A signal detection and extraction method based on a four-dimensional single-potential well-like stochastic resonance system
By constructing a four-dimensional single-potential-well stochastic resonance system and combining Gaussian smoothing and particle swarm optimization algorithms, the problems of high threshold, large output deformation, and low dimension in the double-potential-well system are solved, achieving effective signal extraction and amplification, and making the output signal closer to the characteristic signal.
Patent Information
- Application Number
- CN202310374642.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-10
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2043-04-10
AI Technical Summary
Existing dual-potential-well stochastic resonance systems suffer from problems such as high threshold, large output signal deformation, low dimension, and difficulty in output adjustment when detecting weak signals, making it difficult to effectively extract and amplify feature signals.
A four-dimensional single-potential-well stochastic resonance system is constructed. By combining Gaussian smoothing and particle swarm optimization, the system parameters are optimized through time-domain and frequency-domain signal-to-noise ratio calculations to extract and amplify feature signals.
This approach achieves a greater similarity between the output signal and the characteristic signal waveform and amplitude, while also reducing noise, thus improving signal extraction performance.
Smart Images
Figure CN117454079B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing, specifically providing a signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system. Background Technology
[0002] The detection and extraction of weak feature signals in strong noise environments involves disciplines such as signal processing, electronics, and mechanics. How to extract useful feature signals or detect weak signals from strong noise backgrounds is a problem that needs to be solved in many engineering applications. Traditional signal processing methods separate signal denoising and amplification, which is a cumbersome process and may weaken the feature signals. Weak signal detection methods based on stochastic resonance can utilize noise energy transfer mechanisms to extract and identify weak feature signals submerged in strong noise.
[0003] The theory of weak signal detection based on double-well stochastic resonance is becoming increasingly mature, but it suffers from drawbacks such as high potential barriers and susceptibility to output saturation. Classical double-well stochastic resonance systems can remove some noise from the input signal, but the waveform of the output signal still exhibits significant distortion compared to the characteristic signal. When the amplitude of the input signal exceeds the threshold of the double-well stochastic resonance system, the system's transitions affect the waveform of the output signal; conversely, when the amplitude of the input signal is less than the threshold, the system's output will deviate significantly. In contrast to double-well systems, single-well stochastic resonance systems have only one potential well and do not produce transitions. Therefore, while reducing noise and amplifying weak signals, the waveform of the output signal is also similar to the characteristic signal.
[0004] Low-dimensional stochastic resonant systems have limited adjustable parameters and signal output dimensions, making it difficult to achieve effective noise reduction and diverse output waveform adjustments. In contrast, multi-dimensional stochastic resonant systems offer greater output adjustment flexibility through parameter tuning and output dimension selection, enabling diverse output capabilities. Summary of the Invention
[0005] Based on the aforementioned background problems, and to address the issues of low dimensionality, high threshold for stochastic resonance effects, and easy deformation of the system output in classical stochastic resonance systems, this invention constructs a four-dimensional single-potential-well stochastic resonance system and provides a signal detection and extraction method based on this system. The constructed four-dimensional single-potential-well stochastic resonance system has only one potential well, thus avoiding transitions and threshold phenomena. While reducing noise and amplifying weak signals, the waveform of the output signal closely resembles the characteristic signal. Furthermore, the system has multiple dimensions, each with its own function, enabling simultaneous output of four-dimensional signals. Gaussian smoothing is applied to the system output signal for smoothing filtering. Based on the waveform or frequency of the characteristic signal, two different signal-to-noise ratio (SNR) calculation methods—time-domain and frequency-domain—are used. A particle swarm optimization algorithm is employed, with SNR as the objective function, to optimize the parameters of the four-dimensional single-potential-well stochastic resonance system, outputting a signal with the optimal SNR under the optimal parameters.
