A method for identifying the location of multi-point impact loads on panel-frame structures

Abstract

The present invention relates to the field of identification technology, and more specifically, to an identification method for locating multi-point impact loads on panel-frame structures. This method establishes a finite element model consisting of high-density response points and multiple excitation points to obtain a complete frequency response function matrix. A greedy optimization algorithm based on maximum orthogonality is then introduced to significantly reduce the condition number of the frequency response matrix and improve inversion stability. Furthermore, a non-convex sparse regularized frequency domain identification method (FD-MCP) is proposed, combining the spatial sparsity characteristics of impact loads. This method effectively enhances the noise resistance of load spectrum inversion and achieves complete recovery of the impact load in the time domain through spectrum mirror expansion and inverse Fourier transform. This method significantly reduces the number of response measurement points and improves computational stability while enabling high-precision identification of the spatial location and time history of impact loads, making it suitable for shock response analysis of complex structures.

Description

Technical Field

[0001] The present invention relates to the field of identification technology, in particular to an identification method for positioning multi-point impact loads on a panel frame structure. Background Art

[0002] In large-scale plate-frame structural systems, sudden impact loads can easily lead to localized damage or even total failure. Therefore, accurately identifying the location and duration of impact loads is crucial for structural safety assessment, maintenance strategy formulation, and the development of intelligent monitoring systems. Currently, common load identification methods rely primarily on sensors acquiring response signals and inferring external loads using the structure's frequency response function or dynamic model. However, due to the large spans, multiple degrees of freedom, and complex boundaries of plate-frame structures, identification problems are generally highly ill-posed and pathological.

[0003] Furthermore, impact loads are often non-steady-state, non-periodic, and concentrated over short periods of time, making it difficult for traditional least-squares or regularized solutions to accurately reconstruct their spatiotemporal characteristics. Furthermore, in actual engineering, due to cost and deployment constraints, the number of response measurement points is often far fewer than theoretically required, further exacerbating the model's pathological characteristics. Accurately identifying the time-domain history and spatial location of impact loads in the presence of limited measurement points and noise is one of the current technical challenges facing this field.

[0004] In recent years, the development of sparse representation theory has provided a new approach to solving such high-dimensional ill-posed problems. In particular, in dynamic load identification, by introducing sparse regularization techniques and combining them with prior knowledge of the structure's response to impact loads, the accuracy and robustness of the inverse analysis can be improved while significantly reducing the number of measurement points. However, the performance of such methods often depends on the numerical characteristics of the transfer matrix. Effective optimization during the modeling phase to reduce ill-conditioning and combining advanced sparse solution algorithms to improve identification quality are current research priorities. Therefore, we propose an identification method for locating multi-point impact loads on plate-frame structures. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that traditional solutions based on least squares or regularization are difficult to accurately reconstruct their spatiotemporal characteristics. At the same time, in actual engineering, due to cost and layout limitations, the number of response measurement points is usually far less than the theoretical requirement, further aggravating the pathological characteristics of the model. In dynamic load identification, by introducing sparse regularization technology, the performance of such methods often depends on the numerical characteristics of the transfer matrix, which is effectively optimized in the modeling stage to reduce pathological characteristics, and combined with advanced sparse solution algorithms to improve identification quality.

[0006] To achieve the above object, the present invention provides a method for identifying the location of multi-point impact loads on a panel frame structure, comprising the following steps:

[0007] S1. Establish a finite element model of the panel structure based on the structural dimensions, material properties, and boundary conditions. Arrange multiple excitation points and response measurement points in the model. Apply unit amplitude sinusoidal excitation to each excitation point. Extract the frequency domain response data of all response points. Integrate the frequency response function between the excitation and response into a frequency response matrix.

[0008] S2. Use a greedy algorithm based on maximum orthogonality to screen and optimize the response measurement points. By iteratively constructing the transfer submatrix with the minimum condition number, the pathological condition is reduced, and the optimized response point arrangement scheme and stable transfer matrix are obtained.

[0009] S3. Inverse the optimized transfer matrix with the collected response data to establish a frequency domain impact load identification model. The non-convex MCP regularization term is introduced to enhance the sparse expression capability. The frequency domain impact spectrum of each excitation point is solved through an iterative algorithm.

[0010] S4. Mirror and expand the frequency domain identification results, apply inverse Fourier transform to restore the time domain history of the impact load, obtain the time domain curve of each excitation point, and output the spatial position of each excitation point and the corresponding time domain curve of the impact load.

