Structural modal analysis method based on improved blind source separation

Abstract

The invention provides a structural modal analysis method based on improved blind source separation. The method comprises the following steps: firstly, obtaining a sparse matrix and a time-frequency coefficient of a response signal through multiple synchronous extraction transformation with a sliding window; summing all the time-frequency coefficients along the time direction so as to obtain time-frequency total energy; then locking the position of the maximum time-frequency energy scatter point by adopting a peak value pickup method; calculating energy points having the same distance with each peak value position by using a cosine distance so as to estimate each source frequency band; and finally, performing multiple synchronous extraction inverse transformation with a sliding window on each source frequency band, and reconstructing a single-mode signal.

Description

Technical Field

[0001] The invention belongs to the technical field of structural dynamics, and in particular relates to a structural modal analysis method based on improved blind source separation. Background Art

[0002] Structural modal analysis is an important tool for studying the dynamic characteristics of structures. It describes the structural dynamic system through the modal parameters of the structure (modal frequency, modal damping ratio and modal vibration shape). It is widely used in structural diagnosis and vibration control in the fields of aerospace, machinery, civil engineering, etc. Blind source separation (BSS) refers to estimating the source signal based on the observed mixed signal when the source signal and the mixed signal parameters are unknown. In practical applications, the BSS method only realizes modal decomposition through the response data of the structure, which makes it unique in modal analysis of civil engineering. Since civil structures in working state are subject to environmental excitation, it is usually difficult to obtain the magnitude of the excitation force, and only the response signal affected by environmental factors and test noise can be obtained. In addition, the actual civil structure has large geometric dimensions and complex component forms. The obtained spectrum is often unclear, and aliasing, leakage and false modes are prone to occur. At the same time, due to the large degree of freedom of the structure, there is also a dense mode problem, which brings great difficulties to the practical application of the existing blind source separation method.

[0003] At present, modal analysis involves three categories: experimental modal analysis, operational modal analysis, and operational deformation analysis. In experimental modal analysis, the excitation force can be measured, and together with the response data received by the sensor, the structural modal parameters are identified by constructing a frequency response function; the actual civil engineering structures in service are under random excitations such as wind, vehicles, and ground pulsations, and the excitation force is difficult to measure. Generally, only the structural response can be obtained, which is called operational modal analysis. Operational deformation analysis directly obtains the deformation vibration mode of the structure by superimposing the response of the structure under the working state, which is significantly different from the process of obtaining modal parameters by experiments and operational modal analysis.

[0004] Blind source separation technology can obtain the dynamic characteristics of the system by only analyzing the system response. It has high computational efficiency, is non-parametric, and does not require prior information about the dynamic system, making it widely used in the field of modal analysis of structures. Blind source separation technology is divided into two categories: positive definite and underdetermined. Among them, the positive definite blind source separation method requires that the number of measurement sensors is greater than or equal to the number of structural modes, while the number of structural modes that can be excited in actual engineering is usually unknown. Therefore, this method is subject to certain limitations in practice. When using underdetermined blind source separation technology, the number of sensors can be less than the number of modes, and the application range is wider. As the most representative underdetermined blind source separation method, sparse component analysis separates the mixed signals collected by the sensor array according to the sparse characteristics of the signal in the analysis domain, so the decomposition accuracy will be affected by the sparsity of the analysis domain. However, most of the existing sparse component analysis and its improved methods obtain the sparse transformation matrix through short-time Fourier transform. Since the frequency band identified by short-time Fourier transform will show energy divergence, the sparsity of the acquired time-frequency matrix is ​​insufficient, which in turn affects the modal decomposition accuracy of the sparse component analysis method, especially in the decomposition of complex modes. Summary of the invention

[0005] In view of the above-mentioned deficiencies of the prior art, the present invention proposes a structural modal analysis method based on improved blind source separation to realize structural modal analysis under complex modal conditions. In this method, a multiple synchronous extraction transform with a sliding window is proposed to replace the short-time Fourier transform commonly used in the existing sparse component analysis method, thereby improving the sparsity of the mixing matrix and thus improving the accuracy of modal decomposition.

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

[0007] A structural modal analysis method based on improved blind source separation first obtains the sparse matrix and time-frequency coefficients of the response signal through multiple synchronous extraction transformation with sliding window; then sums all time-frequency coefficients along the time direction to obtain the total time-frequency energy; then uses the peak picking method to lock the position of the maximum time-frequency energy scatter point; then uses the cosine distance to calculate the energy points with the same distance from each peak position to estimate each source frequency band; finally, performs multiple synchronous extraction inverse transformation with sliding window on each source frequency band to reconstruct the single modal signal.

