Time-varying structure vibration signal decomposition method based on experience multiple synchronous extraction

Abstract

The invention provides a time-varying structure vibration signal decomposition method based on experience multiple synchronous extraction, and the method comprises the steps: carrying out the frequency spectrum segmentation through searching a sudden change point of the internal and external energy of a characteristic frequency band in a signal time-frequency spectrum, so as to complete the time-varying signal decomposition: firstly, obtaining the time-frequency spectrum of a signal through the multiple synchronous extraction transformation; summing the time-frequency coefficients of all moments at each frequency position to obtain time-frequency total energy; searching an energy boundary by using an energy segmentation operator, and performing Fourier transform on the signal to obtain a signal frequency spectrum; then, combining a zero-phase filter and an energy boundary position, and extracting a frequency band corresponding to the single-mode signal; and finally, inverse Fourier transform is carried out on each section of frequency spectrum, a single-mode signal is reconstructed, and modal decomposition of the time-varying structure is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of structural dynamics, and in particular relates to a time-varying structural vibration signal decomposition method based on empirical multiple synchronous extraction. Background Art

[0002] Structural vibration modal analysis identifies the modal parameters of the structure (such as modal frequency, modal vibration shape and modal damping ratio) through theoretical analysis, numerical calculation or experimental testing to describe the dynamic characteristics of the structure. Modal analysis is widely used in the fields of health monitoring of engineering structures, finite element model modification and vibration control. One of the key issues is to decompose a series of signals with a single frequency component from the vibration response signal, which is called a single modal signal or a single component signal. However, the classical modal analysis theory is mainly based on the linear and time-invariant assumptions, assuming that the modal parameters of the structure remain unchanged and the structural response conforms to the linear superposition principle. It is currently more mature in application, but modal decomposition methods for time-varying and nonlinear structures are still rare. For example, under extreme loads (such as typhoons, earthquakes and wave impacts), civil engineering structures may be in a time-varying and nonlinear state, the modal parameters will change over time, and the obtained response signal will also show non-stationary characteristics. Therefore, it is very necessary to develop a vibration signal decomposition method suitable for time-varying and nonlinear structures to obtain accurate structural modal parameters in engineering applications.

[0003] When performing structural modal analysis, the first task is to extract a single-mode signal from the vibration response signal of the structure. At this time, signal decomposition methods such as Empirical Mode Decomposition (EMD), Analytical Mode Decomposition (AMD) and Variational Mode Decomposition (VMD) are required. EMD is an adaptive signal decomposition method suitable for non-stationary and nonlinear signals. That is, the modal decomposition of the system is achieved by decomposing the response signal into a series of intrinsic mode functions (IMFs). Each IMF component contains the local characteristic signal of the source signal at different time scales. However, EMD requires that the test signal can be completely decomposed when extracting trend items, otherwise it will cause modal aliasing. At the same time, there is also an endpoint effect problem and a lack of a unified mathematical framework. AMD is essentially a low-pass filter that uses the Fourier spectrum to select the cutoff frequency and then decompose the single-component signal from the source signal. The decomposition effect is better than EMD in the case of multi-component dense modes. However, AMD needs to obtain the cutoff frequency by observing the Fourier spectrum, and the decomposition accuracy is reduced when the spectrum peak is not clear. VMD is an algorithm based on Wiener filtering and variational concepts. It is a non-recursive signal decomposition method that performs signal decomposition under the constraints of a variational model, assuming that all components are concentrated in narrowband signals near each center frequency. However, the number of modes and penalty factors of VMD need to be set manually, and the subjectivity has a great impact on the decomposition results. In addition, the selection of narrowband signals limits the decomposition range of the response signal.

