A method for weak signal enhancement of duffing oscillator with automatic parameter optimization

Abstract

The present application belongs to one-dimensional signal processing technical field, and particularly relates to a Duffing oscillator weak signal enhancement method with automatic parameter optimization. The present application takes a double-stage parallel Duffing random resonance system as a mixed signal processing model, uses a quantum particle swarm algorithm with outstanding performance in optimization solution as a parameter optimization algorithm, converts the double-stage parallel random resonance parameter adjustment problem into a multi-parameter global optimization problem, and performs signal enhancement processing on the signal to be enhanced input into the system according to the best parameters, and outputs the enhanced signal. The present application uses parameter self-adaptive optimization to quickly obtain the best parameters of the double-stage parallel Duffing random resonance system, greatly improves the efficiency and precision of the system best parameter setting, and can quickly and high-quality output the enhanced useful signal.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of one-dimensional signal processing, and particularly relates to a Duffing oscillator weak signal enhancement method with automatic parameter optimization. BACKGROUND

[0002] In the generation, output and processing of signals, unwanted harmful information may be introduced due to external or internal interference, and such noise signals will interfere with the identification of signals, so the enhancement of one-dimensional signals is of great significance. One-dimensional signals include mechanical vibration, brain waves, periodic and non-periodic signals, speech signals and the like.

[0003] The physical model of stochastic resonance signal enhancement includes a first-order Langevin equation model and a second-order Duffing equation model. The Duffing equation is a second-order differential equation, and its physical system is a kind of nonlinear oscillator, which is used to describe the vibration phenomenon under the action of external driving force and nonlinear restoring force. The Duffing equation can exhibit rich dynamic behaviors such as stable periodic solution, period doubling and chaos, and the appearance of these dynamic phenomena depends on the system parameters (such as damping, nonlinearity degree, external driving force, etc.) and initial conditions. When the displacement variable coefficient of the Duffing equation is 0, it becomes a first-order Langevin equation model. Whether it is a first-order Langevin equation or a Duffing equation, both of them come from Brownian random motion, which also lays the foundation for the randomness of signal transition, and both of them have the characteristic of stochastic resonance. When the system is set to different parameters, the disordered signal submerged by noise signal can be changed into an ordered signal. However, when using the stochastic resonance characteristic to detect and enhance weak signals, the model parameters need to be frequently adjusted to adapt to complex signals.

[0004] The traditional signal enhancement method only makes the one-dimensional noisy signal pass through a single Duffing oscillator model, and the input and output are relatively single, which is generally a two-polarization large transition of small signal, and it is difficult to realize multi-level signal gradient transition, and it is difficult to highly restore and enhance the signal. At the same time, the traditional parameter adjustment needs to manually find out the empirical parameter value according to the actual signal through multiple experiments, which is low in efficiency and the parameter may not be the best coefficient. The traditional Duffing model mainly processes frequency domain signal detection, and the time domain signal enhancement method is insufficient. SUMMARY

[0005] The Duffing oscillator weak signal enhancement method with automatic parameter optimization provided by the application takes a double-stage parallel Duffing random resonance system as a mixed signal processing model, uses a quantum particle swarm algorithm with outstanding performance in solving as a parameter optimization algorithm, converts the parameter adjustment problem of the double-stage parallel Duffing random resonance system into a multi-parameter global optimization problem, greatly improves the efficiency and precision of the best parameter setting, can quickly obtain the best parameters of the double-stage parallel Duffing random resonance system, and can quickly and high-quality output the enhanced useful signal.

[0006] To achieve the above object, the application adopts the following technical scheme:

[0007] In the first aspect, the application provides a Duffing oscillator weak signal enhancement method with automatic parameter optimization, comprising the following steps:

[0008] S1, constructing a double-stage parallel Duffing random resonance system;

[0009] S2, inputting the signal to be enhanced into the double-stage parallel Duffing random resonance system, and using a quantum particle swarm algorithm to find the best parameter value of each parameter of the system;

[0010] S3, updating the system according to the best parameter value of each parameter of the system, and performing signal enhancement processing on the input signal to be enhanced with the updated system to output the enhanced signal.

