A stochastic resonance underwater weak signal enhancement method

Abstract

This invention discloses a method for enhancing weak underwater signals using stochastic resonance, belonging to the field of underwater acoustic engineering and signal processing technology. It is used for enhancing weak underwater signals, including constructing and preprocessing an integrated detection and communication signal; constructing a linear potential well wall piecewise tristable stochastic resonance system; inputting the preprocessing results into the linear potential well wall piecewise tristable stochastic resonance system; optimizing the parameters of the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm; numerically solving the system's motion equations using the fourth-order Runge-Kutta method to obtain the enhanced output signal; and performing frequency recovery on the enhanced output signal to generate an output signal with a complete linear frequency modulation structure. This invention fundamentally solves the problems of output saturation and difficulty in improving the signal-to-noise ratio in traditional stochastic resonance systems under strong noise environments through the linear potential well wall piecewise tristable structure, significantly improving the system's adaptability to complex underwater noise.

Description

Technical Field

[0001] This invention discloses a method for enhancing weak underwater signals with random resonance, belonging to the field of underwater acoustic engineering and signal processing technology. Background Technology

[0002] Research on underwater signal enhancement algorithms is of paramount importance to the field of underwater acoustics, particularly underwater time delay estimation. In recent years, stochastic resonance theory has provided a new approach to signal enhancement, transferring some noise energy to the signal frequency band through a nonlinear system, thereby enhancing weak signals. However, this technology still faces a series of challenges in practical application: First, traditional stochastic resonance systems are mostly based on bistable models, which present theoretical matching difficulties when processing high-frequency, large-parameter signals, requiring preprocessing methods such as amplitude compression and scaling transformation for adaptation; second, system parameters significantly affect performance, while manual optimization is inefficient, necessitating the introduction of intelligent optimization algorithms (such as artificial fish swarm algorithms and particle swarm optimization algorithms) for parameter search; furthermore, stochastic resonance processing is often accompanied by signal waveform distortion, requiring recovery through cascaded systems or post-processing.

[0003] To address the aforementioned issues, recent research has proposed various improvement methods. For example, some studies have used mixing and normalization to enable stochastic resonance systems to directly process high-frequency narrow pulse signals and effectively improve detection distance under extremely low signal-to-noise ratio (SNR) conditions. Other works have constructed a composite potential function model, introducing a multistable structure on top of a bistable state, thus expanding the noise energy utilization range and further improving the output SNR. Still other studies have designed a piecewise tristable potential function, which enhances the system's ability to extract acoustic signals in high-noise environments by flexibly adjusting the potential well and barrier morphologies. Experiments show that these improved methods significantly improve the output SNR compared to traditional filtering methods and classical stochastic resonance systems when processing low SNR underwater acoustic signals.

[0004] Nevertheless, existing stochastic resonance enhancement methods generally suffer from problems such as complex system structure, large computational burden for parameter optimization, and insufficient adaptability to different signal types. Their robustness and generalization ability need further improvement, especially in real-time underwater scenarios with high requirements and diverse signal forms. Therefore, there is still a need to research more efficient, adaptive, and easily implemented new signal enhancement methods to better meet the needs of underwater acoustic detection, communication, and positioning applications. Summary of the Invention

[0005] The purpose of this invention is to provide a method for enhancing weak underwater acoustic signals using stochastic resonance, in order to solve the problems in the prior art, such as the difficulty in enhancing weak underwater acoustic signals in noisy backgrounds, the inability of traditional stochastic resonance to directly process broadband detection signals, and the difficulty in adaptively optimizing and matching complex system parameters.

[0006] A method for enhancing weak underwater signals using stochastic resonance includes:

[0007] S1. Receive weak underwater signals through an underwater acoustic measuring instrument, modulate the weak underwater signals onto a linear frequency modulated wave using differential binary phase shift keying, construct an integrated detection and communication signal, preprocess the integrated detection and communication signal to obtain an integrated detection and communication signal with communication information removed and a frequency reduction adaptation step size. The preprocessing includes demodulation, removal of communication information and calculation of the frequency reduction adaptation step size.

[0008] S2. Construct a piecewise tristable stochastic resonance system with a linear potential well wall. Input the integrated detection and communication signal (with communication information removed) into the linear potential well wall piecewise tristable stochastic resonance system to construct the motion equations. Solve the motion equations using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced output signal. Based on the enhanced output signal and the parameters of the linear potential well wall piecewise tristable stochastic resonance system, optimize the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The improved moss growth optimization algorithm includes population initialization, wind direction determination mechanism confirmation, etc. Flight-enhanced spore dispersal mechanism, adaptive dual-propagation search mechanism, and elite preservation and selective cryptidization method;

[0009] S3. Input the integrated detection and communication signal (with communication information removed) into the optimized linear potential well wall segmented tristable stochastic resonance system. Solve the motion equations using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced optimal output signal. Perform inverse frequency scale transformation on the enhanced optimal output signal to generate an output signal with a complete linear frequency modulation structure.

