Bridge influence line identification method combining adaptive dynamic-static separation with automated parameter optimization in typical multi-vehicle operating environment

Abstract

The application proposes a bridge influence line identification method combining adaptive truncated dynamic-static separation and automatic parameter optimization under typical multi-vehicle operation environment, belonging to the field of bridge structure state rapid evaluation and intelligent monitoring. It solves the problems of signal aliasing and matrix ill-conditioning under multi-vehicle load. It includes: obtaining the dynamic response data of the bridge under typical multi-vehicle operation conditions and the corresponding traffic parameters; performing adaptive truncated variational modal decomposition on the dynamic response data to determine the frequency band cutoff position and extract the quasi-static response of the bridge; based on the traffic parameters and the spatial discrete nodes of the bridge, constructing a full space-time vehicle load matrix; establishing an inversion equation between the quasi-static response and the full space-time vehicle load matrix, automatically searching for the optimal regularization parameter by minimizing the generalized cross-validation function, and solving to obtain the discrete influence line of the bridge; using piecewise cubic shape-preserving interpolation to continuously reconstruct the discrete influence line of the bridge to obtain the continuous influence line of the bridge. It is used in the field of bridge management.

Description

Technical Field

[0001] This invention belongs to the field of rapid assessment and intelligent monitoring technology of bridge structural status, and in particular relates to a bridge influence line identification method based on joint adaptive truncation of dynamic and static separation and automated parameter optimization under typical multi-vehicle operation environment. Background Technology

[0002] As a critical node in transportation infrastructure, the health of bridge structures directly impacts road network safety and the efficiency of the national economy. With the shift in bridge maintenance from traditional passive repair to preventative maintenance, the influence line, which quickly and accurately reflects the structural stiffness distribution and load-bearing capacity, has become a core mechanical indicator for structural performance assessment and damage identification. Current technologies primarily rely on the test vehicle loading method. This method involves controlling a dedicated test vehicle to travel at low or ultra-low speeds on a specific lane of the bridge, simultaneously collecting the bridge's displacement or strain response, and then obtaining the influence line shape through mechanical inversion. While this method has some engineering applicability in single-lane, low-traffic, and closed-traffic scenarios, its technical limitations become increasingly apparent in today's high-density, multi-vehicle operating environment.

[0003] Traditional single-vehicle low-speed loading methods face multiple obstacles in practical engineering applications. First, this method typically requires traffic control or even complete closure of the bridge, which not only severely disrupts normal traffic flow but also incurs high road closure costs and complex construction organization difficulties, making it difficult to meet the high-frequency, high-speed maintenance needs of modern urban bridges and highways. Second, the response characteristics obtained from single-vehicle testing cannot simulate the complex load environment of multi-lane, multi-vehicle parallel, and intersecting traffic in actual operation. In real traffic flow, multiple heavily loaded vehicles often travel continuously across the bridge at different speeds and intervals. The bridge response under this typical multi-vehicle load is fundamentally different from the quasi-static response of a single vehicle, causing traditional recognition algorithms based on the single-vehicle assumption to fail in real-world operating environments.

[0004] A more critical technical challenge lies in the extremely high complexity of the bridge dynamic response signals under typical multi-vehicle constant-speed operation conditions. Due to the coupled excitation effect between multiple vehicles and the bridge structure, the original acquired displacement or strain signals not only contain quasi-static components reflecting the structural mechanical properties but also a large number of high-frequency dynamic vibration components and environmental noise. These high-frequency dynamic components and quasi-static responses intertwine in the frequency domain, making the accurate extraction of effective signals from the strong noise background a bottleneck restricting recognition accuracy. Commonly used filtering methods in existing technologies often rely on manual experience to set the cutoff frequency, which easily leads to the loss of effective signals or noise residue, and cannot adapt to the complex and ever-changing actual traffic loads.

[0005] Furthermore, existing technologies face significant mathematical challenges in constructing influence line inversion models under multi-vehicle loads. The multi-vehicle driving process is a complex spatiotemporal superposition process, resulting in a massive and highly ill-conditioned vehicle load matrix. Even minor perturbations in matrix elements can lead to significant deviations in the inversion solution. To address this ill-conditioned problem, regularization techniques are typically introduced. However, existing regularization parameter optimization methods, such as the L-curve method or generalized cross-validation, often rely on prior estimates of noise levels or manual visual judgment of inflection points, lacking automation and robustness. This over-reliance on human experience makes it difficult to achieve standardized and intelligent engineering applications, posing a significant challenge to the implementation of rapid bridge structural performance assessment systems in complex operating environments. Therefore, overcoming signal aliasing and matrix ill-conditioned problems under multi-vehicle loads without traffic control, and achieving high-precision, fully automated bridge influence line identification, is a pressing technical hurdle in this field. Summary of the Invention

[0006] In view of this, the present invention aims to propose a bridge influence line identification method that combines adaptive truncation dynamic-static separation and automated parameter optimization under typical multi-vehicle operation environment, so as to solve the problems of signal aliasing and matrix ill-conditioning under multi-vehicle load.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment, the method comprising: Acquire dynamic response data of the bridge under typical multi-vehicle operation conditions and corresponding traffic parameters, including total vehicle weight, operating speed and time of entry into the bridge. Adaptive truncated variational mode decomposition is performed on the dynamic response data, and the frequency band cutoff position is determined according to the modal cutoff comprehensive discrimination index to extract the quasi-static response of the bridge; wherein, the modal cutoff comprehensive discrimination index ,in: This characterizes the dominant frequency position of the i-th eigenmode function; Let i be the energy of the i-th mode; Based on the traffic parameters and discrete nodes of the bridge space, a full-time and space-time vehicle load matrix is ​​constructed. An inversion equation is established between the quasi-static response and the all-time vehicle load matrix. The optimal regularization parameter is automatically searched by minimizing the generalized cross-validation function, and the discrete influence line of the bridge is obtained by solving the solution. Piecewise cubic conformal interpolation is used to continuously reconstruct the discrete influence lines of the bridge, resulting in continuous influence lines of the bridge.