[0004] The Empirical Fourier Decomposition (EFD) method mainly uses improved spectrum segmentation technology and zero-phase filters to complete signal decomposition. It has high computational efficiency and can be applied to dense modal decomposition. The decomposition accuracy is also higher than VMD. However, EFD still has great limitations in the decomposition of response signals with time-varying characteristics. The reason is that the spectrum segmentation technology of EFD uses the minimum value between adjacent peaks of the spectrum as the boundary to segment, so as to ensure that each segment of the spectrum contains only one peak. Since the single-mode response signal with a time-invariant structure usually has only one peak, this segmentation technology is very applicable. However, the spectrum of a single-mode response signal with time-varying characteristics is likely to contain multiple peaks at the same time, resulting in errors in spectrum segmentation, which in turn affects the decomposition accuracy. Summary of the invention

[0005] In view of the shortcomings of EFD, the present invention proposes a time-varying structural vibration signal decomposition method based on empirical multiple synchronous extraction, abandoning the idea of ​​finding the minimum value between adjacent peaks in the Fourier spectrum, and instead performing spectrum segmentation by searching for the energy mutation points inside and outside the characteristic frequency band in the signal time-frequency spectrum to complete the time-varying signal decomposition.

[0006] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0007] A method for decomposing time-varying structural vibration signals based on empirical multiple simultaneous extraction:

[0008] The spectrum is segmented by searching for the energy mutation points inside and outside the characteristic frequency band in the signal time spectrum to complete the time-varying signal decomposition:

[0009] First, the time-frequency spectrum of the signal is obtained through multiple synchronous extraction transformations; then the time-frequency coefficients of all moments at each frequency position are summed up to obtain the total time-frequency energy; then the energy partition operator is used to find the energy boundary, and the signal is Fourier transformed to obtain the signal spectrum; after that, the frequency band corresponding to the single-mode signal is extracted by combining the zero-phase filter and the energy boundary position; finally, each spectrum segment is inversely Fourier transformed to reconstruct the single-mode signal and realize the modal decomposition of the time-varying structure.

[0010] Furthermore, the time-frequency spectrum of the signal obtained by using multiple synchronous extraction transformations is specifically as follows: first, the partial derivatives with respect to time of the time-frequency coefficients are obtained to estimate the instantaneous frequency; then, the estimated instantaneous frequency is iterated multiple times through the instantaneous frequency iteration operator; then, the synchronous extraction operator is used to retain the time-frequency coefficients that are close to the instantaneous frequency trajectory; finally, with time as the x-axis and frequency as the y-axis, the time-frequency coefficients are mapped to a two-dimensional plane to obtain the time-frequency spectrum of the signal.

[0011] Furthermore, the time-frequency coefficients at all times of each frequency position are summed to obtain the total time-frequency energy:

[0012]

[0013] Where Te is the time-frequency coefficient of the signal after multiple synchronous extraction transformation; t is time; ω is frequency.

[0014] Furthermore, the energy boundary is found by using the energy partition operator as follows: taking the frequency as the x-axis and the total time-frequency energy as the y-axis, the energy at each frequency position is depicted on a two-dimensional plane to obtain the total time-frequency energy spectrum shown in the following formula:

[0015] U={E(ω1),E(ω2),...,E(ω max )}=2π{E(f1),E(f2),...,E(f max )}

[0016] Where ω1 is the starting frequency position; ω i is the end frequency, which is greater than or equal to the upper boundary of the time-frequency spectrum characteristic band and less than half of the sampling frequency. f is the frequency, ω=2πf.

[0017] Then, the frequency position where the time-frequency energy is zero is searched as the energy boundary, so as to divide the time-frequency energy spectrum (U) into multiple intervals. In each interval, the number of characteristic frequency bands can be determined according to the time-frequency spectrum. If each frequency band is decomposed separately, the segmentation is considered to be completed. Otherwise, the interval containing multiple frequency bands needs to be further segmented. Specifically, three frequency positions are selected continuously along the time axis and marked as E(f α ), E(f α+1 ) and E(f α+2 ). E(f α+1 ) to the energy ratio of the other two frequency positions is calculated as follows:

[0018]

[0019] Since there are time-frequency energy fluctuations near the characteristic frequency band, the frequency positions corresponding to the first few maximum energy ratios are taken as energy mutation points to preliminarily determine the approximate position of the characteristic frequency band. Then, these mutation points are arranged in descending order and the frequency positions with the minimum energy between adjacent mutation points are taken as energy boundaries to further divide the frequency interval to ensure that the frequency band of each single component signal can be decomposed separately.

