Time-frequency analysis method for strong time-varying signal

Abstract

The invention discloses a time-frequency analysis method for a strong time-varying signal, and the method comprises the following steps: collecting the strong time-varying signal in a mechanical operation scene, and carrying out the short-time Fourier transform; based on instantaneous frequency estimation, extruding time-frequency energy to be near the instantaneous frequency by adopting a synchronous extrusion S transformation technology; introducing a second-order two-dimensional instantaneous frequency estimation operator to describe the instantaneous frequency of the signal at high precision; iteratively adjusting the position of the time-frequency coefficient through multiple times of synchronous extrusion operation until the energy is concentrated at a real instantaneous frequency position; and outputting a time-frequency representation result with relatively high energy concentration ratio. According to the method, the energy concentration ratio of time-frequency representation can be effectively improved, non-redistribution points can be reduced, and the time-frequency resolution is improved. Compared with a traditional time-frequency analysis method, the method provided by the invention can provide clearer non-stationary signal time-frequency features, and is especially suitable for fault diagnosis and feature extraction scenes of complex mechanical equipment such as engines and heavy oil catalytic units.

Description

Technical Field

[0001] The present invention relates to the field of non-stationary signal time-frequency analysis, and more specifically to a time-frequency analysis method for strongly time-varying signals. Background Art

[0002] Traditional time-frequency analysis methods, such as short-time Fourier transform (ST) and synchronized squeezed S transform (SSST), are limited by the Heisenberg uncertainty principle and are difficult to achieve high resolution in both time and frequency. In particular, for strongly time-varying non-stationary signals with rapidly changing instantaneous frequencies (IFs), the accuracy of their time-frequency representation is limited. SSST improves on traditional ST by squeezing the time-frequency energy near the IF, but it still suffers from energy dispersion for nonlinear frequency modulated signals.

[0003] To solve this problem, the second-order synchronized squeezed S transform (SSST2) and multiple synchronized squeezed S transform (MSSST) methods were proposed to improve the time-frequency energy concentration of the signal. However, these methods still have deviations for strongly non-stationary signals, especially high-order phase modulated signals, resulting in the failure to effectively redistribute some time-frequency coefficients.

[0004] Based on the above content and formula, detailed description:

[0005] First, establish a harmonic signal model:

[0006] x(t)=Acos(ωt) (1)

[0007] Where A and ωt are the instantaneous amplitude and instantaneous phase respectively, and the instantaneous frequency (IF) is defined as the first-order derivative of the instantaneous phase with respect to t. The S transform (ST) of the signal is defined as:

[0008]

[0009] Limited by the Heisenberg uncertainty principle, the time-frequency representation (TFR) result calculated by ST is fuzzy near the IF, and the time-frequency resolution cannot be arbitrarily small in both the time and frequency directions. Therefore, the synchronized squeezed S transform (SSST) is proposed as a post-processing method of ST to squeeze the diffused time-frequency energy to the correct IF position. The formula is as follows:

[0010]

[0011] in is a two-dimensional IF estimate, defined as follows:

[0012]

[0013] In the formula Represents the partial derivative with respect to t. Considering that non-stationary signals in the real world usually have rapidly changing IFs, the first-order IF estimate in equation (4) is derived under the assumption that the analysis signal can only be in pure harmonic form. Therefore, a second-order two-dimensional IF estimation method is proposed, which can accurately describe the rapidly changing IF of the second-order signal. By inserting the second-order two-dimensional IF estimate in the synchronous squeezing operation, a second-order synchronous squeezed S-transform method (SSST2) is proposed. For linear frequency modulated signals FM Section It is expressed as follows:

[0014]

[0015] The ultimate goal of the second-order two-dimensional IF estimation is to obtain the true IF of the signal, which is expressed as:

[0016]

[0017] Before giving the second-order two-dimensional IF estimation expression, define the two-dimensional group delay operator With modulation operator

[0018]

[0019] Where arg[·] represents the argument of the complex number, Re(·) represents the real part, and V(t,f) represents the short-time Fourier transform result. Then, the true IF of the linear frequency modulation signal can be obtained by the second-order two-dimensional IF estimation defined as follows:

[0020]

[0021] By inserting (9) into the synchrosqueezing operator, the second-order synchrosqueezed S-transform (SSST2) can be expressed as:

[0022]

