A multi-component signal time-frequency filtering decomposition method, electronic device and medium
Patent Information
- Application Number
- CN202410166151.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-02-04
- Publication Date
- 2026-10-23
- Estimated Expiration
- 2044-02-04
AI Technical Summary
[0004]为了解决目前对多分量非平稳信号的分解提取存在难以准确提取、计算量大以及分解时间长的技术问题，本发明提供一种分解效果好且分解效率高的多分量信号时频滤波分解方法、电子设备及介质
[0032] The technical advantage of this invention lies in the fact that, based on the fact that each component in a signal has its own specific filtering coefficient, it performs time-frequency domain filtering on the time spectrum of the original signal, thereby achieving accurate separation of various types of components in the original signal, such as adjacent, overlapping, or intermittent components, while also enabling noise reduction and reconstruction. Furthermore, this invention does not require iteration or solving complex optimization problems during the extraction process, thus exhibiting high computational efficiency.
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Figure CN118171039B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing, and in particular to a method for time-frequency filtering and decomposition of multi-component signals, an electronic device, and a medium. Background Technology
[0002] Various signals in nature and engineering, such as biological speech, mechanical vibrations, and radar signals, are typically multi-component, non-stationary, and nonlinear signals. To extract the information contained in such signals, the individual components must first be separated from the original signal. However, these signals generally have complex time-frequency characteristics and low signal-to-noise ratios, making it very difficult to achieve fast and accurate component separation.
[0003] Currently, proposed multi-component non-stationary signal decomposition methods generally rely on the signal's own time-scale characteristics, frequency distribution characteristics, or local time-frequency characteristics. Widely used methods such as empirical mode decomposition, local mean decomposition, and intrinsic time-scale decomposition use the signal's own time-scale characteristics as the basis for decomposition, dividing the signal into a series of single-component components with increasing time scales. Frequency domain decomposition techniques, represented by empirical wavelet transform and variational mode decomposition, construct different types of frequency band filters or filter banks to perform frequency domain filtering based on the signal's frequency domain characteristics, thereby achieving signal decomposition. Theoretically, the non-stationarity and nonlinearity of a signal are reflected in the fact that the instantaneous frequency and amplitude of its components change simultaneously with time and frequency. Furthermore, the instantaneous characteristics may exhibit complex changes such as drastic fluctuations, large frequency spans, and abrupt changes. Therefore, the aforementioned signal decomposition methods based solely on time-scale or frequency characteristics, because they separately consider the signal's time-scale or frequency distribution characteristics, often fail to decompose the signal or mechanically divide the same component into multiple parts, leading to decomposition errors. Decomposition methods based on the joint time-frequency characteristics of signals separate components by calculating time-frequency ridges, vector weighting coefficients, instantaneous frequencies, and other time-frequency features of each component in the signal's time-frequency distribution. These methods, considering both the time and frequency characteristics of the signal, are increasingly used in the decomposition of multi-component non-stationary signals. However, for some signals in nature and practical engineering, the time-frequency characteristics of their components are highly complex due to various interferences such as operating conditions, environment, and shocks. These components may exhibit cross-band, adjacent or even overlapping time-frequency characteristics, and intermittent features, leading to similar or even identical time-frequency characteristics among the components. Furthermore, a large amount of noise may mask some of these characteristics, making it difficult for decomposition methods based solely on differences in signal time-frequency characteristics to decompose components with such complex time-frequency features. In addition, current methods often involve feature matching iterative sieving, solving complex optimization problems, or requiring data from multiple channels simultaneously, resulting in high computational complexity and long decomposition times. Summary of the Invention
[0004] To address the current technical problems of inaccurate extraction, high computational load, and long decomposition time in the decomposition and extraction of multi-component non-stationary signals, this invention provides a multi-component signal time-frequency filtering decomposition method, electronic device, and medium with good decomposition effect and high decomposition efficiency.
[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:
[0006] A time-frequency filtering decomposition method for multi-component signals includes the following steps:
[0007] Step 1: Treat the components in the signal from which the information to be extracted as a set of data points on the time-frequency surface, and select multiple reference data points that can reflect the time-frequency distribution pattern of the corresponding components.
