Structural dynamics model reduction method based on modal shape data clustering and regression

Abstract

The present invention discloses a structural dynamics model reduction method based on modal vibration data clustering and regression, comprising: extracting modal vibration data of a large floating raft structure system, and mining the statistical characteristics of the modal vibration through data statistical analysis. Secondly, the modal vibration modes are grouped according to the vibration mode characteristics by using clustering analysis technology to find the similarities and differences between the vibration modes. The dimension reduction technology is used to reduce the dimension of each cluster cluster to extract the main features of the cluster and determine the nodes after dimensionality reduction. The vibration response of any node is approximately estimated by the regression method using the nodes after dimensionality reduction. Finally, the real signal and the simulated signal are analyzed by vibration response, and the error levels before and after dimensionality reduction are compared to verify the effectiveness and feasibility of the method. The method of the present invention shows an excellent fitting effect as a whole, and can accurately predict the dynamic response of the system in most cases, with high accuracy and reliability.

Description

Technical Field

[0001] The present invention belongs to the field of large-scale structural system modal vibration type analysis and dimensionality reduction, and in particular relates to a structural dynamics model order reduction method based on modal vibration type data clustering and regression. Background Art

[0002] Large floating raft system is an important technical system with wide application in engineering field. Its design and application are aimed at improving the stability and safety of marine engineering facilities. Large floating raft system is usually composed of floating raft, supporting structure, vibration isolation device and control system. With the increase of the scale and complexity of the floating raft system structure, there is a need to more accurately describe the vibration characteristics of the system. In actual engineering, the vibration characteristics of the floating raft system may be affected by a variety of uncertain factors, such as changes in material parameters, uncertainty in environmental loading, etc. These factors lead to the uncertainty of vibration characteristics, and traditional methods are difficult to effectively deal with these uncertainties. The dimensionality reduction method of structural system based on modal vibration statistical analysis has attracted much attention. This method can more comprehensively describe the dynamic response characteristics of the structural system while considering these uncertain factors. By statistically analyzing and reducing the vibration modes of the system structure, high-dimensional vibration data can be converted into a more concise and easier to understand form, thereby reducing the computational complexity, improving the computational efficiency, and providing a more comprehensive description when considering uncertainty factors.

[0003] The structural system dimensionality reduction method based on modal vibration statistical analysis provides a new way to monitor, diagnose and predict the structure of large floating raft systems. By reducing the dimension of the data, analysts can quickly and accurately identify the abnormal vibration mode of the floating raft system, thereby effectively monitoring and evaluating the health status of the floating raft structure. Therefore, it is urgent to propose a new idea and method based on modal vibration statistical analysis and system dimensionality reduction method to meet the challenges in the dynamic response analysis of large floating raft system structures and provide new theoretical and methodological support for the development and practice of structural engineering. Summary of the invention

[0004] The purpose of the present invention is to address the problem of processing high-dimensional vibration data of large-scale floating raft structure systems. In combination with the data statistical analysis of modal vibration shapes, a clustering analysis and system dimensionality reduction method based on modal vibration shapes is proposed, and the accuracy of the method is verified through a set of case dimensionality reduction applications and simulations.

[0005] To achieve the above object, the present invention provides a structural dynamics model reduction method based on modal vibration data clustering and regression, comprising:

[0006] Extracting modal vibration shape data of a large floating raft structure system, and performing logarithmic normalization processing on the modal vibration shape data to obtain normalized node vibration shape vectors;

[0007] Performing cluster analysis on the normalized node vibration mode vectors through KMEANS clustering, taking the node closest to the center of the same class to approximately represent other nodes in the class after clustering, performing data conversion on the normalized data to obtain the cluster center;

[0008] Based on the cluster center replacing other nodes in each cluster, using dimensionality reduction technology to reduce the dimension of each cluster, extracting the main features of the cluster, and determining the nodes after dimensionality reduction and simplification;

[0009] The nodes simplified by dimensionality reduction are used to approximately estimate the vibration response of any node through a regression method. The real signal and the simulated signal are analyzed through the vibration response, and the error levels before and after dimensionality reduction are compared to verify the effectiveness and feasibility of the method.

