JP7140426B2 - Time-varying structure instantaneous frequency determination method, system, device and storage medium - Google Patents

Description

TECHNICAL FIELD The present invention relates to the field of civil engineering structural damage detection technology, and more particularly to a time-varying structural instantaneous frequency determination method, system, device and storage medium.

Civil engineering structural damage detection and identification is one of the necessary means to ensure the normal operation of structures. It has been an important research direction in recent decades to perform damage identification on structures based on the required maintenance and care and on the basis of the measured vibration response (i.e. acceleration, displacement response, etc.). . However, during the actual operation of the structure, extreme impact loads occur due to changes in quality, stiffness, etc. due to material wear or strength deterioration. In the actual detection process, we often encounter structures with changed material attributes (stiffness, quality, etc.), and the vibration characteristics can be expressed according to the changes over time, that is, the time-varying structure, which means the nonlinearity and stiffness of the structure. Due to changes in marginal conditions, the signal is represented as unstable. How to identify the vibrational characteristics of a time-varying system from the measured astable vibration response signal is a problem that structural damage identification must solve. In related work, detection of structural damage can be done by processing the signal using the Hilbert-Huang transform (HHT) or empirical mode decomposition (EMD), but both such methods are susceptible to the mode folding phenomenon. and end effectors. The EEMD method proposed to solve the mode folding phenomenon suppresses the mode folding phenomenon, but the end effector problem still cannot be solved effectively.

The prior art discloses methods for time-varying structural instantaneous frequency identification using empirical wavelet transforms. On the other hand, however, when processing long-period signal components by empirical wavelet transform, the frequency accuracy is insufficient, and the signal distribution is relatively wide and ambiguous on the time spectrum. On the other hand, when processing signals with noise interference by empirical wavelet transform, frequency components appear in the signal spectrum that are not present in the original signal, causing "overdivision", i.e., too many filtering boundary decisions. , After the empirical wavelet transform, we can obtain the components that are not present in the original signal, and if the instantaneous frequency is taken as the index of damage identification, the simple empirical wavelet transform is greatly affected by noise. Therefore, in order to perform damage identification via instantaneous frequency, a relatively accurate time-frequency curve must first be fetched, and when the frequency accuracy is insufficient, a suitable filter can be constructed to separate the multi-component signals. and the structural damage detection results will be inaccurate.

Terminology Interpretation:
Empirical Wavelet Transform (EWT): A method of decomposing a signal into multiple components and performing lesion identification through identification of instantaneous frequencies.
Short Time Fourier Transform (STFT): A mathematical transformation related to the Fourier transform for determining the frequency and phase of a local area sinusoid of a time-varying signal.
Synchro Extracting Transform (SET): A time-frequency analysis method that improves on the short-time Fourier transform.
Time Spectrum: A two-dimensional function of time-frequency, a one-dimensional timing signal can be extended to a two-dimensional plane, and its time-varying characteristics are also clearly represented.

It is an object of the present invention to solve, at least to some extent, one of the technical problems existing in the prior art.

It is therefore an object of embodiments of the present invention to provide a time-varying structural instantaneous frequency determination method. This method uses a synchronous extraction transform to obtain a more accurate and more energy-intensive time spectrum, accurately obtains filtering boundaries based on this time spectrum, and further filters based on this filtering boundaries. Subsequent damage identification can be performed on the time-varying structure by performing an empirical wavelet transform on the structure to obtain the instantaneous frequency of each eigenmode component of the time-varying structure. Embodiments of the present invention improve the accuracy of time-varying structural instantaneous frequency identification and further improve the accuracy of time-varying structural damage identification over the prior art.

It is another object of embodiments of the present invention to provide a time-varying structural instantaneous frequency determination system.

In order to achieve the above technical objectives, the technical solutions used in the embodiments of the present invention are as follows.

According to a first aspect, embodiments of the present invention provide a time-varying structural instantaneous frequency determination method. This method
Performing a time-frequency analysis on a first scheduled signal of time-varying structure using a synchronous extraction transform to obtain a first time spectrum, and determining a first filtering boundary based on the first time spectrum. When,
performing a Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum; performing a division on the first signal spectrum based on the first filtering boundary to obtain a number of spectral pieces; to get and
performing an empirical wavelet transform on the first scheduled signal based on the spectral piece and the first filtering boundary to obtain a number of eigenmode components;
performing demodulation on the eigenmode components to determine a first instantaneous frequency of each eigenmode component.

