A mobile vehicle-mounted identification method and system based on multi-domain dictionary learning

Abstract

The present application relates to the field of mobile vehicle identification technology, and more particularly to a mobile vehicle identification method and system based on multi-domain dictionary learning, the method comprising: decomposing multi-domain representation mobile vehicle signals into constant load components, narrowband vehicle components and broadband vehicle components, and then using constant load component dictionaries, frequency domain dictionaries and time domain dictionaries for corresponding representation, combining system matrices to construct a vehicle-bridge control equation; constructing a mobile vehicle identification model based on vehicle-induced bridge responses and the vehicle-bridge control equation; solving the mobile vehicle identification model through iterative optimization of constant load component identification, sparse coding, frequency domain dictionary updating and time domain dictionary updating to obtain constant load component coefficients, narrowband vehicle component coefficients and broadband vehicle component coefficients; and substituting the obtained constant load component coefficients, narrowband vehicle component coefficients and broadband vehicle component coefficients into the mobile vehicle identification model to achieve mobile vehicle identification; the present application can achieve high-precision identification of mobile vehicles.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mobile vehicle identification technology, and particularly relates to a mobile vehicle identification method and system based on multi-domain dictionary learning. BACKGROUND

[0002] The mobile load caused by vehicles constitutes one of the main live loads in highway bridge structures, and the load exerted by heavy vehicles is widely considered as a key factor to cause bridge damage, which may seriously threaten the safety of the structure. Therefore, it is of great significance to carry out effective identification and monitoring of overweight vehicles for the safe operation and maintenance management of bridges.

[0003] The mobile vehicle identification technology in the related art mainly includes direct identification method and indirect identification method. The direct method usually relies on data reading of vehicle device, back calculation based on vehicle dynamics model, or real-time measurement by means of preset dynamic weighing system. However, such method faces many challenges in practical application, such as high cost investment, model error accumulation, and sensitivity to road conditions, which will affect the identification accuracy and applicability. In comparison, the indirect identification method collects and analyzes the dynamic response of the bridge structure under the action of vehicle load, and calculates the vehicle load characteristics by means of inversion algorithm. This method relies on the sensor system arranged on the structure, does not need to intervene the vehicle, and is more flexible and economical in system design, deployment, implementation and later maintenance, and has become a hot research and application direction.

[0004] The indirect identification method of mobile vehicle based on bridge structure response inversion belongs to the ill-posed problem in structural dynamics, and the solution is often unstable and highly sensitive to measurement noise. SUMMARY

[0005] The present application aims to provide a mobile vehicle identification method and system based on multi-domain dictionary learning, which can realize high-precision identification of mobile vehicle.

[0006] In order to achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] In the first aspect, the present application provides a mobile vehicle identification method based on multi-domain dictionary learning, which comprises the following steps:

[0008] S100, a multi-domain representation mobile vehicle signal is obtained, the multi-domain representation mobile vehicle signal is decomposed into a mobile vehicle load vector containing a constant load component, a narrow-band vehicle load component and a wide-band vehicle load component, and after corresponding representation by using a constant load component dictionary, a frequency domain dictionary and a time domain dictionary respectively, a vehicle-bridge control equation is constructed in combination with a system matrix;

[0009] S200, obtaining a vehicle-induced bridge response, and constructing a moving vehicle load identification model based on multi-domain dictionary learning based on the vehicle-induced bridge response and a bridge-vehicle control equation; the vehicle-induced bridge response includes responses generated by constant load, narrowband load and broadband load respectively; the moving vehicle load identification model is a target function of minimizing reconstruction error between the vehicle-induced bridge response and a moving vehicle load vector;

[0010] S300, solving the moving vehicle load identification model through iterative optimization of constant load component identification, sparse coding, frequency domain dictionary updating and time domain dictionary updating, to obtain constant load component coefficients, narrowband vehicle load component coefficients and broadband vehicle load component coefficients.

[0011] S400, substituting the obtained constant load component coefficients, narrowband vehicle load component coefficients and broadband vehicle load component coefficients into the moving vehicle load identification model to realize identification of the moving vehicle load.

[0012] Optionally, in S100, the multi-domain representation of the moving vehicle load signal is obtained, the multi-domain representation of the moving vehicle load signal is decomposed into a moving vehicle load vector including constant load components, narrowband vehicle load components and broadband vehicle load components, and then represented by using a constant load component dictionary, a frequency domain dictionary and a time domain dictionary respectively, and a bridge-vehicle control equation is constructed in combination with a system matrix, including:

[0013] S110, obtaining a multi-domain representation of a moving vehicle load signal, and decomposing the multi-domain representation of the moving vehicle load signal into constant load components, narrowband vehicle load components and broadband vehicle load components based on a multi-domain dictionary learning model;

[0014] S120, constructing a constant load component dictionary, a frequency domain dictionary and a time domain dictionary of the multi-domain representation of the moving vehicle load signal, and corresponding constant load component coefficients, narrowband vehicle load component coefficients and broadband vehicle load component coefficients; representing the constant load component as a product of the constant load component dictionary and the constant load component coefficients, representing the narrowband vehicle load component as a product of a core dictionary, a frequency domain dictionary and the narrowband vehicle load component coefficients, and representing the broadband vehicle load component as a product of the core dictionary, a time domain dictionary and the broadband vehicle load component coefficients;

[0015] S130, taking a product of the constant load component and a system matrix as a constant load response, taking a product of the narrowband vehicle load component and the system matrix as a narrowband load response, taking a product of the broadband vehicle load component and the system matrix as a broadband load response, and taking a sum of the constant load response, the narrowband load response and the broadband load response as a bridge-vehicle control equation.

[0016] Optionally, in S200, the vehicle-induced bridge response is obtained, and a moving vehicle load identification model based on multi-domain dictionary learning is constructed based on the vehicle-induced bridge response and a bridge-vehicle control equation, including:

[0017] S210, acquiring a vehicle-induced bridge response, and decomposing the vehicle-induced bridge response into responses respectively generated by a constant load, a narrowband load, and a broadband load;

[0018] S220, determining a reconstruction error based on a difference between the response generated by the constant load and a constant load component response, a difference between the response generated by the narrowband load and a narrowband load response, and a difference between the response generated by the broadband load and a broadband load response, constructing a moving vehicle identification model by taking the constant load component coefficient and a sparse representation vector as optimization variables and taking a square of a two-norm of the reconstruction error as an objective function, the sparse representation vector including a narrowband vehicle component coefficient and a broadband vehicle component coefficient, the objective function satisfying a constraint condition that an L0-norm of the narrowband vehicle component coefficient is not more than a target sparsity T1 and an L0-norm of an arbitrary column vector of a frequency domain dictionary is not more than a target sparsity T2.

[0019] Optionally, in S300, the moving vehicle identification model is solved by iterative optimization of the constant load component identification, sparse coding, frequency domain dictionary updating, and time domain dictionary updating to obtain the constant load component coefficient, the narrowband vehicle component coefficient, and the broadband vehicle component coefficient, and the method comprises the following steps:

[0020] S310, converting the moving vehicle identification model into a sparse solving function composed of the vehicle-induced bridge response and the constant load component response, and solving the sparse solving function to obtain the constant load component coefficient, and subtracting the response generated by the constant load component from the vehicle-induced bridge response to obtain a time-varying response component containing only the time-varying load, wherein the sparsity of the constant load component coefficient corresponds to the number of vehicle axles;

[0021] S320, converting the moving vehicle identification model into a sparse coding function composed of the time-varying response component and the time-varying load response, initializing a core dictionary, an initial frequency domain dictionary, and an initial time domain dictionary, and solving the sparse coding function by using an orthogonal matching pursuit algorithm to obtain a sparse representation vector under the condition that the initial frequency domain dictionary and the initial time domain dictionary are fixed;

[0022] S330, determining a position of a non-zero element in the sparse representation vector to locate a to-be-updated frequency domain dictionary atom, calculating a first residual vector after removing a current contribution of the to-be-updated frequency domain dictionary atom, constructing a frequency domain dictionary updating function based on the first residual vector and the to-be-updated frequency domain dictionary atom, and solving the frequency domain dictionary updating function to update the frequency domain dictionary atom to obtain an optimized frequency domain dictionary;

[0023] S340, calculating a second residual vector after removing a contribution of the frequency domain dictionary, constructing a time domain dictionary updating function based on the second residual vector and a to-be-updated time domain dictionary atom, and solving the time domain dictionary updating function to update the time domain dictionary atom to obtain an optimized time domain dictionary;

[0024] S350, updating the extended dictionary matrix based on the optimized frequency domain dictionary and the optimized time domain dictionary to obtain an updated extended dictionary matrix, and jumping to S320;

[0025] S360, repeating S320 to S340 until the reconstruction error of the sparse representation vector is less than a preset threshold or the maximum number of iterations is reached, to obtain a final sparse representation vector and an updated dictionary matrix, and then calculating the constant load component coefficient, the narrowband vehicle load component coefficient and the wideband vehicle load component coefficient through the mobile vehicle identification model.

[0026] Optionally, in S310, the mobile vehicle identification model is converted into a sparse solution function containing only the vehicle-induced bridge response and the constant load component response, including:

[0027] Taking the square of the two-norm of the difference between the vehicle-induced bridge response and the constant load component response as the objective function, and imposing the zero-norm constraint of the constant load component coefficient, a sparse solution function with the constant load component coefficient as the variable is obtained.