[0008] Furthermore, a preferred method is proposed, in which the traffic parameters under the typical multi-vehicle operating conditions are determined through traffic survey data or design load levels, forming a set of vehicle load input parameters. : , in, W i For the first i Total weight of the vehicles. v i For running speed, The moment the vehicle enters the bridge. N This represents the total number of vehicles.

[0009] Furthermore, a preferred method is proposed, wherein the adaptive truncated variational mode decomposition of the dynamic response data includes: The dynamic response data is subjected to detrending processing, outlier removal, and normalization. The processed response data is decomposed into the following values ​​using a variational mode decomposition algorithm: k Individual eigenmodes and residuals ; Based on the modal cutoff comprehensive discrimination index Determine the cutoff order p .

[0010] Furthermore, a preferred method is proposed, wherein the extraction of the quasi-static response of the bridge specifically involves: Using the truncation order p to k The low-frequency modes and residual terms of the first order are reconstructed, and the expression is: , in, The final extracted quasi-static response of the bridge, p This is the frequency band cutoff position. For the first i Each intrinsic mode, k This represents the number of modes.

[0011] Furthermore, a preferred method is proposed, wherein the construction of the all-time-space vehicle load matrix includes: The influence line of the bridge is discretized along the longitudinal direction. n Each node discretizes the response sampling time into... m At that moment; For each vehicle, its spatial position at each sampling time is calculated based on its total weight, operating speed, and the time it enters the bridge, thus constructing a single-vehicle load matrix Q. i ; Superimpose all individual vehicle load matrices to form a unified load matrix: ,

[0012] Where Q is the overall load matrix formed by superimposing multiple vehicle load matrices, Q i For the first i Vehicle load matrix N The total number of vehicles. For the real number field m × n 3D matrix space.

[0013] Furthermore, a preferred approach is proposed, wherein the expression for the generalized cross-validation function is:

[0014] in, It is a generalized cross-validation function; For the influence matrix, I is the identity matrix; For matrix trace, For regularization parameters, It is the identity matrix. For the transpose of the all-time-space vehicle load matrix, This is the quasi-static response vector.

[0015] Furthermore, an optimal method is proposed, wherein the automatic search for the optimal regularization parameter is specifically as follows: The generalized cross-validation function is found by a traversal search strategy. Optimal regularization parameter that achieves minimum value The expression is: ; Substituting these values ​​into the Tikhonov analytical solution expression, the discrete influence lines of the bridge can be obtained.

[0016] Furthermore, a preferred method is proposed, in which piecewise cubic conformal interpolation is used for continuous reconstruction within the interval. x i ≤x≤x i+1 Built-in PCHIP interpolation function:

[0017] in, , The first derivative of the node; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the start of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the beginning of the interval; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the endpoint of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the endpoint of the interval; The starting node of the interpolation interval x i Discrete values ​​of the bridge influence line at the location; The endpoint of the interpolation interval x i+1 Discrete values ​​of the bridge influence line at the location; For the interval [ x i , x i+1 The bridge continuous influence line values ​​obtained from the internal reconstruction. t For interval normalized variables, x These are the actual physical coordinates of the bridge's longitudinal direction.

[0018] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes an event-triggered liquid neural network low-power continuous monitoring and hierarchical wake-up method according to any one of the preceding claims.

