A method for determining the transfer probability of random non-stationary vibration frequency characteristics of multi-modal systems

Abstract

The invention discloses a method for determining the transfer probability of random non-stationary vibration frequency characteristics of a multi-modal system, comprising: extracting the frequency result with the largest energy in each section of the non-stationary vibration power spectrum, taking it as the dominant frequency of the non-stationary vibration section, performing one-dimensional hierarchical clustering on the dominant frequency data of each section of the non-stationary vibration, counting the clusters to which the next non-stationary vibration dominant frequency belongs to each cluster to which the current non-stationary vibration dominant frequency belongs according to the occurrence time of the non-stationary vibration and establishing a transfer probability matrix, calculating the occurrence probability row vector of the cluster cluster and multiplying it with the transfer probability matrix, and then obtaining the transfer probability row vector of each cluster cluster transferred from other cluster clusters, and each transfer probability value in the transfer probability row vector respectively represents the probability size of transferring from other frequency characteristics to each frequency characteristic in a random process. The method of the invention can provide real-time non-stationary vibration frequency and control priority information for the intelligent vibration control of the system.

Description

Technical Field

[0001] The invention relates to a method for determining the transfer probability of random non-stationary vibration frequency characteristics of a multi-modal system, and belongs to the field of structural intelligent monitoring, detection and control. Background Art

[0002] If the dynamic characteristics of a system such as an engineering structure or component have multiple modes, then the system may experience multiple sections of non-stationary vibration dominated by a certain mode during its entire life cycle. The dominant mode of each non-stationary vibration section will convert between the natural modes of each order of the system as the external environment changes. Considering that the vibration frequency is the main characteristic parameter of the vibration mode, determining the dominant frequency of these non-stationary vibration sections and their transition probability in a random process is a prerequisite for vibration control of the system. However, due to the large uncertainty of external environmental changes in real situations, and the fact that the vibration frequency of the system will change slightly with environmental changes, it is difficult to digitally determine the transition probability of the non-stationary vibration frequency characteristics of a multi-modal system in a random process. Relevant technologies are needed to solve this type of problem.

[0003] At present, there are few methods in the civil and mechanical fields for determining the transfer probability of non-stationary vibration frequency characteristics of structures or component systems with multiple modes. Instead, the common method is to ignore the possible potential relationship between the various non-stationary vibration segments in the time history, only regard each non-stationary vibration segment as an independent event, directly identify the frequency of each non-stationary vibration, and manually classify the identification results with similar frequency values, calculate the ratio of the number of each type of identified frequency values ​​to the total number of identified frequency values, and use it as the probability of occurrence of this type (order) of frequency value in the random process. It can be found that the existing technology relies more on the professional knowledge of relevant practitioners, and does not consider the order and potential conversion relationship of each non-stationary vibration segment in the time history, and cannot truly reflect the occurrence and transfer probability of each modal non-stationary vibration frequency in the random process.

[0004] Therefore, it is necessary to develop a method for automatically determining the characteristic transfer probability of random non-stationary vibration frequencies of multi-modal systems, which takes into account the time sequence and the potential relationship between each non-stationary vibration segment, and provide real-time non-stationary vibration frequency and its control priority information for vibration control of civil and mechanical systems. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for determining the transfer probability of random non-stationary vibration frequency characteristics of a multi-modal system, which can provide real-time non-stationary vibration frequency and its control priority information for the intelligent vibration control work of the system.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] The method for determining the transfer probability of the random non-stationary vibration frequency characteristics of a multi-modal system comprises the following steps:

[0008] Step 1, based on multiple sections of non-stationary vibration data of a multi-modal system within a certain time length, frequency domain power spectrum analysis is performed on each section of non-stationary vibration data, and the frequency result with the largest energy in the power spectrum of each section of non-stationary vibration is extracted as the dominant frequency of the non-stationary vibration of this section;

[0009] Step 2, performing one-dimensional hierarchical clustering on the dominant frequency of each segment of non-stationary vibration, the output result of the hierarchical clustering is the clustering result whose sum of square increments of all data points in each cluster is greater than a preset distance value, and the preset distance value is any value between 0.9 and 1 times the minimum distance between the natural frequencies of each order of the system;

[0010] Step 3, according to the occurrence time of the non-stationary vibration, count the clusters to which the next non-stationary vibration dominant frequency belongs to each cluster to which the current non-stationary vibration dominant frequency belongs, and establish a transition probability matrix based on the counting results;

[0011] Step 4: Divide the number of elements in each cluster by the number of elements in all clusters, calculate the occurrence probability of each cluster and store it by row, then multiply the occurrence probability row vector of the cluster by the transition probability matrix to obtain the transition probability row vector of each cluster transferring from other clusters. Each transition probability value in the transition probability row vector represents the probability of transferring from other frequency features to each frequency feature in the random process.

