Time-frequency analysis method for processing multi-component fast-varying time-frequency cross signal

Abstract

The invention discloses a time-frequency analysis method for processing a multi-component fast-changing time-frequency cross signal, relates to the technical field of signal processing, is suitable for processing and analyzing the fast-changing time-frequency cross signal, and can realize accurate characterization and processing of the fast-changing time-frequency cross signal under a strong noise condition. According to the technical scheme, the method comprises the steps that S1, an EMCT is used for processing collected time-frequency cross signals, and an EMCT result of the signals is obtained; and S2, establishing a new frequency redistribution operator, processing an EMCT result of the signal, obtaining an intermediate frequency track of the signal, and carrying out adaptive time-frequency cross ridge extraction. And S3, establishing a time-frequency coefficient compression method for a time-frequency cross signal, and processing an EMCT result of the signal in combination with the obtained intermediate-frequency trajectory to obtain a time-frequency result. And S4, in the generated time-frequency result, extracting a target component of the signal by using an intermediate-frequency track, and representing and reconstructing a time-frequency cross signal.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals. Background Art

[0002] Conducting research on health monitoring and fault diagnosis of large rotating machinery is crucial to improving the feasibility of equipment operation. Among them, large rotating machinery such as aircraft engines and gas turbines have the characteristics of multi-rotor systems and frequent changes in operating conditions. The vibration collection points of such rotating machinery are usually arranged on the casing, so the actual collected signals are multi-source signals; the transmission path of the collected vibration signal contains elastic supports and various thin-walled pillars, so the vibration signal is easily buried in strong interference. In summary, the actual collected vibration signals of rotating machinery show the characteristics of high complexity, strong non-stationarity, strong noise interference, and there is a frequency track crossing phenomenon in the signal. If such signals are not properly processed, it will seriously affect the extraction of rotating machinery fault features, resulting in false alarms or missed detections. In the worst case, it will cause the entire system to paralyze, or even catastrophic failures, causing huge economic losses and safety hazards. Therefore, it is necessary to study the vibration signal analysis and feature extraction of large rotating machinery.

[0003] Traditional time-frequency analysis methods are effective tools for analyzing non-stationary vibration signals and have been widely used in complex large-scale rotating machinery such as aircraft engines and gas turbines. However, the analysis of multi-component fast-changing signals is still one of the challenges faced by existing traditional time-frequency analysis methods. At present, some researchers have developed a variety of improved time-frequency analysis methods based on traditional time-frequency analysis methods to meet this challenge. Among them, the recently proposed entropy matching synchronous compression modulation transform method (EMSSCT) is a representative of advanced time-frequency analysis methods. The accurate analysis and extraction of multi-component fast-changing signals is a highlight of this method. The EMSSCT method is a time-frequency analysis method based on entropy matching modulation transform (EMCT) and local maximum synchronous compression transform (LMSST).

[0004] The entropy matching synchronous compression modulation transform method in the existing advanced time-frequency analysis methods is an upgrade and extension of the classical modulation transform and synchronous compression transform methods, and represents the cutting-edge development direction of time-frequency analysis methods. The frequency redistribution principle used in this method is a frequency redistribution principle based on local maximum values ​​that is widely recognized and applied in the existing compression transform theory. This principle can achieve accurate intermediate frequency estimation of multi-component fast-changing signals, but its applicability requires that the signal components to be processed are well separated in the time-frequency domain. This results in the lack of time-frequency features at the intersection when the method processes multi-component fast-changing signals with time-frequency intersections, because the signal cannot meet the applicable conditions of its frequency redistribution principle, resulting in inaccurate time-frequency results, resulting in incorrect feature representation and incorrect extraction of target components.

[0005] At the same time, the time-frequency coefficient compression method in this method adopts the widely used synchronous compression theory, which can significantly improve the resolution and energy concentration of time-frequency analysis. However, when processing multi-component fast-changing signals with time-frequency intersections, there is a problem of repeated assignment, which causes the component amplitude in the time-frequency results to deviate seriously from the true value, resulting in the problem of incorrect representation of the target component.