[0010] Preferably, the process of performing logarithmic normalization processing on the modal vibration shape data includes:

[0011] The data vector of the modal vibration data is normalized with the first term being positive, and abnormal points are filtered out. The formula expression is:

[0012]

[0013] in, is the modal formation node data of the system before normalization, for The first component of is the normalized modal formation node data.

[0014] Preferably, the process of performing logarithmic normalization processing on the modal vibration shape data further includes:

[0015] The change between adjacent data points is calculated by first-order difference to capture the trend and change speed of the series;

[0016] Calculating the change speed of the first-order difference sequence by second-order difference, thereby obtaining the acceleration and change degree of the first-order difference sequence;

[0017] Among them, the formula expression of the first-order difference is:

[0018]

[0019] The formula expression of the second-order difference is:

[0020]

[0021] in, Indicates the first data points, It represents the difference between adjacent data points. It represents the difference between adjacent first-order difference data points.

[0022] Preferably, the process of performing cluster analysis on the normalized node mode shape vectors by KMEANS clustering includes:

[0023] The Euclidean distance is used to measure the similarity between the node vibration shape vectors, and the unsupervised learning clustering algorithm KMEANS is applied to group the node vibration shape vectors to aggregate similar nodes into the same class;

[0024] Calculate each data point With each centroid distance and the data points Assign to the cluster to which the nearest centroid belongs, for each cluster , recalculate the centroid as the mean of all data points in the cluster;

[0025] Check whether the center has changed or the maximum number of iterations has been reached. If the center has not changed or the preset maximum number of iterations has been reached, the algorithm ends; otherwise, the data points are redistributed to the nearest centroid.

[0026] Preferably, for each data point With each centroid distance and the data points The formula for assigning to the cluster to which the nearest centroid belongs is:

[0027]

[0028] in, represents the Euclidean distance;

[0029]

[0030] in, are the mth component of the data point and centroid respectively.

[0031] Preferably, for each cluster , the formula for recalculating the centroid as the mean of all data points in the cluster is:

[0032] .

[0033] Preferably, the process of performing data conversion on the normalized data to obtain the cluster center includes:

[0034] Take the logarithm of the first-order difference data and the second-order difference data of the logarithm-normalized vibration mode respectively, obtain the total distance first-order difference line graph and the total distance second-order difference line graph, and take the point where the second-order difference in the line graph is zero for the first time to obtain the optimal cluster number ;

[0035] The KMEANS clustering algorithm is used to divide the normalized data into clusters, and group each point according to the clustering results. For a cluster, points, which correspond to points, of which:

[0036]

[0037] set up The cluster center in is , after normalization The cluster center is ,but:

[0038]

[0039] Use normalized cluster centers Approximately Combining the above two equations, we can get The approximate expression of is:

[0040]

[0041] The cluster center for:

[0042] .

[0043] Preferably, the process of approximately estimating the vibration response of any node by using the node simplified by dimensionality reduction through a regression method comprises:

[0044] Assume that there are indivual Mode shape data , clustering After class, we get Cluster center nodes and their corresponding mode shape data ;

[0045] Using clustering After Class The modal vibration shape data of the cluster center nodes for any node Perform regression analysis and approximate estimation;

[0046] Based on the regression theory model, the known modal data and The least squares method is used to estimate the regression model parameters. ;

[0047] The regression model parameters ,use The modal vibration data of the cluster center nodes For Node Estimation of modal vibration data .

[0048] Preferably, clustering is used After Class The modal vibration shape data of the cluster center nodes for any node The formula for regression analysis and approximate estimation is:

[0049]

[0050] It can be expressed as a matrix:

[0051]

[0052] in,

[0053]

[0054] Based on the regression theory model, the known modal data and The least squares method is used to estimate the regression model parameters. The formula expression is:

[0055]

[0056] For Node Estimation of modal vibration data for:

[0057] .

