Ship radiation noise data augmentation method based on frequency spectrum reconstruction, medium and system

Abstract

The invention provides a ship radiation noise data augmentation method based on spectrum reconstruction, a medium and a system, and belongs to the technical field of ship radiation noise processing. After a continuous spectrum and a line spectrum are separated through smooth filtering, a continuous spectrum segmentation parameter, a line spectrum frequency amplitude parameter and a modulation spectrum fundamental frequency parameter are extracted; constructing a continuous spectrum reconstruction game model and a line spectrum detection game model to respectively optimize a filter coefficient and a detection threshold, solving the filter coefficient based on the continuous spectrum reconstruction game model by adopting a variable step size normalized adaptive iterative algorithm, and generating a continuous spectrum reconstruction time domain signal; a line spectrum effective frequency set is determined by adopting a constant false alarm rate adaptive detection algorithm based on a line spectrum detection game model, then a line spectrum reconstruction time domain signal is generated, a modulation pulse sequence is constructed according to the main shaft frequency and the blade number to generate a modulation spectrum reconstruction time domain signal, and the technical problem that the number of ship radiation noise samples is insufficient is solved.

Description

Technical Field

[0001] This invention belongs to the field of ship radiated noise processing technology, and specifically relates to a method, medium and system for augmenting ship radiated noise data based on spectrum reconstruction. Background Technology

[0002] Ship radiated noise identification is an important research direction in underwater acoustic signal processing. Traditional data augmentation methods mainly include techniques such as time-domain waveform superposition, frequency-domain feature transformation, and generative adversarial network (GAN) synthesis. Time-domain waveform superposition generates new data by directly mixing different noise samples; frequency-domain feature transformation expands data by performing operations such as translation and scaling of the spectrum; and GANs generate new noise signals by learning the sample distribution. However, existing methods have significant drawbacks in the data augmentation process: time-domain superposition methods struggle to preserve the physical characteristics and spectral structure of ship radiated noise; frequency-domain transformation methods easily disrupt the energy distribution relationship between the continuous spectrum and the line spectrum; and GANs require a large number of training samples and have poor physical interpretability of the generated signals. In current applications of ship radiated noise identification, the limited number of actual ship noise samples collected and the high cost of acquisition lead to overfitting of deep learning models due to insufficient training samples, making it difficult to improve classification accuracy. In other words, existing technologies suffer from the technical problem of insufficient ship radiated noise samples, making it impossible to train deep learning models. Summary of the Invention

[0003] In view of this, the present invention provides a method, medium and system for augmenting ship radiated noise data based on spectrum reconstruction, which can solve the technical problem in the prior art that the insufficient number of ship radiated noise samples makes it impossible to train deep learning models.

[0004] The present invention is implemented as follows: The first aspect of the present invention provides a method for augmenting ship radiated noise data based on spectrum reconstruction, comprising: acquiring ship radiated noise time-domain signals and preprocessing them to obtain preprocessed time-domain signals; performing discrete Fourier transform on the preprocessed time-domain signals to obtain frequency-domain signals; converting the frequency-domain signals into sound pressure level spectrum signals; performing smoothing filtering on the sound pressure level spectrum signals to separate the continuous spectrum and line spectrum; extracting continuous spectrum segmentation parameters, line spectrum frequency amplitude parameters, and modulation spectrum fundamental frequency parameters; and constructing a continuous spectrum reconstruction game model and a line spectrum detection game model. The continuous spectrum reconstruction game model has the upper-level objective of minimizing filter approximation error and the lower-level objective of maximizing frequency band energy concentration. The line spectrum detection game model has the upper-level objective of maximizing detection probability and the lower-level objective of minimizing false alarm rate. Based on the continuous spectrum reconstruction game model, a variable step-size normalized adaptive iterative algorithm is used to solve the continuous spectrum reconstruction filter coefficients. Gaussian white noise is passed through the digital filter corresponding to the continuous spectrum reconstruction filter coefficients to obtain the continuous spectrum reconstruction time-domain signal. Based on the line spectrum detection game model, a constant false alarm rate adaptive detection algorithm is used to determine the effective frequency set of the line spectrum. The graph theory maximum clique algorithm is used to identify the harmonic relationship to determine the main shaft frequency and the number of blades. The single-frequency signals corresponding to the effective frequency set of the line spectrum are superimposed to obtain the line spectrum reconstruction time-domain signal. A modulation pulse sequence is constructed according to the main shaft frequency and the number of blades. The modulation pulse sequence is multiplied with the continuous spectrum reconstruction time-domain signal to obtain the modulation spectrum reconstruction time-domain signal. The continuous spectrum reconstruction time-domain signal, the line spectrum reconstruction time-domain signal, and the modulation spectrum reconstruction time-domain signal are superimposed to obtain the augmented ship radiated noise time-domain signal.

[0005] Specifically, the step of obtaining the preprocessed time-domain signal involves truncating the long-term ship radiated noise input signal to obtain a truncated time-domain signal, calculating the average value of the truncated time-domain signal and subtracting the average value to obtain a de-DC biased time-domain signal, passing the de-DC biased time-domain signal through a noise reduction filter to obtain a noise-reduced time-domain signal, and downsampling the noise-reduced time-domain signal to obtain the preprocessed time-domain signal.

[0006] The downsampling calculation is performed by determining the downsampled sampling frequency based on the upper limit frequency of the frequency domain of interest, which satisfies the Nyquist sampling theorem, calculating the integer multiple relationship between the original sampling frequency and the downsampled sampling frequency, and performing downsampling according to the integer multiple relationship.

[0007] Specifically, the step of extracting continuous spectrum segmentation parameters involves smoothing the sound pressure level spectrum signal to obtain a smoothed sound pressure level spectrum signal. The smoothed sound pressure level spectrum signal includes a first segment that linearly increases from the starting frequency to the peak frequency according to the first gradient and a second segment that linearly decreases from the peak frequency to the cutoff frequency according to the second gradient. The starting frequency, the corresponding starting sound pressure level, the first gradient, the peak frequency, the peak sound pressure level, the second gradient, the cutoff frequency, and the ending sound pressure level are extracted as continuous spectrum segmentation parameters.

[0008] The extraction step of the line spectrum frequency amplitude parameter specifically involves calculating the difference between the sound pressure level spectrum signal and the smoothed sound pressure level spectrum signal to obtain the difference sound pressure level spectrum signal, setting a uniform threshold to filter the frequencies in the difference sound pressure level spectrum signal that are higher than the uniform threshold to form an effective frequency set, verifying the multiple relationship between the frequencies in the effective frequency set to construct an octave frequency set, and extracting the frequencies and corresponding sound pressure levels in the octave frequency set as the line spectrum frequency amplitude parameter.

[0009] The extraction step of the fundamental frequency parameter of the modulation spectrum specifically involves selecting frequency elements less than 100Hz and greater than 4000Hz from the set of harmonic frequencies, verifying the multiple relationship between the two frequencies, selecting the frequency with the widest and smallest multiple relationship as the main shaft frequency, and calculating the multiple relationship between other frequencies greater than the main shaft frequency in the set of harmonic frequencies and the main shaft frequency to determine the number of blades.

[0010] In the continuous spectrum reconstruction game model, the objective function of the upper-level model is used to measure the weighted mean square error between the expected frequency response and the actual frequency response, while the objective function of the lower-level model is used to measure the weighted combination of the energy concentration of the key frequency band and the uniformity of the energy distribution across the entire frequency band. The two models are coupled through weight coefficients.

[0011] In the line spectrum detection game model, the upper-level objective function is used to measure the weighted combination of the probability of the true line spectrum being correctly detected and the detection stability, while the lower-level objective function is used to measure the weighted combination of the false alarm rate of noise peaks being misclassified as line spectra and the threshold volatility. The two models are coupled through the detection threshold.

[0012] The steps for solving the continuous spectrum reconstruction filter coefficients are as follows: the continuous spectrum reconstruction filter coefficients are initialized as zero vectors, a Gaussian white noise signal is generated, the desired sound pressure level is calculated by linear interpolation based on the continuous spectrum segmentation parameters and multiplied by weighting coefficients to obtain the desired frequency response, the Gaussian white noise signal is passed through the digital filter corresponding to the current continuous spectrum reconstruction filter coefficients to obtain the filtered signal, the filtered signal is subjected to discrete Fourier transform to obtain the actual frequency response, the residual between the desired frequency response and the actual frequency response is calculated, and the continuous spectrum reconstruction filter coefficients are updated using a variable step size normalization adaptive iterative algorithm based on the residual.

[0013] Among them, the variable step size normalized adaptive iterative algorithm updates by adaptively adjusting the variable step size parameter according to the residual. When the residual is large, the step size is larger to speed up the convergence speed, and when the residual is small, the step size is smaller to improve the convergence accuracy.

[0014] Specifically, the steps for obtaining the time-domain signal for line spectrum reconstruction involve calculating the local noise power of each frequency in the differential sound pressure level spectrum signal based on the constant false alarm rate adaptive detection algorithm, determining the adaptive detection threshold based on the local noise power and the set false alarm rate, filtering the frequencies in the differential sound pressure level spectrum signal that are higher than the adaptive detection threshold into a preliminary line spectrum frequency set, and performing morphological filtering on the preliminary line spectrum frequency set to suppress isolated noise peaks to obtain the effective line spectrum frequency set.

[0015] The graph theory maximum clique algorithm calculates the effective frequency set of the line spectrum as the vertices of an undirected graph. If two frequencies satisfy an integer multiple relationship, an edge is connected between the two vertices. All maximal cliques are searched and sorted by size. The maximum clique containing the most harmonic relationships is selected as the harmonic line spectrum set. The greatest common divisor of all frequencies in the harmonic line spectrum set is calculated to determine the candidate values ​​of the principal axis frequency.