[0006] The specific technical solution of this invention is as follows:
[0007] A signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system is proposed. Its main feature is the construction of a multifunctional four-dimensional single-potential-well stochastic resonance system, the expression of which is:
[0008] (1)
[0009] in For system state variables, For system parameters, , For input signal, It is a characteristic signal. It is a noise signal, and the whole system constitutes a monostable stochastic resonance system. Regardless of the input value, the system's motion always tends towards a unique equilibrium point, and when the system is at the equilibrium point, there is always... The relationship between the state variables can be obtained. (2) and the system equilibrium equation (3), thus the relationship between the input S(t) and the y-dimensional expression can be obtained. (4). From the relationship between the state variables (2) and (4), we can obtain the relationship between the input S(t) and the x dimension. (5) The relationship between input S(t) and z-dimensional expression (6) The relationship between input S(t) and w-dimensional expression (7).
[0010] Each dimension of the constructed four-dimensional single-potential-well stochastic resonance system has its own function. From equations (2) to (7), we can see that the y-dimensional of the system is the input dimension of the input signal and also the output dimension of the initial processing of the input signal; the x-dimensional can amplify or reduce the y-dimensional signal and output it; the z-dimensional can square the y-dimensional signal and output it; the w-dimensional can restore the y-dimensional signal and output a signal with a waveform and amplitude similar to the characteristic signal on the basis of noise reduction.
[0011] A signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system is characterized by the fact that the system's w-dimensional output signal can more closely approximate the waveform of the characteristic signal after noise reduction, making it suitable for extracting and restoring the waveform of the characteristic signal. The specific process for characteristic signal extraction and restoration is as follows:
[0012] S1. Discretize the four-dimensional single-potential-well-like stochastic resonance system using the fourth-order Runge-Kutta method, and set the initial parameters of the system as follows. .
[0013] S2. Input signal S(t) is input into a four-dimensional single-potential-well stochastic resonance system through the y-dimensional input, and outputs x-dimensional, y-dimensional, z-dimensional, and w-dimensional signals.
[0014] S3. Perform Gaussian smoothing on the four-dimensional output signal in step S2, and output the processed x-dimensional output signal x(t), y-dimensional output signal y(t), z-dimensional output signal z(t), and w-dimensional output signal w(t).
[0015] S4. Time-domain signal-to-noise ratio of the w-dimensional output signal w(t) For the objective function, adjust parameters a and b, repeat steps S2 and S3, and apply the particle swarm optimization algorithm within the parameter range. The algorithm searches for the optimal parameters a and b. After the optimization is complete, it outputs the optimal parameters a and b. For the corresponding characteristic signal, The length of the input / output signal data.
[0016] S5. Substitute the optimal parameter values of a and b into the system, and after steps S2 and S3, output the time-domain signal-to-noise ratio under the optimal parameters. Optimal signal .
[0017] A signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system is characterized by the fact that the x-dimensional output signal of the system can amplify the spectral amplitude of the feature signal while reducing noise, making it suitable for detecting the presence of feature signals in the input signal. The specific process for feature signal detection is as follows:
[0018] T1. Discretize the four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta method, and set the initial parameters of the system as follows. .
[0019] T2. Input the input signal through the y-dimensional input to the four-dimensional single potential well-like stochastic resonance system, and output x-dimensional, y-dimensional, z-dimensional, and w-dimensional signals.
[0020] T3. Perform Gaussian smoothing on the four-dimensional output signal in step T2, and output the processed x-dimensional output signal x(t), y-dimensional output signal y(t), z-dimensional output signal z(t), and w-dimensional output signal w(t).
[0021] T4, Frequency domain signal-to-noise ratio of the x-dimensional output signal x(t) For the objective function, adjust parameters a and b, repeat steps T2 and T3, and apply the particle swarm optimization algorithm within the parameter range. The algorithm searches for the optimal parameters of a and b. After the optimization is complete, it outputs the optimal parameters of a and b. The frequency of the characteristic signal, For the corresponding characteristic frequency Spectral amplitude, For spectral amplitude, The length of the input signal.