Further, in one embodiment of the present invention, time-frequency analysis is performed on the first schedule signal having the time-varying structure using the above-described synchronous extraction transform to obtain a first time spectrum, Specifically, determining the first filtering boundary based on the time spectrum includes:
performing a short-time Fourier transform on the first schedule signal to obtain a second time spectrum;
estimating a second instantaneous frequency of the first schedule signal based on the second time spectrum;
combining the second instantaneous frequency with a delta function to construct a synchronous extraction operator SEO, and combining the synchronous extraction operator SEO with the second time spectrum to obtain the first time spectrum;
performing calculations based on frequency values of adjacent components in the first time spectrum to determine the first filtering boundary.

Furthermore, in one embodiment of the present invention, the first filtering boundary comprises:

Further, in one embodiment of the present invention, based on the spectral piece and the first filtering boundary, as described above, an empirical wavelet transform is performed on the first scheduled signal to remove some eigenmode components as Specifically, you get
constructing an empirical wavelet function and an empirical scaling function based on the spectral piece and the first filtering boundary;
determining detail coefficients and approximation coefficients based on the empirical wavelet function and the empirical scaling function;
on the first scheduled signal by performing an empirical wavelet transform on the first scheduled signal based on the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients; performing signal decomposition to obtain some eigenmode components.

Furthermore, in one embodiment of the present invention, the time-varying structural instantaneous frequency determination method comprises:
further comprising performing signal reconstruction on the first schedule signal based on the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients to obtain and output a reconstructed signal. .

Furthermore, in one embodiment of the present invention, performing demodulation on the eigenmode components and determining a first instantaneous frequency of each eigenmode component as described above specifically includes:
demodulating the eigenmode components using a Hilbert transform to obtain an instantaneous frequency function of each eigenmode component; and determining a first instantaneous frequency of each eigenmode component based on the instantaneous frequency function. It is to be.

Furthermore, in one embodiment of the present invention, the time-varying structural instantaneous frequency determination method comprises:
Further comprising determining a first time of occurrence of the first instantaneous frequency change based on the instantaneous frequency function, and outputting the first time as a structural damage time.

According to a second aspect, embodiments of the present invention provide a time-varying structural instantaneous frequency determination system. This system
to perform a time-frequency analysis on a first scheduled signal of time-varying structure using a synchronous extraction transform to obtain a first time spectrum, and to determine a first filtering boundary based on the first time spectrum; a filtering boundary determination module of
performing a Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum; performing a division on the first signal spectrum based on the first filtering boundary to obtain a number of spectral pieces; a spectral splitting module for obtaining
an eigenmode component determination module for performing an empirical wavelet transform on the first scheduled signal based on the spectral piece and the first filtering boundary to obtain a number of eigenmode components;
an instantaneous frequency determination module for performing demodulation on the eigenmode components and determining a first instantaneous frequency of each of the eigenmode components.

According to a third aspect, embodiments of the present invention provide a time-varying structural instantaneous frequency determination apparatus. This device
at least one processor;
at least one memory for storing at least one program;
When the at least one program is executed by the at least one processor, it causes the at least one processor to implement the time-varying structure instantaneous frequency determination method.

According to a fourth aspect, embodiments of the present invention further provide a computer-readable storage medium having a processor-executable program stored thereon. When the processor-executable program is executed by the processor, it implements the time-varying structure instantaneous frequency determination method.

Advantages and beneficial effects of the invention will be set forth in part in the description that follows, and in part will be apparent from the description, or may be learned by practice of the invention.

Embodiments of the present invention use a synchronous extraction transform to obtain a more accurate and more energy-intensive time spectrum, accurately obtain filtering boundaries based on the time spectrum, and based on the filtering boundaries, Subsequent damage identification can be performed on the time-varying structure by constructing a filter and performing an empirical wavelet transform to obtain the instantaneous frequency of each eigenmode component of the time-varying structure. Embodiments of the present invention acquire the time spectrum using a synchronous extraction transform to avoid noise interference, thereby providing more accurate filtering so that subsequent filtering of eigenmode components is more accurate and reliable. Boundary can be obtained, compared with the prior art, wide frequency band, high noise signal filtering, improve the positioning inaccuracy situation when determining the boundary, improve the identification accuracy of the time-varying structure instantaneous frequency, It also improves the accuracy of time-varying structural damage identification.

