Signal processing method for weak signal
By using a variable-scale stochastic resonance model and variational mode decomposition algorithm to process weak signals, the problem of signal information loss caused by noise and signal overlap is solved, achieving high efficiency and reliability in signal enhancement and detection, and is applicable to various weak signals.
Patent Information
- Application Number
- CN202511325893.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-17
- Publication Date
- 2025-12-30
AI Technical Summary
When processing weak signals, existing technologies suffer from noise overlapping or aliasing with the signal, which weakens the signal while filtering out noise, resulting in the loss of key information in the signal. Furthermore, the enhancement effect is limited and the fault tolerance rate is low.
By employing a variable-scale stochastic resonance model and variational mode decomposition algorithm, combined with quantum particle swarm optimization, weak signals are processed through a multi-filter system and variational mode decomposition algorithm to improve the signal-to-noise ratio and transfer high-frequency noise energy to low-frequency components to enhance signal strength.
It enables efficient and reliable detection of weak signals under strong background noise, enhances signal strength, and is applicable to different types of weak signals.
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Figure CN121233992A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of rescue equipment, more particularly, the present application relates to a weak signal processing method. BACKGROUND
[0002] With the rapid development of industrial production and information technology in recent years, in the signal collection of various mechanical equipment in industrial production, due to the strong noise background of the working environment and other factors noise, the collected signal exists many interferences, and then the weak signal detection and enhancement are widely concerned.
[0003] In the existing research, wavelet transform, modal decomposition algorithm or stochastic resonance algorithm are mostly used to process weak signals, but the purpose is achieved by suppressing noise signals in weak signals, in practical application, noise and signal exist overlap or aliasing, which will lead to filter noise while weakening signal, so that the key information in the signal is lost, or there are defects such as low fault tolerance and limited enhancement effect, therefore, it is still necessary to study the processing of weak signals. SUMMARY
[0004] The purpose of the present application is to design and develop a weak signal processing method, which improves the signal-to-noise ratio through a variable scale stochastic resonance model, and enhances the intensity of weak signals by combining a variational modal decomposition algorithm.
[0005] The technical scheme provided by the present application is as follows:
[0006] A weak signal processing method, comprising the following steps:
[0007] Step one, collecting original weak signals;
[0008] Step two, constructing a multiple filtering system, inputting the original signals into the multiple filtering system after Hilbert transform into the envelope spectrum of the original signals, and obtaining enhanced low-frequency signals;
[0009] The output of the multiple filtering system is:
[0010]
[0011] In the formula, x i is the output signal of the i-th stochastic resonance model, U li (x i ) is the i-th stochastic resonance model, and t is the time;
[0012] Step three, optimizing the first potential parameter and the second potential parameter in the multiple filtering system by quantum particle swarm algorithm;
[0013] Step four, input the output signal of each stage of the multiple filtering system into the variational mode decomposition algorithm, if the energy loss factor is less than the energy loss factor threshold and the correlation value is greater than the correlation value threshold, output the reconstructed signal;
[0014] Wherein, the energy loss factor satisfies:
[0015]
[0016] In the formula, ∑u k (t) is the energy of the current decomposition component, ∑u k-1 (t) is the energy of the previous decomposition component, and S(t) is the original weak signal.
[0017] Preferably, the multiple filtering system is a plurality of single-stage stochastic resonance models connected in sequence, and the single-stage stochastic resonance model satisfies:
[0018]
[0019] In the formula, x(t) is the Brownian particle trajectory, a is the first potential parameter, b is the second potential parameter, m is the scale coefficient, A1 is the first signal amplitude, f1 is the first signal frequency, is the first initial phase angle, A2 is the second signal amplitude, f2 is the second signal frequency, is the second initial phase angle, and D is the signal strength of the Gaussian white noise.
[0020] Preferably, the quantum particle swarm algorithm specifically includes the following steps:
[0021] Step 1, randomly initialize the initial position of the particle, the population size, the maximum search number, the search space dimension and the optimization range, and the current best position of each particle is P i (0) = X i (0), and the global best position is:
[0022] P g (0) = min{X1(0), X2(0), …, X M (0)};
[0023] In the formula, M is the total number of particles, P g is the global optimal position, X i (0) is the initial position of the i-th particle.
