Time-frequency analysis method based on multiple synchronous compression and inverse differential transformation

Abstract

The invention discloses a time-frequency analysis method based on multiple synchronous compression and inverse differential transformation. The time-frequency analysis method comprises the following steps: S1, selecting any window function and iteration times; s2, initializing a window function and a derivative of the window function to obtain a signal intermediate frequency instantaneous frequency; s3, performing iteration by using a multiple synchronous compression transformation algorithm to obtain an optimal signal intermediate frequency instantaneous frequency; s4, obtaining a difference inverse transformation model by using the optimal intermediate-frequency instantaneous frequency; s5, substituting the input vibration signal to obtain the intermediate-frequency instantaneous frequency of the optimal signal, and performing rounding operation; s6, performing iteration by using the differential inverse transformation model to obtain a minimum differential inverse transformation calculation result; and S7, performing synchronous compression transformation by using a minimum differential inverse transformation calculation result, and obtaining a time-frequency signal analysis result after iteration. According to the method, multi-synchronous compression and differential inverse transformation are combined, and the efficiency and the precision of time-frequency analysis can be considered at the same time, so that the time-frequency signal can be quickly and accurately identified.

Description

Technical Field

[0001] The present invention relates to the field of time-frequency signal analysis and recognition, and in particular to a time-frequency analysis method based on multiple synchronous compression and inverse differential transformation. Background Art

[0002] Rotating machines with bearing defects usually generate pulse signals, which can be recorded by vibration sensors. However, when the machine runs at variable speed, the measured signal usually exhibits strong non-stationary characteristics, that is, the frequency of the signal varies greatly over time. Non-stationary signal analysis is increasingly valued in rotating machinery fault diagnosis. Time-frequency analysis (TFA) technology has a strong ability to solve such challenges.

[0003] Recent studies have shown that energy concentration is a key indicator for evaluating the performance of TFA methods. This is because the concentrated time-frequency representation (TFR) has a better ability to characterize the fault characteristics under the signal. However, limited by the Heisenberg uncertainty principle, the traditional TFA method has difficulty in providing concentrated results when dealing with strong time-varying signals. Various newly developed TFA techniques aim to overcome the shortcomings of various traditional methods. MSST (Multi-Scale Short-Time Fourier Transform) is an advanced time-frequency analysis method that combines the characteristics of short-time Fourier transform (STFT) and multi-scale analysis. It captures the characteristics of the signal at different frequency and time scales by applying windows of multiple scales simultaneously, optimizing the trade-off between frequency resolution and time resolution of the traditional STFT. The specific steps include selecting windows of multiple scales and applying STFT at each scale, and finally integrating the time-frequency representations at different scales to obtain the comprehensive time-frequency characteristics of the signal. However, MSST also faces the challenges of high complexity, strong dependence on scale selection, and cost of algorithm development and understanding. Its applicability and effect may vary under different signal characteristics, noise levels and application scenarios.

[0004] Differential Inverse Transform (DIT) plays an important role in the field of time-frequency analysis, and its main goal is to reconstruct the original signal through time-frequency representation. However, there are several key challenges in the implementation of DIT. The first is complexity and computational overhead, especially when dealing with large amounts of data or high-resolution time-frequency representation, which requires complex mathematical operations, which may lead to performance degradation or real-time limitations. Secondly, differential operations in time-frequency representation may introduce information loss or precision loss, especially when dealing with high-frequency components or signal mutations, making it difficult to fully restore the details of the original signal. Choosing a suitable time-frequency analysis method is also a challenge. Different methods have different abilities to capture signal characteristics, which affects the quality of the reconstructed signal. Finally, dealing with non-stationary signals and local characteristics of time-frequency representation requires overcoming its complexity to ensure the effectiveness and accuracy of the reconstruction process.

[0005] In summary, currently, any of the time-frequency analysis methods based on the multiple synchronous compression method or the differential inverse transformation method is difficult to meet the requirements of actual production. Summary of the invention

[0006] In order to solve the problems existing in the above-mentioned conventional time-frequency analysis methods, the present invention proposes a time-frequency analysis method based on multiple synchronous compression and differential inverse transformation, which improves the energy concentration of the analyzed time-frequency signals and has higher time-frequency feature recognition capability and accuracy, thereby solving the above-mentioned problems.

