A short-term linear canonical transform time-frequency analysis method based on variable sliding window

Abstract

The present invention discloses a short-time linear canonical transform time-frequency analysis method based on a variable sliding window, comprising the following steps: S1: acquiring non-stationary signal data; S2: segmenting the original signal according to the analysis task and the non-stationary signal characteristics, and using different sliding window functions to perform discrete short-time linear canonical transform on the sub-segment signal to obtain the sub-segment signal spectrum; S3: combining the spectrum results of each sub-segment signal; S4: outputting the time-frequency distribution diagram of the time and spectrum change relationship of the combined complete non-stationary signal in an oscilloscope. Based on the characteristics of the non-stationary signal, the present invention selects different sliding window functions for each signal sub-segment to form a short-time linear canonical transform time-frequency analysis method based on a variable sliding window. This method not only retains the advantages of the short-time linear canonical transform, but also obtains a more accurate signal local time-frequency distribution result based on the variable window function analysis.

Description

Technical Field

[0001] The invention relates to the field of non-stationary signal time-frequency analysis, and in particular to a short-time linear canonical transformation time-frequency analysis method based on a variable sliding window. Background Art

[0002] Most of the signals generated by complex industrial production processes have non-stationary characteristics. For example, fault detection and diagnosis in wind power grid-connected systems face a large number of non-stationary signals. Single time domain analysis or frequency domain analysis of these non-stationary signals cannot achieve good results. Traditional short-time Fourier transform (STFT) is one of the most effective methods for time-frequency joint analysis of non-stationary signals. In recent years, short-time linear canonical transform (STLCT) has been introduced into the field of signal processing as a generalized form of short-time Fourier transform.

[0003] However, when applying STLCT signals for time-frequency analysis, generally speaking, for signals with faster frequency changes, it is hoped that they will have higher resolution in the time domain. For example, higher time domain resolution helps to observe the fast-changing frequency part (such as sharp pulse signals). In other words, it is hoped that the time width of observation is smaller, but affected by the uncertainty principle of the STLCT domain, the resolution of the signal in the frequency domain will inevitably decrease, so this is a problem faced by high-frequency signals. Sometimes the high-frequency signal is only a signal in a certain local time period of the entire signal, and the other time periods are low-frequency signals. For the low-frequency signals in these time periods, it is hoped that there will be a higher frequency domain resolution, but similarly, the time resolution will be reduced. Therefore, when the global window function type and width are selected, the area of ​​the time-frequency plane cell formed by the time width and bandwidth (that is, the time-frequency plane resolution) is constant in the entire STLCT time-frequency plane.

[0004] Disadvantages: Currently, STLCT uses a global window function to analyze non-stationary signals, which makes it difficult to accurately obtain the local change characteristics of non-stationary signals.

[0005] Therefore, there is an urgent need for a time-frequency analysis method that can accurately analyze the local frequency characteristics of non-stationary signals. Summary of the invention

[0006] In view of this, the technical problem to be solved by the present invention is to provide a method that can retain the advantages of traditional short-time linear canonical transformation and can accurately reflect the trend of local frequency changes of signals. The method divides the original non-stationary signal into several segments according to the analysis requirements, and uses a suitable window function to perform spectrum analysis based on short-time linear canonical transformation for each segment. A short-time linear canonical transformation time-frequency analysis method based on a variable sliding window is invented, which more accurately reflects the characteristics of local changes in the signal.

[0007] The object of the present invention is achieved in that:

[0008] The present invention provides a short-time linear canonical transformation time-frequency analysis method based on a variable sliding window, comprising the following steps:

[0009] S1: Acquire non-stationary signal data;

[0010] S2: The original signal is segmented according to the analysis task and the characteristics of the non-stationary signal, and the sub-segment signal is discretely short-time linear canonical transformation is performed using different sliding window functions to obtain the sub-segment signal spectrum;

[0011] S3: Perform the transformation in step S2 on each sub-segment of the original signal, and combine the spectrum results of the sub-segment signals;

[0012] S4: Output the time-frequency analysis diagram of the relationship between the time and spectrum changes of the complete non-stationary signal obtained by combination in the oscilloscope.

[0013] Furthermore, in step S2, the original signal is segmented according to the analysis task and the non-stationary signal characteristics, and a discrete short-time linear canonical transformation is performed on the sub-segment signal using different sliding window functions to obtain the sub-segment signal spectrum. The specific steps are as follows:

[0014] S21: According to the acquired non-stationary signal characteristics and analysis tasks, the non-stationary signal is divided into several sub-segments in the time domain, and a different window function is selected for each sub-segment. For example, the first sub-segment signal is analyzed using a rectangular window function. Generally speaking, the rectangular window function expression is

[0015] S22: Multiply the first sub-segment signal by the rectangular window function, and then apply the discrete linear canonical transform (DLCT) to it according to the product result. The general expression is Where a, b, c, d are free parameters satisfying ad-bc = 1, t is time, w is frequency, and j is an imaginary unit. After selecting the free parameters in the above transformation formula, a discrete short-time linear canonical transformation is performed on the first sub-segment signal under a rectangular window to obtain the spectrum of the first sub-segment. The result is

[0016] Furthermore, the step S3 performs the transformation in step S2 on each sub-segment of the original signal, and combines the spectrum results of the sub-segment signals. The specific steps are as follows:

[0017] S31: Based on the original signal characteristics and analysis task, a window function different from that of the first sub-segment is used for the second sub-segment signal, such as a Hanning window function analysis; generally speaking, the expression of the Hanning window function is 1≤n≤M is then applied to obtain the spectrum diagram of the second sub-segment by the method of step S22.

