Load identification and structural response reconstruction method based on denoising regularization

Abstract

The application provides a load identification and structure response reconstruction method based on denoising regularization, comprising the following steps: step one, deducing reconstruction equations of structure dynamic response and external load based on a state space model; step two, introducing a wavelet transform threshold method to perform denoising processing on the measured response; step three, performing interval estimation on the denoised measured response by using a grey mathematical method to determine the interval median and radius of the response; step four, analyzing the ill-posed problem in load identification by means of Tikhonov regularization, so as to inverse the estimation interval of the external load; and step five, realizing interval response reconstruction of the structure by using the dynamic response reconstruction equation. The application has higher effectiveness and applicability, and can quickly and effectively identify the uncertain interval of the load and the response.

Description

Technical Field

[0001] This invention belongs to the field of engineering structural health monitoring, specifically, it relates to a load identification and structural response reconstruction method based on denoising regularization. Background Technology

[0002] External loads and responses at various points on an engineering structure are key indicators for structural health monitoring. Missing response information at critical structural locations can affect the accuracy of the monitoring system. In reality, due to economic constraints and on-site installation limitations, obtaining comprehensive measurement data is difficult, and the external loads on the structure are also difficult to measure directly. Therefore, reconstructing and inverting the responses and external loads at locations where sensors are not installed or cannot be installed, based on limited measurement information, is of great significance.

[0003] To obtain the dynamic response of a structural target location, existing technologies mainly fall into three categories: modal analysis-based, transfer rate matrix-based, and filter-based structural response reconstruction methods. Among these, the transfer rate matrix-based method is the most widely used. Its basic idea is to reconstruct the dynamic response at the target location by establishing a transfer function between the known and unknown responses at the sensor's measurable location. However, all of these methods rely on the premise that the external load is known, while in reality, external loads are often difficult to obtain directly, and the identification of external loads based on the transfer rate matrix is ​​included in the response reconstruction process. Therefore, both aspects should be considered comprehensively. During measurement, the uncertainty of the structural response significantly affects the inversion accuracy, and if the noise contained in the input response is too large, even with regularization methods, the identification results may still diverge significantly.

[0004] In summary, traditional reconstruction techniques suffer from the drawbacks of unknown or difficult-to-measure loads. Furthermore, the noise and uncertainty of the measured vibration response have a significant impact on the results, making it difficult to reconstruct stable external loads and even leading to divergence. Moreover, they cannot obtain accurate structural dynamic responses. Summary of the Invention

[0005] To address the aforementioned issues, a response reconstruction method is proposed that is highly effective and applicable, can effectively identify the uncertainty range of reconstructed loads and responses, and has a wide range of applications.

[0006] This invention provides a load identification and structural response reconstruction method based on denoising regularization, characterized by the following steps.

[0007] Step 1: Derive the structural dynamic response and external load reconstruction equations based on the state-space model.

[0008] Step 2: Wavelet transform thresholding method is introduced to denoise the measurement response.

[0009] Step 3: Use grey mathematics to perform interval estimation on the denoised measurement response to determine the interval median and radius of the response.

[0010] Step four: Use Tikhonov regularization to analyze the ill-posed problem in load identification, thereby inverting the estimation range of the external load.

[0011] Step 5: Use the dynamic response reconstruction equation to reconstruct the interval response of the structure.

[0012] Furthermore, in step one, deriving the structural dynamic response and external load reconstruction equations based on the state-space model includes the following steps.

[0013] (1) Establish a state-space model based on the equation of motion of the structure under external load and its observed response.

[0014] (2) Convert the established state-space model into a discrete-time model.

[0015] (3) The discrete state-space model is transferred to the transfer matrix, and the reconstructed equations of response and external load are constructed iteratively.

[0016] Furthermore, in step two, the wavelet transform thresholding method is introduced to denoise the measurement response, including the following steps.

[0017] (1) Arrange sensors and measure the vibration acceleration response of the structure.

[0018] (2) Perform wavelet transform on the noisy response to obtain wavelet decomposition coefficients, and set the wavelet coefficients caused by noise to zero.

[0019] (3) Perform inverse transform on the wavelet coefficients retained after processing to obtain the denoised vibration acceleration response.

[0020] Furthermore, in step three, the grey mathematical method is used to perform interval estimation on the denoised measurement response, and the midpoint and radius of the response interval are determined by the following steps.

[0021] (1) The gray mathematics method was used to statistically analyze the vibration acceleration response after denoising.

[0022] (2) Based on the mean and the standard deviation of uncertainty, the median and radius of the acceleration response interval are obtained.

[0023] Furthermore, in step four, the ill-posed problem in load identification is analyzed using Tikhonov regularization, thereby inverting the estimated range of the external load, which includes the following steps.

[0024] (1) The Tikhonov regularization is used to invert the interval median and radius of the load.

[0025] (2) Obtain the upper and lower limits of the load based on the median and radius of the load inversion interval.