[0023] In order to distinguish it from the 2D IF estimation in the second-order synchronous squeezed S transform, the multiple synchronous squeezed S transform (MSSST) method uses an iterative process to make the estimated 2D IF closer and closer to the fast-changing IF of the strong frequency signal. To illustrate the principle of MSSST, the original SSST in (3) is rewritten as follows:

[0024]

[0025] Where T [1] The time-frequency representation result calculated using SSST is represented by the superscript [1], which indicates a synchronous extrusion operation. By performing multiple synchronous extrusion operations on the time-frequency representation result calculated by ST, the time-frequency representation result can be expressed as:

[0026]

[0027] Where, T [N] It represents the time-frequency representation result after N times of synchronous squeezing operation. After multiple synchronous squeezing operations, the positions of the time-frequency coefficients are iteratively rearranged according to this relationship:

[0028]

[0029] Fix the position of the time-frequency coefficients until the following relationship is satisfied:

[0030]

[0031] Although the fixed point iteration principle used in MSSST can greatly improve the time-frequency representation results, for strong non-stationary signals (phase greater than 2nd order), the multi-synchronous compression operator in MSSST is a biased two-dimensional IF estimator. The time-frequency representation results calculated using MSSST still retain the unredistributed time-frequency coefficients, and the energy concentration of the time-frequency representation results still needs to be improved.

[0032] In tasks such as heavy oil catalytic unit vibration signal and engine acoustic signal analysis, MSSST is suitable for fault detection and signal feature extraction because it can process multi-component and non-stationary signals, especially nonlinear frequency modulation and transient characteristics. The algorithm can provide a higher time-frequency resolution through multiple synchronous compression technology, making the time-frequency representation clearer and facilitating the capture of key features of fault signals. However, for strong non-stationary signals with a phase greater than the second order, the multi-synchronous compression operator of MSSST has deviations, resulting in insufficient time-frequency energy concentration, and some time-frequency coefficients cannot be effectively redistributed, reducing the accuracy of the time-frequency representation. In addition, the computational complexity of MSSST is high, especially when processing high sampling rate data, which may affect real-time performance. The algorithm needs to be optimized to improve computational efficiency and processing speed to better meet the needs of online monitoring. Summary of the invention

[0033] In view of this, the present invention provides a time-frequency analysis method for strongly time-varying signals, which is a time-frequency analysis method combining second-order two-dimensional IF estimation and multiple synchronous squeezing technology, called second-order multi-synchronous squeezed S transform (MSSST2). By embedding a second-order two-dimensional IF estimation operator, this method can significantly improve the concentration of time-frequency energy and reduce the erroneous redistribution of time-frequency coefficients. At the same time, the present invention is optimized in terms of computational complexity, can effectively process high sampling rate data, and adapt to online monitoring and fault diagnosis tasks.

[0034] In order to achieve the above object, the present invention adopts the following technical solution:

[0035] A time-frequency analysis method for a strong time-varying signal comprises the following steps:

[0036] Collect strong time-varying signals in mechanical operation scenarios and perform short-time Fourier transform;

[0037] Based on the instantaneous frequency estimation, the synchronous squeezed S transform technique is used to squeeze the time-frequency energy to near the instantaneous frequency;

[0038] A second-order two-dimensional instantaneous frequency estimation operator is introduced to describe the instantaneous frequency of the signal with high precision.

[0039] Through multiple synchronous squeezing operations, the positions of the time-frequency coefficients are iteratively adjusted until the energy is concentrated at the real instantaneous frequency position;

[0040] Output the time-frequency representation results with higher energy concentration.

[0041] Further, the position of the time-frequency coefficient is iteratively adjusted through multiple synchronous squeezing operations until the energy is concentrated at the real instantaneous frequency position; including:

[0042] The second-order synchronous extrusion S transform is expressed as follows:

[0043]

[0044] Where Ts [1] is the time-frequency representation result calculated by the second-order synchronous extrusion S, t is the running time, η is the phase, ST x (·) is the S transform of the signal, is the second-order two-dimensional IF defined to estimate the true instantaneous frequency of the signal; δ(·) is the Dirac function used to redistribute the energy of the signal to the instantaneous frequency After one compression, the energy is more concentrated on the calculated real instantaneous frequency;

[0045] The time-frequency representation results after two synchronous extrusion operations are expressed as:

[0046]

[0047] After the second squeezing operation, the energy is more concentrated on the real instantaneous frequency;

[0048] The time-frequency representation result after three synchronous extrusion operations is expressed as:

[0049]

[0050] Finally, after N times of synchronous squeezing operations, the time-frequency representation result is expressed as:

[0051]

[0052] After N times of squeezing operations, the energy of each component on the time-frequency spectrum is basically concentrated on the real instantaneous frequency, which is close to the effect of ideal time-frequency transformation.

