A method and system for optimizing the distribution of measuring points in a dynamic load identification process

Abstract

This invention discloses a method and system for optimizing the distribution of measurement points during dynamic load identification. The method includes: determining the number of measurement points K and the modal cutoff number N; selecting an initial value x1 for the natural mode P = Max(K,N) before solving; and solving the equation to examine whether the equation has P-1 solutions x2, ..., x P If not, the initial value x1 is changed and the solution is solved again until there are P-1 solutions in the solution set. It is then verified whether the initial value and the P-1 solutions ensure that the matrix row vectors are orthogonal and their magnitudes are approximately similar. Based on the P solutions of the equation that satisfy the verification conditions, the measurement point that maximizes load identification stability is obtained. This invention constructs a measurement point location optimization method with the goal of maximizing the stability of the response-load equation. Compared to classical methods, this successfully reduces the ill-conditioned nature of the dynamic calibration matrix.

Description

Technical Field

[0001] This invention belongs to the field of dynamic load identification, and specifically relates to a method and system for optimizing the distribution of measurement points in the dynamic load identification process. Background Technology

[0002] With the continuous improvement of engineering technology, various vibration problems have received increasing attention from the engineering community. Vibration sensing is a discipline that studies the relationship between a structure or system and its excitation and response, and it has wide applications in scientific research and engineering practice. An input, output, and system characteristics together constitute a complete vibration system. Input is the external force acting on the system, i.e., excitation, also known as dynamic load. System characteristics refer to the inherent characteristics of the structural system itself, including the structure's natural frequencies, natural mode shapes, damping, mass characteristics, and stiffness characteristics. Output is the response of the vibration system, including the structure's displacement response, velocity response, and acceleration response.

[0003] Finding a third parameter given two known parameters of a vibrating system constitutes one of the three important research areas in structural dynamics. Finding the response of a system given the excitation and its characteristics is the classic forward problem in vibration. Currently, it is possible to solve vibration problems of various complex structures under arbitrary, accurately describable loads; that is, to apply a certain external excitation to a structure and calculate its dynamic response. Research on dynamic response analysis has been very in-depth, forming a systematic theory and playing an important role in practice. The deepening of research on the forward problem has led to the emergence of inverse problems. Finding the dynamic characteristics of a system given its response and the excitation is the first type of inverse problem in vibration, namely, the parameter identification problem. Parameter identification involves measuring the input and output data of the excited system simultaneously using instruments, processing the data to establish a mathematical model of the vibration system, and then analyzing and identifying the corresponding parameters. This technology has developed significantly and is now quite mature, playing a major role in solving complex engineering problems.

[0004] Dynamic load identification is a type of inverse problem in dynamics. Its basic approach is to derive the response-load equation based on the known relationship between the response and the dynamic load, and then infer the dynamic load by measuring the response. However, according to the research of the currently identified inventors, the distribution of measurement points and the selection of orthogonal polynomials in the dynamic load identification process have received relatively little attention. Regarding measurement point distribution, current methods generally assume that measurement points are evenly distributed throughout the structure to minimize the condition number of the transfer matrix. However, such methods require extensive experimentation and specific measurement point layouts for each structure, making it difficult to arrive at conclusions with practical guiding significance. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a method for optimizing the distribution of measurement points in the dynamic load identification process. By studying the influence of measurement point positions on the dynamic load identification results, a strategy for solving the optimal measurement point positions is proposed, thereby improving the stability of the dynamic calibration matrix and obtaining accurate identification results.

[0006] Technical solution: To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for optimizing the distribution of measurement points during dynamic load identification includes the following steps:

[0008] Step 1: Determine the number of measurement points K and the modal cutoff number N. Let P = Max(K,N), and solve for the first P natural modes. i = 1, 2, ..., P;

[0009] Step 2: Select an initial value x1 as the location of the first measuring point, and solve the equation.

[0010] Step 3: Check if there are P-1 solutions x2,…,x in the solution set of the equation from Step 2. P If not, change the initial value x1 and return to step 2 until the equation has P-1 solutions;

[0011] Step 4: Verify the initial value x1 and the P-1 solutions x2,…,x from the equation in Step 2. P Can the matrix be made If the row vectors are not orthogonal to each other, change the initial value x1 and return to step 2 until the row vectors of the matrix are orthogonal to each other.

