Railway vehicle system structure modal test measuring point optimization method and medium

Abstract

The invention relates to a railway vehicle system structure modal test measuring point optimization method and a medium, and the method comprises the following steps: constructing a modal matrix of a railway vehicle system structure, extracting candidate measuring points of modal test, and forming a candidate measuring point set, the sensor comprises a three-way sensor and a one-way sensor; if a three-way sensor is selected to perform modal testing, calculating measurement values of candidate measurement points in the candidate measurement point set by adopting a multi-dimensional effective independent method based on the modal matrix, and determining final measurement points of the modal testing according to the measurement values; and if the unidirectional sensor is selected for modal testing, constructing an auxiliary matrix based on the modal matrix and the candidate test point set, and determining a final test point of the modal testing according to the auxiliary matrix. Compared with the prior art, the method has the advantages of optimizing measurement point distribution, improving the accuracy of a modal identification result and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration control of rail transit equipment and facilities, and in particular to a method and medium for optimizing measuring points of a rail vehicle system structure modal test. Background Art

[0002] With the increase of rail train operating mileage and the increase of running speed, the train vibration problem has become more serious, which directly affects the running stability of the train. In the actual structural modal test, due to the limitations of environmental factors and experimental conditions, especially the limited number of available sensors, it is necessary to arrange the limited sensors at the key positions of the structure in order to obtain the dynamic response information of the structure more accurately and effectively.

[0003] The arrangement of measuring points in modal test is crucial for subsequent analysis, which directly affects the modification of finite element model, identification of test modal parameters and test modal identification and other related analyses. Due to the limitations of the structure itself and the test conditions, when testing, due to the limitation of the number of sensors, it is impossible to evenly arrange measuring points for the entire structure, and it is unrealistic to arrange sensors for testing in all degrees of freedom.

[0004] In addition, if there are too many sensors, a large amount of redundant data will be collected, which will make it difficult to conduct subsequent data analysis and quickly extract data to observe important modal features. Therefore, when conducting modal testing, the sensor layout strategy needs to be carefully planned to ensure that the dynamic characteristics of the structure can be effectively captured while avoiding excessive redundancy of data, thereby improving the efficiency and accuracy of the test. Summary of the invention

[0005] The purpose of the present invention is to provide a method and medium for optimizing measuring points of a rail vehicle system structure modal test, which provide a more accurate measuring point arrangement.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A method for optimizing measuring points of a rail vehicle system structure modal test comprises the following steps:

[0008] Constructing a modal matrix of the rail vehicle system structure, extracting candidate measuring points for modal testing, and forming a candidate measuring point set, wherein the candidate measuring point positions are candidate positions of sensors during modal testing, and the sensors include three-way sensors and one-way sensors;

[0009] If a three-way sensor is selected for modal testing, then based on the modal matrix, a multi-dimensional effective independence method is used to calculate the measurement values ​​of the candidate measurement points in the candidate measurement point set, and the final measurement points of the modal test are determined according to the measurement values;

[0010] If a unidirectional sensor is selected for modal testing, an auxiliary matrix is ​​constructed based on the modal matrix and the candidate measuring point set, and the final measuring points of the modal test are determined according to the auxiliary matrix.

[0011] Furthermore, the step of constructing the modal matrix includes:

[0012] The vehicle body vibration is approximated as an undamped free vibration system with n degrees of freedom, and the undamped vibration equation is used to calculate the inherent modal characteristics, where the expression of the inherent modal characteristics is:

[0013]

[0014] Where M is the mass matrix, K is the stiffness matrix, x is the displacement column vector, and f(t) is the external load force column vector;

[0015] Based on the natural modal characteristics, the natural frequency of the undamped free vibration system is solved, and the vibration mode vector of the natural frequency is further calculated to obtain the modal matrix of the rail vehicle system structure.

