Measurement point distribution optimization method and system in dynamic load identification process

Abstract

The invention discloses a measuring point distribution optimization method and system in a dynamic load identification process. The method comprises the steps that the number K of measuring points and the modal truncation number N are determined, an initial value x1 is selected before P = Max (K, N) order natural vibration mode # imgabs0 # is solved, an equation # imgabs1 # is solved, whether P-1 solutions x2,..., xP exist in the equation is investigated, if not, the initial value x1 is replaced, and solving is conducted again till P-1 solutions exist in an equation solution set; and verifying whether the initial value and the P-1 solutions can enable the row vectors of the matrix # imgabs2 # to be orthogonal to each other and the modulus lengths of the row vectors to be basically close or not, and obtaining a measuring point enabling the load identification stability to be optimal according to the P solutions of the equation meeting verification conditions. According to the method, the measuring point position optimization method is constructed by enabling the response-load equation to be most stable, and compared with a classical method, the morbidity of a dynamic calibration matrix is successfully reduced.

Description

Technical Field

[0001] The invention belongs to the field of dynamic load identification, and in particular relates to a method and system for optimizing measurement point distribution in a dynamic load identification process. Background Art

[0002] With the continuous improvement of engineering technology, various vibration problems have attracted more and more attention from the engineering community. Vibration perception is a discipline that studies the relationship between a structure or system and its excitation and response, and has a wide range of applications in scientific research and engineering practice. The input part, output part, and system characteristic part together constitute a complete vibration system. The input is the effect of the outside world on the system, that is, excitation, also known as dynamic load or dynamic load. System characteristics refer to the inherent characteristics of the structural system itself, including the natural frequency, natural vibration mode, damping, mass characteristics, and stiffness characteristics of the structure. The output is the response in the vibration system, including the displacement response, velocity response, and acceleration response of the structure.

[0003] Finding the third parameter under the premise of knowing two parameters of the vibration system constitutes three important research contents of structural dynamics. Knowing the excitation and system characteristics and finding its response is a classic direct problem in vibration. Now, people have been able to solve the vibration problems of various complex structures under any load that can be accurately described, that is, applying a certain external excitation to a structure and calculating the dynamic response of the structure. The research on dynamic response analysis has been very in-depth, forming a systematic theory, and has played an important role in practice. The continuous deepening of the research on direct problems has led to the proposal of inverse problems. Under the condition of known system response and excitation, finding the dynamic characteristics of the system is the first type of inverse problem of vibration, that is, parameter identification problem. Parameter identification is to obtain the input and output data of the excited system through instrument measurement, and then process the data to establish a mathematical model of the vibration system, and then analyze and identify the corresponding parameters. This technology has been greatly developed and has been quite mature so far, and has played a great role in solving complex engineering practical problems.

[0004] The dynamic load identification problem belongs to the second type of inverse problem in dynamics. Its basic method is to obtain the response-load equation based on the known relationship between the response and the dynamic load, and infer the dynamic load by measuring the response. However, according to the research work of the currently signed inventor team, the distribution of measuring points and the selection of orthogonal polynomials in the dynamic load identification process have been less studied. Regarding the distribution of measuring points, in the current methods, it is generally assumed that the measuring points are evenly distributed throughout the structure to make the transfer matrix condition number as small as possible. However, such a method requires a lot of attempts and requires a specific measurement point layout for a specific structure, which makes it difficult to form a conclusion with guiding significance. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method for optimizing the distribution of measuring points in the process of dynamic load identification. By studying the influence of measuring point positions on the dynamic load identification results, a strategy for solving the optimal measuring 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 purpose, the present invention adopts the following technical solution:

[0007] A method for optimizing measurement point distribution in a dynamic load identification process comprises the following steps:

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

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

[0010] Step 3: Check whether there are P-1 solutions x2,…,x in the solution set of the equation in step 2. P , if not, replace 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,…,x2 of the equation in step 2. P Can the matrix The row vectors are orthogonal to each other. If not, replace 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,…,x2 of the equation in step 2. P Can the matrix The row vector modulus lengths are basically close. If not, replace the initial value x1 and return to step 2 until the row vector modulus lengths of the matrix are basically close.

[0013] Step 6: Based on the initial value x1 and the P-1 solutions x2,…,x2 that satisfy the equations of Step 4-Step 5 P By identifying the relationship between K and N, the measuring point with the best load identification stability is obtained.

[0014] Furthermore, the judgment matrix The row vectors are orthogonal to each other as follows: the inner product of any two row vectors in the matrix is ​​much smaller than the norm of the two vectors themselves.