[0010] S1 includes, S1.1, receiving weak underwater signals through an underwater acoustic measuring instrument to construct an integrated detection and communication signal. :

[0011] ;

[0012] In the formula, For a moment, It is a complex exponential function. The imaginary unit, The carrier start frequency, To adjust the frequency, , For signal bandwidth, The pulse duration, This is the differential binary phase shift keying baseband symbol sequence after rectangular pulse shaping. ;

[0013] S1 includes, S1.2, and the pair. Demodulation processing is performed, which includes... With reference conjugate linear frequency modulated signal Multiplication, with reference to the conjugate linear frequency modulated signal for:

[0014] ;

[0015] S1 includes S1.3, removing communication information from the demodulated integrated signal, including generating a communication phase compensation factor of the symbol conjugate using the known communication data symbol information in the self-transmitting and self-receiving mode of the underwater acoustic measuring instrument, and multiplying the demodulated integrated signal with the communication phase compensation factor to obtain the detection communication integrated signal with communication information removed. , No. Communication phase compensation factor of each symbol conjugate for:

[0016] ;

[0017] In the formula, For the symbol period, For symbol index, , The total number of code elements. For the first Differential binary phase shift keying transmission code elements.

[0018] S1 includes, S1.4, setting the target low frequency. Calculate the scaling factor :

[0019] ;

[0020] Set sampling frequency Calculate the raw integration step size of the fourth-order Runge-Kutta method. :

[0021] ;

[0022] Determine the secondary sampling frequency :

[0023] ;

[0024] Calculate the frequency reduction adaptation step size :

[0025] .

[0026] S2 includes, S2.1, constructing the potential function of a piecewise tristable stochastic resonance system with a linear potential well wall. :

[0027] ;

[0028] In the formula, The width parameter of the central potential well. The potential well position parameters are on both sides. For the depth of the central potential well, , The potential well depths on both sides, , The slope of the linear potential well wall. , This represents the output signal of a piecewise tristable stochastic resonance system with a linear potential well wall. It is the absolute value symbol;

[0029] To ensure the function is The expression for the continuous constant term is:

[0030] .

[0031] S2 includes, S2.2, and will For a piecewise tristable stochastic resonant system with a linear potential well wall input to underwater acoustic environment noise, the equations of motion are constructed as follows:

[0032] ;

[0033] In the formula, For underwater acoustic environmental noise;

[0034] Using the fourth-order Rungekuta method, The enhanced output signal is obtained by solving the motion equations using the numerical integration step size. ;

[0035] S2 includes S2.3, which involves optimizing the parameters of the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The parameters of the linear potential well wall piecewise tristable stochastic resonance system are used to form moss individuals. Through population initialization, the parameters of each moss individual are calculated. The corresponding output signal-to-noise ratio is used as the fitness value, and the moss individual with the highest fitness value is selected as the current global optimum. The parameters of a linear potential well wall piecewise tristable stochastic resonance system include: , , , and ;

[0036] S2 includes S2.4, utilizing the wind direction determination mechanism, based on... Calculate the wind direction vector based on the distance to other moss individuals. .

[0037] S2 includes, S2.5, and introduction. Flight-enhanced spore dispersal mechanisms update the location of moss individuals, including setting... The characteristic index is Set random number and random number threshold ,when hour, , for:

[0038] ;

[0039] when hour, , for:

[0040] ;

[0041] In the formula, and As a base value parameter, For the current number of assessments, This represents the maximum number of evaluations.

[0042] The formula for updating the location of each individual moss is:

[0043] ;

[0044] ;

[0045] In the formula, For the number of iterations, For the first The next iteration , This is the step size scaling factor. for Random numbers within a range and Let them be independent, standard normally distributed random variables. To obey the symbol, It follows a normal distribution.

[0046] S2 includes S2.6, which employs an adaptive dual-propagation search mechanism to adjust the probability threshold. Perform adaptive design:

[0047] ;

[0048] In the formula, As the initial probability threshold, For the final probability threshold, Parameters for controlling the shape of the curve;

[0049] Calculation parameters :

[0050] ;

[0051] Introducing a decay mechanism to calculate step size parameters :

[0052] ;

[0053] In the formula, yes Random numbers within a range Parameters used to control the step size decay rate;

[0054] The position update formula for the dual-propagation search mechanism is:

[0055] ;

[0056] ;

[0057] In the formula, For the first The new position vector of each individual for Random numbers within a range For randomly selected dimension indexes, For the first The individual in the first A new position vector in dimension, for In the The components of the dimension, The wind direction vector is in the th order. The components of a dimension.