[0053] It can be seen from the above technical solution that compared with the prior art, the present invention has the following advantages:

[0054] The method of the present invention can not only effectively improve the energy concentration of time-frequency representation, but also reduce the unredistributed points and improve the time-frequency resolution. Compared with the traditional time-frequency analysis method, MSSST2 can provide clearer time-frequency characteristics of non-stationary signals, which is particularly suitable for fault diagnosis and feature extraction scenarios of complex mechanical equipment (such as engines and heavy oil catalytic units). BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0056] Figure 1 A diagram showing the evolution of the time-frequency analysis method for strongly time-varying signals and related methods provided by the present invention;

[0057] Figure 2 Schematic diagram of the collected signal waveform and envelope provided by the present invention; (a) signal waveform, (b) envelope;

[0058] Figure 3 Schematic diagram of various time-frequency analysis results: (a) ST result, (b) SSST2 result,

[0059] (c) MSSST result, (d) MSSST2 result, (e) local map of MSSST result, (f) local map of MSSST2 result;

[0060] Figure 4 Results of ridge extraction using various methods; (a) ST, (b) SSST2, (c) MSSST,

[0061] (d) MSSST2;

[0062] Figure 5 This is a simplified structural diagram of a heavy oil catalytic unit;

[0063] Figure 6 The vibration signal waveform and spectrum diagram of Example 2 of the present invention;

[0064] Figure 7The time-frequency representation results of different methods; (a) ST, (b) SSST2, (c) MSSST,

[0065] (d) MSSST2;

[0066] Figure 8 for Figure 7 The M1 ridge extraction results and its spectrum;

[0067] Fig. 9 for Figure 7 The M2 ridge extraction results and its spectrum;

[0068] Fig.10 for Figure 7 M3 ridge extraction results and its spectrum. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] First, the terms involved in the present invention are explained:

[0071] 1.ST (S Transform)

[0072] S transform is a time-frequency analysis method that combines the advantages of short-time Fourier transform and wavelet transform, and can provide localized information of signals in the time domain and frequency domain. ST analyzes the time-varying characteristics of signals by applying window functions of different scales.

[0073] ST can provide a relatively stable time-frequency representation in signals with relatively slow frequency changes, but when processing strong time-varying signals, its time-frequency energy is prone to blurring, resulting in insufficient resolution.

[0074] 2.SSST (Synchronized Squeeze S Transform)

[0075] The synchronous squeezed S transform is a time-frequency post-processing method developed on the basis of the S transform. It concentrates the time-frequency energy at the instantaneous frequency (IF) by synchronously squeezing the result of the S transform.

[0076] SSST improves the time-frequency representation of ST by redistributing time-frequency energy, thereby improving the time-frequency resolution, especially when processing signals with rapidly changing frequencies.

[0077] 3.SSST2 (Second Order Synchronous Squeezed S Transform)

[0078] SSST2 is a further improvement on SSST. It introduces the second-order instantaneous frequency (IF) estimation to more accurately describe the fast-changing characteristics of the signal. It is suitable for the analysis of nonlinear frequency modulated signals.

[0079] SSST2 uses second-order instantaneous frequency estimation to better process signals with complex frequency changes (such as signals with fast phase changes), making the time-frequency energy more concentrated.

[0080] 4.MSSST stands for Multiple Synchrosqueezing S-Transform, which is an extension of the Synchrosqueezing S-Transform (SSST).

[0081] 5. MSSST2 (Second Order Multiple Synchronous Squeezed S Transform) provided by the present invention

[0082] MSSST2 is an extended version of SSST2, which further improves the concentration of time-frequency energy and time-frequency resolution through multiple synchronous squeezing operations. It iteratively adjusts the time-frequency coefficients to eliminate energy points that are not redistributed.

[0083] MSSST2 can perform multiple iterations of synchronous squeezing operations to make the energy of the time-frequency representation more concentrated on the instantaneous frequency. It is particularly suitable for processing strongly time-varying non-stationary signals with higher accuracy and resolution.