[0024] Step 2, calculate the fitness value of each particle initial position, obtain the output signal-to-noise ratio corresponding to each particle, and the global fitness optimal solution is the maximum value of all particle signal-to-noise ratios;
[0025] In the formula, the fitness value of the particle is:
[0026]
[0027] where S(f0) is the amplitude of the signal power spectrum at frequency f0, and N(f0) is the average power of the noise at the same frequency;
[0028] Step 3, if the local optimal solution or the global optimal solution of the single particle in the search space is better than the optimal solution of the last generation particle, the position of the corresponding single particle in the search space is updated, and the local and global optimal solutions are also updated;
[0029] where the new local optimal position of each particle satisfies:
[0030]
[0031] where P i (t+1) is the individual optimal position of particle i after the t+1th iteration, P i (t) is the individual optimal position of particle i after the tth iteration, X i (t+1) is the position of particle i after the t+1th iteration, p is an attractor, a is a contraction and expansion coefficient, Y is the average value of the particle position corresponding to the individual extreme value at the current iteration, X i (t) is the position of particle i after the tth iteration, and v is a random number in [0, 1];
[0032] The global optimal position update satisfies:
[0033] P g (t+1) = min{P1(t+1), P2(t+1), …, P M (t+1)}.
[0034] The individual position update satisfies:
[0035]
[0036] Step 4, stop the iteration process until the maximum number of iterations is reached, and obtain the optimal solution of the first potential parameter and the second potential parameter through the final position of the particle in the search space.
[0037] Preferably, the attractor satisfies:
[0038] p = uP i (t) + (1-u)P g .
[0039] where u is a random number in [0, 1].
[0040] Preferably, the variational mode decomposition algorithm specifically includes the following steps:
[0041] Step I: For each mode function u k Performing a Hilbert transform on (t) yields the analytic signal of the mode function:
[0042]
[0043] In the formula, S′(t) is the signal x i The analytic signal, j is the imaginary unit, δ(t) is the unit impulse function, u k (t) is the mode function;
[0044] Step II: Modulate the analytic signal, that is, modulate the spectrum of each mode function onto its respective fundamental frequency band:
[0045]
[0046] In the formula, To correct the index;
[0047] Step III: Estimate the bandwidth of each modal function to obtain the corresponding constrained variational problem:
[0048]
[0049] Among them, {u k} represents the obtained variational mode components, {u k}={u1,u2,…,u k}, ω k Let ω be the cycle frequency, K be the total number of variational mode component decomposition layers, and {ω} k} is the center frequency corresponding to each component, {ω k}={ω1,ω2,…,ω k}, where t is time, Let be the partial derivative of t;
[0050] Step IV: Transform the constrained variational problem into an unconstrained problem:
[0051]
[0052] In the formula, α is the bandwidth parameter, and λ(t) is the Lagrange multiplier;
[0053] Step V: Each component and its corresponding center frequency are optimized using the alternating direction multiplier method until convergence, obtaining the K IMF components with the smallest sum of bandwidths, and updated as follows:
[0054]
[0055]
[0056] In the formula, and λ n+1 (ω) are respectively u k (t) and λ n+1 The Fourier transform of (t), where ω is the frequency and n is the number of iterations.
[0057] Preferably, the relevant values satisfy:
[0058]
[0059] In the formula, cov(u k S) is u k The covariance of S, and σ s They are u k The variance of S.
[0060] Preferably, the energy loss factor threshold is 0.01.
[0061] Preferably, the correlation threshold is 0.65.
[0062] Preferably, the quantum particle swarm optimization algorithm has 300 iterations.
[0063] Preferably, the optimization interval for the first potential parameter and the second potential parameter is [0,2].
[0064] The beneficial effects of this invention are as follows:
[0065] This invention presents a signal processing method for weak signals. By using a variable-scale stochastic resonance model, the signal-to-noise ratio is improved, and high-frequency noise energy is transferred to low-frequency components to enhance the strength of weak signals, thereby enabling the detection of weak signals. This method achieves efficient and reliable detection of weak signals under strong background noise and is applicable to different types of weak signals. Attached Figure Description
[0066] Figure 1 This is a schematic diagram of the frequency domain of the signal after processing by the multiple filtering system described in this invention.
[0067] Figure 2 This is a schematic diagram of the frequency domain of the signal after VMD processing according to the present invention. Detailed Implementation
[0068] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.
[0069] The signal processing method for weak signals provided by this invention includes the following steps:
[0070] Step 1: Acquire the raw weak signal S(t);
[0071] Step 2: Construct a multiple filtering system. The original signal is transformed by Hilbert to obtain the envelope spectrum of the original signal, which is then input into the multiple filtering system to obtain the enhanced low-frequency signal.