[0012] Step 5: Verify the initial value x1 and the P-1 solutions x2,…,x from the equation in Step 2. P Can the matrix be made If the row vectors are close in magnitude, then change the initial value x1 and return to step 2 until the row vectors of the matrix are close in magnitude.

[0013] Step 6: Based on the initial value x1 and P-1 solutions x2,…,x that satisfy the equations from Steps 4-5… P By identifying the relationship between K and N, the measurement point that best achieves the stability of load identification can be obtained.

[0014] Furthermore, the judgment matrix The method to make row vectors orthogonal to each other is as follows: the inner product of any two row vectors in a matrix is ​​much smaller than their own magnitudes.

[0015] Furthermore, the judgment matrix The method for the lengths of row vectors to be basically close is as follows: If the difference between the lengths of any two row vectors in the matrix is less than a preset threshold, it is determined that the lengths of the row vectors are basically close.

[0016] Further, by identifying the size relationship between K and N, the measuring points that make the load identification stability optimal are obtained in different cases, including: If K > N, then P = K, and at this time, x1, x2, …, x P are the optimal measuring points; if K < N, then K < N = P, and at this time, randomly select K points from x1, x2, …, x P 即可。

[0017] The present invention also provides an optimization system for the distribution of measuring points in the dynamic load identification process, including:

[0018] The natural vibration mode solving module is used to solve the first P natural vibration modes by setting P = Max(K, N) according to the determined number of measuring points K and the modal truncation number N, where i = 1, 2, …, P; i = 1, 2, …, P;

[0019] The equation solving module is used to solve the equation through a selected initial value x1, and this initial value x1 represents the position of the first measuring point;

[0020] The solution quantity checking module is used to check whether there are P - 1 solutions x2, …, x in the solution set of the equation in the equation solving module. If not, replace the initial value x1 and repeat the operation of the equation solving module until the equation has P - 1 solutions; P ,若没有,则更换初始值x1并重复执行方程求解模块的操作,直至该方程有P - 1个解;

[0021] The first verification module is used to verify whether the initial value x1 and the P - 1 solutions x2, …, x of the equation in the equation solving module can make the row vectors of the matrix P 彼此正交,如不能,更换初始值x1并重复执行方程求解模块的操作,直至该矩阵行向量彼此正交; orthogonal to each other. If not, replace the initial value x1 and repeat the operation of the equation solving module until the row vectors of the matrix are orthogonal to each other;

[0022] The second verification module is used to verify whether the initial value x1 and the P - 1 solutions x2, …, x of the equation in the equation solving module can make the row vectors of the matrix P 行向量模长基本接近,如不能,则更换初始值x1并重复执行方程求解模块的操作,直至该矩阵行向量模长基本接近; basically close in length. If not, replace the initial value x1 and repeat the operation of the equation solving module until the row vectors of the matrix are basically close in length;

[0023] The measuring point determination module is used to obtain the measuring points that make the load identification stability optimal in different cases by identifying the size relationship between K and N according to the initial value x1 and the P - 1 solutions x2, …, x of the equation that meet the verification module. P ,通过识别K与N的大小关系分情况获得使载荷识别稳定性最佳的测点。

[0024] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the measurement point distribution optimization method in the dynamic load identification process as described above.

[0025] The present invention also provides a computer storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of the measurement point distribution optimization method in the dynamic load identification process as described above.

[0026] Beneficial Effects: This invention investigates the influence of measurement point location on dynamic load identification results and proposes a measurement point distribution optimization method and system in the dynamic load identification process. By constructing a measurement point location optimization method with the goal of maximizing the stability of the response-load equation, the method first solves for the structure's natural mode shapes, establishes and solves a specific equation, and then verifies and adjusts the solution based on its properties to obtain the measurement points that achieve the best load identification stability. Compared to classical methods, this invention successfully reduces the ill-conditioned nature of the dynamic calibration matrix, thereby improving the accuracy of dynamic load identification. Attached Figure Description

[0027] Figure 1 This is a flowchart of the dynamic load identification method of the present invention;