[0058] Preferably, the process of analyzing the real signal and the simulated signal through vibration response, comparing the error levels before and after dimensionality reduction, and verifying the effectiveness and feasibility of the method includes:

[0059] If the frequencies of each order of the model are , then the signal of the model satisfy:

[0060]

[0061] in for The modal shape data, modal coordinate vector It represents the response amplitude of the system in different modes, which is a function of time;

[0062] Depend on

[0063]

[0064] Where:

[0065]

[0066] Then each modal coordinate A solution of the form:

[0067]

[0068] in and is a constant determined by the initial conditions;

[0069] and then Approximate estimation of actual vibration signal for:

[0070] .

[0071] Compared with the prior art, the present invention has the following advantages and technical effects:

[0072] The present invention extracts the modal vibration data of a large floating raft structure system and mines the statistical characteristics of the modal vibration through data statistical analysis. Secondly, the modal vibration modes are grouped according to the vibration mode characteristics using cluster analysis technology to find the similarities and differences between the vibration modes. The dimension reduction technology is used to reduce the dimension of each cluster cluster to extract the main features of the cluster and determine the nodes after dimensionality reduction and simplification. The vibration response of any node is approximated by the regression method using the nodes after dimensionality reduction. Finally, the real signal and the simulated signal are analyzed through the vibration response, and the error levels before and after dimensionality reduction are compared to verify the effectiveness and feasibility of the method. The method of the present invention shows an excellent fitting effect as a whole, and can accurately predict the dynamic response of the system in most cases. This shows that the cluster analysis based on the modal vibration mode and the system dimensionality reduction method have high accuracy and reliability, and provide strong theoretical support and practical tools for the dynamic analysis of complex structural systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0074] Figure 1 A schematic diagram of a method flow chart of an embodiment of the present invention;

[0075] Figure 2It is a KMEANS clustering flow chart of an embodiment of the present invention;

[0076] Figure 3 A finite element model diagram of a large floating raft system according to an embodiment of the present invention;

[0077] Figure 4 It is a line graph of the first and second order differences of the logarithmically normalized total distance according to an embodiment of the present invention;

[0078] Figure 5 It is a key node diagram of a finite element model of a large floating raft system according to an embodiment of the present invention;

[0079] Figure 6 This is a comparison diagram of the approximate signal and the actual signal of node No. 13931 in an embodiment of the present invention;

[0080] Figure 7 This is a comparison diagram of the approximate signal and the actual signal of node No. 27672 in an embodiment of the present invention;

[0081] Figure 8 This is a comparison diagram between the approximate signal and the actual signal of node No. 34787 in an embodiment of the present invention. DETAILED DESCRIPTION

[0082] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0083] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0084] like Figure 1 As shown, this embodiment provides a structural dynamics model reduction method based on modal vibration data clustering and regression, comprising the following steps:

[0085] Extract the modal vibration shape data of the large floating raft structure system, and perform logarithmic normalization on the modal vibration shape data to obtain the normalized node vibration shape vector;

[0086] The normalized node vibration mode vectors are clustered by KMEANS clustering. After clustering, the node closest to the center of the same class is taken to approximately represent other nodes in the class. The normalized data is converted to obtain the cluster center.

[0087] Based on the cluster center replacing other nodes in each cluster, the dimension reduction technology is used to reduce the dimension of each cluster, extract the main features of the cluster, and determine the nodes after dimensionality reduction and simplification;

[0088] The vibration response of any node is approximately estimated by regression method using the nodes simplified by dimensionality reduction. The real signal and the simulated signal are analyzed by vibration response, and the error levels before and after dimensionality reduction are compared to verify the effectiveness and feasibility of the method.

[0089] Furthermore, step 1: extracting the modal vibration shape data of the large floating raft structure system and performing logarithmic normalization on the modal vibration shape data includes:

[0090] (1) The modal vibration data of the large floating raft structure system are extracted with the help of finite element software.

[0091] (2) In order to make the data more normalized and standardized, improve the efficiency and accuracy of data analysis and processing, and reduce the impact of outliers in the data on the model, the data vector of the modal vibration data is normalized with the first term being positive to filter out outliers. The formula is:

[0092]

[0093] in, is the modal formation node data of the system before normalization, for The first component of is the normalized modal formation node data.

