A structural damage identification method considering mode shape curvature uncertainty

Abstract

The application discloses a structure damage identification method considering mode shape curvature uncertainty, first determines a possible damage area as a query area, measures a structure response under environmental excitation; identifies a modal shape of the query area and its uncertainty through a stochastic subspace method; quantifies the modal shape and its uncertainty, further extends the modal shape and its uncertainty to a modal shape curvature, and calculates a curvature difference and its uncertainty according to the modal shape curvature and its uncertainty before and after damage; calculates a variation coefficient of the curvature difference through the curvature difference and its uncertainty of the query area, combines a weight matrix concept to construct a weight, adjusts the weight of the curvature difference, and proposes a structure damage identification method considering the mode shape curvature uncertainty. The application further quantifies the parameter uncertainty to the damage uncertainty quantification, and integrates the uncertainty into the structure damage identification, and can more stably indicate the structure damage. The application can be used in vibration-based beam structure health monitoring and nondestructive testing.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring and is a method for identifying structural damage that takes into account the uncertainty of mode curvature. Background Technology

[0002] During use, engineering structures inevitably suffer structural damage due to factors such as their own materials or the external environment. To ensure the safety and economy of the structure during use, vibration tests are conducted regularly on structures that have reached a certain service life to check for damage, its location and extent, and to determine whether the structure's safety performance meets the requirements.

[0003] Existing damage identification methods can be broadly categorized into deterministic and uncertain methods. Deterministic methods often utilize the deterministic mapping relationship between structural characteristic parameters (frequency, mode shape, compliance, etc.) and structural damage for damage indication. However, real-world structures are subject to uncertainties such as noise, measurement errors, and model errors, leading to discrepancies between the obtained identification results and the actual damage. Therefore, when using modal parameters for damage identification, it is necessary to consider the uncertainties in the identification process. Currently, uncertainty analysis mostly focuses on structural parameters, with insufficient analysis of damage uncertainty. Furthermore, how to combine the quantified results with damage identification after obtaining structural uncertainties to reduce the interference caused by uncertainty remains a subject of in-depth research. Summary of the Invention

[0004] To address the shortcomings of existing damage indicators that consider uncertainties, this invention proposes a structural damage identification method that takes into account the uncertainty of modal curvature. The method quantifies the uncertainty of structural damage and incorporates the quantification results into the damage identification process, thereby improving the damage indication capability of the parameters.

[0005] To achieve the above objectives, the technical measures adopted by the present invention are as follows:

[0006] 1) Step 1: Determine the potential damage area as the query area and measure the response data under environmental vibration;

[0007] 2) Step Two: Modal mode identification and uncertainty quantification of the query region. Based on the measured response of the query region, the mode shapes and their uncertainties in the region are identified using the random subspace method;

[0008] 3) Step Three: Estimating the covariance of the modal curvature and curvature difference in the query region. Calculate the modal curvature and its uncertainty in the query region, and further calculate the curvature difference and its uncertainty based on the modal curvature and its uncertainty before and after the damage;

[0009] 4) Step Four: Construct damage identification indicators based on the weight matrix to identify the existence and location of damage. Calculate the coefficient of variation of the curvature difference and its covariance, construct weights using the obtained coefficient of variation, adjust the curvature difference, and identify structural damage.

[0010] In step 1, the potentially damaged query area is initially identified. Sensors are deployed in a contact or non-contact manner to measure the structural response under environmental vibration.

[0011] In step 2, based on the collected response data of the query region and matrix perturbation theory, the uncertainty of the parameters can be estimated, and the modal shapes of the query region can be identified through random subspace. And quantify its uncertainty .

[0012] In step 3, based on the obtained identification query region mode shape and its uncertainty, the process is further extended to the quantification of structural mode shape curvature and its uncertainty. The uncertainty of the mode shape curvature is:

[0013] ,

[0014] in and For the integrity of the structural position No. Mode shape and mode curvature, The modal curvature is calculated using the central difference method:

[0015]

[0016] in, This represents the distance between measuring points.

[0017] In step 3, vibration tests are performed on the structures in the state to be evaluated and the reference state. Based on the obtained modal curvatures and their uncertainties in the two states, the curvature difference and its covariance are calculated.

[0018]

[0019] in, Indicates the first The covariance of the curvature difference of the mode shapes The first part represents the damaged structure. The curvature difference of the query region for the mode shape curvature is calculated as follows:

[0020]

[0021] In step 4, during a single identification process, the coefficient of variation of the curvature difference of each mode shape is determined:

[0022]

[0023] in, This represents the coefficient of variation of the difference in mode curvature under noise.

