Nonlinear structure frequency and vibration mode coefficient identification method based on sliding window power spectrum and Polymax

Abstract

The invention discloses a non-linear structure frequency and vibration mode coefficient identification method based on a sliding window power spectrum and Polymax. The method comprises the following steps: 1, testing to obtain an acceleration response of an engineering structure; 2, calculating an auto-power spectrum and a cross-power spectrum of each moment signal in the acceleration response signal of the engineering structure; 3, for each instant, selecting an instant power spectrum function of a specific time period by using a sliding window with a certain length; 4, calculating to obtain a mean power spectrum function of the instantaneous power spectrum functions in the selected time period range; and 5, taking the mean power spectrum function as input of polymax, and combining the stability diagram and clustering analysis to obtain an instantaneous modal frequency and a vibration mode coefficient. According to the non-linear structure frequency and vibration mode coefficient identification method based on the sliding window power spectrum and the Polymax, the outstanding advantages of the Polymax in conventional conditions, large damping and dense modal analysis can be effectively played, and the defects of an existing method in the aspects of analysis parameter selection and model overfitting can be overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of nonlinear frequency and mode coefficient identification of engineering structures, and specifically is a method for identifying frequency and mode coefficient of nonlinear structures based on sliding window power spectrum and Polymax. Background Art

[0002] Engineering structures generally have nonlinear behaviors, which leads to time-varying modal parameters of engineering structures. For example, the interaction between bolts, gaps and boundaries in bridges during load bearing will cause nonlinear behavior; for example, under the action of earthquake motion, the engineering structure will transform from an intact structure to a damaged structure, and the damage location and degree of damage will continue to change. Therefore, during the entire earthquake motion process, the modal parameters of the engineering structure will change with the progress of the load. However, the identification method of time-varying modal parameters of engineering structures is not yet mature, and existing research still has certain deficiencies.

[0003] The existing time-varying modal parameter analysis methods can be roughly divided into three categories, namely the time domain method, the time-frequency domain method and the joint method. The time domain method mainly uses a time series model with time-varying coefficients to establish an equivalent model of the dynamic response of the engineering structure, and extracts the time-varying modal parameters of the engineering structure through the time-varying model coefficients; the time-frequency domain method first performs a wavelet transform on the response signal of the structure, and uses the modulus maximum of the wavelet transform to identify the time-varying frequency of the engineering structure, and uses the wavelet coefficient normalization to obtain the time-varying vibration mode of the structure; the joint method first performs a time-frequency decomposition on the response signal of the engineering structure, decomposes the multi-degree-of-freedom linear time-varying system response into multiple single-modal responses, and then combines the time-varying autoregressive model to extract the time-varying modal parameters.

[0004] Existing methods can realize the identification of time-varying frequency and vibration mode under certain conditions, but the above methods involve the establishment of mathematical models of time-varying autoregressive models, and there are outstanding problems such as lack of objective criteria for the selection of model orders and overfitting of mathematical models; while the time-frequency decomposition method has problems with the selection of basis function types and parameters, and the situation of dense frequencies and large damping has yet to be verified. In addition, the Polymax method has been widely proven to be able to be used not only for modal parameter identification under conventional conditions, but also for modal parameter identification under dense modes and large damping conditions, but due to theoretical limitations, this method is only applicable to linear structures. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a method for identifying the frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax, which can effectively give play to the outstanding advantages of Polymax in conventional cases, large damping and dense modal analysis, and can overcome the shortcomings of existing methods in analysis parameter selection and model overfitting.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for identifying frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax, comprising the following steps:

[0008] Step 1: Test and obtain the acceleration response of the engineering structure;

[0009] Step 2: Calculate the auto-power spectrum and cross-power spectrum of the acceleration response signal of the engineering structure at each moment;

[0010] Step 3: For each instant, use a sliding window of a certain length to select the instantaneous power spectrum function of a specific time period;

[0011] Step 4: Calculate the mean power spectrum function of the instantaneous power spectrum function within the selected time period;

[0012] Step 5: Use the mean power spectrum function as the input of polymax, and combine the stability diagram and cluster analysis to obtain the instantaneous modal frequency and vibration mode coefficient.

[0013] Furthermore, in step 1, an acceleration sensor is used to test the acceleration response of the engineering structure; or a displacement sensor is used to test the displacement response of the engineering structure, and then the displacement response is differentiated twice to obtain the acceleration response of the engineering structure.