[0019] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of a bridge influence line identification method based on joint adaptive truncation of dynamic and static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in any one of the above-mentioned methods.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention addresses the problems of severe dynamic response aliasing, inconsistent vehicle load representation, and unstable ill-conditioned matrix solution in bridge influence line identification under typical multi-vehicle operation conditions. It proposes a bridge influence line identification method based on adaptive band-truncation variational mode decomposition, vehicle matrix construction for typical multi-vehicle operation conditions, and automated GCV parameter optimization. At the signal preprocessing level, this invention abandons traditional fixed threshold filtering or reliance on manual experience to determine the number of modes, instead employing an adaptive band-truncation variational mode decomposition mechanism. The principle is that after variational mode decomposition, the energy and center frequency of each intrinsic mode of the bridge dynamic response exhibit specific evolutionary patterns. This invention introduces a comprehensive discrimination index combining the dominant frequency position and modal energy to objectively quantify the physical contribution of each mode. When this index reflects a sudden change in the energy decay pattern with frequency, the band cutoff position can be automatically locked. This mechanism, in principle, achieves adaptive separation between high-frequency dynamic vibration noise and low-frequency quasi-static response, ensuring that the extracted quasi-static response retains the true contour of the load action while maximally suppressing high-frequency interference caused by vehicle-bridge coupled vibration. At the load modeling level, this invention simplifies complex multi-vehicle, multi-axle traffic flow into an equivalent concentrated moving load model based on the total vehicle weight. By establishing a spatiotemporally unified discretization analysis framework, the operating states of vehicles in different lanes and at different speeds are mapped to a full-spatiotemporal vehicle load matrix. This modeling not only unifies the input of multi-source heterogeneous traffic parameters, but more importantly, it constructs a mathematical carrier capable of fully describing the spatiotemporal superposition effect of multi-vehicles, providing a structured data foundation for subsequent high-dimensional matrix solutions. At the inversion solution level, this invention addresses the inherent ill-conditioned characteristics of the full-spatiotemporal vehicle load matrix by introducing an automated parameter optimization principle based on generalized cross-validation. Unlike the traditional L-curve method, which relies on the subjectivity of manually finding inflection points, this invention utilizes a generalized cross-validation function to construct a balance criterion for measuring model fit and degree-of-freedom penalty. By iteratively searching for the regularization parameter that minimizes the criterion, the optimal damping factor can be adaptively determined, thus achieving an optimal balance between suppressing numerical oscillations caused by matrix ill-conditioning and preserving the physical shape of the influence line. Finally, the discrete solution is reconstructed using the principle of piecewise cubic conformal interpolation, ensuring the continuity and monotonicity of the influence line between nodes and avoiding physical distortions that may be caused by traditional interpolation methods.

[0021] This invention achieves high-precision extraction of the quasi-static response of bridges under typical multi-vehicle operation environments. Through an adaptive truncation mechanism, this invention effectively overcomes the challenge of frequency band aliasing between high-frequency dynamic effects and quasi-static responses in complex traffic flows, significantly improving the signal-to-noise ratio and accuracy of extracting effective structural responses under strong noise backgrounds, and providing high-quality data input for subsequent influence line inversion.

[0022] This invention abstracts the multi-lane, multi-vehicle parallel operation in actual operation into a full-time and space-time vehicle load matrix, which not only greatly simplifies the computational complexity, but also achieves an accurate characterization of the spatiotemporal distribution characteristics of real traffic loads, and solves the defect of existing technologies in handling multi-vehicle coupled load inputs.

[0023] This invention significantly improves the automation and robustness of solving ill-conditioned matrices. By introducing a generalized cross-validation criterion for automatic search of regularization parameters, this invention completely eliminates the reliance on prior knowledge of noise or human experience, achieving full automation and intelligence in the influence line inversion process, and greatly enhancing the adaptability and stability of the algorithm under different bridge structures and traffic conditions.

[0024] This invention ensures the reliability of influence line identification results. By combining piecewise cubic conformal interpolation technology, this invention reconstructs smooth and physically consistent continuous influence lines based on discrete influence lines, avoiding numerical oscillations. Furthermore, this method requires only a small number of response measurement points for identification, without interrupting traffic, significantly reducing on-site testing costs and implementation difficulty, making it particularly suitable for rapid assessment and long-term monitoring of bridges in busy traffic areas. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in this invention. Figure 2 This is a schematic diagram of bridge influence line identification under typical multi-vehicle operation conditions as described in this invention. Figure 3 This is a schematic diagram of the vehicle load matrix construction under typical multi-vehicle operation conditions described in this invention; Figure 4 This is a schematic diagram of the 45-ton heavy-duty test vehicle described in this invention; Figure 5 This is a mid-span cross-sectional view of the 30m simply supported box girder described in this invention; Figure 6 This is a finite element model diagram of the 30m simply supported box girder described in this invention; Figure 7 This is a diagram of the quasi-static response of a bridge after dynamic-static separation as described in this invention. Figure 8 This is a diagram showing the influence of bridge structural displacement under typical multi-vehicle operation conditions as described in this invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0027] Implementation Method 1: This implementation method proposes a bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization under typical multi-vehicle operation environments. The method includes: Acquire dynamic response data of the bridge under typical multi-vehicle operation conditions and corresponding traffic parameters, including total vehicle weight, operating speed and time of entry into the bridge. Adaptive truncated variational mode decomposition is performed on the dynamic response data, and the frequency band cutoff position is determined according to the modal cutoff comprehensive discrimination index to extract the quasi-static response of the bridge; wherein, the modal cutoff comprehensive discrimination index ,in: Characterizing the first i The dominant frequency position of the intrinsic mode function; For the first i Modal energy; Based on the traffic parameters and discrete nodes of the bridge space, a full-time and space-time vehicle load matrix is ​​constructed. An inversion equation is established between the quasi-static response and the all-time vehicle load matrix. The optimal regularization parameter is automatically searched by minimizing the generalized cross-validation function, and the discrete influence line of the bridge is obtained by solving the solution. Piecewise cubic conformal interpolation is used to continuously reconstruct the discrete influence lines of the bridge, resulting in continuous influence lines of the bridge.

[0028] In this embodiment, the traffic parameters under typical multi-vehicle operation conditions are determined through traffic survey data or design load levels, forming a set of vehicle load input parameters. : , in, W i For the first i Total weight of the vehicles. v i For running speed, The moment the vehicle enters the bridge. N This represents the total number of vehicles.

