Reconstruction Method of Impact Load History at Random Positions on Plate Surface Based on Improved Regularization Method

Abstract

The present invention provides a method for reconstructing the impact load history at random positions on the plate surface based on an improved regularization method, including: Step 1, fixing the plate structure to be monitored and arranging an optical fiber FBG sensing network; Step 2, determining four measurement points on the plate surface, conducting an impact measurement experiment, and obtaining a frequency response matrix regarding the measurement points; Step 3, calculating the inverse square value of the distance from the measurement points to the impact position as the weight coefficient; Step 4, constructing an influence matrix; Step 5, determining the optimal regularization parameter and obtaining the improved regularized solution of each measurement point regarding the impact load; Step 6, obtaining the improved regularized weighted solution of the impact load by weighting the weight coefficient of the measurement point and the corresponding improved regularized solution, so as to realize the reconstruction of the impact load history at random positions on the plate surface. The present invention combines the improved regularization technology with the optical fiber Bragg grating sensor, and reconstructs the impact load history by weighting the improved regularized solutions of the measurement points, which is simple and convenient and has a wide range of applicability.

Description

Technical Field

[0001] The present invention belongs to the field of impact load identification in structural health monitoring, and particularly relates to a method for reconstructing the impact load history at random positions on the plate surface based on an improved regularization method. Background Art

[0002] In the field of structural health monitoring technology, there is a strong correlation between the damage mode and degree caused by impact loads on a structure and the magnitude or energy of the impact loads. By accurately identifying the magnitude or energy of the impact loads acting on the surface of a structure through the impact load strain response signals of fiber Bragg grating sensors, it can be used to evaluate the health status and damage degree of composite material structures.

[0003] Currently, extensive research has been carried out on the reconstruction of the impact load history of structures. Ghajari et al. studied the impacts of different impact objects at different impact positions, and decomposed the differences of different impact objects through the impact response frequency domain signals to achieve the reconstruction of the impact load history. Xu used the method of least squares support vector machines to identify the magnitude of impact loads. Atobe et al. used acceleration sensors to obtain impact response signals and proposed an impact load identification method based on the experimental transfer matrix to solve the impact load time history of carbon fiber composite structures.

[0004] Some of the above methods require a large amount of experimental data for system training, and the process is cumbersome; some cannot reconstruct the impact loads at random positions, and the applicable range is relatively narrow. Therefore, in view of the deficiencies of the current methods for reconstructing the impact load history of plate structures, it is necessary to study a new method that does not require system training, is simple, fast, and highly practical. Summary of the Invention

[0005] Object of the Invention: The technical problem to be solved by the present invention is to provide a method for reconstructing the impact load history at random positions on the plate surface based on an improved regularization method in view of the deficiencies of the prior art, including the following steps:

[0006] Step 1: Fix the plate structure to be monitored and arrange fiber Bragg grating sensors (FBG) to form a sensing network.

[0007] Step 2: Determine four measurement points on the plate surface, and conduct impact measurement experiments on the measurement points with an impact force hammer in advance. Obtain the frequency response matrix of the measurement points according to the impact excitation signal and the impact response signal in the impact measurement experiment.

[0008] Step 3: For the impact load at a randomly determined position on the plate surface, calculate the reciprocal of the square of the distance from the measurement point to the impact position as the weight coefficient.

[0009] Step 4: Substitute the response signals of the fiber optic FBG sensing network in the impact load into each frequency response matrix, and use the improved regularization method to introduce a filtering operator to construct an influence matrix;

[0010] Step 5: Use the generalized cross-validation method to determine the optimal regularization parameter, and obtain the improved regularized solution of each measurement point with respect to the impact load;

[0011] Step 6: Weight the weight coefficient and the corresponding improved regularized solution to obtain the improved regularized weighted solution of the impact load, and realize the reconstruction of the impact load history at random positions on the plate surface.