[0028] Optionally, in S320, the mobile vehicle identification model is converted into a sparse coding function composed of a time-varying response component and a time-varying load response, including:

[0029] S321, multiplying the system matrix, the extended dictionary matrix and the sparse representation vector to obtain the time-varying load response;

[0030] S322, taking the square of the two-norm of the difference between the time-varying response component and the time-varying load response as the objective function, and taking the zero-norm of the sparse representation vector not exceeding the target sparsity T1 as the constraint condition, a sparse coding function with the sparse representation vector as the variable is obtained.

[0031] Optionally, in S322, the target sparsity T1 is obtained by the following method:

[0032] S3221, after standardizing the system matrix, transposing it and multiplying it with the residual vector to obtain a covariance vector, and taking the maximum absolute value of the elements in the covariance vector as the path value of the current iteration;

[0033] S3222, by gradually increasing the sparsity level, repeating the steps of feature selection, least squares solution, path value calculation and residual update to generate a series of path values corresponding to different sparsity levels, and obtaining a regularization path composed of a series of path values;

[0034] S3223, calculating the change rate of the path value at the adjacent sparsity level, and when the change rate is less than a set threshold, taking the current sparsity as the target sparsity T1.

[0035] Optionally, in S330, the constructing the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atom to be updated comprises:

[0036] In S331, a ratio of the first residual vector and a corresponding narrowband vehicle-mounted component coefficient is taken as a first target signal vector to be fitted, and a product of a system matrix, a core dictionary and a time domain dictionary atom is taken as a time domain dictionary atom product term.

[0037] In S332, a function of minimizing a square of a two-norm of a difference between the first target signal vector and the time domain dictionary atom product term is taken as an objective function, and a constraint condition that a zero-norm of the time domain dictionary atom does not exceed a target sparsity T2 is taken, to obtain a time domain dictionary update function with the time domain dictionary atom as a variable.

[0038] Optionally, in S340, the constructing the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atom to be updated comprises:

[0039] In S341, a ratio of the second residual vector and a corresponding wideband vehicle-mounted component coefficient is taken as a second target signal vector, and a product of the system matrix, the core dictionary and the time domain dictionary atom is taken as a time domain dictionary atom product term.

[0040] In S342, a log penalty function is constructed based on a difference between the second target signal vector and the time domain dictionary atom product term, to obtain a time domain dictionary update function with the time domain dictionary atom as a variable.

[0041] In a second aspect, an embodiment of the present application provides a mobile vehicle-mounted identification system based on multi-domain dictionary learning, which comprises:

[0042] at least one processor;

[0043] at least one memory configured to store at least one program;

[0044] When the at least one program is executed by the at least one processor, the at least one processor implements the mobile vehicle-mounted identification method based on multi-domain dictionary learning.

[0045] The beneficial effects of the present application are: the present application discloses a mobile vehicle load identification method and system based on multi-domain dictionary learning, the present application obtains a multi-domain representation mobile vehicle load signal, decomposes the multi-domain representation mobile vehicle load signal into a mobile vehicle load vector containing a constant load component, a narrow-band vehicle load component and a wide-band vehicle load component, and uses a constant load component dictionary, a frequency domain dictionary and a time domain dictionary for corresponding representation respectively, then constructs a bridge control equation combined with a system matrix, takes the reconstruction error minimization of the bridge response caused by the vehicle and the response of each load component as an objective function, and through the iterative optimization process of constant load component identification, sparse coding, frequency domain and time domain dictionary updating, accurately solves the constant load component coefficient, the narrow-band and wide-band vehicle load component coefficient, and further accurately identifies the mobile vehicle load. Through the collaborative optimization and sparse constraint of the multi-domain dictionary, the present application effectively improves the accuracy and anti-interference ability of load identification, and can adapt to the load identification requirements under different vehicle models, road conditions and noise levels. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0047] Figure 1 A flowchart of a mobile vehicle load identification method based on multi-domain dictionary learning in an embodiment of the present application is shown;

[0048] Figure 2 A schematic diagram of the solving process of multi-domain dictionary learning in an embodiment of the present application is shown;

[0049] Figure 3 A block schematic diagram of a mobile vehicle load identification system based on multi-domain dictionary learning in an embodiment of the present application is shown;

[0050] Figure 4 A load form and bridge response schematic diagram when the road roughness is 4 in an embodiment of the present application is shown;

[0051] Figure 5 A mobile vehicle load identification result schematic diagram under different sparseness in an embodiment of the present application is shown;

[0052] Figure 6 A time history curve schematic diagram of three methods for identifying mobile vehicle load in an embodiment of the present application is shown;

[0053] Figure 7 A frequency spectrum diagram of three methods for identifying mobile vehicle load in an embodiment of the present application is shown;

[0054] Figure 8 A time-frequency domain identification method in an embodiment of the present application is shown in the contrastive schematic diagram of the moving vehicle. DETAILED DESCRIPTION

[0055] The concept, specific structure and resulting technical effects of the present application will be described clearly and completely in conjunction with the embodiments and the accompanying drawings, so as to fully understand the purpose, scheme and effects of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0056] To overcome the problems in the background art, researchers usually convert the vehicle-mounted identification problem into a convex optimization problem for solution, and existing sparse regularization methods mostly rely on a fixed dictionary constructed by a specific base function. In a scene where the road conditions are stable and the vehicle-mounted features are relatively simple, such a dictionary can achieve a relatively ideal fitting effect. However, in actual engineering, due to the complexity and uncertainty of road conditions, the vehicle load signal often presents significant nonlinearity and variability, and the traditional fixed dictionary is difficult to fully represent the sparse structure and dynamic characteristics thereof, thereby limiting the identification accuracy and adaptability.

[0057] Therefore, providing an adaptive dictionary learning technology capable of dynamic adjustment according to the actual bridge and road response characteristics has important research value and engineering application potential for improving the expression ability and accuracy of sparse representation in moving vehicle identification.

[0058] Dictionary learning (DL) is an efficient signal representation and analysis method, which has excellent complex signal modeling and feature extraction capability, and is widely used in signal reconstruction, classification and identification tasks. Due to the structural restriction introduced by the sparsity constraint in the dictionary update stage in the related art, the dictionary learning often limits the expression ability of the dictionary for high-order and nonlinear load characteristics, thereby affecting the identification accuracy; and in actual application, it may reduce the robustness and generalization ability of the model in complex working conditions.

[0059] On this basis, the present application proposes a novel multi-domain dictionary learning model to realize high-precision identification of the moving vehicle. The innovativeness of the method mainly lies in the following aspects:

[0060] Firstly, a multi-domain dictionary learning framework is constructed, which fuses the feature representation of the frequency domain and the time domain, and breaks through the limitation of the traditional single-domain dictionary learning in the representation ability;

[0061] Secondly, based on the regularization path theory, an adaptive sparsity selection strategy is proposed to realize the dynamic adjustment of sparse parameters and improve the adaptability and robustness of the model under different working conditions.

[0062] In combination with Figure 1 and Figure 2 The embodiment of the present application provides a mobile vehicle load identification method based on multi-domain dictionary learning, which comprises the following steps.

[0063] S100, a multi-domain representation mobile vehicle load signal is obtained, the multi-domain representation mobile vehicle load signal is decomposed into a mobile vehicle load vector containing a constant load component, a narrow-band vehicle load component and a wide-band vehicle load component, and after corresponding representation is performed by using a constant load component dictionary, a frequency domain dictionary and a time domain dictionary respectively, a bridge control equation is constructed in combination with a system matrix; the multi-domain dictionary comprises the constant load component dictionary, the frequency domain dictionary and the time domain dictionary;

[0064] S200, a vehicle-induced bridge response is obtained, and a mobile vehicle load identification model based on multi-domain dictionary learning is constructed based on the vehicle-induced bridge response and the bridge control equation; the vehicle-induced bridge response contains responses generated by constant loads, narrow-band loads and wide-band loads respectively; the mobile vehicle load identification model is a target function for minimizing reconstruction errors between the vehicle-induced bridge response and the mobile vehicle load vector;

[0065] S300, the mobile vehicle load identification model is solved through iterative optimization of constant load component identification, sparse coding, frequency domain dictionary updating and time domain dictionary updating, so as to obtain constant load component coefficients, narrow-band vehicle load component coefficients and wide-band vehicle load component coefficients;

[0066] S400, the constant load component coefficients, the narrow-band vehicle load component coefficients and the wide-band vehicle load component coefficients obtained by solving are substituted into the mobile vehicle load identification model, so as to realize identification of the mobile vehicle load.

[0067] In the embodiments provided by the present application, the mobile vehicle load vector is decomposed into constant load component, narrow-band load component and wide-band load component by the multi-domain dictionary learning model, which correspond to constant load component dictionary, frequency domain dictionary and time domain dictionary respectively, so that the multi-domain characteristics of the mobile vehicle load can be captured more comprehensively. Among them, the constant load component dictionary is used to represent the effect of the constant weight of the vehicle itself on the bridge, the frequency domain dictionary focuses on describing the distribution characteristics of the narrow-band load component in the frequency domain, and the time domain dictionary highlights the dynamic characteristics of the wide-band load component changing with time. Through the synergistic effect of such multi-domain dictionaries, combined with the vehicle-bridge control equation constructed by the system matrix, the mapping relationship between the mobile vehicle load and the vehicle-induced bridge response can be established more accurately, laying a solid foundation for subsequent mobile vehicle load identification. After obtaining the vehicle-induced bridge response, based on the response and the mobile vehicle load identification model constructed by the vehicle-bridge control equation, the objective function of minimizing the vehicle-induced bridge response and the mobile vehicle load vector can effectively utilize the measured bridge response data to deduce the correlation coefficient of the mobile vehicle load. And the process of solving the mobile vehicle load identification model through the steps of constant load component identification, sparse coding, frequency domain dictionary updating and time domain dictionary updating is an iterative process of continuously optimizing the dictionary and the coefficient. The constant load component identification can preliminarily determine the constant load part of the vehicle, the sparse coding can extract the key load features from the complex response data, and the frequency domain dictionary updating and the time domain dictionary updating optimize the frequency domain dictionary and the time domain dictionary respectively, so that they can better adapt to different load working conditions and environmental conditions, so as to finally obtain accurate constant load component coefficients, narrow-band vehicle load component coefficients and wide-band vehicle load component coefficients, and realize high-precision identification of the mobile vehicle load.

