Random subspace method based on machine learning

Abstract

A random subspace method based on machine learning comprises the following steps: pre-collecting partial acceleration response data of a building needing to be identified by using an SHM system, and establishing an SVM classification model in combination with a random subspace method; and combining the established SVM classification model with a K-MEANS algorithm, and analyzing acceleration response data newly collected by the SHM system so as to realize modal parameter identification of the building structure. When the method is used for analyzing the numerical model of the five-degree-of-freedom simulation model, the result shows that the SVM classification model established by the method can automatically and effectively distinguish the structural mode and the non-structural mode of the random subspace method; in addition, the identified modal parameters of the 5DOF model are well matched with theoretical values of the 5DOF model, and the accuracy and effectiveness of the method are verified. According to the method, field actual measurement acceleration response data of a certain 62-floor residential building is analyzed, and the result shows that modal parameters of the residential building can be automatically identified.

Description

Technical Field

[0001] The present invention relates to the technical field of structural operational modal parameter identification, and particularly to a stochastic subspace method based on machine learning. Background Art

[0002] Since it is difficult to obtain the actual forces acting on civil structures, operational modal analysis (OMA) using only output responses is commonly used in health monitoring systems to identify structural modal parameters. In recent years, the stochastic subspace method (SSI) has been widely applied to OMA of civil structures due to its obvious advantages (such as accuracy, solid mathematical foundation, and good performance under non-stationary excitation conditions) (Ubertini et al. 2013, Reynders et al. 2016, He et al. 2021). In SSI, one of the most important concerns is to identify structural modes from spurious (or non-structural) modes ( In 2013, Zhou et al., 2022). Regarding this key issue, some efforts have been made in the past few decades. For example, the traditional stability diagram has been developed as one of the most widely used tools for identifying structural modes, but its performance is not satisfactory, as shown by previous studies (e.g., Faravelli et al., 2011, Liu et al., 2013). Magalhaes et al. (2009) developed a stability diagram based on hierarchical clustering to identify structural modes, in which the cut-off distance parameter must be carefully pre-specified to obtain accurate mode identification results. Wu et al. (2019) developed a double-folded stability diagram, and its analysis process is relatively complex. In addition, several metrics have been proposed to judge whether the identified candidate modes are structural modes. For example, Sarlo & Tarazaga (2019) pointed out that the uncertainty of modal parameters is an effective metric for identifying non-structural modes. Lanslot et al. (2007) verified that the mean phase deviation (MPD) and modal phase collinearity (MPC) are feasible metrics for representing spurious modes or structural modes. Verboven et al. (2002) pointed out that the "pole-zero cancellation pair" can be used to identify non-structural modes. In addition to these metrics, some other metrics have been proposed to distinguish structural modes and non-structural modes, such as the modal scale factor (Allemang & Brown 1982), the modal transfer norm (Reynders & De Roeck 2008), and the modal exceedance complexity value (Heylen et al. 1997), etc. It should be noted that the above metrics or metrics require corresponding thresholds to identify structural or non-structural modes, and the setting of these thresholds usually depends on the judgment and experience of engineers or researchers. In the case where the threshold setting is too strict, several structural modes will be identified as non-structural modes, while when the threshold setting is too loose, several non-structural modes will be wrongly identified as structural modes. The above two cases will have an adverse impact on the mode identification results. In addition, the determination of the artificial intervention threshold is not conducive to the automatic identification of the modes of civil structures. Therefore, it is an urgent task to study an effective method for identifying the working mode parameters of structures based on SSI. Summary of the Invention

[0003] In order to solve the key problem in the above-mentioned prior art that it is impossible to accurately identify structural modes from false (or non-structural) modes, the present invention proposes a random subspace method based on machine learning.

[0004] In one aspect of the present invention, the present invention proposes a random subspace method based on machine learning. According to an embodiment of the present invention, the method includes the following steps:

[0005] A1. Use the SHM system to pre-collect partial acceleration response data of the building to be identified, and establish an SVM classification model in combination with the stochastic subspace method;

[0006] A2. Combine the established SVM classification model with the K-MEANS algorithm to analyze the newly collected acceleration response data of the SHM system, so as to realize the modal parameter identification of the building structure.

