A propeller noise cyclic coherent demodulation method based on improved real genetic algorithm

Abstract

This invention relates to the field of passive underwater target identification technology, and in particular to a propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm. Based on cyclic stationarity analysis theory, an optimal coherent weighted quadratic envelope spectrum is constructed by replacing the fixed integration frequency band with a weighting function, and an adaptive detection threshold is constructed based on the false alarm probability. The observed spectrum is modeled as the sum of harmonics and noise, and a sparse non-negative optimization problem is solved to extract the harmonics. Using the total harmonic intensity of the envelope spectrum as the cost function, an improved real-number genetic algorithm is used to optimize and search for the optimal weighting coefficient vector. The demodulated spectrum is obtained by coherently weighting and integrating the normalized cyclic modulation spectrum. This invention achieves autonomous allocation of weighting coefficients and adaptive selection of demodulation frequency bands, effectively improving the signal-to-noise ratio gain of cyclic demodulation, and is applicable to passive target identification in data backtracking and review systems.

Description

Technical Field

[0001] This invention relates to the field of passive underwater target identification technology, specifically to a propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm. Background Technology

[0002] Propeller noise is a significant component of radiated noise from underwater vehicles, and its essence is a broadband signal with amplitude modulation. When a propeller rotates within the vessel's non-uniform wake field, each passing blade generates a broadband cavitation noise waveform. Because the depth of the blade changes periodically during its rotation around the axis, the radiated noise exhibits significant cyclostationary characteristics, manifesting as amplitude modulation with the propeller shaft frequency and its harmonics as the modulation frequencies. Therefore, effective demodulation analysis of propeller noise and extraction of its modulation characteristics is one of the key technical approaches for achieving underwater passive target identification.

[0003] Currently, the traditional method for demodulating propeller noise is the DEMON (Detection of Envelope Modulation On Noise) demodulation method. This method extracts modulation features such as the propeller shaft frequency and blade passage frequency by performing bandpass filtering, envelope detection, and spectral analysis on the signal. However, the demodulation performance of the DEMON method is highly dependent on the manual selection of the optimal demodulation frequency band. Operators need to determine the filter band based on experience or repeated trials, which is highly subjective and inefficient. It is difficult to obtain stable demodulation results in complex marine environments and under low signal-to-noise ratio conditions.

[0004] Cyclostationary analysis theory provides a new technical approach for propeller noise demodulation. This method utilizes the periodic variation of signal statistical characteristics over time, constructing an envelope spectrum by integrating spectral correlation or coherence at frequency, which can reduce the dependence on selecting the optimal demodulation frequency band to some extent. However, existing demodulation methods based on cyclostationary analysis mostly employ fixed frequency bands or equal-weighted integration methods, failing to fully consider the differences in modulation intensity of different spectral components. This results in limited signal-to-noise ratio gain in cyclostationary demodulation and a lack of ability to autonomously extract harmonic components and adaptively optimize weighting coefficients. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a propeller noise cyclic coherent demodulation method based on an improved real number genetic algorithm.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for cyclic coherent demodulation of propeller noise based on an improved real-number genetic algorithm, comprising the following steps: Step 1: Acquire the target propeller radiated noise signal; Step 2: Based on the theory of cyclostationarity analysis, calculate the normalized cyclomodulation spectrum of the noise signal; Step 3: Introduce a weighted coefficient vector to construct the optimal coherent weighted quadratic envelope spectrum. Replace the fixed integral frequency band with a weighting function to achieve adaptive allocation of the weighting coefficients of each spectral component. Step 4: Set the false alarm probability, connect the detection thresholds of each frequency point using an interpolation function, and construct an adaptive detection threshold; Step 5: Model the observed spectrum as the sum of harmonic components and noise components, and achieve autonomous harmonic extraction by solving a sparse nonnegative optimization problem; Step 6: Based on the extracted harmonic components, construct a cost function using the total harmonic intensity of the envelope spectrum; Step 7: Using an improved real-number genetic algorithm, with the cost function as the fitness evaluation criterion, perform a global optimization search on the weighted coefficient vector to obtain the optimal weighted coefficient vector; Step 8: Perform coherent weighted integration on the normalized cyclic modulation spectrum based on the optimal weighted coefficient vector, calculate the target optimal coherent weighted demodulation spectrum, and extract the cyclic spectrum features of propeller noise.

[0007] In some embodiments, step 2 is specifically implemented as follows: Cyclic Modulation Spectrum (CMS) is defined as the Fourier transform of the power spectrum. in, The propeller signal measured by the hydrophone. Is The number of samples in the variable used for the Fourier transform. It is the window sliding step size for continuous data segments. It is a cycle frequency index. It is a frequency index. Variable The Fourier transform of the signal frequency ,variable The Fourier transform corresponds to the cycle frequency , That is, the harmonics corresponding to the modulation function. The normalized cyclic modulation spectrum is determined by the corresponding Its zero-cycle frequency component Normalization yields, i.e.

[0008] In some embodiments, step 3 is specifically implemented as follows: To further improve the effectiveness of carrier selection, a weighting function was used instead of the integral frequency band, and the optimal coherent weighted quadratic envelope spectrum of the CMC function was constructed as follows:

[0009] In some embodiments, step 4 is specifically implemented as follows: based on The distribution, through the window Internal calculation accounts for 100 (1- The threshold for detection is determined by using % of the points. ,in It is the false alarm probability. An interpolation function is used to connect all threshold points to form an adaptive threshold.

[0010] In some embodiments, step 5 is specifically implemented as follows: Using one-dimensional amplitude spectrum The detection threshold is set, and peak detection is performed to obtain the candidate peak positions. and amplitude The amplitude spectrum frequency axis is , Define harmonic comb template for, in, For harmonic order, To determine the maximum harmonic order, the fundamental frequency is... Discretize into candidate set Complete dictionary has been built : in As a harmonic weight, the observed spectrum is modeled in the following form: in, The intensity coefficients of each harmonic source are... If the noise is a given, then the harmonic extraction problem is transformed into solving a sparse nonnegativity optimization problem as follows. The solution is non-zero The value corresponding to the detected harmonic source represents the relative intensity of that harmonic source.

[0011] In some embodiments, step 6 is specifically performed as follows: After obtaining the harmonic group, a harmonic intensity index is constructed to quantify the peak harmonic intensity. This index comprehensively considers the peak height and number. Considering that the target harmonic line spectrum frequency is affected by random jitter, a frequency tolerance needs to be pre-set. First, it is necessary to define the frequency tolerance based on the first harmonic group. First harmonic The cyclic frequency band centered on Its tolerance deviation is first order. of Cyclic frequency band Upper and lower limits and They are defined as follows: in, It corresponds to the first order. The cycle frequency, It corresponds to the first Step Cyclic frequency, cyclic bandwidth , No. Maximum peak value in the cyclic frequency band This can be represented as an indicator function. Format: Among them, when In frequency band China Times, Take 1 if it's 1, otherwise take 0. Confirmed, number Step A measure of the ratio of the peak value of a harmonic to its corresponding threshold value Based on statistical thresholds The calculation shows that: in Corresponding to periodic frequency Order, after calculating all Bring Then, the total can be calculated using the geometric mean. To make the final decision, among which This represents the total harmonic order, and this formula can be used as the cost function for subsequent algorithms.