[0008] Step 2: Fit the time-frequency coordinates of all reference data points using a polynomial to obtain multiple sets of fitted IF curves that are consistent with the instantaneous frequency of the corresponding component's actual component, i.e., the IF pattern.
[0009] Step 3: Use the time-frequency coordinates of the fitted IF curve as the center frequency coefficients of the time-frequency filter to obtain a group of center frequency coefficients for a time-frequency filter bank; then use the ratio of the vertical axis distance to the component half-bandwidth distance as the corresponding time-frequency coordinate domain threshold condition, and then determine the time-frequency distribution region of the component signal corresponding to the corresponding IF law according to the threshold condition, and retain all time-frequency data points in the time-frequency distribution region to obtain the passband coefficients of the corresponding time-frequency filter.
[0010] Step 4: Based on the time-frequency filter that has obtained the center frequency coefficient and passband coefficient, the signal for which the information to be extracted is filtered in the time-frequency domain. Finally, the filtered time-frequency domain data is subjected to inverse short-time Fourier transform to obtain the corresponding components in the output signal.
[0011] The method, wherein step 1 includes:
[0012] Based on the differences in noise among the signal components on the time-frequency graph, the distribution pattern of the signal components for which the information to be extracted is obtained on the time-frequency graph, and multiple reference data points P that can reflect the distribution pattern are selected. i Where i = 0, 1, ..., m, m is the total number of reference data points, and the coordinates of each reference data point on the time-frequency surface are (x... i ,y i ), where x i The time coordinate value is y. i These are frequency coordinate values.
[0013] In the method described above, step 2, the IF curve is obtained through the following steps:
[0014] Based on a polynomial p(x) of order n:
[0015]
[0016] Where a is the coefficient of the polynomial, j is the order variable, and the value of j ranges from 0 to n;
[0017] p(x) at the reference data point P i The residual at point is e i , where e i =p(x i )-y i ;
[0018] Then, let the vector E = [e0, e1, ..., e m And the square of the L2 norm of E is:
[0019]
[0020] If Q is the L2 norm loss, then when Q reaches its minimum value, the corresponding coefficient a... j To achieve the best agreement between the polynomial curve p(x) and the components represented by the reference data points under the least squares approximation definition, i.e., to solve for the coefficient a... j The system of linear equations:
[0021]
[0022] In the above formula, x0 ≠ x1 ≠ … ≠ x m Solving for a j The unique solution is obtained, thus yielding the expression for p(x), and the fitted IF curve is obtained based on p(x).
[0023] In the method described above, step 3, the time-frequency coordinate domain threshold condition is obtained through the following steps:
[0024] Let the projected coordinates of any point on the three-dimensional time-frequency plot on the two-dimensional time-frequency surface be (x1, y1), and the coordinates of the corresponding point on the fitted IF curve be (x1, p(x1)). Then the ordinate distance d between the two points is:
[0025] d = |y1 - p(x1)|
[0026] The half-bandwidth distance D is determined based on the distribution of the instantaneous amplitude of the component to be decomposed on the time-frequency graph. The threshold condition for the time-frequency coordinate domain is d / D. When d / D≤1, the coordinates and corresponding instantaneous amplitude of the reference data point are retained; otherwise, they are not retained. The half-bandwidth is determined based on the main bandwidth of the component and can be achieved using the Carson criterion.
[0027] An electronic device, comprising:
[0028] One or more processors;
[0029] Storage device for storing one or more programs.
[0030] When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method.
[0031] A computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method.
[0032] The technical advantage of this invention lies in the fact that, based on the fact that each component in a signal has its own specific filtering coefficient, it performs time-frequency domain filtering on the time spectrum of the original signal, thereby achieving accurate separation of various types of components in the original signal, such as adjacent, overlapping, or intermittent components, while also enabling noise reduction and reconstruction. Furthermore, this invention does not require iteration or solving complex optimization problems during the extraction process, thus exhibiting high computational efficiency. Attached Figure Description
[0033] Figure 1 The diagram shows the simulated signal x1(t) of Embodiment 1 of the present invention, where a is the time-domain waveform and b is the STFT time-frequency waveform.