[0007] In addition, according to a stochastic subspace method based on machine learning in the above embodiments of the present invention, the following additional technical features may also be included:

[0008] In some embodiments of the present invention, step A1 includes the following steps:

[0009] (1) Conduct power spectral density analysis to obtain a power spectral density curve to display the modal distribution of the target structure;

[0010] (2) Identify the fundamental natural frequency and the number of structural modes within the relevant frequency range from the determined power spectral density curve;

[0011] (3) Determine the value ranges of two key parameters, the time delay parameter and the system order parameter, in the SSI-COV method;

[0012] (4) Generate s1 groups of random integers [i, n] representing the time delay parameter i and the system order parameter n through Monte Carlo simulation, and obtain s1 groups of candidate modes, namely [Ω 1 , Ω 2 , …, Ω s1 ;

[0013] (5) Based on the acceleration response data pre-collected by the SHM system, determine the labels of the above candidate modes [Ω 1 , Ω 2 , …, Ω s1 ;

[0014] (6) Based on the acceleration response data pre-collected by the SHM system, determine three important evaluation indicators of the candidate modes;

[0015] (7) Regard the evaluation indicators of the candidate modes as the feature data set, regard the labels of the candidate modes as the label data set, and randomly divide the data set into a training set and a test set. Based on the training set, use the Bayesian optimization method to optimize the hyperparameters, so as to construct an SVM classification model; based on the test set, verify the performance of the developed classification model through a confusion matrix.

[0016] In some embodiments of the present invention, in step (3), the two key parameters are the time delay parameter and the system order parameter respectively.

[0017] In some embodiments of the present invention, in the step (5), the process of determining the candidate modal label is specifically as follows. When Ω 1 and the modal label Θ1 can meet the stability criterion in the following equation, the label of Θ1 is defined as the structural modal label; otherwise, it is assigned a non-structural modal label;

[0018] Natural vibration frequency:

[0019] Damping ratio:

[0020] Mode shape: 1 - MAC(φ a , φ b ) ≤ 1%;

[0021] Wherein, the subscripts a and b represent two different modes, f represents the natural vibration frequency, ξ represents the damping ratio, Ω represents the modal set, Θ represents the modal label, and φ represents the modal shape.

[0022] In some embodiments of the present invention, in the step (6): The three important evaluation indexes include the natural frequency uncertainty index, the damping ratio uncertainty index, and the modal shape uncertainty index.

[0023] In some embodiments of the present invention, the calculation formulas of the natural frequency uncertainty index, the damping ratio uncertainty index, and the modal shape uncertainty index are as follows:

[0024]

[0025] Wherein, UIF represents the natural frequency uncertainty index, UID represents the damping ratio uncertainty index, UIM represents the modal shape uncertainty index, Std f represents the standard deviation of the natural frequency, Std ξ represents the standard deviation of the damping ratio, represents the standard deviation of the modal shape of the j-th measuring point, φ j represents the modal shape of the j-th measuring point, f represents the natural vibration frequency, ξ represents the damping ratio, j represents the j-th measuring point, and m is the total number of measuring points.

[0026] In some embodiments of the present invention, the step S2 includes the following steps:

[0027] (1) Combine the established SVM classification model with K - MEANS to analyze the newly collected SHM data for modal parameter identification;

[0028] (2) Generate s2 groups of random integers [i, n] representing the time-delay parameters and the system order parameters through Monte Carlo simulation. Then, s2 groups of candidate modes can be obtained, namely [Ω 1 , Ω2 , …, Ω s2 , and the corresponding evaluation indexes;

[0029] (3) Use the SVM classification model to predict the labels of the candidate modes in group s2, use the K-MEANS algorithm to solve the misclassified mode labels, and cluster different modal parameters;

[0030] (4) Calculate the average value of the clustered modal parameters as the optimal recognition result of the random subspace method based on machine learning.