[0029] In this embodiment, the adaptive truncated variational mode decomposition of the dynamic response data includes: The dynamic response data is subjected to detrending processing, outlier removal, and normalization. The processed response data is decomposed into the following values ​​using a variational mode decomposition algorithm: k Individual eigenmodes and residuals ; Based on the modal cutoff comprehensive discrimination index Determine the cutoff order p .

[0030] Furthermore, the extraction of the quasi-static response of the bridge specifically involves: Using the truncation order p to k The low-frequency modes and residual terms of the first order are reconstructed, and the expression is: , in, The final extracted quasi-static response of the bridge, p This is the frequency band cutoff position. For the first i Each intrinsic mode, k This represents the number of modes.

[0031] In this embodiment, constructing the all-time-space vehicle load matrix includes: The influence line of the bridge is discretized along the longitudinal direction. n Each node discretizes the response sampling time into... m At that moment; For each vehicle, its spatial position at each sampling time is calculated based on its total weight, operating speed, and the time it enters the bridge, thus constructing a single-vehicle load matrix Q. i ; Superimpose all individual vehicle load matrices to form a unified load matrix: ,

[0032] Where Q is the overall load matrix formed by superimposing multiple vehicle load matrices, Q i For the first i Vehicle load matrix N The total number of vehicles. For the real number field m × n 3D matrix space.

[0033] Furthermore, the expression for the generalized cross-validation function is:

[0034] in, It is a generalized cross-validation function; For the influence matrix, I is the identity matrix; For matrix trace, For regularization parameters, It is the identity matrix. For the transpose of the all-time-space vehicle load matrix, This is the quasi-static response vector.

[0035] Furthermore, the automatic search for the optimal regularization parameter specifically involves: The generalized cross-validation function is found by a traversal search strategy. Optimal regularization parameter that achieves minimum value The expression is: ; Substituting these values ​​into the Tikhonov analytical solution expression, the discrete influence lines of the bridge can be obtained.

[0036] In this embodiment, piecewise cubic conformal interpolation is used for continuous reconstruction within the interval. x i ≤x≤x i+1 Built-in PCHIP interpolation function:

[0037] in, , The first derivative of the node; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the start of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the beginning of the interval; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the endpoint of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the endpoint of the interval; The starting node of the interpolation interval x i Discrete values ​​of the bridge influence line at the location; The endpoint of the interpolation interval x i+1 Discrete values ​​of the bridge influence line at the location; For the interval [ x i , x i+1 The bridge continuous influence line values ​​obtained from the internal reconstruction. t For interval normalized variables, x These are the actual physical coordinates of the bridge's longitudinal direction.

[0038] Implementation Method Two: This implementation method is a complete embodiment of the event-triggered liquid neural network low-power continuous monitoring and hierarchical wake-up method described in Implementation Method One, including: Step 1: Develop a bridge operation response test plan; Displacement sensors are deployed at target measurement points on the bridge to collect dynamic response data under bridge operation conditions. Based on bridge structural parameters, traffic survey data, or preset operating conditions, traffic parameters such as vehicle type, axle load, wheelbase, lane distribution, vehicle speed, and vehicle spacing under typical multi-vehicle operating conditions are determined.

[0039] In step 1, The bridge operation response test plan includes a bridge response acquisition plan and a typical multi-vehicle operation condition parameter determination plan.

[0040] Step 1.1, Bridge Response Test Plan Development: Based on the bridge structure, span, testing objectives, and influence line identification locations, displacement, deflection, or acceleration sensors are deployed at the mid-span, quarter-span, or other target sections of the bridge to ensure that the bridge response can fully record the entire process of a typical vehicle crossing the bridge.

[0041] Step 1.2, Determining Typical Multi-Vehicle Operating Conditions: Based on the bridge design load level, highway traffic survey data, or typical operating vehicle parameters, determine the vehicle composition parameters under bridge operating conditions.

[0042] Step 1.3, Establishment of typical vehicle combinations: Establish typical multi-vehicle operation combinations based on the number of bridge lanes, allowing multiple vehicles to be located in different lanes at the same time and maintain a constant speed.

[0043] Step 1.4, Parameter Input: Input the vehicle weight, vehicle speed, vehicle spacing and lane number into the vehicle matrix construction module to provide basic parameters for the subsequent establishment of the all-time and all-space vehicle load matrix.

[0044] Step 2: Perform adaptive truncation and static / dynamic separation of bridge response; Based on the bridge dynamic response data obtained in step 1, the adaptive truncation dynamic-static separation method is used to automatically determine the number of modal decomposition layers and the spectral truncation position, separate the bridge quasi-static response and dynamic response, and extract the quasi-static response required for bridge influence line identification.

[0045] Furthermore, in step 2, Based on the bridge dynamic response data obtained in step 1, the quasi-static response of the bridge is extracted using the adaptive truncation dynamic-static separation method.

[0046] Step 2.1, Bridge response preprocessing: The original dynamic response of the bridge is detrended, outlier removed and normalized to obtain the bridge response sequence.

[0047] The bridge response is expressed as:

[0048] In the formula, The original response of the bridge; Quasi-static response; The dynamic response generated by vehicle excitation; This is environmental noise.

[0049] Step 2.2, Adaptive Band Cutoff Mode Decomposition: The adaptive band-cutoff variational mode decomposition algorithm decomposes the bridge response to obtain:

[0050] In the formula, For the first i One intrinsic mode; k The number of modes; This is a residual term.