[0068] In some embodiments, in S100, the multi-domain representation of the mobile vehicle load signal is obtained, the multi-domain representation of the mobile vehicle load signal is decomposed into a constant load component, a narrow-band vehicle load component and a wide-band vehicle load component, and after corresponding representation is performed by using a constant load component dictionary, a frequency domain dictionary and a time domain dictionary respectively, a vehicle-bridge control equation is constructed in combination with a system matrix, including:

[0069] S110, obtaining a multi-domain representation of the mobile vehicle load signal, and decomposing the multi-domain representation of the mobile vehicle load signal into a constant load component, a narrow-band vehicle load component and a wide-band vehicle load component based on a multi-domain dictionary learning model;

[0070] S120, constructing a constant load component dictionary, a frequency domain dictionary and a time domain dictionary of the multi-domain representation of the mobile vehicle load signal, and corresponding constant load component coefficients, narrow-band vehicle load component coefficients and wide-band vehicle load component coefficients; representing the constant load component as a product of the constant load component dictionary and the constant load component coefficients, representing the narrow-band vehicle load component as a product of the core dictionary, the frequency domain dictionary and the narrow-band vehicle load component coefficients, and representing the wide-band vehicle load component as a product of the core dictionary, the time domain dictionary and the wide-band vehicle load component coefficients;

[0071] S130, the product of the constant load component and the system matrix is taken as the constant load component response, the product of the narrowband vehicle load component and the system matrix is taken as the narrowband load response, and the product of the wideband vehicle load component and the system matrix is taken as the wideband load response, and the sum of the constant load component response, the narrowband load response and the wideband load response is taken as the vehicle-bridge control equation.

[0072] It should be noted that in the vehicle-bridge control equation constructed, the constant load component response, the narrowband load response and the wideband load response are superimposed to obtain the total response of the bridge structure, which needs to be consistent with the measured vehicle-induced bridge response. In the construction process, the constant load component dictionary is in the form of a unit vector matrix to directly represent the constant part of the load; the frequency domain dictionary is generated by Fourier transform of the typical vehicle vibration frequency components to generate initial atoms for capturing the periodic characteristics of the narrowband vehicle load component; and the time domain dictionary is constructed based on the impulse response function, focusing on depicting the transient change characteristics of the wideband vehicle load component. By decomposing the moving vehicle load vector into components with different physical meanings and matching the dedicated dictionary for each component, the fine sparse representation of the load signal in the multi-domain space is realized, which lays a structured foundation for subsequent model solving.

[0073] Firstly, the time-domain control equation for moving vehicle load identification is introduced as follows:

[0074] When identifying the moving vehicle load, a linear relationship between the vehicle load and the bridge response needs to be constructed. According to the principle of linear superposition, the bridge response (p=1,2,…,M) under the action of N moving loads can be expressed in the form of Duhamel convolution integral as follows:

[0075] ;

[0076] In the formula, at time t, represents the time-varying position of the qth moving load ; represents the unit impact response function corresponding to the position when the unit impact force is applied to .

[0077] Based on the finite element method, formula (1) can be re-expressed in the following matrix multiplication form:

[0078] (2);

[0079] wherein, represents the system matrix that obtains the pth response vector under the action of the Nth moving load, which reflects the dynamic behavior of the system. By converting the convolution operation in the continuous time domain into a discrete matrix form, a linear algebra basis is provided for subsequent load identification based on multi-domain dictionary learning, which facilitates the use of sparse optimization algorithms to solve the load components. Equation (2) can be further simplified as:

[0080] (3) ;

[0081] where, represents the system matrix, whose elements are composed of the unit impulse response functions of the bridge structure after discretization, reflecting the transfer relationship between the load at different positions and the responses at each measuring point; F represents the moving vehicle load vector, including the constant load component and the time-varying load component; Y represents the combined response vector of the bridge structure, formed by the bending moment response and acceleration response collected at each measuring point after data fusion. Through equation (3), a linear mapping relationship between the load and the response is established, providing a mathematical modeling basis for mobile vehicle identification based on multi-domain dictionary learning, so that the subsequent sparse coding and dictionary updating process can be efficiently realized through matrix operations under this framework.

[0082] Equation (3) is also called the control equation of the mobile vehicle identification problem. By establishing this control equation, the mobile vehicle identification problem is transformed into a sparse representation problem of the moving force.

[0083] The multi-domain dictionary learning model is constructed as follows:

[0084] According to the distribution characteristics of the mobile vehicle signal in the frequency spectrum, it can be decomposed into zero-frequency components, narrow-band components with obvious periodicity, and wide-band components with obvious time-varying characteristics. Among them, the zero-frequency component corresponds to the constant component of the vehicle load, the narrow-band vehicle signal can be represented by the frequency domain dictionary, and the wide-band vehicle signal can be represented by the time domain dictionary.

[0085] (4) ;

[0086] where, represents the core dictionary of the vehicle signal, which remains unchanged during the dictionary learning process; 、 and represent the constant load component dictionary, the frequency domain dictionary and the time domain dictionary of the multi-domain representation of the mobile vehicle signal, respectively; 、 and represent the atom coefficients of the constant load component, the narrow-band vehicle component and the wide-band vehicle component, respectively. respectively represent the constant load component, the narrowband vehicle load component and the broadband vehicle load component in the vehicle load. By decomposing the moving vehicle load into components with different characteristics and corresponding to different types of dictionaries and coefficients, a structured representation of the load signal is achieved, providing a theoretical basis for the construction and solution of the subsequent multi-domain dictionary learning model.

[0087] Substituting formula (4) into formula (3), the axle control equation can be obtained:

[0088] (5).

[0089] In some embodiments, in S200, the vehicle-induced bridge response is obtained, and a moving vehicle load identification model based on multi-domain dictionary learning is constructed based on the vehicle-induced bridge response and the axle control equation, including:

[0090] In S210, the vehicle-induced bridge response is obtained, and the vehicle-induced bridge response is decomposed into responses respectively generated by the constant load, the narrowband load and the broadband load.

[0091] In S220, the reconstruction error is determined based on the difference between the response generated by the constant load and the constant load component response, the difference between the response generated by the narrowband load and the narrowband load response, and the difference between the response generated by the broadband load and the broadband load response, the constant load component coefficient and the sparse representation vector are taken as the optimization variables, the square of the two-norm of the reconstruction error is taken as the objective function, and a moving vehicle load identification model is constructed; the sparse representation vector includes the narrowband vehicle load component coefficient and the broadband vehicle load component coefficient, and the objective function satisfies the constraint condition that the L0-norm of the narrowband vehicle load component coefficient does not exceed the target sparsity T1 and the L0-norm of any column vector of the frequency domain dictionary does not exceed the target sparsity T2.

[0092] By minimizing the objective function, the joint optimization and solution of the atomic coefficients of the constant load component, the narrowband vehicle load component and the broadband vehicle load component are realized, so that different characteristic components in the moving vehicle load are accurately separated and identified. In the construction process of the objective function, the error terms of each response component are measured by L2 norm to quantify the difference between the actual response and the model predicted response, so as to ensure that the optimization process can effectively reduce the overall reconstruction error. At the same time, the introduction of the sparsity constraint condition enables the model to eliminate redundant information on the premise of ensuring the identification accuracy, improves the physical interpretability of the load component identification result, and conforms to the characteristics of the sparse distribution of the moving vehicle load in the actual engineering scene.

[0093] Correspondingly, the vehicle-induced bridge response can be decomposed into responses respectively generated by the constant load, the narrowband load and the broadband load:

[0094] (6).

[0095] wherein, respectively represent the response components generated by constant load, narrowband load and broadband load acting on the bridge structure, represents the total response of the vehicle to the bridge, i.e., the vehicle-to-bridge response.

[0096] Further, the mobile vehicle-mounted identification model based on multi-domain dictionary learning can be expressed as:

[0097] (7);

[0098] satisfies ;

[0099] wherein the coefficient vector of the narrowband vehicle-mounted component is denoted as The target sparsity of The target sparsity of any column vector in the sparse dictionary is . respectively represent the atom coefficients of the constant load component, the narrowband vehicle-mounted component and the broadband vehicle-mounted component, and the sparsity thereof is controlled by the L0 norm constraint to ensure that the sparse representation of the load signal conforms to the actual physical meaning.

[0100] In the model optimization process, the component coefficients and dictionary atoms are alternately updated, and the iteration is continuously performed until the target function converges, so as to realize the accurate separation and identification of different characteristic components in the mobile vehicle load. The model fully utilizes the advantages of the multi-domain dictionary in representing complex signals, combines the periodic characteristics in the frequency domain with the transient change characteristics in the time domain, effectively improves the overall identification accuracy of the mobile vehicle load, and is especially suitable for load signal analysis scenes containing multiple dynamic characteristics.

