Bridge fundamental frequency and deflection influence line synchronous identification method under vehicle-induced excitation

Abstract

The invention discloses a bridge fundamental frequency and deflection influence line synchronous identification method under vehicle-induced excitation, and relates to the technical field of bridge safety monitoring, and the method comprises the following steps: 1, deducing a fundamental frequency analysis formula through a formula, and setting the fundamental frequency analysis formula as an E-VMD method modal analysis cut-off frequency; 2, stripping a dynamic response component in the deflection response, and identifying a bridge operation frequency through FFT (Fast Fourier Transform); 3, taking the operation frequency as a threshold value, and stripping the dynamic response again; and 4, stripping the axle effect to obtain a static deflection influence line. According to the method, the bridge fundamental frequency obtained through indirect identification based on the dynamic response in the vehicle bridge crossing process has high precision, the relative error between the bridge fundamental frequency and the actually-measured bridge modal fundamental frequency is low, tedious steps of traditional modal testing are avoided, and the analysis efficiency is improved.

Description

Technical Field

[0001] The invention relates to the technical field of bridge safety monitoring, and in particular to a method for synchronously identifying a bridge fundamental frequency and a deflection influence line under vehicle-induced excitation. Background Art

[0002] During the long-term operation of bridges, factors such as traffic loads and even extreme accidents will inevitably cause damage such as degradation of the structural bearing capacity and deterioration of stiffness. Therefore, it is necessary to further improve and perfect the system of rapid detection and assessment methods for bridge safety, timely grasp the status of bridges in service, and take appropriate management and maintenance measures to extend the service life of bridges.

[0003] As an important performance parameter for bridge structure stiffness assessment, influence lines can reflect the deflection, strain, rotation and other responses of specific sections under moving loads. They have been initially applied to the field of bridge health assessment. The application prospects of bridge influence lines are broad, but the recognition accuracy and operability of quasi-static influence lines in actual operations need to be improved.

[0004] Bridge modal frequency identification can be divided into two methods: frequency domain and time domain. The frequency domain method usually uses classical spectrum estimation and is a non-parametric method, while the time domain method belongs to the category of modern spectrum analysis.

[0005] The existing technology includes singular value decomposition of power spectrum density, decoupling the power spectrum density function of the multi-degree-of-freedom system into a series of single-degree-of-freedom power spectrum density functions, and then using the peak method to obtain the frequency; an indirect measurement method based on vehicle response, using the vehicle body response to identify the bridge modal frequency; a bridge modal parameter identification method under a stationary vehicle, converting vibration type identification into frequency identification, using a small number of vibration pickups, and quickly identifying the normalized vibration type of the bridge mass;

[0006] The above methods can obtain modal frequencies with high accuracy, but they all require the use of acceleration or velocity pickups, modal analyzers, etc., which are expensive equipment. In actual engineering, response data is usually quickly obtained by moving a single heavy vehicle for loading. The measured response includes influence line information, bridge vibration components, and test noise. There are relatively mature methods for eliminating vehicle-induced force effects in influence line identification. Among them, modal decomposition methods all require additional dynamic testing to obtain the bridge fundamental frequency as the modal decomposition calculation threshold, and the identification process is relatively cumbersome. Summary of the invention

[0007] The object of the present invention is to provide a method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation, so as to solve the problems mentioned in the above background technology.

[0008] The present invention can be implemented by the following technical solution: a method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation, the method comprising the following steps:

[0009] Step 1: Derivation of the fundamental frequency analytical formula, set as the E-VMD method modal analysis cutoff frequency;

[0010] Step 2: Strip the dynamic response component from the deflection response and identify the bridge operation frequency through FFT transformation;

[0011] Step 3: Use the operating frequency as the threshold and re-strip the power response;

[0012] Step 4: Remove the axle effect and obtain the static deflection influence line.

