A structure damage identification method based on equivalent modal shape derivative
By constructing equivalent mode shapes and their derivatives, and combining frequency response function integration and the strategy of minimizing average curvature, noise-resistant equivalent mode shapes are generated, solving the problems of noise interference and unknown location in existing technologies, and realizing high-precision structural damage identification and location.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-09
- Publication Date
- 2026-04-07
AI Technical Summary
Existing non-destructive testing methods are difficult to accurately identify early structural damage in high-noise environments and require prior knowledge of the damage location, which cannot meet the needs of practical applications.
By constructing equivalent mode shapes and their derivatives, and combining frequency response function integrals and the strategy of minimizing average curvature, noise-resistant equivalent mode shapes are generated, and the damage index FEMSDi is calculated to achieve accurate damage identification.
It can accurately identify structural damage in high-noise environments without prior knowledge of the damage location, and can locate multiple damages simultaneously, adapting to complex damage scenarios.
Smart Images
Figure CN120369611B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of structural health monitoring, and relates to a structural damage identification method, in particular to a structural damage identification method based on equivalent modal shape derivatives. BACKGROUND
[0002] During service, structures are inevitably subjected to various complex loads, such as fatigue loads, low-energy impacts, high pressures, etc. These special external forces may cause internal damage. These micro-damages are often difficult to detect by visual inspection at the initial stage, but they will gradually accumulate over time and with the increase in the number of uses. If these damages are not detected and handled in a timely manner, they may cause sudden failure of the structure, seriously threatening the safety and reliability of the structure.
[0003] In order to effectively detect damage, people have developed various non-destructive testing (NDT) methods. For example, X-ray detection technology, C-scan technology, guided wave technology and thermal imaging technology, etc. Although these technologies have achieved certain results in their respective application scenarios, they generally have some limitations. On the one hand, these methods usually require prior knowledge of the approximate area of the damage, which is often difficult to meet in actual applications, because in many cases the location of the damage is unknown. On the other hand, most of these detection techniques require the measured object to be removed from the working state for offline detection, which not only increases the detection cost and time, but also may affect the normal operation of the equipment. Unlike traditional non-destructive testing methods, vibration-based damage identification methods have unique advantages. This method does not require prior knowledge of the location of the damage, but rather identifies damage by analyzing changes in modal parameters obtained from in-situ vibration testing. Over the past few decades, researchers have developed a variety of damage identification methods based on changes in modal parameters. However, vibration-based damage identification methods still face many challenges in practical applications, with measurement noise being a key issue. In actual measurement processes, experimental data will inevitably be contaminated by noise due to factors such as test environment and equipment precision. Early damage usually only causes minor changes in raw data, which are easily masked by noise, making it difficult to accurately distinguish between damage-induced changes and noise-induced fluctuations. SUMMARY
[0004] The purpose of the present application is to provide a structural damage identification method based on equivalent modal shape derivatives with excellent anti-noise performance and without the need for prior knowledge of the location of the damage. This method obtains the equivalent modal shape and its derivative of the structure by integrating the frequency response function, constructs a damage index to quantify the difference between the equivalent modal shape and its derivative before and after the damage of the structure, and then realizes accurate identification of the damage.