In order to describe the technical solutions in the embodiments of the present invention more clearly, the following introduces the accompanying drawings that should be used in the description of the embodiments of the present invention. It should be understood that the accompanying drawings in the following description are merely some embodiments of the technical solution of the present invention. , other accompanying drawings are also available.

4 is a step flow chart of a time-varying structural instantaneous frequency determination method according to an embodiment of the present invention; 4 is a detailed implementation flow chart of a time-varying structural instantaneous frequency determination method according to an embodiment of the present invention; 1 is a configuration block diagram of a time-varying structural instantaneous frequency determination system according to an embodiment of the present invention; FIG. 1 is a configuration block diagram of a time-varying structural instantaneous frequency determination device according to an embodiment of the present invention; FIG. FIG. 4 is a contrast diagram of a first time spectrum and a second time spectrum according to an embodiment of the present invention; FIG. 2B is a schematic diagram of the time-spectrum crest lines of the first time-spectrum according to an embodiment of the invention; FIG. 4 is a contrast diagram of a first signal spectrum and a reconstructed signal spectrum according to an embodiment of the present invention; Fig. 4 is a schematic diagram of spectral division of a first signal spectrum according to an embodiment of the present invention; FIG. 4 is a schematic diagram of three eigenmode components according to an embodiment of the invention; FIG. 4 is a schematic diagram of a filtered time spectrum of an initial signal according to an embodiment of the invention; FIG. 4 is a contrast diagram of a first signal spectrum and a filtered signal spectrum according to an embodiment of the present invention;

Hereinafter, embodiments of the present invention will be described in detail. Examples in said embodiments are shown in the drawings, where the same or similar reference numbers always denote the same or similar parts or parts with the same or similar functions. The embodiments described below with reference to the drawings are illustrative and are intended to interpret the invention and should not be construed as limiting the invention. In the following examples, the step numbers are merely for convenience of explanation, and the execution order between steps is not particularly limited. The execution order of each step in the embodiment may be adaptively adjusted based on the understanding of those skilled in the art.

In the description of the present invention, the plural means two or more, and the terms "first" and "second" are used to distinguish technical features and to indicate their relative importance. It should not be construed as indicating or suggesting, or specifying the number of technical features indicated, or the context of any technical feature indicated. Also, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art.

First, related descriptions in the embodiments of the present invention will be described.
a first schedule signal--the original schedule signal;
a first time spectrum--the time spectrum obtained by the original schedule signal via SET, abbreviated SET time spectrum;
the first filtering boundary—that is, the one calculated by the first time spectral component, the filtering boundary used for EWT;
a first signal spectrum--a spectrum obtained by subjecting the original signal to a Fourier transform;
first instantaneous frequency—refers to the instantaneous frequency obtained after the eigenmode components have been demodulated;
second time spectrum--the time spectrum obtained by subjecting the original schedule signal to a short-time Fourier transform;
second instantaneous frequency—refers to the original schedule signal instantaneous frequency estimated by the second time spectrum;
first time--the time of occurrence of the first instantaneous frequency change.

Referring to FIG. 1, an embodiment of the present invention provides a time-varying structural instantaneous frequency determination method. This method specifically includes the following steps S101 to S104.

S101, performing time-frequency analysis on the first scheduled signal with time-varying structure using synchronous extraction transform to obtain a first time spectrum, and determining a first filtering boundary based on the first time spectrum; ,
Specifically, embodiments of the present invention perform a time-frequency analysis on the initial signal (i.e., the first scheduled signal) using a synchronous extraction transform to extract only the time-frequency coefficients of the time spectrum at the instantaneous frequency locations. By extracting, a time spectrum can be extracted in which the energy is more concentrated. Processing the signal using a synchronous extraction transform first obtains the time spectrum of the signal by short-time Fourier transform, then uses information on this time spectrum to obtain the instantaneous frequency, and then combines with the Delta function. to construct a synchronous extraction operator, and finally an SEO operator is applied to the time spectrum obtained by the short-time Fourier transform to extract the signal time spectrum where the energy is more concentrated.