[0028] Figure 2 This is a schematic diagram of the beam used in the verification experiment in this embodiment of the invention;

[0029] Figure 3 This is the function when x1 = 100 in the embodiment of the present invention. Images;

[0030] Figure 4 This is the load distribution function in this embodiment of the invention. Detailed Implementation

[0031] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0032] The basic method for dynamic load identification is to derive the response-load equation based on the known relationship between the response and the dynamic load, and then infer the dynamic load by measuring the response. For linear systems, the response-load equation is a matrix equation, and the matrix in the equation is called the dynamic calibration matrix. The location and number of measurement points affect the dynamic calibration matrix, and consequently, the stability and accuracy of the matrix equation.

[0033] Regarding the accuracy of the response-load equation, since all equations in the dynamic load identification process are essentially equations of the load-response relationship when the response takes different values, without considering errors and assuming the total number of measuring points is the same, differences in the distribution of measuring point locations will not invalidate any equation, and therefore will not change the calculation result of the entire matrix equation. Thus, differences in the distribution of measuring point locations do not change the accuracy of the response-load equation.

[0034] Regarding the stability of the response-load equation, different measurement point locations will change the singular values ​​of the dynamic calibration matrix, thereby altering the stability of the overall matrix equation. For example, when the measurement point locations are almost identical, regardless of the number of measurement points, each row in the dynamic calibration matrix is ​​almost the same, and the obtained response-load equation is almost always the same equation. In this case, the stability of the dynamic calibration matrix is ​​extremely poor, making it difficult to obtain accurate identification results.

[0035] The influence of measuring points on dynamic load identification is explained below through formula derivation. The meanings of the symbols involved are shown in Table 1.

[0036] Table 1. Symbol Explanation

[0037]

[0038]

[0039] Taking the identification of distributed dynamic loads on a beam as an example, the load-response relationship is as follows:

[0040]

[0041] The classical method assumes that a set of basis functions φ should be selected. i (x), (i=1,2,…,M) expands the load F(x), i.e. Where a m (i = 1, 2, ..., M) is F(x) according to φ i The coefficients of the expanded basis functions (x), (i = 1, 2, ..., M). Here, M specifies the number of basis functions chosen, hereinafter referred to as the order of the basis functions. If the response u(x) at multiple points is measured... k If k = 1, 2, ..., K, then we have:

[0042] [u(x1),u(x2),…,u(x K )] T K×1 =H·[a1,a2,…,a M ] T M×1 (2)

[0043]

[0044] Although equations (2) and (3) establish the relationship between the multi-point response and the coefficients of the load after expansion according to the basis functions, they cannot directly show the relationship between the measuring point x. k The influence of (k=1,2,…,K) on matrix H. Equation (3) is a complex matrix. For convenience, the integral is written as a function inner product in the form of equation (4).

[0045]

[0046] Clearly, this inner product operator satisfies the principle of linear superposition. For a linear system, the transfer function H(x,x0,ω) is not a random function; it is composed of multiple normalized mode functions. k = 1, 2, 3, ... is a superposition of these values. The transfer function expression for an undamped system is:

[0047]

[0048] Where N is the modal cutoff number. Substituting equation (5) into equation (4), we get:

[0049]

[0050] Choose a set of basis functions φ i Expanding the load F(x), i = 1, 2, ..., we get... If the response u(x) at K points is measured k If k = 1, 2, ..., K, then we have:

[0051]

[0052] Equation (9) establishes the relationship between the response and the coefficients of the orthogonal basis functions to be identified, which involves three matrices, namely and Comparing equations (2) and (9), it can be seen that the so-called dynamic calibration matrix H is actually the product of these three matrices.

[0053]

[0054] This can be achieved by changing the matrix through the distribution of measurement points. This matrix reflects the influence of the measurement point distribution on the dynamic calibration matrix. Therefore, studying the measurement point distribution is equivalent to studying the matrix. The impact of changes on recognition results.

