A method and system for processing weak non-stationary signals

Abstract

The application provides a weak non-stationary signal processing method and system, and relates to the technical field of signal processing, and comprises the following steps: obtaining a weak non-stationary signal; estimating the signal frequency range of the weak non-stationary signal, and estimating the noise intensity according to the estimated signal frequency range; constructing a stochastic resonance model based on a Gaussian mixed potential function, and adaptively optimizing the Gaussian mixed potential function according to the estimated noise intensity, so as to obtain an optimal stochastic resonance model, with the maximum spectral amplification factor of the stochastic resonance model as the target; constructing a parameterized demodulation operator to demodulate the weak non-stationary signal, inputting the demodulated signal into the optimal stochastic resonance model for enhancement, and finally obtaining the enhanced non-stationary signal through inverse demodulation; and the application is based on Gaussian mixed potential function stochastic resonance, and solves the bottleneck problem of weak non-stationary signal processing through a closed-loop process of noise intensity estimation, potential function optimization, frequency estimation and signal enhancement.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, specifically to a method and system for processing weak non-stationary signals. Background Technology

[0002] Non-stationary signals are primarily used to describe the time-varying frequency characteristics of non-stationary physical processes, effectively reflecting the evolution, degradation, or migration patterns of these processes. They have a wide range of applications in rotating machinery, biosignals, radar, and brainwaves. Non-stationary signal processing, also known as time-frequency analysis, follows Pascal's law: for noisy non-stationary signals, the noise robustness of time-frequency analysis is directly proportional to the frequency domain resolution; that is, the larger the analysis window, the higher the noise robustness and frequency domain resolution. However, increasing the analysis window reduces the time domain resolution, making it unsuitable for non-stationary signals with rapidly changing frequencies, especially weak non-stationary signals with a signal-to-noise ratio below -20dB, where the processing effect is even more unstable. Stochastic resonance, as a typical weak signal processing method, can utilize noise energy to enhance signals and has gained widespread attention in enhancing low-frequency stationary signals, but it still has the following drawbacks:

[0003] (1) Traditional random resonance does not make full use of the asymmetry of the potential function, the utilization rate of noise energy is insufficient, and the noise resistance robustness needs to be further improved.

[0004] (2) Traditional random resonance can only process low-frequency stationary signals and cannot process non-stationary signals with a large frequency variation range and a fast frequency variation speed.

[0005] (3) The signal enhancement effect of stochastic resonance is affected by the model parameters. However, the selection of traditional stochastic resonance model parameters relies too much on experience and has poor stability.

[0006] Therefore, existing methods for processing weak, non-stationary signals with a signal-to-noise ratio below -20dB have limitations in terms of accuracy, noise robustness, and stability. Summary of the Invention

[0007] To address the aforementioned problems, this invention proposes a method and system for processing weak non-stationary signals. Based on the random resonance of Gaussian mixture potential functions, it solves the bottleneck problem of weak non-stationary signal processing through a closed-loop process of noise intensity estimation, potential function optimization, frequency estimation, and signal enhancement.

[0008] According to some embodiments, the present invention adopts the following technical solution:

[0009] A method for processing weak non-stationary signals includes:

[0010] Acquire the weak, non-stationary signal to be processed;

[0011] The frequency range of weak, non-stationary signals is estimated, and the noise intensity is estimated based on the estimated frequency range.

[0012] A stochastic resonance model based on a Gaussian mixture potential function is constructed. Based on the estimated noise intensity, the Gaussian mixture potential function is adaptively optimized with the goal of maximizing the spectral amplification factor of the stochastic resonance model, and the optimal stochastic resonance model is obtained.

[0013] A parameterized demodulation operator is constructed to demodulate weak non-stationary signals. The demodulated signal is then input into an optimal stochastic resonance model for enhancement. Finally, the enhanced non-stationary signal is obtained through inverse demodulation.

[0014] According to some embodiments, the present invention adopts the following technical solution:

[0015] A weak non-stationary signal processing system, comprising:

[0016] The signal acquisition module is configured to acquire weak, non-stationary signals to be processed.

[0017] The noise estimation module is configured to: estimate the frequency range of weak, non-stationary signals, and estimate the noise intensity based on the estimated frequency range.