[0022] T5. Substitute the optimal parameter values of a and b into the system, and after steps T2 and T3, output the frequency domain signal-to-noise ratio under the optimal parameters. Optimal signal .
[0023] The specific steps for discretizing the four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta solution method in steps S1 and T1 are as follows:
[0024] 1-1) Solving the equations of a four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta method yields the following expression for the solution:
[0025] 1-2) Obtain the expressions for each recursive parameter: , , , .
[0026] The discrete system formed by the expressions in steps 1-1) and 1-2) is a discretized four-dimensional single potential well stochastic resonance system with an iteration step size h=0.001.
[0027] The Gaussian smoothing processing of the system's four-dimensional output signal in steps S3 and T3 refers to processing the signal data using a Gaussian weighted moving average filter. Specifically, the operation is as follows:
[0028] 2-1) Use a window of length N=35 to scan each data in the signal.
[0029] 2-2) Replace the value of the center data in the window with the weighted average of the data within its neighborhood. The weighting coefficients are a one-dimensional Gaussian distribution function. ,in The distance between the data point and the center data point. denoted as the standard deviation of the Gaussian distribution.
[0030] Each data point of the processed signal is obtained by Gaussian weighted averaging of itself and other data within the window, thus achieving the effect of smoothing the signal.
[0031] The specific steps for finding the optimal parameters of a and b using the particle swarm optimization algorithm in steps S4 and T4 are as follows:
[0032] 3-1) Set the number of particles in the population to m=10, the maximum number of iterations to K=50, the position constraints of parameters a and b to [1,5] and [0,5] respectively, the particle velocity constraint to [1,5], and the inertia weight. Individual learning factor Group learning factor .
[0033] 3-2) Initialize the iteration count k=0, randomly initialize the particle velocity and particle position within the range of position and velocity constraints, and calculate the objective function (time domain signal-to-noise ratio) for parameters a and b corresponding to each particle position. or frequency domain signal-to-noise ratio (to find the best individual position and the best group position).
[0034] 3-3) Through the individual's optimal position and the best position of the group Update the particle's velocity and position, i.e. , in, ; k is the current iteration number; The velocity of the particle; The position of the particle; It is a random number within the interval [0,1].
[0035] 3-4) Calculate the objective function (time-domain signal-to-noise ratio) for individuals and groups. or frequency domain signal-to-noise ratio Update the best individual position and the best group position, and increment k by 1 for each iteration.
[0036] 3-5) Repeat steps 3-3) and 3-4). When the number of iterations k equals the maximum number of iterations k, stop the optimization, obtain the best group position at this time, and output the optimal parameters corresponding to a and b.
[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0038] The four-dimensional single-potential-well stochastic resonance system constructed in this invention has only one potential well, which does not produce transition motion or threshold phenomenon, and can directly process signals with extremely low amplitude.
[0039] The system has multiple dimensions, each with its own function, and can simultaneously output four-dimensional processed signals. The y-dimensional dimension is the input dimension of the input signal and also the initial processing output dimension of the input signal; the x-dimensional dimension can amplify the y-dimensional signal and output it; the z-dimensional dimension can square the y-dimensional signal and output it; the w-dimensional dimension can output a signal with amplitude and waveform similar to the characteristic signal after noise reduction.
[0040] Based on the processing of the four-dimensional single-potential-well stochastic resonance system, Gaussian smoothing is applied to the output signals of each dimension of the system, and the particle swarm optimization algorithm is used to optimize the system parameters according to the signal-to-noise ratio, which further improves the signal-to-noise ratio of the system output signal and enhances the signal extraction effect. Attached Figure Description
[0041] Figure 1 This is a flowchart of a signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system.
[0042] Figure 2 These are the time-domain plots of the characteristic signal m(t) as a sinusoidal signal and the time-domain plots of the input signal S(t) after adding noise.
[0043] Figure 3 yes Figure 2 The time-domain diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) is processed by the system under optimal parameters.
[0044] Figure 4 yes Figure 3 The output time-domain plots of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing.
