A feedforward cascade stochastic resonance weak signal enhancement method
By constructing a feedforward cascaded stochastic resonance system and utilizing signal superposition and phase alignment techniques, the problem of poor signal enhancement in the cascaded stochastic resonance system was solved, achieving a steady improvement in the signal-to-noise ratio and effective signal enhancement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-06-15
- Publication Date
- 2026-06-26
AI Technical Summary
Existing cascaded stochastic resonance systems rely on the effect of the first-stage stochastic resonance, with target information decreasing layer by layer. Furthermore, phase alignment is not performed during superposition, resulting in poor signal enhancement.
By constructing a feedforward cascaded stochastic resonance system, the output of the stochastic resonance system is continuously and reasonably superimposed with the original signal to be enhanced, and phase alignment and weighting are performed to improve the signal-to-noise ratio step by step. The optimal system parameters are found by using genetic algorithms until the set maximum number of cascaded layers or signal-to-noise ratio gain requirement is reached.
It effectively improves the robustness of cascaded stochastic resonance and the ability to process low signal-to-noise ratio signals, with a signal-to-noise ratio gain of up to 8dB. It can handle weak signals with a signal-to-noise ratio as low as -30dB, and significantly improves the signal enhancement effect.
Smart Images
Figure CN116805866B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing, and in particular to a method for enhancing weak resonant signals. Background Technology
[0002] Long-range, high-precision sensing of small underwater targets is fundamental to building a maritime power and is crucial for gaining information initiative. However, with the continuous improvement of vibration and noise reduction technologies for underwater targets such as ships, the level of their radiated noise sources is constantly decreasing, making the research of novel weak signal enhancement methods essential.
[0003] Stochastic resonance is a novel nonlinear signal processing technique that effectively enhances weak signals by matching the nonlinear system, signal, and noise. It abandons the traditional notion that noise is harmful, instead utilizing noise energy to amplify weak signals. Compared to traditional filtering methods, stochastic resonance weak signal processing offers numerous advantages, such as the ability to handle signals with lower signal-to-noise ratios and the capacity to enhance weak signals even when noise and signal frequency bands overlap.
[0004] Cascaded stochastic resonance achieves superior signal enhancement compared to a single stochastic resonance system. However, it suffers from drawbacks such as dependence on the first-stage stochastic resonance effect and a gradual decrease in target information across stages. If the first stage lacks effective stochastic resonance, subsequent stages cannot effectively recover the target signal. Therefore, patent CN114239273A proposes a four-stage cross-stage cascaded stochastic resonance method. This method employs frequency normalization to input the outputs of all preceding stochastic resonance stages into the next stage system, achieving better results than traditional cascaded stochastic resonance. However, this method lacks phase alignment during superposition and employs a search-by-stage approach for the superposition coefficients, which can easily lead to local optima and fail to fully utilize the performance of cascaded stochastic resonance.
[0005] In summary, cascaded stochastic resonance systems have better performance than single stochastic resonance systems. However, existing cascaded stochastic resonance systems still have many imperfections, so it is necessary to conduct in-depth research on cascaded stochastic resonance. Summary of the Invention
[0006] To overcome the shortcomings of existing technologies, this invention provides a method for enhancing weak signals through a feedforward cascaded stochastic resonance system. This invention utilizes the continuous and reasonable superposition of the output of the stochastic resonance system with the original signal to be enhanced to input information to each stage of the stochastic resonance system, thereby continuously and stably improving the signal-to-noise ratio through the stochastic resonance system and achieving the purpose of effectively enhancing weak signals.
[0007] The technical solution adopted by this invention to solve its technical problem includes the following steps:
[0008] Step 1: Obtain the weak signal sn(t) that needs to be enhanced;
[0009] Step 2, construct a feedforward cascaded stochastic resonance system:
[0010]
[0011] Where x1 is the output of the first-order stochastic resonance system, x i Let sn(t) be the output of the i-th level stochastic resonance system, t be time, and sn(t) be the weak input signal to be enhanced. i-1 x i-1 (t) is the signal input to the i-th level stochastic resonance after weighting the output of the (i-1)th level stochastic resonance and superimposing it with the weak signal to be enhanced; n is the maximum number of cascaded layers set; and U(x) is the system potential function.