[0005] The purpose of the present application is achieved by the following technical solutions:
[0006] A structure damage identification method based on equivalent modal mode derivative, comprising the following steps:
[0007] Step 1, generation of equivalent modal mode:
[0008] Step 1-1, obtaining the natural frequency of the structure by modal test;
[0009] Step 1-2, at each natural frequency, select a symmetric integral bandwidth Δω;
[0010] Step 1-3, the FRFs amplitude A i (ω) of each measuring point i is integrated in the frequency band [ω k -Δω,ω k +Δω] to obtain the equivalent amplitude
[0011]
[0012] Wherein, n is the number of measuring points, ω k is the kth natural frequency;
[0013] Step 1-4, divide the equivalent amplitude of each node by the maximum equivalent amplitude to obtain the normalized equivalent modal displacement
[0014]
[0015] Wherein, is the maximum equivalent amplitude of all nodes under the current frequency band;
[0016] Step 1-5, by continuously adjusting the frequency range Δω, calculate the average curvature of equivalent modal mode under different Δω
[0017]
[0018] Step 1-6, determine the optimal integral bandwidth by minimizing the average curvature of equivalent modal mode;
[0019] Step 2, damage index parameter acquisition and calculation:
[0020] Step 2-1, based on the equivalent modal mode Calculate its derivative, the specific steps are as follows:
[0021] For the equivalent modal slope, it is calculated by numerical difference method, for the discrete equivalent modal mode data points (i=1,2,...,n), the equivalent modal slope at the ith point Approximately:
[0022]
[0023] Wherein:
[0024]
[0025] l x and l y is the distance between adjacent nodes in the x, y direction, is the first-order difference of the equivalent modal shape in the x direction, is the first-order difference of the equivalent modal shape in the y direction;
[0026] For the equivalent modal curvature, it is calculated by the numerical difference method, and the equivalent modal curvature at the i th point is Approximately:
[0027]
[0028] Wherein:
[0029]
[0030] is the second-order difference of the equivalent modal shape in the x direction, is the second-order difference of the equivalent modal shape in the y direction;
[0031] Step 2-2, combine the equivalent modal shape derivative information of multiple modes, and calculate the damage index FEMSD by the following formula i :
[0032]
[0033] Wherein:
[0034]
[0035] is the equivalent modal curvature change amount, is the equivalent modal slope change amount, is the equivalent modal shape change amount, N is the number of modes participating in the calculation, h represents the parameter before the structure is damaged, and d represents the parameter after the structure is damaged;
[0036] Step 2-3, in order to eliminate the influence of dimension, the damage index is normalized:
[0037]
[0038] Wherein, nFEMSD i is the normalized damage index, μFEMSD mean(FEMSD FEMSD ) is the mean of damage index;
[0039] Step 3, damage area determination:
[0040] Step 3-1, set dynamic threshold δ = 2·mean(FEMSD i ) / max(FEMSD i ));
[0041] Step 3-2, compare the calculated normalized damage index nFEMSD i with the threshold value, traverse all nodes on the structure, if the nFEMSD i of a node is greater than or equal to δ, then determine that the area where the node is located is a damage area.
[0042] Compared with the prior art, the present application has the following advantages:
[0043] 1. Compared with the traditional damage identification method based on modal derivative, the present application performs well in high noise environment. This is because the equivalent modal shape is constructed by integrating the frequency response function, and the subsequent damage index calculation process fully considers noise suppression and signal feature extraction, effectively reducing the interference of noise on the damage identification result.
[0044] 2. The present application can simultaneously locate and identify multiple damages, and the damage index is constructed by comprehensively utilizing the derivative information of the equivalent modal shape of multiple modes, fully capturing the change characteristics of the modal parameters of the structure under complex damage conditions, effectively meeting the detection needs of complex damage scenarios. BRIEF DESCRIPTION OF DRAWINGS
[0045] Figure 1 It is a flow chart of structure damage identification based on equivalent modal shape derivative;
[0046] Figure 2 It is a schematic diagram of measuring point arrangement of the embodiment;
[0047] Figure 3 It is a schematic diagram of constructing equivalent modal shape by integrating frequency response function;
[0048] Figure 4 It is a schematic diagram of damage identification result. DETAILED DESCRIPTION
[0049] The technical solutions of the present application will be further described below in conjunction with the drawings, but are not limited thereto, any modification or equivalent replacement to the technical solutions of the present application without departing from the spirit and scope of the present application shall be covered in the protection scope of the present application.
[0050] The application provides a structure damage identification method based on equivalent modal shape derivative, and the method provides an equivalent modal shape derivative method based on integral frequency response function (FRFs), noise is suppressed by optimizing frequency band integration, and noise-resistant equivalent modal shapes are generated, so that high-precision damage identification is realized, and the method specifically comprises the following steps:
[0051] Step 1, generation of equivalent modal shape:
[0052] Natural frequencies (such as ω1, ω2,..., ωn) of the structure are obtained through modal testing. n At each natural frequency, such as the kth natural frequency ωk, a symmetrical integral bandwidth Δω is selected. The FRFs amplitude A k (ω) of each measurement point i is integrated in the frequency band [ωk-Δω, ωk+Δω] to obtain the equivalent amplitude i k k
[0053]
[0054] Wherein, n is the number of measurement points.