[0058] S2 includes S2.7, employing an elite preservation and selective cryptophyte method to maintain each moss individual. historical records , For the first The first moss individual historical records, To record the sequence number, when the record reaches... When selecting a line, choose the one with the highest output signal-to-noise ratio from the history records. Replace the current individual, the first A collection of historical records of individual moss plants. for;

[0059] ;

[0060] Set the elite threshold ratio based on the signal-to-noise ratio. Before the signal-to-noise ratio is reduced Individual moss plants are denoted as elite individuals, and the elite set is defined. for:

[0061] ;

[0062] In the formula, The total number of moss individuals. It is a sorting function;

[0063] remove External moss individuals are non-elite individuals, and non-elite individuals are evaluated using probability. Perform a stealth operation:

[0064] ;

[0065] ;

[0066] In the formula, For assignment operation, for random numbers within the range For the first The best historical record of an individual moss. To find the maximum independent variable, To achieve the desired output signal-to-noise ratio;

[0067] right Perform a Fast Fourier Transform (FFT) to obtain the FFT spectrum, and calculate the values ​​in the FFT spectrum. signal amplitude at Calculate the FFT spectrum except for The sum of signal amplitudes at all other frequencies Reassess the fitness values ​​of all moss individuals:

[0068] ;

[0069] In the formula, The target frequency in the FFT spectrum The amplitude of the signal at that location. In the FFT spectrum, except The sum of the signal amplitudes at all other frequencies;

[0070] renew The individual with the highest output signal-to-noise ratio.

[0071] S2 includes S2.8, repeating steps S2.3 to S2.7 until the maximum number of evaluations is reached. Output the optimal parameter configuration.

[0072] S3 includes, S3.1, and Input the optimized linear potential well-walled piecewise tristable stochastic resonance system and apply the fourth-order Runge-Kutta method. Using the numerical integration step size, the motion equations are solved to obtain the enhanced optimal output signal. ;

[0073] S3 includes, S3.2, for Perform inverse frequency scale transform, including using Extend the signal spectrum This yields a high-frequency output signal. :

[0074] ;

[0075] S3 includes, S3.3, and... Perform linear frequency modulation reconstruction with reference linear frequency modulation signal Multiply to generate an output signal with a complete linear frequency modulation structure. :

[0076] ;

[0077] .

[0078] Compared with existing technologies, this invention has the following advantages: The invention fundamentally solves the problems of output saturation and signal-to-noise ratio (SNR) improvement difficulties in traditional stochastic resonance systems under strong noise environments through a segmented tristable structure with linear potential well walls, significantly improving the system's adaptability to complex underwater noise; the combination of an elite retention strategy and a Lévy flight mechanism greatly reduces computational complexity while maintaining signal enhancement effects, creating conditions for deploying resource-constrained underwater embedded devices; it can still effectively enhance weak signal characteristics even in extremely low SNR environments, with output SNR and robustness significantly superior to traditional signal processing methods, and exhibits good generalization ability to different marine environments, providing reliable technical support for integrated underwater detection and communication systems. Attached Figure Description

[0079] Figure 1 This is a detailed flowchart of the present invention;

[0080] Figure 2 It detects the information bits after phase-jump differential coding of the integrated communication signal;

[0081] Figure 3 It is a modulated integrated detection and communication signal;

[0082] Figure 4 This is a diagram illustrating the potential function of a piecewise tristable stochastic resonance system with a linear potential well wall.

[0083] Figure 5 It is the time-domain waveform at the receiving end;

[0084] Figure 6 It is an enhanced LFM signal used for time delay estimation;

[0085] Figure 7 It is the one-sided spectrum of the received signal;

[0086] Figure 8 It is the one-sided spectrum of the output signal of the random resonance system;

[0087] Figure 9 It is an iterative process of an improved moss growth optimization algorithm;

[0088] Figure 10 It is the potential function curve of the linear potential well wall piecewise tristable stochastic resonance system obtained after optimization. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0090] A method for enhancing weak underwater signals using stochastic resonance includes:

[0091] S1. Receive weak underwater signals through an underwater acoustic measuring instrument, modulate the weak underwater signals onto a linear frequency modulated wave using differential binary phase shift keying, construct an integrated detection and communication signal, preprocess the integrated detection and communication signal to obtain an integrated detection and communication signal with communication information removed and a frequency reduction adaptation step size. The preprocessing includes demodulation, removal of communication information and calculation of the frequency reduction adaptation step size.