[0006] Due to the limitations of this method, it is necessary to establish a new time-frequency analysis method for processing multi-component rapidly varying time-frequency crossover signals. Summary of the invention

[0007] In view of this, the present invention provides a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals, which is suitable for the processing and analysis of fast-varying time-frequency crossover signals and can achieve accurate characterization and processing of fast-varying time-frequency crossover signals under strong noise conditions.

[0008] To achieve the above object, the technical solution of the present invention includes:

[0009] S1. Use EMCT to process the collected time-frequency cross signal to obtain the EMCT result of the signal.

[0010] S2. Establish a new frequency redistribution operator, process the EMCT result of the signal, obtain the intermediate frequency trajectory of the signal, and perform adaptive time-frequency cross ridge extraction.

[0011] S3. Establish a time-frequency coefficient compression method for time-frequency crossover signals, combine the obtained intermediate frequency trajectory, process the EMCT results of the signal, and obtain the time-frequency results.

[0012] S4. In the generated time-frequency results, the target component of the signal is extracted using the intermediate frequency trajectory, and the time-frequency cross signal is characterized and reconstructed.

[0013] Furthermore, the EMCT result of the signal obtained in S1 is t is time, ω is frequency. In S2, a new frequency redistribution operator is established as:

[0014]

[0015] Where IF k (t) represents the EMCT image The time-frequency ridge of the extracted k-th component; represents the frequency redistribution operator of the kth component, that is, the intermediate frequency trajectory of the signal; K is the time-frequency result The total number of target components in; Δ is the range of frequency redistribution.

[0016] The following formula is used for adaptive time-frequency cross ridge extraction:

[0017]

[0018] Where s(μ) is the time-frequency result at time μ The frequency information obtained after sequential statistical filtering, is a penalty item, is the probability density distribution function, m is the order of the penalty term, represents a Gaussian probability density function with a mean of Ω and a standard deviation of Ω', where Ω' is the derivative value at the target, E tt-1 (Ω) is the frequency information Ω of the kth component at time t-1 at the target at time t; is the tracking result of the target at the previous moment at moment μ; Ω is the target value at moment μ-1;

[0019]

[0020] Furthermore, in S3, the time-frequency coefficient compression method for the time-frequency cross signal established is specifically established in the following steps:

[0021] S301, divide the time-frequency cross signal in the time-frequency domain into three parts. The first part is the signal satisfying φ'k +1 (t)-φ'k(t)|>Δ, where k∈{1,...,K-1}; the second part is that the signal satisfies The third part is the signal satisfaction

[0022] Determine the number of crossover domains in the EMCT result of the time-frequency crossover signal; for the time-frequency ridge line IF(t), find the positions with the same ridge line value at the same time, and record the number of all positions as N.

[0023] When N=1, there is a single crossover domain in the EMCT result of the time-frequency crossover signal, and the specific determination steps are as follows:

[0024] (1) For the time-frequency ridge line IF(t), find the position with the same ridge line value at the same time, obtain the time at this time as t1, the frequency as ω1, and the component number G1 where there is a time-frequency intersection at this position.

[0025] (2) Get | IF k'+1 (t)-IF k' (t)|=Δ, recorded as T1 and T2, T1<T2, where G1=k',k'+1; get IF G1 The minimum and maximum values ​​of (t) at these two moments are denoted as Ω1 and Ω2, respectively, Ω1<Ω2.

[0026] (3) Define the region where t∈[T1,T2] and ω∈[Ω1-Δ / 2,Ω2+Δ / 2] as the crossover domain.

[0027] When a signal contains multiple cross-domains, the specific steps for determining the cross-domains are as follows:

[0028] (1) For the time-frequency ridge IF(t), find the position with the same ridge value at the same time, and record the time at this time as t1,...,t N , the frequencies are denoted as ω1,...,ω N And the component numbers G1,...,G where time-frequency intersection exists at the corresponding position N .

[0029] (2) For i=1:N

[0030] 1) Get | IF k'+z (t)-IF k' The time when (t)|=Δ is denoted as T 2i-1 and T 2i , T 2i-1 <T 2i , where G i =k',k'+z; Get IF Gi The minimum and maximum values ​​of (t) at these two moments are denoted by Ω 2i-1 and Ω 2i ,Ω 2i-1 <Ω 2i .