[0012] As a preferred embodiment of the present invention, the method of step 1 is specifically as follows:

[0013] Step 1.1, for a structure or component system with multiple modes, based on multiple sections of non-stationary vibration data of the system within a certain time length, a fast Fourier transform method is used to perform frequency domain power spectrum analysis on each section of non-stationary vibration data, wherein the vibration data is acceleration, velocity or dynamic displacement data;

[0014] Step 1.2, extract the frequency result with the largest energy in each segment of the non-stationary vibration power spectrum as the dominant frequency of the non-stationary vibration segment.

[0015] As a preferred solution of the present invention, the calculation formula of the incremental sum of squares of all data points in the cluster in step 2 is as follows:

[0016]

[0017] Where D(r,s) is the incremental sum of squares of cluster r and cluster s, n r and n sare the number of frequency data points in cluster r and cluster s respectively, ||·||2 represents the Euler distance, and are the centroids of cluster r and cluster s respectively; the calculation formula of the centroid of each cluster is as follows:

[0018]

[0019] In the formula, C ri is the frequency value of the i-th frequency data point in cluster r, C si is the frequency value of the i-th frequency data point in cluster s.

[0020] As a preferred embodiment of the present invention, the method of step 3 is as follows:

[0021] Step 3.1, according to the occurrence time of the non-stationary vibration, count the clusters to which the next non-stationary vibration dominant frequency belongs to each cluster to which the current non-stationary vibration dominant frequency belongs;

[0022] Step 3.2: Based on the counting results, define P j,k is the probability that the frequency data of cluster j is followed by the frequency data of cluster k, and the transition probability matrix is ​​established as follows:

[0023]

[0024] Where j = 1,…, N, k = 1,…, N, and N is the total number of clusters output by hierarchical clustering.

[0025] As a preferred embodiment of the present invention, the method of step 4 is as follows:

[0026] Step 4.1: Divide the number of elements in each cluster by the number of elements in all clusters to calculate the probability of occurrence of each cluster P. j , j = 1, ..., N, N is the total number of clusters output by hierarchical clustering, and is stored row by row as a probability row vector as follows:

[0027]

[0028] Step 4.2, multiply the occurrence probability row vector of the cluster by the transition probability matrix to obtain the transition probability row vector of each cluster transferring from other clusters as follows:

[0029]

[0030] Transition probability row vector The transition probability values ​​in to They respectively represent the probability of transferring from other frequency feature clusters to the 1st to Nth frequency feature clusters in a random process.

[0031] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0032] 1. The present invention proposes to use a clustering method to overcome the problem that the same-order vibration frequency may have slight changes when identifying the dominant frequency from the measured vibration data of the system; at the same time, based on the Markov chain principle, it is determined that when the non-stationary vibration occurs at the time, each frequency cluster data is followed by another frequency cluster data The transition probability matrix. The method is logically clear and conforms to the basic principles of mathematics and mechanics.

[0033] 2. The present invention proposes to first determine multiple clusters of the dominant frequencies of each non-stationary vibration segment of the system, then calculate the occurrence probability of each cluster by dividing the number of elements in each cluster by the number of elements in all clusters, and finally multiply the row vector of the probability of occurrence of each cluster by the transition probability matrix to obtain the probability of each cluster transferring from other clusters, which takes into account both the order of each non-stationary vibration segment in the time history and the potential conversion relationship between them. The method is relatively comprehensive, and the results obtained are more in line with engineering practice than traditional methods.