[0016] Furthermore, the step of obtaining the modal matrix of the rail vehicle system structure includes:

[0017] Based on the inherent modal characteristics, let f(t) = 0 and assume that the special solution get:

[0018]

[0019] In the formula, (K-ω 2 M) is the coefficient matrix, ω 2 is the independent variable, is the displacement amplitude column vector of the free response;

[0020] When the determinant of the coefficient matrix is ​​zero, equation (1) has a non-zero solution, and the characteristic equation expression is obtained:

[0021] |K-ω 2 M|=0 (2)

[0022] Among them, the number of positive solutions of the characteristic equation expression is n, which are arranged in ascending order as follows:

[0023] 0<ω 01 <ω 02 <…<ω 0i <...<ω 0n (3)

[0024] In the formula, ω 0i is the i-th natural frequency of the undamped free vibration system;

[0025] Each ω 0i Substituting into formula (2), we can obtain the vibration mode vector of the i-th order natural frequency:

[0026]

[0027] In the formula, is the i-th order vibration mode vector, is the nth-order vibration mode value;

[0028] n Arrange by columns and get the modal matrix of the rail vehicle system structure:

[0029]

[0030] Where Φ is the modal matrix.

[0031] Furthermore, the step of forming a candidate measurement point set includes:

[0032] Determine the target order of the mode;

[0033] For each target order mode, multiple points with the largest displacement are selected from the modal matrix as part of the candidate measuring points, and the remaining candidate measuring points are randomly distributed on the rail vehicle system structure;

[0034] The part of candidate measuring points and the remaining candidate measuring points form a candidate measuring point set.

[0035] Furthermore, the step of determining the final measurement points of the modal test according to the measurement values ​​includes:

[0036] The modal matrix is ​​converted into a three-dimensional modal vibration matrix by using a multi-dimensional effective independence method combined with an intelligent algorithm:

[0037] Φ3=[Φ x , Φ y , Φ z ]

[0038] Where Φ3 is the three-dimensional modal vibration matrix, Φ x , Φ y , Φ z are the mode shapes in the x, y, and z directions;

[0039] The covariance matrix J is constructed based on the three-dimensional modal vibration matrix:

[0040]

[0041] in:

[0042]

[0043] Where E3 is the three-dimensional auxiliary matrix, q is the modal coordinate in the modal space, is the least squares solution of the modal coordinate q, Q is the Fisher information matrix of the artificially defined rail vehicle system structure, is the three-dimensional target modal matrix corresponding to the i-th candidate measurement point, n is the number of candidate measurement points, Q 3i is the Fisher information matrix of the i-th candidate measurement point, σ 2 is the variance;

[0044] Based on the Fisher information matrix Q, the measurement value of each candidate measuring point in the candidate measuring point set is calculated to determine whether there are multiple candidate measuring points with the smallest measurement value. If so, the MAC criterion is used to determine the candidate measuring point with the worst modal recognition effect, and it is removed from the candidate measuring point set to form a new candidate measuring point set. This step is repeated for iterative calculation until the end condition is met to obtain the final modal test measuring point.

[0045] Furthermore, the step of calculating the measurement value of the candidate measurement point includes:

[0046] When the i-th candidate measuring point is deleted from the candidate measuring point set, the EfI value of the three-way sensor corresponding to the i-th candidate measuring point is calculated as the measurement value of the i-th candidate measuring point. The calculation expression of the measurement value of the i-th candidate measuring point is:

[0047] E 3i =1-det(I3-E 3i ) (1)

[0048] In the formula, EfI 3i is the measurement value of the i-th candidate measurement point in three dimensions, I3 is the 3×3 unit matrix, E 3i It is a 3×3 fully filled matrix, containing the EfI value of the sensor corresponding to the i-th candidate measurement point on the diagonal;

[0049] Among them, E 3i The calculation steps include:

[0050] Based on the Fisher information matrix Q, the Fisher information matrix Q of the i-th candidate measurement point is obtained 3i :

[0051]

[0052] In the formula, I k is the k-order unit matrix, k is the number of target modes;

[0053] Based on the Q 3i Get its determinant, which is:

[0054]

[0055] In the formula, is the rth row (r=1, 2, 3) of the target modal partition corresponding to the i-th candidate measurement point;

[0056] Multiply both sides of equation (5) by have to:

[0057]