[0084] In addition, according to the background technology content, although the above post-processing algorithm described attempts to approach the ideal time-frequency representation of non-stationary signals, the effectiveness of existing time-frequency analysis algorithms is limited due to inappropriate signal theory assumptions. Combining the advantages and disadvantages of classical post-processing algorithms, a reliable post-processing algorithm should be able to characterize non-stationary signals with rapidly changing IFs and have the characteristics of low computational complexity.

[0085] Although the second-order two-dimensional IF estimation cannot describe the time-frequency representation results of the typical frequency-modulated signals with a phase greater than the second order in the mechanical operation scenario (such as engine sound signals, heavy oil catalytic unit vibration signals, etc.), it has the ability to characterize the signals with IF with a certain inclination angle on the time-frequency plane. Although the time-frequency representation results of the strong frequency-modulated signals can be iteratively concentrated by multiple synchronous compression operators, the use of the original two-dimensional IF estimation in MSSST will result in many unredistributed time-frequency coefficients in the time-frequency representation results, so the energy concentration of the time-frequency representation results needs to be further improved. Insufficient resolution will lead to insufficient feature extraction for tasks such as fault diagnosis, affecting the accuracy of the task. Considering this, the second-order two-dimensional IF estimation is integrated into the multi-synchronous compression framework, and a new post-processing algorithm called the second-order multi-synchronous squeezed S transform (MSSST2) is proposed.

[0086] The embodiment of the present invention discloses a time-frequency analysis method for a strong time-varying signal, comprising the following steps:

[0087] 1). Collect strong time-varying signals in mechanical operation scenarios and perform short-time Fourier transform;

[0088] 2). Based on the instantaneous frequency estimation, the synchronous squeezed S transform technology is used to squeeze the time-frequency energy to near the instantaneous frequency;

[0089] 3). Introduce a second-order two-dimensional instantaneous frequency estimation operator to describe the instantaneous frequency of the signal with high precision;

[0090] 4). Through multiple synchronous squeezing operations, the position of the time-frequency coefficients is iteratively adjusted until the energy is concentrated at the real instantaneous frequency position;

[0091] 5). Output the time-frequency representation results with higher energy concentration.

[0092] like Figure 1 As shown, the evolution process of the method of the present invention and related methods is demonstrated. First, a harmonic signal model is established and the S transform (ST) is defined to obtain the time-frequency representation result of the signal; then a synchronized squeezing S transform (SSST) post-processing technology is proposed to squeeze the time-frequency energy to the correct IF position based on the first-order IF estimation formula. In order to further improve the accuracy, a second-order two-dimensional IF estimation method is proposed, and the rapidly changing IF of the signal is described by introducing a second-order operator. Then, a second-order synchronized squeezing S transform (SSST2) is proposed to integrate the second-order IF estimation into the squeezing operation, and the energy is more concentrated; finally, based on the multiple synchronized squeezing S transform (MSSST2) proposed in the present invention, the squeezing operation is performed multiple times through an iterative process until the time-frequency coefficient meets certain conditions, thereby achieving a more accurate time-frequency representation.

[0093] Wherein, the above step 4) is specifically implemented as follows:

[0094] Similar to MSSST, the original SSST2 in formula (10) is expressed as:

[0095]

[0096] Where Ts [1] is the time-frequency representation result calculated by the second-order synchronous extrusion S, t is the running time, η is the phase, ST x (·) is the S transform of the signal, is the second-order two-dimensional IF defined to estimate the true instantaneous frequency of the signal; δ(·) is the Dirac function used to redistribute the energy of the signal to the instantaneous frequency After one compression, the energy is more concentrated on the calculated real instantaneous frequency;

[0097] The time-frequency representation results after two synchronous extrusion operations are expressed as:

[0098]

[0099] After the second squeezing operation, the energy is more concentrated on the real instantaneous frequency. For the time-frequency spectrum of the engine sound signal and the vibration signal of the heavy oil catalytic unit, the energy aliasing of each component signal component (such as normal mechanical operation, background noise, fault components, etc.) is reduced, which is convenient for downstream tasks to track and extract signal components.

[0100] Similarly, the time-frequency representation result after three synchronous extrusion operations is expressed as:

[0101]

[0102] Finally, after N times of synchronous squeezing operations, the time-frequency representation result is expressed as:

[0103]

[0104] After N times of squeezing, the energy of each component on the time-frequency spectrum is basically concentrated on the real instantaneous frequency, which is close to the effect of ideal time-frequency transformation.