[0011] As a preferred scheme, in step S1, the double-stage parallel Duffing random resonance system comprises an input module, a first-stage signal enhancement module, a second-stage signal enhancement module and an output module connected in sequence, and the first-stage signal enhancement module and the second-stage signal enhancement module each are composed of n Duffing random resonance models connected in parallel;

[0012] The input module is used for inputting the signal to be enhanced, and the signal to be enhanced is a mixed signal of an effective signal and a noise signal.

[0013] The first-stage signal enhancement module is used for performing first-stage signal enhancement processing on the input signal to be enhanced.

[0014] The second-stage signal enhancement module is used for performing second-stage signal enhancement processing according to the first-stage signal enhancement processing result.

[0015] The output module is used for outputting the second-stage signal enhancement processing result, i.e. the enhanced signal.

[0016] As a preferred scheme, the first-stage signal enhancement processing result and the second-stage signal enhancement processing result are each an average value of the signal enhancement processing results of the n Duffing random resonance models.

[0017] As a preferred solution, the mathematical expression of the first-stage signal enhancement module is:

[0018]

[0019] The mathematical expression of the second-stage signal enhancement module is:

[0020]

[0021] wherein, is an inertia term, is a damping term, k is a damping ratio, a and b are parameters of the Duffing stochastic resonance model, n is the number of parallel Duffing stochastic resonance models, x 1n is the signal enhancement processing result of the nth Duffing stochastic resonance model in the first-stage signal enhancement module, x 2n is the signal enhancement processing result of the nth Duffing stochastic resonance model in the second-stage signal enhancement module, s(t) + ξ(t) is the input signal to be enhanced, s(t) is the real signal part in the signal to be enhanced, ξ(t) is the noise signal part in the signal to be enhanced, x1(t) is the first-stage signal enhancement processing result, i.e., the average value of the signal enhancement processing results of the first-stage n Duffing stochastic resonance models.

[0022] As a preferred solution, in step S2, the quantum particle swarm algorithm is used to find the optimal parameter values of the parameters of the system, including the parameters of the Duffing stochastic resonance model, the step size of the Duffing stochastic resonance model, and the damping ratio of the Duffing stochastic resonance model.

[0023] As a preferred solution, in step S2, the quantum particle swarm algorithm is used to find the optimal parameter values of the parameters of the system, including the following steps:

[0024] S2.1, initialize the parameters of the quantum particle swarm algorithm;

[0025] S2.2, initialize the parameter values of the two-stage parallel Duffing stochastic resonance system, input the signal to be enhanced into the system with the initialized parameters for signal enhancement processing, and calculate the signal-to-noise ratio of the enhanced signal;

[0026] S2.3, update the parameter values of the two-stage parallel Duffing stochastic resonance system, perform signal enhancement processing on the signal to be enhanced using the system with the updated parameters, and calculate the signal-to-noise ratio of the enhanced signal;

[0027] S2.4, repeat step S2.3 until the signal-to-noise ratio of the enhanced signal no longer changes or reaches the maximum iteration step number, to obtain the optimal parameter value of each parameter of the two-stage parallel Duffing stochastic resonance system.

[0028] As a preferred solution, the parameters for initializing the quantum particle swarm algorithm include the maximum iteration step number, the outer wheel number, the particle number, and the optimization range of each parameter of the system.

[0029] As a preferred solution, the position of the particle is obtained by the inverse transformation method, and the calculation formula is:

[0030]

[0031] wherein u is a random sequence between 0 and 1; st is the current iteration step number of the quantum particle swarm algorithm; X(st) is a vector composed of the values of each parameter of the system at the current iteration step number; P is the convergence point of the potential well; and L(st) is the characteristic length of the potential well.

[0032] In a second aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the method according to any one of the above.

[0033] In a third aspect, the present application provides an electronic device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the computer program is executed by the processor to implement the method according to any one of the above.