[0031] 2) Define t∈[T 2i-1 ,T 2i ] and ω∈[Ω 2i-1 -Δ / 2,Ω 2i +Δ / 2] is the crossover domain.

[0032] S302, define the first part of the time-frequency cross signal as a non-cross domain; the non-cross domain is the complement of the cross domain; divide the time-frequency cross signal into two regions in the time-frequency domain, namely, the non-cross domain and the cross domain, respectively denoted as S n and S ci , i=1:N.

[0033] S303, after defining three parts and two regions of the time-frequency cross signal in the time-frequency domain, a new time-frequency coefficient compression method is established as follows:

[0034]

[0035] In the formula is the time-frequency result obtained by the new time-frequency coefficient compression method, δ() is the Dirac function, ζ k is the frequency value of the kth component at time t, is the amplitude recovery value of the target component.

[0036] Furthermore, in S4, the time-frequency ridge IF obtained in S2 is used k (t) Extract the time-frequency image obtained by S3 The specific implementation steps are as follows:

[0037] s k (t)=Real(RCT(t,IF k (t))) / C w

[0038] In the formula, s k (t) is the reconstruction result of the kth target component; Real() is the real part operation, and RCT(t,ω) is the target time-frequency result; w(t) is the window function.

[0039] Beneficial effects:

[0040] 1. The present invention provides a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals, which is suitable for processing and analyzing fast-varying time-frequency crossover signals; it does not use the principle of limiting the local maximum value of the signal component spacing to estimate the intermediate frequency, but uses the frequency redistribution principle based on the component time-frequency ridges when processing time-frequency crossover signals. The present invention can accurately characterize and process fast-varying time-frequency crossover signals under strong noise conditions; when selecting a time-frequency ridge extraction algorithm, in order to address the problem of large noise interference with real signals, based on the idea of ​​establishing amplitude-related terms and penalty terms in existing methods, an algorithm suitable for accurate extraction of time-frequency ridges under strong noise conditions is established, eliminating the interference of noise on the processing of fast-varying time-frequency crossover signals.

[0041] 2. The present invention provides a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals, which solves the problem of repeated compression that exists when existing time-frequency post-processing algorithms process fast-varying time-frequency crossover signals; based on whether repeated compression occurs, the fast-varying time-frequency crossover signals are divided into regions, and a regional compression algorithm is established for the signals in different regions based on accurate compression, thereby achieving accurate characterization and reconstruction of the time-frequency crossover signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flow chart of a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals provided by the present invention;

[0043] Figure 2(a) is the graph of the lg(x) function;

[0044] Figure 2(b) is the graph of the lg(x+1) function;

[0045] Figure 3 This is a graph showing the change in the value of the penalty term under different orders;

[0046] Fig. 4(a) is the EMCT slice diagram of the first part of the time-frequency cross signal;

[0047] Fig. 4(b) is the EMCT slice diagram of the second part of the time-frequency cross signal;

[0048] Fig. 4(c) is the EMCT slice diagram of the third part of the time-frequency cross signal;

[0049] Figure 4(d) is the EMCT slice diagram of the third part (φ' k+1 (t)-φ' k (t)|=0). DETAILED DESCRIPTION

[0050] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0051] The present invention provides a time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals. The method first defines a frequency redistribution operator to solve the problem of missing time-frequency features when the currently widely used frequency redistribution principle processes time-frequency crossover signals. Then, in the newly established frequency redistribution operator, an adaptive time-frequency crossover ridge extraction method is proposed to extract time-frequency crossover ridges under strong noise conditions. In addition, a compression transformation method is also constructed to compress the target component in the time-frequency crossover domain. In summary, the accurate time-frequency representation of multi-component fast-varying time-frequency crossover signals is achieved, and the acquisition process is as follows: Figure 1As shown. Compared with the existing entropy matching synchronous compression modulation transform method (EMSSCT), this method (EMRSCT) has better signal reconstruction ability when processing strong non-stationary signals with crossover frequencies. In addition, it is also better than EMSSCT in terms of energy concentration, noise robustness, accuracy and computational efficiency. The main steps of obtaining and using the specific method are as follows:

[0052] S1. Use EMCT to process the collected time-frequency cross signal x(t) to obtain the EMCT result of the signal;

[0053] S2. Establish a new frequency redistribution operator, use the operator to process the signal EMCT result, obtain the intermediate frequency trajectory of the signal, and propose an improved adaptive time-frequency cross-ridge extraction method in the operator to achieve accurate extraction of the intermediate frequency trajectory under strong noise conditions;

[0054] S3, establish a time-frequency coefficient compression method for time-frequency crossover signals, combine the obtained intermediate frequency trajectory, process the signal EMCT results, and obtain accurate and clear time-frequency results;

[0055] S4. In the generated time-frequency results, the target component of the signal is extracted using the intermediate frequency trajectory to achieve accurate characterization and reconstruction of the time-frequency cross signal.

[0056] First, in S1, the collected time-frequency cross signal is processed by EMCT. In this step, since EMCT is an existing technology, the signal is directly processed by EMCT technology to obtain the corresponding time-frequency result.

[0057]

[0058] Furthermore, a new frequency reallocation principle is defined in S2 as shown in formula (1). Using formula (1) to obtain the time-frequency result The intermediate frequency information of the target component in the image is obtained, and the frequency redistribution operator suitable for time-frequency crossover signals is obtained:

[0059]

[0060] Where IF k (t) represents the EMCT image The time-frequency ridge of the kth component is extracted; represents the frequency redistribution operator of the kth component, that is, the intermediate frequency trajectory of the signal; K is the time-frequency result The total number of target components in; Δ is the range of frequency redistribution.

[0061] It is worth noting that IF k (t) is based on EMCT image Therefore, when the extracted time-frequency ridge is accurate enough, there is IF k (t)≈φ' k (t), and when Sometimes, there is

[0062]

[0063] According to the above analysis, the newly established frequency redistribution operator is suitable for time-frequency cross signals and eliminates the problem of erroneous extraction of the original operator. But obviously, the accurate acquisition of the time-frequency ridge in formula (1) is the basis and premise of this operator. Therefore, the improved time-frequency ridge extraction method that meets the requirements of formula (2) will be established next.

[0064] The existing ridge extraction method for time-frequency cross signals mainly implements its function through formulas (3)-(5), and the specific formulas are as follows:

[0065]

[0066] Where s(μ) is the time-frequency result at time μ Frequency information obtained after sequential statistical filtering. is a penalty item, is the probability density distribution function. According to the probability distribution criterion, the probability density distribution obeys the Gaussian distribution. represents a Gaussian probability density function with mean Ω and standard deviation Ω'. Ω' is the derivative value at the target. E tt-1 (Ω) is the frequency information Ω of the kth component at time t-1, and the target at time t. The algorithm can extract the ridges of the time-frequency cross signal, but it cannot accurately extract the time-frequency features in the time-frequency image under high noise conditions.

[0067] Based on the limitations of the existing ridge extraction algorithm, the present invention establishes a ridge extraction algorithm suitable for time-frequency crossover signals under high noise conditions. First, by observing formula (3), it is found that the penalty function uses Weaken the impact of amplitude fluctuations on ridge target tracking. However, Figure 2(a) shows that the log function is not able to weaken amplitude fluctuations at all times. Specifically, when x>1, assuming that x1 is the amplitude of the target frequency, and x2 is the amplitude after the amplitude fluctuation occurs at the interference frequency. As can be seen from Figure 2(a), the difference calculated by the log function is significantly smaller than the difference between x1 and x2. At this time, the log function has a significant effect in weakening amplitude fluctuations. However, when When , the slope of the log function curve is greater than 1. At this time, assuming that x3 is the amplitude of the target frequency, and x4 is the amplitude after the amplitude fluctuation occurs at the interference frequency. As can be seen from Figure 2(a), the difference calculated by the log function is significantly greater than the difference between x3 and x4. In other words, when the amplitude fluctuates and the amplitude is less than When the log function calculates the fluctuation result, it is obviously greater than the amplitude fluctuation value. At this time, the log function will not be able to weaken the amplitude fluctuation and even highlight the fluctuation to a certain extent. This is consistent with It goes against the original intention.