[0007] The present application discloses a time-frequency analysis method based on multiple synchronous compression and differential inverse transformation, comprising the following steps:

[0008] S1, select any window function and number of iterations;

[0009] S2, initialize the window function obtained by S1 and the derivative of the window function to obtain the instantaneous frequency estimation result of the intermediate frequency of the signal;

[0010] S3, using a multiple synchronous compression transform algorithm to iterate, gradually improving and optimizing the instantaneous frequency in each iteration, and obtaining the best signal intermediate frequency instantaneous frequency after the number of iterations in S1;

[0011] S4, using the best intermediate frequency instantaneous frequency obtained in S3 to obtain the differential inverse transformation model;

[0012] S5, substituting the input vibration signal into S1-S3, obtaining the best signal intermediate frequency instantaneous frequency, and performing rounding operation on the best signal intermediate frequency instantaneous frequency;

[0013] S6, using the inverse differential transformation model to iteratively calculate the instantaneous frequency of the optimal signal intermediate frequency obtained in S5, and then obtain the minimum inverse differential transformation calculation result;

[0014] S7. Use S6 to obtain the minimum inverse differential transformation calculation result to perform synchronous compression transformation, and obtain the result of time-frequency signal analysis after iterative calculation.

[0015] Preferably, the instantaneous frequency of the intermediate frequency of the signal in S2 is:

[0016] The instantaneous frequency of the intermediate frequency of the signal calculated by short-time Fourier transform is:

[0017]

[0018] The instantaneous frequency of the intermediate frequency of the signal calculated by the short-time Fourier transform after windowing is:

[0019]

[0020] Where t is time, ω is frequency, A(t) is instantaneous amplitude, is the instantaneous phase, δ(·) is the Dirac function, is the derivative of the window function, and i is the imaginary part.

[0021] Preferably, S3 comprises the following steps:

[0022] Assuming that the signal is weakly time-varying, the intermediate frequency instantaneous frequency G(t,ψ) of the signal obtained by S2 is compressed into a concentrated area using the reassignment operator. The specific expression is as follows:

[0023]

[0024] in, is the intermediate frequency estimation function, Ts(t,η) is the optimal representation parameter in the time-frequency function;

[0025] The time-frequency analysis results obtained after iterating the multiple synchronous compression transform algorithm are as follows:

[0026]

[0027] The iterative calculation formula is as follows:

[0028]

[0029]

[0030] …

[0031]

[0032] The calculation formula of the best signal intermediate frequency instantaneous frequency obtained after iteration is as follows:

[0033]

[0034] Where g(·) is the window function, N is the number of iterations, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after N iterations, and η is the frequency.

[0035] Preferably, the calculation formula of the inverse differential transformation model is:

[0036]

[0037] in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the N-1th iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the Nth iteration.

[0038] Preferably, the rounding operation in S5 comprises the following steps:

[0039] It is determined whether the calculated best intermediate frequency instantaneous frequency is an integer. If not, the best intermediate frequency instantaneous frequency is adjusted to the nearest integer.

[0040] Preferably, S6 comprises the following steps:

[0041] The inverse differential transformation model is used for iterative calculation, and the calculation formula is as follows:

[0042]

[0043] …

[0044]

[0045] Get the minimum inverse differential transformation calculation result ε min =ε v ∈{ε1,ε2,ε3,…,ε N-1}, ε v The calculation formula is as follows:

[0046]

[0047] in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the vth iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the v-1th iteration, 1≤v≤N-1.

[0048] Preferably, the iterative calculation formula in S7 is as follows:

[0049] Ts [2] (t,η)=Ts [1] (t,η)+ε v ;

[0050] Ts [3] (t,η)=Ts[2] (t,η)+ε v ;

[0051] Ts [4] (t,η)=Ts [3] (t,η)+ε v ;

[0052] …

[0053] Ts [N] (t,η)=Ts [N-1] (t,η)+ε v ;

[0054] Among them, Ts [N] (t,η) is the result of time-frequency signal analysis obtained by iterative calculation.

[0055] Beneficial effects of the present invention:

[0056] (1) The present invention combines the advantages of multi-synchronous compression and differential inverse transformation, integrates the differential inverse transformation algorithm into the parameter selection of the multi-synchronous compression iterative model, and greatly improves the performance of the multi-synchronous compression model.