[0058] Where P i1 It is a vector An oblique projection of the column space spanned by Q 3ir is the information matrix value corresponding to the rth row of the target modal partition of the i-th candidate measurement point;

[0059] The Fisher information matrix Q is decomposed into:

[0060]

[0061] For formula (8), P i1 Multiplying Q on the right yields:

[0062]

[0063] Derived:

[0064]

[0065] In the formula, Q 3jr is the information matrix value corresponding to the rth row of the target modal partition of the jth candidate measurement point;

[0066] To ensure that each item in equation (10) is a zero matrix, we have:

[0067]

[0068] E of formula (4) 3i Restore to:

[0069]

[0070] Furthermore, the step of determining the final measurement points of the modal test according to the auxiliary matrix includes:

[0071] Construct the covariance matrix J based on the modal matrix:

[0072]

[0073] in:

[0074]

[0075] (A-λI)ψ=0

[0076] Where E is the auxiliary matrix, q is the modal coordinate in the modal space, are the true modal coordinates, is the modal matrix, S represents the variance σ 2 Gaussian distributed white noise, Q is the Fisher information matrix of the artificially defined rail vehicle system structure, A is a symmetric positive definite matrix, ψ is the eigenvector matrix of matrix A, and λ is the eigenvalue matrix of matrix A;

[0077] An auxiliary matrix E is constructed based on the covariance matrix J. The contribution of each candidate measuring point in the candidate measuring point set is obtained according to the auxiliary matrix E. It is determined whether there are multiple candidate measuring points with the smallest contribution. If so, the candidate measuring point with the worst modal recognition effect is determined by using the MAC criterion, and it is eliminated from the candidate measuring point set to form a new candidate measuring point set. This step is repeated for iterative calculation until the end condition is met to obtain the final modal test measuring point.

[0078] Furthermore, the auxiliary matrix E is expressed as:

[0079]

[0080] Where E is an idempotent matrix, and its diagonal data E ii The size of represents the modal matrix of the i-th candidate measurement point pair The extent of contribution.

[0081] Furthermore, the expression of the MAC criterion is:

[0082]

[0083] Where MAC is the modal assurance matrix, which represents the angle between the i-th order modal vector and the j-th order modal vector. MAC = mac ij The non-diagonal elements of mac ij The (i≠j) value reflects the correlation between the two modal vibration vectors, that is, the modal identification effect. and They represent the test degree of freedom modal matrix Φ s ∈R s×m The i-th and j-th columns of , s is the test degree of freedom, m is the identifiable mode, and R is a set of real numbers.

[0084] The present invention also provides a computer-readable storage medium, comprising one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the method for optimizing measurement points in a structural modal test of a rail vehicle system as described above.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] (1) For the actual test of the rail vehicle body modal, the present invention starts from the perspective of optimizing the arrangement of measuring points. According to the sensors of different dimensions required for modal testing and the modal matrix of the rail vehicle system structure, the measured values ​​of the candidate measuring points in the candidate measuring point set and the auxiliary matrix representing the contribution of the candidate measuring points are respectively calculated to determine the importance of the candidate measuring points for modal identification, thereby obtaining a more accurate arrangement of measuring points.

[0087] (2) In the process of optimizing candidate measuring points in different dimensions, when there are multiple candidate measuring points with the smallest measurement value and the smallest contribution, the present invention adopts the MAC criterion to identify the candidate measuring points with the worst modal recognition effect and eliminate them, so that the latest candidate test set calculated in each iteration is the best, thereby further improving the measuring point optimization effect.