[0011] Compared with the prior art, the present invention has the following beneficial effects:

[0012] This identification method for locating multi-point impact loads on panel-frame structures constructs a complete frequency response function matrix and introduces a greedy algorithm based on maximum orthogonality to effectively screen the most representative response measurement point combinations from high-dimensional frequency response data. Compared with traditional methods that deploy all measurement points, this strategy significantly reduces the number of measurement points and signal channels while maintaining identification accuracy, significantly reducing hardware costs and data processing pressure, and improving the practicality and deployment efficiency of the identification system.

[0013] During the modeling phase, the original frequency response transfer matrix was structurally optimized, using condition number minimization as the objective function to screen and construct a weakly ill-conditioned matrix. The optimized identification model significantly improved its numerical characteristics, achieving a stable solution even in environments with small impulse signal amplitudes and strong background noise. This solved the common problems of unstable solutions and error amplification in high-dimensional inverse problems, and enhanced the model's adaptability to measured data.

[0014] A non-convex sparse regularization term (MCP) is introduced in the frequency domain identification process to fully utilize the spatial sparsity characteristics of the impact load, achieving more accurate spectrum amplitude inversion. Combined with the inverse Fourier transform, the frequency domain results are mirrored and restored to fully reconstruct the impact load action history, including time domain characteristics such as the start time, peak amplitude, duration, and impact waveform, providing high-fidelity time series information for structural health monitoring and load assessment.

[0015] It has good structural versatility and algorithm scalability, does not rely on specific boundary constraints or structural shape parameters, is applicable to various forms of plate-frame structural systems, and shows excellent adaptability under different structural materials, different excitation paths and different constraint conditions. It is particularly suitable for multi-point impact load identification and historical event backtracking in typical structures such as bridge decks, floor systems, and equipment support surfaces.

[0016] As a further improvement of this technical solution, in S1, the finite element model and the response point arrangement scheme are:

[0017] The finite element model is made of structural steel material with a structural size of 120m×30m×0.1m. Damping parameters and boundary constraints are taken into consideration. The excitation point is set at the center of each unit plate, and the response points are distributed in the plate area in a regular array, covering the entire excitation action area.

[0018] As a further improvement of the present technical solution, in S1, the frequency response function matrix construction process is:

[0019] S1.1.1. Apply a sinusoidal excitation of unit amplitude to each excitation point one by one, and perform a frequency sweep in the frequency range of 0 Hz to 50 Hz;

[0020] S1.1.2. Extract the frequency domain amplitude response of all response points;

[0021] S1.1.3. Integrate the mapping relationship between excitation and response into complex frequency response function values, and construct a frequency response function matrix with the dimension of the number of response points × the number of excitation points.

[0022] The beneficial effect of adopting the above-mentioned further improvements is to quantify the frequency domain mapping relationship between excitation and response and fully capture the dynamic characteristics of the structure. The high-density measurement point arrangement can cover the potential impact area, ensure the comprehensiveness and accuracy of the mapping relationship, and provide a complete data basis for subsequent measurement point optimization. At the same time, the construction of the frequency response matrix transforms the dynamic response problem of complex structures into quantifiable matrix operations, laying a mathematical foundation for the inversion identification of impact loads and solving the problem that the dynamic characteristics of the structure are difficult to directly associate with external loads.

[0023] As a further improvement of this technical solution, S2 adopts a greedy algorithm based on maximum orthogonality to iteratively screen the frequency response matrix to a set target number of response points. The specific steps are as follows:

[0024] S2.1.1. Initialization parameters and sets: Consider the complete frequency response function matrix as the overall matrix, set the number of target response points to p, and initialize an empty measurement point combination set;

[0025] S2.1.2. Iteratively select the optimal response point: From all the response point row vectors of the original frequency response function matrix, select the row vector that is most orthogonal to the currently selected set and can reduce the condition number and add it to the set;

[0026] S2.1.3. Real-time evaluation and optimization of submatrices: Each time a new vector is added, the condition number of the submatrix corresponding to the current combination is calculated and compared with the previous result, and the combination with the smallest condition number is retained;

[0027] S2.1.4. Termination and output: Repeat the above process until the combination contains p response points, and finally obtains the target transfer submatrix with the minimum condition number.

[0028] As a further improvement of the present technical solution, in S2.1.2, the absolute value of the vector dot product between the candidate row vector and the selected row vector in the set is calculated. The smaller the value, the higher the orthogonality. The row vector that is most orthogonal to the currently selected set is determined.