[0031] Compared with the prior art, the beneficial effects of the present invention are:

[0032] (1) The SVM classification model proposed by the present invention is constructed based on the determined candidate mode labels and evaluation indexes, and can effectively determine whether the mode identified by the random subspace method is a structural mode or a non-structural mode.

[0033] (2) The present invention proposes to combine the established classification model with the K-MEANS algorithm, and can realize the automatic identification of the modal parameters of the building structure based on the newly collected SHM acceleration response data. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flowchart of a random subspace method based on machine learning in Embodiment 1 of the present invention;

[0035] Figure 2 It is a 5DOF model in Embodiment 2 of the present invention;

[0036] Figure 3 It is a PSD curve graph of the acceleration response of Segment 1 in Embodiment 2 of the present invention;

[0037] Figure 4 It is a confusion matrix graph of the SVM classification model established in Embodiment 2 of the present invention;

[0038] Figure 5 It is a graph of the natural frequency and damping ratio of the candidate modes in group s2 in Embodiment 2 of the present invention;

[0039] Figure 6 It is a graph of the natural frequency and damping ratio of the candidate modes with "structural mode labels" in Embodiment 2 of the present invention;

[0040] Figure 7 It is a clustering graph of the modal parameters obtained by the K-MEANS algorithm in Embodiment 2 of the present invention;

[0041] Figure 8 It is a graph of the optimal recognition modal parameters of the response of Segment 2 of Modes 1-5 in Embodiment 2 of the present invention;

[0042] Figure 9 This is the modal parameter identification result diagram in Embodiment 2 of the present invention. Among them, a is the natural vibration frequency, b is the damping ratio, and c is the modal vibration mode;

[0043] Figure 10 This is the PSD curve diagram of the acceleration response of Segment 1 (X direction and Y direction) in Embodiment 3 of the present invention;

[0044] Figure 11 This is the confusion matrix diagram of the SVM classification model established in Embodiment 3 of the present invention;

[0045] Figure 12 This is the natural frequency and damping ratio diagram of the candidate modes in Group s2 in Embodiment 3 of the present invention;

[0046] Figure 13 This is the natural frequency and damping ratio diagram of the candidate modes with "structural modal labels" in Embodiment 3 of the present invention;

[0047] Figure 14 This is the clustering diagram of the modal parameters obtained by the K-MEANS algorithm in Embodiment 3 of the present invention;

[0048] Figure 15 This is the best identified modal parameter diagram of the responses of Modes 1-5 of Segment 2 in Embodiment 3 of the present invention;

[0049] Figure 16 This is the natural frequency (left figure) and damping ratio diagram (right figure) of Modes 1-5 from Segment 3 to 216 in Embodiment 3 of the present invention. Detailed implementation manners

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] Embodiment 1

[0052] A random subspace method based on machine learning includes the following steps:

[0053] A1. Use the SHM system to pre-collect part of the acceleration response data of the building to be identified, and establish an SVM classification model in combination with the random subspace method.

[0054] 1) Perform power spectral density (PSD) analysis on the pre-collected part of the acceleration response data to obtain a PSD curve to display the modal distribution of the target structure.

[0055] 2) Identify the basic natural frequency f from the determined PSD curve f and the data acquisition frequency f s .

[0056] 3) Use formulas (1)-(4) to determine the value ranges of two key parameters in the SSI-COV method. The parameters are the time delay parameter i and the system order parameter n respectively.

[0057] n min = N (1)

[0058] n max = 2×N (2)

[0059] i min = f s / f f (3)

[0060] i max = 2×f s / f f (4)

[0061] Among them, N represents the length of the acquired acceleration response data, f f represents the basic natural frequency, f s represents the data acquisition frequency, n min represents the minimum system order parameter, n max represents the maximum system order parameter, i min represents the minimum time delay parameter, i max represents the maximum time delay parameter.