[0013] The further technical improvement of the present invention is that: in step 1, the Rayleigh method frequency derivation is adopted, and in the case of undamped natural vibration, the instantaneous vertical displacement y(x, t) of the bridge is expressed as: y(x, t) = η(x) sin(wt+θ);

[0014] Where: η(x) is the approximate vibration function that satisfies the displacement boundary conditions of the bridge, w is the corresponding frequency, and θ is the phase difference, so the frequency w is derived as

[0015] Where Ep and Ek are the potential energy and kinetic energy of the structural system, EI(x) is the bending stiffness, and m(x) is the mass distribution value.

[0016] A further technical improvement of the present invention is that the kinetic energy of the structural system includes:

[0017] Main beam kinetic energy E k1 , whose expression is

[0018] Kinetic energy of the cable E k2 , whose expression is

[0019] Bridge tower kinetic energy E k3 , whose expression is

[0020] Among them, m G 、m ci 、m T is the linearly distributed mass of the main beam, cables and main tower, then the overall kinetic energy of the bridge is

[0021] The further technical improvement of the present invention is that the potential energy of the structural system is the potential energy of the main beam E p1 、Slope cable potential energy E p2 and the bridge tower potential energy E p3 sum;

[0022] in,

[0023] Where EG I G 、E T I T are the bending stiffness of the main beam and main tower, n, ξ is the vibration mode function of the main beam and main tower;

[0024] The equilibrium equation of cable deformation under unit force increase is constructed, and the cable potential energy is calculated as:

[0025] Where ΔL is the cable deformation, L ci is the original length of the cable, h ci is the cable descent height, a ci is the horizontal inclination angle of the cable;

[0026] When the structural vibration causes the cable inclination angle to change, the secondary potential energy of the cable can be approximately obtained by differentiating the vertical component of the cable force:

[0027]

[0028]

[0029] The overall potential energy of the bridge is:

[0030]

[0031] A further technical improvement of the present invention is that the overall kinetic energy and potential energy are substituted into w to calculate the first-order vertical bending vibration frequency of the bridge as:

[0032]

[0033] A further technical improvement of the present invention is that when the rigidity of the bridge main beam is relatively large, the potential energy of the main tower, the cable, the secondary potential energy of the cable and the kinetic energy of the main tower can be ignored, and the kinetic energy of the cable can also be ignored because the mass of the cable is relatively small compared to the mass of the main beam, w can be simplified to:

[0034]

[0035] Among them, V and G are the unit volume and density of the main beam material, which are the basic vibration mode functions of the bridge.

[0036] A further technical improvement of the present invention is that: the dynamic response in step 2 is the dynamic response of the vehicle crossing the bridge, which is obtained by simplifying the vehicle-bridge coupling system and simplifying the moving vehicle into a single-degree-of-freedom elastic mass block model for analysis;

[0037] Assume the bridge length is L, the mass m and its stiffness EI are evenly distributed, and the existing mass is M v , the stiffness is K v and the damping coefficient is C vThe vehicle model travels across the bridge at a speed v, ignoring the influence of bridge damping, and assuming that the vehicle mass is much smaller than the bridge mass, the motion control equation is established as follows:

[0038]

[0039] Where y v is the vertical displacement of the vehicle body, U v is the dynamic displacement of the bridge, U c is the dynamic displacement of the bridge contact point, δ is the Dirac function, (·) and (′) are the first-order derivatives with respect to time t and distance x, respectively, and g is the gravitational acceleration;

[0040] According to the modal superposition, the dynamic displacement of the bridge is:

[0041]

[0042] The integral from the origin of the bridge length 0 to the total length L establishes the bridge response qb,n solution, and then derives the nth-order vibration frequency wbn of the bridge as:

[0043]

[0044] The further technical improvement of the present invention is that the E-VMD method principle includes:

[0045] A1. Use EMD to adaptively decompose the measured deflection time history response to obtain the intrinsic mode function IMFs components;

[0046] A2. Calculate the correlation coefficient of each IMFs, where M is the number of IMFs and define the correlation threshold l limt :

[0047]

[0048] Among them, ξ is the resolution coefficient, c is the empirical constant;