[0055] (I) Measurement point selection strategy when N=K

[0056] Matrix multiplication does not decrease the condition number of a matrix. However, to ensure that the condition number of matrix H is not increased, the spatial positions of the measurement points should make the matrix H equal to the condition number of matrix H. The singular values ​​should be as equal as possible. The measurement point location should be chosen. matrix It can be written as:

[0057]

[0058] Equation (11) is the matrix A singular value decomposition, That is, a matrix The singular value of . If at this time If the values ​​are exactly close to each other, then at this time... This is the solution that makes the singular values ​​of the matrix as equal as possible. At this point, the matrix... Approximately orthogonal matrices. If the row vectors of a matrix are orthogonal to each other, then:

[0059]

[0060] Right now:

[0061]

[0062] Directly solving equation (13) requires solving for N values ​​simultaneously, which involves a large amount of computation, making direct solution unwise. The first N-1 equations are:

[0063]

[0064] Theoretically, equations (13) and (14) are not equivalent; the solution to equation (13) is a subset of the solution to equation (14). Equation (13) can be solved by finding a set of solutions to equation (14) and substituting them into equation (13) to verify its solution.

[0065] For equation (14), this system of equations has N-1 equations and N unknowns, therefore the solution to equation (14) is not unique. Considering the symmetry of the system of equations (14), a trial value x1 can be selected, and the equation can be solved:

[0066] A series of roots can be used to obtain a set of trial solutions x2, x3, ... x N If equation (15) can be solved to obtain N-1 solutions, then this solution is a set of solutions to equation (14), and we can further substitute it into equation (13) to verify whether it holds true. If x1, x2, x3, ... x N If equation (13) cannot be satisfied, the value of x1 can be adjusted.

[0067] Equation (15) has only one variable x, which is easier to solve than equations (13) and (14) which solve for N unknowns at once.

[0068] In addition, it is necessary to verify whether the matrix can be made The singular values ​​of the matrix should be as equal as possible. The lengths of the row vectors should be as equal as possible.

[0069] (2) Measuring point selection strategy when N ≠ K

[0070] When N > K, the matrix can be written as:

[0071]

[0072] When N < K, the matrix can be written as:

[0073]

[0074] When N > K, the singular values of the matrix depend on the singular values; and when N > K, the singular values of the matrix depend on the singular values. Therefore, when N ≠ K, the singular values of the matrix depend on the singular values.

[0075] Let P = Max(K, N). The measuring point selection strategy when N ≠ K should be to find a set of points x k (k = 1, 2,..., P) such that the singular values of the matrix are close to each other. The specific strategy can be found in the measuring point selection strategy when N = K.

[0076] Based on the above principle analysis, the present invention proposes an optimization method for the measuring point distribution in the dynamic load identification process. Referring to Figure 1 , the method includes the following steps:

[0077] Step 1: Determine the number of measuring points K and the modal truncation number N, denote P = Max(K, N), and solve for the first P natural vibration modes i = 1, 2,..., P.

[0078] Step 2: Select an initial value x1, that is, the position of the first measuring point, and solve the equation

[0079] Step 3: Examine whether the solution set of the equation in Step 2 has P - 1 solutions x2,..., x P . If not, replace the initial value x1 and return to Step 2 until the solution set of the equation has P - 1 solutions.

[0080] Step 4: Verify whether the initial value x1 and the P - 1 solutions x2,..., x P of the equation in Step 2 can make the row vectors of the matrix orthogonal to each other. If not, replace the initial value x1 and return to Step 2 until the row vectors of this matrix are orthogonal to each other.

[0081] Step 5: Verify whether the initial value x1 and the P - 1 solutions x2, …, x of the equation in Step 2 P can make the lengths of the row vectors of the matrix basically close. A threshold can be set to define that if the difference in the lengths of any two row vectors is less than this threshold, it is determined that the lengths of the row vectors are close to each other. If not satisfied, replace the initial value x1 and return to Step 2 until the lengths of the row vectors of the matrix are basically close.

[0082] Step 6: Obtain the points x1, x2, …, x that make the row vectors of the matrix P orthogonal to each other and have close lengths. Based on these P points, obtain the optimal measurement points.

[0083] If K > N, then P = K, and at this time x1, x2, …, x P are the optimal measurement points; if K < N, then K < N = P, and at this time, randomly select K points from x1, x2, …, x P .