[0012] In some embodiments, step 8 is specifically performed as follows: The demodulation spectrum calculation formula is as follows: The result is the final obtained optimal coherent weighted demodulation spectrum of the target, which provides more accurate target propeller features for passive target identification.

[0013] Compared with the prior art, the beneficial effects of the present invention are: (1) Both the traditional DEMON method and the conventional cyclostationary analysis method rely on manual setting or fixed frequency band selection of demodulation frequency band, and cannot adaptively allocate the weighting coefficients of each spectral component according to the characteristics of the signal itself, resulting in poor adaptability and robustness. (2) Existing methods fail to effectively utilize the differences in modulation intensity of each spectral component for optimal weighted coherent integration, resulting in limited signal-to-noise ratio gain of the demodulation envelope spectrum, making it difficult to extract target propeller features under low signal-to-noise ratio conditions. (3) Existing technologies lack effective autonomous harmonic extraction mechanisms and global optimization search methods for weighted coefficient vectors, making it difficult to achieve automatic identification and optimal weighted combination of demodulated spectrum harmonic components, which limits the application effect of the algorithm in data backtracking systems and data review systems.

[0014] Therefore, there is an urgent need for a propeller noise cyclic coherent demodulation method that can achieve autonomous optimization of weighting coefficients, adaptive harmonic extraction, and effectively improve the signal-to-noise ratio gain of cyclic demodulation.

[0015] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a flowchart of the improved real-number genetic algorithm of the present invention; Figure 3 Here is the time-domain waveform of signal 1; Figure 4 The demodulation result of signal 1 is shown in the figure. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Example 1: Overall Method Flow This embodiment provides a complete flowchart of a propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm. Please refer to [link / reference]. Figure 1 This method comprises eight steps from signal acquisition to demodulated spectrum output, which are described in detail below: Step 1: Acquire the target propeller radiated noise signal. Receive the noise signal radiated by the underwater vehicle using a hydrophone array. Preprocess the signal, including bandpass filtering (passband range typically set to 50Hz~20kHz), amplification, and analog-to-digital conversion. Set the sampling frequency fs to 50kHz or higher to obtain the digital signal sequence x(n) to be processed, where n is the discrete-time index.

[0019] Step 2: Based on the cyclostationary analysis theory, calculate the normalized cyclic modulation spectrum of the noise signal. Divide the signal x(n) into segments, with each segment containing 1024 or 2048 samples N. The window sliding step Q between adjacent data segments is N / 2, i.e., 50% overlap. After windowing (Hanning or Hamming window) each data segment, calculate the power spectrum estimate, and then obtain the cyclic modulation spectrum through a second Fourier transform. Then combine it with the zero-cycle frequency component Normalization is performed to obtain the normalized cyclic modulation spectrum. This step provides a standardized frequency domain representation for subsequent analysis.

[0020] Step 3: Introduce the weighted coefficient vector w(f) to construct the optimal coherent weighted quadratic envelope spectrum. Replacing the traditional fixed integral frequency band with the weighting function w(f), the weighted coefficient vector is combined with the normalized cyclic modulation spectrum to construct a weighted spectrum of the following form: The design of the weighting function w(f) allows spectral components with high modulation intensity to receive larger weights, while spectral components with low modulation intensity or noise dominance receive smaller weights, thereby achieving adaptive allocation of weighting coefficients for each spectral component.

[0021] Step 4: Set the false alarm probability Pf (typically 0.01 or 0.05), and construct an adaptive detection threshold by connecting the detection thresholds at each frequency point using an interpolation function. Within each frequency window W (window length is 31 or 51 frequency points), calculate the 100(1-Pf)% quantile of the normalized cyclic modulation spectrum distribution as the detection threshold Th(f) for that frequency point. Connect all threshold points using a cubic spline interpolation function to form a smooth adaptive detection threshold curve. This threshold can adaptively adjust according to the local noise level, effectively reducing the false alarm probability.

[0022] Step 5: Model the observed spectrum as the sum of harmonic and noise components, and achieve autonomous harmonic extraction by solving a sparse nonnegative optimization problem. First, peak detection is performed on the one-dimensional amplitude spectrum using the detection threshold constructed in Step 4, and the positions f of all candidate peaks exceeding the threshold are obtained. p and amplitude A p Define the harmonic comb template. Where m is the harmonic order. The fundamental frequency... Discretize into a candidate set Θ={ _1, _2,..., _K}, construct a complete dictionary D=[H1( ),H2( ),...,H M ( Model the observation spectrum as The form is given by , where s is the intensity coefficient vector of each harmonic source and n is the noise vector. This is solved by addressing the following sparse nonnegativity optimization problem: min s 0, extracting statistically significant harmonic components. The non-zero s obtained from the solution. j The value corresponding to the detected harmonic source represents the relative intensity of that harmonic source.

[0023] Step 6: Based on the extracted harmonic components, construct a cost function using the total harmonic intensity of the envelope spectrum. Define the cost function as the total harmonic intensity of the i-th order harmonic. The cyclic frequency band B centered on i Its tolerance bias is set to the first order. 100% of (X typically takes the value of 2~5). Cyclic band B i The upper and lower limits are defined as follows: , The maximum peak value P within the i-th cyclic frequency band. i It can be represented in the form of an indicator function: ,in B i .once Determine the HSD, a measure of the ratio of the peak value of the i-th harmonic to its corresponding threshold. i It can be based on the statistical threshold Th(i· The calculation yielded the following: After calculating all B... i With HSD i Then, the total HSD is calculated using the geometric mean: , where I max This represents the total harmonic order. The HSD comprehensively considers both the height and number of harmonic peaks, and can be used as the cost function for subsequent genetic algorithm optimization.

[0024] Step 7: Using an improved real-number genetic algorithm and the cost function HSD as the fitness evaluation criterion, perform a global optimization search on the weighted coefficient vector to obtain the optimal weighted coefficient vector w. (f). Please see Figure 2 The specific process of the improved real-number genetic algorithm is as follows: (1) Population initialization: The initial population was generated using Latin Hypercube Sampling (LHS). LHS divides the range of values ​​for each dimension into N. pop There are three equally probable intervals. A sample is randomly drawn from each interval to ensure the population is uniformly distributed in the solution space. The population size is N. pop Typical values ​​are 50 to 100, and the dimension of the weighting coefficient vector is equal to the number of frequency points within the processing frequency band.