[0088] (3) The present invention provides a theoretical basis for vehicle body modal testing by optimizing the vehicle body modal test points, thereby efficiently acquiring the vehicle body modality, and further providing an effective basis for improving the vehicle running stability and improving the vehicle riding comfort. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0090] Figure 2 is the diagonal value of the auxiliary matrix E of the candidate measuring point set of the present invention;

[0091] Figure 3 MAC matrix diagrams after optimization for different numbers of measuring points of the present invention, wherein (a) is for 20 measuring points, (b) is for 40 measuring points, (c) is for 60 measuring points, (d) is for 80 measuring points, (e) is for 120 measuring points, and (f) is for 160 measuring points. DETAILED DESCRIPTION

[0092] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0093] This embodiment provides a method for optimizing measurement points in a rail vehicle system structure modal test. From the perspective of optimizing the measurement point arrangement, for the actual test of the rail vehicle body modal, the measurement point positions obtained by the particle swarm optimization algorithm are adjusted according to the laboratory's test capabilities and the integrity of the vibration mode to maximize the test capability. Figure 1 As shown, the method comprises the following steps:

[0094] S1. Definition of measurement point arrangement for rail vehicle system structural modal test.

[0095] The arrangement of measuring points is a very important part in modal testing. The measuring points are used to set sensors for modal identification. Therefore, the arrangement of measuring points directly determines the effect of modal identification. For the arrangement of measuring points for modal testing of vehicle bodies, some measuring points may be located at modal nodes, which do not contribute much to the identification of modal information. The modal parameters are determined by the mass matrix and stiffness matrix of the structure itself. They are inherent characteristics of the structure and have nothing to do with the excitation characteristics of the external loads. The damping has little effect on the modal frequency and vibration type. Therefore, the vibration of the vehicle body can be approximated as an undamped free vibration system with n degrees of freedom. The undamped vibration equation can be used to calculate the inherent modal characteristics:

[0096]

[0097] Where M is the mass matrix, K is the stiffness matrix, x is the displacement column vector, and f(t) is the external load force column vector.

[0098] If the structure is in free vibration, let f(t) = 0, solve the eigenvalue problem, and assume the special solution:

[0099]

[0100] In the formula, is the displacement amplitude column vector of the free response;

[0101] The solution is:

[0102]

[0103] (K-ω 2 M) is the coefficient matrix. When the determinant of the coefficient matrix is ​​zero, the above formula has a non-zero solution, and we get:

[0104] |K-ω 2 M|=0 (4)

[0105] The above formula is called the characteristic equation expression of the eigenvalue problem. It is an n-order algebraic equation with the independent variable ω 2 , there are n correct solutions, arranged in ascending order:

[0106] 0<ω 01 <ω 02 <…<ω 0n (5)

[0107] ω 0i Represents the i-th order natural frequency of the undamped vibration system. 0i Substituting into the above formula, we can get n The proportional solution of They are linearly independent and are normalized to become the vibration mode vector of the i-th order natural frequency.

[0108]

[0109] Without loss of generality, we will Arranged in columns, it becomes the modal matrix of the system, as shown below:

[0110]

[0111] For forming a candidate measurement point set, the steps include:

[0112] According to the modal analysis, there are several modes that need to be paid special attention to, and the orders of these modes are the target orders;

[0113] For each target order mode, the five points with the largest displacement are selected from the modal matrix as candidate measurement points. These points have the largest vibration amplitude in this mode and are very important for analyzing and optimizing the dynamic characteristics of this mode. In addition to the five maximum displacement points of each mode, the remaining candidate measurement points can be randomly distributed on the rail vehicle system structure. These randomly distributed candidate measurement points help to capture the dynamic behavior of the structure more comprehensively. The candidate measurement points selected based on the maximum displacement are combined with the randomly selected candidate measurement points to form a candidate measurement point set.

[0114] Experimental analysis is to obtain the frequency response function matrix through testing means, and then grasp the structural modal distribution, including measurement point arrangement, application of excitation source, signal acquisition, modal post-processing, modal verification and other steps. Based on the system's excitation and response information, or only based on the system's response information as initial data, the modal parameters of the system are identified through parameter identification methods or non-parameter identification methods, which is called the reverse analysis of modal analysis.

[0115] S2. Optimization of the arrangement of modal test points acting on the rail vehicle system structure.