[0034] Figure 2 This is a schematic diagram of obtaining the IF fitting curve in Embodiment 1 of the present invention, where a is a schematic diagram of the selection of reference data points and b is the fitted IF curve.
[0035] Figure 3 The diagram shows the component region determination and filtering results of Embodiment 1 of the present invention, where a is a schematic diagram of component region determination and b is a filtering result diagram.
[0036] Figure 4 This is the time-domain reconstructed signal of Embodiment 1 of the present invention, where a is the frequency modulation component diagram and b is the amplitude modulation and frequency modulation component diagram.
[0037] Figure 5 The image shows the vibration signal diagram of an industrial gearbox in Embodiment 2 of the present invention, where a is a time-domain waveform diagram and b is an STFT time-frequency diagram.
[0038] Figure 6 The diagram shows the component decomposition results of the gearbox vibration signal in Embodiment 2 of the present invention, where a is component C1, b is component C2, c is component C3, d is component C4, e is component C5, f is component C6, and g is component C7.
[0039] Figure 7 This is a reconstruction of the gearbox vibration signal diagram in Embodiment 2 of the present invention, where a is a time-domain waveform diagram and b is an STFT time-frequency diagram. Detailed Implementation
[0040] This invention is based on the estimation of the IF curves of each component of the signal and the determination of the component regions. This is equivalent to constructing a time-frequency filter bank with the time-frequency coordinates of the estimated IF curve as the center frequency and the region width as the passband width. Therefore, the time-frequency filtering decomposition method based on the time-frequency distribution of the signal proposed in this invention is realized. The method of this invention will be referred to as TFFD.
[0041] In TFFD, the time-frequency filter is actually a frequency bandpass filter at every moment. This frequency bandpass filter can be of the specific type: Infinite Impulse Response (IIR), Finite Impulse Response (FIR), or other classical filters. Alternatively, it can be a formal or generalized form of time-frequency filtering by directly retaining time-frequency domain data that meets the requirements of the time-varying center frequency and passband width parameters. To avoid the influence of too many design parameters on the filtering effect, as well as tedious calculations and excessive computational load, this invention adopts the latter generalized form of time-frequency filtering.
[0042] Example 1
[0043] The steps of this embodiment will be explained by analyzing the noisy simulation signal x1(t) shown in the following formula. x1(t) consists of an amplitude-modulated frequency-modulated component and a line-modulated frequency-modulated component, and n(t) is superimposed Gaussian white noise with a standard deviation of 1.0. The sampling frequency f of x1(t) is... s The frequency is 1000Hz, the sampling time is 7s, and its time-domain waveform is as follows: Figure 1 As shown in a.
[0044] x1(t)=[1+cos(19πt)]sin(100t 2 +150πt)+sin(50πt 2 +300πt)+n(t)
[0045] Where t∈[0:1 / f s :7]
[0046] S1: Establish a three-dimensional time-frequency graph
[0047] TFFD is based on the time-frequency domain data points of a signal. Due to the classic nature of the Short Time Fourier Transform (STFT) and the absence of cross-interference terms, its calculation is simple. Therefore, this embodiment uses STFT to establish the time-frequency diagram of the signal. The STFT time-frequency distribution of x1(t) is as follows: Figure 1 As shown in b, it can be seen that the two components have a large span in the time-frequency domain.
[0048] S2: Obtain the equation of the IF fitting curve.
[0049] Taking the linear frequency modulated component as an example, based on the time-frequency distribution characteristics of the linear frequency modulated component, three reference data points are selected in the time-frequency graph of x1(t), with time-frequency coordinates of P0(0.38, 166.016), P1(3.42, 320.312), and P2(6.06, 451.172), respectively. Figure 2 As shown in Figure a, a polynomial fitting is performed on the reference data points. Since the IF of the linear frequency modulation component changes linearly, the fitting order n is set to 1. The resulting fitted IF curve is shown in Figure a. Figure 2 As shown by the dashed line in b. By comparison... Figure 2 a and Figure 2 As can be seen from b, the fitted IF curve accurately reflects the actual IF law of the component to be determined.