[0016] The generation of single-frequency signals involves calculating the amplitude of a single-frequency signal based on each frequency in the effective frequency set of the line spectrum and its corresponding sound pressure level and the expected sound pressure level of the continuous spectrum, generating a single-frequency signal of the corresponding frequency and setting a random phase, and then superimposing all single-frequency signals to obtain a line spectrum reconstructed time-domain signal.

[0017] Specifically, the steps for obtaining the time-domain signal of the modulation spectrum reconstruction are as follows: calculating the width parameter of a single modulation pulse based on the spindle frequency and the number of blades; calculating the amplitude parameter of a single modulation pulse based on the average amplitude of the single-frequency signal and the attenuation factor in the time-domain signal of the line spectrum reconstruction; generating a single discrete Gaussian pulse signal based on the amplitude parameter and the width parameter; and constructing a modulation pulse sequence by repeating the single discrete Gaussian pulse signal according to the period determined by the spindle frequency and the number of blades.

[0018] In this process, the modulation pulse sequence is multiplied by the continuous spectrum reconstructed time-domain signal by truncating the modulation pulse sequence to make its length the same as the length of the continuous spectrum reconstructed time-domain signal, and then multiplying the truncated modulation pulse sequence with the continuous spectrum reconstructed time-domain signal point by point to obtain the modulation spectrum reconstructed time-domain signal.

[0019] Among them, the acquisition of the time-domain signal of the augmented ship radiated noise is achieved by superimposing the time-domain signal of the continuous spectrum reconstruction, the time-domain signal of the line spectrum reconstruction, and the time-domain signal of the modulation spectrum reconstruction in the time domain.

[0020] A second aspect of the present invention provides a computer-readable storage medium storing program instructions that, when executed in a computer, are used to perform the above-described method for augmenting ship radiated noise data based on spectrum reconstruction.

[0021] A third aspect of the present invention provides a ship radiated noise data augmentation system based on spectrum reconstruction, comprising the aforementioned computer-readable storage medium, wherein the system is a computer, the computer-readable storage medium is disposed within the system, and the system is provided with a microprocessor for executing program instructions stored in the computer-readable storage medium.

[0022] This invention proposes a method for augmenting ship radiated noise data based on spectrum reconstruction. By extracting continuous spectrum segmentation parameters, line spectrum frequency amplitude parameters, and modulation spectrum fundamental frequency parameters, the three spectral components—continuous spectrum, line spectrum, and modulation spectrum—are reconstructed and then superimposed to generate augmented samples. This invention employs a two-layer game model to optimize the spectrum reconstruction process. The continuous spectrum reconstruction game model ensures the energy distribution characteristics of the continuous spectrum through coupled optimization of minimizing the approximation error of the upper-layer filter and maximizing the energy concentration of the lower-layer frequency band. The line spectrum detection game model accurately identifies the harmonic relationships of the line spectrum through coupled optimization of maximizing the detection probability of the upper layer and minimizing the false alarm rate of the lower layer. The modulation spectrum reconstruction simulates the modulation effect by constructing a pulse sequence based on the main shaft frequency and the number of blades. This physics-based spectrum reconstruction method maintains the essential physical properties of ship radiated noise, such as the continuous spectrum envelope characteristics, line spectrum harmonic structure, and modulation spectrum periodic characteristics. Furthermore, it achieves sample diversity through random parameter perturbation. The generated augmented samples are highly consistent with the real samples in terms of spectral structure, effectively expanding the number of training samples while ensuring sample quality. In summary, the present invention solves the technical problem mentioned in the background art of insufficient number of ship radiated noise samples, which prevents deep learning model training. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention.

[0024] Figure 2 The diagram shows the time-domain signal processing of ship radiated noise, which includes four sub-diagrams: (A) frequency domain diagram, (B) spectrum diagram, (C) continuous spectrum diagram, and (D) line spectrum diagram.

[0025] Figure 3 This is a comparison chart of the original sound pressure level spectrum and the smoothed spectrum.

[0026] Figure 4 The image shows the results of identifying the harmonic relationships in the line spectrum.

[0027] Figure 5 The frequency response diagram of the continuous spectrum reconstruction filter.

[0028] Figure 6 This is a comparison chart of the spectra of the augmented signal and the original signal.

[0029] Figure 7The comparison diagram between the augmented signal and the measured signal includes four sub-plots: (E) is the frequency-sound pressure level plot of the augmented signal, (F) is the frequency-sound pressure level plot of the first measured signal, (G) is the frequency-sound pressure level plot of the second measured signal, and (H) is the frequency-sound pressure level plot of the third measured signal. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0031] like Figure 1 The diagram shown is a flowchart of a method for augmenting ship radiated noise data based on spectrum reconstruction, provided in the first aspect of this invention. This method includes the following steps:

[0032] S1. Collect the ship's radiated noise time-domain signal and preprocess it. After extracting the stable signal segment, perform DC bias removal, noise reduction filtering and downsampling processing in sequence to obtain the preprocessed time-domain signal.

[0033] S2. Perform Discrete Fourier Transform on the preprocessed time-domain signal to obtain the frequency-domain signal, convert the frequency-domain signal into a sound pressure level spectrum signal, perform smoothing filtering on the sound pressure level spectrum signal to separate the continuous spectrum and the line spectrum, and extract the continuous spectrum segmentation parameters, the line spectrum frequency amplitude parameters, and the modulation spectrum fundamental frequency parameters.

[0034] S3. Construct a continuous spectrum reconstruction game model and a line spectrum detection game model. The continuous spectrum reconstruction game model takes minimizing the filter approximation error as the upper-level objective and maximizing the frequency band energy concentration as the lower-level objective. The line spectrum detection game model takes maximizing the detection probability as the upper-level objective and minimizing the false alarm rate as the lower-level objective.

[0035] S4. Based on the continuous spectrum reconstruction game model, the variable step size normalization adaptive iterative algorithm is used to solve the continuous spectrum reconstruction filter coefficients. The Gaussian white noise is passed through the digital filter corresponding to the continuous spectrum reconstruction filter coefficients to obtain the continuous spectrum reconstruction time domain signal.

[0036] S5. Based on the line spectrum detection game model, the constant false alarm rate adaptive detection algorithm is used to determine the effective frequency set of the line spectrum. The graph theory maximum clique algorithm is used to identify the harmonic relationship to determine the main shaft frequency and the number of blades. The single-frequency signals corresponding to the effective frequency set of the line spectrum are superimposed to obtain the line spectrum reconstructed time domain signal.

[0037] S6. Construct a modulation pulse sequence based on the main shaft frequency and the number of blades. Multiply the modulation pulse sequence with the continuous spectrum reconstruction time-domain signal to obtain the modulation spectrum reconstruction time-domain signal. Superimpose the continuous spectrum reconstruction time-domain signal, the line spectrum reconstruction time-domain signal, and the modulation spectrum reconstruction time-domain signal to obtain the augmented ship radiated noise time-domain signal.

[0038] The process of acquiring the preprocessed time-domain signal includes: truncating the long-term ship radiated noise input signal, and extracting a time interval of [duration missing] after the input stabilizes. The signal segment of one second is used as the truncated time-domain signal; the average value of the truncated time-domain signal is calculated, and the average value is subtracted from the truncated time-domain signal to obtain the DC-biased time-domain signal; the DC-biased time-domain signal is passed through a noise reduction filter to obtain the noise-reduced time-domain signal; based on the upper limit frequency of the frequency range of interest... Determine the sampling frequency after downsampling Satisfying the Nyquist sampling theorem, calculate the original sampling frequency. Sampling frequency after downsampling Integer multiples The time-domain signal is denoised according to integer multiples. Downsampling is performed to obtain a preprocessed time-domain signal.

[0039] The mathematical expression of the truncated time-domain signal is as follows: ,in , The signal amplitude, For signal frequency, For signal phase, The sampling interval is... For the summation variable. The expression of the DC bias-free time-domain signal is as follows: ,in This indicates an averaging operation. The denoised time-domain signal is represented as follows: ,in This is a noise reduction filter. The downsampling sampling frequency... satisfy Integer multiple relationship ,in This indicates a floor operation. The preprocessed time-domain signal is expressed as follows: ,in .

[0040] The extraction process of the continuous spectrum segmentation parameters, line spectrum frequency amplitude parameters, and modulation spectrum fundamental frequency parameters includes: performing a discrete Fourier transform on the preprocessed time-domain signal to obtain a frequency-domain signal; converting the frequency-domain signal from voltage amplitude to sound pressure amplitude to calculate the sound pressure level spectrum signal; and performing smoothing filtering on the sound pressure level spectrum signal to obtain a smoothed sound pressure level spectrum signal. The smoothed sound pressure level spectrum signal exhibits segmented characteristics, including a first segment and a second segment. The first segment starts from the starting frequency... and corresponding initial sound pressure level Initially, increase with the logarithm of the frequency according to the first gradient. linearly increasing to peak frequency Reaching peak sound pressure level The second paragraph starts from the peak frequency. and peak sound pressure level Initially, increase with the logarithm of the frequency according to the second gradient. linearly decreasing to the cutoff frequency Reaching the final sound pressure level Extract the starting frequency Corresponding initial sound pressure level First gradient Peak frequency Peak sound pressure level Second gradient Cutoff frequency and the final sound pressure level As a continuous spectrum segmentation parameter; the difference between the sound pressure level spectrum signal and the smoothed sound pressure level spectrum signal is calculated to obtain the difference sound pressure level spectrum signal, and a uniform threshold is set. Filtering signals with differential sound pressure levels above a uniform threshold The frequencies constitute the effective frequency set Verify the effective frequency set Constructing a set of harmonic frequencies based on the multiple relationships between intermediate frequencies Extract the set of harmonic frequencies The mid-frequency and corresponding sound pressure level are used as line spectrum frequency amplitude parameters; a set of harmonic frequencies is selected. For frequency elements below 100Hz and above 4000Hz, verify the multiple relationship between the two frequency groups, and select the frequency with the widest and smallest multiple relationship as the principal axis frequency. Calculate the set of harmonic frequencies Medium to high spindle frequency Other frequencies and spindle frequency The multiple relationship determines the number of leaves The spindle frequency and number of leaves As the fundamental frequency parameter of the modulation spectrum.