[0072] The multi-stage filtering system is composed of multiple single-stage stochastic resonance models connected sequentially, which enables high-frequency noise to continuously shift to low frequencies, thereby enhancing low-frequency signals while effectively reducing noise. The single-stage stochastic resonance model satisfies the following:
[0073]
[0074] In the formula, S(t) is the original weak signal, x(t) is the Brownian particle trajectory, a is the first potential parameter, b is the second potential parameter, and both the first and second potential parameters are real numbers that are positive and take relatively small values, and n(t) is the Gaussian white noise signal.
[0075] The original weak signal satisfies the following:
[0076] S(t) = s(t) + n(t);
[0077]
[0078] In the formula, s(t) is a sinusoidal signal, n(t) is a Gaussian white noise signal, A1 is the amplitude of the first signal, f1 is the frequency of the first signal, and t is the time. Let f1 be the first initial phase angle, A2 be the amplitude of the second signal, and f2 be the frequency of the second signal. The second initial phase angle is defined as follows, and the values of the first signal frequency and the second signal frequency are both much greater than 1.
[0079] The Gaussian white noise signal is:
[0080]
[0081] In the formula, D is the signal intensity of Gaussian white noise, and the mean of the Gaussian white noise is 0 and the variance is 1.
[0082] Introducing a substitution variable makes:
[0083] x(t) = z(τ);
[0084] τ=mt;
[0085] Where m is the scaling factor and τ is the intermediate parameter;
[0086] The single-level stochastic resonance model is transformed as follows:
[0087]
[0088] Among them, a, b, mA1, mA2, f1, and f2 are all large parameters.
[0089] Therefore, the multiple filtering system is as follows:
[0090]
[0091] In the formula, x i Let U be the output signal of the i-th level stochastic resonance model. li (x i ) represents the i-th level stochastic resonance model;
[0092] Where, when i = 1:
[0093]
[0094] Step 3: Optimize the first and second potential parameters using the Quantum Particle Swarm Optimization (QPSO) algorithm, specifically including the following steps:
[0095] Step 1: Randomly initialize the initial positions of the particles, population size, maximum number of searches, search space dimension, and optimization range. Let P be the current optimal position of each particle. i (0) = X i (0), the global optimal position is:
[0096] P g (0)=min{X1(0),X2(0),…,X M (0)};
[0097] In the formula, M is the total number of particles, and P g The globally optimal position;
[0098] Step 2: Calculate the fitness value of each particle's initial position and obtain the output signal-to-noise ratio of each particle. The local feasible fitness optimal solution of a single particle in the search space is the signal-to-noise ratio value corresponding to the first generation particle, and the global fitness optimal solution is the maximum value among them.
[0099] The fitness value of the particle is:
[0100]
[0101] In the formula, S(f0) is the amplitude of the signal power spectrum at frequency f0, and N(f0) is the average power of the background noise at the same frequency;
[0102] Step 3: If the local fitness optimal solution or global fitness optimal solution of a single particle in the search space is better than the fitness optimal solution of the previous generation of particles, then update the velocity and position of the corresponding single particle in the search space, and update the local and global fitness optimal solutions at the same time.
[0103] The new local optimal position of each particle satisfies:
[0104]
[0105] In the formula, P i (t+1) represents the optimal position of particle i after the (t+1)th iteration, P i (t) represents the optimal position of particle i after the t-th iteration, X i (t+1) represents the position of particle i after the (t+1)th iteration, p is the attractor, α is the contraction / expansion coefficient, and its value decreases linearly from 1 to 0.5. Y is the average value of the particle position corresponding to the individual extreme value at the current iteration number, and X... i (t) represents the position of particle i after the t-th iteration, and v is a random number in [0,1].
[0106] Wherein, the attractor satisfies:
[0107] p = uP i (t)+(1-u)P g ;
[0108] In the formula, u is a random number within [0,1];
[0109] The global optimal position update satisfies:
[0110] P g (t+1)=min{P1(t+1),P2(t+1),…,P M (t+1)};
[0111] Individual location updates satisfy:
[0112]
[0113] Step 4: Stop the iteration process until the maximum number of iterations is reached, and obtain the optimal solution a by the final position of the particle in the search space. i and b i This is the optimal solution for the first potential parameter and the second potential parameter.
[0114] Step 4: Input the output signal of each stage of the multi-stage filtering system into the variational mode decomposition (VMD) algorithm. If the energy loss factor is less than the energy loss factor threshold and the correlation value is greater than the correlation value threshold, output the reconstructed signal; otherwise, continue to decompose the output signal of the next stage until the conditions are met.