[0055] The integral operation eliminates random noise by statistical averaging and retains the true vibration response characteristics. The equivalent amplitude of each node is divided by the maximum equivalent amplitude to obtain the normalized equivalent modal displacement
[0056]
[0057] Wherein, is the maximum equivalent amplitude of all nodes under the current frequency band.
[0058] In order to accurately determine the optimal integral frequency band, the strategy of minimizing the average curvature of the equivalent modal shape is adopted. The curvature of the equivalent modal shape can reflect the degree of change of its shape, the smaller the average curvature, the smaller the roughness of the equivalent modal shape, and the closer it is to the ideal modal shape and the less it is affected by noise. By continuously adjusting the width Δω of the frequency band range, the average curvature of the equivalent modal shape under different Δω is calculated. The curvature of the equivalent modal shape can be calculated by its second-order difference, and for discrete equivalent modal shape data points The curvature at the ith point is approximately:
[0059]
[0060] Wherein:
[0061]
[0062] l x and ly The distances between adjacent nodes in the x and y directions are... The second-order difference of the equivalent mode shape in the x-direction. This represents the second-order difference of the equivalent mode shape in the y-direction. Mean curvature. This is the average curvature of all points:
[0063]
[0064] The optimal integration bandwidth is determined by minimizing the average curvature of the equivalent modal shapes. In this process, the integration bandwidth is continuously adjusted and the average curvature of the equivalent modal shapes is calculated. The integration bandwidth corresponding to the minimum average curvature is the optimal value. This method effectively suppresses noise while ensuring a high degree of similarity between the equivalent and ideal modal shapes, providing a reliable foundation for accurate calculation of damage indices.
[0065] Step 2: Obtaining and Calculating Damage Index Parameters:
[0066] Based on the constructed equivalent mode shape Calculate its derivative. For the equivalent modal slope (first derivative), it can be calculated using numerical difference methods, for example, for discrete equivalent modal shape data points. (i = 1, 2, ..., n), the equivalent modal slope at the i-th point Approximately:
[0067]
[0068] in:
[0069]
[0070] This is the first-order difference of the equivalent mode shape in the x-direction. This is the first-order difference of the equivalent mode shape in the y-direction.
[0071] For the equivalent modal curvature (second derivative), the equivalent modal curvature at the i-th point is also obtained using the numerical difference method. Approximately:
[0072]
[0073] in:
[0074]
[0075] These derivative information can more sensitively reflect changes in modal parameters caused by structural damage. By combining the equivalent modal shape derivative information of multiple modes, the damage index FEMSD is calculated using a specific formula. i:
[0076]
[0077] in:
[0078]
[0079]
[0080] This represents the equivalent modal curvature change. This represents the change in the slope of the equivalent mode. The formula represents the equivalent modal shape change, where N is the number of modes involved in the calculation, h represents the parameters before structural damage, and d represents the parameters after structural damage. This formula comprehensively considers the changes in the equivalent modal shape derivatives under multiple modes, fully capturing the damage characteristics.
[0081] To eliminate the influence of dimensions, the damage index is normalized:
[0082]
[0083] Among them, nFEMSD i μ is a normalized damage index. FEMSD σ is the mean of the damage index. FEMSD This represents the standard deviation of the damage index. Normalization makes the damage indices comparable under different working conditions, improving the accuracy and versatility of damage identification.
[0084] Step 3, Determining the Damaged Area:
[0085] Set the dynamic threshold δ = 2·mean(FEMSD) i ) / max(FEMSD i The normalized damage index nFEMSD obtained from the calculation is then used. i Compare with a threshold. Traverse all nodes in the structure; if a node's nFEMSD... i If the value is greater than or equal to δ, the region where the node is located is determined to be a damaged area. This method enables precise location of damage. Even in complex scenarios where multiple damages coexist, this method can effectively identify them, accurately determining the number and location of damages by analyzing the distribution and magnitude of damage indicators.