[0101] In actual measurement response, since it is difficult to directly separate the response components generated by different frequency band loads, the above mobile vehicle-mounted identification model can be rewritten as:

[0102] (8);

[0103] satisfies ;

[0104] Let The multi-domain dictionary learning model can be re-expressed as:

[0105] (9);

[0106] satisfies ;

[0107] wherein denotes an extended dictionary matrix consisting of a frequency domain dictionary and a time domain dictionary, the frequency domain dictionary part corresponds to the sparse representation basis of the narrowband vehicle load component, and the time domain dictionary part corresponds to the sparse representation basis of the wideband vehicle load component; x denotes a sparse representation vector composed of narrowband vehicle load component coefficients and wideband vehicle load component coefficients, is a time-varying load response, and denotes a load response part corresponding to the product of the multi-domain dictionary and the sparse representation vector, wherein the product term of the frequency domain dictionary atom and the narrowband coefficient mainly contributes the periodic load response, and the product term of the time domain dictionary atom and the wideband coefficient mainly contributes the transient impact load response, both of which realize the collaborative representation of the multi-domain characteristics through the extended dictionary matrix Θ, and jointly constitute the sparse approximation of the time-varying load response. By linearly superimposing the constant load component response HAc and the multi-domain time-varying load response HΘx, the total response model of the vehicle-bridge system is completely constructed, and a structured objective function form is provided for subsequent load coefficient inversion based on the measured response Y.

[0108] By integrating the multi-domain dictionary and the coefficient vector into a matrix form, the optimization objective of the multi-domain dictionary learning model can be converted into a joint solving problem of the constant load component coefficient c and the sparse representation vector x, further simplifying the calculation complexity of the model and facilitating efficient iterative solving by using optimization algorithms such as the alternating direction method of multipliers. In this matrix representation, the product HΘ of the system matrix H and the joint dictionary Θ reflects the transmission relationship between the multi-domain dictionary atoms and the bridge response, so that the sparse representation error of the load component can be directly quantified through matrix operation, providing a unified mathematical framework for subsequent dictionary updating and sparse coding.

[0109] In some embodiments, in S300, the mobile vehicle load identification model is solved by iterative optimization of constant load component identification, sparse coding, frequency domain dictionary updating, and time domain dictionary updating, to obtain constant load component coefficients, narrowband vehicle load component coefficients, and wideband vehicle load component coefficients, including:

[0110] S310, the mobile vehicle load identification model is converted into a sparse solving function composed of vehicle-bridge response and constant load component response, and the constant load component coefficient is solved by the sparse solving function. The response generated by subtracting the constant load component from the vehicle-bridge response is obtained, which only contains the time-varying response component of the time-varying load, wherein the sparsity of the constant load component coefficient corresponds to the number of vehicle axles;

[0111] S320, the mobile vehicle load identification model is converted into a sparse coding function composed of a time-varying response component and a time-varying load response, the core dictionary, the initial frequency domain dictionary, and the initial time domain dictionary are initialized, and the sparse coding function is solved by using the orthogonal matching pursuit algorithm to obtain the sparse representation vector under the condition of keeping the initial frequency domain dictionary and the initial time domain dictionary fixed;

[0112] S330, determine the positions of non-zero elements in the sparse representation vector to locate the frequency domain dictionary atom to be updated, calculate the first residual vector after removing the current contribution of the frequency domain dictionary atom to be updated, construct the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atom to be updated, solve the frequency domain dictionary update function to update the frequency domain dictionary atom, and obtain the optimized frequency domain dictionary;

[0113] S340, calculate the second residual vector after removing the contribution of the frequency domain dictionary, construct the time domain dictionary update function based on the second residual vector and the time domain dictionary atom to be updated, solve the time domain dictionary update function to update the time domain dictionary atom, and obtain the optimized time domain dictionary;

[0114] S350: Update the extended dictionary matrix based on the optimized frequency domain dictionary and the optimized time domain dictionary to obtain the updated extended dictionary matrix, and then jump to S320;

[0115] S360, repeat S320 to S340 until the reconstruction error of the sparse representation vector is less than the preset threshold or the maximum number of iterations is reached, to obtain the final sparse representation vector and the updated dictionary matrix, and then calculate the constant load component coefficient, narrowband vehicle component coefficient and wideband vehicle component coefficient through the mobile vehicle recognition model.

[0116] By alternately updating the sparse representation vector, frequency domain dictionary, and time domain dictionary, collaborative optimization of the dictionary and coefficients is achieved. After each dictionary update, the sparse representation vector needs to be recalculated. Through alternating optimization of dictionary atoms and coefficient vectors, dynamic adaptation of the dictionary to the characteristics of the load signal is achieved.

[0117] In each iteration, the sparse representation vector is first solved based on the current dictionary parameters. Then, the dictionary atoms that need to be updated are located according to the distribution of non-zero elements in the sparse representation vector. The dictionary atoms are optimized by constructing residual vectors and target signal vectors until the change in the objective function value is less than the set convergence threshold or the maximum number of iterations is reached. This completes the solution of the mobile vehicle recognition model, and finally outputs the constant load component coefficients, narrowband vehicle component coefficients, and wideband vehicle component coefficients. This solution process fully reflects the dynamic optimization characteristics of multi-domain dictionary learning. Through the alternating update of the dictionary and coefficients, the dictionary atoms can adaptively capture the multi-domain features of the load signal, while ensuring that the sparsity of the coefficient vector conforms to physical constraints, thereby improving the recognition accuracy of each component of the mobile vehicle load.

[0118] The frequency domain dictionary update focuses on improving the accuracy of representing periodic load components by adjusting the combined weights of the Fourier basis functions to enhance the ability to capture load energy in different frequency bands. The time domain dictionary update optimizes the shape parameters of the Gaussian derivative function family to better match the waveform characteristics of transient impact loads, especially non-stationary impact signals generated during vehicle start-up, braking, or encountering road bumps. The core dictionary, as a carrier of prior knowledge, constrains the update direction of frequency and time domain dictionary atoms during the dictionary update process to avoid dictionary overfitting caused by local optima, ensuring that the learned dictionary atoms have broader load mode adaptability. Through these multiple rounds of iterative optimization, the final constant load component coefficients, narrowband vehicle load component coefficients, and broadband vehicle load component coefficients accurately reflect the amplitude and temporal distribution characteristics of different characteristic components in moving vehicle loads.

[0119] In some embodiments, S310, converting the mobile vehicle identification model into a sparse solution function containing only the vehicle-induced bridge response and the dead load component response includes:

[0120] The objective function is to minimize the squared 2-norm of the difference between the vehicle-induced bridge response and the dead load component response. A zero-norm constraint is imposed on the dead load component coefficients to obtain a sparse solution function with the dead load component coefficients as variables.

[0121] In this embodiment, by setting the zero-norm constraint of the constant load component coefficient to correspond to the actual number of axles of the vehicle, it is ensured that the constant load component identification result conforms to the physical characteristics of the vehicle's axle weight distribution. By limiting the number of non-zero elements in the constant load component coefficient vector, the constant load component response HAc can accurately reflect the constant weight contribution of each axle of the vehicle, avoiding constant load component identification errors caused by over-parameterization.

[0122] In some embodiments, S320, converting the mobile vehicle identification model into a sparse coding function composed of time-varying response components and time-varying load responses includes:

[0123] S321, multiply the system matrix, the extended dictionary matrix and the sparse representation vector to obtain the time-varying load response;

[0124] S322, with the objective function being the minimization of the squared second norm of the difference between the time-varying response component and the time-varying load response, and with the constraint that the zero norm of the sparse representation vector does not exceed the target sparsity T1, yields a sparse coding function with the sparse representation vector as the variable.

[0125] In this embodiment, by constructing an error function between the time-varying response component and the product of the system matrix, the extended dictionary matrix, and the sparse representation vector, the optimization problem of time-varying load in the mobile vehicle recognition model is transformed into solving the sparse representation vector. Specifically, the time-varying response component is the remainder after subtracting the constant load component response from the total vehicle-induced bridge response, while the time-varying load response is obtained by applying the product of the system matrix and the extended dictionary matrix to the sparse representation vector. Therefore, the core of the sparse coding function is to minimize the L2 norm squared error between the time-varying response component and the time-varying load response. At the same time, by constraining the L0 norm of the narrowband vehicle component coefficient γ in the sparse representation vector x to not exceed the target sparsity T1, it is ensured that the solved sparse representation vector can accurately capture the key feature components in the time-varying load and eliminate redundant information. When solving the sparse coding function using the orthogonal matching pursuit algorithm, the combination of atoms that best matches the response signal is adaptively selected from the extended dictionary matrix based on the characteristics of the time-varying response components. By iteratively updating the position and amplitude of the non-zero coefficients, the optimal sparse representation vector is gradually approximated, thereby achieving a preliminary estimate of the coefficients of the narrowband and wideband vehicle components, laying the foundation for the subsequent dictionary update steps.

[0126] In some embodiments, in S322, the target sparsity T1 is obtained in the following manner:

[0127] S3221, after standardizing the system matrix, transpose it and multiply it with the residual vector to obtain the covariance vector. Take the maximum absolute value of the elements in the covariance vector as the path value of the current iteration.

[0128] S3222, by gradually increasing the sparsity level, repeatedly performing feature selection, least squares solution, path value calculation and residual update steps, a series of path values ​​corresponding to different sparsities are generated, resulting in a regularized path composed of a series of path values;

[0129] S3223, calculate the rate of change of path values ​​under adjacent sparsity levels. When the rate of change is less than the set threshold, the current sparsity is taken as the target sparsity T1.

[0130] This adaptive selection mechanism can effectively avoid overfitting or underfitting caused by traditional empirical sparsity settings. By dynamically adjusting the sparsity parameters through a data-driven approach, the sparse coding results can accurately capture the main load features in the time-varying response components while suppressing the interference of noise and redundant information, thus providing a high-quality sparse representation vector foundation for subsequent dictionary updates.