[0116] In order to evaluate the intersection angle of the modal vector space, an effective tool for evaluating sensor layout is used, namely the modal assurance matrix, also known as the MAC criterion. The MAC matrix can measure the correlation coefficient between the vibration modes and reflect the degree of independence of the vibration modes. Assuming that s sensors are configured in an n-degree-of-freedom system, the identifiable modal end is m, and the test modal vibration matrix of s degrees of freedom is expressed as Φ s ∈R s×m , the test degree of freedom s is less than the system degree of freedom n, and s is a subset of n. Modal assurance matrix MAC = mac ij , which represents the angle between the i-th order modal vector and the j-th order modal vector, can be expressed as:

[0117]

[0118] In the formula, and They represent the i-th and j-th columns of the test freedom modal vibration mode, respectively. It can be deduced that MAC = mac ij The non-diagonal elements of mac ij The closer the (i≠j) value is to 0, the better the orthogonality of the two modal vibration vectors, the higher the linear independence of the modal vibration, the more reasonable the arrangement of the sensors, and the better the modal vibration distribution of the system can be identified. On the contrary, MAC = mac ij The non-diagonal elements of mac ij The closer the (i≠j) value is to 1, the higher the correlation between the two modal vibration vectors is, and the poorer the modal identification effect is.

[0119] (I) For situations where a three-way sensor needs to be set up at the measuring point for modal testing:

[0120] Under the improved multi-dimensional effective independence method, combined with the intelligent algorithm, (7) can be rewritten as:

[0121] Φ3=[Φ x , Φ y , Φ z ] (9)

[0122] The estimated covariance matrix J can be expressed as:

[0123]

[0124] Where q is the modal coordinate in the modal space, is the least squares solution of the modal coordinate q, Φ3 is the three-dimensional modal vibration matrix of the structure, and Q is an artificially defined Fisher information matrix (FIM). It can be decomposed into:

[0125]

[0126] In the formula, is the three-row target modal matrix corresponding to the i-th measuring point, and n is the number of candidate measuring points.

[0127] After deleting the i-th measuring point, it can be written as:

[0128]

[0129] In the formula, I k is the k-order identity matrix, and k is the number of target modes.

[0130] The corresponding determinant can be written as:

[0131]

[0132] In the formula, E 3i is a 3×3 fully filled matrix containing the Effective Independence (EfI) value of the sensor corresponding to the i-th measurement point on the diagonal. In particular, when E 3i With an eigenvalue of λ = 1.0, Q 3i The determinant of is reduced to zero, and the target mode is no longer independent. This indicates that the i-th measurement point is critical to the independence of the target mode. Therefore, at least one of the three degrees of freedom associated with the i-th measurement point must have an EfI value of 1.0. It can be expressed as:

[0133]

[0134] In the formula, is the rth row (r=1,2,3) of the target modal partition corresponding to the ith measurement point. Without loss of generality, let the first degree of freedom of the ith measurement point be crucial to the independence of the target mode. E 3i The corresponding EfI values ​​are given in:

[0135]

[0136] Multiply both sides of formula (15) by have to:

[0137]

[0138] Where P i1 It is a vector An oblique projection of the column space spanned. It can be expressed as:

[0139]

[0140] Formula (11) can be decomposed into:

[0141]

[0142] P i1 Multiplying Q on the right yields:

[0143]

[0144] Formula (18) can be deduced as follows:

[0145]

[0146] According to the relevant theory of matrix calculation, the matrix obtained by multiplying the transpose of a row vector by itself should be a semi-positive definite matrix. It can be deduced that the matrix P i1 and Q 3jris a semi-positive definite matrix, so their product is also semi-positive definite. To ensure that formula (20) holds, all terms in the equation must be zero matrices. Specifically:

[0147] It can be proved that Q 3ir Columns and vectors In parallel, therefore:

[0148]

[0149] By definition, is a non-zero matrix, so:

[0150]

[0151] E 3i The form is reduced to:

[0152]

[0153] Obviously its eigenvalue is 1.0.