[0057] (2) The present invention utilizes multiple synchronous compression and inverse differential transformation methods to identify time-frequency signals, which can take into account both the efficiency and accuracy of time-frequency analysis, thereby achieving rapid and accurate identification of time-frequency signals and can be applied in actual production. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to an embodiment of the present invention;

[0059] Figure 2 is an original signal diagram of an embodiment of the present invention;

[0060] Figure 3 This is a result diagram of time-frequency analysis of an embodiment of the present invention;

[0061] Figure 4 The bat signal time domain and frequency domain diagrams of the embodiment of the present invention;

[0062] Figure 5 It is a time domain and frequency domain diagram of a synthetic signal composed of multiple sinusoidal wave components according to an embodiment of the present invention;

[0063] Figure 6 This is a time-frequency signal fragment diagram of a synthetic signal composed of multiple sinusoidal wave components according to an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0065] The embodiment of the present application discloses a time-frequency analysis method based on multiple synchronous compression and inverse differential transformation, such as Figure 1 As shown, the following steps are included:

[0066] S1. Select any window function and number of iterations.

[0067] By selecting a suitable window function g to truncate the signal in the time domain, the leakage of the signal in the frequency domain can be reduced, and at the same time, a better spectrum analysis rate and dynamic range can be obtained in the time-frequency analysis. The number of iterations N determines the degree of refinement of the time-frequency analysis, which affects the time-frequency resolution of the final time-frequency analysis result.

[0068] S2. Initialize the window function obtained by S1 and the derivative of the window function to obtain the instantaneous frequency estimation result of the intermediate frequency of the signal.

[0069] In the process of initializing the intermediate frequency function of the signal, the window function and the derivative of the window function are initialized first. Due to the limitation of Heisenberg's uncertainty principle, the short-time Fourier transform (STFT) can only provide a fuzzy description of the signal. Therefore, under the premise of assuming that the signal is weakly time-varying, the result of STFT can be expressed by the formula, and then according to the initialized window function and the derivative of the window function, the formula for the instantaneous frequency analysis of the intermediate frequency of the signal is obtained.

[0070] The instantaneous frequency of the intermediate frequency of the signal calculated by STFT is:

[0071]

[0072] The instantaneous frequency of the signal intermediate frequency calculated by the windowed STFT is:

[0073]

[0074] Where t is time, ω is frequency, A(t) is instantaneous amplitude, is the instantaneous phase, δ(·) is the Dirac function, is the derivative of the window function, and i is the imaginary part.

[0075] S3, using the multiple synchronous compression transform algorithm to iterate, gradually improve and optimize the instantaneous frequency in each iteration, and obtain the best signal intermediate frequency instantaneous frequency after the number of iterations in S1.

[0076] Under the assumption that the signal is weakly time-varying, the reassignment operator is used to compress the fuzzy signal intermediate frequency instantaneous frequency G(t,ω) obtained by S2 into a concentrated area. The specific expression is as follows:

[0077]

[0078] in, is the intermediate frequency estimation function, and Ts(t,η) is the optimal representation parameter in the time-frequency function.

[0079] Through the multiple synchronous compression transformation algorithm, the instantaneous frequency is gradually improved and optimized in each iteration. The time-frequency analysis results obtained after iteration of the multiple synchronous compression transformation algorithm are as follows:

[0080]

[0081] The iterative calculation formula is as follows:

[0082]

[0083] …

[0084]

[0085] The above method needs to perform multiple SST operations. In this embodiment, the instantaneous frequency estimation of the intermediate frequency of the signal obtained last is directly taken. To reduce the time of SST operation, the calculation formula of the best signal intermediate frequency instantaneous frequency obtained after iteration is as follows:

[0086]

[0087] Where g(·) is the window function, N is the number of iterations, is the Dirac function, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after N iterations, and η is the frequency.

[0088] S4. Obtain the differential inverse transformation model using the optimal intermediate frequency instantaneous frequency obtained in S3.

[0089] The calculation formula of the inverse difference transformation model is:

[0090]

[0091] in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the N-1th iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the Nth iteration.

[0092] S5, substitute the input vibration signal into S1-S3, obtain the best signal intermediate frequency instantaneous frequency, and perform rounding operation on the best signal intermediate frequency instantaneous frequency. That is, determine whether the calculated best intermediate frequency instantaneous frequency is an integer, if it is an integer, proceed to the next step, if not, adjust the best intermediate frequency instantaneous frequency to the nearest integer.