[0092] S2. Construct a piecewise tristable stochastic resonance system with a linear potential well wall. Input the integrated detection and communication signal (with communication information removed) into the linear potential well wall piecewise tristable stochastic resonance system to construct the motion equations. Solve the motion equations using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced output signal. Based on the enhanced output signal and the parameters of the linear potential well wall piecewise tristable stochastic resonance system, optimize the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The improved moss growth optimization algorithm includes population initialization, wind direction determination mechanism confirmation, etc. Flight-enhanced spore dispersal mechanism, adaptive dual-propagation search mechanism, and elite preservation and selective cryptidization method;

[0093] S3. Input the integrated detection and communication signal (with communication information removed) into the optimized linear potential well wall segmented tristable stochastic resonance system. Solve the motion equations using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced optimal output signal. Perform inverse frequency scale transformation on the enhanced optimal output signal to generate an output signal with a complete linear frequency modulation structure.

[0094] S1 includes, S1.1, receiving weak underwater signals through an underwater acoustic measuring instrument to construct an integrated detection and communication signal. :

[0095] ;

[0096] In the formula, For a moment, It is a complex exponential function. The imaginary unit, The carrier start frequency, To adjust the frequency, , For signal bandwidth, The pulse duration, This is the differential binary phase shift keying baseband symbol sequence after rectangular pulse shaping. ;

[0097] S1 includes, S1.2, and the pair. Demodulation processing is performed, which includes... With reference conjugate linear frequency modulated signal Multiplication, with reference to the conjugate linear frequency modulated signal for:

[0098] ;

[0099] S1 includes S1.3, removing communication information from the demodulated integrated signal, including generating a communication phase compensation factor of the symbol conjugate using the known communication data symbol information in the self-transmitting and self-receiving mode of the underwater acoustic measuring instrument, and multiplying the demodulated integrated signal with the communication phase compensation factor to obtain the detection communication integrated signal with communication information removed. , No. Communication phase compensation factor of each symbol conjugate for:

[0100] ;

[0101] In the formula, For the symbol period, For symbol index, , The total number of code elements. For the first Differential binary phase shift keying transmission code elements.

[0102] S1 includes, S1.4, setting the target low frequency. Calculate the scaling factor :

[0103] ;

[0104] Set sampling frequency Calculate the raw integration step size of the fourth-order Runge-Kutta method. :

[0105] ;

[0106] Determine the secondary sampling frequency :

[0107] ;

[0108] Calculate the frequency reduction adaptation step size :

[0109] .

[0110] S2 includes, S2.1, constructing the potential function of a piecewise tristable stochastic resonance system with a linear potential well wall. :

[0111] ;

[0112] In the formula, The width parameter of the central potential well. The potential well position parameters are on both sides. For the depth of the central potential well, , The potential well depths on both sides, , The slope of the linear potential well wall. , This represents the output signal of a piecewise tristable stochastic resonance system with a linear potential well wall. It is the absolute value symbol;

[0113] To ensure the function is The expression for the continuous constant term is:

[0114] .

[0115] S2 includes, S2.2, and will For a piecewise tristable stochastic resonant system with a linear potential well wall input to underwater acoustic environment noise, the equations of motion are constructed as follows:

[0116] ;

[0117] In the formula, For underwater acoustic environmental noise;

[0118] Using the fourth-order Rungekuta method, The enhanced output signal is obtained by solving the motion equations using the numerical integration step size. ;

[0119] S2 includes S2.3, which involves optimizing the parameters of the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The parameters of the linear potential well wall piecewise tristable stochastic resonance system are used to form moss individuals. Through population initialization, the parameters of each moss individual are calculated. The corresponding output signal-to-noise ratio is used as the fitness value, and the moss individual with the highest fitness value is selected as the current global optimum. The parameters of a linear potential well wall piecewise tristable stochastic resonance system include: , , , and ;

[0120] S2 includes S2.4, utilizing the wind direction determination mechanism, based on... Calculate the wind direction vector based on the distance to other moss individuals. .

[0121] S2 includes, S2.5, and introduction. Flight-enhanced spore dispersal mechanisms update the location of moss individuals, including setting... The characteristic index is Set random number and random number threshold ,when hour, , for:

[0122] ;

[0123] when hour, , for:

[0124] ;

[0125] In the formula, and As a base value parameter, For the current number of assessments, This represents the maximum number of evaluations.

[0126] The formula for updating the location of each individual moss is:

[0127] ;

[0128] ;

[0129] In the formula, For the number of iterations, For the first The next iteration , This is the step size scaling factor. for Random numbers within a range and Let them be independent, standard normally distributed random variables. To obey the symbol, It follows a normal distribution.