[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 with the best load identification stability are obtained in different cases, including: If K > N, then P = K. At this time, x1, x2, …, x P are the optimal measuring points; if K < N, then K < N = P. 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 process of dynamic load identification, 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 by selecting an initial value x1, where the 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 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 lengths of the row vectors of the matrix P 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. 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;

[0023] The measuring point determination module is used to obtain the measuring points with the best load identification stability 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the measurement point distribution optimization method in the dynamic load identification process as described above are implemented.

[0025] 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, the steps of the measuring point distribution optimization method in the dynamic load identification process as described above are implemented.

[0026] Beneficial effects: The present invention studies the influence of the measuring point position on the dynamic load identification results, and proposes a measuring point distribution optimization method and system in the dynamic load identification process. The measuring point position optimization method is constructed by making the response-load equation the most stable. First, the natural vibration mode of the structure is solved, a specific equation is established and solved, and verification and adjustment are performed according to the properties of the solution of the equation to obtain the measuring point with the best load identification stability. Compared with the classical method, the present invention can successfully reduce the pathological nature of the dynamic calibration matrix, thereby improving the accuracy of dynamic load identification. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

[0030] Figure 4 is the load distribution function in the embodiment of the present invention. DETAILED DESCRIPTION

[0031] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

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

[0033] As for 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, the error is not considered. Under the premise that the total number of measuring points is the same, the difference in the distribution of the measuring point positions will not destroy the validity of any equation, and will not change the calculation results of the entire matrix equation. Therefore, the difference in the distribution of the measuring point positions does not change the accuracy of the response-load equation.

[0034] For the stability of the response-load equation, the different measurement point positions will change the singular values ​​of the dynamic calibration matrix, and thus change the stability of the overall matrix equation. For example, when the measurement point positions are almost the same, no matter how many measurement points are taken, each row in the dynamic calibration matrix is ​​almost the same, and the response-load equation obtained is almost the same equation. At this time, the stability of the dynamic calibration matrix is ​​extremely poor, and it is difficult to obtain a more accurate recognition result.

[0035] The following formula is used to derive the influence of the measuring point on the dynamic load identification. The meanings of the symbols involved are shown in Table 1.

[0036] Table 1 Symbols

[0037]

[0038]

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

[0040]

[0041] The classical method is to select a set of basis functions φ i (x), (i=1,2,…,M) expand the load F(x), that is, where a m , (i=1,2,…,M) is F(x) according to φ i (x), (i=1,2,…,M) after expansion. M specifies the number of selected basis functions, which is collectively referred to as the basis function order below. If the response u(x) at multiple points is measured k ),k=1,2,…,K, then:

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

[0043]

[0044] Although the relationship between the multi-point response and the coefficients of the load after expansion according to the basis function is constructed by equations (2) and (3), it is not possible to directly see the relationship between the measurement point x k (k=1,2,…,K) has an influence on the matrix H. Formula (3) is a complex matrix. For convenience, the integral is written as the inner product of a function in the form of formula (4).

[0045]

[0046] Obviously, the inner product operator satisfies the linear superposition principle. For a linear system, the transfer function H(x,x0,ω) is not a random function, but a combination of multiple normalized vibration mode functions. k=1,2,3,… The transfer function expression of the 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 (x), i=1,2,… Expand the load F(x), that is, If the response u(x k ),k=1,2,…,K, then:

[0051]

[0052] Formula (9) establishes the relationship between the response and the orthogonal basis function coefficients to be identified, which involves three matrices, namely and By comparing equation (2) and equation (9), we can see that the so-called dynamic calibration matrix H is actually the product of these three matrices.

[0053]

[0054] Among them, the matrix can be changed by measuring point distribution This matrix reflects the influence of the measurement point distribution on the dynamic calibration matrix. Therefore, studying the measurement point distribution is to study the matrix The impact of changes on the recognition results.

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

[0056] Matrix multiplication does not reduce the matrix condition number. In order to ensure that the condition number of matrix H is not increased, the spatial position of the measurement points should make the matrix The singular values ​​of are as equal as possible. Take the measurement point position matrix It can be written as:

[0057]

[0058] Formula (11) is the matrix A singular value decomposition of That is the matrix The singular value of . The values ​​of are close to each other, then This is the solution that makes the singular values ​​of the matrix as equal as possible. At this time, the matrix Close to an orthogonal matrix. The matrix row vectors are orthogonal to each other, then:

[0059]

[0060] Right now:

[0061]

[0062] Directly solving equation (13) requires solving N values ​​at the same time, which requires a lot of calculations. It is not wise to solve it directly. Take the first N-1 equations as:

[0063]

[0064] Theoretically, equation (13) and equation (14) do not have the same solution, and the solution of equation (13) is a subset of the solution of equation (14). Equation (13) can be solved by solving a set of solutions of equation (14) and substituting them into equation (13) for verification.