[0094] Furthermore, the process of logarithmically normalizing the modal vibration shape data also includes:

[0095] The change between adjacent data points is calculated by first-order difference to capture the trend and change speed of the series;

[0096] The change rate of the first-order difference sequence is calculated by the second-order difference, so as to obtain the acceleration and change degree of the first-order difference sequence;

[0097] Among them, the formula expression of the first-order difference is:

[0098]

[0099] The formula for the second-order difference is:

[0100]

[0101] in, Indicates the first data points, It represents the difference between adjacent data points. It represents the difference between adjacent first-order difference data points.

[0102] Furthermore, step 2: the process of clustering the normalized node vibration mode vectors through KMEANS clustering includes:

[0103] KMEANS clustering is a commonly used unsupervised learning algorithm, which is widely used in various fields. It can divide the data set into groups with similar characteristics. Different groups, such as customer segmentation in marketing, image segmentation in image processing, user segmentation in recommendation systems, risk management in the financial field, etc. By assigning data points to the nearest cluster center and continuously updating the center position, KMEANS clustering can discover potential patterns and structures in the data set, providing strong support for data analysis and decision-making. The specific process of the KMEANS algorithm is as follows: Figure 2 shown.

[0104] The Euclidean distance is used to measure the similarity between node vibration shape vectors, and the unsupervised learning clustering algorithm KMEANS is applied to group the node vibration shape vectors and aggregate similar nodes into the same class.

[0105] Calculate each data point With each centroid distance and the data points Assigned to the cluster of the nearest centroid,

[0106]

[0107] in, represents the Euclidean distance;

[0108]

[0109] in, are the mth component of the data point and centroid respectively.

[0110] For each cluster , recalculate the centroid as the mean of all data points in the cluster;

[0111] .

[0112] Check whether the center has changed or the maximum number of iterations has been reached. If the center has not changed or has changed very little, or the preset maximum number of iterations has been reached, the algorithm ends; otherwise, the data points are redistributed to the nearest centroid.

[0113] Furthermore, step 3: performing data conversion on the normalized data, the process of obtaining the cluster center includes:

[0114] The cluster center is the central point or representative point of each cluster in cluster analysis, reflecting the overall characteristics and typical properties of the cluster. Calculating the cluster center can simplify the data set, highlight the main patterns and structures of the data, and thus perform data analysis and pattern recognition more effectively.

[0115] Due to the large amplitude of data changes, the first and second order difference data in step 1 often present a monotonic curve. Therefore, we take the logarithm of these data to make the data more stable, so as to reduce the volatility and amplitude of data changes, thus facilitating the observation and analysis of its trends and characteristics.

[0116] Take the logarithm of the first-order difference data and the second-order difference data of the logarithm-normalized vibration mode respectively, obtain the total distance first-order difference line graph and the total distance second-order difference line graph, and take the point where the second-order difference in the line graph is zero for the first time to obtain the optimal cluster number ;

[0117] The KMEANS clustering algorithm is used to divide the normalized data into clusters, and group each point according to the clustering results. For a cluster, points, which correspond to points, of which:

[0118]

[0119] set up The cluster center in is , after normalization The cluster center is ,but:

[0120]

[0121] Use normalized cluster centers Approximately Combining the above two equations, we can get The approximate expression of is:

[0122]

[0123] In order to minimize the approximate error of the cluster center, the cluster center for:

[0124] .

[0125] Furthermore, step 4: the process of approximately estimating the vibration response of any node by using the node simplified by dimensionality reduction through regression method includes:

[0126] Assume that there are indivual Mode shape data , clustering After class, we get Cluster center nodes and their corresponding mode shape data ;

[0127] If the modal vibration shape data of the cluster center node of each class is used to directly estimate other non-center nodes in the class, the error will become larger and larger as the number of clusters decreases. After Class The modal vibration shape data of the cluster center nodes for any node Perform regression analysis and approximate estimation; the formula expression is:

[0128]

[0129] It can be expressed as a matrix:

[0130]

[0131] in,

[0132]

[0133] Model parameter determination is the basic part of the regression model. After the regression theory model is established, the known modal data is analyzed based on the regression theory model. and The least squares method is used to estimate the regression model parameters. ;

[0134]

[0135] Through regression model parameters ,use The modal vibration data of the cluster center nodes For Node Estimation of modal vibration data for:

[0136] .