[0012] Step 1 includes: There is a square strain monitoring area inside the fixed plate with side length l, and the sensing network on the plate includes 4 fiber Bragg grating sensors;

[0013] The 4 fiber Bragg grating sensors are numbered FBGi, i ∈ (1, 2, 3, 4). The 4 fiber Bragg grating sensors are respectively arranged at the four vertices of the square strain monitoring area. A rectangular coordinate system is established with the center of the square strain monitoring area as the origin O, and the position coordinates of FBGi are defined as (a i , b i );

[0014] In Step 1, the pasting directions of the fiber Bragg grating sensors are all parallel to the X direction of the rectangular coordinate system on the plate surface to obtain the strain in a single direction on the surface of the plate structure, thereby forming a sensing network.

[0015] Step 2 includes: Determine the midpoint between the fiber Bragg grating sensor FBGi and the origin O as the measurement point i on the plate surface, then the coordinates of the measurement point i are

[0016] Previously, use an impact force hammer to conduct an impact measurement experiment at the measurement point i to determine the frequency response matrix Hi corresponding to each measurement point i;

[0017] When reconstructing the impact load history using two or more fiber Bragg grating sensors, define the impact load signal measured by the impact force hammer as F;

[0018] The impact response signal measured by the fiber Bragg grating sensor FBGi is Y i , then the impact response signal Y of the sensing network is:

[0019] Y = [Y1, Y2, Y3, Y4] T (1)

[0020] When the impact position is the measurement point i, the frequency response matrix Hi obtained from a single impact measurement experiment is expressed as:

[0021] Hi = YF (2)

[0022] Perform more than N impact measurement experiments on measurement point i, and average the frequency response matrices measured in each experiment to obtain the frequency response matrix Hi corresponding to measurement point i;

[0023] Set the frequency response matrix Hi as a P×Q matrix, and P≥Q, where the number of rows P is determined by the dimension of the structural response vector, and the number of columns Q is determined by the dimension of the load vector to be identified;

[0024] The singular value decomposition of the frequency response matrix Hi is expressed as:

[0025] Hi = USV T (3)

[0026] where U = (u1, u2, …, u P ), V = (v1, v2, …, v Q ) are orthogonal matrices composed of left singular value vectors and right singular value vectors respectively, u P represents the Pth left singular value vector, v Q represents the Qth right singular value vector, S is a diagonal matrix composed of non - negative singular values σ i , and T is the matrix transpose symbol.

[0027] Step 3 includes: For the impact load F t randomly determined at a position on the plate surface, let the impact position be A with coordinates (x, y), then the distance L Ai from measurement point i to position A is:

[0028]

[0029] Define the reciprocal of the square of the distance from measurement point i to the impact position A as the weight coefficient W i :

[0030]

[0031] Step 4 includes: Define the response signal of the impact load F t measured by the sensor network as Y Z , combine the singular value decomposition form of the frequency response matrix Hi with the Moore - Penrose generalized inverse to find the direct least - squares solution F m of the impact load as:

[0032]

[0033] where Q0 is the number of singular values greater than zero in the frequency response matrix Hi, so Q0≤P, Q0≤Q; v j is the right singular value vector, u jis the left singular value vector, σ j is a non-negative singular value;

[0034] Introduce improved regularization technology to solve the ill-posed problem and define the filter operator for:

[0035]

[0036] Where λ is the regularization parameter and satisfies λ>0, and γ is the filter operator parameter;

[0037] The filter operator Combined with the frequency response matrix Hi, the influence matrix H is constructed i # :

[0038]

[0039] H i # The role of is to map the input signal of the original problem into an improved regularized solution.

[0040] Step 5 includes: using the generalized cross-validation method to find the optimal regularization parameter, which is expressed as:

[0041]

[0042] Where I is the identity matrix; tr(I-HH # ) is the matrix (I-HH # ), indicating the trace of the matrix (I-HH # ) is the sum of the diagonal elements; in formula (9), λ is the optimal regularization parameter when the function G(λ) is the minimum value;

[0043] After finding the optimal regularization parameter λ, equation (6) and equation (8) are combined to obtain the impact load F t Corresponding to the frequency response matrix Hi, the improved regularization solution F i :

[0044]

[0045] In the impact measurement experiment of step 2, there are four measurement points in total. Each measurement point i corresponds to a frequency response matrix Hi. Therefore, the impact load F is obtained by formula (10): t Four improved regularization solutions, each improved regularization solution F i All correspond to the measurement point i.