[0008] 1. Furthermore, the sparse matrix of the response signal obtained by the multiple synchronous extraction transformation with a sliding window is specifically: the sparse matrix of the response signal is obtained by performing a multiple synchronous extraction transformation with a sliding window on the structural response data; the multiple synchronous extraction transformation with a sliding window is: firstly, a short-time Fourier transform is performed on the response signal to obtain the time-frequency coefficient of the signal, and then, the partial derivative with respect to time is calculated for the time-frequency coefficient to obtain the instantaneous frequency of the signal estimate. Then, the estimated instantaneous frequency is iterated multiple times to improve the estimation accuracy. Next, a sliding window is constructed and the maximum value of the time-frequency coefficient in the window is retained to improve the sparsity of the time-frequency coefficient matrix. Finally, the recognition result of the multiple synchronous extraction transformation with a sliding window can be obtained through the synchronous extraction transformation.

[0009] Furthermore, the sliding window expression is:

[0010]

[0011]

[0012] Where G(t,ω) is the time-frequency coefficient after short-time Fourier transform; G m (t,ω) is the maximum value of the time-frequency coefficient in the window; ω is the frequency, Δω is the window; ω Δ G after N iterations m The corresponding estimated instantaneous frequency;

[0013] ω [N] (t,ω) is defined by the instantaneous frequency iteration operator shown below:

[0014]

[0015] In the formula, is the estimated instantaneous frequency; is the phase; N is the number of iterations.

[0016] Furthermore, the method for calculating the total time-frequency energy is as follows: after the synchronous extraction transformation with a sliding window, the time-frequency energy at each moment is first calculated along the frequency direction (in fact, multiple sensors are usually used when performing power testing, and the response obtained is also a multi-channel signal. Therefore, each channel signal can obtain a corresponding time-frequency energy); on this basis, the time-frequency energies of all channel signals are superimposed to obtain the total time-frequency energy of the mixed signal.

[0017] Furthermore, the method of locking the maximum time-frequency energy scatter point position using the peak picking method is: first, draw a time-frequency total energy graph with time as the x-axis and the time-frequency total energy as the y-axis; then, use the peak picking method to obtain the frequency position corresponding to each peak in the time-frequency total energy graph.

[0018] Furthermore, in the process of estimating the source frequency band: the points with the same cosine distance from the position of each peak in the time-frequency total energy diagram are regarded as the same source point, and the cosine distance is used to estimate all energy points and their positions belonging to the same source, thereby estimating each source frequency band.

[0019] Furthermore, the specific method for reconstructing the unimodal signal is: performing an inverse transformation of the synchronous extraction transformation with sliding window as shown in the following formula on each source frequency band estimated in the center, so as to reconstruct each unimodal signal; the expression of the unimodal signal s(t) is:

[0020]

[0021] Where s(t) is a single-mode signal; g is a window function; [ω0-Δ, ω0+Δ] is the range of the source frequency band; Te is the synchronous extraction transformation recognition result with a sliding window.

[0022] And, a structural modal analysis system based on improved blind source separation, comprising:

[0023] A response signal sparse matrix extraction module is used to obtain the sparse matrix and time-frequency coefficients of the response signal through multiple synchronous extraction transformations with sliding windows;

[0024] A time-frequency total energy calculation module, used for summing all time-frequency coefficients obtained by the response signal sparse matrix extraction module along the time direction to obtain the time-frequency total energy;

[0025] A maximum time-frequency energy scatter point position extraction module is used to lock the maximum time-frequency energy scatter point position by using a peak picking method according to the calculation result of the time-frequency total energy calculation module;

[0026] A source frequency band estimation module is used to calculate energy points with the same distance from each peak position based on the position of the maximum time-frequency energy scatter point using the cosine distance, thereby estimating each source frequency band;

[0027] The single-mode signal reconstruction module is used to perform a multiple synchronous extraction inverse transformation with a sliding window on each source frequency band estimated by the source frequency band estimation module to reconstruct the single-mode signal.

[0028] 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 structural modal analysis method based on improved blind source separation as described above are implemented.

[0029] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the structural modal analysis method based on improved blind source separation as described above.

[0030] Compared with the prior art, the advantages of the present invention and its preferred embodiment include at least the following: (1) The proposed sliding window multi-synchronous extraction transform improves the sparsity of the time-frequency matrix and the accuracy of modal decomposition. (2) The improved blind source separation has better decomposition accuracy for underdetermined and complex modes, and can still maintain good accuracy for dense modal conditions. (3) The modal parameter identification process only requires the response data of the structure.

[0031] This scheme can be used for modal analysis of civil engineering structures under environmental excitation and to identify the modal parameters of structures under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0033] Figure 1 The present invention is a flowchart of a structural modal analysis method based on improved blind source separation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0034] 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:

[0035] 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.