[0062] 4) On this basis, generate s1 groups of random integers [i, n] representing the time delay parameter and the system order parameter through Monte Carlo simulation, and obtain s1 groups of candidate modes, that is

[0063] 5) Based on part of the acceleration response data collected by the SHM system, combined with a mature modal identification method proposed by Magalhaes et al. (2009), determine the labels of the above candidate modes Take Θ1 in Ω 1 as an example to illustrate the determination process. When Ω 1 and Θ1 can meet the stability criteria in equations (5)-(7), then the label of Θ1 is defined as "structural modal label". Otherwise, it is assigned a "non-structural modal label".

[0064] Natural vibration frequency:

[0065] Damping ratio:

[0066] Mode shape: 1 - MAC(φ a , φ b ) ≤ 1% (7)

[0067] where the subscripts a and b represent two different modes, f represents the natural vibration frequency, ξ represents the damping ratio, Ω represents the mode set, Θ represents the mode label, and φ represents the mode shape.

[0068] 6) Based on part of the data collected by the SHM system, calculate three important evaluation indexes of the candidate modes: the natural frequency uncertainty index (UIF), the damping ratio uncertainty index (UID), and the mode shape uncertainty index (UIM). Their calculation formulas are as follows:

[0069]

[0070] where UIF represents the natural frequency uncertainty index, UID represents the damping ratio uncertainty index, UIM represents the mode shape uncertainty index, Std f represents the standard deviation of the natural frequency, Std ξ represents the standard deviation of the damping ratio, represents the standard deviation of the mode shape of the j-th measurement point, φ j represents the mode shape of the j-th measurement point, f represents the natural vibration frequency, ξ represents the damping ratio, j represents the j-th measurement point, and m is the total number of measurement points.

[0071] 7) Regard the evaluation indexes of the candidate modes as the feature data set, and regard the labels of these candidate modes as the label data set. And randomly divide the data set (including the feature data set and the label data set) into a training set (80%) and a test set (20%). Based on the training set, use the Bayesian optimization method to optimize the hyperparameters, so as to construct an SVM classification model; based on the test set, verify the performance of the developed classification model through the confusion matrix.

[0072] A2. Combine the established SVM classification model with the K - MEANS algorithm to analyze the newly collected acceleration response data of the SHM system to realize the modal parameter identification of the building structure.

[0073] 1) Combine the established SVM classification model with K - MEANS to analyze the newly collected SHM data for modal parameter identification.

[0074] 2) Generate s2 groups of random integers [i, n] representing the time - delay parameters and system order parameters through Monte Carlo simulation. Then, s2 groups of candidate modes can be obtained, that is and the corresponding evaluation indexes.

[0075] 3) Use the SVM classification model to predict the labels of the candidate modes in group s2. The K-MEANS algorithm can automatically detect label outliers and cluster the parameters of different modes.

[0076] 4) Calculate the average value of the clustered mode parameters as the optimal recognition result of the random subspace method based on machine learning.

[0077] Example 2

[0078] A 5DOF model was simulated and generated using Matlab software, as Figure 2 shown. The mass m of each mass block is defined as 1 unit, and the stiffness coefficient k is defined as 8 units, obtaining the mass matrix M and the stiffness matrix K as follows:

[0079]

[0080] The damping matrix C is defined as C = 0.003M + 0.01K. A white noise signal excitation is applied to the top of the structure, and the acceleration response of the model is obtained using the Newmark-β method.

[0081] Establish the SVM classification model of this example according to step A1 using the acceleration response of the model. First, divide the 10-hour-long simulated acceleration response of the model into 10 one-hour-long segments. Among them, segment 1 is used to establish the SVM classification model, and other segments are used to prove the effectiveness of the proposed method. Figure 3 Shown is the PSD analysis diagram of the acceleration response of segment 1. Figure 4 For the verification result (i.e., the confusion matrix) of the established SVM classification model. From Figure 4 it can be seen that the established classification model has a very high accuracy (i.e., 96.5%). Only a small part of the non-structural modes may be mispredicted as structural modes by the developed classification model. This problem will be solved by using the K-MEANS algorithm in step A2.