[0018] The potential function optimization module is configured to: construct a stochastic resonance model based on the Gaussian mixture potential function; based on the estimated noise intensity, adaptively optimize the Gaussian mixture potential function with the objective of maximizing the spectral amplification factor of the stochastic resonance model to obtain the optimal stochastic resonance model.

[0019] The signal enhancement module is configured to: construct a parameterized demodulation operator to demodulate the weak non-stationary signal, input the demodulated signal into the optimal stochastic resonance model for enhancement, and finally obtain the enhanced non-stationary signal through inverse demodulation.

[0020] According to some embodiments, the present invention adopts the following technical solution:

[0021] A computer program product includes a computer program that, when executed by a processor, implements the aforementioned weak non-stationary signal processing method.

[0022] According to some embodiments, the present invention adopts the following technical solution:

[0023] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned weak non-stationary signal processing method.

[0024] According to some embodiments, the present invention adopts the following technical solution:

[0025] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a weak non-stationary signal processing method.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. Traditional time-frequency analysis methods are limited by the Heisenberg uncertainty principle. Increasing the analysis window to improve noise immunity and frequency domain resolution inevitably leads to a decrease in time domain resolution, making it impossible to effectively capture rapidly changing frequencies. This invention adopts a stochastic resonance mechanism combined with signal demodulation methods, so that its enhancement effect does not depend on the analysis window. Thus, it can effectively enhance signal components and achieve high-precision frequency positioning while maintaining high time domain resolution, which is particularly suitable for non-stationary signals with rapidly changing frequencies.

[0028] 2. To address the problems of traditional stochastic resonances, such as "not fully utilizing the asymmetry of the potential function" and "insufficient noise energy utilization," this invention actively constructs an asymmetric pentastable Gaussian mixture potential function. Through an optimization strategy aimed at maximizing the spectral amplification factor, it fully explores the potential of the potential function shape to regulate noise energy, converting more noise energy into effective power for signal enhancement. This results in a more stable and significant signal enhancement effect under strong noise conditions.

[0029] 3. Addressing the core deficiency of traditional stochastic resonance models—their inability to handle non-stationary signals—this invention introduces a parametric demodulation operator. This operator first compresses and converts wideband, time-varying non-stationary signals into low-frequency stationary signals, thus meeting the processing requirements of stochastic resonance. After the signal is deeply enhanced, its non-stationary characteristics are recovered through inverse demodulation. This innovation fundamentally solves the limitation of stochastic resonance models on the signal frequency range, achieving effective enhancement of weak non-stationary signals.

[0030] 4. To address the problems of traditional stochastic resonances, such as "parameter selection relying on experience and poor stability," this invention establishes an adaptive optimization mechanism with the output spectrum amplification factor as a clear guide. It can automatically find the optimal parameters of the dominant function and demodulation operator based on the actual situation of the input signal and noise, completely eliminating the reliance on manual experience and ensuring the consistency, high precision, and high stability of the enhancement effect in different application scenarios.

[0031] In summary, this invention combines adaptive stochastic resonance with parametric unmodulation techniques to provide a novel solution for enhancing weak non-stationary signals in a noisy environment. This solution offers high time-frequency resolution, high noise utilization, and high adaptability. In low signal-to-noise ratio environments, its performance is significantly better than traditional time-frequency analysis methods and stochastic resonance models. Attached Figure Description

[0032] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0033] Figure 1 This is a flowchart of a weak non-stationary signal processing method in Example 1.

[0034] Figure 2 The diagram shows the shape of the symmetric pentastable Gaussian mixture potential function and its equilibrium point distribution in Example 1.

[0035] Figure 3 The diagram shows the potential function morphology and spectral amplification factor distribution for different potential well width parameters in Example 1. (a) and (b) represent the spectral amplification factors corresponding to the asymmetric pentastable Gaussian mixture potential function, the symmetric Gaussian mixture potential function under the default parameter set, and the four sets of potential well width parameter variations, respectively.

[0036] Figure 4 The diagram shows the potential function morphology and spectral amplification factor distribution for different potential well depth parameters in Example 1. (a) and (b) represent the spectral amplification factors corresponding to the asymmetric pentastable Gaussian mixture potential function, the symmetric Gaussian mixture potential function under the default parameter set, and the four sets of potential well depth parameter variations, respectively.