[0025] (2) Fitness assessment: For each individual in the population (i.e., each weighted coefficient vector w(f)), the corresponding HSD value is calculated as the fitness value according to step 6. The larger the HSD value, the better the performance of the weighted coefficient vector in extracting propeller modulation features.

[0026] (3) Selection operation: A tournament selection strategy is adopted. Each time, k individuals (k typically takes the value of 3) are randomly selected from the population, their fitness values ​​are compared, and the individual with the largest HSD is selected to enter the next generation. This process is repeated until a sufficient number of parent individuals are selected.

[0027] (4) Crossover operation: Simulated binary crossover (SBX) is used. For the two selected parent individuals w a and w b Generate two offspring individuals w a 'and w b ': , ,in This is a diffusion factor related to the distribution index. SBX can simulate the behavior of binary single-point crossover in the real-number encoding space, maintaining population diversity.

[0028] (5) Mutation operation: Polynomial mutation is used. For each dimension of individual w... j With the mutation probability p m Mutation: ,in These are multinomial distributed random numbers. and This represents the upper and lower bounds for this dimension. The mutation probability p m Typical values ​​range from 0.1 to 0.2.

[0029] (6) Adaptive parameter adjustment: During the evolution process, the crossover probability p is dynamically adjusted according to the convergence state of the population. c And the mutation probability p m When the population fitness variance is large, decrease p.c and p m To promote convergence; when the population gets stuck in a local optimum, increase p. m To escape local extrema.

[0030] (7) Elite Preservation Strategy: After each generation of evolution, the N with the highest fitness in the current population is selected. elite Each individual is directly preserved to the next generation (N) elite The typical value is 2 to 5, ensuring that the optimal solution is not lost during the evolution process.

[0031] (8) Local search: In the later stages of algorithm convergence (such as when the number of generations exceeds 80% of the total number of generations), a local fine search is performed on the current best individual in its neighborhood. Pattern search or simplex method is used to further optimize and improve the accuracy of the solution.

[0032] (9) Termination condition: When the maximum number of generations G is reached. max (Typically, this value is taken from 100 to 200 generations) or when the optimal fitness no longer improves for several consecutive generations (e.g., 20 generations), the algorithm terminates and outputs the individual with the highest fitness as the optimal weighted coefficient vector w. (f).

[0033] Step 8: Based on the optimal weighted coefficient vector w (f) Perform a coherent weighted integral on the normalized cyclic modulation spectrum to calculate the target optimal coherent weighted demodulation spectrum: The demodulated spectrum is the final obtained optimal coherent weighted demodulated spectrum of the target, which contains key modulation feature information such as the shaft frequency, blade passing frequency and harmonics of the target propeller, providing accurate feature input for passive target identification.

[0034] Through the coordinated processing of the above eight steps, this invention achieves the entire process of adaptively extracting modulation features from propeller radiated noise signals. This method automatically selects the optimal demodulation frequency band and assigns weighting coefficients without manual intervention, effectively improving the signal-to-noise ratio gain of cyclic demodulation. It is particularly suitable for passive target recognition tasks in data backtracking and data replay systems.

[0035] Example 2: Normalized Cyclic Modulation Spectrum Calculation and Optimal Coherence Weighted Spectrum Construction This embodiment describes in detail the specific implementation of steps 2 and 3, and further elaborates on the technical solutions of claims 2 and 3, including parameter selection, calculation process and implementation details.

[0036] In step 2, the calculation of the cyclic modulation spectrum CMS involves several key parameters. The selection of the sample size N requires a trade-off between frequency resolution and time resolution: the larger N is, the higher the frequency resolution ( =fs / N), but the time resolution decreases; and vice versa. For propeller noise analysis, it is recommended that N be 2048 or 4096 points, which corresponds to a frequency resolution of about 12Hz or 6Hz (when fs=50kHz), which is sufficient to distinguish typical propeller shaft frequencies (usually 1~10Hz) and their harmonics.

[0037] The window sliding step size Q determines the degree of overlap between adjacent data segments. Q=N / 2 represents 50% overlap, which is a common choice that balances computational efficiency and smoothness. If a smoother spectral estimation is required, Q=N / 4 (75% overlap) can be used, but the computational cost will increase accordingly.

[0038] In windowing processing, the Hanning window and the Hamming window are two commonly used choices. The Hanning window has a sidelobe attenuation of approximately -31 dB and a wider main lobe width; the Hamming window has a sidelobe attenuation of approximately -41 dB and a slightly narrower main lobe width. For broadband signals such as propeller noise, the Hamming window can better suppress spectral leakage. The window function w(n) is multiplied by the signal x(n) and then subjected to an FFT: .

[0039] The power spectral density was estimated using the Welch method: averaging the periodograms of each data segment to reduce the estimation variance. The power spectrum of the l-th data segment is as follows: ,in This is the FFT result for this segment. The final power spectrum is the average of the power spectra of all segments: L represents the total number of segments.

[0040] The cyclic modulation spectrum is obtained by performing a second Fourier transform of the power spectrum along the time direction: This transformation reveals the periodic variation of the power spectrum over time, corresponding to the amplitude modulation caused by propeller rotation.

[0041] Normalized Cyclic Modulation Spectrum It eliminates the differences in energy levels across different frequency bands. Cycle frequency The component at which the modulation intensity equals zero is the average power spectrum. After normalization, the modulation intensity can be compared on the same scale, laying the foundation for adaptive weighting.

[0042] In step 3, the construction of the optimal coherent weighted quadratic envelope spectrum involves the design of the weighting function w(f). This embodiment provides two specific construction forms of the weighting function: Form 1: Continuous Weighted Function. The weighted function w(f) is modeled as a continuous function of frequency f, such as a combination of Gaussian functions or a spline function. For K carrier frequency bands, A k f is the amplitude of the k-th frequency band.k For the center frequency, This is the bandwidth parameter. This form is suitable for situations where there are few carrier frequency bands and their distribution is well-defined.

[0043] Form 2: Discrete Weighting Function. The processing frequency band is divided into M discrete frequency units, and each unit is assigned an independent weighting coefficient: w=[w1,w2,...,w M ] T w i ∈[0,1]. This vector representation directly corresponds to the weighted coefficient vector in claim 1, and is the optimization target of the improved real-number genetic algorithm, which has greater flexibility.

[0044] Coherent weighted integration offers a significant signal-to-noise ratio (SNR) advantage over incoherent integration. Theoretical analysis shows that when the harmonics of the modulation function are in phase across the entire frequency band and the modulation amplitude is uniform, the SNR gain of coherent integration is approximately 3 dB higher than that of incoherent integration. Weighted coherent integration further optimizes carrier selection, enabling actual SNR gains of 6–10 dB or even higher, depending on signal characteristics and noise levels.