Specifically, step S101
S1011, performing a short-time Fourier transform on the first schedule signal to obtain a second time spectrum;
S1012, estimating and obtaining a second instantaneous frequency of the first schedule signal based on the second time spectrum;
S1013, combining the second instantaneous frequency with a delta function to construct a synchronous extraction operator SEO, combining the synchronous extraction operator SEO with a second time spectrum to obtain a first time spectrum;
S1014, performing calculations based on the frequency values of adjacent components in the first time spectrum to determine a first filtering boundary.

そのうち、ｉは虚数単位を表す。 Specifically, an embodiment of the present invention is described as follows, taking the schedule signal x(t) as an example.

Among them, i represents an imaginary unit.

Constructing a synchronous extraction operator SEO by combining the Delta functions to remove the divergent energy around the instantaneous frequency in the second time spectrum to obtain the first time spectrum after synchronous extraction transformation. A specific formula is as follows.

As can be seen, the first time spectrum obtained through the synchronous extraction transform is more accurate than the second time spectrum obtained through the short-time Fourier transform, and the signal The number of components can be made explicit and the filtering boundaries used for subsequent filtering can be accurately determined.

Further, as an alternative embodiment, the first filtering boundary is

S102, performing Fourier spectrum analysis on the first schedule signal to obtain a first signal spectrum, performing division on the first signal spectrum according to the first filtering boundary to obtain some spectral pieces; ,
Specifically, Fourier spectral analysis is performed on the initial first scheduled signal to obtain a first signal spectrum, which is then split on the original signal spectrum based on the filtering boundaries obtained in the previous step. and if there are N−1 first filtering boundaries, divide the first signal spectrum into N consecutive spectral pieces based on this filtering boundary and two initial boundaries 0, π. .

S103, performing an empirical wavelet transform on the first scheduled signal according to the spectral piece and the first filtering boundary to obtain some eigenmode components;
Specifically, embodiments of the present invention employ improved algorithms based on empirical wavelet transforms, and it should be understood that the basis functions used by conventional empirical wavelet transforms are , and the self-adaptive point can construct the filter after determining the filtering boundary based on the conventional frequency band division method, but when the narrowband signal and noise environment are relatively small, is only applicable. Embodiments of the present invention improve upon it, the filtering boundary is calculated by the signal time spectrum after the synchronous extraction transform, and then constructing the filter by the empirical wavelet transform to perform the filtering. Specifically, based on the determined filtering boundaries, an empirical scaling function and an empirical wavelet function can be constructed, and from these two functions approximate and detailed coefficients of the wavelet function can be obtained. On the one hand, the approximation coefficients and detail coefficients may be used to reconstruct the signal, and on the other hand to solve the eigenmode components of the first schedule signal.

Specifically, step S103
S1031, constructing an empirical wavelet function and an empirical scaling function based on the spectral piece and the first filtering boundary;
S1032, determining detailed coefficients and approximate coefficients based on the empirical wavelet function and the empirical scaling function;
S1033, performing signal decomposition on the first scheduled signal by performing an empirical wavelet transform on the first scheduled signal according to the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients; , obtaining some eigenmode components.

以下のとおりである：

Specifically, the empirical wavelet function

are as follows:

Based on the empirical wavelet transform theory, the detailed coefficients w _x (n, t) and approximate coefficients w _x (0, t) of the empirical wavelet transform are obtained by

理解できるように、ｋ＋１は、固有モード成分の数である。 Based on the empirical wavelet transform formula, the first schedule signal may be decomposed into several eigenmode components as follows:

As can be seen, k+1 is the number of eigenmode components.

Further, as an optional embodiment, the time-varying structural instantaneous frequency determination method comprises:
Further comprising performing signal reconstruction on the first schedule signal based on the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients to obtain and output a reconstructed signal.

そのうち、Ｎはスペクトル片の数を表し、Ｆ^-1は、フーリエ逆変換を行うことを表す。 Specifically, the reconstructed signal y(t) of the signal x(t) may be expressed as

Among them, N represents the number of spectral pieces, and F ⁻¹ represents performing inverse Fourier transform.

In an embodiment of the present invention, reconstruction is performed on the first scheduled signal using partial signal values via signal reconstruction to remove the effects of interference, and subsequent differential detection of structural damage. make it easier.