[0050] S3: Determine the boundary of the component region
[0051] Based on the time-frequency coordinates of the fitted IF curve and the proposed threshold conditions, the boundary of the region containing the line-modulated frequency component is determined. Figure 1 b indicates that the main linear frequency modulation component is distributed within a 30Hz frequency band. Therefore, a half-bandwidth distance D = 15Hz is set, and the region determined according to the threshold condition is as follows: Figure 3 The region within the red line in region a. This yields a time-frequency filter with a center frequency equal to the time-frequency coordinate of the fitted IF curve and a passband width of 2D. Figure 3 b is the STFT time-frequency diagram of the filtered component.
[0052] By processing the amplitude-modulated and frequency-modulated components in x1(t) in the same way, a set of time-frequency filter coefficients can also be obtained, thus yielding a time-frequency filter bank for the simulated signal x1(t).
[0053] S4: Reconstruct component signals
[0054] By performing an inverse short-time Fourier transform (ISTFT) on the time-frequency domain data of each filtered component, the time-domain signal of the corresponding component can be obtained. The ISTFT time-domain reconstructed signals of the two components decomposed from the x1(t) filter are as follows: Figure 4 As shown, it can be seen that it accurately corresponds to the two components of x1(t), and the modulation characteristics are consistent with the original signal, except that the noise has a slight effect on the instantaneous amplitude.
[0055] To quantitatively evaluate the algorithm's performance and analyze its robustness to noise, three information entropies—singular spectral entropy, fuzzy entropy, and envelope entropy—were used as quantitative indicators. The information entropy values of x1(t) were calculated for the TFFD decomposition results under Gaussian white noise with standard deviations of 0.5, 1.0, 1.5, and 2.0, as well as under noise-free conditions. The results are shown in Table 1. Table 1 shows that under different noise standard deviations, i.e., different noise intensities, the three entropy values of the decomposition results are very close to those under noise-free conditions (standard deviation of 0), with the maximum difference not exceeding 8.8%, indicating that the algorithm's decomposition and denoising effects are good. Furthermore, it can be seen that the three information entropy values are very stable under different noise intensities, demonstrating the algorithm's good noise robustness.
[0056] Table 1 Information entropy of TFFD decomposition results under different noise intensities
[0057]
[0058] Example 2
[0059] Numerous multi-component nonstationary nonlinear signals exist in nature and engineering practice, exhibiting complex time-frequency characteristics and severe noise interference. This embodiment describes the extraction of component parts from gearbox vibration signals in engineering applications.
[0060] Gearbox vibration signals are typical multi-component non-stationary signals. Due to the complex structure and operating conditions of the gearbox, the numerous and interconnected moving parts, and the interference from impact and noise, the components not only possess complex time-frequency instantaneous characteristics but also contain rich state information such as gearbox structure, operation, and operating conditions. To extract this state characteristic information, it is necessary to decompose each component from the original vibration signal. Figure 5 The data is a set of measured vibration acceleration signals of an industrial gearbox. It can be seen that the signal contains multiple components, each of which has complex time-frequency characteristics such as being adjacent, overlapping, and having a large time-frequency domain span, and has a low signal-to-noise ratio.
[0061] The vibration acceleration signal of the gearbox was decomposed using this method. The signal sampling frequency was 4096 Hz, and the sampling time was 11.375 s. The main components were labeled C1-C7. Since the gearbox was under uniform acceleration starting condition when the vibration signal was measured, the components mainly consist of the meshing vibration components of each gear stage, which vary linearly with the rotational frequency, as well as the inherent vibration components of the structural components at a constant frequency and the AC interference components. That is, each component IF exhibits linear characteristics. Therefore, during the decomposition process, the fitting order of each component was set to 1. Figure 5In the time-frequency graph of b, the unaffected portions of each component show that their bandwidths are basically consistent. Therefore, to improve decomposition efficiency, a uniform half-bandwidth distance D = 45Hz is determined. The time-frequency filter designed based on this parameter yields the following time-frequency filtering decomposition result: Figure 6 As shown, each component is completely decomposed, and its instantaneous features are clearly displayed. Further superposition and reconstruction of the extracted components yields the following results: Figure 7 As shown, comparison Figure 7 and Figure 5 It can be seen that the reconstructed signal not only retains the characteristics of the original gearbox vibration signal, but also improves the signal-to-noise ratio.