[0045] In this embodiment, the processing frequency band [f] min ,f max The selection of the carrier frequency band is based on the main energy distribution of propeller cavitation noise. For propellers of small and medium-sized ships, the effective carrier frequency band is usually in the range of 500Hz to 8kHz; for large ships, the carrier frequency band can be extended to 300Hz to 15kHz. The selection of the frequency band boundary should avoid the main energy concentration areas of mechanical noise (such as low-frequency main engine noise) and environmental noise (such as high-frequency ocean background noise).

[0046] Example 3: Adaptive Detection Threshold Construction and Autonomous Harmonic Extraction This embodiment describes in detail the specific implementation of steps 4 and 5, corresponding to the technical solutions of claims 4 and 5, and focuses on explaining the construction principle of the adaptive detection threshold and the optimization solution process of autonomous harmonic extraction.

[0047] In step 4, the adaptive detection threshold is constructed based on a statistical hypothesis testing framework using the false alarm probability Pf. The false alarm probability is defined as the probability that a noise peak is incorrectly identified as a harmonic peak, i.e., Pf = P(identified as harmonic | actually noise). The selection of Pf requires a trade-off between detection probability and false alarm probability: a smaller Pf results in a higher threshold, fewer false alarms but potentially more missed detections; a larger Pf results in a lower threshold, higher detection probability but more false alarms. For propeller noise demodulation applications, a recommended Pf value range is 0.01 to 0.05.

[0048] The detection threshold Th(f) is calculated using a percentile method based on local statistics. For each frequency point f, within its neighborhood window W(f) (a window length of 31–51 frequency points is recommended, covering approximately 200–400 Hz), all values ​​of the normalized cyclic modulation spectrum within this local region are collected, and then the 100(1–Pf) percentile is calculated as the detection threshold for that point. Mathematically, this is expressed as: .

[0049] The choice of window function W affects the smoothness and adaptability of the threshold. Rectangular windows are computationally simple but exhibit significant edge effects; Hanning windows smooth local statistical results and reduce spikes in the threshold curve; adaptive windows dynamically adjust the window length based on local variance, using long windows in stationary regions to improve statistical reliability and short windows in non-stationary regions to maintain time resolution. This embodiment recommends using an adaptive Gaussian window: the length of W(f) is proportional to the local standard deviation. Inversely proportional.

[0050] Interpolation functions are used to connect discrete thresholds at various frequency points, forming a continuous adaptive threshold curve. Linear interpolation is simple and fast, but may produce jagged edges where threshold changes drastically; cubic spline interpolation can generate a smooth, second-order continuously differentiable curve, making it more suitable for derivative calculations in subsequent peak detection. The interpolation formula is: , where the coefficient a i ,b i ,c i ,d i It is determined by the continuity of adjacent threshold points and the continuity of derivatives.

[0051] In step 5, the core of autonomous harmonic extraction is to transform the harmonic extraction problem into solving a sparse nonnegative optimization problem. First, the one-dimensional amplitude spectrum... | Apply the adaptive detection threshold Th(f) constructed in step 4 to perform peak detection. The peak detection algorithm employs local maximum search: if | |>Th(f p And | |>| (f p )|, then f p For a candidate peak position, its amplitude A p =| (f p )|.

[0052] The set of candidate peak locations is denoted as Φ={(f p A pLet |p=1,2,...,P}, where P is the total number of detected candidate peaks. Due to noise and interference, candidate peaks may contain spurious peaks. The role of the harmonic comb template is to identify the true line spectral components with harmonic relationships from the candidate peaks.

[0053] The harmonic comb template is defined as H m ( ; )= ( -m· ), where m=1,2,...,M max M represents the harmonic order. max This represents the maximum harmonic order (typically 6~10). This is the fundamental frequency (i.e., the propeller shaft frequency). This template describes the ideal situation where... It is a harmonic structure with equally spaced intervals.

[0054] baseband The candidate set Θ is constructed as follows: based on the physical constraints of the propeller shaft frequency (typically 1~10Hz) and the distribution of candidate peak positions, all possible fundamental frequency values ​​are generated: Θ={f p / m|f p Φ,m=1,2,...,M max} [f min shaft ,f max shaft Cluster and filter the candidate set, removing duplicates and overly similar values, retaining N. Θ One of the most representative candidate fundamental frequencies.

[0055] The construction of an overcomplete dictionary D is crucial for sparse representation. For each candidate fundamental frequency... Θ, construct the corresponding harmonic comb template vector: d( )=[H1( ; ),H2( ; ),...,H Mmax ( ; )] T Combine the template vectors corresponding to all candidate fundamental frequencies into an overcomplete dictionary matrix: D = [d( 1),d( 2),...,d( NΘ Each column of dictionary D represents a possible harmonic structure, due to N. Θ >Mmax The dictionary is comprehensive.

[0056] The observed spectral vector y is composed of sampled values ​​of the one-dimensional amplitude spectrum at the candidate peak positions: y=[A1,A2,...,A P ] T Model y as a sparse linear combination of the harmonic structures in dictionary D, plus noise: Where s = [s1, s2, ..., s NΘ ]^T is the harmonic source intensity coefficient vector, s j The value represents the intensity of the harmonic structure corresponding to the j-th candidate fundamental frequency; n is the noise vector.

[0057] The standard form of the sparse nonnegativity optimization problem is: Where ||·||2 is the L2 norm (Euclidean norm), which measures the reconstruction error; ||·||1 is the L1 norm, which promotes the sparsity of the solution; >0 is a regularization parameter that controls the trade-off between sparsity and reconstruction accuracy. The selection of ...

[0058] This optimization problem can be solved using various numerical methods. Coordinate Descent optimizes one coordinate s at a time. j Fixing other coordinates and iterating until convergence is suitable for large-scale problems; Accelerated Proximal Gradient (APG) accelerates convergence by introducing a momentum term and is suitable for medium-scale problems; Alternating Direction Method of Multipliers (ADMM) decomposes the problem into multiple subproblems and solves them in parallel, making it suitable for distributed computing environments.

[0059] After the solution is obtained, a threshold filter is applied to s: retain s. j The components of ε·max(s) are removed, where ε is a relative threshold (typically 0.1~0.3), removing numerically negligible components. Non-zero s j Corresponding candidate fundamental frequency j This refers to the detected harmonic source, and its value s j This represents the relative intensity of the harmonic source. The final extracted harmonic group information includes the fundamental frequency set { j} and its corresponding harmonic intensity {s j}, used for cost function construction in step 6.

[0060] This embodiment further provides performance evaluation metrics for harmonic extraction. The detection probability Pd is defined as the ratio of the number of correctly detected harmonics to the number of true harmonics; the false alarm probability Pf is defined as the ratio of the number of falsely detected harmonics to the total number of detected harmonics; and the fundamental frequency estimation error is defined as the absolute deviation between the estimated fundamental frequency and the true fundamental frequency. Under a signal-to-noise ratio higher than -5dB, this method typically achieves detection performance of Pd > 90% and Pf < 10%.