[0018] S32: According to the result of segmenting the original signal in step S2, the above steps S21 and S22 are repeated (the window function type can be changed according to the spectrum analysis requirements) until the analysis is completed.

[0019] The advantages of the present invention are: the present invention analyzes the spectrum information of non-stationary signals based on short-time linear canonical transform with variable window. On the one hand, short-time linear canonical transform is a more general short-time Fourier transform, which has advantages in analyzing non-stationary signals such as multi-component signals and radar signals. On the other hand, short-time linear canonical transform, like the classical short-time Fourier transform, selects a global window function, that is, once the window function is selected, it can be changed. The present invention divides the original signal according to the signal spectrum analysis requirements, and then selects a suitable window function for different analysis tasks, avoiding the disadvantage that the traditional method cannot accurately describe the local spectrum characteristics of the signal due to the use of a global window function. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0021] Figure 1 It is a flow chart of the short-time linear canonical transformation time-frequency analysis method with a variable sliding window;

[0022] Figure 2 Flowchart for slicing a signal for a variable sliding window.

[0023] Specific implementation details

[0024] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings; it should be understood that the preferred embodiments are only for illustrating the present invention rather than for limiting the protection scope of the present invention.

[0025] Figure 1 The flowchart of the short-time linear canonical transformation time-frequency analysis method with a variable sliding window is shown in Figure 2. Figure 2 The flow chart of the variable sliding window segmentation signal is shown in the figure: A short-time linear canonical transform time-frequency analysis method based on a variable sliding window provided by the present invention comprises the following steps:

[0026] S1: Acquire non-stationary signal data;

[0027] S2: The original signal is segmented according to the analysis task and the characteristics of the non-stationary signal, and the sub-segment signal is discretely short-time linear canonical transformation is performed using different sliding window functions to obtain the sub-segment signal spectrum;

[0028] S21: According to the acquired non-stationary signal characteristics and analysis tasks, the non-stationary signal is divided into several sub-segments in the time domain, and a different window function is selected for each sub-segment. For example, the first sub-segment signal is analyzed using a rectangular window function. Generally speaking, the rectangular window function expression is

[0029] S22: Multiply the first sub-segment signal by the rectangular window function, and then apply the discrete linear canonical transform (DLCT) to it according to the product result. The general expression is Where a, b, c, d are free parameters satisfying ad-bc = 1, t is time, w is frequency, and j is an imaginary unit. After selecting the free parameters in the above transformation formula, a discrete short-time linear canonical transformation is performed on the first sub-segment signal under a rectangular window to obtain the spectrum of the first sub-segment. The result is

[0030] S3: Perform the transformation in step S2 on each sub-segment of the original signal, and combine the spectrum results of the sub-segment signals;

[0031] S31: Based on the original signal characteristics and analysis task, a window function different from that of the first sub-segment is used for the second sub-segment signal, such as a Hanning window function analysis; generally speaking, the expression of the Hanning window function is 1≤n≤M is then applied to obtain the spectrum diagram of the second sub-segment by the method of step S22.

[0032] S32: According to the result of segmenting the original signal in step S2, the steps S21 to S22 are repeated (the window function type can be changed according to the spectrum analysis requirements) until the analysis is completed.

[0033] S4: Output the time-frequency analysis diagram of the relationship between the time and spectrum changes of the complete non-stationary signal obtained by combination in the oscilloscope.

[0034] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A short-term linear canonical transform time-frequency analysis method based on a variable sliding window, characterized in that: The following steps are involved: S1: Acquisition of non-stationary signals for fault detection and diagnosis in wind power grid-connected systems; S2: The original signal is segmented according to the analysis task and the characteristics of the non-stationary signal, and the sub-segment signal is discretely short-time linear canonical transformation is performed using different sliding window functions to obtain the sub-segment signal spectrum; S3: Perform the transformation in step S2 on each sub-segment of the original signal, and combine the spectrum results of the sub-segment signals; S4: Outputting the time-frequency analysis diagram of the relationship between the time and spectrum changes of the complete non-stationary signal obtained by combination on an oscilloscope; In the step S2, the original signal is segmented according to the analysis task and the non-stationary signal characteristics, and a discrete short-time linear canonical transformation is performed on the sub-segment signal using different sliding window functions to obtain the sub-segment signal spectrum. The specific steps are as follows: S21: according to the acquired non-stationary signal characteristics and analysis tasks, the non-stationary signal is divided into several sub-segments in the time domain by user-defined methods, and a different window function is selected for each sub-segment; S22: Multiply the first sub-segment signal by the rectangular window function, and then apply a discrete linear canonical transform to it according to the product result. The general expression is Among them, a, b, c, d are free parameters that satisfy ad-bc = 1, t is time, w is frequency, and j is an imaginary unit. After selecting the free parameters in the above transformation formula, a discrete short-time linear canonical transformation is performed on the first sub-segment signal under a rectangular window to obtain the spectrum of the first sub-segment. The result is The step S3 performs the transformation in step S2 on each sub-segment of the original signal, and combines the spectrum results of the sub-segment signals. The specific steps are as follows: S31: applying a window function different from that of the first sub-segment to the second sub-segment signal according to the original signal characteristics and the analysis task, and then applying the method of step S22 to obtain a spectrum diagram of the second sub-segment; S32: According to the result of segmenting the original signal in step S2, the above steps S21 and S22 are repeated, and the window function type is changed according to the spectrum analysis requirements until the analysis is completed.

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