[0046] Step 6 includes: i And the corresponding weight coefficient W i The impact load F can be reconstructed by superposition. tImproved Regularized Weighted Solution F r :

[0047]

[0048] Improved Regularized Weighted Solution F r , which is the finally obtained impact load F t 's history reconstruction solution, thereby realizing the impact load history reconstruction at random positions on the plate surface.

[0049] The present invention also provides a storage medium storing a computer program or instruction, which when the computer program or instruction is run, implements the method for reconstructing the impact load history at random positions on the plate surface based on the improved regularization method.

[0050] Beneficial effects: The method of the present invention realizes the history reconstruction of the impact load through the impact load response signals measured by the fiber Bragg grating sensing network arranged on the plate structure. The present invention is applicable to engineering application fields such as load identification of plate structures, and has the following advantages: First, only 4 fiber Bragg grating sensors are required to form a sensing network, which has the advantages of simple circuit layout and strong anti-electromagnetic interference ability compared with traditional sensing methods. Second, an improved regularization technique is used to introduce a filtering operator and construct an influence matrix to solve the ill-posed problem existing in the frequency response matrix, improving the load reconstruction accuracy. Finally, the present invention sets multiple impact measurement points on the plate surface, measures the frequency response matrices of these points, and weights the improved regularization solution according to the position relationship between the measurement points and the impact load by introducing an inverse distance weighting function, realizing the history reconstruction of the impact load at random positions on the plate surface. Description of the Drawings

[0051] The following further specifically describes the present invention in conjunction with the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0052] Figure 1 is the layout diagram of the fiber Bragg grating sensors on the plate surface.

[0053] Figure 2 is the schematic diagram of the positions of the FBG sensors, measurement points and impact load on the plate surface.

[0054] Figure 3 is the flow chart of the impact load history reconstruction. Specific Embodiments

[0055] As Figure 3 shown, the present invention provides a method for reconstructing the impact load history at random positions on the plate surface based on the improved regularization method, including the following steps:

[0056] Step 1: Fix the plate structure to be monitored and arrange the fiber optic FBG sensing network; specifically:

[0057] There is a square strain monitoring area within the fixed plate surface with side length l. The fiber optic FBG sensing network on the plate surface includes 4 FBG sensors; the fiber Bragg grating sensors are numbered as FBGi, i ∈ (1, 2,... 4) in sequence, and FBGi are respectively arranged at the four vertices of the square. Taking the center of the square monitoring area as the origin O, a rectangular coordinate system is established, and the position coordinates of FBGi are defined as (a i , b i ). The sticking directions of the above fiber Bragg grating sensors are all parallel to the X direction of the plate surface to obtain the strain in a single direction on the surface of the plate structure, thus constituting the fiber Bragg grating sensor network on the plate surface;

[0058] Step 2: Determine four measurement points on the plate surface. The measurement points are usually evenly arranged on the plate surface, as Figure 1 shown. First, conduct impact measurement experiments on the measurement points with an impact hammer. According to the impact excitation signal and impact response signal in the impact measurement experiment, obtain the frequency response matrix of the measurement points; specifically:

[0059] Determine the midpoint between FBGi and the origin O as the measurement point on the plate surface, and define them as measurement point i, i ∈ (1, 2,... 4) respectively. Then the coordinates of measurement point i are First, use an impact hammer to conduct impact measurement experiments at measurement point i to determine the frequency response matrix Hi corresponding to each measurement point i. The frequency response matrix Hi is the impact system information characterized by the FBG sensing network at measurement point i. When reconstructing the impact load history using multiple FBG sensors, define the impact load signal measured by the impact hammer as F, and F is a discrete time-domain signal. The impact response signal measured by sensor FBGi is Y i , Y i is a discrete time-domain signal. Then the impact response signal Y of the FBG sensing network is:

[0060] Y = [Y1, Y2, Y3, Y4] T (1)

[0061] When the impact position is measurement point i, the frequency response matrix Hi obtained from a single impact measurement experiment is expressed as:

[0062] Hi = YF (2)

[0063] To reduce the measurement error, conduct impact measurement experiments on measurement point i three times or more, and average the frequency response matrices measured in each experiment to obtain the frequency response matrix Hi corresponding to measurement point i.