[0084] To verify the performance of this method, in one embodiment, taking a cantilever beam as an example, the measurement point distribution is optimized according to this method. The beam schematic diagram and the corresponding coordinate system are as Figure 2 shown. Without loss of generality, assume that the length of the cantilever beam L = 100 mm, the elastic modulus E = 210 GPa, the density ρ = 7.85 g / cm 3 , the width w = 5 mm, the thickness t = 1 mm, and the flexural rigidity I = wt 3 / 12.

[0085] The natural frequency of the cantilever beam is:

[0086]

[0087] where s n L is the nth positive solution of the equation cosh(x)cos(x) = -1. The normalized vibration mode function of the cantilever beam is:

[0088]

[0089] Take N = K = 5.

[0090] Select the initial measurement point at 100 mm, that is, x1 = 100. Use the graphical method to solve the function The image of which is as Figure 3 shown. It can be seen that the equation (15) has four solutions, and the solution set is {189, 283, 380, 468}. Then it is judged that the condition in Step 3 is satisfied, and the verification of the row vectors of the matrix is carried out.

[0091] Let {x1,x2,x3,x4,x5} = {100,189,283,380,468} be an experimental solution. Let vectors l1, l2,…,l be... N The pairwise inner product is:

[0092]

[0093] Vectors l1, l2, ..., l N The order of magnitude of the square of the modulus is stable at 10. -2 The order of magnitude of the pairwise inner product is 10. -4 ~10 -6 This indicates that vectors l1, l2, ..., l N The dot product of any two vectors is much smaller than their magnitudes, which means that the angle between any two vectors is close to 90°, i.e., the angle between vectors l1, l2, ..., l... N Both can be considered orthogonal.

[0094] Vectors l1, l2, ..., l N The modulus length is:

[0095]

[0096] A threshold of 0.01 is set. The maximum difference between the moduli is 0.008, and the moduli can be considered to be basically equal. Singular value decomposition shows that the matrix at this point... The singular values ​​are {0.116, 0.108, 0.104, 0.102, 0.101}. This is similar to {||l1||,||l2||,…,||l N The values ​​of ||} are basically close.

[0097] Finally, the measurement points {x1,x2,x3,x4,x5} that achieve the best load identification stability are obtained as {100,189,283,380,468}.

[0098] In contrast, if the measurement point selection strategy is to uniformly select points according to geometric dimensions, i.e., {y1,y2,y3,y4,y5}={L / 6,L / 3,L / 2,2L / 3,5L / 6}, singular value decomposition shows that the matrix in this case... The singular values ​​are {0.115, 0.111, 0.109, 0.109, 0.019}.

[0099] By adjusting the measurement points, the small singular value of 0.019 introduced by the measurement points was successfully removed. In terms of matrix condition number, the condition number of the transfer matrix with measurement points {x1,x2,x3,x4,x5} is 1.14, and the condition number of the transfer matrix with measurement points {y1,y2,y3,y4,y5} is 6.12. Compared to classical methods, this invention successfully reduces the ill-conditioned nature of the dynamic calibration matrix.

[0100] As described in the calculation in the above embodiment, the modal cutoff number N = 5, the number of measurement points K = 5, and the basis function φ i (x), (i = 1, 2, ..., M) are Legendre orthogonal basis functions defined on the beam, with order M = 5.

[0101] Define an external load Load(x,t) on the beam as sin[π(x / L)]. 2 cos(60t), the load distribution function is as follows Figure 4 As shown. The load distribution function expands according to the Legendre basis function defined on it as follows: The coefficients are shown in Table 2.

[0102] Table 2. Legendre basis function coefficients

[0103]

[0104] The process of determining the measuring points is as described above. The transfer matrix obtained with measuring points {x1,x2,x3,x4,x5} = {100,189,283,380,468} is defined as H, and the response at measuring points {x1,x2,x3,x4,x5} is defined as U = {u1,u2,u3,u4,u5}. In the traditional method, measuring points are uniformly selected on the beam. The transfer matrix obtained with uniformly distributed measuring points {y1,y2,y3,y4,y5} = {L / 6,L / 3,L / 2,2L / 3,5L / 6} is defined as H0, and the response at measuring points {y1,y2,y3,y4,y5} is defined as...