[0037] Figure 5 The diagram shows the potential function morphology and spectral amplification factor distribution corresponding to different potential well position parameters in Example 1. (a) and (b) are the spectral amplification factors corresponding to the asymmetric pentastable Gaussian mixture potential function and the symmetric Gaussian mixture potential function under the default parameter set, respectively, and the four sets of potential well position parameter changes.

[0038] Figure 6 The distribution of spectral amplification factors for the random resonance of Gaussian mixed potential functions and the random resonance of classical bistable potential functions in Example 1 is shown.

[0039] Figure 7 The diagram shows the verification effect of Example 1, where (a), (b), and (c) represent the parameter optimization process, frequency estimation result, and signal enhancement effect, respectively. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0042] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0043] Example 1

[0044] One embodiment of the present invention provides a method for processing weak non-stationary signals. Based on the random resonance of a Gaussian mixture potential function, it solves the bottleneck problem of weak non-stationary signal processing through a closed-loop process of noise intensity estimation, potential function optimization, frequency estimation, and signal enhancement. Figure 1 As shown, it includes:

[0045] Step S1: Obtain the weak non-stationary signal to be processed.

[0046] Step S2: Estimate the frequency range of the weak non-stationary signal, and estimate the noise intensity based on the estimated frequency range.

[0047] Specifically, a noise intensity estimation method based on signal frequency range pre-estimation is proposed, the steps of which are as follows:

[0048] (1) Pre-estimate the signal frequency range, specifically:

[0049] The model for a noisy frequency-modulated signal is established, and the calculation method is as follows:

[0050] (1)

[0051] in, u ( t () represents the weak, non-stationary signal to be processed. t For time variables, A For a fixed amplitude, f ( t () represents a time-varying frequency. n ( t ) is Gaussian white noise.

[0052] The original signal is processed using short-time Fourier transform to obtain its time-frequency distribution. The calculation method is as follows:

[0053] (2)

[0054] in, This represents the time-frequency distribution of the original signal. s This represents the standard deviation of the Gaussian window function. t For time integration variables, j The imaginary unit, f It is the frequency constant of the Fourier transform.

[0055] The signal frequencies identified from the generated time-frequency distribution are:

[0056] (3)

[0057] The estimated signal frequency range is:

[0058] (4)

[0059] (2) Based on the range of signal frequency variation, a switching noise intensity estimation method is adopted, specifically:

[0060] For frequency variation range is small ( <10H z For non-stationary signals, the noise intensity is estimated using the synchronous averaging method, specifically:

[0061] Determining the signal period based on the peak value of the Fast Fourier Transform spectrum. T Segment the signal into M ≥ 10 periodic segments, each segment having a length of T One sampling point.

[0062] Calculate the position of each signal segment relative to all segments. The residual of the average signal, i.e., the phase synchronization residual. ,in, Indicates the first Section 1 The value of each sampling point, =1, 2,…, T , =1,2, …, M .

[0063] Output noise intensity , where Δ t The sampling interval is denoted as .

[0064] For frequencies with a large range of variation ( ≥ 10H z For non-stationary signals, the noise intensity is estimated using the polynomial residual method, specifically:

[0065] The order of the polynomial used to fit the overall trend of the original signal is optimized using the Akaike information criterion. p Polynomial fitting of the signal yields ,in, The order is the degree of the polynomial. The coefficients are polynomials; calculate the fitting residuals. Estimate residual variance ,in, t θ Indicates the first i The estimated output noise intensity at each sampling point is... , L For signal length, Δ t The sampling interval is denoted as .

[0066] Step S3: Construct a stochastic resonance model based on a Gaussian mixture potential function. Based on the estimated noise intensity, and with the objective of maximizing the spectral amplification factor of the stochastic resonance model, adaptively optimize the Gaussian mixture potential function to obtain the optimal stochastic resonance model. Specifically:

[0067] (1) To address the problem of low noise energy utilization caused by low potential function asymmetry, an asymmetric pentastable Gaussian mixture potential function is designed, and the potential function shape is flexibly controlled by multiple parameters, specifically:

[0068] The piecewise asymmetric pentastable Gaussian mixture potential function is designed and calculated as follows:

[0069] (5)

[0070] (6)

[0071] (7)

[0072] In the formula, w i This represents the potential well depth parameter. s i This represents the potential well width parameter. m i Indicates the potential well location parameters. x These are the state variables of the stochastic resonance system, i.e., the output signal of the stochastic resonance model. X 1, X 2 represents the endpoint of the piecewise asymmetric pentastable Gaussian mixture potential function. It is a Gaussian function. k 1, k 2 represent the potential function at the endpoints. X 1, X The slope at point 2.