[0029] As a further improvement of the present technical solution, in S2.1.3, if the condition number of the new submatrix is ​​smaller than the result of the previous round, the current set is retained; otherwise, the optimal combination of the previous round is traced back to ensure that the iterative process always converges to the "minimization of the condition number".

[0030] The beneficial effect of adopting the above-mentioned further improvements is that the morbidity of the original frequency response matrix is ​​significantly reduced, and the inversion stability is improved. At the same time, the number of response measurement points is greatly reduced, while reducing hardware costs and data redundancy, the most valuable response information is retained, and the output optimized measurement point layout plan is more in line with the actual engineering layout requirements.

[0031] As a further improvement of the present technical solution, in S3, the steps of establishing the frequency domain impact load identification model are as follows:

[0032] S3.1.1. Construct the load inversion objective function based on the least squares error;

[0033] S3.1.2. Introduce a sparse regularization term into the objective function to enhance the sparse expression capability;

[0034] S3.1.3. Solve the load frequency domain spectrum through an iterative optimization algorithm so that the inversion results have sparsity and robustness while satisfying the response constraints.

[0035] As a further improvement of the present technical solution, in S3.1.3, the load frequency domain spectrum is solved by an iterative optimization algorithm, and the forward and backward splitting iterative algorithm is adopted to solve the optimization objective function of the frequency domain impact identification model. The load spectrum distribution that satisfies the "spatial sparsity" is obtained through iterative calculation, and finally the load amplitude and phase information of each excitation point are output, providing a basis for subsequent time domain reconstruction.

[0036] The beneficial effect of adopting the above-mentioned further improvement is to make full use of the spatial sparsity characteristics of the impact load, strongly penalize small-amplitude interference (noise or non-impact signals) to achieve sparse suppression, and weakly penalize large-amplitude real impacts to avoid amplitude distortion. This not only solves the problem of excessive compression of the impact amplitude by traditional regularization methods, but also improves the noise resistance of the model. At the same time, the low condition number characteristics of the optimized transfer matrix are combined with the efficient solution of the iterative algorithm to ensure the accurate distinction of the frequency domain spectrum of each excitation point in the multi-point impact coupling scenario.

[0037] As a further improvement of the present technical solution, in S4, the steps of the mirror expansion operation and spectrum reconstruction are:

[0038] S4.1.1. Expand the frequency domain identification results symmetrically around the Nyquist frequency on the frequency axis.

[0039] S4.1.2. Complement the negative frequency components by conjugate symmetric expansion to ensure that the inverse Fourier transform result is a real time series;

[0040] S4.1.3. During the expansion process, the high-frequency truncation problem is automatically handled to improve the accuracy of time domain reconstruction.

[0041] As a further improvement of the present technical solution, in said S4, the output time domain curve of the impact load is: each excitation point corresponds to a time domain load curve, and the load curve contains the starting time, peak amplitude, duration and complete waveform shape, which is used for subsequent structural response analysis, impact event backtracking and fatigue life assessment.

[0042] The beneficial effect of adopting the above-mentioned further improvement is that the negative frequency components are complemented by the conjugate symmetry characteristics of the spectrum, the time domain distortion problem caused by frequency domain truncation is solved, and the reconstructed time domain curve accurately reflects the starting time, peak amplitude, duration and waveform characteristics of the impact load; the spatial position of each excitation point and the corresponding time domain curve are output, which not only realizes the complete correlation between the spatial position and time history of the impact load, but also provides high-fidelity time domain characteristic data for subsequent structural response analysis, fatigue assessment and impact event backtracking.

[0043] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0045] Figure 2 This is a complete response measurement point arrangement diagram before optimization of the present invention;

[0046] Figure 3 This is a graph showing the condition number change of the frequency response function matrix before optimization of the present invention;

[0047] Figure 4 Schematic diagram of the process of the greedy optimization algorithm for response measurement points of the present invention;

[0048] Figure 5 This is a schematic diagram of the arrangement of optimized response measurement points obtained by using the greedy algorithm of the present invention;

[0049] Figure 6 This is a graph showing the condition number change of the frequency response function matrix after greedy optimization of the present invention;

[0050] Figure 7 This is a process flow chart for frequency domain identification and time domain reconstruction based on the FD-MCP method of the present invention;

[0051] Figure 8 This is a comparison diagram of the recognition results of the present invention under different noise levels and the actual impact load time history. DETAILED DESCRIPTION

[0052] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0053] At present, traditional solutions based on least squares or regularization are difficult to accurately reconstruct its spatiotemporal characteristics. At the same time, in actual engineering, due to cost and layout limitations, the number of response measurement points is usually far less than the theoretical requirement, further aggravating the pathological characteristics of the model. In dynamic load identification, by introducing sparse regularization technology, the performance of such methods often depends on the numerical characteristics of the transfer matrix. Effective optimization is performed in the modeling stage to reduce pathological characteristics, and combined with advanced sparse solution algorithms to improve identification quality.