[0045] Figure 5 yes Figures 2 to 4 A comparison of the time-domain signal-to-noise ratio of the sinusoidal output signal at each stage.
[0046] Figure 6 These are the time-domain plots of the characteristic signal m(t) as an amplitude-modulated signal and the time-domain plots of the input signal S(t) after adding noise.
[0047] Figure 7 yes Figure 6 The time-domain diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) is processed by the system under optimal parameters.
[0048] Figure 8 yes Figure 7 The output time-domain plots of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing.
[0049] Figure 9 yes Figures 6 to 8 A comparison of the time-domain signal-to-noise ratio of the amplitude-modulated output signal at each stage.
[0050] Figure 10 These are the time-domain plots of the characteristic signal m(t) as a superimposed signal and the time-domain plots of the input signal S(t) after adding noise.
[0051] Figure 11 yes Figure 10 The time-domain diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) is processed by the system under optimal parameters.
[0052] Figure 12 yes Figure 11 The output time-domain plots of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing.
[0053] Figure 13 yes Figures 10 to 12 A comparison of the time-domain signal-to-noise ratio of the superimposed output signals at each stage.
[0054] Figure 14 These are the time-domain plots of the characteristic signal m(t) as a class-coded signal and the time-domain plots of the input signal S(t) after adding noise.
[0055] Figure 15 yes Figure 14 The time-domain diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) is processed by the system under optimal parameters.
[0056] Figure 16 yes Figure 15 The output time-domain plots of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing.
[0057] Figure 17 yes Figures 14 to 16 A comparison of the time-domain signal-to-noise ratio of the output signals at each stage.
[0058] Figure 18 These are the time-domain plot and spectrum of the input signal S(t) as the bearing vibration signal.
[0059] Figure 19 yes Figure 18 The spectrum diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) is processed by the system with optimal parameters.
[0060] Figure 20 yes Figure 19 The spectrum of the output signal after Gaussian smoothing of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals. Detailed Implementation
[0061] The technical solution of the present invention will be further described below with reference to the accompanying drawings and actual experiments.
[0062] Figure 1 Here is a flowchart of a signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system, including the following steps:
[0063] Step 1: Determine if the time domain of the characteristic signal m(t) in the input signal S(t) is known. If known, select the time domain signal-to-noise ratio of the output signal w(t) in w dimensions. Given the objective function, the Particle Swarm Optimization (PSO) algorithm is applied within the parameter range. Find the optimal parameters for a and b within the context. For the corresponding characteristic signal, This represents the data length of the input and output signals. If unknown, the frequency domain signal-to-noise ratio of the x-dimensional output signal x(t) is chosen. Given the objective function, the Particle Swarm Optimization (PSO) algorithm is applied within the parameter range. Find the optimal parameters for a and b within the context. The frequency of the characteristic signal, For the corresponding characteristic frequency Spectral amplitude, For spectral amplitude, The length of the input / output signal data.
[0064] Step 2: Discretize the four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta solution method, and set the initial parameters of the system to a=2 and b=1.
[0065] Step 3: The system will process the input signal with initial parameters for the first time, and then update the system parameters according to the particle swarm optimization algorithm. The input signal will be input into the four-dimensional single potential well stochastic resonance system through the y-dimensional input, and the output signals will be x-dimensional, y-dimensional, z-dimensional, and w-dimensional signals.
[0066] Step 4: Perform Gaussian smoothing on the four-dimensional output signals of the system, and output the processed x-dimensional output signal x(t), y-dimensional output signal y(t), z-dimensional output signal z(t), and w-dimensional output signal w(t).
[0067] Step 5: After the particle swarm optimization algorithm finishes its optimization process, substitute the optimal parameters of a and b into the system and output the signal with the best frequency domain signal-to-noise ratio or the signal with the best time domain signal-to-noise ratio under the optimal parameters.