[0041] The frequency domain signal after the discrete Fourier transform is expressed as follows: ,in , For the length of the preprocessed time-domain signal, For discretized frequencies, The imaginary unit is used. The sound pressure level spectral signal is expressed as... ,in The frequency domain signal corresponds to the sound pressure amplitude. For reference sound pressure level, This indicates the absolute value operation. The smoothed sound pressure level spectrum signal is described as follows: ,in This is a smoothing filter. The differential sound pressure level spectral signal is expressed as follows: The effective frequency set satisfy ,in The set of all frequencies. The set of harmonic frequencies. satisfy ,in The number of blades is a positive integer. Verification conditions are .

[0042] The continuous spectrum reconstruction game model comprises an upper-level model and a lower-level model. The upper-level model aims to minimize the filter approximation error, while the lower-level model aims to maximize the frequency band energy concentration. The two models are coupled through weight coefficients. The objective function of the upper-level model measures the weighted mean square error between the desired and actual frequency responses. Its inputs include continuous spectrum segmentation parameters, actual frequency responses, and weight coefficients, and its output is the filter approximation error. The objective function of the lower-level model measures a weighted combination of the energy concentration in the key frequency band and the uniformity of energy distribution across the entire frequency band. Its inputs include the frequency response energy distribution, the key frequency band range, and weight coefficients, and its output is the frequency band energy concentration. The coupling term between the two models is the weight coefficient, which is adaptively adjusted based on the distance between the key frequency band and the current frequency.

[0043] The objective function of the upper-level model is: ,in For weighting coefficients, For the desired frequency response, This is the actual frequency response. and We are concerned with the lower and upper limits of the frequency band. The objective function of the lower-level model is: ,in For the key frequency band range, and The weighting coefficients are defined as follows: the first term represents the energy proportion of the key frequency band, and the second term represents the reciprocal of the energy distribution uniformity. The weighting coefficients are expressed as follows: when hour, Otherwise, among them Peak frequency, This represents the frequency offset.

[0044] The line spectrum detection game theory model comprises an upper-level model and a lower-level model. The upper-level model aims to maximize the detection probability, while the lower-level model aims to minimize the false alarm rate. The two models are coupled through a detection threshold. The objective function of the upper-level model measures a weighted combination of the probability of correctly detecting a true line spectrum and detection stability. Its inputs include the difference sound pressure level spectrum signal, the detection threshold, and local noise power estimation; the output is the detection probability. The objective function of the lower-level model measures a weighted combination of the false alarm rate of noise peaks being misidentified as line spectra and threshold fluctuations. Its inputs include local noise power estimation, the detection threshold, and noise statistical characteristics; the output is the false alarm rate. The coupling term between the two models is the detection threshold, which is dynamically adjusted based on the local noise power to achieve a constant false alarm rate.

[0045] The objective function of the upper-level model is: ,in For detection probability, To test the stability of the probability variance representation. These are weighting coefficients. The detection probability is expressed as... ,in It is the set of true line spectrum frequencies. For indicator functions, To detect threshold, This represents the number of elements in the set. The objective function of the lower-level model is... ,in False alarm rate For threshold volatility, The weighting coefficient is used. The false alarm rate is expressed as... ,in This is the set of pure noise frequencies. The detection threshold is expressed as... ,in This represents the average local noise power. The standard deviation of local noise power. This is the threshold factor.

[0046] The process of solving the continuous spectrum reconstruction filter coefficients includes: initializing the continuous spectrum reconstruction filter coefficients as a zero vector, generating a vector of length... The Gaussian white noise signal is used as the input signal; the desired sound pressure level corresponding to any frequency in the band of interest is calculated by linear interpolation based on the continuous spectrum segmentation parameters, and the desired sound pressure level is multiplied by the weighting coefficient to obtain the desired frequency response; the Gaussian white noise signal is passed through the digital filter corresponding to the current continuous spectrum reconstruction filter coefficient to obtain the filtered signal, and the filtered signal is subjected to discrete Fourier transform to obtain the actual frequency response; the residual between the desired frequency response and the actual frequency response is calculated, and the continuous spectrum reconstruction filter coefficient is updated using a variable step size normalization adaptive iterative algorithm based on the residual; it is determined whether the residual is less than the convergence threshold. If not, the filtering step is returned to continue iterating; if so, the continuous spectrum reconstruction filter coefficient is output; the new Gaussian white noise signal is passed through the digital filter corresponding to the continuous spectrum reconstruction filter coefficient to obtain the continuous spectrum reconstruction time domain signal.

[0047] The desired sound pressure level is expressed as when hour, when The desired frequency response is expressed as follows: The filtered signal is described as follows: ,in It is a Gaussian white noise signal. These are the coefficients of the continuous spectrum reconstruction filter. The actual frequency response is expressed as... The update formula for the variable step-size normalized adaptive iterative algorithm is as follows: , , ,in For convolution operators, For residuals, For variable step size parameters, To prevent small constants from being divided by zero, the variable step size parameter is expressed as follows: , For the maximum step size, This is the step size adjustment factor.

[0048] The process of acquiring the time-domain signal for line spectrum reconstruction includes: calculating the local noise power of each frequency in the differential sound pressure level spectrum signal based on a constant false alarm rate adaptive detection algorithm; determining the adaptive detection threshold based on the local noise power and the set false alarm rate; selecting frequencies in the differential sound pressure level spectrum signal above the adaptive detection threshold as a preliminary line spectrum frequency set; performing morphological filtering on the preliminary line spectrum frequency set to suppress isolated noise peaks to obtain the effective line spectrum frequency set; constructing the effective line spectrum frequency set as vertices of an undirected graph; connecting edges between vertices if two frequencies satisfy an integer multiple relationship; using a graph theory maximum clique algorithm to search for all maximal cliques and sorting them by size; selecting the maximum clique containing the most harmonic relationships as the harmonic line spectrum set; calculating the greatest common divisor of all frequencies in the harmonic line spectrum set to determine the candidate values ​​for the principal axis frequency; verifying the effectiveness of the candidate values ​​for the principal axis frequency by combining the mapping relationship between the low-frequency and high-frequency line spectra; and determining the principal axis frequency. and number of leaves The amplitude of a single-frequency signal is calculated based on each frequency in the effective frequency set of the line spectrum, its corresponding sound pressure level, and the expected sound pressure level of the continuous spectrum. A single-frequency signal of the corresponding frequency is generated and a random phase is set. All single-frequency signals are superimposed to obtain the time-domain signal of the line spectrum reconstruction.

[0049] The local noise power is expressed as the frequency of the differential sound pressure level spectral signal. The average power is calculated using a sliding window within the neighborhood. The adaptive detection threshold satisfies the constant false alarm rate condition. ,in To set the false alarm rate, the following is obtained: The morphological filtering employs opening operations to remove isolated small peaks while preserving the continuous spectral structure. The graph theory maximum clique algorithm uses the Bron-Kerbosch recursive algorithm, utilizing vertex degree for pruning to reduce the search space. The criterion for determining the multiple relationship is... ,in This indicates rounding to the nearest integer. Tolerance for multiple relationships. The greatest common divisor is calculated using the Euclidean algorithm to find the greatest common divisor of all frequencies in the octave line spectrum set. The amplitude of the single-frequency signal is expressed as... when hour, Otherwise, among them This is the sound pressure level to voltage amplitude conversion factor. The effective frequency set. The time-domain signal reconstructed from the line spectrum is expressed as: ,in From 0 to Random phases between.

[0050] The process of acquiring the modulation spectrum reconstruction time-domain signal includes: based on the principal axis frequency. and number of leaves The width parameter of a single modulation pulse is calculated. The amplitude parameter of a single modulation pulse is calculated based on the average amplitude of the single-frequency signal and the attenuation factor in the time-domain signal reconstructed from the line spectrum. The attenuation factor is randomly selected between 0 and 0.6. A single discrete Gaussian pulse signal is generated based on the amplitude and width parameters, according to the principal axis frequency. and number of leaves A modulated pulse sequence is constructed by repeatedly generating a single discrete Gaussian pulse signal with a defined period; the length of the modulated pulse sequence is truncated to be the same as the length of the continuous spectrum reconstructed time-domain signal, and the truncated modulated pulse sequence is multiplied point by point with the continuous spectrum reconstructed time-domain signal to obtain the modulated spectrum reconstructed time-domain signal.

[0051] The single discrete Gaussian pulse signal is expressed as follows: ,in The amplitude of the pulse signal. The pulse signal width is defined as follows. The pulse signal amplitude is expressed as... ,in This is the average amplitude of a single-frequency signal. It is the attenuation factor and The pulse signal width is described as follows: The modulation pulse sequence is described as follows: ,in subscript Indicates the first A pulse. The time-domain signal reconstructed from the modulation spectrum is expressed as: .

[0052] The process of acquiring the augmented ship radiated noise time-domain signal is as follows: the continuous spectrum reconstructed time-domain signal, the line spectrum reconstructed time-domain signal, and the modulation spectrum reconstructed time-domain signal are superimposed in the time domain. The superimposed signal is the augmented ship radiated noise time-domain signal. The augmented ship radiated noise time-domain signal is described as follows: ,in This is the index for time-domain sampling points.