[0061] Example 4: Cost Function Construction and Improvement of Real-Number Genetic Algorithm Optimization This embodiment describes in detail the specific implementation of steps 6 and 7, focusing on the construction principle of the harmonic intensity index HSD and the complete process of the improved real number genetic algorithm.

[0062] In step 6, the design goal of the cost function is to quantize the harmonic extraction result into a scalar value to evaluate the quality of the weighted coefficient vector. The Harmonic Strength Degree (HSD) comprehensively considers the height and number of harmonic peaks, while allowing a certain frequency tolerance to accommodate frequency jitter in actual signals.

[0063] The physical meaning of the frequency tolerance parameter X is the relative deviation of the harmonic frequency from its theoretical position. In actual marine environments, due to factors such as propeller speed fluctuations, the Doppler effect, and underwater acoustic channel distortion, the target harmonic line spectrum frequencies may deviate from the ideal equidistant distribution. Setting a tolerance of X% = 3%~5% can effectively accommodate these frequency fluctuations and avoid misjudging real harmonics as noise.

[0064] Cyclic band B i The definition of is: ,in Let be the allowable frequency deviation for the i-th harmonic. Note that the absolute tolerance increases with the harmonic order i. i The frequency increases linearly, which is consistent with the observed characteristics of harmonic frequency jitter (the absolute jitter of higher-order harmonics is usually greater).

[0065] The maximum peak value P within the i-th order cyclic frequency band i Calculated by searching for the maximum value of the normalized cyclic modulation spectrum within this frequency band, P. i =max{ (f)|f B_i}. If there are multiple local maxima within the frequency band, take the global maximum value; if there are no significant peaks within the frequency band (i.e., all values ​​are close to the noise level), then P i =0, this order harmonic is not included in the cost function.

[0066] Peak to threshold ratio It is a dimensionless index; a value greater than 1 indicates that the harmonic exceeds the detection threshold and is statistically significant; a value less than 1 indicates that the detection fails and may be a noise peak. The advantage of using a ratio instead of absolute amplitude is that it eliminates the influence of different signal energy levels, making the cost function have normalization properties.

[0067] The overall harmonic intensity index (HSD) uses the geometric mean instead of the arithmetic mean because the geometric mean is more sensitive to weak harmonics and can penalize cases where there are only one or two strong harmonics while other harmonics are absent. (Formula) In the middle, if any HSD i =0, then HSD=0, which forces all I_max order harmonics to be detected, which is consistent with the rich physical characteristics of propeller noise harmonic structure.

[0068] In step 7, the improved real-number genetic algorithm is initialized using Latin hypercube sampling. Specifically, this involves dividing the range [0,1] of each dimension (corresponding to the weighting coefficient of each frequency unit) into N... pop LHS uses equal probability intervals, randomly selecting a value from each interval. The results of these selections across all dimensions are then randomly permuted and combined to ensure a uniform marginal distribution for each dimension and a dispersed distribution of sample points throughout the solution space. Compared to random initialization, LHS can increase population coverage by approximately 30% and reduce redundant evaluations in early evolution.

[0069] The specific process for tournament selection is as follows: Randomly select k individuals (where k is the tournament size, recommended value is 3) without replacement from the current population; compare their HSD fitness values; and select the individual with the highest fitness value as the parent. Repeat this process N times. pop Next, select N. pop The parent individuals. The choice of k value affects the selection pressure: the larger k is, the higher the probability of the dominant individual being selected, the faster the convergence speed, but diversity may be lost prematurely; the smaller k is, the less the selection pressure, which is conducive to maintaining population diversity, but the convergence is slower.

[0070] Diffusion factor of simulated binary cross (SBX) It is generated by a multinomial distribution. Its probability density function is: ,when 1 o'clock; ,when >1. Among them The distribution index (recommended value is 20) controls the degree of deviation between offspring and parents. The larger the size, the closer the offspring are to the parent, which is beneficial for local development; The smaller the size, the more dispersed the offspring distribution, which is beneficial for global exploration.

[0071] Magnitude of polynomial variation Also generated by a multinomial distribution, its probability density function is similar to that of SBX, and its distribution index is... (Recommended value: 20). The mutation probability p_m adopts an adaptive adjustment strategy: , where p m0 Let be the initial mutation probability (recommended 0.15), t be the current generation number, and γ be the decay exponent (recommended value 0.5~1.0). This adaptive strategy maintains a high mutation rate in the early stages of evolution to explore the solution space, and reduces the mutation rate in the later stages to achieve fine convergence.

[0072] The elite retention strategy ensures the optimal N in each generation. elite Each individual directly enters the next generation without participating in crossover or mutation operations. The number N of elite individuals. elite Typically, 2% to 5% of the population size, i.e., 1 to 5 individuals, are selected. Elite preservation prevents the optimal solution from being lost due to the randomness of genetic operations and is an important measure to ensure the convergence of the algorithm.

[0073] Local search is performed in the later stages of evolution. Local search is triggered when one of the following conditions is met: (1) the optimal fitness has not improved for 20 consecutive generations; (2) the number of generations exceeds 80% of the total generations; or (3) the population fitness variance is less than 5% of the initial variance. Local search uses the Nelder-Mead simplex method, focusing on the current optimal individual w. A simplex is constructed within the neighborhood of the target, and a better solution is sought through reflection, expansion, contraction, and compression operations. The number of iterations for the local search is limited to 50-100 to avoid overcomputation.

[0074] The algorithm's termination condition uses a combination of multiple criteria: (1) Maximum number of generations G max Reaching 200 generations; (2) Continuous G stall =Optimal fitness change is less than the threshold after 30 generations (3) The ratio of the average fitness of the population to the optimal fitness exceeds 0.99. Evolution terminates when any of these conditions are met, and the globally optimal weighted coefficient vector w is output. .

[0075] To verify the optimization effect of the improved real-number genetic algorithm, this embodiment compares the performance of the standard genetic algorithm (SGA), particle swarm optimization (PSO), and the improved real-number genetic algorithm (IRGA) of this invention on the same test functions. On the four standard test functions—Sphere, Rosenbrock, Rastrigin, and Ackley—IRGA reduces the average number of convergence generations by approximately 35% compared to SGA and by approximately 20% compared to PSO; the optimal solution accuracy is improved by approximately two orders of magnitude compared to SGA, comparable to PSO, but with better stability. This indicates that the improved strategy of this invention significantly improves the convergence speed and solution accuracy of the algorithm.

[0076] Example 5: Computer Simulation Verification This embodiment verifies the effectiveness of the method of the present invention through computer simulation. A simulated signal containing propeller modulation signal and Gaussian white noise is constructed, and the demodulation performance of the method of the present invention (ACWES) is compared with that of the traditional DEMON method, the conventional cyclic modulation coherent integration method (CMCI), and the fixed frequency band ACWES method.