[0068] Therefore, the present invention re-establishes the amplitude-related term on this basis, namely The details are shown in Figure 2(b). Generally speaking, the newly established amplitude-related term can achieve the function of weakening the amplitude fluctuation in the full amplitude range of the time-frequency image.

[0069] Continue to observe formula (3), where the penalty term of the penalty function is Since the existing penalty term may lead to the wrong extraction of the time-frequency ridge under strong noise conditions, the present invention improves the penalty term and converts the original first-order dimensionless variable into an m-order dimensionless variable. Figure 3 The change of penalty value under different orders is shown. Figure 3 It can be seen that as the order increases, the penalty for the same interference position gradually increases, that is, the difficulty of incorrectly extracting the time-frequency ridge line increases. This helps to achieve accurate extraction of the time-frequency ridge line under strong noise interference.

[0070] In summary, the improved penalty function is shown in formula (6):

[0071]

[0072] Where m is the order of the penalty term.

[0073] The mathematical expression of the time-frequency ridge extracted by the improved method is shown in formula (7):

[0074]

[0075] The improved formulas (6) and (7) are substituted into the newly defined formula (1), so that the accurate extraction of the intermediate frequency trajectory under strong noise conditions and the acquisition of the frequency redistribution operator can be achieved through the obtained frequency redistribution principle.

[0076] Furthermore, in S3, unlike the classical time-frequency coefficient compression method which selects synchronous compression technology, the present invention establishes a new time-frequency coefficient compression method for processing. First, the limitations of synchronous compression technology in processing time-frequency crossover signals are explained.

[0077] The time-frequency cross signal is divided into three parts. The first part is when the signal φ' k+1 (t)-φ' k (t)|>Δ, where k∈{1,...,K-1}. The EMCT slice of this part of the signal at a certain moment is plotted, as shown in Figure 4(a). As shown in Figure 4(a), there is enough spacing between the components in the first part of the signal, so that when the components are synchronously compressed, no other interference components are introduced. Therefore, when this part of the signal is synchronously compressed, the amplitude is very close to the true value.

[0078] The second part is when the signal When the EMCT slice of this part of the signal at a certain moment is plotted, as shown in Figure 4(b). As shown in Figure 4(b), the time-frequency cross-components in the second part of the signal begin to affect each other, but the local maximum of each component remains independent and unaffected. This causes the related components to introduce some other components as interference when synchronous compression is performed. Therefore, when synchronous compression is performed on this part of the signal, the amplitude deviates from the true value.

[0079] The third part is when the signal When the EMCT slice of this part of the signal at a certain moment is drawn, as shown in Figure 4(c). As shown in Figure 4(c), the time-frequency cross-components in the third part of the signal affect each other very obviously, and the local maximum of each component is also affected. This makes the time-frequency cross-component introduce a large number of other components as interference when performing synchronous compression. Therefore, when this part of the signal is synchronously compressed, the amplitude is obviously deviated from the true value. In particular, when the signal's φ' k+1 (t)-φ' k When (t)|=0, the EMCT slice of the signal is shown in Figure 4(d). It can be seen from Figure 4(d) that the time-frequency cross-components have merged into one. At this time, synchronous compression cannot distinguish the components. Therefore, other components are inevitably introduced as interference, causing the final amplitude to deviate significantly from the true value.

[0080] In summary, the synchronous compression technology has obvious limitations when processing time-frequency crossover signals. Based on this, the present invention establishes a new compression method, and the specific establishment steps are as follows:

[0081] 1. The time-frequency cross signal in the time-frequency domain is divided into three parts, as described above. Next, the second and third parts are uniformly defined as the cross domain. The specific steps to determine the single cross domain of the time-frequency cross signal are as follows:

[0082] (1) For the time-frequency ridge IF(t), find the position with the same ridge value at the same time, obtain the time at this time as t1, the frequency as ω1, and the component number G1 (for example, G1 = k', k'+1) at this position where the time-frequency intersection exists;

[0083] (2) Get | IF k'+1 (t)-IF k' =Δ(G1=k',k'+1), denoted as T1 and T2 (T1<T2), to obtain The minimum and maximum values ​​at these two moments are recorded as Ω1 and Ω2 (Ω1<Ω2);

[0084] (3) Define the region where t∈[T1,T2] and ω∈[Ω1-Δ / 2,Ω2+Δ / 2] as the crossover domain.