[0131] In some embodiments, S330, the construction of the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atoms to be updated includes:

[0132] S331, the ratio of the first residual vector to the corresponding narrowband vehicle component coefficient is taken as the first target signal vector to be fitted, and the product of the system matrix, the core dictionary and the frequency domain dictionary atom is taken as the frequency domain dictionary atom product term;

[0133] S332, with the objective function being the square of the second norm of the difference between the first target signal vector and the product terms of the frequency domain dictionary atoms, and with the constraint that the zero norm of the frequency domain dictionary atoms does not exceed the target sparsity T2, yields a frequency domain dictionary update function with frequency domain dictionary atoms as variables.

[0134] In this embodiment, the optimization objective is to minimize the error between the product term of the first target signal vector and the frequency domain dictionary atom. Simultaneously, by constraining the L0 norm of the frequency domain dictionary atom to not exceed T², the updated frequency domain dictionary atom ensures that, while retaining the core load periodic characteristics, it possesses a sparse structure matching the load frequency distribution. Specifically, the first residual vector reflects the uninterpreted portion of the current frequency domain dictionary atom's time-varying response components. By calculating the ratio with the corresponding narrowband coefficient, the residual signal can be focused onto the contribution frequency band of the atom to be updated, thereby constructing a more targeted first target signal vector. The product term of the system matrix and the core dictionary provides a physical constraint basis for the frequency domain dictionary atom, ensuring that its update process always follows the dynamic transmission characteristics of the bridge structure and avoids dictionary atom patterns that contradict the actual physical meaning of the load. When solving this update function, gradient descent or coordinate descent methods are typically used. The element values ​​of the frequency domain dictionary atom are iteratively adjusted until the objective function converges, ultimately obtaining an optimized frequency domain dictionary atom that fits the first target signal vector and satisfies the sparsity constraints. This process enables the frequency domain dictionary to adaptively learn the characteristics of periodic loads, allowing dictionary atoms to dynamically track changes in load frequency components and improve the characterization accuracy of narrowband load responses under different vehicle speeds and models.

[0135] In some embodiments, S340, the construction of the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atoms to be updated includes:

[0136] S341, the ratio of the second residual vector to the corresponding broadband vehicle component coefficient is taken as the second target signal vector, and the product of the system matrix, the core dictionary and the time-domain dictionary atom is taken as the time-domain dictionary atom product term;

[0137] S342, a logarithmic penalty function is constructed based on the difference between the second target signal vector and the product terms of the time-domain dictionary atoms, resulting in a time-domain dictionary update function with minimizing the logarithmic penalty function as the objective function and the time-domain dictionary atoms as variables.

[0138] In this embodiment, by introducing a logarithmic penalty function, a nonlinear constraint can be applied to the amplitude changes of the time-domain dictionary atoms, which is particularly suitable for capturing the steep changes in transient impact loads in broadband vehicle components. The second residual vector is the remaining response obtained after removing the contribution of the frequency domain dictionary, reflecting the main effect of the broadband vehicle components. Dividing it by the corresponding broadband coefficient can highlight the impact signal characteristics that the time-domain dictionary atom to be updated should represent, forming the second target signal vector. The product term of the system matrix and the core dictionary ensures that the update of the time-domain dictionary atoms conforms to the transmission law of transient loads in the bridge structure, avoiding physical distortion of the atomic mode. When constructing the logarithmic penalty function, the element values ​​of the time-domain dictionary atoms are usually logarithmized and then L1 norm regularized. This processing method can effectively suppress noise interference in the atoms and enhance the ability to capture sparse high-frequency impact components.

[0139] The solution process for the mobile vehicle recognition model is as follows:

[0140] Existing research has shown that in mobile vehicle identification, employing a strategy of separating and identifying dynamic and static load components helps improve identification accuracy. Based on this, the solution process of the multi-domain dictionary learning method proposed in this invention mainly includes four key steps: constant load component identification, sparse coding, frequency domain dictionary update, and time domain dictionary update (see...). Figure 2 ), Figure 2 In this context, OMP stands for Orthogonal Matching Pursuit Algorithm, and GD stands for Gradient Descent Algorithm with Adaptive Moment Estimation. The following section will elaborate on the specific implementation methods and theoretical basis of these four steps.

[0141] (1) Identification of dead load components

[0142] Because constant loads do not change with time, they can be identified relatively accurately even without considering time-varying loads. In this case, formula (9) can be transformed into:

[0143] (10);

[0144] satisfy ;

[0145] Formula (10) is solved using the Orthogonal Matching Pursuit (OMP) algorithm, where the sparsity of the constant load component coefficient c corresponds to the number of axles of the vehicle. After obtaining the constant load component coefficient, the corresponding time-varying response components can be further calculated.

[0146] (11);

[0147] in, This represents the time-varying response component separated from the constant load component identification results. This component contains only the dynamic effects of the narrowband vehicle-mounted component and the broadband vehicle-mounted component on the bridge structure.

[0148] In one embodiment, during the identification of constant load components, by setting the sparsity of the constant load coefficient vector c to be equal to the number of vehicle axles, it is possible to effectively ensure that the identified constant load components match the actual axle load distribution characteristics of the vehicle, laying the foundation for the accurate separation and identification of subsequent time-varying load components. The orthogonal matching pursuit algorithm iteratively selects the atoms most relevant to the residuals, gradually approximating the optimal sparse solution. When dealing with the constant load component identification problem with clearly defined sparsity characteristics, it not only has high computational efficiency but also effectively suppresses the impact of noise interference on the constant load component extraction results while ensuring identification accuracy.

[0149] (2) Sparse coding

[0150] Before updating the dictionary, a sparse encoding step must be performed first, and the two steps are iterated alternately until the algorithm converges. First, the core dictionary is initialized. And design an initial frequency domain dictionary. and the initial time-domain dictionary While maintaining the initial frequency domain dictionary and the initial time-domain dictionary Under fixed conditions, sparse representation vectors The solution is then transformed into a sparse coding problem. Substituting equation (11) into equation (9) and using the Orthogonal Matching Pursuit (OMP) algorithm, the sparse representation vector can be obtained. .

[0151] (12);

[0152] satisfy ;

[0153] in, The initial sparse representation vector is the sparse representation vector obtained from the first sparse coding iteration. Its non-zero elements correspond to the main contributing atoms of the narrowband and wideband onboard components in the time-varying response components.

[0154] To further improve the accuracy of sparse coding, this invention introduces an adaptive target sparsity selection mechanism based on regularized paths. This mechanism dynamically adjusts the target sparsity T1 by constructing a regularized path to balance the fitting accuracy and sparsity of the sparse coding function. Specifically, it first calculates the covariance vector between the current residual vector and the system matrix, defining its infinite norm as the path value. By tracking the trend of the path value's change with increasing sparsity, when the rate of change of the path value is lower than a preset threshold (e.g., 1%), the sparsity is determined to be optimal, thus avoiding overfitting due to excessively high sparsity or underfitting due to excessively low sparsity. After determining the optimal sparsity, the orthogonal matching pursuit algorithm is re-executed to optimize and update the sparse representation vector x, obtaining a sparse coding result that better reflects the actual load characteristics. During this process, the number of non-zero elements in the narrowband component coefficient γ is strictly controlled within the target sparsity T1 to ensure that the periodic characteristics of the narrowband vehicle component are accurately captured. Meanwhile, the target sparsity T2 of the frequency domain dictionary atoms guarantees the localization characteristics of the dictionary column vectors, providing a reliable coefficient basis for subsequent dictionary updates.

[0155] (3) Frequency domain dictionary update

[0156] In obtaining sparse representation vectors Then, keeping it fixed, the initial frequency domain dictionary can be adjusted. Perform column-by-column updates. The update process for each column includes the following steps:

[0157] Sub-step one: First, determine the sparse representation vector. The positions of non-zero elements in the frequency domain dictionary. The column vectors in the array represent the atoms to be updated.

[0158] Sub-step two involves updating the dictionary atoms in the i-th column. When doing so, it is necessary to first calculate the first residual vector after removing the current contribution of the atom. This is used to extract the residual information that needs to be fitted to the current atom.

[0159] (13);

[0160] in, This indicates the removal of the i-th column of the frequency domain dictionary atoms. and its corresponding narrowband vehicle component coefficient The first residual vector after contribution, This represents the contribution of the product term of the frequency domain dictionary atom and its corresponding coefficient in the j-th column to the time-varying response component. This represents the contribution of the product term of the time-domain dictionary and the broadband coefficients. By removing interference from other atoms, Focus on atoms to be updated The signal features to be fitted provide a pure target residual for atomic optimization.

[0161] Sub-step three, due to the corresponding sparsity coefficient It is known that equation (13) can be rewritten in the following form, and the OMP algorithm is used to... Update.

[0162] ;satisfy ;

[0163] Let represent the updated i-th column of the frequency domain dictionary atom. The optimization objective is to minimize the reconstruction error between the product term of the first residual vector and the frequency domain dictionary atom. The ratio of the first residual vector to the corresponding narrowband vehicle component coefficient is used as the target signal vector to be fitted. The product of the system matrix, the core dictionary, and the frequency domain dictionary atoms is taken as the product term of the frequency domain dictionary atoms. .

[0164] The orthogonal matching pursuit algorithm iteratively selects the residual vector. The most relevant frequency domain basis functions are used to gradually construct sparse dictionary atoms. At the same time, a zero-norm constraint is applied to the atoms ( This allows the updated atoms to more accurately capture the periodic frequency characteristics of narrowband onboard components.