[0049] When l1(m)≥l limt , the mth IMF component is defined as a useful component, otherwise it is noise; all useful components are superimposed to obtain the preprocessed signal, recorded as x0(n);

[0050] The signal is subjected to variational modal decomposition (VMD) processing at different K values. Each decomposition obtains a set of narrowband IMFs components. The relationship between narrowband IMFs and x0(n) is determined by calculating the correlation coefficient, which satisfies l2(k)≥l limtThe reconstructed signal x1(n) is obtained by superimposing the narrowband IMFs components of (k=1, 2, ...K). The mutual information relationship between the preprocessed signal x0(n) and the reconstructed signal x1(n) is calculated by the mutual information method, and the mutual information (MI) index is proposed:

[0051] MI[x1,x0]=H(x1)+H(x0)-H(x1,x0);

[0052] Where: H(x1), H(x0) and H(x1,x0) are the information entropy and joint entropy of x0(n) and x1(n), denoted as:

[0053]

[0054] Where x1(n), and are the probability mass function and joint probability mass function of x0(n) and x1(n) respectively;

[0055] When the mutual information index MI reaches the maximum value, the corresponding K value is the optimal number of modes obtained by variational mode decomposition. Reconstruct the optimal number of modes when x0(n) satisfies l2(k)≥l limt By using narrow-band IMFs of (k=1, 2, ...K), the quasi-static component of the vehicle-induced time-history response can be obtained.

[0056] A further technical improvement of the present invention is that the method for stripping the axle effect comprises:

[0057] B1. Solve the influence line ill-conditioned equation using Tikhonov regularization;

[0058] B2, after E-VMD decomposition and processing of the time history response, the error e is introduced to establish the influence line identification model Rs;

[0059] Where Rs is the quasi-static response of the bridge, L is the vehicle information matrix, and Φ is the influence line coefficient of the bridge node;

[0060] R s =LΦ+e;

[0061] The Tikhonov regularization method uses the L2 norm as a penalty function to constrain the least squares expression, thereby solving the pathological mathematical equation of the influence line identification model caused by the error term. The regularization equation is as follows: λ is the regularization coefficient;

[0062] The regularized experience matrix is:

[0063]

[0064] B3. The vehicle information matrix is ​​determined by parameters such as sampling frequency, vehicle axle weight, number of axles, wheelbase and vehicle speed. The vehicle speed and sampling frequency determine the number of matrix columns, and the sensor sampling frequency determines the number of rows of the regularized experience matrix.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The bridge fundamental frequency obtained by the indirect identification of the dynamic response of the vehicle crossing the bridge in the present invention has high accuracy and low relative error with the measured bridge modal fundamental frequency, thus avoiding the cumbersome steps of traditional modal testing and improving the analysis efficiency;

[0067] The measured bridge modal fundamental frequency is used as the decomposition threshold to pre-process the measured deflection response and simultaneously identify the influence line, which has a low relative error and simplifies the steps of testing the modal frequency in advance in traditional influence line identification. The test has high accuracy and is easy to operate.

[0068] At the same time, the present invention only requires the installation of a "non-contact" deflection meter under the bridge, avoiding the installation of a vibration pickup, effectively shortening the time for closing traffic in the impact line test, and providing a more economical new idea for rapid bridge detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0070] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0071] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0072] See also Figure 1 The present invention provides a method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation, the method comprising the following steps:

[0073] Step 1: Derivation of the fundamental frequency analytical formula, set as the E-VMD method modal analysis cutoff frequency;

[0074] In this embodiment, the Rayleigh method frequency derivation is adopted, and in the case of undamped natural vibration, the instantaneous vertical displacement y(x, t) of the bridge is expressed as: y(x, t) = η(x) sin(wt+θ);

[0075] Where: η(x) is the approximate vibration function that satisfies the displacement boundary conditions of the bridge, w is the corresponding frequency, and θ is the phase difference, so the frequency w is derived as

[0076] In the formula, Ep and Ek are the potential energy and kinetic energy of the structural system, EI(x) is the bending stiffness, and m(x) is the mass distribution value;