[0036] 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.

[0037] To achieve the above object, the technical solution adopted by the present invention is: a structural modal analysis method based on improved blind source separation, the specific process is as follows Figure 1 shown.

[0038] The following steps are involved:

[0039] Step 1: Obtain a sparse matrix of the response signal. Perform a multiple synchronous extraction transform with a sliding window on the structural response data to obtain a sparse matrix of the response signal. It is preferred to use a multiple synchronous extraction transform with a sliding window: first, perform a short-time Fourier transform on the response signal to obtain the time-frequency coefficients of the signal, then calculate the partial derivatives with respect to time for the time-frequency coefficients to obtain the instantaneous frequency of the signal estimate. Then, perform multiple iterations on the estimated instantaneous frequency to improve the estimation accuracy. Next, construct a sliding window and retain the maximum value of the time-frequency coefficients in the window to improve the sparsity of the time-frequency coefficient matrix. Finally, the recognition result of the multiple synchronous extraction transform with a sliding window can be obtained through the synchronous extraction transform.

[0040] Specifically:

[0041] In theory, the instantaneous frequency of a signal is equal to the first-order derivative of its phase with respect to time. However, errors will occur in the actual derivation process, thereby affecting the estimation accuracy of the instantaneous frequency. To address this problem, the embodiment of the present invention introduces the instantaneous frequency iteration operator shown in formula (1) to improve the estimation accuracy of the frequency, while indirectly reducing the energy divergence of the frequency band:

[0042]

[0043] In the formula, is the estimated instantaneous frequency; is the phase; N is the number of iterations.

[0044] From formula (1), we can see that when N is large enough, will tend to 0, making the estimated instantaneous frequency equal to the first-order derivative of the phase. The existing synchronous extraction transformation process improves the time-frequency aggregation by constructing a synchronous extraction operator to retain only the time-frequency coefficients closest to the instantaneous frequency. Compared with the short-time Fourier transform, the frequency band energy identified by the synchronous extraction transform is more concentrated. However, the synchronous extraction operator operates on the entire time-frequency spectrum, which inevitably causes interference points outside the frequency band, thereby affecting the sparsity of the time-frequency matrix.

[0045] To this end, the embodiment of the present invention provides a solution of sliding the window and retaining the maximum value of the time-frequency coefficient in the window, further improving the sparsity of the time-frequency matrix. The sliding window expression is:

[0046]

[0047]

[0048] Where G(t,ω) is the time-frequency coefficient after short-time Fourier transform; G m (t,ω) is the maximum value of the time-frequency coefficient in the window; ω is the frequency, Δω is the window; ω Δ G after N iterations mThe corresponding estimated instantaneous frequency.

[0049] Finally, the recognition result of multiple synchronous extraction transformations with sliding windows can be obtained through synchronous extraction transformation.

[0050] Step 2: Calculate the total time-frequency energy. After the synchronous extraction transformation with a sliding window, the time-frequency coefficients of the signal can be obtained. In this step, the time-frequency energy at each moment is first calculated along the frequency direction. Since the present invention belongs to the underdetermined blind source separation method, the number of sensors less than the number of modes can be used for modal analysis. In addition, since the input signal is a multi-channel signal, each channel signal can obtain a time-frequency energy. On this basis, the time-frequency energies of all channel signals are superimposed to obtain the total time-frequency energy of the mixed signal.

[0051] Step 3: Lock the maximum time-frequency energy scatter point position. First, draw the time-frequency total energy graph with time as the x-axis and the time-frequency total energy as the y-axis. Then, use the peak picking method to obtain the frequency position corresponding to each peak in the time-frequency total energy graph.

[0052] Step 4: Estimate the source frequency band. Points with the same cosine distance from the position of each peak in the time-frequency total energy graph are the same source points. Therefore, the cosine distance can be used to estimate all energy points and their positions belonging to the same source, thereby estimating each source frequency band.

[0053] Step 5: Reconstruct the unimodal signal. Perform the inverse transform of the sliding window synchronous extraction transform as shown in equation (4) on each source frequency band estimated in step 4 to reconstruct each unimodal signal, that is, a signal containing only a single frequency component. The improved unimodal signal s(t) is expressed as

[0054]

[0055] Where s(t) is a single-mode signal; g is a window function; [ω0-Δ, ω0+Δ] is the range of the source frequency band; Te is the synchronous extraction transformation recognition result with a sliding window.

[0056] 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.

[0057] 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.