[0082] Next, use segments 2 to 10 to prove the effectiveness of the proposed method. Figure 5 Shown are the natural frequencies and damping ratios of the candidate modes in group s2. There are some non-structural modes in the figure. Then, the evaluation indexes of the identified candidate modes in group s2 are regarded as the input of the SVM classification model developed in step A1, and the labels of these candidate modes (i.e., structural mode labels or false mode labels) can be predicted. Figure 6 Shows the natural frequencies and damping ratios of the candidate modes with the predicted "structural mode labels", indicating that the vast majority of non-structural modes have been automatically eliminated. Then, take the structural mode parameters with the predicted "structural mode labels" as the input of the K-MEANS algorithm, and the result is as Figure 7As shown, it indicates that several outliers are effectively detected. The results in the figure show that the combination of the SVM classification model and the K-MEANS algorithm can automatically and effectively distinguish structural modes and non-structural modes. In addition, as Figure 7 shown, the modal parameters belonging to different modes are well clustered, and the average values of these clustered modal parameters can be calculated accordingly ( Figure 8 ), which can be regarded as the identification of the optimal structural modal parameters. According to the same procedure, the structural modal parameters of other segments can be well determined, and the results are as Figure 9 shown. Among them Figure 9 (a) is the natural vibration frequency, 9(b) is the damping ratio, and 9(c) is the modal vibration shape. For simplicity, only the identified modal shape of the first-order mode is provided here. The identified structural modal parameters are in good agreement with the theoretical values, indicating that the proposed machine learning-based stochastic subspace method can provide accurate modal identification results.

[0083] Example 3

[0084] Operational modal parameter analysis based on the measured acceleration response signals of a 62-story residential building: A SHM system was installed in the residential building, which has 72 sensors and can transmit real-time acceleration data from multiple floors to monitor its structural performance.

[0085] To prove the applicability and effectiveness of the present invention for OMA of civil structures, the acceleration responses of the 18th, 36th, 48th, 53rd, and 62nd floors along two orthogonal directions (i.e., the X direction and the Y direction) were adopted in this example. First, the 216-hour measured acceleration response was divided into 216 one-hour-long segments. Segment 1 was used to establish the SVM classification model, and the other segments were used to prove the effectiveness of the proposed method. Figure 10 Shown is the PSD analysis diagram of the acceleration responses of Segment 1 (X direction and Y direction). Figure 11 The verification result (i.e., the confusion matrix) of the established SVM classification model. Next, Segments 2 to 216 were used to prove the effectiveness of the proposed method. Figure 12 Shows the natural frequencies and damping ratios of the candidate modes in Group s2, indicating that there are some non-structural modes among the candidate modes. Then, the evaluation indexes of the candidate modes in Group s2 were used as the input of the SVM classification model established in Step A1, and the labels of the candidate modes in Group s2 (i.e., the structural mode label or the false mode label) could be predicted. Figure 13 Shows the diagram of the natural frequencies and damping ratios of the candidate modes with the predicted "structural mode label", indicating that the vast majority of non-structural modes are automatically eliminated. Then, the structural modal parameters with the predicted "structural mode label" were used as the input of the K-MEANS algorithm, and the results are as Figure 14As shown. The results show that several outliers are effectively detected, and the modal parameters belonging to different modes are well clustered. Next, the average values of these clustered modal parameters can be easily calculated ( Figure 15 ), which can be regarded as the best identification result of Segment 2.

[0086] Table 1 Identification Results of Modal Parameters of Residential Buildings

[0087]

[0088] a Relative Error = |Value of the Present Invention - Value of the Reference Method| / Value of the Reference Method

[0089] For easy comparison, a reference method developed by Magalhaes et al. (2009) was adopted to identify the structural modal parameters based on the building responses of Segment 2. The results in Table 1 show that the modal parameters of the residential building identified by the proposed method are in good agreement with those of the reference method, indicating that the proposed method can provide accurate modal identification results. According to the same procedure, the structural modal parameters of Segments 3 to 216 were well identified, and the results are as Figure 16 shown. The above results clearly show that the proposed method is applicable and effective for OMA of civil structures.

[0090] The above content is only an example and explanation of the structure of the present invention. Those skilled in the art of this technology make various modifications or supplements to the described specific embodiments or use similar ways to replace them. As long as they do not deviate from the structure of the present invention or exceed the scope defined by this claims, they should fall within the protection scope of the present invention.