[0086] Example:
[0087] This embodiment uses a plain weave composite material board as an example to illustrate the specific implementation process of the present invention in detail. The implementation process is as follows: Figure 1 As shown.
[0088] In this embodiment, the dimensions of the plain weave composite material sheet are 150mm × 100mm × 4.4mm. To simulate potential damage during actual use, the specimen is subjected to an optimized high-speed ice impact test, which introduces delamination damage without completely penetrating the sheet.
[0089] A plain-weave composite panel was suspended from a steel frame using flexible ropes to simulate free boundary conditions. The suspension status of the specimen was checked to ensure it was in a stable, stationary state (without initial swaying). A Philips SPA5270W loudspeaker was used as the excitation source. This loudspeaker is capable of generating stable acoustic excitation within the frequency range of 20Hz-20,000Hz. With its frequency accuracy set to 0.1Hz, the emitted sound waves acted on the plain-weave composite panel, exciting the specimen to vibrate. A Polytec PSV-500-3D scanning laser Doppler vibrometer was used to accurately collect key modal parameters such as the specimen's natural frequencies, mode shapes, and frequency response functions (FRFs). Based on the specimen's structural characteristics and the distribution of areas prone to damage, 88 measurement points were strategically placed on the specimen surface. Figure 2 As shown in the figure. Eleven points are evenly distributed along the length direction and eight points are evenly distributed along the width direction to ensure that the possible damage area can be fully covered and sufficient vibration response data can be obtained.
[0090] With the specimen in an undamaged state, the excitation and measurement systems were activated for the initial modal test. The excitation system excited the specimen according to a pre-set frequency range and scanning pattern, while the measurement system sequentially collected vibration response data at each measurement point, acquiring modal data such as FRFs under the undamaged state. After completing the undamaged state test, the specimen underwent a high-speed ice impact test to introduce delamination damage. The excitation and measurement systems were then activated again, and modal data under the damaged state were collected under the exact same excitation conditions and measurement environment as the undamaged test.
[0091] In-depth analysis of the acquired modal data under undamaged conditions yielded the equivalent modal shapes. Where h represents the healthy state and k represents the equivalent mode shape corresponding to the k-th natural frequency.
[0092] Initially select a symmetrical integration bandwidth Δω, for example, starting with 0.2Hz. Calculate the FRF amplitude A at each measurement point i. i (ω) in the frequency band [ω k -Δω,ω k Integrating within [+Δω], we obtain the equivalent amplitude:
[0093]
[0094] Where n is the number of measurement points.
[0095] The integral operation eliminates random noise through statistical averaging, preserving the true vibration response characteristics. Dividing the equivalent amplitude of each node by the maximum equivalent amplitude yields the normalized equivalent modal displacement:
[0096]
[0097] in, This represents the maximum equivalent amplitude of all nodes within the current frequency band.
[0098] First-order equivalent mode shape such as Figure 3 As shown.
[0099] To accurately determine the optimal integration frequency band, a strategy of minimizing the average curvature of the equivalent modal shape is adopted. The curvature of the equivalent modal shape reflects the degree of change in its shape; the smaller the average curvature, the closer the equivalent modal shape is to the true mode shape.
[0100] The curvature of the equivalent mode shape can be approximated by its second-order difference for discrete equivalent mode shape data points. (i = 1, 2, ..., n), the curvature at the i-th point is approximately:
[0101]
[0102] in:
[0103]
[0104] l x and l y The distances between adjacent nodes in the x and y directions are... The second-order difference of the equivalent mode shape in the x-direction. This represents the second-order difference of the equivalent mode shape in the y-direction. The mean curvature is then the average of the curvatures at all points.
[0105]
[0106] By continuously adjusting the bandwidth Δω of the frequency band, the average curvature of the equivalent mode shape under different Δω values is calculated. When the average curvature reaches its minimum value, the Δω at this point is determined to be the optimal integration bandwidth. In the test of this plain weave composite material plate, the optimal integration bandwidth was determined to be 20Hz for the first natural frequency.
[0107] Similarly, by conducting in-depth analysis of the acquired modal data under damaged conditions, equivalent modal shapes are obtained. Where d represents the damage state, and k represents the equivalent mode shape corresponding to the k-th natural frequency.