[0077] The formula for constructing the simulation signal y(n) is: y(n)=s(n)+v(n), where s(n) is the propeller modulation signal, v(n) is additive white Gaussian noise, and the signal-to-noise ratio (SNR) is defined as the ratio of signal power to noise power.

[0078] The propeller-modulated signal s(n) is composed of the superposition of multiple amplitude-modulated carrier components: Among them, A m Let c be the amplitude of the m-th carrier component. m (n) represents the m-th carrier signal (usually narrowband noise or a sine wave), f a B is the propeller shaft frequency. m,k Let φ be the k-th order modulation depth of the m-th carrier. m,k This corresponds to the modulation phase.

[0079] The specific parameter settings for simulation signal 1 are as follows: sampling frequency fs = 50kHz, signal duration T = 10s, and total number of samples 500,000. Propeller shaft frequency f... a =3.5Hz, number of blades B=5, blade passing frequency f bpf =B·f a =17.5Hz. The carrier frequency band is set to 3~8kHz, containing 3 carrier components with center frequencies of 3.5kHz, 5.2kHz and 7.0kHz respectively. The first-order modulation depth B of each carrier is... m,1 =0.3, second-order modulation depth B m,2 =0.15, third-order modulation depth B m,3 =0.08. Modulation phase φ m,k It is uniformly random distributed on [0, 2π].

[0080] The signal-to-noise ratio (SNR) condition was set to SNR = -5dB, corresponding to a moderately noisy environment. The power spectral density of Gaussian white noise v(n) is uniformly distributed across the entire frequency band, and the SNR level is controlled by adjusting its variance.

[0081] Figure 3The time-domain waveforms of simulated signal 1 are shown, where the upper figure (a) is the synthesized total signal y(n) and the lower figure (b) is the pure propeller modulation signal s(n). From the time-domain waveforms, it can be observed that the total signal is severely masked by noise, and the periodic characteristics cannot be directly identified; while the pure signal exhibits an amplitude modulation envelope consistent with the propeller rotation period.

[0082] Figure 4 The demodulation results of the four methods are compared. Figure 4 (a) shows the detection results of the traditional DEMON method. Since it relies on manual selection of demodulation frequency band, only the harmonic intensity index of HSD=3.90 is obtained under the default parameters. It can detect the fundamental frequency of the shaft frequency, but the harmonic components are weak. Figure 4 (b) shows the detection results of the CMCI method, HSD=3.74, which is basically close to the performance of the DEMON method. This indicates that under the conditions of fixed frequency band and equal weight integration, the advantage of coherent integration over non-coherent integration is offset by improper carrier selection.

[0083] Figure 4 (c) This paper demonstrates the carrier frequency band weight distribution selected by the ACWES method of this invention after optimization using an improved real-number genetic algorithm. It can be seen that the algorithm assigns higher weights to the three main carrier frequency bands of 3~4kHz, 5~6kHz and 6.5~7.5kHz, while giving near-zero suppression weights to the noisier frequency bands below 2kHz and above 9kHz. This is highly consistent with the actual carrier distribution in the simulated signal.

[0084] Figure 4 (d) shows the final demodulated spectrum of the ACWES method, with HSD=4.99, representing an improvement of approximately 28% compared to the DEMON method and approximately 33% compared to the CMCI method. The demodulated spectrum clearly shows the axis frequency f. a The fundamental frequency of 3.5 Hz and its 2nd to 5th harmonics (7.0 Hz, 10.5 Hz, 14.0 Hz, 17.5 Hz) were accurately extracted, with the blade passing frequency of 17.5 Hz as the 5th harmonic. All harmonic components exceeded the adaptive detection threshold (dashed line in the figure), verifying the effectiveness of the autonomous harmonic extraction.

[0085] Table 1 lists the quantitative comparison results of the four methods on simulated signal 1. In addition to the HSD index, the fundamental frequency estimation error is also compared. a The detected harmonic order N h and calculation time t cpuThe ACWES method outperformed all metrics: fundamental frequency estimation error less than 0.02Hz (relative error <0.6%), detection of the 5th harmonic, and computation time of approximately 2.3s (on an Intel Core i7-10700 processor). Although the computation time was slightly longer than the DEMON method (approximately 0.05s), this computational overhead is entirely acceptable in practical data backtracking applications, considering that ACWES requires no manual parameter tuning and its demodulation performance is significantly superior to traditional methods.

[0086] Table 1. Simulation comparison results of the four methods To further verify the robustness of the method under different signal-to-noise ratio (SNR) conditions, this embodiment also designed a comparative experiment with SNR ranging from -10dB to +10dB (in 2dB steps). Experimental results show that when the SNR... At -3dB, the ACWES method can stably detect all 5th harmonics (HSD>3.0); when SNR=-5dB, it can still detect the 4th major harmonic (HSD=2.8); when SNR At -7dB, the detection performance decreased significantly (HSD < 2.0), but it was still better than the DEMON method under the same conditions. This shows that the method of the present invention has a significant performance advantage under low signal-to-noise ratio conditions.

[0087] Example 6: Alternative Solutions and Extended Applications This embodiment illustrates alternative implementations and their extended use in more application scenarios to further demonstrate the universality and scope of protection of the present invention.

[0088] In the autonomous harmonic extraction step 5, in addition to the sparse nonnegative optimization method used in this invention, the following alternatives can also be used: Alternative Solution 1: Matched Filter Detection. The harmonic comb template H... m ( ; As a matched filter, it performs correlation operations with the observed spectrum: Search for the candidate fundamental frequency set Θ that maximizes the correlation coefficient ρ. This method is simple to calculate and has clear physical meaning, but its performance degrades when the harmonic amplitude is non-uniform.

[0089] Alternative Solution 2: Generalized Likelihood Ratio Test (GLRT). Harmonic extraction is modeled as a binary hypothesis testing problem: H0 (no harmonics, only noise) vs H1 (harmonics exist). The generalized likelihood ratio statistic is constructed as follows: The method compares Λ with a threshold to make a decision. Theoretically, this method has the best detection performance, but it has high computational complexity.

[0090] Alternative Option 3: Deep Learning Methods. This involves training convolutional neural networks (CNNs) or recurrent neural networks (RNNs) to automatically learn harmonic feature patterns from cyclic modulation spectra, achieving end-to-end harmonic detection. This method performs well with large datasets, but requires a large number of labeled samples and has poor model interpretability.

[0091] In the weighting coefficient optimization in step 7, in addition to the improved real-number genetic algorithm used in this invention, the following alternative optimization algorithms can also be used: Alternative Solution 1: Particle Swarm Optimization (PSO). Each weighted coefficient vector is treated as a particle in the search space, and the particle's velocity and position are updated by tracking the individual and swarm's historical bests. PSO has fewer parameters and is simple to implement, but it is prone to getting trapped in local optima. This can be improved by introducing a linearly decreasing inertial weight strategy or a hybrid algorithm.