[0026] Furthermore, in step five, the interval response reconstruction of the structure using the dynamic response reconstruction equation includes the following steps.

[0027] (1) The response reconstruction equation derived in step one is used to calculate the interval midpoint and radius of the response at the location to be reconstructed.

[0028] (2) Obtain the upper and lower bounds of the dynamic response at the location to be reconstructed based on the interval midpoint and radius of the response at the location to be reconstructed.

[0029] Compared with existing technologies, this invention has the following advantages: First, this method improves inversion accuracy from two aspects: denoising the response data and regularization. On the one hand, it denoises the measured response to reduce the influence of high-frequency noise; on the other hand, it uses regularization to analyze the ill-conditioned nature of the transfer matrix and obtain a stable solution. Then, by combining interval analysis to consider the uncertainty of the measured response, it performs step-by-step inversion and reconstruction of the interval median and interval radius of the external load and the structural dynamic response. Attached Figure Description

[0030] Figure 1 This is a step diagram of a load identification and structural response reconstruction method based on denoising regularization.

[0031] Figure 2 This is a site structural diagram of an example cantilever beam.

[0032] Figure 3 This is a diagram showing the layout of measurement points for an example cantilever beam.

[0033] Figure 4 This is a diagram showing the load identification results.

[0034] Figure 5 This is a diagram showing the reconstruction results of the vertical velocity at 8 nodes.

[0035] Figure 6 This is a diagram showing the reconstructed vertical velocity results for the 17 nodes.

[0036] Figure 7 This is a diagram showing the reconstruction results of the 8-node vertical acceleration.

[0037] Figure 8 This is a diagram showing the reconstruction results of the vertical acceleration at 17 nodes. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific examples.

[0039] This invention provides a load identification and structural response reconstruction method based on denoising regularization, such as... Figure 1 As shown, it includes the following steps.

[0040] Step 1: Derive the structural dynamic response and external load reconstruction equations based on the state-space model.

[0041] Step 2: Wavelet transform thresholding method is introduced to denoise the measurement response.

[0042] Step 3: Use grey mathematics to perform interval estimation on the denoised measurement response to determine the interval median and radius of the response.

[0043] Step four: Use Tikhonov regularization to analyze the ill-posed problem in load identification, thereby inverting the estimation range of the external load.

[0044] Step 5: Use the dynamic response reconstruction equation to reconstruct the interval response of the structure.

[0045] In step one, the derivation of the structural dynamic response and external load reconstruction equations based on the state-space model includes the following steps.

[0046] (1) Establish the state-space model of the structure based on the equation of motion of the structure under external load and its observed response.

[0047] (2) Convert the established state-space model into a discrete-time model.

[0048] (3) The discrete state-space model is transferred to the transfer matrix, and the reconstructed equations of response and external load are constructed iteratively.

[0049] The external load identification equation is The reconstruction equation of the structural dynamic response is: .

[0050] Among them, subscript m This represents the response vector at the measurement location; To measure the dynamic response at the measurement location; The transfer matrix at the measurable location; subscript r This indicates that the response vector at the location that needs to be reconstructed; For the dynamic response at the location that needs to be reconstructed; This is the transfer matrix at the location where reconstruction is needed.

[0051] In step two, the wavelet transform thresholding method is introduced to denoise the measurement response, which includes the following steps.

[0052] (1) Deploy sensors and measure uncertainties. n Group structure vibration acceleration response .

[0053] .

[0054] (2) Perform wavelet transform on the noisy response to obtain wavelet decomposition coefficients, and set the wavelet coefficients caused by noise to zero.

[0055] (3) Perform inverse transform on the wavelet coefficients retained after processing to obtain the denoised vibration acceleration response. .

[0056] .

[0057] In step three, the grey mathematical method is used to perform interval estimation on the denoised measurement response to determine the interval median of the response. With radius It includes the following steps.

[0058] (1) The gray mathematics method was used to statistically analyze the vibration acceleration response after denoising.

[0059] (2) Based on the mean and the standard deviation of uncertainty, the median and radius of the acceleration response interval are obtained.

[0060] .

[0061] Among them, superscript Represents a range; superscript Represents the median; and These are the lower and upper bounds of the vibration acceleration response after denoising, respectively.

[0062] In step four, the ill-posed problem in load identification is analyzed using Tikhonov regularization, thereby inverting the estimated range of the external load, which includes the following steps.

[0063] (1) The Tikhonov regularization is used to invert the interval median and radius of the load.

[0064] First, the GCV function is used to initially select the regularization parameters for the median and radius of the response.

[0065] To avoid the excitation recognition results from diverging, the regularization parameters for the median and radius of the response were redefined.

[0066] .

[0067] in, and These are the median and radius regularization parameters of the initially calculated response interval, respectively. and These are the final determined interval midpoint and radius regularization parameters, respectively.

[0068] Using regularization methods to target the midpoint of the load interval and radius Inversion was performed separately.

[0069] , .