[0105] For clarity, the vector formed by the true values ​​of the first 5 Legendre basis function coefficients is denoted as A = {a1, a2, a3, a4, a5}, and these true values ​​are shown in Table 2. Let the vector formed by the Legendre basis function coefficients identified by the measurement points {x1, x2, x3, x4, x5} be denoted as B = {b1, b2, b3, b4, b5}; let the vector formed by the Legendre basis function coefficients identified by the measurement points {y1, y2, y3, y4, y5} be denoted as C = {c1, c2, c3, c4, c5}.

[0106] This example demonstrates the superiority of the proposed measurement point layout optimization method over traditional methods by showing that vector B is closer to vector A than vector C, even when U and U0 have errors.

[0107] According to equation (2), the matrix equation can be obtained:

[0108] U = H·B (21)

[0109] U0=H0·C (22)

[0110] Matrix H and H0 can be obtained from equation (10). The actual response values ​​at measurement points {x1,x2,x3,x4,x5} and {y1,y2,y3,y4,y5} are shown in Table 3.

[0111] Table 3 shows the responses at the two measurement points.

[0112]

[0113] The matrix equations (21) and (22) were processed using Tikhonov regularization theory after multiple errors of U and U0.1%. The calculation results are shown in Table 4.

[0114] Table 4. Results of Matrix Equation Calculation

[0115]

[0116] The matrix equations (21) and (22) were processed using Tikhonov regularization theory after multiple errors of U and U02%. The calculation results are shown in Table 5.

[0117] Table 5 Calculation Results of Matrix Equations (Part 2)

[0118]

[0119] Calculation results show that the optimized measurement point layout can reduce the condition number of the transfer matrix during dynamic load identification. This reduces the errors caused by the instability of the matrix equations during identification under different error scales, thus improving the accuracy of dynamic load identification.

[0120] Based on the same technical concept as the method embodiments, the present invention also provides a measurement point distribution optimization system in the dynamic load identification process, comprising:

[0121] The natural mode shape solving module is used to solve for the first P natural modes, given a determined number of measurement points K and modal cutoff number N, assuming P = Max(K,N). i = 1, 2, ..., P;

[0122] The equation solving module is used to solve equations using a selected initial value x1. The initial value x1 represents the position of the first measuring point;

[0123] The solution quantity check module is used to check whether there are P-1 solutions x2,…,x in the solution set of the equation solving module. P If not, change the initial value x1 and repeat the operation of the equation solving module until the equation has P-1 solutions;

[0124] The first verification module is used to verify whether the initial value x1 and the P-1 solutions x2, …, x of the equation in the equation solving module can make the row vectors of the matrix P orthogonal to each other. If not, replace the initial value x1 and repeat the operation of the equation solving module until the row vectors of the matrix are orthogonal to each other;

[0125] The second verification module is used to verify whether the initial value x1 and the P-1 solutions x2, …, x of the equation in the equation solving module can make the lengths of the row vectors of the matrix P basically close. If not, replace the initial value x1 and repeat the operation of the equation solving module until the lengths of the row vectors of the matrix are basically close;

[0126] The measuring point determination module is used to obtain the measuring points that optimize the load identification stability in different cases by identifying the size relationship between K and N according to the initial value x1 and the P-1 solutions x2, …, x of the equation that satisfy the verification module. P

[0127] If K > N, then P = K, and at this time, x1, x2, …, x P are the optimal measuring points; if K < N, then K < N = P, and at this time, randomly select K points from x1, x2, …, x P

[0128] The present invention also provides a computer device, including: one or more processors; a memory; and one or more programs, where the one or more programs are stored in the memory and are configured to be executed by the one or more processors. When the program is executed by the processor, it implements the steps of the method for optimizing the measuring point distribution in the dynamic load identification process as described above.

[0129] The present invention also provides a computer storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the method for optimizing the measuring point distribution in the dynamic load identification process as described above.

[0130] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a device, a computer device, or a computer program product. Therefore, the present invention can adopt the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0131] ​​​​This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 Means for a function specified in one or more processes. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that are implemented in the process. Figure 1 The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 Steps of a specified function in one or more processes.