[0034] 3. The implementation process of the present invention is basically based on the processing and calculation of sensor test data, with few empirical factors. Any technician with a certain foundation in mathematics, mechanics, and computers can determine the transfer probability of the random non-stationary vibration frequency characteristics of the multi-modal system according to the present invention. The method is highly reproducible and easy to apply and promote. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the method of the present invention;

[0036] Figure 2 is a schematic diagram of 68 sections of non-stationary vibration data of a cable system according to an embodiment of the present invention;

[0037] Figure 3 It is a schematic diagram of determining a typical non-stationary vibration segment of a system and its dominant frequency in an embodiment of the present invention;

[0038] Figure 4 Schematic diagram of clustering results of non-stationary vibration dominant frequencies according to an embodiment of the present invention;

[0039] Figure 5 It is a schematic diagram of transition probability corresponding to the transition probability matrix of an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0041] like Figure 1 As shown, the method for determining the transfer probability of the random non-stationary vibration frequency characteristics of a multi-modal system described in the present invention mainly includes the following steps:

[0042] Step 1: For a structure or component system with multiple modes, based on multiple non-stationary vibration data of the system within a certain time length, use methods such as fast Fourier transform to perform frequency domain power spectrum analysis on each segment of non-stationary vibration data; extract the frequency result with the largest energy in each segment of the non-stationary vibration power spectrum, and use it as the dominant frequency of the non-stationary vibration segment.

[0043] Step 2: Perform one-dimensional hierarchical clustering on the dominant frequency data of each segment of non-stationary vibration. The output result of the hierarchical clustering is the clustering result where the sum of the square increments of all data points in each cluster is greater than the preset distance value. The preset distance value is recommended to be any value between 0.9 and 1 times the minimum distance between the natural frequencies of each order of the system. The calculation formula for the sum of the square increments of all data points in the cluster is as follows:

[0044]

[0045] Where D(r,s) is the incremental sum of squares of cluster r and cluster s, n r and n s are the number of data points in cluster r and cluster s respectively, ||·||2 represents the Euler distance, and are the centroids of cluster r and cluster s respectively; the calculation formula of the centroid of each cluster is as follows:

[0046]

[0047] In the formula, C ri is the frequency value of the i-th frequency data point in cluster r, C si is the frequency value of the i-th frequency data point in cluster s.

[0048] Step 3: According to the occurrence time of non-stationary vibration, count the clusters of the next non-stationary vibration dominant frequency of each cluster to which the current non-stationary vibration dominant frequency belongs; define P based on the counting results j,k is the probability that the frequency data of cluster j is followed by the frequency data of cluster k, and the transition probability matrix is ​​established as follows:

[0049]

[0050] Step 4: Divide the number of elements in each cluster by the number of elements in all clusters to calculate the probability of occurrence P of each cluster. N , and stored row by row as as follows:

[0051]

[0052] By multiplying the occurrence probability row vector of the cluster cluster with the transition probability matrix, we can get the transition probability row vector of each cluster cluster from other cluster clusters. as follows:

[0053]

[0054] Transition probability row vector The transition probability values ​​in to They respectively represent the probability of transferring from other frequency feature clusters to the 1st to Nth frequency feature clusters in a random process.

[0055] Example

[0056] The specific implementation process of the present invention is described below by taking the non-stationary vibration segment of the acceleration monitoring data of a certain cable of a certain long-span cable-stayed bridge in Jiangsu Province as an example.

[0057] (1) For a cable-stayed bridge cable system with multiple modes, based on 68 non-stationary vibration data of the cable system from the 3rd to the 16th of a certain month (e.g. Figure 2 As shown in the figure, the frequency domain power spectrum analysis of each segment of non-stationary vibration data is performed using fast Fourier transform; the frequency result with the largest energy in each segment of non-stationary vibration power spectrum is extracted (as shown in the figure). Figure 3 As shown in Figure 2, it is taken as the dominant frequency of this section of non-stationary vibration.

[0058] (2) Perform one-dimensional hierarchical clustering on the dominant frequency data of each segment of non-stationary vibration. The output of the hierarchical clustering is the 17 cluster results whose sum of square increments of all data points in each cluster is greater than the preset distance value of 0.2 Hz (e.g. Figure 4 As shown in the figure, the dotted lines are the data centroid values ​​of each cluster).

[0059] (3) According to the occurrence time of non-stationary vibration, the clusters of the next non-stationary vibration dominant frequency of each cluster to which the current non-stationary vibration dominant frequency belongs are counted, and a transition probability matrix is ​​established based on the counting results. The transition probability diagram corresponding to the transition probability matrix is ​​shown in the figure below: Figure 5 shown.