[0073] It can be seen that the potential function at the endpoints X 1 and X The function is continuously differentiable at two points. The purpose of using a piecewise function is to ensure the unsaturation of the stochastic resonance output.

[0074] To demonstrate the morphological characteristics of the asymmetric pentstable Gaussian mixture potential function, a set of symmetric pentstable Gaussian mixture potential functions is generated as a comparative example of the asymmetric pentstable Gaussian mixture potential function. Its default parameter set is... , s i = 1.0, w i = 0.2, i =1, 2, 3, 4, 5 Figure 2 This is a graph showing the shape of a symmetric pentastable Gaussian mixture potential function and its equilibrium point distribution, with the horizontal axis... x The vertical axis represents the state variables of the stochastic resonance system, i.e., the output signal of the stochastic resonance model. U ( x ) represents the potential function, such as Figure 2 As shown, the potential well is at the equilibrium point ( x mi ,0), i It reaches a minimum at points 1, 2, 3, 4, 5, and at the equilibrium point ( x ni , U ( x ni )), i The maximum value is obtained at positions 1, 2, 3, and 4.

[0075] Combining the Gaussian mixture potential function with second-order stochastic resonance, the resulting stochastic resonance model is as follows:

[0076] (8)

[0077] In the formula, c The damping coefficient is... oh ω is the angular frequency of the input signal.

[0078] According to the Ford-Planck equation, the generalized potential function of this stochastic resonance model is obtained as follows:

[0079] (9)

[0080] (2) Based on the adiabatic approximation theory, the spectral amplification factor of the random resonance of the asymmetric five-stable Gaussian mixture potential function is derived as follows:

[0081] The following linearization condition is satisfied near the equilibrium point:

[0082] (10)

[0083] In the formula, x ∗ This represents extreme points, including minimum points. x mi ( i = 1, 2, 3, 4, 5) and the maximum point x ni ( i = 1,2,3,4).

[0084] When amplitude A When = 0, equation (8) can be linearized near the equilibrium point as follows:

[0085] (11)

[0086] in, H For the characteristic matrix, y State variables x right t The derivative, i.e. It transforms a second-order system into two first-order equations, which facilitates analysis and numerical solutions.

[0087] Feature matrix H The eigenvalues ​​are:

[0088] (12)

[0089] The transition rate between different potential wells is:

[0090] (13)

[0091] (14)

[0092] In the formula, k i,i+1 Indicates a potential well i to potential well i +1 transition rate, k i+1,i Indicates a potential well i +1 to potential well i The transition rate, , , , for A = 0, x The generalized potential function when taking each extreme value.

[0093] The stochastic resonance model of Equation (8) can be mapped to a discrete-state Markovian transition process describing the probability transitions between five stable states, with its probability transition vector... = [ p 1( t ), p 2( t ), p 3( t ), p 4( t ), p 5( t The following conditions must be met:

[0094] (15)

[0095] in, The Markovian transition matrix is ​​represented by the following method:

[0096] (16)

[0097] Under the linear approximation condition, the following condition must be satisfied:

[0098] (17)

[0099] Substituting formula (17) into formula (15) yields:

[0100] (18)

[0101] (19)

[0102] In the formula, and They are A = 0 and t The Markovian transition matrix and steady-state probability transition vector when = 0.

[0103] Suppose that the solution to formula (18) has the following form:

[0104] (20)

[0105] In the formula, q = [ q 1, q 2, q 3, q 4, q 5] T , l = [ l 1, l 2, l 3, l 4, l 5] T .

[0106] Substituting formula (20) into formula (18) yields:

[0107] (twenty one)

[0108] To avoid finding the inverse matrix in formula (21), an approximate solution is given as follows:

[0109] (twenty two)

[0110] In the formula, and = [ , , , , ] T yes The eigenvalues ​​and eigenvectors that satisfy... , a k satisfy .