[0034] The present application has the following advantages:

[0035] 1. A single Duffing stochastic resonance system has insufficient rectification fluctuation characteristics for a noisy signal, and the potential well transition is single, which is difficult to meet the multi-gradient data signal effect. The present application uses a two-stage parallel Duffing stochastic resonance system to perform signal enhancement processing on the input signal, enhances the multi-gradient useful signal, converts the noise signal as transition energy, converts the adverse factors into useful signals, and further improves the signal-to-noise ratio and the signal preprocessing value.

[0036] 2. In the two-stage parallel Duffing stochastic resonance system, both the first-stage and second-stage signal enhancement models are composed of n Duffing systems connected in parallel. Each stage of the signal enhancement model has multiple inputs. Therefore, a highly efficient, fast, and globally searchable quantum particle swarm adaptive multi-parameter synchronous optimization method is adopted. This method overcomes the shortcomings of traditional systems that suffer from poor detection results due to manual parameter setting or single-parameter optimization. While fully preserving the synergistic effect between the system parameters, it greatly improves the efficiency and accuracy of optimal parameter setting. It can quickly obtain the optimal parameters of the two-stage parallel Duffing stochastic resonance system and output the enhanced useful signal quickly and with high quality, effectively improving the efficiency of signal processing. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a method for enhancing weak signals using a Duffing oscillator with automatic parameter optimization.

[0039] Figure 2 This is a schematic diagram of the structure of a two-stage parallel Duffing stochastic resonance system.

[0040] Figure 3 This is a flowchart illustrating the adjustment of parameters in a two-stage parallel Duffing stochastic resonance system using the quantum particle swarm optimization algorithm.

[0041] Figure 4 This is a signal diagram of a noisy signal with noise intensity D=5.

[0042] Figure 5 This is the spectrum of a noisy signal.

[0043] Figure 6 This is an optimization curve for the quantum particle swarm optimization algorithm to find the optimal parameters for a bi-parallel Duffing stochastic resonance system.

[0044] Figure 7 It is a time-domain plot obtained by processing a one-dimensional sinusoidal noisy signal using the Duffing oscillator weak signal enhancement method with automatic parameter optimization.

[0045] Figure 8 The signal spectrum is obtained by processing a one-dimensional sinusoidal noisy signal using the Duffing oscillator weak signal enhancement method with automatic parameter optimization.

[0046] Figure 9 is a signal phase diagram obtained by processing a one-dimensional sinusoidal noise signal by the Duffing oscillator weak signal enhancement method with automatic parameter optimization.

[0047] Figure 10 is a structural schematic diagram of a computer readable storage medium.

[0048] Figure 11 is a structural schematic diagram of an electronic device. DETAILED DESCRIPTION

[0049] The present application will be described in more detail by the following specific embodiments. A person skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in the specification. The present application can also be implemented or applied by different specific embodiments, and the details in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0050] Referring to Figure 1 , the embodiment provides a Duffing oscillator weak signal enhancement method with automatic parameter optimization, comprising the following steps:

[0051] S1, constructing a double-stage parallel Duffing stochastic resonance system;

[0052] S2, inputting the signal to be enhanced into the double-stage parallel Duffing stochastic resonance system, and using a quantum particle swarm algorithm to find the optimal parameter value of each parameter of the system;

[0053] S3, updating the system according to the optimal parameter value of each parameter of the system, and performing signal enhancement processing on the input signal to be enhanced by using the updated system, to output the enhanced signal.

[0054] Further, referring to Figure 2 , in step S1, the double-stage parallel Duffing stochastic resonance system constructed includes an input module, a first-stage signal enhancement module, a second-stage signal enhancement module and an output module connected in sequence, and the first-stage signal enhancement module and the second-stage signal enhancement module each are composed of n Duffing stochastic resonance models connected in parallel;

[0055] The input module is used for inputting the signal to be enhanced, and the signal to be enhanced is a mixed signal of an effective signal and a noise signal.

[0056] The first-stage signal enhancement module is used for performing first-stage signal enhancement processing on the input signal to be enhanced.