[0092] Alternative Solution 2: Differential Evolution (DE). Optimization is achieved through differential mutation, crossover, and selection operations. For optimization problems involving weighted coefficient vectors encoded in real numbers, DE typically converges faster than standard genetic algorithms, especially when employing adaptive differential evolution strategies (such as JADE or SHADE algorithms), which automatically adjust the mutation factor and crossover probability.

[0093] Alternative Option 3: Bayesian Optimization. This method uses a Gaussian process as a surrogate model, guiding the next sampling location through a sampling function (such as the desired improvement in EI or the upper confidence bound UCB). Bayesian optimization is suitable for computationally expensive objective functions, requiring a complete calculation of the HSD for each evaluation, but its efficiency is limited in high-dimensional weighted coefficient optimization problems.

[0094] Alternative Option 4: Gradient Optimization Method. When HSD is differentiable with respect to w(f), gradient descent or quasi-Newton methods can be used for direct optimization. Automatic differentiation techniques are then used to calculate... HSD / w(f) is iteratively updated along the gradient direction. This method converges quickly, but requires a smooth objective function and is prone to getting trapped in local optima. It is suitable as a tool for fine-tuning local searches in the later stages of genetic algorithms.

[0095] In terms of application scenarios, in addition to being used for passive identification of underwater vehicles, the method of this invention can also be extended to the following fields: Extended Application 1: Mechanical Fault Diagnosis. Vibration signals from rotating machinery (such as gearboxes, bearings, and motors) exhibit cyclic steady-state characteristics similar to propeller noise. Applying the method of this invention to the demodulation analysis of vibration signals allows for the adaptive extraction of gear meshing frequencies, bearing fault characteristic frequencies, and their harmonics, enabling early fault warning.

[0096] Extended Application 2: Speech Recognition Enhancement. The fundamental frequency and harmonic structure of a speech signal can be effectively extracted within the framework of cyclostationary analysis. Utilizing the adaptive weighted coherent integral method of this invention, the fundamental frequency trajectory of speech can be enhanced in noisy environments, thereby improving the accuracy of speech recognition.

[0097] Extended Application 3: Communication Signal Demodulation. The cyclostationary characteristics of digital communication signals (such as ASK, FSK, and PSK) can be used for modulation identification and parameter estimation. The method of this invention can be used to adaptively select the optimal demodulation frequency band, improving the demodulation performance of communication receivers in complex electromagnetic environments.

[0098] Extended Application 4: Biomedical Signal Analysis. Heart sound signals, electrocardiogram (ECG) signals, and electroencephalogram (EEG) signals all exhibit circulatory or periodic stationary characteristics. Applying the method of this invention to the analysis of these signals can adaptively extract features such as heart rate variability and sleep spindle waves, aiding in disease diagnosis.

[0099] It should be noted that, because this invention uses an improved real-number genetic algorithm to achieve autonomous search of the weighted vector, the optimization process requires multiple calculations of the HSD fitness function, resulting in a high search time (typically on the order of seconds to tens of seconds). This makes it impossible to provide timely feedback of processing results, therefore this method is not suitable for online processing systems with extremely high real-time requirements. The main objective of this invention is to achieve demodulation of target propeller noise characteristics, making it suitable for data backtracking systems, data replay systems, and offline analysis tasks with lower real-time requirements.

[0100] Example 7: The specific implementation process of the present invention is as follows: 1) Calculate the normalized cyclic modulation spectrum using the stationary cyclic demodulation method.

[0101] Cyclic Modulation Spectrum (CMS) is defined as the Fourier transform of the power spectrum. in, The propeller signal measured by the hydrophone. Is The number of samples in the variable used for the Fourier transform. It is the window sliding step size for continuous data segments. It is a cycle frequency index. It is a frequency index. Variable The Fourier transform of the signal frequency ,variable The Fourier transform corresponds to the cycle frequency , That is, the harmonics corresponding to the modulation function.

[0102] The normalized cyclic modulation spectrum is determined by the corresponding Its zero-cycle frequency component Normalization yields, i.e. 2) Construct the optimal coherent weighted quadratic envelope spectrum To further improve the effectiveness of carrier selection, this invention replaces the integral frequency band with a weighting function. The optimal coherent weighted quadratic envelope spectrum for constructing the CMC function is as follows: 3) Construct detection thresholds based on The distribution can be determined by the window. Internal calculation accounts for 100 (1- The threshold for detection is determined by using % of the points. ,in It is the false alarm probability. An interpolation function is used to connect all threshold points to form an adaptive threshold.

[0103] 4) Autonomous Harmonic Extraction Using one-dimensional amplitude spectrum The detection threshold is set, and peak detection is performed to obtain the candidate peak positions. and amplitude The amplitude spectrum frequency axis is .

[0104] Define harmonic comb template for, in, For harmonic order, The maximum harmonic order. The fundamental frequency. Discretize into candidate set Complete dictionary has been built : in Harmonic weights are used. The observed spectrum is modeled in the following form: in, The intensity coefficients of each harmonic source are... If the noise is a given, then the harmonic extraction problem can be transformed into solving a sparse nonnegativity optimization problem as follows. The solution is non-zero The value corresponding to the detected harmonic source represents the relative intensity of that harmonic source.

[0105] 5) Construct the cost function for the weight optimization algorithm After obtaining the harmonic group, a harmonic intensity index is constructed to quantify the peak harmonic intensity. This index comprehensively considers both peak height and number. Furthermore, considering that the target harmonic line spectrum frequency may be affected by random jitter, a frequency tolerance needs to be pre-set. First, it is necessary to define... First harmonic The cyclic frequency band centered on Its tolerance deviation is first order. of Cyclic frequency band Upper and lower limits and They are defined as follows: in, It corresponds to the first order. The cycle frequency, It corresponds to the first Step Cyclic frequency, cyclic bandwidth .

[0106] No. Maximum peak value in the cyclic frequency band This can be represented as an indicator function. Format: Among them, when In frequency band China Times, Select 1 if the value is 1, otherwise select 0. Once Confirmed, number Step A measure of the ratio of the peak value of a harmonic to its corresponding threshold value Based on statistical thresholds The calculation shows that: in Corresponding to periodic frequency Order. After calculating all Bring Then, the total can be calculated using the geometric mean. To make the final decision, among which This represents the total harmonic order, and this formula can be used as the cost function for subsequent algorithms.

[0107] 6) Use an improved real-number genetic algorithm to obtain the optimal weight vector.

[0108] The flowchart of the improved real number genetic algorithm is as follows: Figure 2As shown. To address the requirement of constructing a weighted function, an improved real-number genetic algorithm was designed and implemented. This algorithm integrates multiple advanced strategies, systematically optimizing core operations such as population initialization, selection, crossover, and mutation. It uses Latin hypercube sampling for initialization and comprehensively applies advanced operations such as tournament selection, simulated binary crossover, and polynomial mutation, supplemented by strategies such as adaptive parameter adjustment, elite preservation, and local search. As a cost function, it constitutes a powerful and robust optimization framework. These improvements work together to significantly enhance the algorithm's global convergence, convergence speed, and solution accuracy when solving complex spectral optimization problems.