[0093] S6. Perform iterative calculation using the inverse differential transformation model, and then obtain the minimum inverse differential transformation calculation result.

[0094] The inverse differential transformation model is used for iterative calculation, and the calculation formula is as follows:

[0095]

[0096] …

[0097]

[0098] For the input vibration signal, the result of the iterative calculation is rounded off, and the result output by the inverse differential transformation model is adjusted to the nearest integer to simplify the result and meet the specific numerical representation requirements.

[0099] Get the minimum inverse differential transformation calculation result ε min =ε v ∈{ε1,ε2,ε3,…,ε N-1}, to reduce the impact of noise, ε v The calculation formula is as follows:

[0100]

[0101] in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the vth iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the v-1th iteration, 1≤v≤N-1.

[0102] S7. Perform synchronous compression transformation using the minimum inverse differential transformation calculation result obtained in S6, and obtain the result of time-frequency signal analysis after iterative calculation.

[0103] The result of the inverse differential transform is used for synchronous compression transform, and analysis and conversion are performed between the time domain and the frequency domain to better understand the characteristics of the signal in time and frequency, and the minimum value of the inverse differential transform result is taken. v To Ts [N] (t,η) is optimized for multiple iterations to gradually improve the accuracy of signal separation and tracking. Using the best result of the above inverse differential transform, the fuzzy STFT result can be compressed into a relatively concentrated area using the reassignment operator, and the best time-frequency analysis result can be obtained by performing appropriate iterations.

[0104] The iterative calculation formula is as follows:

[0105] Ts [2] (t,η)=Ts [1] (t,η)+ε v ;

[0106] Ts [3] (t,η)=Ts [2] (t,η)+ε v ;

[0107] Ts [4] (t,η)=Ts [3] (t,η)+ε v ;

[0108] …

[0109] Ts [N] (t,η)=Ts [N-1] (t,η)+ε v ;

[0110] Among them, Ts [N] (t,η) is the result of time-frequency signal analysis obtained by iterative calculation.

[0111] Finally, the time-frequency signal analysis results are output.

[0112] because

[0113] In this application, the inverse differential transform is used to enhance the weak signal components of the time-frequency representation function to highlight the weak features in the original signal. [N] The value of (t,η) is increased to highlight the weak components of the signal, and the iterative process of MSST is combined to further concentrate the signal energy. In order to reduce the impact of noise on the results, the minimum value of the inverse differential transform is selected to ensure that the noise is minimized while enhancing the signal. The principle of this method is to optimize the parameters of the inverse differential transform and finally obtain a clear and definite time-frequency representation result.

[0114] In a specific embodiment, the above embodiment is further described by performing time-frequency analysis and identification on a certain signal.

[0115] The specific expression of the signal is:

[0116] s(t)=sin(2π(25t+10sin(1.5t)))+0.01sin(120πt);

[0117] The data are sampled at a rate of 200 samples per second. The original signal is as follows: Figure 2 shown.

[0118] The signal is analyzed and identified by the time-frequency analysis method based on multiple synchronous compression and differential inverse transformation proposed in this application. The final signal identification result is as follows: Figure 3 shown. Figure 3 for Figure 2The red border of the truncation diagram, Figure 2 Although it seems that the weak signal has poor aggregation and the signal is truncated, according to Figure 2 It can be clearly seen that the characterization of the weak signal 0.01sin(120πt) verifies that the high-resolution time-frequency analysis method based on multi-synchronous compression and inverse differential transformation has high accuracy and aggregation. Then, according to the time-frequency analysis method based on multi-synchronous compression and inverse differential transformation proposed in this application, the bat signal and the synthetic signal composed of multiple sinusoidal wave components are subjected to time-frequency analysis and identification. Figure 4 The time-frequency diagram of bat signals processed by the time-frequency analysis method based on multiple synchronous compression and differential inverse transformation proposed in this application is shown. The characteristics of bat signals are clearly shown in the figure. Compared with previous methods, the method proposed in this application better reveals the ductility of the signal and provides a clear and complete representation of the main components of the signal. The energy distribution of TFRs represented in the time-frequency domain is also clearer, showing higher analysis accuracy. Figure 5 The time-frequency diagram of a signal composed of multiple sinusoidal components is shown, and it can be clearly seen that the method of the present application is superior in signal characterization. No matter how weak the signal is, its characteristics can be clearly displayed. Figure 6 yes Figure 5 The enlarged image of the red border area further highlights the high analytical accuracy of this method, which accurately captures the subtle features of the signal.