[0051] Step 2.3, Quasi-static response reconstruction: Reconstruct the bridge's quasi-static response using the retained low-frequency modes.

[0052] In the formula, This is the final extracted quasi-static response of the bridge; p At the frequency band cutoff position, high-frequency dynamic vibration modes are automatically truncated, retaining only the frequency band cutoff position. p arrive k The energy of the lower-order modes of the first order.

[0053] Step 3: Construct a full-time and space vehicle load matrix for typical multi-vehicle operation conditions; Based on the typical operational traffic parameters determined in step 1, a typical multi-lane, multi-vehicle uniform speed driving model is established using vehicle weight, vehicle speed, vehicle spacing, and lane distribution as inputs. Based on the spatiotemporal positional relationship of vehicles on the bridge, a spatiotemporal distribution matrix of multi-vehicle loads is constructed, and a full-time-space vehicle load matrix under typical multi-vehicle operating conditions is formed, providing a unified load input model for bridge influence line inversion.

[0054] Furthermore, in step 3, Based on the typical multi-vehicle operating condition parameters determined in step 1, a method for constructing the vehicle load matrix for typical multi-vehicle operating conditions is proposed. The vehicle load matrix uses the total vehicle weight as the concentrated load, without considering the axle load distribution and wheelbase influence. The vehicle load matrix under typical multi-vehicle operating conditions is established based on the total vehicle weight, vehicle speed, vehicle spacing, and lane distribution.

[0055] Step 3.1, Establish the discrete model of the bridge: Discretize the influence line of the bridge along the longitudinal direction of the bridge.n Each node, the bridge response sampling time is discrete. m At each sampling time, the influence line of the bridge can be represented as:

[0056] In the formula, Φ represents the influence line of the bridge structure. For the first j Influence line values ​​corresponding to each discrete node; n This represents the number of discrete nodes along the bridge's influence line.

[0057] Step 3.2, Construct a vehicle matrix for each individual vehicle. Let the first i The total weight of the vehicles is W i The running speed is v i The time when the vehicle enters the bridge is The vehicle's position at each sampling time is calculated based on its speed.

[0058] Step 3.3, Construct a typical multi-vehicle operating condition vehicle matrix: Assume that the bridge has a total of [number missing] vehicles within the response time. N If multiple vehicles participate in the influence line identification, then all vehicle matrices are superimposed to form a typical multi-vehicle operating condition vehicle matrix Q:

[0059] Where Q is the vehicle load matrix under typical multi-vehicle operation conditions, each row is the vehicle load state corresponding to a sampling time, and each column corresponds to the vehicle load at the discrete node of the bridge influence line. Let be the vehicle matrix of the i-th vehicle.

[0060] Step 4: Solve for the ill-conditioned matrix of the bridge influence line; Based on the quasi-static response of the bridge obtained in step 2 and the all-time vehicle load matrix established in step 3, the inversion equation of the bridge influence line is established; the optimal regularization parameter is automatically searched using the generalized cross-validation method to achieve stable solution of the bridge influence line and obtain the discrete influence line of the bridge.

[0061] Based on the quasi-static response obtained in step 2 Using the all-time-space vehicle load matrix Q established in step 3, a bridge influence line inversion model is established.

[0062] Step 4.1, establish the influence line equation: The bridge's quasi-static response satisfies:

[0063] Where R is the quasi-static response. Q represents the vehicle load matrix. This is the influence line of the bridge.

[0064] Step 4.2, construct the generalized cross-validation function:

[0065] In the formula, It is a generalized cross-validation function; For the influence matrix, I is the identity matrix; It is the trace of the matrix.

[0066] Step 4.3, Automatically search for the optimal regularization parameters:

[0067] In the formula, This is the optimal regularization parameter.

[0068] The influence line stability solution is completed using the optimal parameters, and the discrete influence line of the bridge is obtained.

[0069] Step 5: Perform continuous reconstruction of the bridge influence line; Based on the discrete influence line data obtained in step 4, a piecewise cubic conformal interpolation method is used for continuous reconstruction to obtain the continuous influence line of the bridge, thereby realizing the identification of the bridge influence line under typical multi-vehicle operation conditions.

[0070] Furthermore, in step 5, Based on the discrete bridge structure influence line node data obtained in step 4, piecewise cubic conformal interpolation (PCHIP) is used to continuously reconstruct the bridge influence line. Within the interval... x i ≤x≤x i+1 Built-in PCHIP interpolation function:

[0071] In the formula, , The first derivative of the node; , , , , , ; t For interval normalization variables.

[0072] Finally, the continuous influence line of the bridge is obtained and output as the bridge influence line identification result.

[0073] Implementation Method 3, see below Figures 1 to 8 This embodiment describes a specific application example of the event-triggered liquid neural network low-power continuous monitoring and hierarchical wake-up method described in Embodiment 1, including: Step 1: Develop a bridge operation response test plan; The bridge operation response testing scheme is used to acquire real dynamic response information of the bridge structure under typical multi-vehicle operation conditions, and to provide basic data support for subsequent bridge influence line identification and vehicle load matrix construction. The bridge operation response testing scheme includes a bridge response acquisition scheme and a typical multi-vehicle operation condition parameter determination scheme.