[0053] The continuous spectrum segmentation parameters are a combination of parameters describing the segmentation characteristics of the smooth sound pressure level spectrum signal, including the starting frequency. Corresponding initial sound pressure level First gradient Peak frequency Peak sound pressure level Second gradient Cutoff frequency and the final sound pressure level The line spectrum frequency amplitude parameter is a combination of parameters describing the characteristics of the line spectrum, including a set of harmonic frequencies. Mid-frequency and corresponding sound pressure level The fundamental frequency parameter of the modulation spectrum is a combination of parameters describing the characteristics of the modulation spectrum, including the principal axis frequency. and number of leaves The constant false alarm rate adaptive detection algorithm is a detection method that dynamically adjusts the detection threshold based on local noise power to maintain a constant false alarm rate. The graph theory maximum clique algorithm is an algorithm for searching the largest complete subgraph in an undirected graph, used to identify harmonic relationships between frequencies. The Bron-Kerbosch recursive algorithm is a recursive algorithm that enumerates all maximal cliques in an undirected graph. The morphological filtering is a filtering method based on mathematical morphology, which removes isolated noise peaks through opening operations. The single-frequency signal is a sinusoidal signal with a fixed frequency.

[0054] The specific implementation methods of the above steps are described in detail below.

[0055] Step S1 involves systematically preprocessing the acquired raw ship radiated noise signal to extract stable and effective signal segments. The purpose of this step is to eliminate non-stationary interference and redundant information in the signal, providing a high-quality time-domain data foundation for subsequent frequency domain analysis. First, the stability of the long-term input signal is assessed. The moment the signal enters a stable state is determined by calculating the time-varying characteristics of the signal energy. From this moment, a segment is extracted for a duration of... The signal segment, typically 10 to 30 seconds long, is used for subsequent processing to ensure sufficient spectral information while avoiding excessive computational complexity. The time-domain average of the truncated signal segment is then calculated, and this average is subtracted point-by-point from the signal to remove the DC bias component. This operation is based on the principle that signal mean drift affects the accuracy of frequency domain analysis, and centering the signal to make it fluctuate around zero. Next, the de-DC signal is denoised using a digital filter designed based on bandpass filtering principles. Its passband range is determined according to the frequency range of interest, typically 10Hz to 10000Hz. A filter order of 64 to 128 is recommended to balance filtering effect and phase distortion. Finally, the new sampling frequency after downsampling is determined according to the Nyquist sampling theorem. This frequency is at least twice the upper limit of the frequency of interest, and is usually set to 2.5 times the upper limit of the frequency of interest to leave a margin. After calculating the integer multiple relationship between the original sampling frequency and the new sampling frequency, the signal is downsampled according to this multiple relationship. This operation, based on multi-rate signal processing principles, effectively reduces the amount of data and lowers the computational burden.

[0056] Step S2 involves performing frequency domain transformation and feature parameter extraction on the preprocessed time-domain signal. The purpose of this step is to convert the time-domain signal into a frequency-domain representation and separate the key parameters of the three components: continuous spectrum, line spectrum, and modulation spectrum. First, a Discrete Fourier Transform (DFT) is performed on the preprocessed time-domain signal. This transform maps the time-domain signal to the frequency domain based on the principle of signal spectrum decomposition. The transform length is equal to the number of sampling points of the preprocessed signal; a Fast Fourier Transform (FFT) algorithm is typically used to improve computational efficiency. Then, the frequency-domain signal is converted from voltage amplitude units to sound pressure level (SPL) amplitude units. This conversion requires determining the conversion coefficients based on the sensor sensitivity and preamplifier gain of the acquisition system. After the conversion, the SPL spectrum relative to a reference SPL is calculated, where the reference SPL value is 2 × 10⁻⁶. Pascal. Next, a smoothing filter is applied to the sound pressure level spectrum using a moving average filter principle. The sliding window length is set to 5 to 10 times the frequency resolution. The purpose of this operation is to extract the envelope characteristics of the spectrum while preserving the peak information of the line spectrum. The smoothed spectrum exhibits obvious piecewise linear characteristics. By identifying three key points in the smoothed spectrum—the start frequency, peak frequency, and cutoff frequency—the logarithmic frequency gradient from the start frequency to the peak frequency and from the peak frequency to the cutoff frequency are calculated. These parameters constitute the set of continuous spectrum piecewise parameters. The difference between the original sound pressure level spectrum and the smoothed spectrum is calculated to obtain the residual spectrum. This residual spectrum reflects the degree of convexity of the line spectrum components relative to the continuous spectrum background. A uniform threshold value is set to filter the peak frequencies in the residual spectrum; the threshold value is usually set to 3 to 6 dB. The selected frequency set is then verified for multiples of frequency. A clique detection algorithm from graph theory is used to identify frequency groups with integer multiples of frequency. This algorithm is based on the principle of constructing frequencies as vertices of a graph and multiples of frequency as edges. Searching the largest complete subgraph in the graph will find the frequency group with the richest multiples of frequency. Low-frequency components less than 100Hz and high-frequency components greater than 4000Hz are selected from this harmonic frequency group. The candidate value of the main shaft frequency is determined by calculating the greatest common divisor. The multiple relationship between the candidate value and other frequencies is verified to determine the number of blades. The number of blades is usually an integer and between 3 and 7.

[0057] The specific implementation of step S3 involves constructing two coupled game-theoretic optimization models to guide the continuous spectrum reconstruction and line spectrum detection processes. The purpose of this step is to establish a multi-objective optimization framework to balance the contradictory relationships between different performance indicators. The continuous spectrum reconstruction game-theoretic model adopts a two-layer optimization architecture. The upper-layer objective is to minimize the weighted mean square error between the desired frequency response and the actual frequency response. This objective ensures that the reconstructed continuous spectrum approximates the original spectrum in its overall shape. The weight coefficients are adaptively adjusted based on the distance between the frequency point and the peak frequency. The weight coefficients near the peak frequency are set to 1.0 to enhance the approximation accuracy, while those far from the peak frequency are set to 0.1 to relax the constraints. The frequency offset threshold is recommended to be set to 5% to 10% of the peak frequency. The lower-layer objective is to maximize the energy concentration of the key frequency band while minimizing the unevenness of the energy distribution across the entire frequency band. This objective is achieved through a weighted combination of two terms: the first term calculates the proportion of energy in the key frequency band to the total energy, and the second term calculates the ratio of the maximum to the minimum energy value as the reciprocal of the uniformity. The weight coefficients for these two terms are recommended to be set to 0.7 and 0.3, respectively. The line spectrum detection game theory model also employs a two-layer optimization architecture. The upper-layer objective is to maximize the detection probability of the true line spectrum while minimizing the variance of the detection probability to improve detection stability. A weighting coefficient of 0.8 is recommended to prioritize ensuring the detection probability. The lower-layer objective is to minimize the false alarm rate while minimizing the volatility of the detection threshold. The false alarm rate reflects the probability of a noise peak being misidentified as a line spectrum, while threshold volatility reflects the stability of the detection threshold with frequency. A weighting coefficient of 0.9 is recommended to prioritize controlling the false alarm rate. The two game theory models are coupled through the weighting coefficients and the detection threshold. The weighting coefficients affect the frequency response of the continuous spectrum reconstruction, thus influencing the background noise estimation for line spectrum detection. The detection threshold is dynamically adjusted based on local noise power to achieve a constant false alarm rate characteristic.

[0058] Step S4 is specifically implemented by solving the digital filter coefficients and generating a continuous spectrum reconstructed signal based on a continuous spectrum reconstruction game model. The purpose of this step is to shape Gaussian white noise into a continuous spectrum signal with desired spectral characteristics using an adaptive filtering algorithm. First, the filter coefficients are initialized as zero vectors. The filter length is typically set to 128 to 256 to balance frequency resolution and computational complexity. Gaussian white noise of the same length as the preprocessed signal is generated as the input excitation signal. Based on the continuous spectrum segmentation parameters, the desired sound pressure level at each frequency point within the band of interest is calculated using piecewise linear interpolation. In logarithmic frequency coordinates, the sound pressure level increases linearly from the starting frequency to the peak frequency segment according to the first gradient, and decreases linearly from the peak frequency to the cutoff frequency segment according to the second gradient. The desired sound pressure level is multiplied by weighting coefficients to obtain the weighted desired frequency response. The Gaussian white noise is passed through a finite impulse response digital filter corresponding to the current filter coefficients to obtain the filtered output signal. A discrete Fourier transform is performed on the filtered output signal to obtain the actual frequency response. The residual vector between the weighted desired frequency response and the actual frequency response is calculated. This residual vector represents the approximation error of the current filter coefficients. A variable-step-size normalized least mean square adaptive filtering algorithm is used to update the filter coefficients. This algorithm is based on the principle of stochastic gradient descent. The step size parameter is adaptively adjusted according to the instantaneous power of the residual. When the residual power is large, the step size is increased to accelerate the convergence speed, and when the residual power is small, the step size is decreased to improve the steady-state accuracy. The maximum step size is recommended to be set to 0.01 to 0.05, and the step size adjustment factor is recommended to be set to 100 to 500. The normalization process normalizes the update amount by the input signal power, which can effectively avoid the influence of the input signal power variation on the convergence performance. The zero-prevention constant is recommended to be set to 10. The algorithm checks if the mean square value of the residual is less than the convergence threshold, which is recommended to be set to 0.1% to 1% of the mean square value of the desired frequency response. If convergence is not achieved, the algorithm returns to the filtering step and continues iterating until convergence is achieved or the maximum number of iterations is reached, which is recommended to be set to 1000 to 5000. After convergence, the optimal filter coefficients are output, and new Gaussian white noise is generated and passed through this filter to obtain the continuous spectrum reconstructed time-domain signal.