[0108] Based on the obtained equivalent mode shapes, the equivalent mode slopes and curvatures are calculated using the numerical difference method based on the discrete equivalent mode shape data points:
[0109]
[0110] in, This is the first-order difference of the equivalent mode shape in the x-direction. This is the first-order difference of the equivalent mode shape in the y-direction.
[0111] By performing the above calculations at each node, the slope φ' of the mode shape of the entire plate under both healthy and damaged conditions can be obtained. (i,k) and curvature φ″ (i,k) :
[0112]
[0113]
[0114] h represents the parameters before structural damage, and d represents the parameters after structural damage.
[0115] Combining the equivalent modal shape derivative information of multiple modes (e.g., selecting the first two modes, N=2), the damage index is calculated according to the formula:
[0116]
[0117] in:
[0118]
[0119] After the calculation is completed, the damage index is normalized:
[0120]
[0121] Where, μ FEMSD σ is the mean of the damage index. FEMSD This represents the standard deviation of the damage index.
[0122] Set the dynamic threshold δ = 2·mean(FEMSD) i ) / max(FEMSD i Iterate through the 54 nodes on the plain weave composite material plate and set the nFEMSD of each node. i Compare each value with the threshold δ one by one. If the nFEMSD of a certain node... iIf the value is greater than or equal to δ, the area where the node is located is determined to be a damaged area. After all nodes have been assessed, a damage area distribution map is drawn based on the assessment results to visually display the location and extent of the damage on the board. In this embodiment, the calculated δ is 0.286, and the damage identification result is as follows: Figure 4 As shown.
Claims
1. A structural damage identification method based on equivalent modal derivatives, characterized in that... The method includes the following steps: Step 1: Generation of equivalent mode shapes: Step 1-1: Obtain the natural frequencies of the structure through modal testing; Step 1-2: At each natural frequency, select a symmetrical integration bandwidth. ; Steps 1-3: For each measurement point FRFs amplitude In frequency band Integrating within the range yields the equivalent amplitude. : in, The number of measurement points. For the first One natural frequency; Steps 1-4: Divide the equivalent amplitude of each node by the maximum equivalent amplitude to obtain the normalized equivalent modal displacement. : in, This represents the maximum equivalent amplitude of all nodes in the current frequency band. Steps 1-5: By continuously adjusting the frequency band range Calculate different Mean curvature of the lower equivalent mode shape : Steps 1-6: Determine the optimal integration bandwidth by minimizing the average curvature of the equivalent modal shape; Step 2: Obtaining and Calculating Damage Index Parameters: Step 2-1: Based on the constructed equivalent mode shape Calculate its derivative; Step 2-2: Calculate the damage index by combining the equivalent modal shape derivative information of multiple modes. The damage index The calculation formula is: in: This represents the equivalent modal curvature change. This represents the change in the slope of the equivalent mode. This represents the change in equivalent mode shape. The number of modes involved in the calculation. The representative parameter is the parameter before structural damage. The representative parameter is the parameter after structural damage; Steps 2-3: To eliminate the influence of dimensions, the damage index is normalized. Step 3, Determining the Damaged Area: Step 3-1: Set dynamic threshold ); Step 3-2: Calculate the normalized damage index Compare with a threshold, traverse all nodes in the structure, and if a node's... Greater than or equal to If so, the area where the node is located is determined to be a damaged area.
2. The structural damage identification method based on equivalent modal derivatives according to claim 1, characterized in that... The specific steps of step 2-1 are as follows: The equivalent modal slope is calculated using the numerical difference method for discrete equivalent modal data points. , No. Equivalent modal slope at each point Approximately: in: and for , The distance between adjacent nodes in the direction. For equivalent mode shapes in First-order difference in direction, For equivalent mode shapes in First-order difference in direction; The equivalent modal curvature is calculated using the numerical difference method. Equivalent modal curvature at each point Approximately: in: For equivalent mode shapes in Second-order difference in direction, For equivalent mode shapes in Second-order difference in direction.
3. The structural damage identification method based on equivalent modal derivatives according to claim 1, characterized in that... The normalized damage index The calculation formula is: in, The mean of the damage index. This represents the standard deviation of the damage index.