[0057] The second-stage signal enhancement module is configured to perform second-stage signal enhancement processing according to the first-stage signal enhancement processing result.

[0058] The output module is configured to output the second-stage signal enhancement processing result, i.e., the enhanced signal.

[0059] Specifically,

[0060] The first-stage signal enhancement processing result and the second-stage signal enhancement processing result are both average values of n Duffing random resonance model signal enhancement processing results.

[0061] The mathematical expression of the first-stage signal enhancement module is as follows:

[0062]

[0063] The mathematical expression of the second-stage signal enhancement module is as follows:

[0064]

[0065] wherein, is an inertia term, is a damping term, k is a damping ratio, a and b are parameters of the Duffing random resonance model, n is the number of parallel Duffing random resonance models, x 1n is the n-th Duffing random resonance model signal enhancement processing result in the first-stage signal enhancement module, x 2n is the n-th Duffing random resonance model signal enhancement processing result in the second-stage signal enhancement module, s(t)+ξ(t) is the input signal to be enhanced, s(t) is the real signal part in the signal to be enhanced, ξ(t) is the noise signal part in the signal to be enhanced, and x1(t) is the first-stage signal enhancement processing result, i.e., the average value of the first-stage n Duffing random resonance model signal enhancement processing results.

[0066] A single Duffing random resonance model has the random resonance characteristic, and can perform noise reduction and nonlinear stretching of the signal to highlight the contrast. However, the signal enhancement effect of a single Duffing random resonance model is not very ideal. When the output of the system is required to be high, a single Duffing system is difficult to meet the requirements, while a system formed by interconnecting multiple Duffing systems can compensate for the defects to some extent and improve the output quality. The two-stage parallel Duffing random resonance system is adopted to perform signal enhancement processing on the input signal, which can enhance the useful signal in multiple gradients, convert the noise signal as transition energy, convert the adverse factors into useful signals, and further improve the signal-to-noise ratio and the value of signal preprocessing.

[0067] Further, in step S2, finding the optimal parameter values of the system parameters using the quantum particle swarm algorithm includes the parameters a and b of the Duffing stochastic resonance model, the step size h of the Duffing stochastic resonance model, and the damping ratio k of the Duffing stochastic resonance model.

[0068] Further, in step S2, finding the optimal parameter values of the system parameters using the quantum particle swarm algorithm includes the following steps:

[0069] S2.1, initializing the parameters of the quantum particle swarm algorithm, which includes initializing the maximum iteration step number T max , the outer wheel number R, the particle number M, and the optimization range of the system parameters.

[0070] In the process of finding the optimal parameter values of the system parameters, the finding ranges of the parameters of the double-stage parallel Duffing stochastic resonance system are respectively: a∈[0.1, 5], b∈[0.1, 5], h∈[0.01, 0.5], and k∈[1, 4]; the maximum iteration step number T max of the quantum particle swarm algorithm is initialized to 30, the outer wheel number R is set to 3, and the particle number M is set to 30.

[0071] S2.2, initializing the parameter values of the double-stage parallel Duffing stochastic resonance system, inputting the signal to be enhanced into the system with the initialized parameters for signal enhancement processing, and calculating the signal-to-noise ratio of the enhanced signal.

[0072] S2.3, updating the parameter values of the double-stage parallel Duffing stochastic resonance system, performing signal enhancement processing on the signal to be enhanced by using the system with the updated parameters, and calculating the signal-to-noise ratio of the enhanced signal.

[0073] For a one-dimensional signal, the signal-to-noise ratio SNR is selected to measure the effect of the enhanced signal output by the system with adjusted parameters, and the calculation formula of the signal-to-noise ratio SNR is as follows:

[0074]

[0075] Wherein, P s is the power of the input signal to be enhanced, and P N is the total power of the mixed signal of the input signal to be enhanced and the interference noise.