[0014] Furthermore, in step 2, for an engineering structure with n measuring points, the i-th measuring point is k The instantaneous auto-power spectrum function is expressed as:

[0015]

[0016] The i-th and j-th measuring points are at the t-th k The instantaneous cross power spectrum function is expressed as:

[0017]

[0018] Where: X i (ω,t k ) indicates that the signal of the i-th measuring point is at t k The instantaneous Fourier spectrum function; Represents X i (ω,t k ) is the conjugate of the function.

[0019] Furthermore, in step three, the length of the sliding window is set, the current instant is taken as the midpoint of the sliding window, and a time point within the sliding window is selected to realize the selection of the instantaneous power spectrum function in a specific time period.

[0020] Further, in step 4, the mean power spectrum function is expressed as:

[0021]

[0022] in: Indicates that the signals of the i-th and j-th measuring points are at t k The cross-spectral function of the mean power spectrum at an instant; L is the length of the sliding window.

[0023] In the step 5, the t k The instantaneous mean power spectrum function is used as the input of polymax, combined with the stability diagram and cluster analysis, to obtain the tth k The instantaneous modal frequencies and vibration coefficients.

[0024] The beneficial effects of the present invention are:

[0025] The present invention is based on a nonlinear structural frequency and vibration mode coefficient identification method based on a sliding window power spectrum and Polymax. First, the acceleration response of the engineering structure is subjected to instantaneous power spectrum analysis. Then, for each instant, a sliding window of a certain length is used to select the instantaneous power spectrum function of a specific time period, and then the mean power spectrum function of the instantaneous power spectrum function within the range is calculated. The mean power spectrum function is then used as the input of Polymax, and the frequency and vibration mode coefficient of the engineering structure at the current instant are automatically picked up in combination with a stability diagram and a cluster analysis method. The method of the present invention can effectively give play to the outstanding advantages of Polymax in conventional situations, large damping and dense modal analysis, and can overcome the shortcomings of existing methods in analysis parameter selection and model overfitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0027] Figure 1 It is a flow chart of the method for identifying the frequency and mode coefficient of a nonlinear structure based on the sliding window power spectrum and Polymax of the present invention;

[0028] Figure 2 This is the schematic diagram of the time sliding window;

[0029] Figure 3 The following are two waveform diagrams of the simulated signals; (a) waveform diagram of signal 1; (b) waveform diagram of signal 2;

[0030] Figure 4 The frequency and mode coefficient identification results when the sliding window length is 1000 data points; (a) is the natural frequency identification result; (b) is the mode coefficient identification result. DETAILED DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0032] like Figure 1 As shown, the nonlinear structure frequency and mode coefficient identification method based on sliding window power spectrum and Polymax in this embodiment includes the following steps.

[0033] Step 1: Test and obtain the acceleration response of the engineering structure.

[0034] Specifically, an acceleration sensor may be used to test the acceleration response of the engineering structure; or a displacement sensor may be used to test the displacement response of the engineering structure, and then the displacement response is secondarily differentiated to obtain the acceleration response of the engineering structure. In this embodiment, an acceleration sensor is used to test the acceleration response of the engineering structure.

[0035] Step 2: Calculate the auto-power spectrum and cross-power spectrum of the acceleration response signal of the engineering structure at each moment.

[0036] Specifically, for an engineering structure with n measuring points, the i-th measuring point is k The instantaneous auto-power spectrum function is expressed as:

[0037]

[0038] The i-th and j-th measuring points are at the t-th k The instantaneous cross power spectrum function is expressed as:

[0039]

[0040] Where: X i (ω,t k ) indicates that the signal at the i-th measuring point is k The instantaneous Fourier spectrum function; Represents X i (ω,t k ) is the conjugate of the function.

[0041] Step 3: For each instant, use a sliding window of a certain length to select the instantaneous power spectrum function of a specific time period.

[0042] Specifically, the method of selecting a specific time period using a sliding window is as follows: set the length of the sliding window, take the current instant as the midpoint of the sliding window, select a time point within the sliding window range, and realize the instantaneous power spectrum function selection of a specific time period, such as Figure 2As shown. Specifically, the length of the sliding window is selected according to the severity of the frequency component changes in the signal. Generally, the length of the sliding window can be qualitatively judged more clearly by the frequency changes of the engineering structure to be investigated. Usually, for signals with relatively gentle frequency changes, the length of the sliding window can be 500 to 1000 data points; for signals with relatively drastic frequency changes, a smaller number of data points can be taken.

[0043] Step 4: Calculate the mean power spectrum function of the instantaneous power spectrum function within the selected time period.