[0054] Therefore, the present invention proposes to establish a finite element model according to the structural dimensions, material properties and boundary conditions, apply unit amplitude sinusoidal excitation to each excitation point, extract the frequency domain response data of all response points, use a greedy algorithm based on maximum orthogonality to screen and optimize the response measurement points, combine the optimized transfer matrix with the collected response data for inversion, establish a frequency domain impact load identification model, mirror the frequency domain identification results, apply inverse Fourier transform to restore the time domain history of the impact load, obtain the time domain curve of each excitation point, and output the spatial position of each excitation point and the corresponding impact load time domain curve.

[0055] The details are as follows:

[0056] like Figure 1 As shown, the present invention provides a method for identifying the location of multi-point impact loads on a panel frame structure, comprising the following steps:

[0057] S1. Establish a finite element model of the panel structure based on the structural dimensions, material properties, and boundary conditions. Arrange multiple excitation points and response measurement points in the model. Apply unit amplitude sinusoidal excitation to each excitation point. Extract the frequency domain response data of all response points. Integrate the frequency response function between the excitation and response into a frequency response matrix.

[0058] S2. Use a greedy algorithm based on maximum orthogonality to screen and optimize the response measurement points. By iteratively constructing the transfer submatrix with the minimum condition number, the pathological condition is reduced, and the optimized response point arrangement scheme and stable transfer matrix are obtained.

[0059] S3. Inverse the optimized transfer matrix with the collected response data to establish a frequency domain impact load identification model. The non-convex MCP regularization term is introduced to enhance the sparse expression capability. The frequency domain impact spectrum of each excitation point is solved through an iterative algorithm.

[0060] S4. Mirror and expand the frequency domain identification results, apply inverse Fourier transform to restore the time domain history of the impact load, obtain the time domain curve of each excitation point, and output the spatial position of each excitation point and the corresponding time domain curve of the impact load.

[0061] In order to better establish the finite element model of the plate-frame structure, a finite element model of the plate-frame structure is first established, and a large number of initial response measurement points are arranged on the surface of the structure to comprehensively obtain the response information of the structure under multi-point impact. In this way, an initial frequency response function matrix that can accurately describe the mapping relationship between impact load and response is constructed, as follows:

[0062] A high-density response point arrangement scheme is constructed to comprehensively collect the response information of the structure under excitation. Figure 2 As shown, the frame structure is divided into 9 × 14 blocks, totaling 126 unit areas. Each unit is equipped with 23 response measurement points, forming a large-scale measurement set containing 2898 response points in total. The response points are distributed in an array form, evenly covering the surface of the structure to ensure complete perception of the excitation impact area.

[0063] In order to better construct the frequency response function matrix, in S1, the frequency response function matrix construction process is:

[0064] S1.1.1. Apply a sinusoidal excitation of unit amplitude to each excitation point one by one, and perform a frequency sweep in the frequency range of 0 Hz to 50 Hz;

[0065] S1.1.2. Extract the frequency domain amplitude response of all response points;

[0066] S1.1.3. Integrate the mapping relationship between excitation and response into complex frequency response function values, and construct a frequency response function matrix with the dimension of the number of response points × the number of excitation points.

[0067] An excitation point is preset at the center of each plate element, totaling 126 points, to simulate the impact load application location. Each excitation point stimulates the structural response, and the corresponding frequency response function values ​​are measured at all response points. This constructs a frequency response function matrix with a dimension of 2898 × ​​126. This matrix fully describes the mapping relationship between excitation points and response points and is the core input of the load identification mathematical model.