[0020] Furthermore, the method of extracting the frequency band corresponding to the single-mode signal is as follows: performing Fourier transform on the signal to obtain the spectrum of the signal, then segmenting the spectrum according to energy boundary lines, and extracting each segment of the spectrum using a zero-phase filter.

[0021] And, a time-varying structural vibration signal decomposition system based on empirical multiple synchronous extraction, comprising:

[0022] A multiple synchronous extraction and transformation module, used for obtaining the time-frequency spectrum of the signal through multiple synchronous extraction and transformation;

[0023] A time-frequency total energy calculation module, used to sum the time-frequency coefficients at all moments of each frequency position in the time-frequency spectrum obtained by the multiple synchronous extraction and transformation module to obtain the time-frequency total energy;

[0024] An energy boundary extraction module is used to find the energy boundary by using the energy partition operator based on the total time-frequency energy;

[0025] A frequency band extraction module is used to perform Fourier transform on the signal to obtain a signal spectrum; and then extract the frequency band corresponding to the single-mode signal by combining the zero-phase filter and the energy boundary position obtained by the energy boundary extraction module;

[0026] The reconstruction module is used to perform inverse Fourier transform on each frequency spectrum obtained by the frequency band extraction module, reconstruct a single-mode signal, and realize modal decomposition of the time-varying structure.

[0027] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction as described above are implemented.

[0028] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction as described above.

[0029] Compared with the prior art, the advantages of the present invention and its preferred embodiment include at least the following: (1) the response signal with time-varying characteristics can be decomposed with high precision; (2) the constructed energy segmentation operator improves the segmentation accuracy of the existing improved spectrum segmentation technology, and can still maintain good decomposition accuracy when analyzing signals with strong interference outside the frequency band; (3) only the output response data of the structure is required to complete the modal decomposition.

[0030] This scheme can be used for the decomposition of vibration signals of civil, mechanical and aerospace engineering structures in time-varying and nonlinear conditions, and for the identification of structural modal parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0032] Figure 1 The present invention is a flowchart of a method for decomposing a time-varying structural vibration signal based on empirical multiple synchronous extraction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to make the features and advantages of this patent more obvious and easy to understand, the following embodiments are specifically described in detail as follows:

[0034] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0035] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0036] In the scheme provided by the present invention, the time-frequency spectrum of the signal is first obtained through multiple synchronous extraction transformations; then the time-frequency coefficients of each frequency position at all times are summed to obtain the total time-frequency energy; then the energy partition operator is used to find the energy boundary, and the signal is Fourier transformed to obtain the signal spectrum; then the zero-phase filter and the energy boundary position are combined to extract the frequency band corresponding to the single-mode signal; finally, each frequency spectrum segment is inversely Fourier transformed to reconstruct the single-mode signal, thereby realizing the modal decomposition of the time-varying structure and obtaining the structural modal parameters.

[0037] like Figure 1 As shown, the implementation process includes the following steps:

[0038] Step 1: Use multiple synchronous extraction transformations to obtain the time-frequency spectrum of the signal. The existing synchronous extraction transformation algorithm improves the time-frequency energy concentration of the frequency band by retaining only the time-frequency coefficients that are close to the instantaneous frequency trajectory. However, this method requires the partial derivative of the time-frequency coefficient to estimate the instantaneous frequency, which causes errors when estimating the instantaneous frequency, thereby affecting the accuracy of instantaneous frequency estimation. To this end, this step proposes a multiple synchronous extraction transformation algorithm. This method first estimates the instantaneous frequency by taking the partial derivative of the time with respect to the time of the time-frequency coefficient. Then, the instantaneous frequency is iterated multiple times by the instantaneous frequency iteration operator to improve the accuracy of instantaneous frequency estimation. Next, the existing synchronous extraction operator is used to retain the time-frequency coefficients that are close to the instantaneous frequency trajectory. Specifically: the synchronous extraction operator retains the time-frequency coefficients that are close to the instantaneous frequency trajectory by setting the difference between the estimated instantaneous frequency and the instantaneous frequency and returns the remaining coefficients to zero. Finally, with time as the x-axis and frequency as the y-axis, the time-frequency coefficients are mapped to a two-dimensional plane to obtain the time-frequency spectrum of the signal.