[0077] The kinetic energy of the structural system includes:

[0078] Main beam kinetic energy E k1 , whose expression is

[0079] Kinetic energy of the cable E k2 , whose expression is

[0080] Bridge tower kinetic energy E k3 , whose expression is

[0081] Among them, m G 、m ci 、m T is the uniformly distributed mass of the main beam, cables and main tower, then the overall kinetic energy of the bridge is

[0082] The potential energy of the structural system is the potential energy of the main beam E p1 、Slope cable potential energy E p2 and the bridge tower potential energy E p3 sum;

[0083] in,

[0084] Where E G I G 、E T I T are the bending stiffness of the main beam and main tower, n, ξ is the vibration mode function of the main beam and main tower;

[0085] The equilibrium equation of cable deformation under unit force increase is constructed, and the cable potential energy is calculated as:

[0086] Where ΔL is the cable deformation, L ci is the original length of the cable, h ci is the cable descent height, a ci is the horizontal inclination angle of the cable;

[0087] When the structural vibration causes the cable inclination angle to change, the secondary potential energy of the cable can be approximately obtained by differentiating the vertical component of the cable force:

[0088]

[0089] The overall potential energy of the bridge is:

[0090]

[0091] Substituting the overall kinetic energy and potential energy into w, the first-order vertical bending vibration frequency of the bridge is calculated as:

[0092]

[0093] When the stiffness of the bridge main beam is large, the potential energy of the main tower, the cable, the secondary potential energy of the cable and the kinetic energy of the main tower can be ignored, and the kinetic energy of the cable can also be ignored because the mass of the cable is small relative to the mass of the main beam, w can be simplified to:

[0094]

[0095] Among them, V and G are the unit volume and bulk density of the main beam material, which is the basic vibration mode function of the bridge;

[0096] Assuming that the first-order positive symmetric vertical bending vibration is satisfied, the vibration mode functions of the main beam and side span are:

[0097]

[0098] By transforming the coordination equation The fundamental frequency analytical solution of the low-tower cable-stayed bridge can be derived as:

[0099]

[0100] The principles of the E-VMD method include:

[0101] A1. Use EMD to adaptively decompose the measured deflection time history response to obtain the intrinsic mode function IMFs components;

[0102] A2. Calculate the correlation coefficient of each IMFs, where M is the number of IMFs and define the correlation threshold l limt :

[0103]

[0104] Among them, ξ is the resolution coefficient, c is the empirical constant;

[0105] When l1(m)≥l limt , the mth IMF component is defined as a useful component, otherwise it is noise; all useful components are superimposed to obtain the preprocessed signal, recorded as x0(n);

[0106] The signal is subjected to variational modal decomposition (VMD) processing at different K values. Each decomposition obtains a set of narrowband IMFs components. The relationship between narrowband IMFs and x0(n) is determined by calculating the correlation coefficient, which satisfies l2(k)≥l limtThe reconstructed signal x1(n) is obtained by superimposing the narrowband IMFs components of (k=1, 2, ...K). The mutual information relationship between the preprocessed signal x0(n) and the reconstructed signal x1(n) is calculated by the mutual information method, and the mutual information (MI) index is proposed:

[0107] MI[x1,x0]=H(x1)+H(x0)-H(x1,x0);

[0108] Where: H(x1), H(x0) and H(x1,x0) are the information entropy and joint entropy of x0(n) and x1(n), denoted as:

[0109]

[0110]

[0111] Where x1(n), and are the probability mass function and joint probability mass function of x0(n) and x1(n) respectively;

[0112] When the mutual information index MI reaches the maximum value, the corresponding K value is the optimal number of modes obtained by variational mode decomposition. Reconstruct the optimal number of modes when x0(n) satisfies l2(k)≥l limt The narrow-band IMFs of (k=1, 2, ...K) can be used to obtain the quasi-static components of the vehicle-induced time-history response;

[0113] Step 2: Strip the dynamic response component from the deflection response and identify the bridge operation frequency through FFT transformation;