[0154] Therefore, if one of the sensor orientations associated with the ith measurement point is critical to the independence of the target mode, then E 3i has an eigenvalue of 1.0, and I3-E 3i The determinant of becomes 0. On the contrary, if I3-E 3i The determinant of FIM is 1.0. Deleting the i-th measurement point has no effect on the determinant of FIM. Q of FIM is positive definite, Q 3i is at least positive semidefinite. The expression It is also at least semidefinite. 3i The measured value of is given by:

[0155] E 3i =1-det(I3-E 3i ) (twenty four)

[0156] The value range is 0≤EfI 3i ≤1. 3i The value of represents the fractional change in the determinant if the i-th measurement point is removed from the candidate measurement point set. If a measurement point is critical to the independence of the target mode, the corresponding EfI3 value is 1.0; if a measurement point does not contribute to independence, its corresponding EfI3 value is 0.0. This measure can be used to rank and sort the candidate measurement points, and delete the lowest ranked measurement points. In an iterative manner, the candidate measurement point set can match the required number of three-dimensional sensors for modal testing.

[0157] If there are multiple candidate measuring points with the smallest measurement values, the MAC criterion in formula (8) is used to judge the correlation of the modal vibration vectors between the two candidate measuring points, determine the candidate measuring points that need to be eliminated in the end, and form a new set of candidate measuring points.

[0158] (II) For situations where a unidirectional sensor needs to be set up at the measuring point for modal testing:

[0159] Once the vehicle system dynamics parameters are determined, the modal parameters are constants, so an auxiliary matrix can be constructed for evaluation. The optimal estimate of is used to obtain the optimal modal result. The unbiased estimation method is used to retain the linear independence of the structure to the greatest extent, and a covariance matrix J of the estimation error is defined:

[0160]

[0161] In the formula, S represents the variance σ 2 Gaussian distributed white noise, Q is the artificially defined Fisher information matrix.

[0162]

[0163] According to statistical principles, the smaller the covariance matrix, the more accurate the indicator estimation. When the determinant of matrix A reaches a maximum value, the Fisher information matrix also reaches a maximum value at the same time, and the covariance matrix of the estimation error becomes smaller. Therefore, the properties of matrix A are further discussed below.

[0164] (A-λI)ψ=0 (27)

[0165] Where λ is the eigenvalue matrix of matrix A, ψ is the eigenvector matrix of matrix A, and the modal matrix of the system is assumed to be If they are linearly independent, then A is a symmetric positive definite matrix, the eigenvector matrix ψ is a normalized matrix, and the eigenvalues ​​are positive definite real numbers.

[0166] but:

[0167] ψ T Aψ=λ (28)

[0168] ψ T ψ=I (29)

[0169] From the above formula, we can deduce that

[0170] ψ T λ -1 ψ=A -1 (30)

[0171] Construct the auxiliary matrix E matrix:

[0172]

[0173] Matrix E is an idempotent matrix. Assuming that the system has i measurement points, the matrix E is an i-order square matrix, and its diagonal data E ii The size represents the modal matrix of the i-th measurement point pair The extent of contribution.

[0174] Eliminate the candidate measuring point with the smallest contribution from the candidate measuring points to form a new candidate measuring point. Through iteration, the candidate measuring point set can match the required number of unidirectional sensors for modal testing.

[0175] If there are multiple candidate measuring points with the smallest contribution, the MAC criterion in formula (8) is used to judge the correlation of the modal vibration vector between two candidate measuring points, determine the candidate measuring points that need to be eliminated in the end, and form a new set of candidate measuring points.

[0176] This embodiment takes a certain type of subway vehicle as an example, and the diagonal values ​​of the auxiliary matrix E obtained according to the candidate measurement point set are as follows: Figure 2 As shown in the figure, the MAC matrix diagram after optimization of different measurement point numbers is as follows Figure 3 As shown. In this example, the modal vibration matrix of the candidate measuring point obtained by finite element simulation is extracted to perform MAC matrix calculation, and the maximum value of the non-diagonal elements of the MAC matrix is ​​compared. Under the premise of ensuring that the maximum value of the non-diagonal elements of the MAC matrix is ​​not higher than 0.25 and the number of sensors is higher than the target modal order of interest, the number of sensors required is reduced as much as possible to make full use of the test resources.

[0177] In summary, this embodiment optimizes the vehicle body modal test measurement points and combines the vehicle body vibration to provide a theoretical basis for the vehicle body modal test, thereby efficiently acquiring the vehicle body modality, and further providing an effective basis for improving the vehicle running stability and improving the vehicle ride comfort.

