A DEMON spectrum analysis frequency band selection method and device based on holographic hilbert spectrum analysis

Abstract

The application discloses a DEMON spectrum analysis frequency band selection method and device based on holographic Hilbert spectrum analysis, which utilizes short-time Fourier transform to perform time-frequency analysis on a signal, and combines a time-domain graph to intercept stable time-domain signals; the intercepted signals are subjected to holographic Hilbert spectrum analysis, a nested empirical mode decomposition and Hilbert-Huang transform method is used, an additional dimension is added in a frequency spectrum result, a high-dimensional representation method is used to establish a corresponding relationship between a modulation frequency and a carrier frequency; then, a holographic Hilbert amplitude modulation spectrum is combined to determine a frequency band range of a band-pass filter in DEMON spectrum analysis; finally, the signal is subjected to DEMON spectrum analysis to accurately estimate parameter information such as an axial frequency, a blade frequency and a number of blades of an underwater target propeller. The application directly obtains the corresponding relationship between the modulation frequency and the carrier frequency by using the holographic Hilbert spectrum decomposition technology, and solves the problem that it is difficult to select the band-pass filter in the DEMON spectrum analysis process.

Description

Technical Field

[0001] This invention relates to the field of underwater target recognition technology, and in particular to a method and apparatus for selecting frequency bands in DEMON spectrum analysis based on holographic Hilbert spectrum analysis. Background Technology

[0002] Underwater target radiated noise signals typically contain many features that reflect the nature of the target. Feature extraction methods based on underwater target radiated noise are an effective means of achieving accurate underwater target detection. Therefore, the key to detecting and identifying underwater targets lies in whether effective features reflecting the nature of underwater vehicles can be accurately extracted from their radiated noise.

[0003] Radiated noise from underwater targets such as ships and underwater vehicles can be categorized into three types: mechanical noise generated by the vibration of various internal mechanical devices (e.g., propulsion machinery); propeller noise generated by the rotation of the propeller in water, including propeller cavitation noise and propeller rotation noise; and hydrodynamic noise generated by the interaction between the vehicle's hull and the water body during underwater navigation. The low-frequency line spectra of the shaft frequency, blade frequency, and their harmonic frequencies generated by propeller rotation often exist in the form of modulation within the high-frequency cavitation noise continuous spectrum. Detection of Envelope Modulation On Noise (DEMON) analysis is a method that obtains the low-frequency modulation spectrum characteristics by demodulating a received broadband high-frequency signal with modulation characteristics and performing spectral analysis on the envelope signal. DEMON analysis can obtain characteristic information such as the target's shaft frequency and blade frequency.

[0004] When using the DEMON spectrum analysis method for underwater vehicle classification and tracking, the choice of bandpass filter bandwidth significantly impacts algorithm performance. Traditional DEMON spectrum analysis methods require manual selection of the bandpass filter bandwidth, which is highly arbitrary in practical applications. When the selected bandwidth lacks modulation characteristics or has weak modulation characteristics, useful information in the signal may be filtered out, making it difficult to extract characteristic lines reflecting propeller shaft frequency, blade frequency, and number of blades from the obtained DEMON spectrum.

[0005] Therefore, accurately selecting the frequency band range of the bandpass filter is a problem that the DEMON spectral analysis algorithm urgently needs to solve. Summary of the Invention

[0006] To address the aforementioned technical problems in the prior art, this invention provides a DEMON spectrum analysis frequency band selection method and apparatus based on holographic Hilbert spectrum analysis, thereby solving the problem of difficulty in selecting the bandpass filter frequency band range in the prior art DEMON spectrum analysis method.

[0007] To achieve the above objectives, the technical solution of this invention is as follows:

[0008] The first aspect of the present invention provides a DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis, the method comprising:

[0009] The obtained underwater target radiated noise signal is subjected to spectral analysis to obtain the main frequency range of the radiated noise signal, and the radiated noise signal is downsampled to obtain a simplified radiated noise signal;

[0010] The simplified radiated noise signal is subjected to time-frequency analysis by short-time Fourier transform, and the signal is truncated by combining the time-domain plot to obtain the truncated radiated noise signal.