[0105] SSST2 and MSSST can generate energy-concentrated time-frequency representations for signals with IFs that have a certain inclination angle on the time-frequency plane. However, when the phase of the signal cannot be approximated to the second order, the results of these two methods have the phenomenon of energy divergence. Therefore, in this embodiment, the present invention embeds the second-order IF estimation operator into a multiple synchronous extrusion framework, and the present invention simultaneously considers the advantages of second-order two-dimensional IF estimation and iterative two-dimensional IF estimation under a multiple synchronous extrusion framework. Compared with the existing time-frequency analysis algorithms, the method of the present invention can eliminate the unreassigned time-frequency points to a large extent, and can provide more concentrated energy time-frequency representation results. After multiple synchronous extrusion operations, the original strong time-varying non-stationary signal has a clearer representation in the time-frequency domain. Compared with the original MSSST, the processed time-frequency spectrum of the present invention distinguishes the time-frequency components of the non-stationary signal more clearly. In application scenarios such as engine sound signals and heavy oil catalytic units, it is manifested as higher signal resolution and reduced aliasing of components such as mechanical operation, faults, and background noise.

[0106] Embodiment 1:

[0107] This embodiment verifies the effectiveness of the proposed method by analyzing the acoustic signals of the engine at variable speeds. We rationally arrange microphones around the car engine to obtain detailed acoustic characteristic information. As a key acoustic sensing device, the microphone can convert the vibration of the surrounding sound waves into corresponding electrical signals, thereby accurately capturing the acoustic behavior of the engine. These signals contain important information such as engine speed, which plays a vital role in monitoring the engine status. The sampling frequency of the acquisition signal is set to 48000Hz, and the sampling duration is 16 seconds.

[0108] Figure 2 The waveform and envelope of the signal are shown. In order to obtain the engine speed information, different time-frequency analysis methods are used to process the signal envelope. The results are as follows: Figure 3 As shown in Figure 2. It can be seen that due to the Heisenberg uncertainty principle, the ST result has serious energy divergence. SSST2 sharpens the ST result through the frequency redistribution operator, but the first-order redistribution operator still makes the energy concentration of the result low. MSSST and MSSST2 provide energy-concentrated time-frequency representations. Although the two results look very similar, Figure 3 In (e), the enlarged features show that the MSSST results are seriously affected by the problem of unassigned points. In such a short time, the unassigned points affect the representation of time-frequency features. It is difficult to determine more precise instantaneous information, such as instantaneous amplitude and instantaneous frequency, from the ambiguous MSSST results. MSSST2 provides Figure 3 (f) shows the highly concentrated results. It can be observed that there seems to be only one time-frequency coefficient that represents the time-varying characteristics of the signal at each moment. From the concentrated MSSST2 results, the precise frequency information at each moment can be determined. Then, the ridge extraction algorithm is used to extract the time-frequency ridges of the four methods. The results are shown in Figure 4 As shown. Figure 4 It can be seen that MSSST( Figure 4 Part c) and MSSST2 ( Figure 4 The ridge line of SSST2 (part d in the middle) is smooth, which can better reflect the engine speed information, so the effect is ideal. Figure 4 There are some glitches in the part b), which results in inaccurate reflection of engine speed information and poor performance. Figure 4 The ridge burrs in the middle part (a) are the most serious, contain the least useful information, and have the worst effect. Therefore, the proposed MSSST2 is more suitable for state monitoring and feature extraction using engine acoustic signals.

[0109] Embodiment 2:

[0110] The abnormal vibration of a heavy oil catalytic unit is taken as the research object. Figure 5 As shown. The bearing housings (1#, 2#, 3# and 4#) are used to support the corresponding shafts. The vibration sensors are mounted on the bearing housings with a sampling frequency of 2000 Hz. It is known that the vibration of bearing 2# is greater than the alarm limit, which is due to a friction fault between the rotor and the static element. The main focus is on the instantaneous time-frequency characteristics of the signal recorded from bearing 2#. The gas turbine speed is 5381 r / min (where the rotation frequency is approximately equal to 90 Hz).