[0074] In actual implementation, bridge response testing needs to fully consider the impact of bridge structural form, traffic operation status and environmental factors on structural response. Therefore, the test plan not only includes sensor deployment and data acquisition parameter design, but also needs to build a reasonable vehicle operation condition model in combination with typical traffic flow characteristics.

[0075] Step 1.1, Develop a bridge response test plan: In this embodiment, structural displacement gauges and strain sensors are installed at the mid-span, 1 / 4-span, or moment and shear force control sections of the bridge to collect dynamic response data of the bridge under vehicle action in real time.

[0076] Step 1.2, Determine typical uniform-speed multi-vehicle operating conditions: Further, in this embodiment, based on the bridge design load level, highway traffic survey data, and the operating patterns of typical uniform-speed vehicles, the parameters of typical uniform-speed multi-vehicle operating conditions under bridge operation are determined. These operating condition parameters include key influencing factors such as vehicle type, total vehicle weight, lane distribution, vehicle speed, and vehicle spacing.

[0077] Step 1.3, Establishing a Typical Uniform Speed ​​Vehicle Combination: In this embodiment, a typical uniform speed multi-vehicle operation combination model is constructed based on the number of bridge lanes and traffic flow distribution patterns. In this model, multiple vehicles are allowed to be located in different lanes at the same time and maintain a uniform speed within their respective lanes, thus forming a multi-lane coupled operation condition.

[0078] Step 1.4, Input vehicle matrix parameters: In this embodiment, all vehicle operation parameters determined in Step 1.2 and Step 1.3 are uniformly input into the vehicle matrix construction module for subsequent construction of the all-time-space vehicle load matrix.

[0079] Through the implementation of step 1 above, standardized modeling and parameterized expression of bridge vehicle operation status under typical multi-vehicle operation conditions are realized, transforming complex traffic flow into a calculable unified input form.

[0080] Step 2: Perform adaptive truncation and static / dynamic separation of bridge response; Based on the bridge dynamic response data obtained in step 1, an adaptive truncated variational mode decomposition method is used to separate the dynamic and static components of the bridge response signal, thereby extracting the quasi-static response components. Frequency band separation is achieved through variational mode decomposition, and adaptive mode truncation is realized by combining energy evolution laws and frequency abrupt change characteristics, thus achieving stable extraction of the quasi-static response.

[0081] First, the original response signal is preprocessed, including trend term elimination, outlier removal, and amplitude normalization, so that the signal meets the stability requirements of subsequent decomposition in terms of statistical characteristics.

[0082] Furthermore, the filtered signal is introduced into a variational mode decomposition framework, representing the complex non-stationary signal as the sum of several mode functions with finite bandwidth characteristics. This invention further introduces an adaptive truncation mechanism based on energy evolution discrimination to achieve automatic mode classification. Through this mechanism, low-frequency modes can be automatically identified as components of the quasi-static response, while high-frequency modes are identified as dynamic vibration and noise components. Based on this, truncation and reconstruction are performed to ultimately obtain a stable quasi-static response signal for the bridge. This method avoids the uncertainty of manually selecting the number of modes and significantly improves the robustness and consistency of signal separation in complex multi-vehicle operating environments.

[0083] In this embodiment, the center frequency of each mode is first calculated, then the modal energy is calculated, and a comprehensive modal cutoff discrimination index is constructed:

[0084] in, To comprehensively evaluate the criteria, the intrinsic mode order at this point is the learned cutoff order. p ; Characterizing the first i The dominant frequency position of the intrinsic mode function; For the first i Modal energy.

[0085] The method proposed in this embodiment essentially achieves adaptive determination of the number of modes through an energy attenuation mechanism and achieves stable extraction of the quasi-static response through low-frequency mode reconstruction.

[0086] Through the implementation of step 2 above, this method can effectively suppress high-frequency vibration interference and environmental noise under complex excitation conditions of multi-vehicle coupling, improve the accuracy and stability of bridge quasi-static response extraction, and provide high-quality input data for subsequent bridge influence line inversion.

[0087] Step 3: Construct a full-time and space vehicle load matrix for typical multi-vehicle operation conditions; Based on the typical multi-vehicle operating condition parameters determined in step 1 and combined with the bridge quasi-static response information obtained in step 2, this embodiment further proposes a method for constructing a bridge vehicle load matrix under multi-lane uniform speed operating conditions. This method is used to convert the complex multi-vehicle coupling effect into a unified spatiotemporal discrete load expression form, providing structured input for bridge influence line inversion.

[0088] Under typical multi-vehicle operation conditions, the bridge structure is simultaneously affected by multiple vehicles traveling at uniform speeds in different lanes. The spatial location and temporal evolution of each vehicle differ significantly, resulting in strong time-varying and spatially distributed loads. For example... Figure 3 As shown, in order to achieve a unified expression of this complex physical process, the vehicle load modeling in this embodiment is simplified from "axle-level distribution model" to "vehicle total weight equivalent concentrated moving load model", thereby realizing the matrix expression of multi-vehicle coupling effect.

[0089] In this embodiment, based on the unified modeling concept of spatial and temporal discretization of bridges, the response domain of a continuous bridge structure is divided into several spatially discrete nodes, and the entire vehicle operation process is divided into discrete-time sampling points, thereby constructing a unified spatiotemporal analysis framework. By superimposing the single-vehicle load matrices, an overall vehicle load matrix under typical multi-vehicle operating conditions is formed, thus achieving a unified description of the bridge's stress state under multi-vehicle, multi-lane conditions.