[0011] Based on empirical mode decomposition in holographic Hilbert spectral analysis, the truncated radiated noise signal is decomposed into multiple intrinsic mode functions, and Hilbert spectral analysis is performed on each intrinsic mode function to obtain the amplitude variation function and carrier frequency variation function of each intrinsic mode function.

[0012] The envelope of each intrinsic mode function is calculated, and empirical mode decomposition and Hilbert spectrum analysis are performed on each envelope to obtain the envelope amplitude variation function and the modulation frequency variation function.

[0013] Integrating the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function yields the holographic Hilbert amplitude modulation spectrum.

[0014] Based on the holographic Hilbert amplitude modulation spectrum, the correspondence between the modulation frequency and the carrier frequency of the truncated radiated noise signal is obtained, the frequency band range of the bandpass filter in the DEMON spectrum analysis is determined, and the DEMON spectrum analysis is performed on the truncated radiated noise signal to obtain the DEMON spectrum.

[0015] Feature extraction was performed on the DEMON spectrum to obtain estimates of the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

[0016] This invention provides a DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis, the device comprising:

[0017] The downsampling module is used to perform spectral analysis on the obtained underwater target radiated noise signal to obtain the main frequency range of the radiated noise signal, and to perform downsampling processing on the radiated noise signal to obtain a simplified radiated noise signal;

[0018] The signal interception module is used to perform time-frequency analysis on the simplified radiated noise signal through short-time Fourier transform, and to intercept the signal by combining the time domain diagram to obtain the intercepted radiated noise signal.

[0019] The first analysis module is used to decompose the truncated radiated noise signal into multiple intrinsic mode functions based on empirical mode decomposition in holographic Hilbert spectral analysis, and to perform Hilbert spectral analysis on each intrinsic mode function to obtain the amplitude variation function and carrier frequency variation function of each intrinsic mode function.

[0020] The second analysis module is used to calculate the envelope of each intrinsic mode function, and to perform empirical mode decomposition and Hilbert spectrum analysis on each envelope to obtain the envelope amplitude variation function and the modulation frequency variation function.

[0021] An integration module is used to integrate the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function to obtain the holographic Hilbert amplitude modulation spectrum.

[0022] The third analysis module is used to obtain the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum, determine the frequency band range of the bandpass filter in DEMON spectrum analysis, and perform DEMON spectrum analysis on the truncated radiated noise signal to obtain the DEMON spectrum.

[0023] The feature extraction module is used to extract features from the DEMON spectrum to obtain estimates of the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

[0024] In some embodiments, when performing spectral analysis on the obtained underwater target radiated noise signal, the Fourier transform calculation formula is as follows:

[0025]

[0026] Where f(t) is the original received signal, ω is the signal frequency, t represents time, and j is the imaginary unit.

[0027] In some embodiments, when performing time-frequency analysis on the simplified radiated noise signal using short-time Fourier transform, the calculation formula for the short-time Fourier transform is as follows:

[0028]

[0029] Where x1(t) is the downsampled signal, h(t) is the window function, f is the signal frequency, t represents time, and j is the imaginary unit.

[0030] In some embodiments, the empirical mode decomposition based on holographic Hilbert spectral analysis decomposes the truncated radiated noise signal into multiple eigenmode functions, wherein the truncated radiated noise signal is represented as follows:

[0031]

[0032] Among them, c j (t) represents the j-th intrinsic mode function, and the amplitude a of each IMF component is... j (t) and frequency ω j (t) represents a function of time, and N is the number of intrinsic moduli;

[0033] The nested expression for the amplitude change function is:

[0034]

[0035] Where Ω represents the slowly varying envelope frequency.