[0111] The steady-state time response of the system is:

[0112] (twenty three)

[0113] The spectral amplification factor of the stochastic resonance model is defined as:

[0114] (twenty four)

[0115] Substituting equations (22) and (23) into equation (24), the spectral amplification factor can be rewritten as:

[0116] (25)

[0117] (3) Based on formula (25), the influence of the potential function on the spectral amplification factor of the stochastic resonance model is analyzed as follows:

[0118] like Figure 3 to Figure 5 As shown, with noise intensity D The increase of spectral magnification factor It exhibits a non-monotonic trend, characterized by an initial increase followed by a decrease, exhibiting a typical stochastic resonance phenomenon.

[0119] Potential well width parameter s 1 and s Under the change of 2, the asymmetric pentastable Gaussian mixture potential function and the symmetric Gaussian mixture potential function under the default parameter set are as follows: Figure 3 As shown in (a), the spectral amplification factors corresponding to the four sets of parameter changes are as follows: Figure 3As shown in (b), the black curve represents the symmetric Gaussian mixture potential function, and the other colors represent the asymmetric pentastable Gaussian mixture potential function. s i =1.4, i When = 1, 2, at the equilibrium point ( x mi ,0), i At positions 1 and 2, the potential well widens and becomes shallower, and the barrier height decreases. The potential function becomes flatter, corresponding to the largest peak value of the spectral amplification factor. It performs well under weak noise but poorly under strong noise. s i =0.6, i When = 1,2, at the equilibrium point ( x mi ,0), i At points 1 and 2, the potential well becomes narrower and deeper, and the barrier height increases, resulting in a steeper potential function and the smallest peak value of the corresponding spectral amplification factor, leading to poor overall performance. s 1 = 1.4, s 2 = 0.6 and s 1 = 0.6, s When 2=1.4, one potential function becomes more gradual and the other becomes more steep, resulting in better performance under strong noise.

[0120] The results show that simultaneously increasing s 1. s 2. This is beneficial for increasing the peak value of the spectral amplification factor while reducing... s 1. s 2 performed poorly, increasing s 1 decrease s 2 or reduce s 1. Increase s 2. It is beneficial to the overall improvement of signal enhancement effect under various noise intensities.

[0121] Potential well depth parameters w 1 and w 2. Under the change ( w 1 and w The sum of 2 is fixed at 0.4). The asymmetric pentastable Gaussian mixture potential function and the symmetric Gaussian mixture potential function under the default parameter set are as follows: Figure 4 As shown in (a), the spectral amplification factors corresponding to the four sets of parameter changes are as follows: Figure 4 As shown in (b) above, for w 1 = 0.25 w 2 = 0.15 and w 1 = 0.15 w 2 = 0.25, at the equilibrium point ( x mi ,0),i As the potential well depth at points =1 and 2 increases or decreases, the peak value of the spectral amplification factor shifts upward, resulting in better performance under strong noise; for w 1 = 0.35 w 2 = 0.05, at the equilibrium point ( x m1 At point 0, the potential well is shallow, and at the equilibrium point ( x m2 At position 0), the potential well is deeper, the peak value of the spectral amplification factor shifts downward, and it performs better under strong noise; for w 1 = 0.05 w 2 = 0.35, at the equilibrium point ( x m1 At point 0, the potential well of the potential function is relatively deep, and at the equilibrium point ( x m2 At ,0), the potential well of the potential function is shallow, the peak value of the spectral amplification factor shifts further downward, and the performance is poor under strong noise.

[0122] The results show that w 1. The smaller the increase, the better the signal enhancement effect. w 2. The smaller the increase, the better the signal enhancement effect.

[0123] Potential well location parameters m 1 and m Under the change of 2, the asymmetric pentastable Gaussian mixture potential function and the symmetric Gaussian mixture potential function under the default parameter set are as follows: Figure 5 As shown in (a), the spectral amplification factors corresponding to the four sets of parameter changes are as follows: Figure 5 As shown in (b) above, for m 1 = -11, m 2 = -6 and m 1 = -9, m 2 = -4, that is m 1 and m 2. When both increase or both decrease simultaneously, the equilibrium point ( x m1 ,0) and ( x m2 ,0) move to the left or right simultaneously, at the equilibrium point ( x mi ,0), i At positions 1 and 2, the potential well of the potential function widens or narrows, the peak value of the spectral amplification factor increases, and it performs better under strong noise; m 1 = -11, m 2 = -4 and m 1 = -9, m 2 = -6, that is m 1 and m 2. When the value increases and decreases respectively, the equilibrium point (x m1 ,0) and ( x m2 ,0) move to the left or right respectively, at the equilibrium point ( x mi ,0), i At positions 1 and 2, the potential well of the potential function becomes wider or narrower, respectively, the peak value of the spectral amplification factor decreases, and the performance is poor under strong noise.