[0165] Iteratively update all frequency domain dictionary atoms column by column to complete one full frequency domain dictionary update process, resulting in the updated frequency domain dictionary. By optimizing column by column, each atom is precisely adjusted for the signal frequency band it is responsible for representing, gradually reducing the overall reconstruction error and improving the frequency domain dictionary's ability to represent narrowband periodic loads.

[0166] This process effectively reduces the reconstruction error between the dictionary and the sparse representation by iteratively optimizing each column of the frequency domain dictionary atoms, thereby improving the accuracy of signal representation. After updating all column vectors, the updated frequency domain dictionary is obtained. .

[0167] (4) Time-domain dictionary update

[0168] Since the time-domain dictionary contains only one atom to be updated, its update process is relatively simplified, requiring only two key steps: calculating the second residual vector and updating the dictionary atom. The specific operations are as follows:

[0169] Sub-step one: Calculate the second residual vector after removing the frequency domain dictionary contribution.

[0170] (15);

[0171] in, This represents the updated narrowband vehicular component coefficients, where HD represents the product of the system matrix and the core dictionary. This represents the optimized frequency domain dictionary. This represents the second residual vector after removing the contribution of the frequency domain dictionary. This vector only contains the contribution of the product term of the time domain dictionary atoms and the broadband vehicle component coefficients to the time-varying response components. By removing the influence of the frequency domain dictionary, the second residual vector E focuses on the broadband random load characteristics that the time domain dictionary atoms need to fit, providing a clear optimization objective for subsequent atom updates.

[0172] Sub-step two involves updating the time-domain dictionary. Since time-domain dictionaries typically lack sparsity, this invention employs a logarithmic penalty function to update the time-domain dictionary. Constraints are applied. As a smooth and relatively robust loss function, the logarithmic penalty function effectively reduces sensitivity to outliers without requiring additional regularization parameters. Given the given conditions, equation (15) can be expressed as the following optimization problem:

[0173] (16);

[0174] in, This represents the updated time-domain dictionary atom, where HB represents the product term of the system matrix and the core dictionary. Let n represent the second target signal vector, where n is the number of sampling points. Represents the atomic product terms in the time-domain dictionary;

[0175] The log-sum loss function is solved using a gradient descent (AGD) strategy that incorporates an adaptive moment estimation optimizer, in order to balance convergence speed and numerical stability.

[0176] After updating both the frequency domain and time domain dictionaries once, the updated extended dictionary matrix can be obtained. Subsequently, this extended dictionary matrix... Substituting into equation (12), we solve for the new sparse representation vector. If the algorithm terminates after the k-th iteration, we obtain a set of... .

[0177] Will Substituting into equation (4), the finally identified mobile vehicle can be represented as:

[0178] (16);

[0179] Adaptive target sparsity selection based on regularized paths:

[0180] In solving dictionary learning models, the target sparsity parameter T has a significant impact on recognition accuracy. However, there is currently a lack of effective strategies for adaptively determining the optimal sparsity. Therefore, this invention proposes an adaptive sparsity selection method based on regularized paths.

[0181] A regularization path refers to the trajectory formed by the continuous change of model parameters as the regularization parameter gradually increases from zero to a certain maximum value. When the regularization parameter is represented by sparsity, this path characterizes the changing trend of parameter coefficients as the model evolves from low to high sparsity. By analyzing this regularization path, we can identify which features gradually become important in the model and which feature coefficients rapidly shrink to zero, thus enabling the selection of optimal sparsity. Therefore, the appropriate selection of model parameters to serve as path values ​​is crucial.

[0182] The proposed regularized path construction method mainly comprises four processes: feature selection, least squares solution, path value calculation, and residual update. Feature selection, least squares solution, and residual update are all standard procedures of the orthogonal matching pursuit algorithm. It should be noted that to improve the effectiveness of feature selection, the system matrix needs to be standardized before this step. In this invention, each column of data is standardized to have a mean of 0 and a standard deviation of 1.

[0183] In this invention, the path value uses the infinite norm (i.e., the maximum absolute inner product) of the covariance vector between the system matrix and the residual vector as the metric. The mathematical expression of the path value is as follows:

[0184] (17);

[0185] in, Let represent the standardized system matrix, where n and p represent the number of samples and the number of columns in the system matrix, respectively, and r represents the residual vector of the current iteration, i.e., the difference between the model's predicted value and the true value. Indicates the path value.

[0186] By standardizing the residual vector, the influence of dimensional differences on covariance calculation is eliminated, ensuring that the path value can accurately reflect the correlation strength between each column of the system matrix and the residual vector.

[0187] After obtaining the regularized path, another key issue is how to adaptively select the sparsity parameter. As the importance of the selected features gradually decreases, the regularized path value usually tends to stabilize, meaning the path curve gradually converges. Considering this key characteristic, this invention uses the rate of change of the regularized path value as the criterion for selecting the sparsity parameter. The calculation expression for the sparsity parameter is as follows:

[0188] (18);

[0189] in, This represents the rate of change of the regularized path value in the k-th iteration. and These are the path values ​​for the k-th and (k-1)-th iterations, respectively. This represents the path value corresponding to the k-th sparsity level. When the rate of change is less than a certain threshold ε, the current sparsity is considered the optimal target sparsity.

[0190] and Figure 1 The corresponding method is referenced. Figure 3 This invention provides a mobile vehicle recognition system based on multi-domain dictionary learning, comprising:

[0191] At least one processor;

[0192] At least one memory for storing at least one program;

[0193] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0194] It is evident that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0195] To verify the effectiveness of this invention, experiments are conducted below;

[0196] To verify the effectiveness and robustness of the proposed multi-domain dictionary learning model in identifying moving vehicle loads with high complexity and uncertainty, this invention constructs a system based on... Figure 1 The vehicle-bridge coupled power system model shown is used to generate simulated vehicle load data.

[0197] 1. Parameter settings

[0198] Based on the definition of road surface roughness in the international standard ISO 8608, five different levels (levels A to E) of road surface power spectral density are introduced as excitation inputs.

[0199] The key structural characteristics and dynamic parameters of the vehicle-bridge system are listed in Table 1. To simplify the problem and control computational complexity, the vehicle speed is set to a constant 15 m / s. Considering the span of the simulated bridge and the vehicle's geometry, the total time for the vehicle to traverse the entire bridge is 2.4 seconds.

[0200] Table 1: Detailed Axle Parameters

[0201]

[0202] Figure 4 The study demonstrates the vertical response history of the vehicle load and bridge structure generated by the vehicle-bridge coupling system when the vehicle is traveling under Level 4 road surface unevenness conditions. Figure 4 (a) shows a simply supported bridge model in an embodiment of the present invention; Figure 4 (b) shows the load form when the road surface roughness is D in an embodiment of the present invention; Figure 4 (c) in the embodiment of the invention shows the bridge response when the road surface roughness is level D; it can be observed that under this poor road condition, the load signal applied to the bridge by the vehicle has high amplitude uncertainty and frequency fluctuation, reflecting the significant influence of road surface excitation on the vehicle-bridge system coupling behavior.

[0203] To reduce reliance on the original dictionary and improve the model's generalization ability and interpretability under different load scenarios, this invention constructs a core dictionary. It is derived solely from the expansion of cosine basis functions. The core dictionary form is as follows:

[0204] (19);

[0205] in, This represents a discrete time point, where n is the number of columns in the dictionary, controlling its frequency resolution.

[0206] In the proposed multi-domain dictionary learning framework, the frequency domain dictionary and the time domain dictionary need to be initialized. Specifically, the initial frequency domain dictionary... The identity matrix is ​​set, and the initial time-domain dictionary B0 is set as a randomly generated vector. It is worth noting that during the initial sparse coding process, because the initial time-domain dictionary is randomly generated, it is often difficult to effectively match the measured response signal within the set target sparsity. Therefore, the time-domain dictionary ξ and the time-domain atomic coefficients s need to be replaced with:

[0207] (20);

[0208] (twenty one);

[0209] In the formula, and Representing the frequency domain dictionary The T1 column of the vector of atoms and coefficients The corresponding elements in.

[0210] The actual measured response is inevitably affected by noise interference. The present invention adopts the method proposed in related technologies to superimpose Gaussian white noise on the bridge response obtained by numerical simulation in order to construct signal data with actual measurement characteristics.

[0211] (twenty two);

[0212] in, and These represent the bridge responses with and without noise, respectively. The noise level is represented by P; the number of elements in vector Y is represented by P; and rand is a white noise vector that conforms to a standard normal distribution.

[0213] Furthermore, to quantify the accuracy and stability of the proposed method in identifying moving loads, this invention introduces "Relative Percentage Error" (RPE) as a performance evaluation metric to measure the relative deviation between the identification result and the actual moving load. The mathematical definition of RPE is as follows:

[0214] (twenty three);

[0215] (twenty four);

[0216] in, and These represent the actual vehicle load and the identified vehicle load, respectively. (Superscript) This represents the constant load component.

[0217] 2. Verification of the proposed method

[0218] To comprehensively evaluate the performance of the proposed multi-domain dictionary learning method (DL-MD) in mobile vehicle recognition tasks, it is systematically compared with two benchmark methods: one is the traditional sparse representation method (OMP) without dictionary learning, and the other is the recognition method using a single-domain dictionary learning strategy (DL-SD). Since the bridge bending moment response and acceleration response are sensitive to the low-frequency and high-frequency components of vehicle loads, respectively, and they complement each other in the frequency domain, joint observations of the two types of responses are used as input data in this invention. Furthermore, except for specifically noted subsections, 5% Gaussian white noise is uniformly superimposed on the simulated structural response, and the road surface roughness level is set to Class D according to the ISO standard.