[0085] 2. When the signal contains multiple cross-domains, the specific steps for determining the cross-domains are as follows:

[0086] (1) For the time-frequency ridge IF(t), find the position with the same ridge value at the same time, and record the time at this time as t1,...,t N , the frequencies are denoted as ω1,...,ω N And the component numbers G1,...,G where time-frequency intersection exists at the corresponding position N ;

[0087] (2) For i=1:N

[0088] 1) Get | IF k'+z (t)-IF k' (t)|=Δ(G i = k', k'+z), denoted as T 2i-1 and T 2i (T 2i-1 <T 2i ), get IF Gi The minimum and maximum values ​​of (t) at these two moments are denoted by Ω 2i-1 and Ω 2i (Ω 2i-1 <Ω 2i );

[0089] 2) Define t∈[T 2i-1 ,T 2i ] and ω∈[Ω 2i-1 -Δ / 2,Ω 2i +Δ / 2] is the crossover domain.

[0090] 3. Define the first part of the time-frequency cross signal as the non-cross domain. Obviously, the non-cross domain is the complement of the cross domain.

[0091] In summary, the present invention divides the time-frequency cross signal into two regions in the time-frequency domain, namely, the non-cross domain and the cross domain, which are respectively denoted as S n and S ci (i=1:N).

[0092] 4. After defining three parts and two regions of the time-frequency cross signal in the time-frequency domain, a new time-frequency coefficient compression method is established as follows:

[0093]

[0094] In the formula is the time-frequency result obtained by the new time-frequency coefficient compression method, δ() is the Dirac function, ζ k is the frequency value of the kth component at time t, is the amplitude recovery value of the target component.

[0095] It can be seen from formula (8) that the newly established time-frequency coefficient squeezing method realizes the processing of the time-frequency cross signal by taking different squeezing operations on different parts of the time-frequency cross signal. The specific meaning of formula (8) is as follows:

[0096] (1) When the time-frequency coefficients to be squeezed are located in the non-crossing domain, that is, the first part of the time-frequency cross signal, since there is enough interval between the components in this part of the signal, the time-frequency coefficients can be directly squeezed synchronously. The specific squeezing operation is shown in the first part of formula (8).

[0097] (2) When the time-frequency coefficients that need to be squeezed are located in the cross domain, since the signal components in this area will interfere with each other, direct synchronous squeezing cannot meet the needs. At this time, it is necessary to squeeze the time-frequency cross signals in different parts of this area separately, so the specific squeezing operations in the cross domain are as follows:

[0098] 1) When the time-frequency coefficients to be squeezed belong to the second part of the time-frequency cross signal, firstly, according to the description of STFT, EMCT is described as:

[0099]

[0100] From formula (9), we can see that the time-frequency energy of the kth component in the signal is [ω k (t)-Δ g ,ω k (t)+Δ g ] area and diffuses at frequency ω k (t) reaches its maximum value. Since the window function g(t) used in the EMCT method is a real even window function, its Fourier transformed It is also a real even window function, and the real even function is based on ω k (t) is the center. At the same time, for the kth component of the signal at time t, Value in ω k In summary, the EMCT result of the kth component of the signal at time t is along ω=ω k (t) Axisymmetric.

[0101] For the second part of the time-frequency cross signal, the time-frequency cross components affect each other and cannot be squeezed synchronously. However, the local maximum of each component remains independent and unaffected, that is, at least half of the range of each component in the window of the corresponding window function is unaffected. Since the EMCT results of each component are respectively along ω=ω k (t) axisymmetric. Therefore, the unaffected half of the EMCT result in the window can be used to characterize the affected EMCT result. For the newly established frequency redistribution principle, ω k (t) = IF k (t). Therefore, the specific extrusion operation is shown in the second part of formula (8).