[0068] Since the number of response points is much larger than the number of excitation points, the original frequency response matrix has serious ill-conditioned problems. Figure 3 As shown in the figure, the condition number of the initial frequency response function matrix changes with frequency. It can be seen from the figure that the maximum condition number is about 6000, which is significantly higher than the generally acceptable numerical solution range. Such a high condition number indicates that there are a large number of linearly correlated or redundant response row vectors in the matrix, which makes it extremely sensitive to input errors, the inversion process is unstable, and the recognition results are easily distorted.

[0069] It can be seen that although the frequency response matrix has complete information, the initial inverse problem model constructed is significantly ill-conditioned due to its high dimension and serious data redundancy, making it difficult to solve directly.

[0070] To reduce matrix pathology and improve system stability, S2 uses a greedy algorithm based on maximum orthogonality to iteratively screen the frequency response matrix to the set target number of response points. The specific steps are as follows:

[0071] S2.1.1. Initialization parameters and sets: Consider the complete frequency response function matrix as the overall matrix, set the number of target response points to p, and initialize an empty measurement point combination set;

[0072] S2.1.2. Iteratively select the optimal response point: From all the response point row vectors of the original frequency response function matrix, select the row vector that is most orthogonal to the currently selected set and can reduce the condition number and add it to the set;

[0073] S2.1.3. Real-time evaluation and optimization of submatrices: Each time a new vector is added, the condition number of the submatrix corresponding to the current combination is calculated and compared with the previous result, and the combination with the smallest condition number is retained;

[0074] S2.1.4. Termination and output: Repeat the above process until the combination contains p response points, and finally obtains the target transfer submatrix with the minimum condition number.

[0075] like Figure 4, which is a flow chart of the greedy optimization algorithm for response measurement points in the present invention.

[0076] This optimization method takes minimizing the frequency response matrix condition number as the objective function and gradually selects the optimal subset from the 2898 original response points based on the orthogonality maximization principle. The specific process is as follows:

[0077] First, the target number of response points is set to 126, matching the number of excitation points. A blank combination set is initialized. Then, in each iteration, the row vector that is most orthogonal to the selected set and can further reduce the condition number is selected from the remaining candidate response points and added to the current set. After each selection, the condition number of the current submatrix is ​​calculated in real time, and the combination with the smallest condition number is continuously retained. This process is repeated until the target number of response points is reached.

[0078] To better determine the row vector that is most orthogonal to the currently selected set, in S2.1.2, the row vector that is most orthogonal to the currently selected set is determined by calculating the absolute value of the vector dot product between the candidate row vector and the selected row vector in the set. The smaller the value, the higher the orthogonality.

[0079] The degree of orthogonality between a candidate row vector and the set of selected row vectors is measured by the absolute value of the vector dot product. Specifically, for the set of currently selected row vectors and the candidate row vector to be evaluated, the absolute value of the dot product between the candidate vector and each selected vector in the set is calculated. The smaller the absolute value of the dot product, the closer the angle between the two vectors is to 90°, and the higher the orthogonality. Conversely, the larger the absolute value of the dot product, the closer the angle between the two vectors is to 0° or 180°, and the lower the orthogonality.

[0080] To ensure that the iterative process always converges to the "minimization of the condition number", in S2.1.3, if the condition number of the new submatrix is ​​smaller than the result of the previous round, the current set is retained. Otherwise, the optimal combination of the previous round is backtracked to ensure that the iterative process always converges to the "minimization of the condition number";

[0081] During the iterative selection of response points, each time a new response point row vector is added to the current set, the condition number of the newly constructed submatrix must be calculated in real time and compared with the condition number of the submatrix obtained in the previous iteration. If the condition number of the new submatrix is ​​smaller than the result from the previous iteration, it indicates that the newly added response point has improved the numerical stability of the matrix, and the current set of measurement points is retained. If the condition number of the new submatrix is ​​greater than or equal to the result from the previous iteration, it indicates that the newly added response point has introduced redundancy or correlation, causing the matrix to become more ill-conditioned. In this case, the newly added points must be discarded and the optimal combination of measurement points from the previous iteration must be returned to.

[0082] The final optimization result is as follows Figure 5 As shown in the figure, it is a schematic diagram of the optimized response measurement point arrangement obtained by the greedy algorithm of the present invention. Figure 2 Compared with the original arrangement scheme in , the optimized response points are mainly concentrated in the area around the excitation point, which has stronger local response representativeness and physical correlation, and effectively removes redundant measurement points, thereby reducing the system dimension and improving data quality.