S104, demodulate the eigenmode components to determine the first instantaneous frequency of each eigenmode component.

Specifically, the obtained eigenmode components are all in the form of amplitude modulation-frequency modulation and need to be demodulated to obtain the instantaneous frequency function.

Optionally, demodulate the eigenmode components using a Hilbert transform to obtain an instantaneous frequency function of each eigenmode component, and determine a first instantaneous frequency of each eigenmode component based on the instantaneous frequency function. do.

Further, as an optional embodiment, the time-varying structural instantaneous frequency determination method comprises:
Further comprising determining a first time of occurrence of the first instantaneous frequency change based on the instantaneous frequency function and outputting the first time as the structural damage time.

Specifically, based on the instantaneous frequency function of the eigenmode component obtained above, the time of occurrence of time-varying structural instantaneous frequency change, that is, the time of occurrence of structural damage, can be rudimentarily observed. Methods such as the Hilbert transform can be combined to build a damage index and further determine the damage location and damage extent of the structure.

The method steps of the present invention have been described above, and the implementation flow of one specific embodiment of the present invention will now be described in conjunction with the drawings.

Referring to FIG. 2, the embodiment of the present invention first performs time-frequency analysis on the first schedule signal using synchronous extraction transform to obtain a first time spectrum with more concentrated energy. determines the number of signal components and also determines the first filtering boundary. Simultaneously, performing Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum, performing division on the first signal spectrum based on the determined first filtering boundary to obtain some spectra obtaining a piece, then constructing an empirical scaling function, an empirical wavelet function, determining detail coefficients and approximation coefficients, based on the obtained spectral piece and the first filtering boundary, then the empirical scaling function, Based on the empirical wavelet function, the detail coefficients and the approximation coefficients, perform signal decomposition on the first schedule signal to obtain some eigenmode components, at the same time perform signal reconstruction to obtain the reconstructed signal, and output You can also Furthermore, by performing a Hilbert transform on the obtained eigenmode components and obtaining an instantaneous frequency function of each eigenmode component, the instantaneous frequency of each eigenmode component at each time is determined, that is, the time-varying structural instantaneous frequency complete the determination of

It should be appreciated that the prior art extracts each mode directly from the vibration response signal by the empirical wavelet transform (EWT), but the filtering bounds used when constructing the filter by the empirical wavelet transform are the usual It was obtained based directly on the Fourier spectrum. Embodiments of the present invention obtain a time spectrum with better accuracy and more concentrated energy, based on this time spectrum, the filtering boundary used in the structure of the filter can be clearly obtained, wide frequency band, It improves the situation of positioning inaccuracy, improves the accuracy of identifying time-varying structure instantaneous frequencies, and improves the accuracy of time-varying structure damage identification when determining high noise signal filtering boundaries.

Hereinafter, the method of the present invention will be described and verified for reliability by connecting specific examples. It should be understood that the invention is not limited to this example.

1) A primitive signal containing three frequency components was constructed and Gaussian white noise was added, SNR=10 dB, three frequency components were 5 Hz, 25 Hz and 40 Hz.

2) A synchronous extraction transform was performed on this original signal to obtain a first time spectrum after synchronous extraction conversion. FIG. 5(a) shows the second time spectrum obtained after the short-time Fourier transform, and (b) shows the first time spectrum obtained after the synchronous extraction transform. The time spectrum energy after synchronous extraction transformation becomes more concentrated, the time spectrum crest line is clear, but the second time spectrum suggests obvious frequency components, but its energy spread is serious, It was found to be unfavorable for further signal analysis.

3) Extract crest lines for the first time spectrum, as shown in FIG. 6, which is a schematic diagram of the time spectrum crest lines of the first time spectrum, the signal has three time spectrum crest lines , that is, it is clearly seen that there are three main frequency components. Based on the three time-spectral crest lines, the formula allowed us to determine two first filtering boundaries, which were 15.1875 Hz and 32.7500 Hz, respectively.

4) perform Fourier spectrum analysis on the original signal, the resulting first signal spectrum is shown in FIG. 7(a); A segmentation was performed on the signal spectrum to divide the first signal spectrum into three segments by a total of four boundaries, adding initial boundaries 0 and π, as shown in FIG.