[0064] Assume that the frequency response matrix Hi is a P×Q matrix, and P≥Q, where the number of rows P is determined by the dimension of the structural response vector, and the number of columns Q is determined by the dimension of the load vector to be identified. The singular value decomposition (SVD) of the frequency response matrix Hi can be expressed as:

[0065] Hi = USV T (3)

[0066] where U = (u1, u2, …, u P ), V = (v1, v2, …, v Q ) are orthogonal matrices composed of left and right singular value vectors respectively, and S is a diagonal matrix composed of non-negative singular values σ i .

[0067] Step 3: For the impact load randomly determined at a position on the plate surface, find the inverse square value of the distance from the measurement point to the impact position as the weight coefficient; specifically:

[0068] For the impact load F t randomly determined at a position on the plate surface, its impact load signal is unknown. Let the impact position be A with coordinates (x, y), as Figure 2 shown. Then the distance L Ai from the measurement point i to the position A is:

[0069]

[0070] Define the inverse square value of the distance from the measurement point i to the impact position A as the weight coefficient W i , which can be expressed as:

[0071]

[0072] Step 4: Substitute the response signal of the FBG sensing network in this impact load into each frequency response matrix, and use the improved regularization method to introduce a filtering operator to construct an influence matrix; specifically:

[0073] Define the response signal measured by the FBG sensing network in this impact load as Y Z , and the direct least squares solution F m of the impact load can be obtained by combining the singular value decomposition form of the frequency response matrix Hi with the Moore-Penrose generalized inverse as:

[0074]

[0075] In Equation (6), Q0 is the number of singular values greater than zero in the frequency response matrix Hi, v j is the right singular value vector, u j is the left singular value vector, and σ j is the non-negative singular value.

[0076] Due to the ill-posedness of the frequency response matrix Hi, the direct least-squares solution F m is much larger than the true impact load F t . The solution F m obtained by directly inverting the least squares cannot obtain the true information of the impact load F t . Therefore, this method introduces an improved regularization technique to solve the ill-posedness problem and defines a filtering operator as:

[0077]

[0078] In equation (7), λ is the regularization parameter and satisfies λ > 0, γ is the filtering operator parameter. The larger the filtering operator parameter γ, the higher the convergence order of the improved regular solution relative to the data error.

[0079] Here, let the filtering operator parameter γ = 5, and combine the filtering operator with the frequency response matrix Hi to construct the influence matrix H i # , H i # can be expressed as:

[0080]

[0081] H i # The role of H is to map the input signal to be solved in the original problem to the improved regular solution, and the input signal to be solved is the impact load F t ;

[0082] Step 5: Use the generalized cross-validation method to determine the optimal regularization parameter and obtain the improved regular solution of each measurement point regarding the impact load; specifically:

[0083] Use the generalized cross-validation method (GCV) to find the optimal regularization parameter. The expression of the GCV method is:

[0084]

[0085] In the formula, I is the identity matrix, tr(I - HH # ) is the trace of the matrix (I - HH # ), representing the sum of the diagonal elements of the matrix (I - HH # ). In equation (9), the λ that makes the function G(λ) the minimum value is the optimal regularization parameter.

[0086] After obtaining the optimal regularization parameter λ, by combining equation (6) and equation (8), the impact load F t corresponding to the improved regular solution F of the frequency response matrix Hi can be obtainedi :

[0087]

[0088] Since there are four measurement points in the impact measurement experiment of Step 2, and each measurement point i corresponds to the frequency response matrix Hi. Therefore, the impact load F can be obtained through Equation (10). t Four improved regularized solutions, and each improved regularized solution F i corresponds to the measurement point i.