[0024] In step 4, based on the parameter uncertainty analysis, different weights are assigned to different modes at each location:

[0025]

[0026] in, The weighting coefficients for single-mode parameters are taken into account under uncertainty.

[0027] In step 4, the obtained uncertainty is incorporated into the damage identification based on the constructed weighting coefficients. The weight of areas with greater uncertainty is reduced, and the adjusted damage index is as follows:

[0028]

[0029] in, The coefficient of variation of curvature difference represents the parameters after weight adjustment. It includes the standard deviation and mean of the parameters. When the mean identification has a certain accuracy, the damaged area has a stronger ability to resist uncertainty interference compared with the undamaged area due to the existence of damage information. The parameters are adjusted by using the coefficient of variation of curvature difference. The reliability of the identification process is reduced by the reciprocal of the coefficient of variation for areas with a large degree of uncertainty.

[0030] Beneficial effects: This invention quantifies the uncertainty of damage based on the uncertainty of parameters, obtaining the covariance and coefficient of variation of the curvature difference. Based on the concept of a weighted matrix for the covariance, the coefficient of variation is used to adjust the weights of the curvature difference, resulting in a curvature damage index optimized for uncertain locations. This method achieves good damage localization results even in noise interference, providing an effective new method for damage identification in beam structures. Attached Figure Description

[0031] Figure 1 Flowchart of the present invention

[0032] Figure 2. Schematic diagram of vibration test of simply supported beam bridge

[0033] Figure 3. The first two vibration modes of the simply supported beam and their uncertainty boundaries.

[0034] Figure 4 First two curvature difference and standard deviation plot

[0035] Figure 5 Comparison of damage identification between the first two order parameters Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0037] See Figure 1 The present invention provides a structural damage identification method considering the uncertainty of mode curvature, the specific steps of which are as follows:

[0038] Step 1: Identify the potentially damaged area as the query area and measure the response data under environmental vibration;

[0039] Step 2: Modal shape identification and uncertainty quantification of the query region. Based on the measured response of the query region, the mode shapes and their uncertainties in the region are identified using the random subspace method;

[0040] Step 3: Estimate the covariance of the modal curvature and curvature difference of the query region. Calculate the modal curvature and its uncertainty of the query region, and further calculate the curvature difference and its uncertainty based on the modal curvature and its uncertainty before and after the damage;

[0041] Step 4: Construct damage identification indicators based on the weight matrix to identify the existence and location of damage. Calculate the coefficient of variation of the curvature difference and its covariance, construct weights using the obtained coefficient of variation, adjust the curvature difference, and identify structural damage.

[0042] In step 1, the potentially damaged query area is initially identified. Sensors are deployed in a contact or non-contact manner to measure the structural response under environmental vibration.

[0043] In step 2, based on the collected response data, the discrete-time random spatial state model of the query region is as follows:

[0044]

[0045] in Indicates a point in time The measurement vector, It is the system state vector. and It is the system matrix. In the random subspace, let... and Let be a sequence of white noise with an expected value of zero, representing process noise and measurement noise, respectively. Assume the number of reference sensors is . The output covariance matrix of the query region can be displayed as follows:

[0046]

[0047] in This indicates the corresponding measurement value from the reference sensor.

[0048] In step 2, based on the output covariance matrix of the query region, a block matrix of the corresponding region is constructed and feature vectors are identified:

[0049]

[0050] in By outputting the covariance matrix The exported block matrix, for Singular value decomposition is performed to obtain an extended observability matrix, which is then used to identify the system matrix. and .

[0051] In step 2, the obtained system matrix Characteristic equation: It can identify the modal frequencies of the structure. and damping eigenvectors Combined with system matrix You can obtain the modal shapes of the query area:

[0052]

[0053] in For position No. Mode shape The maximum normalized mode shape is obtained by identifying the mode shape: The uncertainty of the normalized mode shape at the maximum value is:

[0054]

[0055] in For the covariance of the mode shape, It is the covariance of the block matrix. yes Relative to the sensitivity of the system matrix, and These are system matrices and Sensitivity relative to block matrices.

[0056] Taking a simply supported beam as an example, the vibration test model for a simply supported beam is shown below. Figure 2 Damage to the structure is simulated by reducing the stiffness of local elements, and the damage location is... Figure 2 At the location shown, Gaussian white noise is applied to the measured response. The mode shape and its uncertainty of the state to be evaluated are as follows: Figure 3 .

[0057] In step 3, based on the obtained identification query region mode shape and its uncertainty, the process is further extended to the quantification of structural mode shape curvature and its uncertainty. The uncertainty of the mode shape curvature is:

[0058] ,

[0059] in and For the integrity of the structural position No. Mode shape and mode curvature, The modal curvature is calculated using the central difference method:

[0060]

[0061] in, This represents the distance between measuring points.