5) A filter family was constructed via an empirical wavelet transform using the first filtering boundary to classify the original signal into three eigenmode components, as shown in FIG. At the same time, signal reconstruction is performed to obtain a reconstructed signal spectrum of the original signal. As shown in FIG. It has been found that the interference frequencies are significantly reduced compared to the first signal spectrum obtained, ie there is a "noise reduction" effect after the signal is synchronously extracted transformed.

6) The Hilbert transform was performed on each of the three eigenmode components, the instantaneous frequency of each eigenmode component was obtained, and a filtered time spectrum as shown in FIG. 10 was obtained. Three frequency components were clearly visible, and the filtered time spectrum was clearer and more accurate than the second time spectrum and the first time spectrum. The three components varied slightly around 5 Hz, 25 Hz and 40 Hz, respectively.

7) As shown in FIG. 11, comparing the first signal spectrum with the spectrum of the three component signals extracted by the improved EWT method of the present invention, the improvement of the present invention, even under the influence of noise. It was found that the proposed EWT method has a good signal resolution effect.

8) From the three eigenmode components extracted by the above method, it is possible to rudimentarily observe that the time of occurrence of instantaneous structural frequency change is the time of occurrence of structural damage. can be combined to construct a damage index, which can further determine the damage location and damage extent of the structure.

As can be seen from the above description, by adopting the method of the embodiment of the present invention, the frequency components of the original signal can be accurately determined, the noise interference is avoided, the robustness is good, and the component filtering is good. Accurate and advantageous for subsequent damage identification.

Referring to FIG. 3, an embodiment of the present invention provides a time-varying structural instantaneous frequency determination system. This system
performing a time-frequency analysis on the first scheduled signal of time-varying structure using a synchronous extraction transform to obtain a first time spectrum; and determining a first filtering boundary based on the first time spectrum. a filtering boundary determination module;
performing a Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum, performing a division on the first signal spectrum based on a first filtering boundary to obtain a number of spectral pieces; a spectral splitting module;
an eigenmode component determination module for performing an empirical wavelet transform on the first scheduled signal based on the spectral piece and the first filtering boundary to obtain a number of eigenmode components;
an instantaneous frequency determination module for performing demodulation on the eigenmode components and determining a first instantaneous frequency of each eigenmode component.

The contents in the above method embodiments are all applicable to the system embodiments, the functions specifically implemented by the system embodiments are the same as the above method embodiments, and the beneficial effects achieved are also the same as the above method embodiments. The same beneficial effect achieved by the method embodiment.

Referring to FIG. 4, an embodiment of the present invention provides a time-varying structural instantaneous frequency determination device. This device
at least one processor;
at least one memory for storing at least one program;
When the at least one program is executed by the at least one processor, it causes the at least one processor to implement the time-varying structural instantaneous frequency determination method.

The contents in the above method embodiments are all applicable to the present apparatus embodiments, the functions specifically implemented by the present apparatus embodiments are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as the above method embodiments. The same beneficial effect achieved by the method embodiment.

Embodiments of the invention further provide a computer-readable storage medium on which a processor-executable program is stored. When this processor-executable program is executed by the processor, it implements the time-varying structure instantaneous frequency determination method.

The computer-readable storage medium of the embodiments of the present invention is capable of executing the time-varying structural instantaneous frequency determination method according to the method embodiments of the present invention, and is capable of executing any combination of implementation steps of the method embodiments; It has functions and beneficial effects corresponding to the method.

Embodiments of the present invention further disclose a computer program product or computer program. The computer program product or computer program comprises computer instructions stored on a computer readable storage medium. A processor of a computer device may read computer instructions from a computer-readable storage medium. The processor executes the computer instructions, thereby causing the computer equipment to perform the method shown in FIG.

In some alternative implementations, the functions/acts noted in the block diagrams need not occur in the order noted in the operational illustrations. For example, two blocks shown in succession may actually be executed more or less concurrently, or the blocks may be executed in the reverse order, depending on the functionality/acts involved. Also, the embodiments disclosed and described in the flow charts of the present invention are provided in an example manner for the purpose of a more thorough understanding of the technology. The methods disclosed herein are not limited to the acts and logic flows disclosed herein. Alternative embodiments are envisioned in which various operations are reordered and sub-operations described as part of a larger operation are independently performed.