[0070] Among them, superscript Represents conjugate transpose; It is an identity matrix.

[0071] (2) Obtain the upper and lower limits of the load based on the median and radius of the load inversion interval.

[0072] .

[0073] in, and These are the lower and upper bounds for identifying the load, respectively.

[0074] In step five, the interval response reconstruction of the structure is achieved using the dynamic response reconstruction equation, which includes the following steps.

[0075] (1) The interval median of the response at the location to be reconstructed is obtained by using the response reconstruction equation derived in step one. With radius Perform the calculation.

[0076] , .

[0077] (2) Obtain the upper and lower bounds of the dynamic response at the location to be reconstructed based on the midpoint and radius of the response at the location to be reconstructed.

[0078] .

[0079] In the formula, To reconstruct the upper boundary of the response, To reconstruct the lower boundary of the response.

[0080] Experimental examples.

[0081] The invention will be further illustrated below using the constructed cantilever beam test bench as an example. The cantilever beam is 2000mm long, 100mm wide, and 10mm thick, and is divided into 20 elements and 21 nodes. Only the Y-direction degree of freedom of each node is considered. The on-site structure of the example cantilever beam is as follows. Figure 2 As shown.

[0082] The cantilever beam is fixed at 2 nodes and simply supported at 20 nodes. A hammer load is applied vertically at node 9. Vertical acceleration signals at nodes 5, 11, and 14 are measured for external load identification and response reconstruction. Additional vertical acceleration signals at nodes 8 and 17 are collected and compared with the reconstructed signals. The specific measurement point arrangement is as follows. Figure 3 As shown. Figure 4 The identification results of the external load are presented. As shown in the figure, identifying the upper and lower bounds of the dynamic load at the impact point can basically encapsulate the actual measured load. The regularization parameter is: . Figure 5 and Figure 6 The results of the vertical velocity interval reconstruction for nodes 8 and 17 are shown, and compared with the actual velocity. Figure 7 and Figure 8 The reconstructed vertical acceleration intervals for nodes 8 and 17 are shown below, and compared with the measured acceleration. It can be seen that the reconstructed response intervals describe the time history of the dynamic response changes, and the actual response is mostly within the upper and lower boundaries. Therefore, the method of this invention can fully consider the uncertainty of the measured response and effectively identify external loads and reconstruct the structural response.

[0083] The above description is merely a specific embodiment of the present invention. The method proposed in this invention is not limited to the embodiments described in the specific embodiments. Any changes made to the technical solution of this invention that do not exceed the scope of the technical solution of this invention are all within the protection scope of this invention.

Claims

1. A load identification and structural response reconstruction method based on denoising regularization, characterized in that, Includes the following steps: Step 1: Derive the structural dynamic response and external load reconstruction equations based on the state-space model; Step 2: Introduce wavelet transform thresholding method to denoise the measurement response; Step 3: Use grey mathematics to perform interval estimation on the denoised measurement response to determine the interval median and radius of the response; Step four: Use Tikhonov regularization to analyze the ill-posed problem in load identification, thereby inverting the estimation range of the external load; Step 5: Use the dynamic response reconstruction equation to reconstruct the interval response of the structure; In step one, deriving the structural dynamic response and the reconstruction equations of external loads based on the state-space model includes the following steps: (1) Establish a state-space model based on the equation of motion of the structure under external loads and its observed response; (2) Convert the established state-space model into a discrete-time model; (3) Transform the discrete state-space model into the transfer matrix and iteratively construct the reconstructed equations of response and external load; In step three, the grey mathematical method is used to perform interval estimation on the denoised measurement response, and the determination of the interval median and radius of the response includes the following steps: (1) The grey mathematical method was used to statistically analyze the denoised vibration acceleration response; (2) Based on the mean and the standard deviation of uncertainty, obtain the median and radius of the acceleration response interval; In step four, the ill-posed problem in load identification is analyzed using Tikhonov regularization, thereby inverting the estimation interval of the external load, which includes the following steps: (1) Tikhonov regularization is used to invert the interval median and radius of the load; (2) Obtain the upper and lower bounds of the load based on the median and radius of the load inversion interval; In step five, the interval response reconstruction of the structure using the dynamic response reconstruction equation includes the following steps: (1) The response reconstruction equation derived in step one is used to calculate the interval midpoint and radius of the response at the location to be reconstructed; (2) Obtain the upper and lower bounds of the dynamic response at the location to be reconstructed based on the midpoint and radius of the response at the location to be reconstructed.

2. The load identification and structural response reconstruction method based on denoising regularization according to claim 1, characterized in that: In step two, the wavelet transform thresholding method is introduced to denoise the measurement response, including the following steps: (1) Arrange sensors and measure the vibration acceleration response of the structure; (2) Perform wavelet transform on the noisy response to obtain wavelet decomposition coefficients, and set the wavelet coefficients caused by noise to zero; (3) Perform inverse transform on the wavelet coefficients retained after processing to obtain the denoised vibration acceleration response.

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