[0039] Among them, the instantaneous frequency iteration operator is specifically:

[0040]

[0041] In the formula, is the estimated instantaneous frequency; is the phase; N is the number of iterations.

[0042] Theoretically, the instantaneous frequency of a signal should be the first-order derivative of the phase with respect to time, but in practice, an error term will be generated during the derivation process. From formula (1), we can see that when N is large enough, It will tend to 0, making the estimated instantaneous frequency equal to the first-order derivative of the phase, thereby reducing the estimation error.

[0043] Step 2: Sum the time-frequency coefficients at all times of each frequency position to obtain the total time-frequency energy of each frequency position.

[0044]

[0045] Where Te is the time-frequency coefficient of the signal after multiple synchronous extraction transformation; t is time; ω is frequency.

[0046] Step 3: Construct an energy segmentation operator to find the energy spectrum boundary. Specifically, with frequency as the x-axis and the total time-frequency energy as the y-axis, the energy at each frequency position is plotted on a two-dimensional plane to obtain the total time-frequency energy spectrum shown in formula (3).

[0047] U={E(ω1),E(ω2),…,E(ω max )}=2π{E(f1),E(f2),…,E(f max )} (3)

[0048] Where ω1 is the starting frequency position, which is usually 0Hz. i is the termination frequency, which is usually greater than or equal to the upper boundary of the time-frequency spectrum characteristic band. At the same time, it should also be less than half of the sampling frequency. f is the frequency, ω=2πf.

[0049] In fact, the energy of the signal inside and outside the instantaneous frequency band will suddenly change. The energy inside the characteristic frequency band is usually more obvious, while the energy outside the frequency band is relatively small or even 0. This phenomenon is more obvious after the energy at all moments is superimposed. Based on this, we first search for all frequency positions with 0 energy in the energy spectrum, and preliminarily divide the energy spectrum U into multiple intervals.

[0050] According to the time-frequency spectrum, if each characteristic frequency band is decomposed separately, these positions can be directly used as energy boundaries. If there are multiple characteristic frequency bands in one or more intervals, three energy points are selected from the smallest to the largest frequency along the positive direction of the frequency axis in the interval, and the energy at the middle frequency position is used as the divisor, and the quotient is calculated with the energy of the other two positions, and the quotient value is recorded.

[0051]

[0052] Repeat this operation for all frequency points in the interval to obtain the energy quotients of all frequency points, and then sort the quotients in descending order, and select the number of quotients according to the number of frequency bands in the interval. Then, search for the frequency positions corresponding to these quotients, and use the frequency positions with the minimum energy value within these positions as the energy boundary line, so that the interval containing multiple frequency bands can be divided again to ensure that each characteristic frequency band can be solved separately.

[0053] Step 4: Extract the frequency band corresponding to the single-mode signal. Perform Fourier transform on the signal to obtain the spectrum of the signal, then segment the spectrum using the energy boundary line obtained in step 3, and use a zero-phase filter to extract each spectrum segment.

[0054] Step 5: Perform inverse Fourier transform on each spectrum segment to reconstruct all single-mode responses and obtain the modal parameters of the time-varying structure.

[0055] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0056] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0057] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0058] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0059] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0060] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0061] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive other forms of time-varying structural vibration signal decomposition methods based on empirical multiple synchronous extraction under the inspiration of this patent. All equal changes and modifications made according to the scope of the patent application of the present invention should be covered by this patent.

Claims

1. A method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction, characterized in that: The spectrum is segmented by searching for the energy mutation points inside and outside the characteristic frequency band in the signal time spectrum to complete the time-varying signal decomposition: First, the time-frequency spectrum of the signal is obtained through multiple synchronous extraction transformations; then the time-frequency coefficients of all moments at each frequency position are summed up to obtain the total time-frequency energy; then the energy partition operator is used to find the energy boundary, and the signal is Fourier transformed to obtain the signal spectrum; after that, the frequency band corresponding to the single-mode signal is extracted by combining the zero-phase filter and the energy boundary position; finally, each spectrum segment is inversely Fourier transformed to reconstruct the single-mode signal and realize the modal decomposition of the time-varying structure.