[0137] Step 5: Perform vibration response analysis on the model, select the key nodes of the model, and compare and analyze the actual signal with the approximate signal.

[0138] The following is implemented with reference to the accompanying drawings and examples. Figure 3 As shown in Figure 2, the modal vibration data of the large floating raft structure system was extracted using commercial software, and the finite element diagram of the model was extracted using CAD software. The model has 35646 nodes, focus on the z vibration direction of each node, and capture the vibration characteristics of the structure in the vertical direction. According to step 1, extract the front of each node Mode shape data , and its corresponding vibration signal is , and the modal vibration data Perform logarithmic normalization.

[0139] Then, according to steps 2 and 3, KMEANS clustering is used to perform cluster analysis on the normalized node vibration mode vectors. Figure 4 The point where the second-order difference in the line graph of the first and second-order differences of the logarithmic total distance is zero for the first time can be obtained as the optimal number of clusters, which is 1000. After determining the number of clusters, the cluster center of each class is obtained, and the cluster center is used to replace other nodes in each cluster to achieve dimensionality reduction.

[0140] According to step 4, the nodes after dimension reduction are used to obtain the previous value of each node through regression method. Approximate estimation of the modal shape data . Follow step 5, such as Figure 5 As shown, the center point of the original large valve rack, i.e. the 27672th point, and the two interface intersection points, i.e. the 13931st and 34787th points, are selected as key points. The actual signal obtained needs to be compared with the approximate signal to verify the accuracy and effectiveness of the model.

[0141] If the frequencies of each order of the model are , then the signal of the model satisfy:

[0142]

[0143] in for The modal shape data, modal coordinate vector It represents the response amplitude of the system in different modes, which is a function of time;

[0144] Depend on

[0145]

[0146] Where:

[0147]

[0148] Then each modal coordinate A solution of the form:

[0149]

[0150] in and is a constant determined by the initial conditions. To avoid loss of generality, and , then simplify to get:

[0151]

[0152] and then Approximate estimation of actual vibration signal for:

[0153] .

[0154] The processed approximate signal is compared with the actual signal, and the error level before and after dimensionality reduction is compared, such as Figure 6-8 As shown in the figure, the simulated signal fits the real signal well. The average errors of the three nodes are 7.77e-12, 1.34e-10 and 1.81e-10, and the maximum errors are 2.06e-11, 4.38e-10 and 5.83e-10, respectively. The model shows an excellent fitting effect as a whole and can accurately predict the dynamic response of the system in most cases. This shows that the clustering analysis and system dimensionality reduction method based on modal vibration shapes have high accuracy and reliability, and provide strong theoretical support and practical tools for the dynamic analysis of complex structural systems.