[0059] The specific implementation of step S5 is based on a line spectrum detection game model to identify effective line spectrum frequencies and reconstruct the line spectrum time-domain signal. The purpose of this step is to accurately extract line spectrum components from the residual spectrum while suppressing noise interference. First, a constant false alarm rate (CFAR) adaptive detection algorithm is used to calculate the local noise power at each frequency point in the differential sound pressure level spectrum. This algorithm sets a sliding window at each frequency point, with a recommended window length of 20 to 50 times the frequency resolution. The average power of all frequency points within the window, excluding the center frequency, is calculated as the local noise power estimate. An adaptive detection threshold is then calculated based on a preset CFAR rate, which is recommended to be set to 10. Up to 10 The detection threshold is equal to the product of the mean local noise power plus the threshold factor and the standard deviation of the local noise power. The threshold factor is determined by the negative logarithm of the false alarm rate. Frequencies exceeding the detection threshold in the differential sound pressure level spectrum are selected as a preliminary line spectrum frequency set. Morphological opening filtering is applied to this set. This filtering, based on mathematical morphology principles of erosion followed by dilation, effectively removes isolated noise spikes while preserving a continuous line spectrum structure. The recommended length of the structuring element is 3 to 5 frequency points. The filtered effective frequency set is constructed as a vertex set of an undirected graph. The ratio of any two frequency points is calculated. If the deviation of the ratio from the nearest integer is less than the tolerance, the two frequencies are considered to satisfy a multiple relationship, and an edge is connected between the corresponding vertices. The recommended tolerance is 0.05 to 0.1. A recursive enumeration algorithm is used to search for all maximal complete subgraphs in the graph. This algorithm gradually expands the candidate vertex set through a depth-first search strategy, using vertex degree information for pruning to reduce the search space. All found maximal cliques are sorted by the number of vertices they contain, and the maximal clique with the most vertices is selected as the octave line spectrum set. The greatest common divisor (GCD) of all frequencies in the octave line spectrum set is calculated using the Euclidean algorithm as a candidate value for the principal axis frequency. This algorithm recursively calculates the GCD of two numbers based on the Euclidean division principle and then extends it pairwise to the entire set. The existence of a frequency equal to the candidate principal axis frequency in the low-frequency line spectrum and an integer multiple of the product of the principal axis frequency and the number of blades in the high-frequency line spectrum are verified. If the verification passes, the validity of the principal axis frequency and the number of blades is confirmed. The amplitude of the single-frequency signal is calculated based on the residual sound pressure level and the expected continuous spectrum sound pressure level at each frequency point in the effective frequency set. This amplitude is determined by the conversion factor of the sound pressure level to voltage amplitude, which is obtained based on the calibration parameters of the acquisition system. A corresponding single-frequency sinusoidal signal is generated for each effective frequency, with the phase uniformly and randomly distributed between 0 and 2π to simulate the random phase characteristics of the actual signal. All single-frequency signals are superimposed point by point to obtain the time-domain signal for line spectrum reconstruction.

[0060] The specific implementation of step S6 involves constructing a modulation pulse sequence and synthesizing the final augmented ship radiated noise signal. The purpose of this step is to simulate the modulation effect generated by the periodic cutting of water flow by propeller blades and to fuse the three spectral components into a complete signal. First, the width parameter of a single modulation pulse is calculated based on the main shaft frequency and the number of blades. This width parameter is equal to the product of 60 and the main shaft frequency, divided by the number of blades. This calculation is based on the physical principle that the blade passage frequency equals the product of the main shaft frequency and the number of blades. The average amplitude of all single-frequency signals in the line spectrum reconstruction signal is calculated. This average is multiplied by an attenuation factor to obtain the amplitude parameter of the modulation pulse. The attenuation factor is randomly selected between 0 and 0.6 to simulate the variation in modulation depth under different operating conditions; a larger attenuation factor indicates a stronger modulation effect. Based on the calculated amplitude and width parameters, a single discrete Gaussian pulse signal is generated. This pulse uses a Gaussian function to realistically reflect the pressure pulsation characteristics when the blades cut the water flow. The peak value of the Gaussian function is located at the time origin, and the standard deviation is determined by the width parameter. Based on the pulse repetition period determined by the spindle frequency and the number of blades, a single Gaussian pulse is periodically copied to construct a modulation pulse sequence. The pulse repetition period is equal to the reciprocal of the spindle frequency, and the time interval between adjacent pulses is equal to the pulse repetition period divided by the number of blades. The modulation pulse sequence is truncated to a length consistent with the length of the continuous spectrum reconstructed signal. The truncated modulation pulse sequence is multiplied with the continuous spectrum reconstructed signal point by point to obtain the modulation spectrum reconstructed signal. This multiplication operation achieves the modulation effect in the time domain, corresponding to the convolution operation in the frequency domain. Finally, the continuous spectrum reconstructed signal, the line spectrum reconstructed signal, and the modulation spectrum reconstructed signal are superimposed in the time domain. The three signals are added point by point to obtain the final augmented ship radiated noise time-domain signal, which simultaneously contains three typical ship radiated noise spectral components: broadband continuous spectrum, discrete line spectrum, and modulation sideband spectrum.

[0061] It should be noted that the key technical ideas of this invention are reflected in the following three aspects. First, a two-layer game optimization model is used to guide the continuous spectrum reconstruction and line spectrum detection processes respectively. This model achieves synergistic optimization of multiple performance indicators through the coupling of upper-layer and lower-layer objectives. Compared with traditional single-objective optimization methods, it can achieve a better balance between approximation accuracy and computational stability. At the same time, the adaptive adjustment mechanism of weight coefficients and detection thresholds improves the algorithm's adaptability to different signal-to-noise ratio conditions. Second, the robust identification of line spectrum octave relationships and accurate extraction of principal axis frequencies are achieved by combining graph theory maximum clique algorithm and Euclidean algorithm. This method maps the multiple relationships between frequencies to the topological structure of a graph. By searching the maximal complete subgraph, the most important octave group is automatically discovered. Compared with traditional threshold determination methods, it has stronger anti-noise interference capability and higher identification accuracy, and can reliably extract key parameters such as propeller speed and number of blades in complex spectrum environments. Third, physical modeling of the modulation spectrum is achieved by temporally modulating the continuous spectrum using a modulation pulse sequence. This method is based on the physical mechanism of propeller blades periodically cutting water flow. Gaussian pulse sequences are used to simulate the pressure pulsations generated by the blades passing through. A modulation sideband structure is naturally formed through time-domain multiplication, which, compared to traditional frequency-domain synthesis methods, can more realistically reproduce the time-frequency and statistical characteristics of the modulation spectrum. The synergistic effect of these three key technologies lies in constructing a complete data augmentation framework from spectral parameter extraction and component separation and reconstruction to physical mechanism modeling. Game theory optimization ensures the accuracy of each spectral component, graph theory algorithms ensure the robustness of parameter extraction, and physical modeling ensures the authenticity of the generated signal. These three elements support each other to form a closed loop, resulting in augmented ship radiated noise data that is highly consistent with real data in multiple dimensions, including frequency domain characteristics, time domain waveform, and statistical distribution. This is significantly superior to existing augmentation methods such as simple superposition or random perturbation.

[0062] It should be noted that this invention also solves the following technical problem: existing data augmentation methods struggle to maintain the consistency of the physical characteristics of ship radiated noise. Traditional methods generate new samples through simple time-domain superposition or frequency-domain transformation, often disrupting the inherent physical properties of ship radiated noise, such as the shape of the continuous spectrum envelope, the harmonic structure of the line spectrum, and the periodic characteristics of the modulation spectrum. This results in significant differences in spectral structure between the generated samples and the real samples. Such non-physical augmented samples introduce false features, thereby reducing the model's generalization ability. This invention optimizes the reconstruction process of the continuous spectrum and the line spectrum by constructing a two-layer game model. The continuous spectrum reconstruction game model achieves accurate approximation of the spectral envelope through adaptive adjustment of weight coefficients. The line spectrum detection game model accurately identifies harmonic relationships through constant false alarm rate detection and graph theory maximum clique algorithm. The modulation spectrum reconstruction simulates the propeller modulation effect based on the physical mechanism of pulse sequences. The reconstruction of all three spectral components follows the physical generation mechanism of ship radiated noise, ensuring that the augmented samples maintain a high degree of consistency with the real samples in terms of spectral structure and energy distribution, thereby guaranteeing the effectiveness of the augmented data and the reliability of model training.

[0063] A second aspect of the present invention provides a computer-readable storage medium storing program instructions that, when executed in a computer, are used to perform the above-described method for augmenting ship radiated noise data based on spectrum reconstruction.

[0064] A third aspect of the present invention provides a ship radiated noise data augmentation system based on spectrum reconstruction, comprising the aforementioned computer-readable storage medium. The system is any one of a computer, a server, or a microcontroller. The computer-readable storage medium is disposed within the system, and the system is provided with a microprocessor that executes the program instructions stored in the computer-readable storage medium.

[0065] Specifically, the principle of this invention is as follows: This invention solves the technical problem of insufficient sample quantity for ship radiated noise. Its principle lies in achieving physical mechanism-driven data augmentation through spectral decomposition and reconstruction. Ship radiated noise consists of three components: continuous spectrum, line spectrum, and modulation spectrum. This invention first extracts the characteristic parameters of these three spectral components through smoothing filtering, then reconstructs each component separately and superimposes them to generate new samples. Continuous spectrum reconstruction employs a two-layer game theory model to design an adaptive filter. The upper layer optimizes the filter approximation error to ensure the accuracy of the spectral envelope, while the lower layer optimizes the frequency band energy concentration to ensure the rationality of the energy distribution. The two-layer coupled optimization ensures that the generated continuous spectrum conforms to both the target spectral shape and the energy distribution constraints. Line spectrum detection uses a constant false alarm rate adaptive algorithm to dynamically adjust the detection threshold. After accurately extracting the line spectrum frequency, a graph theory maximum clique algorithm is used to identify the harmonic relationships, ensuring the physical correctness of the line spectrum structure. Modulation spectrum reconstruction generates a periodic pulse sequence based on the main shaft frequency and the number of blades, simulating the propeller modulation effect. This decomposition and reconstruction strategy not only maintains the physical characteristics of ship radiated noise, but also achieves sample diversity through parameter randomization, thereby effectively expanding the sample quantity while ensuring sample quality.