[0219] Regarding the target sparsity setting, the target sparsity T2 has a relatively small impact on recognition accuracy; therefore, T2 is set to 5 in this invention. For the target sparsity T1, three sparsity levels (T1=5, 15, 25) and an adaptive sparsity based on regularization paths are set to systematically evaluate the impact of different sparsities on recognition performance. The average relative percentage error (RPE) and computation time statistics of the three methods under the above settings are summarized in Table 2. All experiments were run on a unified hardware platform with an Intel i9-11900K processor at a clock speed of 3.5GHz to ensure fairness of different methods in a comparable computing environment.

[0220] It should be noted that the recognition results and time consumption of the proposed method in Table 2 are based only on the results of a single dictionary learning iteration. This setting is based on the fact that the proposed method has shown significant load feature extraction capabilities in the initial learning, and that multiple training iterations may actually lead to a decrease in training efficiency in actual testing.

[0221] Table 2: RPE values ​​of moving loads identified by different methods at a 5% noise level

[0222]

[0223] As can be seen from the data in Table 2, under all set working conditions and sparsity conditions, the multi-domain dictionary learning method (DL-MD) proposed in this invention is significantly better than the single-domain dictionary learning method (DL-SD) and the traditional OMP method, whether for static load or total mobile vehicle load.

[0224] In static load identification, the proposed method employs a separate identification strategy for static and dynamic loads, which increases the weight of static load identification and thus significantly improves its accuracy and stability. The sparsity setting primarily affects the dynamic load component. However, existing DL-SD methods cannot improve static load accuracy compared to OMP methods. This is because the dictionary atom sequence (all elements are 1) corresponding to the static load already conforms to its distribution pattern, resulting in the same static load identification results from the single-domain dictionary learning method (DL-SD) and the traditional OMP method. For the overall moving vehicle load, due to the high mismatch between the considered moving vehicle load and the preset core dictionary, the single-domain dictionary learning DL-SD method exhibits significant limitations, and its identification accuracy does not show a significant improvement compared to the OMP method. Specifically, the optimal recognition accuracy of the OMP method without dictionary learning for the front and rear axles is 9.56% and 12.05%, respectively, while the optimal recognition accuracy of the DL-SD method for the front and rear axles is 9.97% and 11.79%, respectively. The optimal recognition accuracy of the proposed method for the front and rear axles under all working conditions is 7.08% and 6.01%, respectively. This shows that the proposed method has better learning ability for unknown and complex moving vehicle rigs.

[0225] Furthermore, the setting of the sparsity level has a significant impact on the recognition performance of the three methods—both in terms of accuracy and computational efficiency—demonstrating the key regulatory role of this parameter in the sparse modeling framework.

[0226] On the one hand, lower sparsity means that the model selects only a small number of atoms for reconstruction in each sparse encoding process, which helps to significantly reduce computation time and thus improve overall recognition efficiency. However, because it ignores the expression of some important payload components, the reconstruction results are prone to underfitting, leading to a significant decrease in recognition accuracy. On the other hand, while excessively high sparsity can enhance the ability to capture signal details, it also carries the risk of overfitting. The improvement in recognition accuracy is not always linear, and recognition efficiency will also decrease significantly.

[0227] Taking the typical measurement point combination "1 / 4m&1 / 2m&1 / 2a&3 / 4a" as an example, all methods—OMP, DL-SD, and the proposed DL-MD—achieved their highest computational efficiency when the target sparsity was set to T1=5. However, the corresponding moving load identification accuracy was the worst among the four sparsity settings. As the sparsity increased to 15 and 25, the identification accuracy of each method improved significantly. However, further increasing the sparsity led to a saturation of accuracy improvement, and in some cases, a rebound in identification error occurred, reflecting that high sparsity may introduce redundant atoms, which in turn interferes with the accurate extraction of load features.

[0228] To address the aforementioned trade-off in sparsity selection, this invention introduces an adaptive sparsity adjustment strategy. This strategy dynamically adjusts the sparsity level based on the feature complexity of the input response and the dictionary fitting error, thereby suppressing unnecessary computational overhead while ensuring recognition accuracy. Results show that under this strategy, all three methods can achieve better recognition results within a finite timeframe, with the DL-MD method exhibiting a particularly superior accuracy-efficiency balance.

[0229] Figure 5 The paper presents the sparsity selection process corresponding to different sparsity settings under the above measurement point combinations, as well as the moving load time history curves identified by the DL-MD method. Figure 5 (a) in the figure illustrates the adaptive selection process of sparsity T1 in an embodiment of the present invention; Figure 5 (b) shows the mobile vehicle recognition result when the sparsity T1=5 in an embodiment of the present invention; Figure 5 (c) shows the mobile vehicle recognition result when the sparsity T1=15 in an embodiment of the present invention; Figure 5Figure (d) shows the mobile vehicle identification results in an embodiment of the invention with sparsity T1=25. It can be observed that when the sparsity is low (e.g., T1=5), the vehicle axle load fluctuation range cannot be effectively fitted, resulting in an underestimation of the amplitude of the dynamic load response. However, as the sparsity is gradually increased, the identified vehicle load can not only accurately track the vehicle's static load characteristics but also more completely capture its time-varying dynamic load components. It is important to emphasize that when the sparsity exceeds a certain threshold, the load curve remains essentially unchanged, indicating that the model has captured the main vehicle load characteristics. Further increasing the sparsity may introduce unnecessary disturbances.

[0230] In summary, sparsity is a key parameter affecting load identification performance. A reasonable sparsity setting, especially a strategy based on adaptive adjustment of structural response characteristics, is crucial for ensuring identification accuracy, optimizing computational efficiency, and improving model generalization ability.

[0231] Figure 6 The on-board time history curves of front and rear axle movement identified by three methods are shown under the measurement point combination of "1 / 4m&1 / 2m&1 / 2a&3 / 4a" and adaptive sparsity control. Figure 6 In this context, OMP stands for Orthogonal Matching Pursuit, and DL-SD stands for Single Domain Dictionary Learning. Figure 6 (a) shows the time history curve of the OMP method for identifying mobile vehicle in an embodiment of the present invention; Figure 6 (b) shows the time history curve of the DL-SD method for identifying mobile vehicle in an embodiment of the present invention; Figure 6 Figure (c) shows the time history curve of the DL-MD method for identifying the moving vehicle load in this embodiment of the invention. It can be clearly observed from the figure that the proposed DL-MD method can accurately capture the evolution trend of the real load in the time domain, especially in terms of peak amplitude, vibration mode, and phase characteristics, which are highly consistent with the real vehicle load. In contrast, the OMP method, limited by a static and unupdated frequency domain basis, shows significant deviations in waveform details and dynamic amplitude changes. Although the DL-SD method has been improved through learning, its performance is still inferior to the DL-MD method due to insufficient modeling information.

[0232] Figure 7 Furthermore, spectral analysis diagrams of the recognition results of the three methods under the above conditions are provided, quantitatively demonstrating the differences in frequency domain reconstruction capabilities among the different methods. Figure 7 In this context, OMP stands for Orthogonal Matching Pursuit, and DL-SD stands for Single Domain Dictionary Learning. Figure 7 (a) shows a spectrum of the OMP method for identifying a mobile vehicle in an embodiment of the present invention; Figure 7 (b) shows a spectrum of the DL-SD method for identifying a mobile vehicle in an embodiment of the present invention; Figure 7Figure (c) shows the spectrum of the mobile vehicle identified by the DL-MD method in the embodiment of the present invention. It can be clearly seen from the figure that the frequency distribution identified by the DL-MD method is highly consistent with the spectrum of the real vehicle and can effectively recover multiple dominant frequency components and their energy distribution characteristics. Although the DL-SD method has a certain degree of frequency adaptability, its resolution in the mid-to-high frequency band is weak. The OMP method is obviously limited by the initial cosine fundamental frequency distribution, with a narrow spectrum range and lack of ability to express the frequency structure of complex time-varying loads.

[0233] Figure 8 Further comparisons show the recognition results of the proposed method for mobile vehicles under three strategies: frequency domain dictionary learning, time domain dictionary learning, and joint time-frequency domain dictionary learning, respectively, to explore the applicability and limitations of different domain dictionaries in complex vehicle recognition tasks. Figure 8 (a) shows a mobile vehicle-mounted system for frequency domain dictionary recognition in an embodiment of the present invention; Figure 8 (b) illustrates a mobile vehicle-mounted system for time-domain dictionary recognition in an embodiment of the present invention; Figure 8 Figure (c) shows the spectrum of mobile vehicle recognition using time-domain and frequency-domain dictionaries in an embodiment of the present invention. As can be seen from the figure, when learning is done solely using the frequency-domain dictionary, its expressive power is significantly limited by the initial frequency composition. Although the frequency-domain dictionary has strong filtering and feature extraction capabilities, its learning process mainly involves weight adjustments based on the original frequency components, making it difficult to overcome the bandwidth limitations of the initial frequency domain configuration.

[0234] In comparison, time-domain dictionary learning is more sensitive to depicting the time-varying dynamics of moving vehicles, and can better reflect the trend of load changes over time, especially in terms of the overall structure and amplitude changes of load carrier shape. However, its local recognition ability is still insufficient, especially at the boundary between the vehicle and the bridge, where the time-domain dictionary recognition results are prone to error shifts, affecting the overall recognition accuracy.

[0235] In summary, the combined use of time-domain and frequency-domain dictionaries (i.e., multi-domain dictionaries) can effectively overcome the limitations of single-domain dictionaries. The time-domain dictionary provides adaptability to dynamic trends and non-stationary changes, while the frequency-domain dictionary enhances the robust extraction of dominant frequency bands and periodic features. The fusion of these two dictionaries enables joint analysis and accurate reconstruction of the time-frequency features of mobile vehicle-mounted systems, significantly improving the modeling and identification capabilities for unknown and complex loads.