[0068] The specific steps for discretizing the four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta solution method in step 2 are as follows:
[0069] 1-1) Solving the equations of a four-dimensional single-potential-well stochastic resonance system using the fourth-order Runge-Kutta method yields the following expression for the solution:
[0070] 1-2) Obtain the expressions for each recursive parameter: , , , .
[0071] The discrete system formed by the expressions in steps 1-1) and 1-2) is a discretized four-dimensional single potential well stochastic resonance system with an iteration step size h=0.001.
[0072] Step 4, Gaussian smoothing of the system's four-dimensional output signal, refers to processing the signal data using a Gaussian-weighted moving average filter. The specific operation is as follows:
[0073] 2-1) Use a window of length N=35 to scan each data in the signal.
[0074] 2-2) Replace the value of the center data in the window with the weighted average of the data within its neighborhood. The weighting coefficients are a one-dimensional Gaussian distribution function. ,in The distance between the data point and the center data point. denoted as the standard deviation of the Gaussian distribution.
[0075] Each data point of the processed signal is obtained by Gaussian weighted averaging of itself and other data within the window, thus achieving the effect of smoothing the signal.
[0076] The specific steps for finding the optimal parameters of a and b using the particle swarm optimization algorithm in step 5 are as follows:
[0077] 3-1) Set the number of particles in the population to m=10, the maximum number of iterations to K=50, the position constraints of parameters a and b to [1,5] and [0,5] respectively, the particle velocity constraint to [1,5], and the inertia weight. Individual learning factor Group learning factor .
[0078] 3-2) Initialize the iteration count k=0, randomly initialize the particle velocity and particle position within the range of position and velocity constraints, and calculate the objective function (time domain signal-to-noise ratio) for parameters a and b corresponding to each particle position. or frequency domain signal-to-noise ratio (to find the best individual position and the best group position).
[0079] 3-3) Through the individual's optimal position and the best position of the group Update the particle's velocity and position, i.e. , in, ; k is the current iteration number; The velocity of the particle; The position of the particle; It is a random number within the interval [0,1].
[0080] 3-4) Calculate the objective function (time-domain signal-to-noise ratio) for individuals and groups. or frequency domain signal-to-noise ratio Update the best individual position and the best group position, and increment k by 1 for each iteration.
[0081] 3-5) Repeat steps 3-3) and 3-4). When the number of iterations k equals the maximum number of iterations k, stop the optimization, obtain the best group position at this time, and output the optimal parameters corresponding to a and b.
[0082] Let the input signal ,in It is a characteristic signal. , It is a white noise signal with a mean of 0 and a variance of 1. Let the noise amplitude be... .
[0083] like Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, Figure 2 The characteristic signal m(t) is a sinusoidal signal. The time-domain plot of the input signal S(t) after adding noise and the time-domain plot of the input signal S(t) are derived from... Figure 2 It can be seen that the characteristic signal waveform is completely masked by noise. Figure 3 This is a time-domain graph of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) has been processed by a four-dimensional single-potential-well stochastic resonance system with optimal parameters. Figure 3It can be seen that after system processing, the y-dimensional output signal has removed most of the noise in the input signal. The x-dimensional output signal further amplifies the signal amplitude based on the y-dimensional processing, and the w-dimensional output signal is restored based on the y-dimensional processing, making it closer to the characteristic signal amplitude and waveform. Figure 4 The figures show the time-domain outputs of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing. As can be seen from the figures, the smoothing process further removes noise, making the output signal waveform closer to the characteristic signal. In particular, the w-dimensional output signal is similar to the characteristic signal in both waveform and amplitude. Figure 5 yes Figures 2 to 4 The graph compares the time-domain signal-to-noise ratio (SNR) of the sinusoidal output signals at each stage, where 1 represents the time-domain SNR of the input signal, 2 represents the time-domain SNR of the x-dimensional output signal, 3 represents the time-domain SNR of the x-dimensional output signal after smoothing, 4 represents the time-domain SNR of the y-dimensional output signal, 5 represents the time-domain SNR of the y-dimensional output signal after smoothing, 6 represents the time-domain SNR of the z-dimensional output signal, 7 represents the time-domain SNR of the z-dimensional output signal after smoothing, 8 represents the time-domain SNR of the w-dimensional output signal, and 9 represents the time-domain SNR of the w-dimensional output signal after smoothing. Figure 5 It can be seen that the time-domain signal-to-noise ratio of the w-dimensional output signal after smoothing is the highest.