2. The time-varying structural vibration signal decomposition method based on empirical multiple synchronous extraction according to claim 1 is characterized in that: The method of using multiple synchronous extraction transformations to obtain the time-frequency spectrum of the signal is specifically as follows: first, the partial derivatives with respect to time of the time-frequency coefficients are obtained to estimate the instantaneous frequency; then, the estimated instantaneous frequency is iterated multiple times through the instantaneous frequency iteration operator; then, the synchronous extraction operator is used to retain the time-frequency coefficients that are close to the instantaneous frequency trajectory; finally, with time as the x-axis and frequency as the y-axis, the time-frequency coefficients are mapped to a two-dimensional plane to obtain the time-frequency spectrum of the signal.

3. The method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction according to claim 1, characterized in that: The time-frequency coefficients at all moments of each frequency position are summed to obtain the total time-frequency energy: Where Te is the time-frequency coefficient of the signal after multiple synchronous extraction transformation; t is time; ω is frequency.

4. The method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction according to claim 1, characterized in that: The specific method of finding the energy boundary by using the energy partition operator is as follows: taking the frequency as the x-axis and the total time-frequency energy as the y-axis, the energy at each frequency position is depicted on a two-dimensional plane to obtain the total time-frequency energy spectrum shown in the following formula: U6{E(ω1),E(ω2),...,E(ω max )}S2π{E(f1),E(f2),...,E(f max )} Where ω1 is the starting frequency position; ω i is the termination frequency, which is greater than or equal to the upper boundary of the time-frequency spectrum characteristic frequency band and less than half of the sampling frequency; f is the frequency, ω=2πf; Then, the frequency position where the time-frequency energy is zero is searched as the energy boundary, so as to divide the time-frequency energy spectrum (U) into multiple intervals; in each interval, the number of characteristic frequency bands is determined according to the time-frequency spectrum; if each frequency band is decomposed separately, the segmentation is considered to be completed; otherwise, the interval containing multiple frequency bands needs to be further segmented: specifically, three frequency positions are selected continuously along the time axis and marked as E(f α ), E(f α+1 ) and E(f α+2 ); E(f α+1 ) to the energy ratio of the other two frequency positions is calculated as follows: Since there are time-frequency energy fluctuations near the characteristic frequency band, the frequency positions corresponding to the first few maximum energy ratios are taken as energy mutation points to preliminarily determine the approximate position of the characteristic frequency band; then, these mutation points are arranged in descending order and the frequency positions with the smallest energy between adjacent mutation points are used as energy boundaries to further divide the frequency interval to ensure that the frequency band of each single-component signal is decomposed separately.

5. The method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction according to claim 1, characterized in that: The method of extracting the frequency band corresponding to the single-mode signal is: performing Fourier transform on the signal to obtain the spectrum of the signal, then segmenting the spectrum according to energy boundary lines, and extracting each segment of the spectrum using a zero-phase filter.

6. A time-varying structural vibration signal decomposition system based on empirical multiple synchronous extraction, characterized in that: include: A multiple synchronous extraction and transformation module, used for obtaining the time-frequency spectrum of the signal through multiple synchronous extraction and transformation; A time-frequency total energy calculation module, used to sum the time-frequency coefficients at all moments of each frequency position in the time-frequency spectrum obtained by the multiple synchronous extraction and transformation module to obtain the time-frequency total energy; An energy boundary extraction module is used to find the energy boundary by using the energy partition operator based on the total time-frequency energy; A frequency band extraction module is used to perform Fourier transform on the signal to obtain a signal spectrum; and then extract the frequency band corresponding to the single-mode signal by combining the zero-phase filter and the energy boundary position obtained by the energy boundary extraction module; The reconstruction module is used to perform inverse Fourier transform on each frequency spectrum obtained by the frequency band extraction module, reconstruct a single-mode signal, and realize modal decomposition of the time-varying structure.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the time-varying structural vibration signal decomposition method based on empirical multiple synchronous extraction as described in any one of claims 1 to 5 are implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for decomposing time-varying structural vibration signals based on empirical multiple synchronous extraction as described in any one of claims 1 to 5 are implemented.

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