[0102] 2) When the time-frequency coefficients that need to be squeezed belong to the third part of the time-frequency cross signal, it is found that serious interference has occurred between the time-frequency cross components, and the squeezing method in the second part of formula (8) can no longer be used for processing. If the components of this part are squeezed synchronously, the time-frequency result of the combined component is finally obtained. Therefore, the present invention decides to separate the time-frequency result of the target component from the time-frequency result of the combined component to achieve the purpose. Through observation, it is found that the time-frequency ridge intervals between the components are much smaller than those of other parts. Therefore, let the time of the third part of the time-frequency cross signal be t', and assume that IF k' (t')≈IF k'+z (t')(G i = k', k'+z). For the component x k' (t') and x k'+z For (t'), we can get Right now The combined components can be expressed as Under the premise of knowing the combined components, the target components can be obtained by the following formula:

[0103]

[0104] From formula (10), we know that the combined component x k' (t')+x k'+z (t') and its amplitude A k' (t')+Ak'+z (t'), but x k' (t') amplitude information A k' (t') cannot be directly obtained from it. Similar to the situation in formula (10), the same problem exists between the time-frequency result of the combined component and the time-frequency result of the target component. Therefore, in order to obtain the time-frequency result of the target component, it is necessary to obtain the amplitude information of the target component. Here, the present invention introduces compressed sensing technology to obtain the amplitude of this part of the target component. By setting the signal of the third part of the time-frequency cross signal to zero, A k' (t') can be regarded as a lossy signal, and the process of restoring the lossy signal to a complete signal can be regarded as a reconstruction process of compressed sensing to achieve the purpose. The specific steps are as follows:

[0105] Let A k' (t') = 0; and the observed signal A is obtained by the following formula k ”(t):

[0106] A k ”(t)=ΦA k' (t)(11)

[0107] Among them A k' (t) is x k' (t) amplitude information, there is A k' (t')∈A k' (t), Φ is the measurement matrix in the compressed sensing theory, the purpose is to remove A k' (t) while keeping the size and order of other elements unchanged.

[0108] Assumption A k' (t) can be sparsed by the dictionary matrix Ψ, that is:

[0109] Θ=Ψ·A k' (t)(12)

[0110] Where Θ is the sparse representation coefficient vector, then:

[0111] A k ” (t) = ΦΨ -1 Θ=BΘ(13)

[0112] At this time, it is known that the observed signal A k "(t) and the measurement matrix B, in order to obtain the final repair signal, it is necessary to reconstruct Θ, and Θ is sparse. In view of this, there are currently some reconstruction algorithms that can meet the corresponding requirements. The present invention selects the orthogonal matching pursuit algorithm (OMP) to realize the reconstruction of Θ. When using the OMP algorithm to obtain the estimated value of Θ After that, the recovered signal can be further calculated as follows:

[0113]

[0114] make Finally, the restored information of the amplitude of the target component in the third part of the time-frequency cross signal is obtained.

[0115] In summary, according to the idea of ​​formula (10) combined with the restored amplitude information, the specific extrusion operation is shown in the third part of formula (8).

[0116] Further, in S4, the intermediate frequency trajectory IF obtained in S2 is used k (t) Extract the time-frequency image obtained by S3 The specific implementation steps are as follows:

[0117] s k (t)=Real(RCT(t,IF k (t))) / C w (15)

[0118] In the formula, s k (t) is the reconstruction result of the kth target component; Real() is the real part operation, and RCT(t,ω) is the target time-frequency result. w(t) is the window function.

[0119] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals, characterized in that: include: S1. Use EMCT to process the collected time-frequency cross signal to obtain the EMCT result of the signal; S2, establish a new frequency redistribution operator, process the EMCT result of the signal, obtain the intermediate frequency trajectory of the signal, and perform adaptive time-frequency cross ridge extraction; S3, establishing a time-frequency coefficient compression method for time-frequency crossover signals, combining the obtained intermediate frequency trajectory, processing the EMCT results of the signal, and obtaining the time-frequency results; S4. In the generated time-frequency results, the target component of the signal is extracted using the intermediate frequency trajectory, and the time-frequency cross signal is characterized and reconstructed.