[0083] like Figure 6 As shown in the figure, the condition number change diagram of the frequency response function matrix after greedy optimization of the present invention is compared. Figure 3 As can be seen, the maximum condition number of the optimized frequency response function matrix dropped significantly from approximately 6000 to approximately 140, a decrease of over 97%. This significant improvement in pathological conditions verifies the effectiveness of the greedy algorithm. Through this optimization method, the original non-square matrix (2898×126) is compressed into a square matrix (126×126), further simplifying the inversion model solution process and enhancing the load identification system's robustness to noise interference.

[0084] Among them, in S3, the steps of establishing the frequency domain impact load identification model are as follows:

[0085] S3.1.1. Construct the load inversion objective function based on the least squares error;

[0086] S3.1.2. Introduce a sparse regularization term into the objective function to enhance the sparse expression capability;

[0087] S3.1.3. Solve the load frequency domain spectrum through an iterative optimization algorithm so that the inversion results have sparsity and robustness while satisfying the response constraints.

[0088] like Figure 7 The figure shows the processing flow chart of frequency domain identification and time domain reconstruction based on the FD-MCP method in the present invention. To further improve the accuracy and anti-interference ability of impact load identification, after completing the response measurement point optimization and frequency response matrix preprocessing, the minimax non-convex sparse regularization method (FD-MCP) and the impact load inversion method are proposed. It mainly includes two stages: frequency domain load identification and time domain response reconstruction;

[0089] First, a sparse inversion model is constructed in the frequency domain. Since the impact load is short-lived and localized in space, it is sparse in the frequency domain. Therefore, this characteristic can be used to construct a frequency domain inverse problem solving model. Under the premise of knowing the optimized frequency response function matrix and response vector, the construction form is The linear equations are , where H is the 126×126 dimension optimized frequency response matrix, y is the frequency domain response vector measured at the optimized response point, and f is the frequency domain sparse coefficient vector of the impact load to be determined;

[0090] To improve the stability and accuracy of the solution, a sparsity regularization term (MCP) is introduced into the model, constructing an objective function with a sparsity constraint and solving it through an iterative algorithm. Compared with traditional L1 norm regularization, this method is more suitable for impact load identification scenarios with highly sparse but drastically varying amplitudes.

[0091] In order to better solve the load frequency domain spectrum, in S3.1.3, the load frequency domain spectrum is solved by an iterative optimization algorithm. The forward and backward splitting iterative algorithm is used to solve the optimization objective function of the frequency domain impact identification model. The load spectrum distribution that meets the "spatial sparsity" is obtained through iterative calculation. Finally, the load amplitude and phase information of each excitation point are output to provide a basis for subsequent time domain reconstruction.

[0092] By alternating between forward and backward steps, the algorithm gradually approaches a solution that satisfies spatial sparsity. Specifically, the forward step, based on the principle of gradient descent, optimizes the least squares error term in the objective function that reflects the deviation between the response and the load, adjusting the intermediate variables to align with the measured response. The backward step, based on the constraints of the non-convex MCP regularization term, performs a sparse projection on the intermediate variables, imposing a strong penalty on small-amplitude interference (noise or non-impact signals) to suppress their influence, while weakening the penalty on large-amplitude true impact signals to avoid amplitude distortion, thus ensuring the sparsity and accuracy of the solution.

[0093] After completing the frequency domain identification, the identified frequency domain load vector is reconstructed in the time domain using the inverse Fourier transform to obtain a complete impact load time history curve, which is convenient for load spectrum analysis and structural response simulation in engineering applications.

[0094] Among them, in S4, the steps of the mirror extension operation and spectrum reconstruction are:

[0095] S4.1.1. Expand the frequency domain identification results symmetrically around the Nyquist frequency on the frequency axis.

[0096] S4.1.2. Complement the negative frequency components by conjugate symmetric expansion to ensure that the inverse Fourier transform result is a real time series;

[0097] S4.1.3. During the expansion process, the high-frequency truncation problem is automatically handled to improve the accuracy of time domain reconstruction.

[0098] In order to evaluate the accuracy of the present invention in spatial positioning, the positioning error of the excitation point in the recognition results was quantitatively analyzed. As shown in the following table,

[0099] Table 1: Comparison of spatial positioning errors of impact loads

[0100]

[0101] This table is based on the statistical results of the identification results of multiple impact load application points under typical working conditions. The Euclidean distance between the identification value and the actual load application position is calculated as a measure of spatial error.