[0115] The VMD solution method primarily involves updating the center frequency and bandwidth of each IMF component as the number of iterations increases, using the minimum sum of k bandwidths to evaluate the mode function u.k (t) is adaptively decomposed, and the input signal can be transformed into the sum of k modal functions, specifically including:
[0116] Step I: For each mode function u k Performing a Hilbert transform on (t) yields the analytic signal of the mode function:
[0117]
[0118] In the formula, S′(t) is the signal x i The analytic signal, j is the imaginary unit, δ(t) is the unit impulse function, u k (t) is the mode function;
[0119] Step II: Modulate the analytic signal, that is, modulate the spectrum of each mode function onto its respective fundamental frequency band:
[0120]
[0121] In the formula, To correct the index;
[0122] Step III: Estimate the bandwidth of each modal function to obtain the corresponding constrained variational problem:
[0123]
[0124] Among them, {u k} represents the obtained variational mode components, {u k}={u1,u2,…,u k}, ω k Let ω be the cycle frequency, K be the total number of variational mode component decomposition layers, and {ω} k} is the center frequency corresponding to each component, {ω k}={ω1,ω2,…,ω k}, where t is time, Let be the partial derivative of t;
[0125] Step IV: Transform the constrained variational problem into an unconstrained problem:
[0126]
[0127] In the formula, α is the bandwidth parameter, and λ(t) is the Lagrange multiplier;
[0128] Step V: Each component and its corresponding center frequency are optimized using the alternating direction multiplier method until convergence, obtaining the K IMF components with the smallest sum of bandwidths, and updated as follows:
[0129]
[0130] In the formula, and λ n+1 (ω) are respectively u k (t) and λ n+1 The Fourier transform of (t), where ω is the frequency and n is the number of iterations;
[0131] The bandwidth parameter and the number of decompositions are determined by the energy loss factor and the correlation value, wherein the energy loss factor satisfies:
[0132]
[0133] In the formula, ∑u k (t) represents the energy of the current component, ∑u k-1 (t) represents the energy of the previous component;
[0134] The relevant values satisfy:
[0135]
[0136] In the formula, cov(u k S) is u k The covariance of S, and σ s They are u k The variance of S;
[0137] In this embodiment, the energy loss factor threshold is 0.01 and the correlation value threshold is 0.65.
[0138] In this embodiment, the original weak signal is the bearing vibration signal due to cracks in the inner and outer rings of the bearing. The intensity of the added Gaussian white noise is 0.1047. The time scale of the multiple filtering system is 3000, the number of iterations of the quantum particle swarm optimization algorithm is 300, the population size is 100, and the optimization interval of the first and second potential parameters is [0,2]. After two-stage stochastic resonance modeling, the first potential parameter is 1.98, the second potential parameter is 1.90, the output signal-to-noise ratio is 18.05dB, and the output spectrum is obtained as follows. Figure 1 As shown, the amplitude of the characteristic signal was enhanced, but the fault frequency still could not be clearly identified. Further reconstruction of the weak signal was performed. Experiments determined the energy loss factor to be 0.006, thus determining the initial VMD decomposition level to be 7 IMF components. The signal was decomposed into 3 levels by VMD. The correlation of IMF1 was 0.93, IMF2 was 0.87, and IMF3 was 0.68. The signal-to-noise ratio after enhancement was 18.24 dB. The reconstructed signal is shown below. Figure 2 As shown, the fault frequency can be clearly observed.
[0139] This invention presents a signal processing method for weak signals. By using a variable-scale stochastic resonance model, it improves the signal-to-noise ratio and transfers high-frequency noise energy to low-frequency components, thereby enhancing the strength of weak signals and enabling their detection. Moreover, it is applicable to different types of weak signals.
[0140] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and embodiments shown and described herein.
Claims
1. A signal processing method of a weak signal, characterized by, It comprises the following steps: Step one, collecting original weak signals; Step two, constructing a multiple filtering system, inputting the original signals into the multiple filtering system after Hilbert transform into the envelope spectrum of the original signals, and obtaining enhanced low-frequency signals; Wherein, the output of the multiple filtering system is: In the formula, x i is the output signal of the i-th level stochastic resonance model, U li (x i ) is the i-th level stochastic resonance model, and t is the time. Step three, optimizing the first potential parameter and the second potential parameter in the multiple filtering system through a quantum particle swarm algorithm; Step four, inputting the output signal of each level of the multiple filtering system into a variational mode decomposition algorithm, if the energy loss factor is less than the energy loss factor threshold and the correlation value is greater than the correlation value threshold, then outputting the reconstructed signal; Wherein, the energy loss factor satisfies: where ∑u k (t) is the energy of the current decomposition component, ∑u k-1 (t) is the energy of the previous decomposition component, S(t) is the original weak signal.