[0119] Therefore, it can be judged that the test signal recognition result is consistent with the solution proposed in the embodiment of the present application, which proves the effectiveness of the embodiment.

[0120] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A time-frequency analysis method based on multiple synchronous compression and inverse differential transformation, characterized in that: The following steps are involved: S1, select any window function and number of iterations; S2, initialize the window function obtained by S1 and the derivative of the window function to obtain the instantaneous frequency estimation result of the intermediate frequency of the signal; S3, using a multiple synchronous compression transform algorithm to iterate, gradually improving and optimizing the instantaneous frequency in each iteration, and obtaining the best signal intermediate frequency instantaneous frequency after the number of iterations in S1; S4, using the best intermediate frequency instantaneous frequency obtained in S3 to obtain the differential inverse transformation model; S5, substituting the input vibration signal into S1-S3, obtaining the best signal intermediate frequency instantaneous frequency, and performing rounding operation on the best signal intermediate frequency instantaneous frequency; S6, using the inverse differential transformation model to iteratively calculate the instantaneous frequency of the optimal signal intermediate frequency obtained in S5, and then obtain the minimum inverse differential transformation calculation result; S7. Use S6 to obtain the minimum inverse differential transformation calculation result to perform synchronous compression transformation, and obtain the result of time-frequency signal analysis after iterative calculation.

2. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 1 is characterized in that: The instantaneous frequency of the intermediate frequency signal in S2 is: The instantaneous frequency of the intermediate frequency of the signal calculated by short-time Fourier transform is: The instantaneous frequency of the intermediate frequency of the signal calculated by the short-time Fourier transform after windowing is: Where t is time, ω is frequency, A(t) is instantaneous amplitude, is the instantaneous phase, δ(·) is the Dirac function, is the derivative of the window function, and i is the imaginary part.

3. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 2 is characterized in that: The S3 comprises the following steps: Assuming that the signal is weakly time-varying, the intermediate frequency instantaneous frequency G(t,ω) of the signal obtained by S2 is compressed into a concentrated area using the reassignment operator. The specific expression is as follows: in, is the intermediate frequency estimation function, Ts(t,η) is the optimal representation parameter in the time-frequency function; The time-frequency analysis results obtained after iterating the multiple synchronous compression transform algorithm are as follows: The iterative calculation formula is as follows: The calculation formula of the best signal intermediate frequency instantaneous frequency obtained after iteration is as follows: Where g(·) is the window function, N is the number of iterations, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after N iterations, and η is the frequency.

4. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 3 is characterized in that: The calculation formula of the inverse difference transformation model is: in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the N-1th iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the Nth iteration.

5. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 4 is characterized in that: The rounding operation in S5 includes the following steps: It is determined whether the calculated best intermediate frequency instantaneous frequency is an integer. If not, the best intermediate frequency instantaneous frequency is adjusted to the nearest integer.

6. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 5 is characterized in that: The S6 comprises the following steps: The inverse differential transformation model is used for iterative calculation, and the calculation formula is as follows: Get the minimum inverse differential transformation calculation result ε min =ε v ∈{ε1,ε2,ε3,…,ε N-1 }, ε v The calculation formula is as follows: in, is the instantaneous frequency of the optimal intermediate frequency of the signal obtained after the vth iteration, is the instantaneous frequency of the optimal signal intermediate frequency obtained after the v-1th iteration, 1≤v≤N-1.

7. The time-frequency analysis method based on multiple synchronous compression and inverse differential transformation according to claim 6 is characterized in that: The iterative calculation formula in S7 is as follows: Ts [2] (t,η)=Ts [1] (t,η)+ε v ; Ts [3] (t,η)=Ts [2] (t,η)+ε v ; Ts [4] (t,η)=Ts [3] (t,η)+ε v ; …… Ts [N] (t,η)=Ts [N-1] (t,η)+ε v ; Among them, Ts [N] (t,η) is the result of time-frequency signal analysis obtained by iterative calculation.

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