[0102] The results show that the spatial positioning error of the vast majority of identification points is within 0.5 structural units, with the maximum error not exceeding 0.9 unit plate lengths. Compared to traditional sparse inversion methods, this method significantly improves spatial identification accuracy by combining response point optimization with the FD-MCP identification model, ensuring the accurate positioning of the impact source under multi-point coupling conditions.

[0103] In actual engineering applications, structural responses are often inevitably affected by measurement noise. In order to verify the robustness of the identification method in a noisy environment, typical excitation points were selected and identification tests were carried out under different signal-to-noise ratio (SNR) conditions. The load history obtained by identification was compared with the actual impact input. Figure 8 As shown in the figure, the time history curve comparison between the impact load identified by the FD-MCP method and the actual load under 25dB noise conditions is shown.

[0104] As can be seen from the figure, the identified curve is highly consistent with the true curve in terms of peak position, start and end times, and waveform trend, with no significant delay, drift, or amplitude distortion. This result demonstrates that even under high noise levels, the proposed frequency domain identification and regularized reconstruction scheme maintains excellent anti-interference capabilities and can stably recover time domain information of impact loads.

[0105] In order to better output the impact load time domain curve, in S4, the output impact load time domain curve is: each excitation point corresponds to a time domain load curve, and the load curve contains the starting time, peak amplitude, duration and complete waveform shape, which is used for subsequent structural response analysis, impact event backtracking and fatigue life assessment;

[0106] The starting moment marks the time point when the impact begins to act, the peak amplitude reflects the maximum intensity of the impact load, the duration reflects the duration of the impact, and the complete waveform shape shows the change pattern of the entire process of the impact from occurrence, enhancement, attenuation to end;

[0107] Structural response analysis can simulate the dynamic impact of impact on the structure based on waveform characteristics; impact event backtracking can accurately restore the timing of the impact through the starting time, duration, etc.; fatigue life assessment can quantify the contribution of impact loads to the cumulative damage of the structure based on peak amplitude and waveform characteristics, thereby providing high-fidelity load data for the safe maintenance, life prediction and impact-resistant design of plate-frame structures.

[0108] In summary, the working principle of this solution is as follows:

[0109] This identification method for locating multi-point impact loads on panel-frame structures constructs a complete frequency response function matrix and introduces a greedy algorithm based on maximum orthogonality to effectively screen the most representative response measurement point combinations from high-dimensional frequency response data. Compared with traditional methods that deploy all measurement points, this strategy significantly reduces the number of measurement points and signal channels while maintaining identification accuracy, significantly reducing hardware costs and data processing pressure, and improving the practicality and deployment efficiency of the identification system.

[0110] During the modeling phase, the original frequency response transfer matrix was structurally optimized, using condition number minimization as the objective function to screen and construct a weakly ill-conditioned matrix. The optimized identification model significantly improved its numerical characteristics, achieving a stable solution even in environments with small impulse signal amplitudes and strong background noise. This solved the common problems of unstable solutions and error amplification in high-dimensional inverse problems, and enhanced the model's adaptability to measured data.

[0111] A non-convex sparse regularization term (MCP) is introduced in the frequency domain identification process to fully utilize the spatial sparsity characteristics of the impact load, achieving more accurate spectrum amplitude inversion. Combined with the inverse Fourier transform, the frequency domain results are mirrored and restored to fully reconstruct the impact load action history, including time domain characteristics such as the start time, peak amplitude, duration, and impact waveform, providing high-fidelity time series information for structural health monitoring and load assessment.

[0112] It has good structural versatility and algorithm scalability, does not rely on specific boundary constraints or structural shape parameters, is applicable to various forms of plate-frame structural systems, and shows excellent adaptability under different structural materials, different excitation paths and different constraint conditions. It is particularly suitable for multi-point impact load identification and historical event backtracking in typical structures such as bridge decks, floor systems, and equipment support surfaces.