Also, while the invention has been described in the context of functional modules, it should be understood that, unless indicated to the contrary, one or more of the above functions and/or features may be implemented in a single physical device and/or It may be integrated into software modules, or one or more functions and/or features may be implemented in a single physical device or software module. Moreover, it should be understood that a detailed discussion of the actual implementation of each module is not necessary for understanding the invention. Rather, given the attributes, functions and interrelationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the modules will be understood within the prior art of engineers. Thus, those skilled in the art will be able to implement the claimed invention using common techniques and without the need for undue experimentation. Further, it should be understood that the specific concepts disclosed are exemplary only and are not intended to limit the scope of the invention. The scope of the invention is determined by the appended claims and their full scope of equivalents.

The functions described above may be implemented in the form of software functional units and stored on a single computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention may be realized in the form of a software product in substance, or a part that contributes to the prior art, or a part of this technical solution. This computer software product is stored in one storage medium, and all or part of the method described in each embodiment of the present invention can be implemented in one computer device (which may be a personal computer, a server, or a network device). contains some instructions to cause the steps of The above storage media include media capable of storing various program codes such as U disk, removable hard disk, read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk. include.

The logic and/or steps represented in a flow chart or otherwise described herein may be considered, for example, an ordered list of executable instructions for implementing the logic function, and may be considered an instruction execution system. , any computer-readable medium for use in a device or apparatus (e.g., a computer-based system, a system comprising a processor or an instruction execution system, or other system capable of obtaining and executing instructions from the apparatus or apparatus) or may be used in combination with these instruction execution systems, devices or devices. As used herein, a "computer-readable medium" stores, stores, communicates, transmits, or transmits a program for use in combination with an instruction execution system, device, or device, or with these instruction execution systems, devices, or devices. It may be any device capable of

More specific examples (non-exhaustive list) of computer-readable media include the following. Electrical connections with one or more wires (electronic equipment), portable computer disk boxes (magnetic equipment), random access memory (RAM), read-only memory (ROM), erasable editable read-only memory (EPROM or flash) memory), fiber optic devices, and portable read-only memory (CDROM). A computer readable medium also means that a program is obtained electronically, for example, by optically scanning paper or other suitable medium and then compiling, interpreting, or processing in other suitable manner as desired. It may also be paper or other suitable medium on which the program can be printed, as it can then be stored in computer memory.

It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or any combination thereof. In the above embodiments, steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, when implemented in hardware, discrete logic circuitry with logic gate circuitry for implementing logic functions on data signals, specific logic circuitry with suitable combinatorial logic gate circuitry, as well as other embodiments. It can be implemented in any one or combination of technologies well known in the art such as application-specific integrated circuits, programmable gate arrays (PGA), field programmable gate arrays (FPGA).

In the above description of this specification, descriptions that refer to terms such as “one embodiment/example,” “another embodiment/example,” or “any of the embodiments/examples” refer to this embodiment or example. is meant to be included in at least one embodiment or example of the invention. As used herein, the exemplary expressions of the terms do not necessarily refer to the same embodiment or example. Moreover, the particular features, structures, materials or characteristics described may be combined in any suitable combination in any one or more embodiments or examples.

Although embodiments of the present invention have been illustrated and described, it will be appreciated by those skilled in the art that various changes, modifications, and alterations may be made to these embodiments without departing from the principles and spirit of the invention. Substitutions and modifications may be made, and the scope of the invention is defined by the claims and their equivalents.

Although the preferred embodiments of the present invention have been specifically described above, the present invention is not limited to the above embodiments. or substitutions may be made, all of which are within the scope of the claims of this application.

Claims (9)

A time-varying structural instantaneous frequency determination method comprising:
Performing a time-frequency analysis on a first scheduled signal of time-varying structure using a synchronous extraction transform to obtain a first time spectrum, and determining a first filtering boundary based on the first time spectrum. When,
performing Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum; performing division on the first signal spectrum based on the first filtering boundary to obtain a plurality of spectral pieces; to get and
performing an empirical wavelet transform on the first scheduled signal based on the spectral piece and the first filtering boundary to obtain a plurality of eigenmode components;
performing demodulation on the eigenmode components to determine a first instantaneous frequency of each eigenmode component ;
Performing a time-frequency analysis on the first scheduled signal with time-varying structure using the synchronous extraction transform described above to obtain a first time spectrum, and determining a first filtering boundary based on the first time spectrum. to decide
performing a short-time Fourier transform on the first schedule signal to obtain a second time spectrum;
estimating a second instantaneous frequency of the first schedule signal based on the second time spectrum;
combining the second instantaneous frequency with a delta function to construct a synchronous extraction operator SEO, and combining the synchronous extraction operator SEO with the second time spectrum to obtain the first time spectrum;
performing calculations based on frequency values of adjacent components in the first time spectrum to determine the first filtering boundary to avoid noise interference and to narrow the first filtering boundary. A time-varying structure instantaneous frequency determination method characterized in that it can be obtained accurately . The first filtering boundary is