[0066] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0067] The specific implementation of step S1 is as follows: The ship's radiated noise time-domain signal is acquired and preprocessed. After truncating a stable signal segment, DC bias removal, noise reduction filtering, and downsampling are performed sequentially to obtain the preprocessed time-domain signal. The long-term ship radiated noise input signal is truncated, and a segment with a duration of [duration missing] is truncated after the input stabilizes. The signal segment of one second is treated as a truncated time-domain signal. The mathematical expression of the truncated time-domain signal is: In the formula, index of time-domain sampling points and , The unit of signal amplitude is volts. The signal angular frequency is expressed in radians per second. The unit for signal phase is radians. The sampling interval is in seconds. For the summation variable, To extract duration in seconds, The original sampling frequency is in Hertz. Calculate the average value of the truncated time-domain signal, and subtract this average value from the truncated time-domain signal to obtain the de-DC biased time-domain signal. The de-DC biased time-domain signal is expressed as... In the formula, This indicates the calculation of the average. The unit is volts. The de-DC biased time-domain signal is passed through a noise reduction filter to obtain the denoised time-domain signal, which is expressed as follows: In the formula, The coefficients of the noise reduction filter are dimensionless. The unit is volts. Based on the upper frequency limit of the range of interest. Determine the sampling frequency after downsampling Satisfies the Nyquist sampling theorem, where, To determine the upper frequency range of interest, with the unit being Hertz, the downsampling sampling frequency satisfies the following conditions: Calculate the original sampling frequency Sampling frequency after downsampling Integer multiples In the formula, This indicates the floor function. It is a dimensionless integer. The unit is Hertz. The time-domain signals are denoised according to integer multiples. Downsampling is performed to obtain a preprocessed time-domain signal, which is expressed as follows: In the formula, , The unit is volts.

[0068] The specific implementation of step S2 is as follows: A discrete Fourier transform is performed on the preprocessed time-domain signal to obtain a frequency-domain signal. This frequency-domain signal is then converted into a sound pressure level (SPL) spectrum signal. The SPL spectrum signal is then smoothed and filtered to separate the continuous spectrum and line spectrum. The continuous spectrum segmentation parameters, line spectrum frequency amplitude parameters, and modulation spectrum fundamental frequency parameters are extracted. The frequency-domain signal after the discrete Fourier transform is expressed as follows: In the formula, For discrete frequency index and , To preprocess time-domain signals with dimensionless length, The imaginary unit, The unit is volts. After converting the frequency domain signal from voltage amplitude to sound pressure amplitude, the sound pressure level spectrum signal is calculated. The sound pressure level spectrum signal is expressed as... In the formula, The unit for the sound pressure amplitude of the frequency domain signal is Pascal. The reference unit for sound pressure is Pascal. This indicates the absolute value operation. The unit is decibels. This represents the logarithm to base 10. Smoothing the sound pressure level spectrum signal with a smooth filter yields a smoothed sound pressure level spectrum signal, which is expressed as... In the formula, The coefficients of the smoothing filter are dimensionless. The unit is decibels (dB). A smooth sound pressure level spectrum signal exhibits segmented characteristics, including a first segment and a second segment. The first segment starts from the initial frequency... and corresponding initial sound pressure level Initially, increase with the logarithm of the frequency according to the first gradient. linearly increasing to peak frequency Reaching peak sound pressure level The second paragraph starts from the peak frequency. and peak sound pressure level Initially, increase with the logarithm of the frequency according to the second gradient. linearly decreasing to the cutoff frequency Reaching the final sound pressure level In the formula, The starting frequency is in Hertz. The corresponding initial sound pressure level is in decibels. The first gradient unit is decibels. The peak frequency is measured in Hertz. Peak sound pressure level is measured in decibels (dB). The second gradient unit is decibels. The cutoff frequency is expressed in Hertz. The starting frequency is extracted with the final sound pressure level in decibels. Corresponding initial sound pressure level First gradient Peak frequency Peak sound pressure level Second gradient Cutoff frequency and the final sound pressure level As a continuous spectrum segmentation parameter, the difference between the sound pressure level spectrum signal and the smoothed sound pressure level spectrum signal is calculated to obtain the difference sound pressure level spectrum signal, which is expressed as... In the formula, The unit is decibels. A uniform threshold is set. Filtering signals with differential sound pressure levels above a uniform threshold The frequencies constitute the effective frequency set In the formula, To standardize the threshold unit to decibels, values ​​typically range from 3 to 5, and the effective frequency set satisfies... In the formula, For the set of all frequencies and Verify the effective frequency set. Constructing a set of harmonic frequencies based on the multiple relationships between intermediate frequencies The set of harmonic frequencies satisfies In the formula, Positive integers represent frequencies and The multiple relationship, and For frequency indexing. Extract the set of harmonic frequencies. Mid-frequency and corresponding sound pressure level are used as line spectrum frequency amplitude parameters. A set of octave frequencies is selected. For frequency elements below 100Hz and above 4000Hz, verify the multiple relationship between the two frequency groups, and select the frequency with the widest and smallest multiple relationship as the principal axis frequency. Calculate the set of harmonic frequencies Medium to high spindle frequency Other frequencies and spindle frequency The multiple relationship determines the number of leaves In the formula, The spindle frequency is measured in Hertz (Hz). The number of blades is a dimensionless positive integer, and the verification condition for the number of blades is: Spindle frequency and number of leaves As the fundamental frequency parameter of the modulation spectrum.

[0069] The specific implementation of step S3 involves constructing a continuous spectrum reconstruction game model and a line spectrum detection game model. The continuous spectrum reconstruction game model includes an upper-level model and a lower-level model. The upper-level model aims to minimize the filter approximation error, and its objective function is... In the formula, The weighting coefficients are dimensionless. For the desired frequency response to be dimensionless, The actual frequency response is dimensionless. and For the frequency indices of the lower and upper bounds of the frequency band, the lower-level model aims to maximize the energy concentration within the frequency band. The objective function of the lower-level model is: In the formula, For the key frequency band range, and The weighting coefficients are dimensionless and typically take a value of 0.5. The first term represents the dimensionless proportion of energy in the key frequency band, and the second term represents the dimensionless reciprocal of the energy distribution uniformity. The coupling term between the two models is the weighting coefficient, which is expressed as... when hour, Otherwise, in the formula, The peak frequency is measured in Hertz. The frequency offset is expressed in Hertz, and the empirical value is the peak frequency. 5%. The line spectrum detection game model consists of an upper-level model and a lower-level model. The upper-level model aims to maximize the detection probability, and its objective function is... In the formula, The detection probability is dimensionless. To detect the dimensionless stability of the probability variance representation, The weighting coefficient is dimensionless and typically takes a value of 0.7. The detection probability is expressed as... In the formula, It is the set of true line spectrum frequencies. This is an indicator function that takes the value 1 if the condition is met and 0 otherwise; it is dimensionless. The detection threshold is in decibels. The number of elements in the set is dimensionless. The lower-level model aims to minimize the false alarm rate, and its objective function is: In the formula, The false alarm rate is dimensionless. The threshold fluctuation is dimensionless. The weighting coefficient is dimensionless and typically takes a value of 0.6. The false alarm rate is expressed as... In the formula, This is the set of pure noise frequencies. The coupling term between the two models is the detection threshold, which is expressed as... In the formula, The local noise power mean is expressed in decibels. The standard deviation of local noise power is expressed in decibels. The threshold factor is dimensionless and typically takes values ​​of 2 to 4.

[0070] The specific implementation of step S4 is as follows: Based on the continuous spectrum reconstruction game model, a variable step-size normalized adaptive iterative algorithm is used to solve for the continuous spectrum reconstruction filter coefficients. Gaussian white noise is then passed through the digital filter corresponding to the continuous spectrum reconstruction filter coefficients to obtain the continuous spectrum reconstruction time-domain signal. The continuous spectrum reconstruction filter coefficients are initialized as a zero vector, and a length of [missing information] is generated. The Gaussian white noise signal is used as the input signal. Based on the continuous spectrum segmentation parameters, the desired sound pressure level corresponding to any frequency within the band of interest is calculated through linear interpolation. The desired sound pressure level is expressed as... when hour, when When, in the formula, The reference frequency is in Hertz, usually taken as 1 Hz for frequency normalization. The unit is decibels (dB). The desired frequency response is obtained by converting the desired sound pressure level to a normalized amplitude and then multiplying it by weighting coefficients. The desired frequency response is expressed as... In the formula, The frequency response is dimensionless. The Gaussian white noise signal is passed through a digital filter corresponding to the coefficients of the current continuous spectrum reconstruction filter to obtain the filtered signal, which is expressed as... In the formula, The signal is Gaussian white noise, measured in volts. The coefficients of the continuous spectrum reconstruction filter are dimensionless. The unit is volts. The actual frequency response is obtained by performing a discrete Fourier transform on the filtered signal and normalizing it. The actual frequency response is expressed as... In the formula, The dimensionless normalized frequency response, This represents the modulo operation. The residual between the desired and actual frequency responses is calculated. Based on the residual, the coefficients of the continuous spectrum reconstruction filter are updated using a variable step-size normalized adaptive iterative algorithm. The update formula for the variable step-size normalized adaptive iterative algorithm is as follows: , In the formula, The residual is dimensionless. For the dimensionless step size parameter, To prevent the division by zero of dimensionless small constants, a value of is usually taken. , express The transpose of the variable step size parameter is expressed as In the formula, The maximum step size is dimensionless and is usually taken as 0.01. The step size adjustment factor is dimensionless and typically takes the value 0.001. It checks if the residual is less than the convergence threshold; if not, it returns to the filtering step to continue iteration; otherwise, it outputs the continuous spectrum reconstruction filter coefficients. The new Gaussian white noise signal is then passed through the digital filter corresponding to the continuous spectrum reconstruction filter coefficients to obtain the continuous spectrum reconstructed time-domain signal.