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

[0066] A series of roots of can obtain a set of trial solutions x2,x3,…x N If equation (15) can be solved to obtain N-1 solutions, then the solution is a set of solutions to equation (14), which can be further substituted into equation (13) to verify whether it is true. N If equation (13) cannot be satisfied, simply adjust the value of x1.

[0067] Formula (15) has only one variable x, and is easier to solve than Formula (13) and Formula (14) which need to solve N unknown quantities at one time.

[0068] In addition, it is necessary to verify whether the matrix The singular values ​​of the matrix 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. For the specific strategy, refer to 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 the first P-order 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. If the difference between 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 orthogonal to each other and have close lengths. Based on these P points, obtain the optimal measurement points. P If K > N, then P = K. At this time, x1, x2, …, x

[0083] are the optimal measurement points; if K < N, then K < N = P. At this time, randomly select K points from x1, x2, …, x P . P For example, in one embodiment, to verify the performance of this method, the measurement point distribution of a cantilever beam is optimized according to this method. The schematic diagram of the beam and the corresponding coordinate system are as shown in

[0084] . Let's assume the length of the cantilever beam L = 100 mm, the elastic modulus E = 210 GPa, the density ρ = 7.85 g / cm Figure 2 , the width w = 5 mm, the thickness t = 1 mm, and the flexural rigidity I = wt 3 / 12. 3 The natural frequency of the cantilever beam is:

[0085]

[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. Solve the function using the graphical method. The image of the function is as shown in Figure 3 . 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 conditions in Step 3 are satisfied, and the verification of the row vectors of the matrix is carried out.

[0091] Take the trial solution {x1,x2,x3,x4,x5} = {100,189,283,380,468}. Vectors l1,l2,…,l N The pairwise inner product is:

[0092]

[0093] Vector l1,l2,…,l N The magnitude of the square of the modulus length is stable at 10 -2 , while the order of magnitude of the pairwise inner product is 10 -4 ~10 -6 This shows that the vectors l1,l2,…,l N The inner product of any two vectors is much smaller than their own modulus, which means that the angle between any two vectors is close to 90°, that is, the vectors l1, l2, ..., l N Any two can be considered orthogonal.

[0094] Vector l1,l2,…,l N The modulus length is:

[0095]

[0096] The threshold is set to 0.01. The maximum difference between the modulus lengths is 0.008, and the modulus lengths can be considered to be basically equal. The singular value decomposition shows that the matrix The singular values ​​of are {0.116, 0.108, 0.104, 0.102, 0.101}. N The values ​​of ||} are basically close.

[0097] Finally, the measuring points {x1,x2,x3,x4,x5}={100,189,283,380,468} that optimize load identification stability are obtained.

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

[0099] By adjusting the measuring points, the small singular value 0.019 caused by the measuring points was successfully removed. From the perspective of the matrix condition number, the transfer matrix condition number of the {x1, x2, x3, x4, x5} measuring points is 1.14, and the transfer matrix condition number of the {y1, y2, y3, y4, y5} measuring points is 6.12. Compared with the classical method, the present invention successfully reduces the morbidity of the dynamic calibration matrix.

[0100] As described in the calculation of 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, and the basis function order M=5.

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

[0102] Table 2 Legendre basis function coefficients

[0103]

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

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

[0106] This example verifies the superiority of the proposed measurement point layout optimization method over the traditional method by using the fact that vector B is closer to vector A than vector C when there are errors in U and U0.

[0107] According to formula (2), we can get the matrix equation:

[0108] U=H·B (21)

[0109] U0=H0·C (22)

[0110] The matrices H and H0 can be obtained by equation (10). The true values ​​of the responses at the measuring points {x1, x2, x3, x4, x5} and {y1, y2, y3, y4, y5} are shown in Table 3.

[0111] Table 3 Responses of two measuring points

[0112]

[0113] The error of U and U01% is given many times, and the matrix equations (21) and (22) are processed by Tikhonov regularization theory. The calculation results are shown in Table 4.

[0114] Table 4 Matrix equation calculation results 1

[0115]

[0116] The error of U and U02% is given many times, and the matrix equations (21) and (22) are processed by Tikhonov regularization theory. The calculation results are shown in Table 5.