[0084] like Figure 6 , Figure 7 , Figure 8 and Figure 9 As shown, Figure 6 The characteristic signal m(t) is an amplitude-modulated signal. The time-domain plot of the input signal S(t) after adding noise and the time-domain plot of the input signal S(t) are derived from... Figure 6 It can be seen that the characteristic signal waveform is completely masked by noise. Figure 7 This is a time-domain graph of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) has been processed by a four-dimensional single-potential-well stochastic resonance system with optimal parameters. Figure 7 It can be seen that after system processing, the y-dimensional output signal has removed most of the noise in the input signal. The x-dimensional output signal further amplifies the signal amplitude based on the y-dimensional processing, and the w-dimensional output signal is restored based on the y-dimensional processing, making it closer to the characteristic signal amplitude and waveform. Figure 8 The figures show the time-domain outputs of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing. As can be seen from the figures, the smoothing process further removes noise, making the output signal waveform closer to the characteristic signal. In particular, the w-dimensional output signal is similar to the characteristic signal in both waveform and amplitude. Figure 9 yes Figures 6 to 8The graph compares the time-domain signal-to-noise ratio (SNR) of the amplitude-modulated (AM) signals at each stage of the output signal. Here, 1 represents the time-domain SNR of the input signal, 2 represents the time-domain SNR of the x-dimensional output signal, 3 represents the time-domain SNR of the x-dimensional output signal after smoothing, 4 represents the time-domain SNR of the y-dimensional output signal, 5 represents the time-domain SNR of the y-dimensional output signal after smoothing, 6 represents the time-domain SNR of the z-dimensional output signal, 7 represents the time-domain SNR of the z-dimensional output signal after smoothing, 8 represents the time-domain SNR of the w-dimensional output signal, and 9 represents the time-domain SNR of the w-dimensional output signal after smoothing. Figure 9 It can be seen that the time-domain signal-to-noise ratio of the w-dimensional output signal after smoothing is the highest.
[0085] like Figure 10 , Figure 11 , Figure 12 and Figure 13 As shown, Figure 10 The characteristic signal m(t) is a superimposed signal. The time-domain plot of the input signal S(t) after adding noise and the time-domain plot of the input signal S(t) are derived from... Figure 6 It can be seen that the characteristic signal waveform is completely masked by noise. Figure 11 This is a time-domain graph of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) has been processed by a four-dimensional single-potential-well stochastic resonance system with optimal parameters. Figure 11 It can be seen that after system processing, the y-dimensional output signal has removed most of the noise in the input signal. The x-dimensional output signal further amplifies the signal amplitude based on the y-dimensional processing, and the w-dimensional output signal is restored based on the y-dimensional processing, making it closer to the characteristic signal amplitude and waveform. Figure 12 The figures show the time-domain outputs of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing. As can be seen from the figures, the smoothing process further removes noise, making the output signal waveform closer to the characteristic signal. In particular, the w-dimensional output signal is similar to the characteristic signal in both waveform and amplitude. Figure 13 yes Figures 10 to 12 The graph compares the time-domain signal-to-noise ratio (SNR) of the amplitude-modulated (AM) signals at each stage of the output signal. Here, 1 represents the time-domain SNR of the input signal, 2 represents the time-domain SNR of the x-dimensional output signal, 3 represents the time-domain SNR of the x-dimensional output signal after smoothing, 4 represents the time-domain SNR of the y-dimensional output signal, 5 represents the time-domain SNR of the y-dimensional output signal after smoothing, 6 represents the time-domain SNR of the z-dimensional output signal, 7 represents the time-domain SNR of the z-dimensional output signal after smoothing, 8 represents the time-domain SNR of the w-dimensional output signal, and 9 represents the time-domain SNR of the w-dimensional output signal after smoothing. Figure 13 It can be seen that the time-domain signal-to-noise ratio of the w-dimensional output signal after smoothing is the highest.