[0071] The specific implementation of step S5 is as follows: Based on the line spectrum detection game model, a constant false alarm rate (CFAR) adaptive detection algorithm is used to determine the effective frequency set of the line spectrum. The graph theory maximum clique algorithm is used to identify the harmonic relationships to determine the main shaft frequency and the number of blades. The single-frequency signals corresponding to the effective frequency set of the line spectrum are superimposed to obtain the line spectrum reconstructed time-domain signal. Based on the CFAR adaptive detection algorithm, the local noise power of each frequency in the difference sound pressure level spectrum signal is calculated. The mean local noise power is expressed as... The standard deviation of local noise power is expressed as In the formula, The dimensionless half-width of the sliding window is typically taken as 5 to 10. The unit is decibels. The unit is decibels. An adaptive detection threshold is determined based on the local noise power and the set false alarm rate, and the adaptive detection threshold satisfies the constant false alarm rate condition. In the formula, To set the dimensionless false alarm rate, it is usually taken as a value of 1. to Thus we obtain The frequencies above the adaptive detection threshold in the differential sound pressure level spectrum signal are selected as a preliminary line spectrum frequency set. Morphological filtering is then applied to this preliminary line spectrum frequency set to suppress isolated noise peaks, resulting in the effective line spectrum frequency set. This effective line spectrum frequency set is then constructed as vertices of an undirected graph. If two frequencies satisfy an integer multiple relationship, an edge is connected between the two vertices. The multiple relationship determination condition is... In the formula, This indicates rounding to the nearest integer. For multiple relationships, the tolerance is dimensionless and typically takes a value of 0.05. and For frequency indexing, a graph-theoretic maximum clique algorithm is used to search all maximal cliques and sort them by size. The maximum clique containing the most octave relationships is selected as the octave line spectrum set. The greatest common divisor of all frequencies in the octave line spectrum set is calculated to determine candidate values ​​for the principal axis frequency. The validity of the candidate values ​​for the principal axis frequency is verified by combining the mapping relationship between the low-frequency and high-frequency line spectra, and the principal axis frequency is determined. and number of leaves The amplitude of a single-frequency signal is calculated based on each frequency in the effective frequency set of the line spectrum, its corresponding sound pressure level, and the expected sound pressure level of the continuous spectrum. The amplitude of a single-frequency signal is expressed as... when hour, Otherwise, in the formula, The sound pressure level to voltage amplitude conversion factor is determined based on the sensor sensitivity and is usually [value missing]. to The constant within the range is in volts per pascal. For the effective frequency set, The unit is volts. Single-frequency signals of corresponding frequencies are generated and set with random phases. All single-frequency signals are superimposed to obtain the line spectrum reconstructed time-domain signal. The line spectrum reconstructed time-domain signal is expressed as... In the formula, From 0 to The random phase between them is in radians. The frequency resolution unit is Hertz. , The unit is volts.

[0072] The specific implementation of step S6 is as follows: A modulation pulse sequence is constructed based on the main shaft frequency and the number of blades. This modulation pulse sequence is multiplied by the continuous spectrum reconstruction time-domain signal to obtain the modulation spectrum reconstruction time-domain signal. The continuous spectrum reconstruction time-domain signal, the line spectrum reconstruction time-domain signal, and the modulation spectrum reconstruction time-domain signal are then superimposed to obtain the augmented ship radiated noise time-domain signal. Based on the main shaft frequency... and number of leaves Calculate the width parameter of a single modulation pulse, where the pulse signal width is expressed as... In the formula, The unit is seconds. The amplitude parameters of a single modulation pulse are calculated based on the average amplitude of the single-frequency signal and the attenuation factor in the time-domain signal reconstructed from the line spectrum. The average amplitude of the single-frequency signal is expressed as... In the formula, The unit is volts, and the amplitude of the pulse signal is expressed as... In the formula, The unit is volts. The attenuation factor is dimensionless and A single discrete Gaussian pulse signal is generated based on the amplitude and width parameters. This single discrete Gaussian pulse signal is described as follows: In the formula, The sampling interval after downsampling is in seconds and , The unit is volts. According to the spindle frequency... and number of leaves A modulated pulse sequence is constructed by repeatedly sending a single discrete Gaussian pulse signal at a defined period. The period of the modulated pulse is expressed as... In the formula, The unit is seconds, and the modulated pulse sequence is expressed as follows: In the formula, The pulse number is dimensionless. The total number of pulses is dimensionless. The unit is volts. The modulated pulse sequence is truncated to the same length as the continuous spectrum reconstructed time-domain signal. The truncated modulated pulse sequence is then multiplied point-by-point by the continuous spectrum reconstructed time-domain signal to obtain the modulated spectrum reconstructed time-domain signal, which is expressed as: In the formula, The unit is volts. The time-domain superposition of the continuous spectrum reconstructed time-domain signal, the line spectrum reconstructed time-domain signal, and the modulation spectrum reconstructed time-domain signal results in the augmented ship radiated noise time-domain signal expressed as follows: In the formula, For time-domain sampling point index, The unit is volts.

[0073] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To address the problem of insufficient training samples for ship radiated noise, technicians used the method of this invention to perform data augmentation processing on the collected ship radiated noise signals. Technicians used an underwater acoustic acquisition system to collect a 60-second raw signal of ship radiated noise in a certain sea area. The original sampling frequency was 51200Hz, and the signal amplitude fluctuated between -0.8 and +0.8.

[0074] Technicians first preprocessed the original signal. Through energy time-varying characteristic analysis, they determined that the signal reached a stable state after 8 seconds. A 20-second segment of the signal was extracted from this point as the processing target. The time-domain average value of this signal segment was calculated to be 0.0023. This average value was then subtracted point-by-point from the signal to remove the DC bias. The de-DC signal was then passed through a 128th-order bandpass filter for noise reduction, with the filter's passband range set to 10Hz to 10000Hz. Based on the upper limit of the desired frequency range (10000Hz), the downsampled sampling frequency was determined to be 25600Hz. The calculated integer multiple relationship was 2. The noise-reduced signal was downsampled by a factor of 2 to obtain the preprocessed time-domain signal, which had 512,000 sampling points. Figure 2 As shown, the preprocessed time-domain signal exhibits stable random fluctuation characteristics, with the signal amplitude concentrated in the range of -0.6 to +0.6, and periodic amplitude modulation can be observed in the waveform.

[0075] Technicians performed a 512,000-point Discrete Fourier Transform on the preprocessed time-domain signal to obtain the frequency-domain signal. Based on the sensor sensitivity of the acquisition system (-170 dB) and the preamplifier gain of 40 dB, conversion coefficients were calculated to convert the frequency-domain signal into a sound pressure level (SPL) spectrum signal. The SPL spectrum signal was then smoothed using a moving average filter with a window length of 50 frequency points, resulting in a smoothed SPL spectrum exhibiting obvious piecewise linear characteristics. For example... Figure 3 As shown, the smoothed spectrum starts at a sound pressure level of 82 dB at a starting frequency of 150 Hz, and linearly increases with the logarithm of the frequency by a gradient of 18 dB per octave, reaching a peak sound pressure level of 106 dB at a peak frequency of 800 Hz. It then linearly decreases with a gradient of -22 dB per octave to a final sound pressure level of 68 dB at a cutoff frequency of 8500 Hz. Technicians extracted these parameters as continuous spectrum segmentation parameters, and the specific values ​​are shown in Table 1.

[0076] Table 1 Continuous Spectrum Segmentation Parameter Table

[0077]

[0078] Technicians calculated the difference between the original sound pressure level spectrum and the smoothed spectrum to obtain the difference sound pressure level spectrum. A uniform threshold of 4.5 dB was set to filter the difference spectrum, extracting 237 frequency points above the threshold to form an effective frequency set. These frequencies were constructed as vertices of an undirected graph, with a tolerance of 0.08 for the multiple relationship. The ratio of any two frequencies was calculated iteratively, and when the deviation of the ratio from the nearest integer was less than the tolerance, an edge was connected between the corresponding vertices. A recursive enumeration algorithm was used to search all maximal complete subgraphs in the graph, finding 18 maximal cliques. After sorting by the number of vertices contained, the largest clique containing 42 vertices was selected as the octave line spectrum set. Figure 4As shown, the frequencies in this octave spectrum set are distributed in the range of 48Hz to 7200Hz, exhibiting a clear octave structure. Technicians used the Euclidean algorithm to calculate the greatest common divisor of all frequencies in the set, obtaining a candidate value of 12Hz for the main axis frequency. Verification confirmed the existence of a 12Hz frequency point with a sound pressure level of 88 dB in the low-frequency spectrum, and the presence of frequency points at 240Hz, 480Hz, and 720Hz in the high-frequency spectrum, confirming the main axis frequency as 12Hz. Calculating the multiples between the high-frequency spectrum and the main axis frequency revealed that 240Hz is 20 times the main axis frequency, 480Hz is 40 times, and 720Hz is 60 times, determining the number of blades to be 5.

[0079] Technicians constructed a continuous spectrum reconstruction game model and a line spectrum detection game model to guide the subsequent reconstruction process. In the continuous spectrum reconstruction game model, the weight coefficients of the upper-level targets were set to 1.0 within an 80Hz range around the peak frequency of 800Hz, and 0.1 for other frequencies. The key frequency range for the lower-level targets was set to 500Hz to 1500Hz, with weight coefficients of 0.7 and 0.3 respectively. In the line spectrum detection game model, the weight coefficients of the upper-level targets were set to 0.8, and the weight coefficients of the lower-level targets were set to 0.9, with a preset false alarm rate of 10%. .

[0080] Technicians initialized the continuous spectrum reconstruction filter coefficients of length 256 as a zero vector and generated a Gaussian white noise signal of length 512000 as the input excitation. Based on the continuous spectrum segmentation parameters, the desired sound pressure level at each frequency point within the band of interest (150Hz to 8500Hz) was calculated using piecewise linear interpolation, and multiplied by weighting coefficients to obtain the weighted desired frequency response. A variable-step-size normalized least mean square adaptive filtering algorithm was used to solve for the filter coefficients, with the maximum step size set to 0.03, the step size adjustment factor set to 300, and the zero-prevention constant set to 10. The convergence threshold was set to 0.5% of the mean square value of the desired frequency response. After 2847 iterations, the mean square value of the residuals converged below the threshold, yielding the optimal filter coefficients. Figure 5 As shown, the frequency response of the continuous spectrum reconstruction filter closely matches the desired response near the peak frequency, with an approximation error of less than 2 dB. Passing the newly generated Gaussian white noise through this filter yields a continuous spectrum reconstruction time-domain signal with a length of 512,000 sampling points.