[0114] The dynamic response is the dynamic response of the vehicle crossing the bridge, which is obtained by simplifying the vehicle-bridge coupling system and simplifying the moving vehicle into a single-degree-of-freedom elastic mass block model for analysis;

[0115] Assume the bridge length is L, the mass m and its stiffness EI are evenly distributed, and the existing mass is M v , the stiffness is K v and the damping coefficient is C v The vehicle model travels across the bridge at a speed v, ignoring the influence of bridge damping, and assuming that the vehicle mass is much smaller than the bridge mass, the motion control equation is established as follows:

[0116]

[0117] Where y v is the vertical displacement of the vehicle body, U v is the dynamic displacement of the bridge, U cis the dynamic displacement of the bridge contact point, δ is the Dirac function, (·) and (′) are the first-order derivatives with respect to time t and distance x, respectively, and g is the gravitational acceleration;

[0118] According to the modal superposition, the dynamic displacement of the bridge is:

[0119]

[0120] The integral from the origin of the bridge length 0 to the total length L establishes the bridge response qb,n solution, and then derives the nth-order vibration frequency wbn of the bridge as:

[0121]

[0122] right Solve the nonhomogeneous differential equation, set the deflection and velocity at the bridge boundary to 0, and substitute the result to derive Then Substitution The vibration displacement response of the bridge is obtained as follows

[0123] It can be seen that when the mass of the test loading vehicle is much smaller than the mass of the bridge, the natural frequency of the bridge can be theoretically identified from the dynamic deflection response;

[0124] Step 3: Use the operating frequency as the threshold and re-strip the power response;

[0125] Step 4: Strip off the axle effect and obtain the static deflection influence line;

[0126] Methods for removing the axle effect include:

[0127] B1. Solve the influence line ill-conditioned equation using Tikhonov regularization;

[0128] B2, after E-VMD decomposition and processing of the time history response, the error e is introduced to establish the influence line identification model Rs;

[0129] Where Rs is the quasi-static response of the bridge, L is the vehicle information matrix, and Φ is the influence line coefficient of the bridge node;

[0130] R s =LΦ+e;

[0131] The Ti khonov regularization method uses the L2 norm as a penalty function to constrain the least squares expression, thereby solving the pathological mathematical equation of the influence line identification model caused by the error term. The regularization equation is as follows: λ is the regularization coefficient;

[0132] The regularized experience matrix is:

[0133]

[0134] B3. The vehicle information matrix is ​​determined by parameters such as sampling frequency, vehicle axle weight, number of axles, wheelbase and vehicle speed. The vehicle speed and sampling frequency determine the number of matrix columns, and the sensor sampling frequency determines the number of rows.

[0135] In this embodiment, the timing start and end points are the front axle of the vehicle going onto the bridge and the last axle going off the bridge, and the vehicle information matrix is:

[0136]

[0137] Ai is the vehicle axle weight;

[0138] Substitute the regularized empirical matrix into the regularized equation to solve Φ, and the influence line solution equation is:

[0139] Φ=(L T L+λ 2 T T T) -1 L T R s .

[0140] Implementation Cases:

[0141] An actual three-span low-tower cable-stayed bridge was used as the research object for experimental research. The span of the bridge is (105+180+105)m. The longitudinal main beam adopts a corrugated steel web-PC composite box beam. The main beam concrete is C50 and the top plate width is 35.5m. In order to obtain the influence line of bridge deflection, the test is carried out by idling vehicle loading. The loading path selects the center line of the bridge. The four-axle test vehicle with a full load of 35T is driven along the loading route. The deflection response data of the bridge under the idle loading test is measured to identify the deflection influence line of the bridge structure. The main geometric dimension information of the bridge section is reviewed on site in combination with the design drawings. A non-contact bridge dynamic displacement acquisition instrument is used to test the dynamic deflection of the mid-span section of the cable-stayed bridge. The bridge modal test is carried out by a 941B acceleration sensor. The measured bridge fundamental frequency is 0.843Hz.