[0117] Table 5 Matrix equation calculation results II

[0118]

[0119] The calculation results show that the optimized measurement point layout can reduce the condition number of the transfer matrix in the dynamic load identification process, thereby reducing the error caused by the instability of the matrix equation in the identification process under different error scales and improving the accuracy of dynamic load identification.

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

[0121] The natural vibration mode solving module is used to solve the first P order natural vibration modes according to the determined number of measurement points K and the modal truncation number N, assuming P = Max (K, N) i=1,2,…,P;

[0122] The equation solving module is used to solve the equation by selecting an initial value x1. The initial value x1 represents the first measuring point position;

[0123] The solution quantity check module is used to check whether there are P-1 solutions x2,…,x in the equation solution set in the equation solving module. P If not, replace 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 the initial value x1 and the P-1 solutions x2,…,x in the equation solving module.P Whether the matrix row vectors are 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 the initial value x1 and the P - 1 solutions x2,..., x of the equation in the equation solving module P Whether the matrix row vector norms are basically close. If not, replace the initial value x1 and repeat the operation of the equation solving module until the row vector norms 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 meet the verification module P ,

[0127] If K > N, then P = K. At this time, x1, x2,..., x P are the optimal measuring points; if K < N, then K < N = P. At this time, randomly select K points from x1, x2,..., x P 即可。

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

[0129] The present invention also provides a computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the measuring point distribution optimization method in the dynamic load identification process as described above are implemented.

[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 complete hardware embodiment, a complete 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] The present invention is described with reference to a flowchart of a method according to an embodiment of the present invention. It should be understood that each process in the flowchart and a combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the process in the flowchart. Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the functions specified in the process. Figure 1 The steps of a specified function in a process or multiple processes.

Claims

1. A method for optimizing the distribution of measuring points in a dynamic load identification process, characterized in that: The following steps are involved: Step 1: Determine the number of measurement points K and the modal cutoff number N, set P = Max(K,N), and solve the first P order natural vibration modes Step 2: Select an initial value x1 as the first measuring point and solve the equation Step 3: Check whether there are P-1 solutions x2,…,x in the solution set of the equation in step 2. P , if not, replace 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,…,x2 of the equation in step 2. P Can the matrix The row vectors are orthogonal to each other. If not, replace 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,…,x2 of the equation in step 2. P Can the matrix The row vector modulus lengths are basically close. If not, replace the initial value x1 and return to step 2 until the row vector modulus lengths of the matrix are basically close. Step 6: Based on the initial value x1 and the P-1 solutions x2,…,x2 that satisfy the equations of Step 4-Step 5 P By identifying the relationship between K and N, the measuring point with the best load identification stability is obtained.

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

3. The method according to claim 1, characterized in that Judgment Matrix The method for determining that the moduli of row vectors are substantially close is as follows: if the difference between the moduli of any two row vectors in the matrix is ​​less than a preset threshold, it is determined that the moduli of row vectors are substantially close.

4. The method according to claim 1, characterized in that: Obtain the measuring points that optimize the load identification stability by identifying 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。 5. A measuring point distribution optimization system in the process of dynamic load identification, characterized in that: include: The natural vibration mode solving module is used to solve the first P order natural vibration modes according to the determined number of measurement points K and the modal truncation number N, assuming P = Max (K, N) The equation solving module is used to solve the equation by selecting an initial value x1. The initial value x1 represents the first measuring point position; The solution quantity check module is used to check whether there are P-1 solutions x2,…,x in the equation solution set in the equation solving module. P If not, replace 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 The row vectors are 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. 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 The row vector modulus length is basically close. If not, replace the initial value x1 and repeat the operation of the equation solving module until the row vector modulus length of the matrix is ​​basically close; The measurement point determination module is used to determine the P-1 solutions x2,…,x2 based on the initial value x1 and the equations that satisfy the verification module. P By identifying the relationship between K and N, the measuring point with the best load identification stability is obtained.

6. The system according to claim 5, characterized in that Judgment Matrix The row vectors are orthogonal to each other as follows: the inner product of any two row vectors in the matrix is ​​much smaller than the norm of the two vectors themselves.

7. The system according to claim 5, characterized in that Judgment Matrix The method for determining that the moduli of row vectors are substantially close is as follows: if the difference between the moduli of any two row vectors in the matrix is ​​less than a preset threshold, it is determined that the moduli of row vectors are substantially close.

8. The system according to claim 5, characterized in that Obtain the measuring points that optimize the load identification stability by distinguishing cases based on 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。 9. 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the method for optimizing the distribution of measuring points in the dynamic load identification process as described in any one of claims 1 to 4 are implemented.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for optimizing the distribution of measuring points in the dynamic load identification process according to any one of claims 1 to 4 are implemented.

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