2. The method of claim 1, wherein the weak signal is a signal having a signal-to-noise ratio of 0 dB or less. The multiple filtering system is a plurality of single-stage stochastic resonance models connected in turn, and the single-stage stochastic resonance model satisfies: wherein x(t) is a Brownian particle trajectory, a is a first potential parameter, b is a second potential parameter, m is a scaling factor, A1 is a first signal amplitude, f1 is a first signal frequency, is a first initial phase angle, A2 is a second signal amplitude, f2 is a second signal frequency, is a second initial phase angle, and D is a signal strength of a Gaussian white noise.
3. The method for processing a weak signal according to claim 2, wherein The quantum particle swarm algorithm specifically comprises the following steps: Step 1, randomly initialize the initial position of the particle, population size, maximum search number, search space dimension and optimization range, the current best position of each particle is P i (0) = X i (0), the global best position is: P g (0) = min{X1(0), X2(0),..., X M (0)}; where M is the total number of particles, P g is the global optimal position, X i (0) is the initial position of the i-th particle; Step 2, calculate the fitness value of the initial position of each particle, obtain the corresponding output signal-to-noise ratio of each particle, and the global optimal solution is the maximum value of the signal-to-noise ratio of all particles; Wherein, the fitness value of the particle is: In the formula, S(f0) is the amplitude of the signal power spectrum at frequency f0, and N(f0) is the average power of the same frequency background noise; Step 3, if the local fitness optimal solution or the global fitness optimal solution of a single particle in the search space is better than the fitness optimal solution of the last generation particle, update the position of the corresponding single particle in the search space, and update the local and global fitness optimal solution; Wherein, the new local optimal position of each particle satisfies: where P i (t + 1) is the individual optimal position of particle i after the t+1th iteration, P i (t) is the individual optimal position of particle i after the tth iteration, X i (t + 1) is the position of particle i after the t+1th iteration, p is an attractor, a is a contraction expansion coefficient Y is the average of the particle positions corresponding to the individual extreme values at the current iteration, X i (t) is the position of particle i after the tth iteration, v is a random number in [0, 1] The global optimal position update satisfies: P g (t+1) = min{P1(t+1), P2(t+1),..., P M (t+1)}; The individual position update satisfies: Step 4, stop the iteration process until the maximum iteration number is reached, and obtain the optimal solution of the first potential parameter and the second potential parameter through the final position of the particle in the search space.
4. The method for processing a weak signal according to claim 3, wherein The attractor satisfies: p = uP i (t) + (1 - u)P g ; In the formula, u is a random number in [0,1].
5. The method for processing a weak signal according to claim 4, wherein, The variational mode decomposition algorithm specifically comprises the following steps: Step I, for each modal function u k (t) is Hilbert transformed to obtain the analytic signal of the modal function as where S'(t) is the analytic signal of the signal x i j is the imaginary unit, and δ(t) is the unit impulse function, and u k (t) is the modulating function. Step II, modulate the analytical signal, that is, modulate the frequency spectrum of each modal function to the respective base frequency band: In the formula, is a correction index; Step III, estimate the bandwidth of each modal function to obtain the corresponding constrained variational problem: Among them, {u k } represents the obtained variational mode components, {u k }={u1,u2,…,u k }, ω k Let ω be the cycle frequency, K be the total number of variational mode component decomposition layers, and {ω} k } is the center frequency corresponding to each component, {ω k }={ω1,ω2,…,ω k }, where t is time, Let be the partial derivative of t; Step IV, convert the constrained variational problem into an unconstrained problem: In the formula, alpha is the bandwidth parameter, and lambda(t) is the Lagrange multiplier; Step V, each component and the corresponding center frequency is optimized and solved through the alternating direction multiplier method until convergence, and the IMF component with the minimum sum of K bandwidths is obtained, and the update is as follows: wherein and λ n+1 (ω) are the Fourier transforms of uk(t) and λ uk(t) and λ n+1 (t), respectively, ω is the frequency, and n is the number of iterations.
6. The method for processing a weak signal according to claim 5, wherein, The correlation value satisfies: where cov(u k , S) is the covariance of u k and S, and σ s are the variances of u k and S, respectively.
7. The method for processing a weak signal according to claim 6, wherein The energy loss factor threshold is 0.
01.
8. The method for processing a weak signal according to claim 7, wherein, The correlation value threshold is 0.
65.
9. The method for processing a weak signal according to claim 8, wherein, The iteration number of the quantum particle swarm algorithm is 300.
10. The method of processing a weak signal according to claim 9, wherein, The optimization interval of the first potential parameter and the second potential parameter is [0,2].