[0142] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technical personnel in this field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation, characterized in that: The method comprises the following steps: Step 1: Derivation of the fundamental frequency analytical formula, set as the E-VMD method modal analysis cutoff frequency; Step 2: Strip the dynamic response component from the deflection response and identify the bridge operation frequency through FFT transformation; Step 3: Use the operating frequency as the threshold and re-strip the power response; Step 4: Remove the axle effect and obtain the static deflection influence line.

2. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 1 is characterized in that: In step 1, the Rayleigh method frequency derivation is used. In the case of undamped natural vibration, the instantaneous vertical displacement y(x, t) of the bridge is expressed as: y(x, t) = η(x)sin(wt+θ); Where: η(x) is the approximate vibration function that satisfies the displacement boundary conditions of the bridge, w is the corresponding frequency, and θ is the phase difference, so the frequency w is derived as Where Ep and Ek are the potential energy and kinetic energy of the structural system, EI(x) is the bending stiffness, and m(x) is the mass distribution value.

3. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 2 is characterized in that: The kinetic energy of the structural system includes: Main beam kinetic energy E k1 , whose expression is Kinetic energy of the cable E k2 , whose expression is Bridge tower kinetic energy E k3 , whose expression is m G 、m ci 、m T The uniform distribution quality of the main beam, cable and main tower; The overall kinetic energy is 4. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 3 is characterized in that: The potential energy of the structural system is the potential energy of the main beam E p1 、Slope cable potential energy E p2 and the bridge tower potential energy E p3 sum; in, Where E G I G 、E T I T are the bending stiffness of the main beam and main tower, n, ξ is the vibration mode function of the main beam and main tower; The equilibrium equation of cable deformation under unit force increase is constructed, and the cable potential energy is calculated as: Where ΔL is the cable deformation, L ci is the original length of the cable, h ci is the cable descent height, a ci is the horizontal inclination angle of the cable; When the structural vibration causes the cable inclination angle to change, the secondary potential energy of the cable can be approximately obtained by differentiating the vertical component of the cable force: The overall potential energy of the bridge is:

5. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 4 is characterized in that: Substituting the overall kinetic energy and potential energy into w, the first-order vertical bending vibration frequency of the bridge is calculated as:

6. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 1 is characterized in that: The dynamic response in step 2 is the dynamic response of the vehicle crossing the bridge, which is obtained by simplifying the vehicle-bridge coupling system and simplifying the moving vehicle into a single-degree-of-freedom elastic mass block model for analysis.

7. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 1 is characterized in that: The principles of the E-VMD method include: A1. Use EMD to adaptively decompose the measured deflection time history response to obtain the intrinsic mode function IMFs components; A2. Calculate the correlation coefficient of each IMFs, where M is the number of IMFs and define the correlation threshold l limt : Among them, ξ is the resolution coefficient, c is the empirical constant; When l1(m)≥l limt , the mth IMF component is defined as the useful component, otherwise it is noise; The preprocessed signal obtained by superimposing all useful components is denoted as x0(n).

8. The method for synchronously identifying the fundamental frequency and deflection influence line of a bridge under vehicle-induced excitation according to claim 1 is characterized in that: Methods for removing the axle effect include: B1. Solve the influence line ill-conditioned equation using Tikhonov regularization; B2, after E-VMD decomposition and processing of the time history response, the error e is introduced to establish the influence line identification model Rs; R s =LΦ+e; Where Rs is the quasi-static response of the bridge, L is the vehicle information matrix, and Φ is the influence line coefficient of the bridge node; The Tikhonov regularization method uses the L2 norm as a penalty function to constrain the least squares expression, thereby solving the pathological mathematical equation of the influence line identification model caused by the error term. The regularized equation is as follows: λ is the regularization coefficient; The regularized experience matrix is: B3. The vehicle information matrix is ​​determined by parameters such as sampling frequency, vehicle axle weight, number of axles, wheelbase and vehicle speed. The vehicle speed and sampling frequency determine the number of matrix columns, and the sensor sampling frequency determines the number of rows of the regularized experience matrix.

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