[0090] By implementing the above step 3, the traditional discrete analysis based on individual vehicle parameters is transformed into a matrix-based overall modeling method. This matrix representation method significantly improves the stability and well-posedness of subsequent influence line inversion calculations, providing a high-quality input data foundation for bridge structural condition identification.

[0091] Step 4: Solve for the ill-conditioned matrix of the bridge influence line; Based on the bridge quasi-static response sequence obtained in step 2 and the vehicle load matrix of typical multi-vehicle operation conditions constructed in step 3, a bridge influence line inversion model is established. The generalized cross-validation (GCV) criterion is introduced to achieve adaptive optimization of parameters, thereby improving the stability and noise resistance of influence line identification.

[0092] During the calculation, a regularization parameter that minimizes the GCV function is found through a search strategy that involves either traversal or optimization. Then, by substituting this into the Tikhonov analytical solution expression, a stable discrete influence line solution for the bridge is obtained.

[0093] In this embodiment, the explicit expansion formula for the GCV function residual is as follows:

[0094] in, To the regularization parameter Influence line solution obtained under control; , represents the bridge response value predicted by the GCV model. For the first j The actual observed response value of a time or space sampling point; No. j The model's predicted response value corresponding to each sampling point; m The total number of sampling points for the response data.

[0095] Through the implementation method described in step 4 above, this implementation method first introduces the generalized cross-validation (GCV) criterion based on the linear mapping relationship between the vehicle load matrix Q and the bridge quasi-static response R. By constructing a comprehensive evaluation function based on the residual norm and the degree of freedom penalty term, it achieves adaptive optimization selection of the regularization parameter, thereby obtaining the global optimal solution. Finally, by combining the optimized parameters, the discrete influence line solution of the bridge is obtained, realizing the stable inversion and high-precision identification of the bridge influence line under complex conditions of multi-vehicle operation, and providing reliable basic data support for subsequent structural status assessment.

[0096] Step 5: Perform continuous reconstruction of the bridge influence line; Based on the discrete influence line results of the bridge obtained in step 4, this embodiment uses the piecewise cubic conformal interpolation (PCHIP) method to continuously reconstruct the discrete influence line in order to obtain a smooth bridge influence line function expression that maintains monotonicity.

[0097] By implementing the above-described step 5, the oscillation phenomenon that may occur with traditional cubic spline interpolation can be effectively avoided, thereby improving the stability of the influence line in bridge engineering applications.

[0098] The bridge type in this embodiment is a conventional span bridge.

[0099] The following section describes the identification of bridge influence lines under multi-vehicle operation conditions based on actual circumstances: To verify the effectiveness and engineering applicability of the bridge influence line identification method proposed in this invention under typical multi-vehicle operation conditions, such as... Figure 5 and Figure 6 As shown, a 30-m span prestressed concrete continuous box girder bridge was selected as the actual bridge test object for loading test research. The bridge structure is a typical small-to-medium span highway bridge with a two-lane transverse arrangement. The overall structural stiffness is moderate, and the dynamic response characteristics are obvious, making it suitable for influence line inversion and multi-vehicle coupled load identification tests.

[0100] like Figure 4As shown, the test conditions were designed for two 45-ton heavy-duty test vehicles to drive at a constant speed on the bridge under load. Both vehicles entered the bridge sequentially in the same direction of travel, with a stable distance between them. They crossed the bridge at idle speed, 5 km / h, 10 km / h, 20 km / h, and 30 km / h from the first lane. During the test, displacement sensors were deployed at the mid-span section of the bridge to collect the dynamic response signals of the structure as the vehicles passed. Continuous data acquisition was performed throughout the entire process from the vehicles entering the bridge to completely exiting it, ensuring a complete record of the bridge's time-varying response under the coupled action of the two vehicles.

[0101] In this dual-vehicle uniform speed loading test of a 30m box girder bridge, the original dynamic response signal of the bridge was first processed based on the adaptive truncation dynamic-static separation method proposed in step 2, and the quasi-static response components of the bridge were successfully extracted. For example... Figure 7 As shown, the results indicate that after decomposition and low-frequency mode reconstruction, the extracted quasi-static response curve exhibits a smooth, continuous trend consistent with the changes in vehicle load, effectively reflecting the equivalent effect of vehicle load on the bridge structure.

[0102] Furthermore, based on the bridge influence line inversion results obtained in step 4, the identified influence lines are compared and analyzed with the theoretical or actual bridge reference influence lines under calibration conditions. For example... Figure 8 As shown, the results indicate that the influence lines identified by the method of the present invention have a high degree of consistency with the actual influence lines in terms of overall shape. In particular, near the mid-span control section, the peak positions of the influence lines are basically consistent, indicating that the method of the present invention has strong structural identification ability and stability.

[0103] To quantitatively evaluate the accuracy of influence line recognition, this implementation further constructs an error evaluation index based on peak characteristics. The peak relative error is defined as:

[0104] In the formula, This represents the relative error of the peak value. This represents the peak value of the actual influence line. To identify the peak value of the influence line.

[0105] The actual influence line values ​​are obtained by identifying the quasi-static response of the bridge when vehicles cross it at idle speed (below 5 km / h, close to zero speed). Experimental results show that under the condition of two vehicles following each other at a constant speed, the peak error of the influence line identified by the method of this invention remains within 5%, indicating that the proposed inversion method can effectively suppress the noise amplification effect caused by multi-vehicle coupling, thereby achieving high-precision influence line identification.