[0086] like Figure 14 , Figure 15 , Figure 16 and Figure 17 As shown, Figure 14 The characteristic signal m(t) is a class-coded signal (amplitude). The time-domain plot of the input signal S(t) and the time-domain plot of the input signal S(t) after adding noise are obtained from... Figure 14 It can be seen that the characteristic signal waveform is completely masked by noise. Figure 15 This is a time-domain graph of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal S(t) has been processed by a four-dimensional single-potential-well stochastic resonance system with optimal parameters. Figure 15 It can be seen that after system processing, the y-dimensional output signal has removed most of the noise in the input signal. The x-dimensional output signal further amplifies the signal amplitude based on the y-dimensional processing, and the w-dimensional output signal is restored based on the y-dimensional processing, making it closer to the characteristic signal amplitude and waveform. Figure 16 The figures show the time-domain outputs of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after Gaussian smoothing. As can be seen from the figures, the smoothing process further removes noise, making the output signal waveform closer to the characteristic signal. In particular, the w-dimensional output signal is similar to the characteristic signal in both waveform and amplitude. Figure 17 yes Figures 14 to 16 The graph compares the time-domain signal-to-noise ratio (SNR) of the amplitude-modulated (AM) signals at each stage of the output signal. Here, 1 represents the time-domain SNR of the input signal, 2 represents the time-domain SNR of the x-dimensional output signal, 3 represents the time-domain SNR of the x-dimensional output signal after smoothing, 4 represents the time-domain SNR of the y-dimensional output signal, 5 represents the time-domain SNR of the y-dimensional output signal after smoothing, 6 represents the time-domain SNR of the z-dimensional output signal, 7 represents the time-domain SNR of the z-dimensional output signal after smoothing, 8 represents the time-domain SNR of the w-dimensional output signal, and 9 represents the time-domain SNR of the w-dimensional output signal after smoothing. Figure 17 It can be seen that the time-domain signal-to-noise ratio of the w-dimensional output signal after smoothing is the highest.
[0087] like Figure 18 , Figure 19 and Figure 20 As shown, Figure 18 The input signal S(t) is the time-domain plot and spectrum of the bearing vibration signal. The bearing vibration signal used comes from the bearing data center of Case Western Reserve University (CWRU), labeled IR007_0, and contains a fault signal characteristic frequency of 161.699Hz. Figure 19 yes Figure 18 The spectrum diagrams of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals after the input signal is processed by a four-dimensional single-potential-well stochastic resonance system. Figure 18 It can be seen that the spectral amplitude of the fault signal characteristic frequency of 161.699Hz in the bearing vibration signal is 0.0146. The fault signal is masked by signals of other frequencies and is not well represented in the overall spectrum. Figure 19It can be seen that after the bearing vibration signal is processed by the four-dimensional single potential well type random resonance system, the spectral amplitude of the fault signal characteristic frequency 161.699Hz in the output signal is significantly higher than that of other frequencies. In particular, the spectral amplitude of the characteristic frequency 161.699Hz in the x-dimensional output signal is 0.0969, which is significantly improved compared with the spectral amplitude of the characteristic frequency of the input signal before processing, which is 0.0146. Figure 20 They are Figure 19 The spectrum of the output signal after Gaussian smoothing of the x-dimensional, y-dimensional, z-dimensional, and w-dimensional output signals. The smoothing process further removes noise in the high-frequency part of the signal.