[0076] It is assumed that the enhanced signal output by the double-stage parallel Duffing stochastic resonance system is sampled to obtain a discrete sequence S(n), and the frequency spectrum distribution is obtained by performing FFT transformation on the discrete sequence, which is specifically as follows:

[0077]

[0078] Let W(k0) be the amplitude of the f0 frequency component in the spectrum, k0=f0*N / f0; therefore the SNR of the system is:

[0079]

[0080] Where N is the total number of points of signal discretization.

[0081] S2.4, repeat step S2.3 until the signal-to-noise ratio of the enhanced signal no longer changes or reaches the maximum iteration step number, to obtain the optimal parameter value of each parameter of the two-stage parallel Duffing random resonance system.

[0082] The first stage signal enhancement model and the second stage signal enhancement model in the two-stage parallel Duffing random resonance system are each composed of 4 Duffing systems in parallel, and each stage signal enhancement model is a multi-layer input, therefore a quantum particle swarm adaptive multi-parameter synchronization optimization method with high efficiency, speed and global search capability is adopted, which overcomes the defects of poor detection effect of manual parameter setting or single parameter optimization of traditional systems, while fully retaining the synergistic effect between the parameters of the system, greatly improving the efficiency and precision of the optimal parameter setting, and quickly obtaining the optimal parameters of the two-stage parallel Duffing random resonance system, and quickly and high-quality output the enhanced useful signal.

[0083] The application takes the two-stage parallel Duffing random resonance system as a mixed signal processing model, uses the quantum particle swarm algorithm with outstanding optimization solving performance as a parameter optimization algorithm, converts the two-stage parallel Duffing random resonance parameter adjustment problem into a multi-parameter global optimization problem, and performs signal enhancement processing on the signal to be enhanced input into the system according to the optimal parameters, and outputs the enhanced signal, the specific process is shown in Figure 3 .

[0084] Further, when updating the parameter values of the two-stage parallel Duffing random resonance system, the vector composed of the parameter values is obtained by the inverse transformation method, and the calculation formula is:

[0085]

[0086] Where u is a random sequence between 0 and 1; st is the current iteration step number of the quantum particle swarm algorithm; X(st) is the position vector of each particle, that is, the vector composed of the parameter values of the system at the current iteration step number; P is the convergence point of the potential well; and L(st) is the characteristic length of the potential well.

[0087] In the quantum particle swarm algorithm, the potential well is used to describe the aggregation behavior of particles in the search space, which is similar to a potential field in physics and can attract particles to the lowest point (convergence point).

[0088] Convergence point of potential well refers to the position near the optimal solution where the particle swarm gradually gathers in the search process, which represents the best solution or the position close to the best solution of the problem. In the particle swarm algorithm, the position and velocity of the particles are adjusted so that the particles gradually approach the convergence point of the potential well.

[0089] Characteristic length of potential well refers to the size or range of potential well, which can be understood as the diameter or radius of potential well, indicating the extension degree of potential well in the search space. The larger the characteristic length of potential well, the wider the range of potential well, and the range of movement of particles in the search space will also increase accordingly. The adjustment of characteristic length can affect the search strategy and convergence speed of particles.

[0090] The calculation formula of characteristic length L(st) of potential well is:

[0091] L(st+1)=2*β*|mbest-X(st)|,

[0092]

[0093]

[0094] Where β is the contraction-expansion factor; T max is the maximum number of iterations; M is the number of particles, each particle representing a solution of the parameters of the system; P i is the signal-to-noise ratio of the enhanced signal obtained by the system using the parameter values of the i-th particle; mbest is the mean value of the signal-to-noise ratio of the enhanced signal obtained by the solution of the parameters of the system; D dim is the number of parameters to be optimized;

[0095] Finally, the calculation formula of the vector composed of the values of the parameters of the system is as follows:

[0096] X(st+1)=P±β*|mbest-X(st)|*ln(1 / u)。

[0097] The actual effect of the automatic parameter optimization Duffing oscillator weak signal enhancement method is verified by specific examples:

[0098] The input of the two-stage parallel Duffing stochastic resonance system is a sinusoidal noise signal, and the mixed signal of the input is sn(t)=Acos(2πft)+ξ(t), where f=0.01HZ, A=0.7, and ξ(t) is a Gaussian white noise with mean value 0 and intensity D=5.