[0111] Vibration signal waveform and spectrum Figure 6 As shown. It can be seen that the first-order rotation frequency is the largest component, corresponding to the main fault cause. However, the main focus should not be only on the largest component, but also on the weak components. This is because the weak component may contain more basic information that is closely related to the early fault characteristics. In order to enhance the time-frequency characteristics of the weak component, we show the analysis results of different time-frequency analysis methods (see Figure 7 ). For comparison, Figure 7 In Figure 1, the time-frequency representations generated by ST, SSST2, MSSST, and MSSST2 are shown. It can be observed that the ST result is very blurry. Since SSST2 cannot provide enough distance to redistribute the blurred time-frequency coefficients to the true IF region, its result cannot provide accurate time-frequency information. The concentration of the MSSST result has been greatly improved compared with ST and SSST2, but there are still a few points of redistribution errors, resulting in multiple frequency components at a specific moment. In contrast, MSSST2 has the highest energy concentration, with only one frequency component at each moment. In addition, the Renyi entropy of the corresponding methods is shown in Table 1.

[0112] Table 1 Renyi entropy of different methods

[0113] method ST SSST2 MSSST MSSST2 Renyi entropy 16.9497 12.1296 11.0649 10.5803

[0114] Renyi entropy is an indicator that can quantitatively evaluate the energy concentration of time-frequency representation. Generally speaking, the smaller the Renyi entropy, the higher the energy concentration. Table 1 shows that MSSST2 has the smallest Renyi entropy, which means that MSSST2 can generate a more concentrated time-frequency representation. From the MSSST2 results, it can be clearly observed that the three modes M1, M2, and M3 and their oscillation time-frequency characteristics. Then the ridge detection algorithm is used to estimate the IF of the three modes, such as Figure 8-10 As shown in Figure 2, the oscillation frequency of the IF trajectory is further revealed by the spectrum. Figure 8 It can be seen that the IF of the M1 mode oscillates periodically around the first-order rotation frequency, with a frequency of 89.94Hz. This is because the rubbing fault causes the rotor to run at an unstable speed. Fig. 9 and Fig.10In the figure, modes M2 and M3 are high-order components with weaker amplitudes and more irregular oscillation characteristics. For example, 62.5 Hz cannot be found in the M1 mode, but it becomes the dominant motion in the M3 mode. The results show that the rubbing fault should occur in the early stage and therefore does not cause violent irregular vibration of the shaft. However, more attention should be paid to irregular high-order motions to avoid further development of the fault and the occurrence of major damage. The concentrated time-frequency representation results generated by the MSSST2 method proposed in the present invention provide an effective method for extracting the time-varying characteristics of weak components.

[0115] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0116] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A time-frequency analysis method for strongly time-varying signals, characterized in that: The following steps are involved: Collect strong time-varying signals in mechanical operation scenarios and perform short-time Fourier transform; Based on the instantaneous frequency estimation, the synchronous squeezed S transform technique is used to squeeze the time-frequency energy to near the instantaneous frequency; A second-order two-dimensional instantaneous frequency estimation operator is introduced to describe the instantaneous frequency of the signal with high precision. Through multiple synchronous squeezing operations, the positions of the time-frequency coefficients are iteratively adjusted until the energy is concentrated at the real instantaneous frequency position; Output the time-frequency representation results with higher energy concentration.

2. A time-frequency analysis method for strongly time-varying signals according to claim 1, characterized in that: Through multiple synchronous squeezing operations, the position of the time-frequency coefficients is iteratively adjusted until the energy is concentrated at the real instantaneous frequency position; including: The second-order synchronous extrusion S transform is expressed as follows: Where Ts [1] is the time-frequency representation result calculated by the second-order synchronous extrusion S, t is the running time, η is the phase, ST x (·) is the S transform of the signal, is the second-order two-dimensional IF defined to estimate the true instantaneous frequency of the signal; δ(·) is the Dirac function used to redistribute the energy of the signal to the instantaneous frequency After one compression, the energy is more concentrated on the calculated real instantaneous frequency; The time-frequency representation results after two synchronous extrusion operations are expressed as: After the second squeezing operation, the energy is more concentrated on the real instantaneous frequency; The time-frequency representation result after three synchronous extrusion operations is expressed as: Finally, after N times of synchronous squeezing operations, the time-frequency representation result is expressed as: After N times of squeezing operations, the energy of each component on the time-frequency spectrum is basically concentrated on the real instantaneous frequency, which is close to the effect of ideal time-frequency transformation.

Images