[0130] S2 includes S2.6, which employs an adaptive dual-propagation search mechanism to adjust the probability threshold. Perform adaptive design:

[0131] ;

[0132] In the formula, As the initial probability threshold, For the final probability threshold, Parameters for controlling the shape of the curve;

[0133] Calculation parameters :

[0134] ;

[0135] Introducing a decay mechanism to calculate step size parameters :

[0136] ;

[0137] In the formula, yes Random numbers within a range Parameters used to control the step size decay rate;

[0138] The position update formula for the dual-propagation search mechanism is:

[0139] ;

[0140] ;

[0141] In the formula, For the first The new position vector of each individual for Random numbers within a range For randomly selected dimension indexes, For the first The individual in the first A new position vector in dimension, for In the The components of the dimension, The wind direction vector is in the th order. The components of a dimension.

[0142] S2 includes S2.7, employing an elite preservation and selective cryptophyte method to maintain each moss individual. historical records , For the first The first moss individual historical records, To record the sequence number, when the record reaches... When selecting a line, choose the one with the highest output signal-to-noise ratio from the history records. Replace the current individual, the first A collection of historical records of individual moss plants. for;

[0143] ;

[0144] Set the elite threshold ratio based on the signal-to-noise ratio. Before the signal-to-noise ratio is reduced Individual moss plants are denoted as elite individuals, and the elite set is defined. for:

[0145] ;

[0146] In the formula, The total number of moss individuals. It is a sorting function;

[0147] remove External moss individuals are non-elite individuals, and non-elite individuals are evaluated using probability. Perform a stealth operation:

[0148] ;

[0149] ;

[0150] In the formula, For assignment operation, for random numbers within the range For the first The best historical record of an individual moss. To find the maximum independent variable, To achieve the desired output signal-to-noise ratio;

[0151] right Perform a Fast Fourier Transform (FFT) to obtain the FFT spectrum, and calculate the values ​​in the FFT spectrum. signal amplitude at Calculate the FFT spectrum except for The sum of signal amplitudes at all other frequencies Reassess the fitness values ​​of all moss individuals:

[0152] ;

[0153] In the formula, The target frequency in the FFT spectrum The amplitude of the signal at that location. In the FFT spectrum, except The sum of the signal amplitudes at all other frequencies;

[0154] renew The individual with the highest output signal-to-noise ratio.

[0155] S2 includes S2.8, repeating steps S2.3 to S2.7 until the maximum number of evaluations is reached. Output the optimal parameter configuration.

[0156] S3 includes, S3.1, and Input the optimized linear potential well-walled piecewise tristable stochastic resonance system and apply the fourth-order Runge-Kutta method. Using the numerical integration step size, the motion equations are solved to obtain the enhanced optimal output signal. ;

[0157] S3 includes, S3.2, for Perform inverse frequency scale transform, including using Extend the signal spectrum This yields a high-frequency output signal. :

[0158] ;

[0159] S3 includes, S3.3, and... Perform linear frequency modulation reconstruction with reference linear frequency modulation signal Multiply to generate an output signal with a complete linear frequency modulation structure. :

[0160] ;

[0161] .

[0162] The process of this invention is as follows Figure 1 As shown, the receiver receives the integrated detection and communication signal, and then performs preprocessing, including demodulation, removal of communication information, and calculation of the frequency reduction adaptation step size. The preprocessing result is then subjected to stochastic resonance, i.e., a linear potential well wall piecewise tristable stochastic resonance system. The system output result is then optimized for parameters, including initializing the moss population, evaluating the signal-to-noise ratio and recording the optimal solution, and determining whether the number of evaluations has reached the upper limit. If the upper limit has not been reached, the IMGO core optimization mechanism is executed, including wind guidance, Lévy flying spore dispersal, and adaptive dual propagation. The optimization result is then evaluated sequentially for the new solution's signal-to-noise ratio, elite retention and population update, application of cryptic mechanisms, and updating of FEs, and then the number of evaluations is evaluated again to see if the upper limit has been reached. If the number of evaluations has reached the upper limit, the optimal solution is output.