[0124] The results show that simultaneously increasing or decreasing m 1. m 2. It helps to increase the peak value of the spectral amplification factor and increase... m 1 decrease m 2 or reduce m 1. Increase m 2. It can only slightly improve the signal enhancement effect under weak noise.

[0125] (4) Based on the above analysis results, the potential function is adaptively optimized according to the estimated noise intensity and the derived spectral amplification factor, as follows:

[0126] To save optimization time and feasibility, the potential function parameters { s i , w i , m i} ( i = 3, 4, 5) Use the default parameter set data to reduce the dimensionality of the parameter search space and avoid local optima. Set the noise intensity. oh = 0, c =5, with the goal of maximizing the spectral amplification factor, the potential function parameter set is... Q = { s i , w i , m i} ( i Optimizing = 1, 2) results in:

[0127] (26)

[0128] like Figure 6As shown, after optimization of the potential function parameters, under the same noise intensity, the spectral amplification factor of the Gaussian mixture potential function stochastic resonance is always greater than that of the adaptive classical bistable stochastic resonance. For the case where the spectral amplification factor is greater than 20, the noise range corresponding to the Gaussian mixture potential function stochastic resonance is 0.05 ~ 0.2, and the maximum spectral amplification factor is 80, while the noise range of the adaptive classical bistable stochastic resonance is 0.05 ~ 0.08, and the maximum spectral amplification factor is 32.

[0129] The results show that the Gaussian mixture potential function stochastic resonance has a wider signal-to-noise ratio range and stronger noise robustness. The three potential function subplots represent the optimal Gaussian mixture potential function and its parameter values ​​corresponding to the maximum, 20, and minimum values ​​of the spectral amplification factor, respectively. It can be seen that as the noise intensity increases, the optimal function adopted at the equilibrium point ( x m1 The potential well at (0) becomes shallower, and at the equilibrium point ( x m2 The potential well at (0) becomes deeper, and particles transition between potential wells with large height differences, thereby enhancing the stochastic resonance output signal.

[0130] Step S4: Construct a parameterized demodulation operator to demodulate the weak non-stationary signal, input the demodulated signal into an optimized Gaussian mixture potential function stochastic resonance model for enhancement, and finally obtain the enhanced non-stationary signal through inverse demodulation.

[0131] Specifically, this embodiment proposes a method for frequency estimation and signal enhancement of weak non-stationary signals, the steps of which are as follows:

[0132] (1) Construct a parameterized demodulation operator to demodulate the original signal, including the following:

[0133] To address the diversity of time-varying frequencies of non-stationary signals, a parametric unmodulation operator is constructed based on the Chebyshev polynomial interpolation method. l ( t ; P ), expressed by the formula:

[0134] (27)

[0135] Among them, frequency f d ( t ; P The calculation method for ) is as follows:

[0136] (28)

[0137] in, P = [ p ( t 1),..., p (t K ] represents the parameter to be optimized, i.e., the Chebyshev interpolation frequency, ( t k , p ( t k )) represents the nodes of the Chebyshev interpolation polynomial. t k For the first k The time points corresponding to each interpolation node. l k ( t ) represents a Lagrange polynomial. K The order of the Chebyshev interpolation polynomial can be determined based on the application scenario and the estimated signal frequency.

[0138] (2) Combining the parametric unmodulation operator and the Gaussian mixture potential function stochastic resonance model, a method for frequency estimation and enhancement of non-stationary signals is proposed, including the following:

[0139] The original signal is demodulated using a parametric demodulation operator to reduce its frequency. The calculation method is as follows:

[0140] (29)

[0141] The demodulated signal is input into the optimized Gaussian mixture potential function stochastic resonance model, which is expressed as:

[0142] (30)

[0143] According to formula (30) and the theory of stochastic resonance, it can be seen that f ( t )- f d ( t ; P The smaller the value of the demodulation factor, the better the signal enhancement effect of the stochastic resonance model. Similarly, when the energy of the stochastic resonance output signal is strongest, the lower the frequency of the demodulated signal, the closer the frequency of the demodulation factor is to the frequency of the signal. f ( t ) = f d ( t ; P Based on this, the frequency of the signal can be estimated using the random resonance output signal.