and
Among them

represents the maximum value of the frequency of the nth component in the first time spectrum, and

2. The time-varying structure instantaneous frequency determination method according to claim 1 , wherein is the minimum value of the frequency of the n+1th component in the first time spectrum, and ω _n is the first filtering boundary. Specifically, performing an empirical wavelet transform on the first scheduled signal to obtain a plurality of eigenmode components based on the spectral piece and the first filtering boundary, as described above, specifically includes:
constructing an empirical wavelet function and an empirical scaling function based on the spectral piece and the first filtering boundary;
determining detail coefficients and approximation coefficients based on the empirical wavelet function and the empirical scaling function;
on the first scheduled signal by performing an empirical wavelet transform on the first scheduled signal based on the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients; performing signal decomposition to obtain a plurality of eigenmode components. The time-varying structure instantaneous frequency determination method includes:
further comprising performing signal reconstruction on the first schedule signal based on the empirical wavelet function, the empirical scaling function, the detail coefficients and the approximation coefficients to obtain and output a reconstructed signal. 4. The time-varying structural instantaneous frequency determination method according to claim 3 , characterized by: Specifically, performing demodulation on the eigenmode components and determining the first instantaneous frequency of each eigenmode component as described above includes:
demodulating the eigenmode components using a Hilbert transform to obtain an instantaneous frequency function of each eigenmode component; and determining a first instantaneous frequency of each eigenmode component based on the instantaneous frequency function. The time-varying structure instantaneous frequency determination method according to any one of claims 1 to 4 , characterized in that: The time-varying structure instantaneous frequency determination method includes:
6. Further comprising determining a first time of occurrence of said first instantaneous frequency change based on said instantaneous frequency function, and outputting said first time as a structural damage time. The time-varying structural instantaneous frequency determination method according to . A time-varying structural instantaneous frequency determination system comprising:
to perform a time-frequency analysis on a first scheduled signal of time-varying structure using a synchronous extraction transform to obtain a first time spectrum, and to determine a first filtering boundary based on the first time spectrum; a filtering boundary determination module of
performing Fourier spectral analysis on the first scheduled signal to obtain a first signal spectrum; performing division on the first signal spectrum based on the first filtering boundary to obtain a plurality of spectral pieces; a spectral splitting module for obtaining
an eigenmode component determination module for performing an empirical wavelet transform on the first scheduled signal based on the spectral piece and the first filtering boundary to obtain a plurality of eigenmode components;
an instantaneous frequency determination module for performing demodulation on the eigenmode components to determine a first instantaneous frequency of each of the eigenmode components;
The filtering boundary determination module comprises:
performing a short-time Fourier transform on the first schedule signal to obtain a second time spectrum;
estimating a second instantaneous frequency of the first schedule signal based on the second time spectrum;
combining the second instantaneous frequency with a delta function to construct a synchronous extraction operator SEO; combining the synchronous extraction operator SEO with the second time spectrum to obtain the first time spectrum;
calculating based on the frequency values of adjacent components in the first time spectrum to determine the first filtering boundary to avoid noise interference and obtain the first filtering boundary more accurately; A time-varying structural instantaneous frequency determination system characterized by: A time-varying structure instantaneous frequency determination device, comprising:
at least one processor;
at least one memory for storing at least one program;
The at least one program, when executed by the at least one processor, causes the at least one processor to implement the time-varying structure instantaneous frequency determination method according to any one of claims 1 to 6 . and the time-varying structure instantaneous frequency determination device. A computer-readable storage medium storing a processor-executable program, the time-varying structural instantaneous frequency determination according to any one of claims 1 to 6 , when said processor-executable program is executed by a processor. A computer-readable storage medium embodying a method.

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