[0012] Step 3: Input the weak signal sn(t) to be enhanced into the first-order stochastic resonance system to find the optimal system parameters and the optimal output x. opt , and save;
[0013] Step 4, for the obtained x opt Phase alignment with the signal to be enhanced, sn(t);
[0014] Step 5, weighted summation, applying the weighted summation to the X obtained in Step 4. opt Multiply (ω) by the weight ω obtained from formula (2) to get the weighted signal ωX. opt (ω), and superimposed with SN(ω) to obtain ωX opt (ω)+SN(ω);
[0015] Step 6, for the ωX obtained in step 5 opt Performing an inverse Fourier transform on (ω)+SN(ω) yields the input signal x for the next level of stochastic resonance. input (t);
[0016] Step 7, take the x obtained in step 6 input (t) is input into the next stage of the stochastic resonance system, and the same parameter optimization process as in step 3 is performed to obtain the optimal output x. opt ;
[0017] Step 8: Repeat steps 4 to 7, saving the optimal output of each stage of the stochastic resonance system until the set maximum number of cascaded layers N is reached or other set stopping conditions are met.
[0018] Step 9: Select the signal corresponding to the optimal metric index from the optimal output of each stage of the stochastic resonance system as the final output of the feedforward cascaded stochastic resonance.
[0019] The system potential function U(x) is the potential function of various stochastic resonance systems.
[0020] The weight ω i-1 Let ω be a variable that gradually increases with the number of cascaded layers i. As a preferred value, ω i-1 Set as:
[0021] ω i-1 =k*m i-p (2)
[0022] Among them, k adjusts the final size of the weight coefficient, m determines the trend of weight change, and p adjusts the timing of the weight change trend.
[0023] Preferably, k = 0.1, m = 1.2, and p = 2;
[0024] In step 3, the method for finding the optimal system parameters is either traversal optimization or various intelligent algorithms, including genetic algorithm optimization, particle swarm optimization algorithm, and simulated annealing algorithm, which does not affect the performance of the proposed method.
[0025] In step 3, the parameter optimization metric can be selected from the following: signal-to-noise ratio, cross-correlation coefficient, zero-crossing rate, and spectral warp.
[0026] The phase alignment process involves performing the following two steps sequentially:
[0027] 4.1: Perform a Fourier transform on the weak signal sn(t) to be enhanced, and take the modulus and phase of the Fourier transform result to obtain SN(ω) and save it.
[0028] 4.2: For the optimal output x opt Perform a Fourier transform, and then take the modulus and phase of the Fourier transform result to obtain X. opt (ω).
[0029] The phase alignment in step 4 and the superposition in step 5 are frequency domain phase alignment, but time domain phase alignment has the same effect as frequency domain phase alignment.
[0030] The optimal measurement index is as follows: when the measurement index is signal-to-noise ratio (SNR), the maximum SNR is optimal; when the measurement index is entropy, the minimum entropy is optimal.
[0031] The beneficial effects of this invention lie in its utilization of noise energy to enhance weak signals. Through feedforward of the original noisy signal and a reasonable weighted cascading method, the signal-to-noise ratio (SNR) is steadily improved. This solves the problems of dependence on the first-stage random resonance and the gradual decrease in target information in cascaded random resonance, effectively enhancing the robustness of cascaded random resonance and its ability to process low SNR signals. Compared with traditional cascaded random resonance, the feedforward cascaded random resonance can improve the SNR gain by up to 8 dB, and can handle a minimum SNR as low as -30 dB, showing broad application prospects in the field of weak signal processing. Attached Figure Description
[0032] Figure 1 This is a schematic diagram of the principle of the present invention.
[0033] Figure 2 This is a flowchart of an example program of the present invention.
[0034] Figure 3 This is a flowchart of a stochastic resonance parameter optimization procedure based on a genetic algorithm.
[0035] Figure 4 These are the time-domain and frequency-domain plots of the weak signal to be enhanced. Figure 4 (a) is the time-domain plot of the weak signal to be enhanced. Figure 4 (b) is the frequency domain diagram of the weak signal to be enhanced.
[0036] Figure 5 These are the time-domain and frequency-domain output plots of the first-order stochastic resonance system. Figure 5 (a) is the time-domain output diagram of the first-order stochastic resonance system. Figure 5 (b) is the frequency domain diagram of the output of the first-order stochastic resonance system.
[0037] Figure 6 It is the optimal output time-domain and frequency-domain plot of a traditional cascaded stochastic resonance system.
[0038] Figure 7 This is the optimal output time-domain diagram and frequency-domain diagram of the feedforward cascaded stochastic resonance system of this invention. Detailed Implementation
[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. The present invention includes, but is not limited to, the following embodiments.