[0099] The signal diagram of the noisy signal (mixed signal of the input) is shown in Figure 4 The frequency spectrum diagram of the noisy signal is shown in Figure 5 ObserveFigure 4 It can be observed that the useful signal has been contaminated by noise, making its signal characteristics completely undetectable. Observation Figure 5 As can be seen in the figure, its main frequency characteristics are affected by noise, with frequency components of varying amplitudes interfering with the signal. This is detrimental to the frequency identification of the main characteristics of the original effective signal.

[0100] Figure 6 This is an optimization curve plot of the quantum particle swarm optimization algorithm for finding the optimal parameters of a two-stage parallel Duffing stochastic resonance system. According to... Figure 6 It can be seen that after optimization by the quantum particle swarm optimization algorithm, the fitness value of the two-stage parallel Duffing stochastic resonance system begins to converge after about 12 processing iterations, and the convergence value of the fitness is 6.6dB. The optimal parameters of the two-stage parallel Duffing stochastic resonance system are output as follows: a = 1.0120, b = 2.1059, k = 2.800, h = 0.0800.

[0101] Figure 7 , Figure 8 , Figure 9 These are the time-domain diagram, signal spectrum diagram, and signal phase diagram obtained by processing a one-dimensional sinusoidal noisy signal using the Duffing oscillator weak signal enhancement method.

[0102] from Figure 7 As can be seen, the effective signal in the time domain is significantly prominent, with very little noise and a smooth signal with almost no glitches. Because the dual-parallel Duffing stochastic resonant system can utilize noise to transfer its own energy to the effective signal, the amplitude increases by approximately 1.8 compared to the original signal amplitude of 0.7. Through comparison... Figure 8 and Figure 5 It can be seen that the frequency amplitude at 0.01Hz is more uniform and prominent compared to the original noisy signal, with very few random frequency components in the noise signal. Through comparison... Figure 9 and Figure 4 It can be observed that the quantum particle swarm adaptive stochastic resonance parameter optimization is highly efficient and effectively improves the signal enhancement quality of the dual-parallel Duffing stochastic resonance system.

[0103] Reference Figure 10This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the automatic parameter optimization Duffing oscillator weak signal enhancement method described in the above embodiments. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0104] Reference Figure 11 This application also provides an electronic device, including at least one processor, at least one memory, and a computer program stored in the memory and executable on the processor.

[0105] The processor may include one or more processing cores. It connects various parts of the electronic device via interfaces and circuits, performing various functions and processing data by running or executing instructions, programs, code sets, or instruction sets stored in memory, and by accessing data stored in memory. Optionally, the processor may be implemented using at least one hardware form of DSP, FPGA, or PLA. The processor may integrate one or more of the following: CPU, GPU, and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content required for display on the screen.

[0106] The memory may include RAM or ROM. Optionally, the memory may include a non-transitory computer-readable medium. The memory can be used to store instructions, programs, code, code sets, or instruction sets. The memory may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-described method embodiments, etc.; the data storage area may store data involved in the above-described method embodiments, etc. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor. As a computer storage medium, the memory may include an operating system, a network communication module, a user interface module, and an application program for executing the Duffing oscillator weak signal enhancement method with automatic parameter optimization of the above embodiments.