[0044] The instantaneous power spectrum function of a specific time period is used to calculate the mean of the instantaneous power spectrum function to obtain the mean power spectrum function. Specifically, the mean power spectrum function is expressed as:

[0045]

[0046] in: Indicates that the signals of the i-th and j-th measuring points are at t k The cross-spectral function of the mean power spectrum at an instant; L is the length of the sliding window.

[0047] Step 5: Use the mean power spectrum function as the input of polymax, and combine the stability diagram and cluster analysis to obtain the instantaneous modal frequency and vibration mode coefficient. k The instantaneous mean power spectrum function is used as the input of polymax, combined with the stability diagram and cluster analysis, to obtain the tth k The instantaneous modal frequencies and vibration coefficients.

[0048] This embodiment is based on the nonlinear structural frequency and mode coefficient identification method of sliding window power spectrum and Polymax. First, the acceleration response of the engineering structure is subjected to instantaneous power spectrum analysis. Then, for each instant, a sliding window of a certain length is used to select the instantaneous power spectrum function of a specific time period, and then the mean power spectrum function of the instantaneous power spectrum function within the range is calculated. The mean power spectrum function is then used as the input of Polymax, and combined with the stability diagram and cluster analysis method, the frequency and mode coefficient of the engineering structure at the current instant are automatically picked up. The method of this embodiment can effectively give play to the outstanding advantages of Polymax in conventional situations, large damping and dense modal analysis, and can overcome the shortcomings of existing methods in analysis parameter selection and model overfitting.

[0049] The technical effect of the method of this embodiment is verified below with reference to specific examples.

[0050] White noise excitation is applied to a signal containing a frequency and a modal coefficient that varies linearly with time. The frequency varies with time in the range of 0.56 to 0.66 Hz. The ratio of the modal coefficient of signal 2 to the modal coefficient of signal 1 is time-varying, and the ratio of the modal coefficients varies in the range of 1.76 to 1.21. Figure 3 The following are two signal waveforms obtained by simulation. Figure 4 The calculation results of the frequency and mode coefficients when the sliding window length is 1000 data points. The scattered points in the figure represent the recognition results, and the dotted line represents the theoretical value. The results show that the method proposed in this embodiment can effectively describe the changing characteristics of time-varying frequency and mode coefficients, and the recognition results have high accuracy.

[0051] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for identifying frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax, characterized in that: The steps include: Step 1: Test and obtain the acceleration response of the engineering structure; Step 2: Calculate the auto-power spectrum and cross-power spectrum of the acceleration response signal of the engineering structure at each moment; Step 3: For each instant, use a sliding window of a certain length to select the instantaneous power spectrum function of a specific time period; Step 4: Calculate the mean power spectrum function of the instantaneous power spectrum function within the selected time period; Step 5: Use the mean power spectrum function as the input of polymax, and combine the stability diagram and cluster analysis to obtain the instantaneous modal frequency and vibration mode coefficient.

2. The method for identifying nonlinear structural frequency and mode coefficients based on sliding window power spectrum and Polymax according to claim 1, characterized in that: In the step 1, an acceleration sensor is used to test the acceleration response of the engineering structure; or a displacement sensor is used to test the displacement response of the engineering structure, and then the displacement response is differentiated twice to obtain the acceleration response of the engineering structure.

3. The method for identifying frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax according to claim 1, characterized in that: In the step 2, for an engineering structure with n measuring points, the i-th measuring point is k The instantaneous auto-power spectrum function is expressed as: The i-th and j-th measuring points are at the t-th k The instantaneous cross power spectrum function is expressed as: Where: X i (ω,t k ) indicates that the signal at the i-th measuring point is k The instantaneous Fourier spectrum function; Represents X i (ω,t k ) is the conjugate of the function.

4. The method for identifying frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax according to claim 1, characterized in that: In the step three, the length of the sliding window is set, the current instant is taken as the midpoint of the sliding window, and a time point within the sliding window is selected to realize the selection of the instantaneous power spectrum function in a specific time period.

5. The method for identifying frequency and mode coefficients of nonlinear structures based on sliding window power spectrum and Polymax according to claim 1, characterized in that: In step 4, the mean power spectrum function is expressed as: in: Indicates that the signals of the i-th and j-th measuring points are at t k The cross-spectral function of the mean power spectrum at an instant; L is the length of the sliding window.

6. Identification of nonlinear structural frequency and mode coefficients based on sliding window power spectrum and Polymax according to claim 1 The method is characterized in that: In the step 5, the t k The instantaneous mean power spectrum function is used as the input of polymax, Combining the stability diagram and cluster analysis, we get k The instantaneous modal frequencies and vibration coefficients.

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