[0155] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A structural dynamics model reduction method based on modal vibration data clustering and regression, characterized in that: include: Extracting modal vibration shape data of a large floating raft structure system, and performing logarithmic normalization processing on the modal vibration shape data to obtain normalized node vibration shape vectors; Performing cluster analysis on the normalized node vibration mode vectors through KMEANS clustering, taking the node closest to the center of the same class to approximately represent other nodes in the class after clustering, performing data conversion on the normalized data to obtain the cluster center; Based on the cluster center replacing other nodes in each cluster, using dimensionality reduction technology to reduce the dimension of each cluster, extracting the main features of the cluster, and determining the nodes after dimensionality reduction and simplification; The nodes simplified by dimensionality reduction are used to approximately estimate the vibration response of any node through a regression method, and the real signal and the simulated signal are analyzed through the vibration response, and the error levels before and after dimensionality reduction are compared to verify the effectiveness and feasibility of the method; The process of performing logarithmic normalization processing on the modal vibration shape data also includes: The change between adjacent data points is calculated by first-order difference to capture the trend and change speed of the series; Calculating the change speed of the first-order difference sequence by second-order difference, thereby obtaining the acceleration and change degree of the first-order difference sequence; Among them, the formula expression of the first-order difference is: The formula expression of the second-order difference is: in, Indicates the first data points, It represents the difference between adjacent data points. It represents the difference between adjacent first-order difference data points; The process of clustering analysis of the normalized node vibration mode vectors by KMEANS clustering includes: The Euclidean distance is used to measure the similarity between the node vibration shape vectors, and the unsupervised learning clustering algorithm KMEANS is applied to group the node vibration shape vectors to aggregate similar nodes into the same class; Calculate each data point With each centroid distance and the data points Assign to the cluster to which the nearest centroid belongs, for each cluster , recalculate the centroid as the mean of all data points in the cluster; Check whether the center has changed or the maximum number of iterations has been reached. If the center has not changed or the preset maximum number of iterations has been reached, the algorithm ends; otherwise, the data points are redistributed to the nearest centroid; The process of converting the normalized data and obtaining the cluster center includes: Take the logarithm of the first-order difference data and the second-order difference data of the logarithm-normalized vibration mode respectively, obtain the total distance first-order difference line graph and the total distance second-order difference line graph, and take the point where the second-order difference in the line graph is zero for the first time to obtain the optimal cluster number ; The KMEANS clustering algorithm is used to divide the normalized data into clusters, and group each point according to the clustering results. For a cluster, points, which correspond to points, of which: set up The cluster center in is , after normalization The cluster center is ,but: Use normalized cluster centers Approximately Combining the above two equations, we can get The approximate expression of is: The cluster center for: The process of approximately estimating the vibration response of any node by using the node simplified by dimensionality reduction through a regression method includes: Assume that there are indivual Mode shape data , clustering After class, we get Cluster center nodes and their corresponding mode shape data ; Using clustering After Class The modal vibration shape data of the cluster center nodes for any node Perform regression analysis and approximate estimation; Based on the regression theory model, the known modal data and The least squares method is used to estimate the regression model parameters. ; The regression model parameters ,use The modal vibration data of the cluster center node For Node Estimation of modal vibration data ; The process of analyzing the real signal and the simulated signal through vibration response and comparing the error level before and after dimensionality reduction to verify the effectiveness and feasibility of the method includes: If the frequencies of each order of the model are , then the signal of the model satisfy: in for The modal shape data, modal coordinate vector It represents the response amplitude of the system in different modes, which is a function of time; Depend on Where: Then each modal coordinate A solution of the form: in and is a constant determined by the initial conditions; and then Approximate estimation of actual vibration signal for: 。 2. The structural dynamics model reduction method based on modal vibration data clustering and regression according to claim 1, characterized in that: The process of performing logarithmic normalization processing on the modal vibration shape data includes: The data vector of the modal vibration data is normalized with the first term being positive, and abnormal points are filtered out. The formula expression is: in, is the modal formation node data of the system before normalization, for The first component of is the normalized modal formation node data.

3. The structural dynamics model reduction method based on modal vibration data clustering and regression according to claim 1, characterized in that: Calculate each data point With each centroid distance and the data points The formula for assigning to the cluster to which the nearest centroid belongs is: in, represents the Euclidean distance; in, are the mth component of the data point and centroid respectively.

4. The structural dynamics model reduction method based on modal vibration data clustering and regression according to claim 1, characterized in that: For each cluster , the formula for recalculating the centroid as the mean of all data points in the cluster is: 。 5. The structural dynamics model reduction method based on modal vibration data clustering and regression according to claim 1, characterized in that: Using clustering After Class The modal vibration shape data of the cluster center nodes for any node The formula for regression analysis and approximate estimation is: It can be expressed as a matrix: in, Based on the regression theory model, the known modal data and The least squares method is used to estimate the regression model parameters. The formula expression is: For Node Estimation of modal vibration data for: 。

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