Claims

1. A method for optimizing the distribution of measuring points during the identification of dynamic loads on beams, characterized in that, Includes the following steps: Step 1: Determine the number of measuring points K on the beam and the modal cutoff number N. Let P = Max(K,N), and solve for the first P natural modes. Step 2: Select an initial value x1 as the location of the first measuring point, and solve the equation. Step 3: Check if there are P-1 solutions x2,…,x in the solution set of the equation from Step 2. P If not, change the initial value x1 and return to step 2 until the equation has P-1 solutions; Step 4: Verify the initial value x1 and the P-1 solutions x2,…,x from the equation in Step 2. P Can the matrix be made If the row vectors are not orthogonal to each other, change the initial value x1 and return to step 2 until the row vectors of the matrix are orthogonal to each other. Step 5: Verify the initial value x1 and the P-1 solutions x2,…,x from the equation in Step 2. P Can the matrix be made If the row vector magnitudes are close enough, then change the initial value x1 and return to step 2 until the row vector magnitudes of the matrix are close enough; where the judgment matrix... The method for determining that the magnitudes of row vectors are basically similar is as follows: if the difference between the magnitudes of any two row vectors in the matrix is ​​less than a preset threshold, then the magnitudes of the row vectors are determined to be basically similar. Step 6: Based on the initial value x1 and P-1 solutions x2,…,x that satisfy the equations from Steps 4-5… P By identifying the relationship between K and N, the measurement point that best achieves the stability of load identification can be obtained.

2. The method according to claim 1, characterized in that, Judgment Matrix The method to make row vectors orthogonal to each other is as follows: the inner product of any two row vectors in a matrix is ​​much smaller than their own magnitudes.

3. The method according to claim 1, characterized in that, Obtain the measuring points that make the load identification stability optimal by distinguishing cases according to the magnitude relationship between K and N, including: if K > N, then P = K, and at this time, x1, x2, …, x P are the optimal measuring points; if K < N, then K < N = P, and at this time, randomly select K points from x1, x2, …, x P 即可。 4. A measurement point distribution optimization system for dynamic load identification on beams, characterized in that, include: The mode shape solving module is used to solve for the first P natural modes, given a determined number of measuring points K on the beam and the modal cutoff number N, assuming P = Max(K,N). The equation solving module is used to solve equations using a selected initial value x1. The initial value x1 represents the position of the first measuring point; The solution quantity check module is used to check whether there are P-1 solutions x2,…,x in the solution set of the equation solving module. P If not, change the initial value x1 and repeat the operation of the equation solving module until the equation has P-1 solutions; The first verification module is used to verify the initial value x1 and the P-1 solutions x2,…,x in the equation solving module. P Can the matrix be made If the row vectors are not orthogonal to each other, change the initial value x1 and repeat the operation of the equation solving module until the row vectors of the matrix are orthogonal to each other. The second verification module is used to verify the initial value x1 and the P-1 solutions x2,…,x in the equation solving module. P Can the matrix be made If the row vector magnitudes are close enough, then change the initial value x1 and repeat the operation of the equation solving module until the row vector magnitudes of the matrix are close enough; among them, the judgment matrix The method for determining that the magnitudes of row vectors are basically similar is as follows: if the difference between the magnitudes of any two row vectors in the matrix is ​​less than a preset threshold, then the magnitudes of the row vectors are determined to be basically similar. The measurement point determination module is used to determine the measurement point based on the initial value x1 and P-1 solutions x2,…,x that satisfy the equation of the verification module. P By identifying the relationship between K and N, the measurement point that best achieves the stability of load identification can be obtained.

5. The system according to claim 4, characterized in that, Judgment Matrix The method to make row vectors orthogonal to each other is as follows: the inner product of any two row vectors in a matrix is ​​much smaller than their own magnitudes.

6. The system according to claim 4, characterized in that, Obtain the measuring points that make the load identification stability optimal by distinguishing cases according to the size relationship between K and N, including: if K > N, then P = K, and at this time, x1, x2, …, x P are the optimal measuring points; if K < N, then K < N = P, and at this time, randomly select K points from x1, x2, …, x P 即可。 7. A computer device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the measurement point distribution optimization method in the beam dynamic load identification process as described in any one of claims 1-3.

8. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the measurement point distribution optimization method in the beam dynamic load identification process as described in any one of claims 1-3.

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