[0060] (4) Divide the number of elements in each cluster by the number of elements in all clusters, calculate the occurrence probability of each cluster and store it row by row, then multiply the occurrence probability row vector of the cluster by the transition probability matrix, and we can get the transition probability row vector of the 1st to 17th clusters from other clusters as [0.0147, 0.0147, 0.0147, 0.0478, 0.0882, 0.0478, 0.0147, 0, 0.1360, 0.0588, 0.0735, 0.0882, 0.0735, 0.0772, 0.0588, 0.1765]. Theoretically, the sum of the transition probability row vector of the obtained cluster is 1, but there will be a slight error due to rounding. Each transition probability value in the transition probability row vector represents the probability of transferring from other frequency features to each frequency feature in the random process.

[0061] The above embodiments are only for illustrating the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for determining the transfer probability of random non-stationary vibration frequency characteristics of a multi-modal system, characterized in that: The steps include: Step 1, based on multiple sections of non-stationary vibration data of a multi-modal system within a certain time length, frequency domain power spectrum analysis is performed on each section of non-stationary vibration data, and the frequency result with the largest energy in the power spectrum of each section of non-stationary vibration is extracted as the dominant frequency of the non-stationary vibration of this section; Step 2, performing one-dimensional hierarchical clustering on the dominant frequency of each segment of non-stationary vibration, the output result of the hierarchical clustering is the clustering result whose sum of square increments of all data points in each cluster is greater than a preset distance value, and the preset distance value is any value between 0.9 and 1 times the minimum distance between the natural frequencies of each order of the system; The calculation formula for the incremental sum of squares of all data points in the cluster is as follows: Where D(r,s) is the incremental sum of squares of cluster r and cluster s, n r and n s are the number of frequency data points in cluster r and cluster s respectively, ||·||2 represents the Euler distance, and are the centroids of cluster r and cluster s respectively; the calculation formula of the centroid of each cluster is as follows: In the formula, C ri is the frequency value of the i-th frequency data point in cluster r, C si is the frequency value of the i-th frequency data point in cluster s; Step 3, according to the occurrence time of the non-stationary vibration, count the clusters to which the next non-stationary vibration dominant frequency belongs to each cluster to which the current non-stationary vibration dominant frequency belongs, and establish a transition probability matrix based on the counting results; Step 4: Divide the number of elements in each cluster by the number of elements in all clusters, calculate the occurrence probability of each cluster and store it by row, then multiply the occurrence probability row vector of the cluster by the transition probability matrix to obtain the transition probability row vector of each cluster transferring from other clusters. Each transition probability value in the transition probability row vector represents the probability of transferring from other frequency features to each frequency feature in the random process.

2. The method for determining the transition probability of the random non-stationary vibration frequency characteristics of a multi-modal system according to claim 1 is characterized in that: The method of step 1 is as follows: Step 1.1, for a structure or component system with multiple modes, based on multiple sections of non-stationary vibration data of the system within a certain time length, a fast Fourier transform method is used to perform frequency domain power spectrum analysis on each section of non-stationary vibration data, wherein the vibration data is acceleration, velocity or dynamic displacement data; Step 1.2, extract the frequency result with the largest energy in each segment of the non-stationary vibration power spectrum as the dominant frequency of the non-stationary vibration segment.

3. The method for determining the transfer probability of the random non-stationary vibration frequency characteristics of a multi-modal system according to claim 1, characterized in that: The method of step 3 is as follows: Step 3.1, according to the occurrence time of the non-stationary vibration, count the clusters to which the next non-stationary vibration dominant frequency belongs to each cluster to which the current non-stationary vibration dominant frequency belongs; Step 3.2: Based on the counting results, define P j,k is the probability that the frequency data of cluster j is followed by the frequency data of cluster k, and the transition probability matrix is ​​established as follows: Where j = 1,…, N, k = 1,…, N, and N is the total number of clusters output by hierarchical clustering.

4. The method for determining the transfer probability of the random non-stationary vibration frequency characteristics of a multi-modal system according to claim 1 is characterized in that: The method of step 4 is as follows: Step 4.1: Divide the number of elements in each cluster by the number of elements in all clusters to calculate the probability of occurrence of each cluster P. j , j = 1, ..., N, N is the total number of clusters output by hierarchical clustering, and is stored row by row as a probability row vector as follows: Step 4.2, multiply the occurrence probability row vector of the cluster by the transition probability matrix to obtain the transition probability row vector of each cluster transferring from other clusters as follows: Transition probability row vector The transition probability values ​​in to They respectively represent the probability of transferring from other frequency feature clusters to the 1st to Nth frequency feature clusters in a random process.

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