[0062] In step 3, vibration tests are performed on the structures in the state to be evaluated and the reference state. Based on the obtained modal curvatures and their uncertainties in the two states, the curvature difference and its covariance are calculated.

[0063]

[0064] in, Indicates the first The covariance of the curvature difference of the mode shapes The first part represents the damaged structure. The curvature difference of the query region for the mode shape curvature is calculated as follows:

[0065]

[0066] The difference in curvature between the first two orders and its uncertainty are visible. Figure 4 .

[0067] In step 4, during a single identification process, the coefficient of variation of the curvature difference of each mode shape is determined:

[0068]

[0069] in, It represents the coefficient of variation of the difference in mode curvature under noise.

[0070] In step 4, weighting coefficients are constructed based on the coefficient of variation of the curvature difference, and the parameters of the query region are adjusted accordingly.

[0071]

[0072] in, To account for the weighting coefficients of single-modal parameters under uncertainty, the parameters of the query region are adjusted and a damage identification index is constructed.

[0073] In step 4, the obtained uncertainty is incorporated into the damage identification based on the constructed weighting coefficients. The weight of areas with greater uncertainty is reduced, and the adjusted damage index is as follows:

[0074]

[0075] in, This represents the parameters after weight adjustment. The identification results of the first two curvature differences before and after adjustment are shown in [link to documentation]. Figure 5 .

[0076] The above describes how the present invention constructs weights based on the uncertainty of curvature difference, corrects the curvature difference of the query region, and constructs a damage index. However, the present invention is not limited to the above embodiments. All equivalent changes or modifications made according to the spirit and essence of the present invention should be covered within the protection scope of the present invention.

Claims

1. A structural damage identification method considering the uncertainty of modal curvature, characterized in that... Includes the following steps: 1) Step 1: Determine the potential damage area as the query area and measure the response data under environmental vibration; 2) Step Two: Modal mode identification and uncertainty quantification of the query region. Based on the measured response of the query region, the mode shape and its uncertainty in the region are identified using the random subspace method. 3) Step 3: Estimate the covariance of the modal curvature and curvature difference of the query area, calculate the modal curvature and its uncertainty of the query area, and further calculate the location based on the modal curvature and its uncertainty before and after the damage. First Step mode curvature difference and its uncertainty ; 4) Step Four: Construct damage identification indicators based on the weight matrix to identify the existence and location of damage. In a single identification process, based on the location... First Step mode curvature difference Its covariance determines the coefficient of variation of the curvature difference of each mode: in, For position First Difference in curvature of mode shapes Indicates position under noise First The coefficient of variation of the curvature difference of the mode shapes; based on parametric uncertainty analysis, different weights are assigned to different modes at each location, with the weighting coefficients being: in, For position First The single-mode parameter weighting coefficients are determined after considering uncertainties in the first-order modal analysis. Based on the constructed weighting coefficients, the obtained uncertainties are incorporated into the damage identification process, and the weights of locations with significant uncertainties are reduced. The adjusted damage identification index is as follows: in, For position First The curvature difference damage identification index, adjusted by uncertainty weights for the first mode, is used to identify whether structural damage exists and its location.

2. The structural damage identification method considering mode curvature uncertainty according to claim 1, characterized in that: In step 1, the potentially damaged query area is initially identified. Sensors are deployed in a contact or non-contact manner to measure the structural response under environmental vibration.

3. The structural damage identification method considering mode curvature uncertainty according to claim 1, characterized in that: In step 2, based on the collected response data of the query region and matrix perturbation theory, the uncertainty of the parameters is estimated, and the modal shapes of the query region are identified through a random subspace. And quantify its uncertainty .

4. The structural damage identification method considering mode curvature uncertainty according to claim 1, characterized in that: In step 3, based on the obtained identification query region mode shape and its uncertainty, the process is further extended to the quantification of structural mode shape curvature and its uncertainty. The uncertainty of the mode shape curvature is: ， in, and For the integrity of the structural position No. Mode shape and mode curvature, , The central difference method is used to calculate the mode shape curvature to determine the spacing between measuring points. .

5. The structural damage identification method considering mode curvature uncertainty according to claim 1, characterized in that: In step 3, vibration tests are performed on the structures in the state to be evaluated and the reference state. Based on the obtained modal curvatures and their uncertainties in the two states, the curvature difference and its covariance are calculated. in, Indicates the first The covariance of the curvature difference of the mode shapes The first part represents the damaged structure. The curvature difference of the query region for the mode shape curvature is calculated as follows: .

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