[0089] Step 6: The improved regularized weighted solution of the impact load is obtained by weighting the measurement point weight coefficient and the corresponding improved regularized solution, realizing the reconstruction of the impact load history at random positions on the plate surface. Specifically:

[0090] In Step 3, the weight coefficient is obtained according to the positional relationship between the measurement point and the impact load, and in Step 5, the improved regularized solution F i corresponding to the measurement point is obtained. The improved regularized solution F i , Hi and the impact response signal Y obtain the inverse solution through the improved regularization technique. Since a filtering operator is introduced in the solution process, the ill-posedness error between F i and the true impact load F t is small, but the error caused by the distance L Ai from the measurement point i to position A still exists.

[0091] Superimpose F i and the corresponding weight coefficient W i , and thus the improved regularized weighted solution F t of the impact load F r can be reconstructed, and its formula is:

[0092]

[0093] The improved regularized weighted solution F r is the inverse distance squared weighted solution of the improved regularized solutions F i corresponding to 4 different position measurement points i with respect to the true impact position. Regarding the obtained F r as the history reconstruction solution of the impact load F t , it can significantly reduce the error caused by the distance L Ai from the measurement point i to position A, and thus realize the reconstruction of the impact load history at random positions on the plate surface.

[0094] The method of the present invention can solve the problem of solving the impact load history in practical engineering when the position of the impact load on the plate surface is known. Solving the history of the impact load helps to determine the degree of impact damage or the impact damage mode, providing a basis for the detection and repair of impact damage in structural health monitoring.

[0095] In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit. Among them, the computer storage medium can store a computer program, and when the computer program is executed by the data processing unit, it can run the inventive content of the method for reconstructing the impact load history at random positions on the plate surface based on the improved regularization method and some or all of the steps in each embodiment. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), or the like.

[0096] Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of a computer program and its corresponding general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the parts that contribute to the prior art can be embodied in the form of a computer program, that is, a software product. The computer program software product can be stored in a storage medium and includes several instructions to enable a device including a data processing unit (which can be a personal computer, a server, a single-chip microcomputer, a MUU, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments of the present invention.

[0097] The present invention provides a method for reconstructing the impact load history at random positions on the plate surface based on the improved regularization method. There are many methods and ways to specifically implement this technical solution. The above is only the preferred implementation mode of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the prior art.

Claims

1. A method for reconstructing the impact load history at random positions on the plate surface based on an improved regularization method, characterized in that, It includes the following steps: Step 1: Fix the plate structure to be monitored and arrange fiber Bragg grating sensors to form a sensing network; Step 2: Determine four measurement points on the plate surface. Conduct impact measurement experiments on the measurement points in advance with an impact force hammer. Obtain the frequency response matrix of the measurement points according to the impact excitation signal and the impact response signal in the impact measurement experiment; Step 3: For the impact load randomly located on the plate surface, calculate the inverse square value of the distance from the measurement point to the impact position as the weight coefficient; Step 4: Substitute the response signal of the fiber FBG sensing network in the impact load into each frequency response matrix, and use the improved regularization method to introduce a filtering operator to construct an influence matrix; Step 5: Use the generalized cross-validation method to determine the optimal regularization parameter and obtain the improved regularized solution of each measurement point for the impact load; Step 6: Weight the weight coefficient and the corresponding improved regularized solution to obtain the improved regularized weighted solution of the impact load, and realize the reconstruction of the impact load history at random positions on the plate surface.

2. The method according to claim 1, characterized in that, Step 1 includes: There is a square strain monitoring area in the fixed plate surface with side length l. The sensing network on the plate surface includes 4 fiber Bragg grating sensors; The 4 fiber Bragg grating sensors are numbered FBGi, where i ∈ (1, 2, 3, 4). The 4 fiber Bragg grating sensors are respectively arranged at the four vertices of a square strain monitoring area. Taking the center of the square strain monitoring area as the origin O, a rectangular coordinate system is established, and the position coordinates of FBGi are defined as (a i , b i ).

3. The method according to claim 2, characterized in that, In Step 1, the pasting directions of the fiber Bragg grating sensors are all parallel to the X direction of the right-angle coordinate system on the plate surface to obtain the strain in a single direction on the surface of the plate structure, thereby forming a sensing network.