[0163] The following description, in conjunction with embodiments and accompanying drawings, provides further details. First, an integrated detection and communication signal is constructed, reflecting information bits from the phase-jump differential coding, such as… Figure 2 As shown, there are 20 bits in total, and their amplitude is... The level transitions between these bits reflect the information bits after phase differential encoding; a level transition corresponds to a bit "1", while remaining unchanged corresponds to a bit "0". The modulated integrated detection and communication signal is as follows: Figure 3 As shown, Figure 2 The differentially coded bits are modulated onto the LFM carrier using DBPSK (Differential Binary Phase Shift Keying) to form a composite signal with time-frequency characteristics. Specific parameters include the time width... It takes 20ms. 2kHz It is 11kHz. 100kHz / s for , for Based on the NOF1 channel impulse response from the real underwater channel dataset Watermark, a weak integrated signal at the receiver under low signal-to-noise ratio is generated:

[0164] ;

[0165] In the formula, This represents the channel impulse response in the watermark. For integration variables;

[0166] right Preprocessing is performed first, including demodulation and adjustment. and Multiplication converts a time-varying frequency linear frequency modulated signal into a fixed frequency cosine signal. :

[0167] ;

[0168] Secondly, for Communication information removal is performed, including using known communication data symbol information in the self-transmitting and self-receiving mode of the underwater delay estimation device to generate a communication phase compensation factor with symbol conjugate, and then... and Multiplying them yields a detection and communication integrated signal with phase transition removed. :

[0169] ;

[0170] The final step in preprocessing is to calculate the down-adaptation step size:

[0171] ;

[0172] ;

[0173] The numerical integration step size of the equations of motion for stochastic resonance is correspondingly amplified to... Use frequency reduction adaptation step size When performing the fourth-order Runge-Kutta method, it is equivalent to... The frequency domain is compressed, and the original signal Stretched proportionally on the timeline The new duration is times, Within this stretched domain, the original 220 complete cycles are preserved, but exhibit the following characteristics: for Slowly changing signals.

[0174] Construct a piecewise tristable stochastic resonance system with linear potential well walls, and set the parameters as follows: , , , and The integrated detection and communication signal, after removing communication information, is input together with the underwater acoustic environment noise into a linear potential well wall segmented tristable stochastic resonance system. The fourth-order Runge-Kutta method (RK4) is used to numerically solve the system's equations of motion.

[0175] The improved moss growth optimization algorithm (IMGO) is used to optimize the system parameters. First, the population is initialized by randomly generating populations within the parameter space. Individual moss, set ,set up For individual moss indexes, , For the first Individual moss, at the search boundary Uniformly distributed within, with a lower bound vector of . The upper bound vector is , respectively represent , , , and The lower and upper limits of the value are defined. The fitness value is calculated using the objective function. :

[0176] ;

[0177] Determine the current global optimal solution based on the output signal-to-noise ratio. .

[0178] Wind direction determination mechanism, including random selection The dominant groups are divided according to each dimension, and the intersection of these groups forms a set. , , The floor symbol is used for rounding down. The problem dimension refers to the number of parameters in the stochastic resonance system that need to be optimized. Each division is based on In selected dimensions The value is a threshold, which divides the population into... and Two subsets are selected, with the larger subset chosen as the dominant group for that dimension. This mechanism simulates the natural process of wind blowing from dense moss areas to the optimal growth environment, guiding the population to evolve towards areas with high output signal-to-noise ratio. The wind direction vector is calculated. :

[0179] ;

[0180] ;

[0181] ;

[0182] In the formula, for arrive The distance vector, It is a set of distance vectors. for The number of elements, This serves as a reference set for wind direction.

[0183] set up , Range of values , , , Perform Lévy flight-enhanced spore dispersal. (Settings) , , , Perform adaptive double propagation; set , , To preserve elites and selectively camouflage, Perform a Fast Fourier Transform (FFT) to obtain the FFT spectrum:

[0184] ;

[0185] In the formula, for FFT spectrum, yes Spectrum index, No. Each sample value, , for The total number of sampling points.

[0186] In calculating the FFT spectrum signal amplitude at :

[0187] ;

[0188] In the formula, , and They are respectively The real and imaginary parts, To match the target frequency The corresponding discrete spectrum index is calculated as follows:

[0189] ;

[0190] In the formula, 0.5 is added to achieve rounding.

[0191] Calculate the FFT spectrum except The sum of signal amplitudes at all other frequencies :

[0192] ;

[0193] use and Reassess the fitness values ​​of all moss individuals.

[0194] After fitness evaluation and global optimum update, the final converged parameters are obtained. , , , and .set up ,right Perform linear frequency modulation reconstruction with reference linear frequency modulation signal Multiply to generate an output signal with a complete linear frequency modulation structure. .