[0113] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely preferred examples of the present invention and are not intended to limit the present invention. Various changes and improvements may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and improvements fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying the location of multi-point impact loads on a panel frame structure, characterized in that: The following steps are involved: S1. Establish a finite element model of the panel structure based on the structural dimensions, material properties, and boundary conditions. Arrange multiple excitation points and response measurement points in the model. Apply unit amplitude sinusoidal excitation to each excitation point. Extract the frequency domain response data of all response points. Integrate the frequency response function between the excitation and response into a frequency response matrix. S2. Use a greedy algorithm based on maximum orthogonality to screen and optimize the response measurement points. By iteratively constructing the transfer submatrix with the minimum condition number, the pathological condition is reduced, and the optimized response point arrangement scheme and stable transfer matrix are obtained. S3. Inverse the optimized transfer matrix with the collected response data to establish a frequency domain impact load identification model. The non-convex MCP regularization term is introduced to enhance the sparse expression capability. The frequency domain impact spectrum of each excitation point is solved through an iterative algorithm. S4. Mirror and expand the frequency domain identification results, apply inverse Fourier transform to restore the time domain history of the impact load, obtain the time domain curve of each excitation point, and output the spatial position of each excitation point and the corresponding time domain curve of the impact load; S2 uses a greedy algorithm based on maximum orthogonality to iteratively screen the frequency response matrix to set the target number of response points. The specific steps are as follows: S2.1.

1. Initialization parameters and sets: Consider the complete frequency response function matrix as the overall matrix, set the number of target response points to p, and initialize an empty measurement point combination set; S2.1.

2. Iteratively select the optimal response point: From all the response point row vectors of the original frequency response function matrix, select the row vector that is most orthogonal to the currently selected set and can reduce the condition number and add it to the set; S2.1.

3. Real-time evaluation and optimization of submatrices: Each time a new vector is added, the condition number of the submatrix corresponding to the current combination is calculated and compared with the previous result, and the combination with the smallest condition number is retained; S2.1.

4. Termination and output: Repeat the above process until the combination contains p response points, and finally obtains the target transfer submatrix with the minimum condition number.

2. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: The finite element model and response point arrangement scheme in S1 are: The finite element model is made of structural steel material with a structural size of 120m×30m×0.1m. Damping parameters and boundary constraints are taken into consideration. The excitation point is set at the center of each unit plate, and the response points are distributed in the plate area in a regular array, covering the entire excitation action area.

3. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: The frequency response function matrix construction process in S1 is: S1.1.

1. Apply a sinusoidal excitation of unit amplitude to each excitation point one by one, and perform a frequency sweep in the frequency range of 0 Hz to 50 Hz; S1.1.

2. Extract the frequency domain amplitude response of all response points; S1.1.

3. Integrate the mapping relationship between excitation and response into complex frequency response function values, and construct a frequency response function matrix with the dimension of the number of response points × the number of excitation points.

4. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: In S2.1.2, the row vector that is most orthogonal to the currently selected set is determined by calculating the absolute value of the vector dot product between the candidate row vector and the selected row vector in the set. The smaller the value, the higher the orthogonality.

5. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: In S2.1.3, if the condition number of the new submatrix is ​​smaller than the result of the previous round, the current set is retained; otherwise, the optimal combination of the previous round is backtracked to ensure that the iterative process always converges to "minimizing the condition number".

6. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: The steps of establishing the frequency domain impact load identification model in S3 are as follows: S3.1.

1. Construct the load inversion objective function based on the least squares error; S3.1.

2. Introduce a sparse regularization term into the objective function to enhance the sparse expression capability; S3.1.

3. Solve the load frequency domain spectrum through an iterative optimization algorithm so that the inversion results have sparsity and robustness while satisfying the response constraints.

7. The identification method for locating multi-point impact loads on a panel frame structure according to claim 6, characterized in that: In S3.1.3, the load frequency domain spectrum is solved by an iterative optimization algorithm, and the forward and backward splitting iterative algorithm is adopted to solve the optimization objective function of the frequency domain impact identification model. The load spectrum distribution that meets the "spatial sparsity" is obtained through iterative calculation, and finally the load amplitude and phase information of each excitation point are output to provide a basis for subsequent time domain reconstruction.

8. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: In S4, the steps of the mirror extension operation and spectrum reconstruction are: S4.1.

1. Expand the frequency domain identification results symmetrically around the Nyquist frequency on the frequency axis. S4.1.

2. Complement the negative frequency components by conjugate symmetric expansion to ensure that the inverse Fourier transform result is a real time series; S4.1.

3. During the expansion process, the high-frequency truncation problem is automatically handled to improve the accuracy of time domain reconstruction.

9. The identification method for locating multi-point impact loads on a panel frame structure according to claim 1, characterized in that: The impact load time domain curve output in S4 is: each excitation point corresponds to a time domain load curve, and the load curve contains the starting time, peak amplitude, duration and complete waveform shape, which is used for subsequent structural response analysis, impact event backtracking and fatigue life assessment.

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