4. The method according to claim 3, characterized in that, Step 2 includes: determining the midpoint between the fiber Bragg grating sensor FBGi and the origin O as the measurement point i on the plate surface, and the coordinates of the measurement point i are Conduct an impact measurement experiment on the measurement point i in advance with an impact force hammer to determine the frequency response matrix Hi corresponding to each measurement point i; When reconstructing the impact load history using more than two fiber Bragg grating sensors, define the impact load signal measured by the impact force hammer as F; The impact response signal measured by the fiber optic Bragg grating sensor FBGi is Y i , then the impact response signal Y of the sensing network is: Y = [Y1, Y2, Y3, Y4] T (1) When the impact position is the measurement point i, the frequency response matrix Hi obtained from a single impact measurement experiment is expressed as: Hi = YF (2) Conduct more than N impact measurement experiments on the measurement point i, and average the frequency response matrices measured in each experiment to obtain the frequency response matrix Hi corresponding to the measurement point i; Set the frequency response matrix Hi as a P×Q matrix, and P≥Q, where the number of rows P is determined by the dimension of the structural response vector, and the number of columns Q is determined by the dimension of the load vector to be identified; The singular value decomposition of the frequency response matrix Hi is expressed as: Hi = USV T (3) where \(U=(u_1, u_2, \ldots, u\) P ), \(V=(v_1, v_2, \ldots, v\) Q ) are the orthogonal matrices composed of left singular value vectors and right singular value vectors respectively, \(u\) P represents the \(P\)th left singular value vector, \(v\) Q represents the \(Q\)th right singular value vector, \(S\) is the diagonal matrix composed of non - negative singular values \(\sigma\) i , and \(T\) is the matrix transpose symbol.

5. The method according to claim 4, characterized in that, Step 3 includes: randomly determining the position of the impact load F on the plate surface t , setting the impact position as A with coordinates (x, y), then the distance L from the measurement point i to the position A Ai is as follows: Define the inverse square value of the distance from the measurement point i to the impact position A as the weight coefficient W i :

6. The method according to claim 5, characterized in that, Step 4 includes: the impact load F measured by the sensing network t The response signal is defined as Y Z , combined with the singular value decomposition form of the frequency response matrix Hi and the Moore-Penrose generalized inverse, to obtain the direct least squares solution F of the impact load m which is: where Q0 is the number of singular values greater than zero in the frequency response matrix Hi, so Q0 ≤ P and Q0 ≤ Q; v j is the right singular value vector, u j is the left singular value vector, σ j is the non - negative singular value; An improved regularization technique is introduced to solve the ill-posed problem, and the filtering operator is defined as follows: where λ is the regularization parameter and satisfies λ>0, and γ is the parameter of the filtering operator; Combine the filtering operator with the frequency response matrix Hi to construct the influence matrix H i # : H i # functions to map the input signal of the original problem into an improved regularized solution.

7. The method according to claim 6, wherein, Step 5 includes: Use the generalized cross-validation method to find the optimal regularization parameter, and the expression is: where I is the identity matrix; tr(I - HH # ) is the trace of the matrix (I - HH # ), representing the sum of the diagonal elements of the matrix (I - HH # ); in Equation (9), λ that minimizes the function G(λ) is the optimal regularization parameter; After finding the optimal regularization parameter λ, equation (6) and equation (8) are combined to obtain the impact load F t Corresponding to the frequency response matrix Hi, the improved regularization solution F i : In the impact measurement experiment of Step 2, there are a total of four measurement points, and each measurement point i corresponds to a frequency response matrix Hi. Therefore, the impact load F is obtained through Equation (10). t Four improved regularized solutions of i each correspond to the measurement point i.

8. The method according to claim 7, wherein, Step 6 includes: adding F i to the corresponding weight coefficient W i to reconstruct the improved regularized weighted solution F t of the impact load F r : Improved Regularized Weighted Solution F r , which is the reconstructed solution of the impact load F obtained finally t , thus realizing the reconstruction of the impact load history at random positions on the plate surface.

9. A storage medium, wherein, Stored with computer programs or instructions, when the computer programs or instructions are run, the method described in any one of claims 1 to 8 is implemented.

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