[0195] Figure 4 The potential function of a piecewise tristable stochastic resonance system with linear potential well walls is shown, with parameters set as follows: , , , and This forms a tristable structure with a central shallow well and two side deep wells, which have linear potential well walls. Figure 5 The time-domain waveform of the receiver in a low signal-to-noise ratio underwater acoustic environment is shown. The useful signal is completely submerged by strong noise, making it difficult to extract directly and use for underwater positioning scenarios such as time delay estimation. Figure 6 The time-domain waveform of the LFM signal after random resonance enhancement is shown for scenarios such as time delay estimation. The signal-to-noise ratio is significantly improved and the signal outline is clearly visible, providing a reliable basis for subsequent time delay estimation. Figure 7 The single-sided power spectrum of the received signal is shown. The spectral characteristics are not obvious, making it difficult to identify the effective signal components, reflecting the concealment of the signal in a low signal-to-noise ratio environment. Figure 8 The single-sided power spectrum of the output signal of the random resonance system is shown. A significant energy peak appears in the low-frequency band, indicating that high-frequency noise is effectively suppressed and transferred to the low-frequency region, and the weak signal is enhanced. Figure 9 The convergence process of the improved moss growth optimization algorithm is demonstrated. It achieves a rapid increase in signal-to-noise ratio from -15dB to over -7dB in only 30 iterations, showing good convergence speed and optimization performance. In the figure, IMGO represents the improved moss growth optimization algorithm. Figure 10 The potential function curve of the optimized linear potential well wall piecewise tristable stochastic resonance system is shown. The optimized parameters are: , , , and Compared with the initial settings, the optimized barrier height, well depth and symmetry better match the target signal characteristics, forming a clear tristable structure, which effectively enhances the ability of the stochastic resonance system to enhance weak underwater detection and communication signals.

[0196] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for enhancing a weak underwater signal by stochastic resonance, characterized in that, include: S1. Receive weak underwater signals through an underwater acoustic measuring instrument, modulate the weak underwater signals onto a linear frequency modulated wave using differential binary phase shift keying, construct an integrated detection and communication signal, preprocess the integrated detection and communication signal to obtain an integrated detection and communication signal with communication information removed and a frequency reduction adaptation step size. The preprocessing includes demodulation, removal of communication information and calculation of the frequency reduction adaptation step size. S2. Construct a piecewise tristable stochastic resonance system with a linear potential well wall. Input the integrated detection and communication signal (with communication information removed) into the linear potential well wall piecewise tristable stochastic resonance system to construct the motion equations. Solve the motion equations using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced output signal. Based on the enhanced output signal and the parameters of the linear potential well wall piecewise tristable stochastic resonance system, optimize the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The improved moss growth optimization algorithm includes population initialization, wind direction determination mechanism confirmation, etc. Flight-enhanced spore dispersal mechanism, adaptive dual-propagation search mechanism, and elite preservation and selective cryptidization method; S3. Input the integrated detection and communication signal (with communication information removed) into the optimized linear potential well wall segmented tristable stochastic resonance system. Solve the motion equation using the fourth-order Runge-Kutta method and frequency reduction adaptation step size to obtain the enhanced optimal output signal. Perform inverse frequency scale transformation on the enhanced optimal output signal to generate an output signal with a complete linear frequency modulation structure. S2 comprises, S2.1, constructing a linear potential well wall piecewise bistable stochastic resonance system potential function : ； In the formula, The width parameter of the central potential well. The potential well position parameters are on both sides. For the depth of the central potential well, , The depth of the potential wells on both sides , The slope of the linear potential well wall. , This represents the output signal of a piecewise tristable stochastic resonance system with a linear potential well wall. It is the absolute value symbol; To ensure that the function is continuous at the constant term, the expression is: ； S2 comprises, S2.2, providing With the underwater ambient noise input linear potential well wall piece three-stable random resonance system, the motion equation is constructed: ； In the formula, is the ambient noise of the underwater acoustic environment; The fourth order Runge-Kutta method is used to solve the motion equation to obtain the enhanced output signal with a numerical integration step size of ; S2 includes S2.3, which involves optimizing the parameters of the linear potential well wall piecewise tristable stochastic resonance system using an improved moss growth optimization algorithm. The parameters of the linear potential well wall piecewise tristable stochastic resonance system are used to form moss individuals. Through population initialization, the parameters of each moss individual are calculated. The corresponding output signal-to-noise ratio is used as the fitness value, and the moss individual with the highest fitness value is selected as the current global optimum. The parameters of a linear potential well wall piecewise tristable stochastic resonance system include: , , , and ; S2 comprises, S2.4, using a wind direction determination mechanism, determining a wind direction vector based on The distance to other bryophyte individuals is used to calculate the wind direction vector .