2. A time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals as claimed in claim 1, characterized in that: The EMCT result of the signal obtained in S1 is t is time, ω is frequency; In S2, a new frequency reallocation operator is established as: Where IF k (t) represents the EMCT image The time-frequency ridge of the extracted k-th component; represents the frequency redistribution operator of the kth component, that is, the intermediate frequency trajectory of the signal; K is the time-frequency result The total number of target components; Δ is the range of frequency redistribution; The following formula is used for adaptive time-frequency cross ridge extraction: Where s(μ) is the time-frequency result at time μ The frequency information obtained after sequential statistical filtering, is a penalty item, is the probability density distribution function, m is the order of the penalty term, represents a Gaussian probability density function with a mean of Ω and a standard deviation of Ω', where Ω' is the derivative value at the target, E tt-1 (Ω) is the frequency information Ω of the kth component at time t-1 at the target at time t; is the tracking result of the target at the previous moment at moment μ; Ω is the target value at moment μ-1; 3. A time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals as claimed in claim 1, characterized in that: In S3, the time-frequency coefficient compression method for the time-frequency cross signal is established, and the specific establishment steps are as follows: S301, divide the time-frequency cross signal in the time-frequency domain into three parts. The first part is the signal satisfying φ'k +1 (t)-φ'k(t)|>Δ, where k∈{1,...,K-1}; the second part is that the signal satisfies The third part is the signal satisfaction Determine the number of crossover domains in the EMCT result of the time-frequency crossover signal; for the time-frequency ridge line IF(t), find the positions with the same ridge line value at the same time, and record the number of all positions as N; When N=1, there is a single crossover domain in the EMCT result of the time-frequency crossover signal, and the specific determination steps are as follows: (1) For the time-frequency ridge line IF(t), find the position with the same ridge line value at the same time, and obtain the time at this time as t1, the frequency as ω1, and the component number G1 where there is a time-frequency intersection at this position; (2) Get | IF k'+1 (t)-IF k' (t)|=Δ, recorded as T1 and T2, T1<T2, where G1=k',k'+1; get IF G1 (t) The minimum and maximum values ​​at these two moments are denoted as Ω1 and Ω2, respectively, Ω1<Ω2; (3) Define the region where t∈[T1,T2] and ω∈[Ω1-Δ / 2,Ω2+Δ / 2] as the crossover domain; When a signal contains multiple cross-domains, the specific steps for determining the cross-domains are as follows: (1) For the time-frequency ridge IF(t), find the position with the same ridge value at the same time, and record the time at this time as t1,...,t N , the frequencies are denoted as ω1,...,ω N And the component numbers G1,...,G where time-frequency intersection exists at the corresponding position N ; (2) For i=1:N 1) Get | IF k'+z (t)-IF k' The time when (t)|=Δ is denoted as T 2i-1 and T 2i , T 2i-1 <T 2i , where G i = k', k'+z, get IF Gi The minimum and maximum values ​​of (t) at these two moments are denoted by Ω 2i-1 and Ω 2i ,Ω 2i-1 <Ω 2i ; 2) Define t∈[T 2i-1 ,T 2i ] and ω∈[Ω 2i-1 -Δ / 2,Ω 2i +Δ / 2] is the crossover domain; S302, define the first part of the time-frequency cross signal as a non-cross domain; the non-cross domain is the complement of the cross domain; divide the time-frequency cross signal into two regions in the time-frequency domain, namely, the non-cross domain and the cross domain, respectively denoted as S n and S ci , i=1:N; S303, after defining three parts and two regions of the time-frequency cross signal in the time-frequency domain, a new time-frequency coefficient compression method is established as follows: In the formula is the time-frequency result obtained by the new time-frequency coefficient compression method, δ() is the Dirac function, ζ k is the frequency value of the kth component at time t, is the amplitude recovery value of the target component.

4. A time-frequency analysis method for processing multi-component fast-varying time-frequency crossover signals as claimed in claim 3, characterized in that: In S4, the time-frequency ridge IF obtained in S2 is used k (t) Extract the time-frequency image obtained by S3 The specific implementation steps are as follows: s k (t)=Real(RCT(t,IF k (t))) / C w In the formula, s k (t) is the reconstruction result of the kth target component; Real() is the real part operation, and RCT(t,ω) is the target time-frequency result; w(t) is the window function.

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