[0081] Technicians used a constant false alarm rate adaptive detection algorithm to process the differential sound pressure level spectrum, setting the sliding window length to 1500 frequency points, and calculated the mean and standard deviation of local noise power at each frequency point. Based on a preset false alarm rate of 10... An adaptive detection threshold was calculated, with the threshold value adaptively varying between 3.2 dB and 5.8 dB with frequency. Frequencies exceeding the detection threshold in the difference spectrum were selected as a preliminary line spectrum frequency set, containing 189 frequency points. A morphological opening filter with a structuring element length of 4 was applied to this set to remove isolated noise peaks, resulting in a line spectrum effective frequency set containing 156 frequencies. Based on the difference sound pressure level and the desired continuous spectrum sound pressure level for each frequency in this set, the technicians calculated the amplitude of the single-frequency signal, with the phase uniformly and randomly distributed between 0 and 2π. The corresponding single-frequency sinusoidal signals were generated and superimposed point-by-point to obtain the line spectrum reconstructed time-domain signal, which contains 156 single-frequency components of different frequencies.

[0082] Based on the spindle frequency of 12Hz and the number of blades of 5, technicians calculated the width parameter of a single modulation pulse to be 100. The average amplitude of all single-frequency signals in the line spectrum reconstruction signal was calculated to be 0.078, and a randomly generated attenuation factor of 0.42 was used, resulting in a modulation pulse amplitude parameter of 0.033. After generating a single discrete Gaussian pulse signal, it was periodically replicated with a pulse repetition period of 83.3 milliseconds and an adjacent pulse time interval of 16.7 milliseconds to construct a modulation pulse sequence. The modulation pulse sequence was truncated to a length of 512,000 sampling points and multiplied point-by-point with the continuous spectrum reconstruction time-domain signal to obtain the modulation spectrum reconstruction time-domain signal. Finally, the continuous spectrum reconstruction signal, the line spectrum reconstruction signal, and the modulation spectrum reconstruction signal were time-domain superimposed to obtain the augmented ship radiated noise time-domain signal. Figure 6 As shown, the spectrum of the augmented signal simultaneously contains three components: a wideband continuous spectrum, a discrete line spectrum, and a modulation sideband spectrum. The spectral shape is highly consistent with the original signal, but differences exist in waveform details and phase distribution, thus achieving effective data augmentation. Technicians compared the augmented signal with three measured signals, as detailed below. Figure 7 As shown.

[0083] This invention represents a significant advancement in technical principles compared to traditional ship radiated noise data augmentation methods. Traditional methods typically generate new samples using simple time-domain superposition or frequency-domain random perturbation. These methods only simulate the original signal at a superficial level and cannot accurately reproduce the intrinsic physical mechanisms and spectral structure characteristics of ship radiated noise. The generated samples often lack realism and diversity. This invention employs a game-theoretic optimization model to finely reconstruct both the continuous spectrum and line spectrum. It achieves an optimal balance between approximation accuracy and stability by utilizing the coupling mechanism of a two-layer objective function, ensuring the accuracy of each spectral component. A graph-theoretic maximum clique algorithm is used to automatically identify the harmonic relationships between line spectra, avoiding the sensitivity to noise interference inherent in traditional thresholding methods and significantly improving the reliability of extracting key parameters such as spindle frequency and blade number. The physical mechanism-based modulation spectrum modeling method simulates the pressure pulsation process of propeller blades cutting water flow using Gaussian pulse sequences. This ensures that the generated signal not only matches the real signal in frequency domain characteristics but also maintains a high degree of similarity in time domain waveform and statistical distribution characteristics, fundamentally improving the quality and usability of the augmented data.

[0084] It should be noted that the variables involved in this invention are explained in detail in Tables 2 and 3.

[0085] Table 2. Variable Explanation Table (Part 1)

[0086]

[0087] Table 3. Variable Explanation Table (Part Two)

[0088]

[0089] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for augmenting ship radiated noise data based on spectrum reconstruction, characterized in that, The process includes acquiring and preprocessing the ship's radiated noise time-domain signal to obtain a preprocessed time-domain signal; performing a Discrete Fourier Transform (DFT) on the preprocessed time-domain signal to obtain a frequency-domain signal; converting the frequency-domain signal into a sound pressure level (SPL) spectrum signal; performing smoothing filtering on the SPL spectrum signal to separate the continuous spectrum and line spectrum; extracting continuous spectrum segmentation parameters, line spectrum frequency amplitude parameters, and modulation spectrum fundamental frequency parameters; and constructing a continuous spectrum reconstruction game model and a line spectrum detection game model. The continuous spectrum reconstruction game model aims to minimize the filter approximation error as its upper-level objective and maximize the frequency band energy concentration as its lower-level objective. The line spectrum detection game model aims to maximize the detection probability as its upper-level objective and minimize the false alarm rate as its lower-level objective. Based on the continuous spectrum reconstruction game model, a variable step-size normalization algorithm is employed. An adaptive iterative algorithm is used to solve for the coefficients of the continuous spectrum reconstruction filter. Gaussian white noise is passed through the digital filter corresponding to the coefficients of the continuous spectrum reconstruction filter to obtain the continuous spectrum reconstruction time-domain signal. Based on the line spectrum detection game model, a constant false alarm rate adaptive detection algorithm is used to determine the effective frequency set of the line spectrum. The graph theory maximum clique algorithm is used to identify the harmonic relationship to determine the main shaft frequency and the number of blades. The single-frequency signals corresponding to the effective frequency set of the line spectrum are superimposed to obtain the line spectrum reconstruction time-domain signal. A modulation pulse sequence is constructed according to the main shaft frequency and the number of blades. The modulation pulse sequence is multiplied with the continuous spectrum reconstruction time-domain signal to obtain the modulation spectrum reconstruction time-domain signal. The continuous spectrum reconstruction time-domain signal, the line spectrum reconstruction time-domain signal and the modulation spectrum reconstruction time-domain signal are superimposed to obtain the augmented ship radiated noise time-domain signal.

2. The method of claim 1, wherein, The steps for obtaining the preprocessed time-domain signal are as follows: truncating the long-term ship radiated noise input signal to obtain a truncated time-domain signal; calculating the average value of the truncated time-domain signal and subtracting the average value to obtain a de-DC biased time-domain signal; passing the de-DC biased time-domain signal through a noise reduction filter to obtain a noise-reduced time-domain signal; and downsampling the noise-reduced time-domain signal to obtain the preprocessed time-domain signal.

3. The method of claim 2, wherein, The downsampling calculation is performed by determining the downsampled sampling frequency based on the upper limit frequency of the frequency domain of interest, which satisfies the Nyquist sampling theorem. The integer multiple relationship between the original sampling frequency and the downsampled sampling frequency is calculated, and downsampling is performed according to the integer multiple relationship.

4. The method of claim 3, wherein, The extraction steps for continuous spectrum segmentation parameters specifically involve smoothing the sound pressure level spectrum signal to obtain a smoothed sound pressure level spectrum signal. The smoothed sound pressure level spectrum signal includes a first segment that linearly increases from the starting frequency to the peak frequency according to the first gradient and a second segment that linearly decreases from the peak frequency to the cutoff frequency according to the second gradient. The starting frequency, the corresponding starting sound pressure level, the first gradient, the peak frequency, the peak sound pressure level, the second gradient, the cutoff frequency, and the ending sound pressure level are extracted as continuous spectrum segmentation parameters.

5. The method of claim 4, wherein, The extraction steps for line spectrum frequency amplitude parameters are as follows: calculate the difference between the sound pressure level spectrum signal and the smoothed sound pressure level spectrum signal to obtain the difference sound pressure level spectrum signal; set a uniform threshold to filter the frequencies in the difference sound pressure level spectrum signal that are higher than the uniform threshold to form an effective frequency set; verify the multiple relationship between the frequencies in the effective frequency set to construct an octave frequency set; and extract the frequencies and corresponding sound pressure levels in the octave frequency set as line spectrum frequency amplitude parameters.

6. The method of claim 5, wherein, The extraction steps for the fundamental frequency parameters of the modulation spectrum are as follows: select frequency elements less than 100Hz and greater than 4000Hz from the set of harmonic frequencies, verify the multiple relationship between the two frequencies, select the frequency with the widest and smallest multiple relationship as the main shaft frequency, and calculate the multiple relationship between other frequencies greater than the main shaft frequency in the set of harmonic frequencies and the main shaft frequency to determine the number of blades.

7. The method of claim 6, wherein, The upper-level objective function of the continuous spectrum reconstruction game model is used to measure the weighted mean square error between the expected frequency response and the actual frequency response, while the lower-level objective function is used to measure the weighted combination of the energy concentration in the key frequency band and the uniformity of the energy distribution across the entire frequency band. The two models are coupled through weight coefficients.

8. The method of claim 7, wherein, The objective function of the upper-level model of the line spectrum detection game model is used to measure the weighted combination of the probability of the true line spectrum being correctly detected and the detection stability, while the objective function of the lower-level model is used to measure the false alarm rate of noise peaks being misclassified as line spectra and the weighted combination of threshold volatility. The two models are coupled through the detection threshold.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program instructions that, when executed in a computer, are used to perform the ship radiated noise data augmentation method based on spectrum reconstruction as described in any one of claims 1-8.

10. A ship radiated noise data augmentation system based on spectrum reconstruction, characterized in that, The system comprises the computer-readable storage medium of claim 9, wherein the system is a computer, the computer-readable storage medium is disposed within the system, and the system is provided with a microprocessor that executes program instructions stored in the computer-readable storage medium.

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