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of structural modal analysis methods based on improved blind source separation 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 structural modal analysis method based on improved blind source separation, characterized in that: Firstly, the sparse matrix and time-frequency coefficients of the response signal are obtained through multiple synchronous extraction transformation with sliding windows; then all time-frequency coefficients are summed along the time direction to obtain the total time-frequency energy; Then the peak picking method is used to lock the position of the maximum time-frequency energy scatter point; then the cosine distance is used to calculate the energy points with the same distance from each peak position, so as to estimate each source frequency band; Finally, a multiple synchronous extraction inverse transform with sliding window is performed on each source frequency band to reconstruct the single-modal signal.

2. The structural modal analysis method based on improved blind source separation according to claim 1, characterized in that: The method of obtaining the sparse matrix of the response signal through the multiple synchronous extraction transformation with a sliding window is specifically as follows: the sparse matrix of the response signal is obtained by performing the multiple synchronous extraction transformation with a sliding window on the structural response data; the multiple synchronous extraction transformation with a sliding window is as follows: first, the response signal is short-time Fourier transformed to obtain the time-frequency coefficients of the signal, and then, the partial derivatives with respect to time of the time-frequency coefficients are calculated to obtain the instantaneous frequency of the signal estimate; then, the estimated instantaneous frequency is iterated multiple times to improve the estimation accuracy; then, a sliding window is constructed and the maximum value of the time-frequency coefficients in the window is retained to further improve the sparsity of the time-frequency matrix; finally, the recognition result of the multiple synchronous extraction transformation with a sliding window is obtained through the synchronous extraction transformation.

3. The structural modal analysis method based on improved blind source separation according to claim 2 is characterized in that: The sliding window expression is: Where G(t,ω) is the time-frequency coefficient after short-time Fourier transform; G m (t,ω) is the maximum value of the time-frequency coefficient in the window; ω is the frequency, Δω is the window; ω Δ G after N iterations m The corresponding estimated instantaneous frequency; ω [N] (t,ω) is defined by the instantaneous frequency iteration operator shown below: In the formula, is the estimated instantaneous frequency; is the phase; N is the number of iterations.

4. The structural modal analysis method based on improved blind source separation according to claim 1, characterized in that: The method for calculating the total time-frequency energy is as follows: after synchronous extraction transformation with a sliding window, the time-frequency energy at each moment is calculated along the frequency direction; the time-frequency energies of all channel signals are superimposed to obtain the total time-frequency energy of the mixed signal.

5. The structural modal analysis method based on improved blind source separation according to claim 1, characterized in that: The method for locking the maximum time-frequency energy scatter point position by using the peak picking method is as follows: first, a time-frequency total energy diagram is drawn with time as the x-axis and the time-frequency total energy as the y-axis; then, the peak picking method is used to obtain the frequency position corresponding to each peak in the time-frequency total energy diagram.

6. The structural modal analysis method based on improved blind source separation according to claim 1, characterized in that: In the process of estimating the source frequency band: the points with the same cosine distance from the position of each peak in the time-frequency total energy diagram are regarded as the same source points, and the cosine distance is used to estimate all energy points and their positions belonging to the same source, thereby estimating each source frequency band.

7. The structural modal analysis method based on improved blind source separation according to claim 1 is characterized in that: The specific method for reconstructing the unimodal signal is: performing an inverse transformation of the synchronous extraction transformation with sliding window as shown in the following formula on each source frequency band estimated in the center, so as to reconstruct each unimodal signal; the expression of the unimodal signal s(t) is: Where s(t) is a single-mode signal; g is a window function; [ω0-Δ, ω0+Δ] is the range of the source frequency band; Te is the synchronous extraction transformation recognition result with a sliding window.

8. A structural modal analysis system based on improved blind source separation, characterized in that: include: A response signal sparse matrix extraction module is used to obtain the sparse matrix and time-frequency coefficients of the response signal through multiple synchronous extraction transformations with sliding windows; A time-frequency total energy calculation module, used for summing all time-frequency coefficients obtained by the response signal sparse matrix extraction module along the time direction to obtain the time-frequency total energy; A maximum time-frequency energy scatter point position extraction module is used to lock the maximum time-frequency energy scatter point position by using a peak picking method according to the calculation result of the time-frequency total energy calculation module; A source frequency band estimation module is used to calculate energy points with the same distance from each peak position based on the position of the maximum time-frequency energy scatter point using the cosine distance, thereby estimating each source frequency band; The single-mode signal reconstruction module is used to perform a multiple synchronous extraction inverse transformation with a sliding window on each source frequency band estimated by the source frequency band estimation module to reconstruct the single-mode signal.

9. 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 structural modal analysis method based on improved blind source separation as described in any one of claims 1 to 7 are implemented.

10. 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 structural modal analysis method based on improved blind source separation as described in any one of claims 1 to 7 are implemented.

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