[0107] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for enhancing weak signals using a Duffing oscillator with automatic parameter optimization, characterized in that, Including the following steps: S1. Construct a two-stage parallel Duffing stochastic resonance system; S2. Input the signal to be enhanced into a two-stage parallel Duffing stochastic resonance system, and use the quantum particle swarm optimization algorithm to find the optimal parameter values ​​of each parameter of the system. The signal to be enhanced is a speech signal. S3. Update the system according to the optimal parameter values ​​of each parameter, and use the updated system to perform signal amplification processing on the input signal to be amplified, so as to output the amplified signal; In step S1, the constructed two-stage parallel Duffing stochastic resonance system includes an input module, a first-stage signal enhancement module, a second-stage signal enhancement module, and an output module connected in sequence. The first-stage signal enhancement module and the second-stage signal enhancement module are each composed of n Duffing stochastic resonance models connected in parallel. An input module is used to input the signal to be enhanced, which is a mixture of a valid signal and a noise signal; The first-stage signal enhancement module is used to perform first-stage signal enhancement processing on the input signal to be enhanced; The second-level signal enhancement module is used to perform second-level signal enhancement processing based on the results of the first-level signal enhancement processing. The output module is used to output the result of the second-stage signal enhancement processing, that is, to output the enhanced signal; Step S2, which uses the quantum particle swarm optimization algorithm to find the optimal parameter values ​​for each system parameter, includes the following steps: S2.1 Initialize the parameters of the quantum particle swarm algorithm; S2.2 Initialize the parameter values ​​of the two-stage parallel Duffing stochastic resonance system, input the signal to be enhanced into the system after parameter initialization for signal enhancement processing, and calculate the signal-to-noise ratio of the enhanced signal; S2.3 Update the parameter values ​​of the two-stage parallel Duffing stochastic resonance system, use the updated system to perform signal enhancement processing on the signal to be enhanced, and calculate the signal-to-noise ratio of the enhanced signal; S2.4 Repeat step S2.3 until the signal-to-noise ratio of the enhanced signal no longer changes or the maximum number of iterations is reached, in order to obtain the optimal parameter values ​​of each parameter of the two-stage parallel Duffing stochastic resonance system.

2. The automatic parameter optimization method for weak signal enhancement of a Duffing oscillator according to claim 1, characterized in that, The results of the first-level signal enhancement processing and the second-level signal enhancement processing are both averages of the signal enhancement processing results of n Duffing stochastic resonance models.

3. The automatic parameter optimization method for weak signal enhancement of a Duffing oscillator according to claim 2, characterized in that, The mathematical expression for the first-level signal enhancement module is: The mathematical expression for the second-level signal enhancement module is: in, For inertia, Here, k is the damping term, a and b are parameters of the Duffing stochastic resonance model, n is the number of parallel components in the Duffing stochastic resonance model, and x is the damping ratio. 1n x represents the signal enhancement result of the nth Duffing stochastic resonance model in the first-level signal enhancement module. 2n s(t)+ξ(t) is the signal enhancement result of the nth Duffing stochastic resonance model in the second-level signal enhancement module, s(t)+ξ(t) is the input signal to be enhanced, s(t) is the real signal part in the signal to be enhanced, ξ(t) is the noise signal part in the signal to be enhanced, and x1(t) is the signal enhancement result of the first level, that is, the average value of the signal enhancement results of the nth Duffing stochastic resonance model in the first level.

4. The automatic parameter optimization method for weak signal enhancement of a Duffing oscillator according to claim 1, characterized in that, In step S2, the quantum particle swarm optimization algorithm is used to find the optimal parameter values ​​for each parameter of the system, including the parameters of the Duffing stochastic resonance model, the step size of the Duffing stochastic resonance model, and the damping ratio of the Duffing stochastic resonance model.

5. The automatic parameter optimization method for weak signal enhancement of a Duffing oscillator according to claim 1, characterized in that, The parameters for initializing the quantum particle swarm optimization algorithm include the maximum number of iterations, the number of outer wheels, the number of particles, and the optimization range of each system parameter.

6. The automatic parameter optimization method for weak signal enhancement of a Duffing oscillator according to claim 1, characterized in that, When updating the parameter values ​​of a two-stage parallel Duffing stochastic resonance system, the vector composed of the parameter values ​​is obtained using the inverse transform method, and the calculation formula is as follows: Where u is a random sequence between [0,1]; st is the current iteration step of the quantum particle swarm optimization algorithm; X(st) is a vector composed of the system parameter values ​​at the current iteration step; P is the convergence point of the potential well; and L(st) is the characteristic length of the potential well.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 6.

8. An electronic device, characterized in that, The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of claims 1 to 6.

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