[0144] Specifically, with the objective of minimizing the negative value of the random resonance output signal energy, the demodulation operator is solved using an optimization algorithm, expressed as:

[0145] (31)

[0146] in, The energy value of the output signal of the stochastic resonance model. f s Indicates the sampling frequency.

[0147] Finally, the random resonance output signal is inversely demodulated to obtain an enhanced weak non-stationary signal. The calculation method is as follows:

[0148] (32)

[0149] The method described in this embodiment was verified by simulation, specifically as follows:

[0150] A non-stationary simulation signal is constructed with a sampling frequency of 3000 Hz, 1000 sampling points, a signal length of 0.33 s, and a parabolic frequency response curve. Gaussian white noise is added, and the signal-to-noise ratio is -20 dB. Figure 7 As shown in (a) of this embodiment, the method can converge to the theoretical optimal solution, indicating that it works well in a noisy environment; Figure 7 As shown in (b) of this embodiment, the estimated signal frequency by the method basically coincides with the actual signal frequency; as Figure 7 As shown in (c), the target signal is completely submerged by noise. Through the method described in this embodiment, the weak target signal is effectively enhanced and basically matches the target signal.

[0151] Example 2

[0152] One embodiment of the present invention provides a weak non-stationary signal processing system, comprising:

[0153] The signal acquisition module is configured to acquire weak, non-stationary signals to be processed.

[0154] The noise estimation module is configured to: estimate the frequency range of weak, non-stationary signals, and estimate the noise intensity based on the estimated frequency range.

[0155] The potential function optimization module is configured to: construct a stochastic resonance model based on the Gaussian mixture potential function; based on the estimated noise intensity, adaptively optimize the Gaussian mixture potential function with the objective of maximizing the spectral amplification factor of the stochastic resonance model to obtain the optimal stochastic resonance model.

[0156] The signal enhancement module is configured to: construct a parameterized demodulation operator to demodulate the weak non-stationary signal, input the demodulated signal into the optimal stochastic resonance model for enhancement, and finally obtain the enhanced non-stationary signal through inverse demodulation.

[0157] Example 3

[0158] One embodiment of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned weak non-stationary signal processing method.

[0159] Example 4

[0160] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned weak non-stationary signal processing method.

[0161] Example 5

[0162] One embodiment of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a weak non-stationary signal processing method.

[0163] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure one One or more processes and / or boxes Figure one A device that provides the functions specified in one or more boxes.

[0164] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure one One or more processes and / or boxes Figure one The steps of the function specified in one or more boxes.

[0165] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for processing weak non-stationary signals, characterized in that, The method comprises the following steps: acquiring a weak non-stationary signal to be processed; estimating a signal frequency range of the weak non-stationary signal, and estimating noise intensity according to the estimated signal frequency range; constructing a stochastic resonance model based on a Gaussian mixed potential function, and adaptively optimizing the Gaussian mixed potential function according to the estimated noise intensity, so as to maximize a spectral amplification factor of the stochastic resonance model, and obtaining an optimal stochastic resonance model; the construction of the stochastic resonance model based on the Gaussian mixed potential function comprises the following steps: designing an asymmetric five-stable Gaussian mixed potential function, flexibly regulating a potential function form by using multiple parameters, and combining the Gaussian mixed potential function with second-order stochastic resonance, so as to obtain the stochastic resonance model; wherein w i denotes the potential well depth parameter, the asymmetric five-stable Gaussian mixed potential function is designed by using a calculation method as follows: i denotes the potential well width parameter, σ i denotes the potential well position parameter, x is the state variable of the stochastic resonance system, i.e. the output signal of the stochastic resonance model, X 1, X 2 are the end points of the piecewise asymmetrically five-stable Gaussian mixture potential function, is the Gaussian function, k 1, k 2 are the slopes of the potential function at the end points X 1, X 2 respectively; μ wherein, D is the noise intensity, the adaptive optimization of the Gaussian mixed potential function is performed by using a formula as follows: is the spectral amplification factor, η is the damping coefficient, γ is the angular frequency of the signal, Q is the potential function parameter to be optimized in the stochastic resonance model; ω constructing a parameterized demodulation operator to demodulate the weak non-stationary signal, inputting the demodulated signal into the optimal stochastic resonance model for enhancement, and finally obtaining an enhanced non-stationary signal through inverse demodulation; wherein is a parametric demodulation operator, P = [ p ( t 1),…, p ( t K ) denotes a parameter to be optimized, K denotes the order of the Chebyshev interpolation polynomial, is a frequency of the parametric demodulation operator, A is the amplitude of the original signal, n ( t ) is a Gaussian white noise.