[0041] like Figure 1 and Figure 2 As shown in the figure, this invention proposes a method for enhancing weak signals using a feedforward cascaded random resonance. The technical solution mainly includes the following steps:
[0042] Step 1: Obtain the weak signal to be enhanced, sn(t) = Asin(2πf0t) + ξ(t), where A and f0 are the amplitude and frequency of the signal, respectively. In this example, the signal amplitude and frequency are A = 0.1 Hz and f0 = 0.01 Hz, respectively, the sampling frequency is 5 Hz, t is time, the signal length is 5000 points, and ξ(t) represents Gaussian white noise with a mean of 0 and a variance of 5. The time-domain and frequency-domain plots of sn(t) are shown below. Figure 4As shown, the signal-to-noise ratio is -30dB at this time, which shows that the target signal is submerged by noise in both the time and frequency domains.
[0043] Step 2: Construct a feedforward cascaded stochastic resonance system.
[0044]
[0045] Where x1 is the output of the first-order stochastic resonance system, x i Let sn(t) be the output of the i-th level stochastic resonance system, t be time, and sn(t) be the weak input signal to be enhanced. i-1 x i-1 (t) is the signal input to the i-th stochastic resonance after weighting and other operations on the (i-1)th stage stochastic resonance output, n is the maximum number of cascaded layers set, and U(x) is the system potential function;
[0046] In step 2, the potential function U(x) can be chosen as the potential function of various stochastic resonance systems. Here, we take the classical bistable system as an example:
[0047]
[0048] Where a and b are system parameters, which are real numbers greater than zero.
[0049] In step 2, the weight ω i-1 Let ω be a variable that gradually increases with the number of cascaded layers i. As a preferred value, ω i-1 It can be set to
[0050] ω i-1 =k*m i-p (4)
[0051] Among them, k adjusts the final size of the weight coefficient, m determines the trend of weight change, and p adjusts the timing of weight change.
[0052] As a preferred option, k = 0.1, m = 1.2, p = 2.
[0053] Step 3: Input the weak signal sn(t) to be enhanced into the first-order stochastic resonance system to find the optimal system parameters and the optimal output x. opt , and save;
[0054] In step 3, the methods for finding the optimal system parameters include various methods such as traversal optimization, genetic algorithm optimization, and particle swarm optimization, which do not affect the performance of the proposed method.
[0055] In step 3, the parameter optimization measurement index includes any method such as signal-to-noise ratio and cross-correlation coefficient;
[0056] This example uses a genetic algorithm to jointly optimize system parameters a and b. The genetic algorithm program flow is as follows: Figure 3 As shown. The signal-to-noise ratio (SNR) is used as the fitness value of the genetic algorithm. The SNR is calculated as shown in formula (5). Where N is the signal length, A f The amplitude of the power spectrum signal is the energy of the signal. Represents the total energy of the output signal. Energy representing noise;
[0057]
[0058] The search range for the system parameters is set to a∈[0,5], b∈[0,5]. The population size in the genetic algorithm is 50, the crossover probability is 0.6, the mutation probability is 0.05, and the maximum number of iterations is set to 50. This allows the stochastic resonance system to obtain a better output and the optimal system parameters a. opt b opt and the optimal output x opt .
[0059] The output of the first-order stochastic resonance system is as follows: Figure 5 As shown, the target signal is still submerged in noise, indicating that a single random resonance system cannot effectively enhance the weak signal at this time.
[0060] Step 4, for the obtained x opt Phase alignment with the signal to be enhanced, sn(t), is primarily aimed at ensuring a positive effect in subsequent superposition. A simple method for phase alignment is employed here:
[0061] The phase alignment method in step 4 includes the following two steps.
[0062] (1) Perform a Fourier transform on the signal sn(t) to be enhanced, and take the modulus and phase of the Fourier transform result to obtain SN(ω) and save it;
[0063] (2) For the optimal output x opt Perform a Fourier transform, and then take the modulus and phase of the Fourier transform result to obtain X. opt (ω)
[0064] Step 5, weighted summation, applying the weighted summation to the X obtained in Step 4. opt Multiply (ω) by the weight ω obtained from formula (2) to get the weighted signal ωX. opt (ω), and superimposed with SN(ω) to obtain ωX opt (ω)+SN(ω);
[0065] The operations in steps 4-5 can be summarized as phase alignment and weighted superposition. Here, weighted superposition is performed in the frequency domain, or it can be performed in the time domain. Their functions are basically the same.
[0066] Step 6, for the ωX obtained in step 5 opt Subtracting the mean from (ω)+SN(ω) and performing an inverse Fourier transform yields the input signal x for the next level of stochastic resonance. input (t);
[0067] Step 7, take the x obtained in step 6 input (t) is input into the next stage of the stochastic resonance system, and parameter optimization is performed to obtain the optimal output x. opt The parameters are consistent with step 3 in the specific implementation process;
[0068] Step 8: Repeat steps 4 to 7, saving the optimal output of each stage of the stochastic resonance system until the set maximum number of cascaded layers N is reached or until other set stopping conditions are met, such as stopping after the signal-to-noise ratio gain reaches the set requirements.