[0178] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0179] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present invention may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0180] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, 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 processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0181] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0182] 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 process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0183] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0184] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for optimizing measurement points of a rail vehicle system structure modal test, characterized in that: The following steps are involved: Constructing a modal matrix of the rail vehicle system structure, extracting candidate measuring points for modal testing, and forming a candidate measuring point set, wherein the candidate measuring point positions are candidate positions of sensors during modal testing, and the sensors include three-way sensors and one-way sensors; If a three-way sensor is selected for modal testing, then based on the modal matrix, a multi-dimensional effective independence method is used to calculate the measurement values ​​of the candidate measurement points in the candidate measurement point set, and the final measurement points of the modal test are determined according to the measurement values; If a unidirectional sensor is selected for modal testing, an auxiliary matrix is ​​constructed based on the modal matrix and the candidate measuring point set, and the final measuring points of the modal test are determined according to the auxiliary matrix.

2. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 1, characterized in that: The steps of constructing the modal matrix include: The vehicle body vibration is approximated as an undamped free vibration system with n degrees of freedom, and the undamped vibration equation is used to calculate the inherent modal characteristics, where the expression of the inherent modal characteristics is: Where M is the mass matrix, K is the stiffness matrix, x is the displacement column vector, and f(t) is the external load force column vector; Based on the natural modal characteristics, the natural frequency of the undamped free vibration system is solved, and the vibration mode vector of the natural frequency is further calculated to obtain the modal matrix of the rail vehicle system structure.

3. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 2, characterized in that: The step of obtaining the modal matrix of the rail vehicle system structure comprises: Based on the inherent modal characteristics, let f(t) = 0 and assume that the special solution get: In the formula, (K-ω 2 M) is the coefficient matrix, ω 2 is the independent variable, is the displacement amplitude column vector of the free response; When the determinant of the coefficient matrix is ​​zero, equation (1) has a non-zero solution, and the characteristic equation expression is obtained: |K-oh 2 M|=0 (2) Among them, the number of positive solutions of the characteristic equation expression is n, which are arranged in ascending order as follows: 0<ω 01 <ω 02 <…<ω 0i <...<ω 0n (3) In the formula, ω 0i is the i-th natural frequency of the undamped free vibration system; Each ω 0i Substituting into formula (2), we can obtain the vibration mode vector of the i-th order natural frequency: In the formula, is the i-th order vibration mode vector, is the nth-order vibration mode value; n Arrange by columns and get the modal matrix of the rail vehicle system structure: Where Φ is the modal matrix.

4. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 1, characterized in that: The step of forming a candidate measurement point set comprises: Determine the target order of the mode; For each target order mode, multiple points with the largest displacement are selected from the modal matrix as part of the candidate measuring points, and the remaining candidate measuring points are randomly distributed on the rail vehicle system structure; The part of candidate measuring points and the remaining candidate measuring points form a candidate measuring point set.

5. The method for optimizing measuring points of a rail vehicle system structure modal test according to claim 1, characterized in that: The step of determining the final modal test measurement point according to the measurement value comprises: The modal matrix is ​​converted into a three-dimensional modal vibration matrix by using a multi-dimensional effective independence method combined with an intelligent algorithm: Φ3=[Φ x ,F y ,F z ] Where Φ3 is the three-dimensional modal vibration matrix, Φ x , Φ y , Φ z are the mode shapes in the x, y, and z directions; The covariance matrix J is constructed based on the three-dimensional modal vibration matrix: in: Where E3 is the three-dimensional auxiliary matrix, q is the modal coordinate in the modal space, is the least squares solution of the modal coordinate q, Q is the Fisher information matrix of the artificially defined rail vehicle system structure, is the three-dimensional target modal matrix corresponding to the i-th candidate measurement point, n is the number of candidate measurement points, Q 3i is the Fisher information matrix of the i-th candidate measurement point, σ 2 is the variance; Based on the Fisher information matrix Q, the measurement value of each candidate measuring point in the candidate measuring point set is calculated to determine whether there are multiple candidate measuring points with the smallest measurement value. If so, the MAC criterion is used to determine the candidate measuring point with the worst modal recognition effect, and it is removed from the candidate measuring point set to form a new candidate measuring point set. This step is repeated for iterative calculation until the end condition is met to obtain the final modal test measuring point.

6. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 5, characterized in that: The step of calculating the measurement value of the candidate measuring point comprises: When the i-th candidate measuring point is deleted from the candidate measuring point set, the EfI value of the three-way sensor corresponding to the i-th candidate measuring point is calculated as the measurement value of the i-th candidate measuring point. The calculation expression of the measurement value of the i-th candidate measuring point is: Efi 3i =1-det(I3-E 3i ) (1) In the formula, EfI 3i is the measurement value of the i-th candidate measurement point in three dimensions, I3 is the 3×3 unit matrix, E 3i It is a 3×3 fully filled matrix, containing the EfI value of the sensor corresponding to the i-th candidate measurement point on the diagonal; Among them, E 3i The calculation steps include: Based on the Fisher information matrix Q, the Fisher information matrix Q of the i-th candidate measurement point is obtained 3i : In the formula, I k is the k-order unit matrix, k is the number of target modes; Based on the Q 3i Get its determinant, which is: In the formula, is the rth row (r=1, 2, 3) of the target modal partition corresponding to the i-th candidate measurement point; Multiply both sides of equation (5) by have to: Where P i1 It is a vector An oblique projection of the column space spanned by Q 3ir is the information matrix value corresponding to the rth row of the target modal partition of the i-th candidate measurement point; The Fisher information matrix Q is decomposed into: For formula (8), P i1 Multiplying Q on the right yields: Derived: In the formula, Q 3jr is the information matrix value corresponding to the rth row of the target modal partition of the jth candidate measurement point; To ensure that each item in equation (10) is a zero matrix, we have: E of formula (4) 3i Restore to:

7. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 1, characterized in that: The step of determining the final modal test points according to the auxiliary matrix includes: Construct the covariance matrix J based on the modal matrix: in: (A-λI)ψ=0 Where E is the auxiliary matrix, q is the modal coordinate in the modal space, are the true modal coordinates, is the modal matrix, S represents the variance σ 2 Gaussian distributed white noise, Q is the Fisher information matrix of the artificially defined rail vehicle system structure, A is a symmetric positive definite matrix, ψ is the eigenvector matrix of matrix A, and λ is the eigenvalue matrix of matrix A; An auxiliary matrix E is constructed based on the covariance matrix J. The contribution of each candidate measuring point in the candidate measuring point set is obtained according to the auxiliary matrix E. It is determined whether there are multiple candidate measuring points with the smallest contribution. If so, the candidate measuring point with the worst modal recognition effect is determined by using the MAC criterion, and it is eliminated from the candidate measuring point set to form a new candidate measuring point set. This step is repeated for iterative calculation until the end condition is met to obtain the final modal test measuring point.

8. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 7, characterized in that: The expression of the auxiliary matrix E is: Where E is an idempotent matrix, and its diagonal data E ii The size represents the modal matrix of the i-th candidate measurement point pair The extent of contribution.

9. A method for optimizing measuring points of a rail vehicle system structure modal test according to claim 5 or 7, characterized in that: The expression of the MAC criterion is: Where MAC is the modal assurance matrix, which represents the angle between the i-th order modal vector and the j-th order modal vector. MAC = mac ij The non-diagonal elements of mac ij The (i≠j) value reflects the correlation between the two modal vibration vectors, that is, the modal identification effect. and They represent the test degree of freedom modal matrix Φ s ∈R s×m The i-th and j-th columns of , s is the test degree of freedom, m is the identifiable mode, and R is a set of real numbers.

10. A computer-readable storage medium, characterized in that: It comprises one or more programs executed by one or more processors of an electronic device, wherein the one or more programs comprise instructions for executing the method for optimizing measuring points of a rail vehicle system structure modal test as claimed in any one of claims 1 to 9.

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