2. The stochastic resonance underwater weak signal enhancement method according to claim 1, characterized in that, S1 includes, S1.1, receiving weak underwater signals through an underwater acoustic measuring instrument to construct an integrated detection and communication signal. : ； In the formula, For a moment, It is a complex exponential function. The imaginary unit, The carrier start frequency, To adjust the frequency, , For signal bandwidth, The pulse duration, This is the differential binary phase shift keying baseband symbol sequence after rectangular pulse shaping. ; S1 comprises, S1.2, multiplying with a reference conjugate chirp signal is:​​ ； S1 includes S1.3, removing communication information from the demodulated integrated signal, including generating a communication phase compensation factor of the symbol conjugate using the known communication data symbol information in the self-transmitting and self-receiving mode of the underwater acoustic measuring instrument, and multiplying the demodulated integrated signal with the communication phase compensation factor to obtain the detection communication integrated signal with communication information removed. , No. Communication phase compensation factor of each symbol conjugate for: ； In the formula, For the symbol period, For symbol index, , The total number of code elements. For the first Differential binary phase shift keying transmission code elements.

3. The stochastic resonance underwater weak signal enhancement method according to claim 2, characterized in that, S1 comprises, S1.4, setting a target low frequency , calculating a scale factor : ； Setting a sampling frequency Computing a fourth order Runge-Kutta method's raw integration step : ； Determining a subsampling frequency : ； Computing a down- frequency adaptation step : 。 4. The stochastic resonance underwater weak signal enhancement method according to claim 3, characterized in that, S2 includes, S2.5, and introduction. Flight-enhanced spore dispersal mechanisms update the location of moss individuals, including setting... The characteristic index is Set random number and random number threshold ,when hour, , for: ； When time, , is: ； wherein and is a base value parameter, is the current evaluation number, is the maximum evaluation number; The formula for updating the location of each individual moss is: ； ； In the formula, For the number of iterations, For the first The next iteration , This is the step size scaling factor. for Random numbers within a range and Let them be independent, standard normally distributed random variables. To obey the symbol, It follows a normal distribution.

5. The stochastic resonance underwater weak signal enhancement method according to claim 4, characterized in that, S2 comprises, S2.6, employing an adaptive double propagation search mechanism to adjust the probability threshold Adaptive design: ； wherein is an initial probability threshold, is a final probability threshold, is a parameter controlling the shape of the curve. Computing parameters : ； Introducing a damping mechanism to compute step size parameters : ； wherein is a random number in the range is a parameter controlling the step attenuation rate; The position update formula for the dual-propagation search mechanism is: ； ； In the formula, For the first The new position vector of each individual for Random numbers within a range For randomly selected dimension indexes, For the first The individual in the first A new position vector in dimension, for In the The components of the dimension, The wind direction vector is in the th order. The components of a dimension.

6. The stochastic resonance underwater weak signal enhancement method according to claim 5, characterized in that, S2 includes S2.7, employing an elite preservation and selective cryptophyte method to maintain each moss individual. historical records , For the first The first moss individual historical records, To record the sequence number, when the record reaches... When selecting a line, choose the one with the highest output signal-to-noise ratio from the history records. Replace the current individual, the first A collection of historical records of individual moss plants. for; ； Set the elite threshold ratio based on the signal-to-noise ratio. Before the signal-to-noise ratio is reduced Individual moss plants are denoted as elite individuals, and the elite set is defined. for: ； wherein is the total number of moss individuals, is the ranking function; Except Bryophyte individuals are non-elite individuals, and the non-elite individuals are selected with a probability Perform a crypto operation: ； ； wherein is an assignment operation, is a random number in the range is the optimal history record of the th moss individual, is the maximum argument, is the output signal-to-noise ratio; right Perform a Fast Fourier Transform (FFT) to obtain the FFT spectrum, and calculate the values ​​in the FFT spectrum. signal amplitude at Calculate the FFT spectrum except for The sum of the signal amplitudes at all other frequencies Reassess the fitness values ​​of all moss individuals: ； In the formula, The target frequency in the FFT spectrum The amplitude of the signal at that location. In the FFT spectrum, except The sum of the signal amplitudes at all other frequencies; update individuals for highest output signal-to-noise ratio.

7. The stochastic resonance underwater weak signal enhancement method according to claim 6, characterized in that, S2 comprises, S2.8, repeating steps S2.3 to S2.7 until a maximum number of evaluations is reached outputting the optimal parameter configuration.

8. The stochastic resonance underwater weak signal enhancement method according to claim 7, characterized in that, S3 includes, S3.1, and Input the optimized linear potential well-walled piecewise tristable stochastic resonance system and apply the fourth-order Runge-Kutta method. Using the numerical integration step size, the motion equations are solved to obtain the enhanced optimal output signal. ; S3 comprises, S3.2, performing a frequency scale inverse transform, including utilizing :​​​ ； S3 comprises, S3.3, multiplying the reference chirp signal with the reconstructed chirp signal :​ ； 。

Images