[0062] According to embodiments of the present invention, the present invention also provides an electronic device and a computer-readable medium.
[0063] Electronic devices include:
[0064] One or more processors;
[0065] Storage device for storing one or more programs.
[0066] When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned multi-component signal time-frequency filtering decomposition method.
[0067] In practical use, users can interact with servers, which are also electronic devices, via a network to receive or send messages. Terminal devices are generally various electronic devices equipped with a display and used through a human-computer interface, including but not limited to smartphones, tablets, laptops, and desktop computers. Various specific application software can be installed on these terminal devices as needed, including but not limited to web browsers, instant messaging software, social media platforms, and shopping apps.
[0068] A server is a network service provider that offers various services, such as a backend server that provides corresponding computing services for signal data received from terminal devices. This includes extracting components from the received signal data and returning the extraction results to the terminal device.
[0069] Similarly, the computer-readable medium of the present invention stores a computer program thereon, which, when executed by a processor, implements the multi-component signal time-frequency filtering decomposition method of the embodiments of the present invention.
Claims
1. A time-frequency filtering decomposition method for multi-component signals, characterized in that, Includes the following steps: Step 1: Treat the components in the signal from which the information to be extracted as a set of data points on the time-frequency surface, and select multiple reference data points that can reflect the time-frequency distribution pattern of the corresponding components. Step 2: Fit the time-frequency coordinates of all reference data points using a polynomial to obtain multiple sets of fitted IF curves that are consistent with the instantaneous frequency of the corresponding component's actual component, i.e., the IF pattern. Step 3: Use the time-frequency coordinates of the fitted IF curve as the center frequency coefficients of the time-frequency filter to obtain a group of center frequency coefficients for a time-frequency filter bank; then use the ratio of the vertical axis distance to the component half-bandwidth distance as the corresponding time-frequency coordinate domain threshold condition, and then determine the time-frequency distribution region of the component signal corresponding to the corresponding IF law according to the threshold condition, and retain all time-frequency data points in the time-frequency distribution region to obtain the passband coefficients of the corresponding time-frequency filter. Step 4: Based on the time-frequency filter that has obtained the center frequency coefficient and passband coefficient, the signal for which the information to be extracted is filtered in the time-frequency domain. Finally, the filtered time-frequency domain data is subjected to inverse short-time Fourier transform to obtain the corresponding components in the output signal. The signal is a gearbox vibration signal; In step 3, the time-frequency coordinate domain threshold condition is obtained through the following steps: Let the projected coordinates of any point on the three-dimensional time-frequency graph onto the two-dimensional time-frequency surface be... The coordinates of the points corresponding to the fitted IF curve are... The vertical distance between the two points is... for: Half-bandwidth distance D The threshold condition in the time-frequency coordinate domain is determined based on the distribution of the instantaneous amplitude of the component to be decomposed on the time-frequency graph. d / D ,when d / D If the value is ≤ 1, then the coordinates of the reference data point and the corresponding instantaneous amplitude are retained; otherwise, they are not retained.
2. The method according to claim 1, characterized in that, Step 1 includes: Based on the differences in noise among the signal components on the time-frequency graph, the distribution pattern of the signal components from which the information to be extracted is obtained on the time-frequency graph, and multiple reference data points that can reflect the distribution pattern are selected. ,in , The total number of reference data points is given, and the coordinates of each reference data point on the time-frequency surface are given by the given values. ,in For time coordinate values, These are frequency coordinate values.
3. The method according to claim 2, characterized in that, In step 2, the fitted IF curve is obtained through the following steps: Based on the order n polynomial p ( x ): in a The coefficients of the polynomial, j For order variables, j The value range is 0- n ; by p ( x At the baseline data point The residual at the location is ,in ; Then use vectors And there are E The square of the L2 norm for: Right now For L2 norm loss, then we have When the minimum value is taken, the corresponding coefficient Make polynomial curve p ( x The IF of the components represented by the baseline data points has the best consistency under the least squares approximation definition, i.e., solving for the coefficients The system of linear equations: In the above formula Solving for The unique solution is obtained, thus yielding p ( x The expression, and based on p ( x The fitted IF curve is obtained.
4. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-3.
5. A computer-readable medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-3.