Claims

1. A random subspace method based on machine learning, characterized in that, It includes the following steps: A1. Use the SHM system to pre-collect the acceleration response data of the building to be identified, and establish an SVM classification model in combination with the stochastic subspace method; A2. Then combine the established SVM classification model with the K-MEANS algorithm to analyze the newly collected acceleration response data of the SHM system to realize the identification of the modal parameters of the building structure.

2. The random subspace method based on machine learning according to claim 1, wherein The step A1 includes the following steps: (1) Conduct power spectral density analysis to obtain the power spectral density curve to display the modal distribution of the target structure; (2) Identify the fundamental natural frequency and the number of structural modes within the relevant frequency range from the determined power spectral density curve; (3) Determine the value ranges of the two key parameters, the time delay parameter and the system order parameter, in the SSI-COV method; (4) Generate s1 groups of random integers [i, n] representing the time-delay parameter i and the system order parameter n through Monte Carlo simulation, obtaining s1 groups of candidate modes, namely (5) Determine the labels of the above candidate modes based on the acceleration response data pre-collected by the SHM system ; (6) Based on the acceleration response data pre-collected by the SHM system, determine three important evaluation indexes for the candidate modes; (7) Regard the evaluation indexes of the candidate modes as the feature data set, regard the labels of the candidate modes as the label data set, and randomly divide the data set into a training set and a test set. Based on the training set, use the Bayesian optimization method to optimize the hyperparameters, thereby constructing an SVM classification model; based on the test set, verify the performance of the developed classification model through the confusion matrix.

3. The random subspace method based on machine learning according to claim 2, characterized in that: In the step (3), the two key parameters are the time delay parameter and the system order parameter respectively.

4. A random subspace method based on machine learning according to claim 2, characterized in that: In the step (5), the process of determining the candidate modal tags is specifically as follows. When Ω 1 and the modal tag Θ1 can meet the stability criteria in the following equation, the tag of Θ1 is defined as the structural modal tag; otherwise, it is assigned a non-structural modal tag. Natural vibration frequency: Damping ratio: Mode shape: 1 - MAC(φ a , φ b ) ≤ 1%; Among them, the subscripts a and b represent two different modes, f represents the natural vibration frequency, ξ represents the damping ratio, Ω represents the modal set, Θ represents the modal label, and φ represents the modal vibration mode.

5. A random subspace method based on machine learning according to claim 2, characterized in that, In the step (6): The three important evaluation indexes include the natural frequency uncertainty index, the damping ratio uncertainty index, and the modal vibration mode uncertainty index.

6. The random subspace method based on machine learning according to claim 5, wherein The calculation formulas of the natural frequency uncertainty index, the damping ratio uncertainty index, and the modal vibration mode uncertainty index are as follows: Among them, UIF represents the natural frequency uncertainty index, UID represents the damping ratio uncertainty index, UIM represents the mode shape uncertainty index, Std f represents the standard deviation of the natural frequency, Std ξ represents the standard deviation of the damping ratio, represents the standard deviation of the mode shape at the j-th measurement point, j represents the mode shape at the j-th measurement point, f represents the natural vibration frequency, ξ represents the damping ratio, j represents the j-th measurement point, and m is the total number of measurement points.

7. A random subspace method based on machine learning according to claim 1, characterized in that, The step S2 includes the following steps: (1) Combine the established SVM classification model with K-MEANS to analyze the newly collected SHM data for modal parameter identification; (2) Generate s2 groups of random integers [i, n] representing time-delay parameters and system order parameters through Monte Carlo simulation. Then, s2 groups of candidate modes can be obtained, that is and the corresponding evaluation metrics; (3) Use the SVM classification model to predict the labels of the candidate modes in the s2 group, use the K-MEANS algorithm to solve the misclassified modal labels, and cluster different modal parameters; (4) Calculate the average value of the clustered modal parameters as the optimal identification result of the stochastic subspace method based on machine learning.

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