[0236] Furthermore, embodiments of the present invention also disclose a computer program product or computer program stored in a computer-readable storage medium. A processor of a computer device can read the computer program from the computer-readable storage medium, and the processor executes the computer program, causing the computer device to perform the described method. Similarly, the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0237] It will be understood by those skilled in the art that all or some of the methods and systems disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0238] The above is a detailed description of the preferred embodiments of this disclosure. However, this disclosure is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this disclosure. All such equivalent modifications or substitutions are included within the scope defined by the claims of this disclosure.

Claims

1. A mobile vehicle recognition method based on multi-domain dictionary learning, characterized in that, The method includes the following steps; S100, acquire the multi-domain representation of the mobile vehicle signal, decompose the multi-domain representation of the mobile vehicle signal into a mobile vehicle load vector containing constant load component, narrowband vehicle component and wideband vehicle component, and represent them respectively using constant load component dictionary, frequency domain dictionary and time domain dictionary, and construct the vehicle-bridge control equation in combination with the system matrix; S200, Obtain the vehicle-induced bridge response, and construct a moving vehicle recognition model based on multi-domain dictionary learning based on the vehicle-induced bridge response and the vehicle-bridge control equation; the vehicle-induced bridge response includes the responses generated by constant load, narrow-band load and wide-band load respectively; the moving vehicle recognition model is the objective function of minimizing the reconstruction error between the vehicle-induced bridge response and the moving vehicle load vector. S300, through iterative optimization of constant load component identification, sparse coding, frequency domain dictionary update and time domain dictionary update, the mobile vehicle identification model is solved to obtain constant load component coefficients, narrowband vehicle component coefficients and wideband vehicle component coefficients; S400: Substitute the obtained constant load component coefficients, narrowband vehicle component coefficients, and broadband vehicle component coefficients into the mobile vehicle identification model to achieve mobile vehicle identification. S200 includes: S210, Obtain the vehicle-induced bridge response, and decompose the vehicle-induced bridge response into responses generated by constant load, narrow-band load and wide-band load respectively; S220, the reconstruction error is determined based on the difference between the response generated by constant load and the response of constant load component, the difference between the response generated by narrowband load and the response of narrowband load component, and the difference between the response generated by broadband load and the response of broadband load component. The constant load component coefficient and the sparse representation vector are used as optimization variables, and the objective function is to minimize the squared L2 norm of the reconstruction error. A mobile vehicle recognition model is constructed. The sparse representation vector includes narrowband vehicle component coefficients and broadband vehicle component coefficients. The objective function satisfies the constraint that the L0 norm of the narrowband vehicle component coefficients does not exceed the target sparsity T1 and the L0 norm of any column vector of the frequency domain dictionary does not exceed the target sparsity T2.

2. The method according to claim 1, characterized in that, In S100, the process of acquiring the multi-domain representation of the mobile vehicle-mounted signal involves decomposing the multi-domain representation of the mobile vehicle-mounted signal into a mobile vehicle load vector containing a constant load component, a narrowband vehicle-mounted component, and a wideband vehicle-mounted component. After representing these components using a constant load component dictionary, a frequency domain dictionary, and a time domain dictionary, the vehicle-bridge control equations are constructed in conjunction with the system matrix, including: S110, acquire the multi-domain representation of the mobile vehicle signal, and decompose the multi-domain representation of the mobile vehicle signal into constant load component, narrowband vehicle component and wideband vehicle component based on the multi-domain dictionary learning model; S120, construct a multi-domain dictionary representing the constant load component, frequency domain dictionary, and time domain dictionary of the mobile vehicle signal, as well as the corresponding constant load component coefficients, narrowband vehicle component coefficients, and wideband vehicle component coefficients; represent the constant load component as the product of the constant load component dictionary and the constant load component coefficients, represent the narrowband vehicle component as the product of the core dictionary, the frequency domain dictionary, and the narrowband vehicle component coefficients, and represent the wideband vehicle component as the product of the core dictionary, the time domain dictionary, and the wideband vehicle component coefficients; S130, the product of the constant load component and the system matrix is ​​taken as the constant load component response, the product of the narrowband vehicle load component and the system matrix is ​​taken as the narrowband load response, and the product of the broadband vehicle load component and the system matrix is ​​taken as the broadband load response. The sum of the constant load component response, the narrowband load response and the broadband load response is taken as the vehicle-bridge control equation.

3. The method according to claim 1, characterized in that, In S300, the iterative optimization of solving the mobile vehicle recognition model through constant load component identification, sparse coding, frequency domain dictionary update, and time domain dictionary update to obtain constant load component coefficients, narrowband vehicle component coefficients, and broadband vehicle component coefficients includes: S310, the mobile vehicle identification model is converted into a sparse solution function composed of vehicle-induced bridge response and dead load component response. The dead load component coefficient is obtained by solving the sparse solution function. The response generated by the dead load component is subtracted from the vehicle-induced bridge response to obtain a time-varying response component that only contains the time-varying load action. The sparsity of the dead load component coefficient corresponds to the number of vehicle axles. S320 converts the mobile vehicle recognition model into a sparse coding function composed of time-varying response components and time-varying load response, initializes the core dictionary, initial frequency domain dictionary and initial time domain dictionary, and, while keeping the initial frequency domain dictionary and initial time domain dictionary fixed, uses the orthogonal matching pursuit algorithm to solve the sparse coding function to obtain the sparse representation vector. S330, determine the positions of non-zero elements in the sparse representation vector to locate the frequency domain dictionary atom to be updated, calculate the first residual vector after removing the current contribution of the frequency domain dictionary atom to be updated, construct the frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atom to be updated, solve the frequency domain dictionary update function to update the frequency domain dictionary atom, and obtain the optimized frequency domain dictionary; S340, calculate the second residual vector after removing the contribution of the frequency domain dictionary, construct the time domain dictionary update function based on the second residual vector and the time domain dictionary atom to be updated, solve the time domain dictionary update function to update the time domain dictionary atom, and obtain the optimized time domain dictionary; S350: Update the extended dictionary matrix based on the optimized frequency domain dictionary and the optimized time domain dictionary to obtain the updated extended dictionary matrix, and then jump to S320; S360, repeat S320 to S340 until the reconstruction error of the sparse representation vector is less than the preset threshold or the maximum number of iterations is reached, to obtain the final sparse representation vector and the updated dictionary matrix, and then calculate the constant load component coefficient, narrowband vehicle component coefficient and wideband vehicle component coefficient through the mobile vehicle recognition model.

4. The method according to claim 3, characterized in that, In S310, the conversion of the mobile vehicle identification model into a sparse solution function composed of the vehicle-induced bridge response and the dead load component response includes: The objective function is to minimize the squared 2-norm of the difference between the vehicle-induced bridge response and the dead load component response. A zero-norm constraint is imposed on the dead load component coefficients to obtain a sparse solution function with the dead load component coefficients as variables.

5. The method according to claim 3, characterized in that, In S320, the conversion of the mobile vehicle identification model into a sparse coding function composed of time-varying response components and time-varying load response includes: S321, multiply the system matrix, the extended dictionary matrix and the sparse representation vector to obtain the time-varying load response; S322, with the objective function being the minimization of the squared second norm of the difference between the time-varying response component and the time-varying load response, and with the constraint that the zero norm of the sparse representation vector does not exceed the target sparsity T1, yields a sparse coding function with the sparse representation vector as the variable.

6. The method according to claim 5, characterized in that, In S322, the target sparsity T1 is obtained in the following way; S3221, after standardizing the system matrix, transpose it and multiply it with the residual vector to obtain the covariance vector. Take the maximum absolute value of the elements in the covariance vector as the path value of the current iteration. S3222, by gradually increasing the sparsity level, repeatedly performing feature selection, least squares solution, path value calculation and residual update steps, a series of path values ​​corresponding to different sparsities are generated, resulting in a regularized path composed of a series of path values; S3223, calculate the rate of change of path values ​​under adjacent sparsity levels. When the rate of change is less than the set threshold, the current sparsity is taken as the target sparsity T1.

7. The method according to claim 3, characterized in that, In S330, the step of constructing a frequency domain dictionary update function based on the first residual vector and the frequency domain dictionary atoms to be updated includes: S331, the ratio of the first residual vector to the corresponding narrowband vehicle component coefficient is taken as the first target signal vector to be fitted, and the product of the system matrix, the core dictionary and the frequency domain dictionary atom is taken as the frequency domain dictionary atom product term; S332, with the objective function being the square of the second norm of the difference between the first target signal vector and the product terms of the frequency domain dictionary atoms, and with the constraint that the zero norm of the frequency domain dictionary atoms does not exceed the target sparsity T2, yields a frequency domain dictionary update function with frequency domain dictionary atoms as variables.

8. The method according to claim 3, characterized in that, In S340, the construction of the time-domain dictionary update function based on the second residual vector and the time-domain dictionary atoms to be updated includes: S341, the ratio of the second residual vector to the corresponding broadband vehicle component coefficient is taken as the second target signal vector, and the product of the system matrix, the core dictionary and the time-domain dictionary atom is taken as the time-domain dictionary atom product term; S342, a logarithmic penalty function is constructed based on the difference between the second target signal vector and the product terms of the time-domain dictionary atoms, resulting in a time-domain dictionary update function with minimizing the logarithmic penalty function as the objective function and the time-domain dictionary atoms as variables.

9. A mobile vehicle recognition system based on multi-domain dictionary learning, characterized in that, The system includes: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 8.

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