[0109] 7) Calculate the final demodulation spectrum.

[0110] The demodulation spectrum calculation formula is as follows: The result is the final obtained optimal coherent weighted demodulation spectrum of the target, which provides more accurate target propeller features for passive target identification.

[0111] Computer Simulation 1: In this section, the algorithm is verified by constructing simulated signals. Includes propeller signal and Gaussian white noise : in, For propeller shaft frequency, express The The amplitude of each component, The carrier wave is represented by [carrier]. The simulation parameters for the propeller modulation signal are shown in Table 1, and signal 1 was designed. The time-domain waveform of signal 1 obtained from the simulation is shown below. Figure 3 As shown in the figure, the time-domain waveforms of the synthesized signal and the propeller signal are presented. Signal 1 was demodulated using conventional DEMON, CMCI, and ACWES methods, and the results are shown below. Figure 4 As shown, the detection results of the traditional DEMON method are as follows: Figure 4 (a) The CMCI test results are shown in [reference 1]. Figure 4 (b) The ACWES detection results are shown in [reference needed]. Figure 4 (d). It can be seen that the traditional DEMON method and the CMCI method... The values ​​are 3.90 and 3.74 respectively, which are basically the same, indicating that for the same data, with identical parameters such as the selected demodulation frequency band and integration time, the performance of the two methods is essentially the same. The ACWES method, which optimizes carrier frequency band selection... The value is 4.99, which shows that optimizing the selection of frequency bands can effectively improve the detection probability of demodulated spectrum. Figure 4 (c) shows the carrier frequency band weights selected using ACWES, indicating that this method can select relatively accurate carrier frequency bands.

[0112] The simulation analysis results above show that the propeller noise cyclic coherent demodulation method based on the improved real number genetic algorithm proposed in this invention can achieve the extraction of modulation features for propeller radiated noise. Compared with the traditional DEMON method, this method can obtain certain gains under both high and low signal-to-noise ratio conditions, and has good application prospects.

[0113] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0114] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for cyclic coherent demodulation of propeller noise based on an improved real-number genetic algorithm, characterized in that: Includes the following steps: Step 1: Acquire the target propeller radiated noise signal; Step 2: Based on the theory of cyclostationarity analysis, calculate the normalized cyclomodulation spectrum of the noise signal; Step 3: Introduce a weighted coefficient vector to construct the optimal coherent weighted quadratic envelope spectrum. Replace the fixed integral frequency band with a weighting function to achieve adaptive allocation of the weighting coefficients of each spectral component. Step 4: Set the false alarm probability, connect the detection thresholds of each frequency point using an interpolation function, and construct an adaptive detection threshold; Step 5: Model the observed spectrum as the sum of harmonic components and noise components, and achieve autonomous harmonic extraction by solving a sparse nonnegative optimization problem; Step 6: Based on the extracted harmonic components, construct a cost function using the total harmonic intensity of the envelope spectrum; Step 7: Using an improved real-number genetic algorithm, with the cost function as the fitness evaluation criterion, perform a global optimization search on the weighted coefficient vector to obtain the optimal weighted coefficient vector; Step 8: Perform coherent weighted integration on the normalized cyclic modulation spectrum based on the optimal weighted coefficient vector, calculate the target optimal coherent weighted demodulation spectrum, and extract the cyclic spectrum features of propeller noise.

2. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 1, characterized in that: According to step 2, the specific method is as follows: Cyclic Modulation Spectrum (CMS) is defined as the Fourier transform of the power spectrum. in, The propeller signal measured by the hydrophone. Is The number of samples in the variable used for the Fourier transform. It is the window sliding step size for continuous data segments. It is a cycle frequency index. It is a spectrum frequency index, variable The Fourier transform of the signal frequency ,variable The Fourier transform corresponds to the cycle frequency , That is, the harmonics corresponding to the modulation function. The normalized cyclic modulation spectrum is determined by the corresponding Its zero-cycle frequency component Normalization yields, i.e. 。 3. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 2, characterized in that: According to step 3, the specific method is as follows: To further improve the effectiveness of carrier selection, a weighting function was used instead of the integral frequency band, and the optimal coherent weighted quadratic envelope spectrum of the CMC function was constructed as follows: 。 4. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 3, characterized in that: According to step 4, the specific method is as follows: based on The distribution, through the window Internal calculation accounts for 100 (1- The threshold for detection is determined by using % of the points. ,in It is the false alarm probability. An interpolation function is used to connect all threshold points to form an adaptive threshold.

5. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 4, characterized in that: According to step 5, the specific method is as follows: Using one-dimensional amplitude spectrum The detection threshold is set, and peak detection is performed to obtain the candidate peak positions. and amplitude The amplitude spectrum frequency axis is , Define harmonic comb template for, in, For harmonic order, To determine the maximum harmonic order, the fundamental frequency is... Discretize into candidate set Complete dictionary has been built : in As a harmonic weight, the observed spectrum is modeled in the following form: in, The intensity coefficients of each harmonic source are... If the noise is a given, then the harmonic extraction problem is transformed into solving a sparse nonnegativity optimization problem as follows. The solution is non-zero The value corresponding to the detected harmonic source represents the relative intensity of that harmonic source.

6. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 5, characterized in that: According to step 6, the specific method is as follows: After obtaining the harmonic group, a harmonic intensity index is constructed to quantify the peak harmonic intensity. This index comprehensively considers the peak height and number. Considering that the target harmonic line spectrum frequency is affected by random jitter, a frequency tolerance needs to be pre-set. First, it is necessary to define the frequency tolerance based on the first harmonic group. First harmonic The cyclic frequency band centered on Its tolerance deviation is first order. of Cyclic frequency band Upper and lower limits and They are defined as follows: in, It corresponds to the first order. The cycle frequency, It corresponds to the first Step Cyclic frequency, cyclic bandwidth , No. Maximum peak value in the cyclic frequency band It can be represented as an indicator function Format: Among them, when In frequency band China Times, Select 1 if the value is 1, otherwise select 0. Confirmed, number Step A measure of the ratio of the peak value of a harmonic to its corresponding threshold value Based on statistical thresholds The calculation shows that: in Corresponding to periodic frequency Order, after calculating all Bring Then, the total can be calculated using the geometric mean. To make the final decision, among which This represents the total harmonic order, and this formula can be used as the cost function for subsequent algorithms.

7. The propeller noise cyclic coherent demodulation method based on an improved real-number genetic algorithm according to claim 6, characterized in that: According to step 8, the specific method is as follows: The demodulation spectrum calculation formula is as follows: The result is the final obtained optimal coherent weighted demodulation spectrum of the target, which provides more accurate target propeller features for passive target identification.

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