefficient. W=2 is the frequency index, that is, the frequency of the slope in the log-logarithmic coordinates, which determines the frequency structure of the roughness power spectral density. Considering that the road surface roughness is a kind of limited bandwidth noise, the time-domain road surface roughness with the desired power spectral density of the road surface can be simulated by using specific white noise through first-order filtering:

Where n ₁ =0.01m ^-1 represents the lowest cutoff frequency, ω(t) represents zero-mean white noise, u _r (t) represents vertical excitation, and v represents the formal speed of the vehicle (v=10m/s). The power spectrum diagram of E-class pavement is shown in Fig. 2.

Under the Matlab environment, the method proposed by the present invention is applied to the road roughness signal set produced by white noise filtering to calculate the vertical acceleration responses of the vehicle body, front wheels and rear wheels at vehicle speeds. The sampling frequency of the simulation is 200Hz, and the dynamic response of the vehicle is shown in Figure 3.

An important feature of the method proposed by the present invention is how to determine parameters, including covariance and initial values. [1e-4 1e-4 1e-2 1e-2 1e-4 1e-8 1e-8 1e-7 1e-7 1e-8] is set to the diagonal element of Q in the example of the present invention, the pair of R The corner elements are set to [1e-4 1e-4 1e-2 1e-2 1e-4]. The initial value of P _0|-1 is set to 5e-5. Acceleration sensors are installed at the bottom of the vehicle body, the center of the front and rear wheels, and the vertical acceleration signals of the wheels are collected during vehicle driving, and then the algorithm is applied to the measurement data to obtain the dynamic response of the vehicle to identify road surface roughness information. Compared with the road profile in the above simulation case, it is shown in Figure 4. It can be seen from the figure that the road contour recognition is relatively accurate, which proves the effectiveness of the method.

Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be construed as limitations to the present invention. Variations, modifications, substitutions, and modifications to the above-described embodiments are possible within the scope of the present invention.

Claims (2)

1. a road surface roughness recognition method based on Kalman filter theory, is characterized in that concrete steps are as follows: Step 1: Acquiring actual data to be identified, the actual data to be identified is to collect the vertical acceleration of the vehicle body, front wheels and rear wheels on the calibration road surface; Step 2: Input the data collected in Step 1 into the established road surface roughness recognition algorithm to obtain road surface roughness information; The road surface roughness identification algorithm is established based on the Kalman filter theory, specifically: a) Establish a half-vehicle two-dimensional model considering the vehicle and the objects it carries, and the motion equation of the half-vehicle model excited by the road surface is expressed as:

where M, C and K represent the mass, damping and stiffness matrices of the structure, respectively;

and Y represent the acceleration, velocity and displacement of the structure, respectively; S _p is the load distribution matrix corresponding to F(t), and F(t) represents the external force vector; b) Select the displacement and velocity as the state quantity on the calibrated road surface, select the acceleration sensor as the observation quantity, introduce the state vector X(t) and the measured response vector Z(t) into the motion equation of the semi-vehicle model, and then deduce respectively The state equation and observation equation of the system are: X _k+1 ＝A _c X _k +B _c F _k +w _k (11) Z _k ＝GX _k +JF _k +v _k (12) Wherein, w _k and v _k represent system uncertainty and measurement noise respectively; X _k ＝X(kDt), F _k ＝F(kDt), Z _k ＝Z(kDt), k＝1,..., N),A _c ＝exp(AΔt),B _c ＝[A _c -I]A ^-1 B; the state variable is set as

The response vector is Z=[y ₁ ,y ₂ ,y ₃ ,y ₄ ,θ] ^T ; the output influence matrix and direct transmission matrix are defined as: G=[S _d -S _a M ^-1 KS _v -S _a M ^{- 1} C], J＝[S _a M ^-1 S _p ]; t represents time,

represent state transition matrix and control matrix respectively, S _a , S _v and S _d are selection matrices of acceleration, velocity and displacement respectively; c) According to the state equation and observation equation obtained in step b), introduce the augmented state vector

The augmented state equation and observation equation are obtained as follows:

in,

G _a =[GJ],

η _k represents disturbance; d) Based on the Kalman filter theory, the recursive prediction scheme is applied to the augmented observation equation. Through time update and measurement update, the estimate is updated by the observed variable, and the measurement estimate is calculated according to the vehicle parameter conditions, that is, the body under the given state vector, Vertical acceleration response of front and rear wheels; Time update process:

in,

and P _k|k represent the prior estimates of the state vector and error covariance, respectively,

Status update process:

The error covariance matrix of the estimated value and the true value is updated as follows: P _k|k ＝P _k|k-1 -L _k G _a P _k|k-1 (19) Among them, the Kalman gain formula is:

R represents the matrix of observation noise; Through the vehicle dynamic response obtained through the above process, reverse the road surface excitation u ₁ (t) and u ₂ (t) to identify road surface roughness information, u ₁ (t) and u ₂ (t) represent the front wheel and rear wheel respectively The road excitation of the wheels; assuming that the front and rear wheels of the vehicle are running on the same straight line, so the road excitation u ₁ (t) and u ₂ (t) are the same, and the excitation time is different, therefore, u ₁ (t) and u ₂ The relationship between (t) in the time domain is expressed as: u ₁ (t)=u ₂ (t-Δt),

In the second step, the establishment of the semi-vehicle two-dimensional model is as follows: Firstly, it is set that the transportation equipment is placed on the center line symmetrical with the longitudinal direction of the vehicle, and the swaying vibration of the vehicle is ignored; Then, the model is simplified to a two-dimensional planar model; There are 6 degrees of freedom in the model, respectively representing the movement of the suspension, body and equipment in the x and y directions; the coordinate system is established on the moving vehicle, which involves the stiffness kt of the tire, the tire stiffness and the road surface displacement u( t) and assuming that the damping of the tires is negligible; the parameters on each axis of the two suspension systems of the actual vehicle are combined to obtain the following six-degree-of-freedom differential equation of motion:

Equations (1)-(6) are six-degree-of-freedom nonlinear coupled dynamical differential equation systems; in equation (1), θ ² (t) and

Solve after ignoring; when studying the vibration of vehicles and equipment, consider solving and calculating equations (2)-(5); where L ₁ is the distance from the center of gravity of the vehicle to the rear wheels, and L ₂ is the distance from the center of gravity of the vehicle to the front wheels distance, e is the eccentricity of vehicle mass, m ₁ is the weight of vehicle equipment, m ₂ is the weight of vehicle body, m ₃ and m ₄ are the weight of vehicle tires, I is the moment of inertia of the vehicle, k ₁ and k ₂ are the lateral stiffness of the vehicle, k ₃ is the vehicle vertical stiffness, k ₄ is the vehicle suspension stiffness, k ₅ is the vehicle tire stiffness, c ₁ and c ₂ are the vehicle lateral damping, c ₃ is the vehicle vertical damping, and c ₄ is the vehicle suspension damping; Write equations (1)-(6) in the form of a matrix such as formula (7), where:

and

2. The road surface roughness identification method based on Kalman filter theory according to claim 1, characterized in that: in the step 1, the method for obtaining the data to be identified is, in advance, at the bottom of the vehicle body, the center of the front wheel and the rear wheel An acceleration sensor is installed at the place, and the vehicle collects the vertical acceleration signal of the wheel during driving on the calibrated road surface.

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