[0106] Implementation Method 4: This implementation method proposes a computer device, including a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes an event-triggered liquid neural network low-power continuous monitoring and hierarchical wake-up method according to any one of Implementation Methods 1 to 3.

[0107] Implementation Method 5: This implementation method proposes a computer-readable storage medium storing a computer program. When the computer program is run by a processor, it executes the steps of a bridge influence line identification method in a typical multi-vehicle operation environment, as described in any one of Implementation Methods 1 to 3.

[0108] The specific embodiments of the present invention disclosed above are merely illustrative of the invention. These embodiments do not exhaustively describe all details, nor do they limit the invention to the specific embodiments described. Many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment, characterized in that, The method includes: Acquire dynamic response data of the bridge under typical multi-vehicle operation conditions and corresponding traffic parameters, including total vehicle weight, operating speed and time of entry into the bridge. Adaptive truncated variational mode decomposition is performed on the dynamic response data, and the frequency band cutoff position is determined according to the modal cutoff comprehensive discrimination index to extract the quasi-static response of the bridge; wherein, the modal cutoff comprehensive discrimination index ,in: Characterizing the first i The dominant frequency position of the intrinsic mode function; For the first i Modal energy; Based on the traffic parameters and discrete nodes of the bridge space, a full-time and space-time vehicle load matrix is ​​constructed. An inversion equation is established between the quasi-static response and the all-time vehicle load matrix. The optimal regularization parameter is automatically searched by minimizing the generalized cross-validation function, and the discrete influence line of the bridge is obtained by solving the solution. Piecewise cubic conformal interpolation is used to continuously reconstruct the discrete influence lines of the bridge, resulting in continuous influence lines of the bridge.

2. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 1, characterized in that, The traffic parameters under typical multi-vehicle operating conditions are determined through traffic survey data or design load levels, forming a set of vehicle load input parameters. : ， in, W i For the first i Total weight of the vehicles. v i For running speed, The moment the vehicle enters the bridge. N This represents the total number of vehicles.

3. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 1, characterized in that, The adaptive truncated variational mode decomposition of the dynamic response data includes: The dynamic response data is subjected to detrending processing, outlier removal, and normalization. The processed response data is decomposed into the following values ​​using a variational mode decomposition algorithm: k Individual eigenmodes and residuals ; Based on the modal cutoff comprehensive discrimination index Determine the cutoff order p .

4. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 3, is characterized in that... The extraction of the quasi-static response of the bridge specifically includes: Using the truncation order p to k The low-frequency modes and residual terms of the first order are reconstructed, and the expression is: ， in, The final extracted quasi-static response of the bridge, p This is the frequency band cutoff position. For the first i Each intrinsic mode, k This represents the number of modes.

5. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 1, characterized in that, The construction of the all-time-space vehicle load matrix includes: The influence line of the bridge is discretized along the longitudinal direction. n Each node discretizes the response sampling time into... m At that moment; For each vehicle, its spatial position at each sampling time is calculated based on its total weight, operating speed, and the time it enters the bridge, thus constructing a single-vehicle load matrix Q. i ; Superimpose all individual vehicle load matrices to form a unified load matrix: ， Where Q is the overall load matrix formed by superimposing multiple vehicle load matrices, Q i For the first i Vehicle load matrix N The total number of vehicles. For the real number field m × n 3D matrix space.

6. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 5, is characterized in that... The expression for the generalized cross-validation function is: in, It is a generalized cross-validation function; For the influence matrix, I is the identity matrix; For matrix trace, For regularization parameters, It is the identity matrix. For the transpose of the all-time-space vehicle load matrix, This is the quasi-static response vector.

7. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 6, is characterized in that... The automatic search for the optimal regularization parameter is specifically as follows: The generalized cross-validation function is found by a traversal search strategy. Optimal regularization parameter that achieves minimum value The expression is: ； Substituting these values ​​into the Tikhonov analytical solution expression, the discrete influence lines of the bridge can be obtained.

8. The bridge influence line identification method based on joint adaptive truncation dynamic-static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in claim 1, characterized in that, The method employs piecewise cubic conformal interpolation for continuous reconstruction within the interval. x i ≤x≤x i+1 Built-in PCHIP interpolation function: in, , The first derivative of the node; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the start of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the beginning of the interval; These are cubic polynomial basis functions used to control the function values ​​of the interpolation curve at the endpoint of the interval; These are basis functions for a cubic polynomial, used to control the derivative at the endpoint of the interval; The starting node of the interpolation interval x i Discrete values ​​of the bridge influence line at the location; The endpoint of the interpolation interval x i+1 Discrete values ​​of the bridge influence line at the location; For the interval [ x i , x i+1 The bridge continuous influence line values ​​obtained from the internal reconstruction. t For interval normalized variables, x These are the actual physical coordinates of the bridge's longitudinal direction.

9. A computer device, characterized in that: The device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes an event-triggered liquid neural network low-power continuous monitoring and hierarchical wake-up method according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a bridge influence line identification method based on joint adaptive truncation of dynamic and static separation and automated parameter optimization in a typical multi-vehicle operation environment as described in any one of claims 1-8.

Images