[0069] Step 9: Select the most suitable result from the optimal output of each stage of the stochastic resonance system as the final output of the feedforward cascaded stochastic resonance.
[0070] The optimal output result of traditional cascaded stochastic resonance is as follows Figure 6 As shown, comparison Figure 5 The output results of the first-stage stochastic resonance system show that the cascaded stochastic resonance system merely shifts high-frequency noise to low frequencies, making the signal waveform smoother. However, it loses some information in the time domain and remains submerged in low-frequency noise in the frequency domain, failing to effectively enhance weak signals. In contrast, the output results of the feedforward cascaded stochastic resonance method proposed in this invention are as follows... Figure 7 As shown, the method proposed in this invention effectively enhances weak signals in both the time and frequency domains, and recovers the time and frequency domain characteristics of the signal very well.
Claims
1. A method for enhancing weak signals using a feedforward cascaded stochastic resonance, characterized in that... Includes the following steps: Step 1: Obtain the weak signal sn(t) that needs to be enhanced; Step 2, construct a feedforward cascaded stochastic resonance system: Where x1 is the output of the first-order stochastic resonance system, x i Let sn(t) be the output of the i-th level stochastic resonance system, t be time, and sn(t) be the weak input signal to be enhanced. i-1 x i-1 (t) is the signal input to the i-th level stochastic resonance after being weighted and superimposed with the weak signal to be enhanced, where n is the maximum number of cascaded layers set, and U(x) is the system potential function. Step 3: Input the weak signal sn(t) to be enhanced into the first-order stochastic resonance system to find the optimal system parameters and the optimal output x. opt , and save; Step 4, for the obtained x opt Phase alignment with the signal to be enhanced, sn(t); Step 5, weighted summation, applying the weighted summation to the X obtained in Step 4. opt Multiply (ω) by the weight ω obtained from formula (2) to get the weighted signal ωX. opt (ω), and superimposed with SN(ω) to obtain ωX opt (ω)+SN(ω); Step 6, for the ωX obtained in step 5 opt Performing an inverse Fourier transform on (ω)+SN(ω) yields the input signal x for the next level of stochastic resonance. input (t); Step 7, take the x obtained in step 6 input (t) is input into the next stage of the stochastic resonance system, and the same parameter optimization process as in step 3 is performed to obtain the optimal output x. opt ; Step 8: Repeat steps 4 to 7, saving the optimal output of each stage of the stochastic resonance system until the set maximum number of cascaded layers N is reached or other set stopping conditions are met. Step 9: Select the signal corresponding to the optimal metric index from the optimal output of each stage of the stochastic resonance system as the final output result of the feedforward cascaded stochastic resonance.
2. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: The system potential function U(x) is the potential function of various stochastic resonance systems.
3. The feedforward cascaded stochastic resonance weak signal enhancement method according to claim 1, characterized in that: The weight ω i-1 Let ω be a variable that gradually increases with the number of cascaded layers i. i-1 Set as: oh i-1 =k*m i-p (2) Among them, k adjusts the final size of the weight coefficient, m determines the trend of weight change, and p adjusts the timing of the weight change trend.
4. The feedforward cascaded stochastic resonance weak signal enhancement method according to claim 3, characterized in that: The values are k = 0.1, m = 1.2, and p = 2.
5. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: In step 3, the method for finding the optimal system parameters is traversal optimization and various intelligent algorithms, including any one of genetic algorithm optimization, particle swarm optimization algorithm and simulated annealing algorithm.
6. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: In step 3, the parameter optimization metric can be selected from the following: signal-to-noise ratio, cross-correlation coefficient, zero-crossing rate, and spectral warp.
7. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: The phase alignment process involves performing the following two steps sequentially: 4.1: Perform a Fourier transform on the weak signal sn(t) to be enhanced, and take the modulus and phase of the Fourier transform result to obtain SN(ω) and save it. 4.2: For the optimal output x opt Perform a Fourier transform, and then take the modulus and phase of the Fourier transform result to obtain X. opt (ω).
8. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: The phase alignment in step 4 and the superposition in step 5 are frequency domain phase alignment, but time domain phase alignment has the same effect as frequency domain phase alignment.
9. The method for enhancing weak signals via feedforward cascaded stochastic resonance according to claim 1, characterized in that: The optimal measurement index is: when the measurement index is signal-to-noise ratio (SNR), the maximum SNR is optimal; when the measurement index is entropy, the minimum entropy is optimal.