2. The method of processing a weak non-stationary signal as claimed in claim 1, wherein, the parameterized demodulation operator is constructed to demodulate the weak non-stationary signal by using a formula as follows: the estimation of the signal frequency range of the weak non-stationary signal comprises the following steps: establishing a frequency modulation signal model containing noise; processing the weak non-stationary signal by using short-time Fourier transform based on the frequency modulation signal model, and generating a time-frequency distribution of the signal; 3. The method of processing a weak non-stationary signal as claimed in claim 1, wherein, identifying a signal frequency range from the generated time-frequency distribution. the estimation of the noise intensity according to the estimated signal frequency range is performed by using a switching noise intensity estimation method, which comprises the following steps: when the signal frequency range is less than a threshold value, estimating the noise intensity by using a synchronous average method; 4. A weakly non-stationary signal processing system characterized by, when the signal frequency range is not less than the threshold value, estimating the noise intensity by using a polynomial residual method. The method comprises the following steps: a signal acquisition module is configured to acquire a weak non-stationary signal to be processed; a noise estimation module is configured to estimate a signal frequency range of the weak non-stationary signal, and estimate noise intensity according to the estimated signal frequency range; a potential function optimization module is configured to construct a stochastic resonance model based on a Gaussian mixed potential function, and adaptively optimize the Gaussian mixed potential function according to the estimated noise intensity, so as to maximize a spectral amplification factor of the stochastic resonance model, and obtain an optimal stochastic resonance model; the construction of the stochastic resonance model based on the Gaussian mixed potential function comprises the following steps: wherein w i represents a potential well depth parameter, designing an asymmetric five-stable Gaussian mixed potential function, flexibly regulating a potential function form by using multiple parameters, and combining the Gaussian mixed potential function with second-order stochastic resonance, so as to obtain the stochastic resonance model; i represents a potential well width parameter, the asymmetric five-stable Gaussian mixed potential function is designed by using a calculation method as follows: i represents a potential well position parameter, x is a state variable of the stochastic resonance system, i.e. the output signal of the stochastic resonance model, X 1, X 2 are end points of the piecewise asymmetrically five-stable Gaussian mixture potential function, is a Gaussian function, k 1, k 2 are slopes of the potential function at the end points X 1, X 2, respectively; σ wherein, D is the noise intensity, μ is the spectral amplification factor, the adaptive optimization of the Gaussian mixed potential function is performed by using a formula as follows: is the damping coefficient, η is the angular frequency of the signal, Q is the potential function parameter to be optimized in the stochastic resonance model; γ ω a signal enhancement module is configured to construct a parameterized demodulation operator to demodulate the weak non-stationary signal, input the demodulated signal into the optimal stochastic resonance model for enhancement, and finally obtain an enhanced non-stationary signal through inverse demodulation; The parameterized demodulation operator is used to demodulate the weak non-stationary signal, and is expressed by a formula as follows: wherein is a parametric demodulation operator, P = [ p ( t 1),…, p ( t K ) denotes a parameter to be optimized, K denotes the order of the Chebyshev interpolation polynomial, is a frequency of the parametric demodulation operator, A is the amplitude of the original signal, n ( t ) is a Gaussian white noise.

5. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the weak non-stationary signal processing method in any one of claims 1-3.

6. A non-transitory computer-readable storage medium, comprising, The non-transitory computer readable storage medium is used to store computer instructions, and the computer instructions are executed by the processor to implement the weak non-stationary signal processing method in any one of claims 1-3.

7. An electronic device, comprising: Comprise: A processor, a memory and a computer program; wherein the processor is connected with the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the weak non-stationary signal processing method in any one of claims 1-3.

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