Claims
1. A signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system, characterized in that, A multifunctional four-dimensional single-potential-well stochastic resonance system was constructed. The system expression is as follows: （1）， in For system state variables, For system parameters, , For input signal, It is a characteristic signal. It is a noise signal, and the whole system constitutes a monostable stochastic resonance system; regardless of the input value, the system's motion always tends to a unique equilibrium point, and when the system is at the equilibrium point, there is always... The relationship between the state variables can be obtained. (2) and the system equilibrium equation (3), thus the relationship between the input S(t) and the y-dimensional expression can be obtained. (4); From the relationship between the state variables (2) and (4), we can obtain the relationship between the input S(t) and the x dimension. (5) The relationship between input S(t) and z-dimensional expression (6) The relationship between input S(t) and w-dimensional expression (7); Each dimension of the constructed four-dimensional single-potential-well stochastic resonance system has its own function. From equations (2) to (7), we can see that the y-dimensional of the system is the input dimension of the input signal and also the output dimension of the initial processing of the input signal; the x-dimensional can amplify or reduce the y-dimensional signal and output it; the z-dimensional can square the y-dimensional signal and output it; the w-dimensional can restore the y-dimensional signal and output a signal with waveform and amplitude similar to the characteristic signal on the basis of noise reduction. The system's w-dimensional output signal can more closely approximate the waveform of the feature signal after noise reduction, making it suitable for extracting and restoring the waveform of the feature signal. The specific process for feature signal extraction and restoration is as follows: S1. Discretize the four-dimensional single-potential-well-like stochastic resonance system using the fourth-order Runge-Kutta method, and set the initial parameters of the system as follows. ; S2. Input signal S(t) is input into a four-dimensional single-potential-well stochastic resonance system through the y-dimensional input, and outputs x-dimensional, y-dimensional, z-dimensional, and w-dimensional signals; S3. Perform Gaussian smoothing on the four-dimensional output signal in step S2, and output the processed x-dimensional output signal x(t), y-dimensional output signal y(t), z-dimensional output signal z(t), and w-dimensional output signal w(t). S4. Time-domain signal-to-noise ratio of the w-dimensional output signal w(t) For the objective function, adjust parameters a and b, repeat steps S2 and S3, and apply the particle swarm optimization algorithm within the parameter range. The algorithm searches for the optimal parameters a and b. After the optimization is complete, it outputs the optimal parameters a and b. For the corresponding characteristic signal, The data length of the input and output signals; S5. Substitute the optimal parameter values of a and b into the system, and after steps S2 and S3, output the time-domain signal-to-noise ratio under the optimal parameters. Optimal signal .
2. A signal detection and extraction method based on a four-dimensional single-potential-well stochastic resonance system according to claim 1, characterized in that, The system's x-dimensional output signal can amplify the spectral amplitude of the feature signal while reducing noise, making it suitable for detecting the presence of feature signals in the input signal. The specific process for feature signal detection is as follows: T1. Discretize the four-dimensional single-potential-well-like stochastic resonance system using the fourth-order Runge-Kutta method, and set the initial parameters of the system as follows. ; T2. Input the input signal through the y-dimensional input to the four-dimensional single potential well-like stochastic resonance system, and output x-dimensional, y-dimensional, z-dimensional, and w-dimensional signals; T3. Perform Gaussian smoothing on the four-dimensional output signal in step T2, and output the processed x-dimensional output signal x(t), y-dimensional output signal y(t), z-dimensional output signal z(t), and w-dimensional output signal w(t). T4, Frequency domain signal-to-noise ratio of the x-dimensional output signal x(t) For the objective function, adjust parameters a and b, repeat steps T2 and T3, and apply the particle swarm optimization algorithm within the parameter range. The algorithm searches for the optimal parameters of a and b. After the optimization is complete, it outputs the optimal parameters of a and b. The frequency of the characteristic signal, For the corresponding characteristic frequency Spectral amplitude, For spectral amplitude, The length of the input signal; T5. Substitute the optimal parameter values of a and b into the system, and after steps T2 and T3, output the frequency domain signal-to-noise ratio under the optimal parameters. Optimal signal .