[0036] In some embodiments, the integration module is further configured to integrate the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function using edge expressions to obtain a frequency-only spectrum, and perform multiple iterations until the amplitude change function no longer has cyclic characteristics in the envelope, thereby obtaining a pure frequency high-dimensional full-information representation of the signal amplitude, i.e., the holographic Hilbert amplitude modulation spectrum; wherein, the formula for calculating the edge spectrum is:

[0037]

[0038] Where T is the integration time range, ω is the signal frequency, and t represents time.

[0039] In some embodiments, the third analysis module is further configured to: obtain the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum; determine the frequency band range in which modulation characteristics exist in the truncated radiated noise signal based on the correspondence; select a suitable frequency band range to perform bandpass filtering on the truncated radiated noise signal in conjunction with the holographic Hilbert amplitude modulation spectrum to obtain a filtered radiated noise signal; perform envelope demodulation on the filtered radiated noise signal using the Hilbert transform demodulation method to obtain an envelope signal; and perform low-pass filtering and spectral analysis on the envelope signal to obtain a DEMON spectrum.

[0040] This invention provides an electronic device, including: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement the above-mentioned DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis.

[0041] This invention provides a computer-readable storage medium storing executable instructions, which, when executed by a processor, implement the aforementioned DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis.

[0042] The DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis provided by this invention first performs empirical mode decomposition on the target radiated noise signal, decomposing the signal into multiple intrinsic mode functions (IMFs), and then performs Hilbert spectrum analysis to obtain the amplitude and frequency of each IMF component as functions of time. Next, the envelope of each IMF is calculated, and empirical mode decomposition and Hilbert spectrum analysis are performed again on each envelope to obtain the amplitude and frequency of the envelope as functions of time. Then, the time variable of each layer of Hilbert spectrum analysis results is integrated to obtain a frequency-only spectrum. Finally, multiple iterations are performed as needed until the amplitude function falls within the specified range. The network no longer exhibits cyclic properties, ultimately yielding a pure frequency high-dimensional full-information representation of the signal amplitude, namely the holographic Hilbert amplitude modulation spectrum. Holographic Hilbert spectral decomposition technology uses nested empirical mode decomposition and Hilbert-Huang transform methods to identify amplitude and frequency modulations frequently occurring in nonlinear and non-stationary systems. By adding an extra dimension to the spectral results and utilizing high-dimensional representation to establish the correspondence between modulation frequency and carrier frequency, it is possible to quantitatively study complex signal modulation mechanisms. Holographic Hilbert spectral analysis can directly obtain the bandpass filter range in DEMON spectral analysis, avoiding the difficulty in selecting the bandpass filter during DEMON spectral analysis. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating a DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis provided by the present invention;

[0044] Figure 2 This invention provides another method for selecting frequency bands in DEMON spectral analysis based on holographic Hilbert spectral decomposition technology;

[0045] Figure 3 This is a schematic diagram of the holographic Hilbert spectral analysis process provided by the present invention;

[0046] Figure 4 This is a time-domain diagram of the radiated noise of an AUV performing a task, provided in the experimental example of this invention.

[0047] Figure 5 This is a time-frequency diagram of radiated noise provided in the experimental examples of this invention;

[0048] Figure 6 This is a 30-second segment of a stable AUV radiation noise time-domain plot provided in the experimental example of this invention;

[0049] Figure 7 This is the holographic Hilbert amplitude modulation spectrum of the intercepted signal provided in the experimental example of this invention;

[0050] Figure 8 This is the curve showing the correspondence between the integral value of the holographic spectrum amplitude modulation frequency and the FM frequency provided in the experimental examples of this invention;

[0051] Figure 9 This is the DEMON spectrum of the intercepted signal after bandpass filtering provided in the experimental example of this invention;

[0052] Figure 10 This is a schematic diagram of the composition structure of the DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis provided in an embodiment of the present invention;

[0053] Figure 11 This is a schematic diagram of the composition structure of the DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis provided in an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be regarded as limitations on the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] In the following description, references to "some embodiments" refer to a subset of all possible embodiments; however, it is understood that "some embodiments" may be the same or different subsets of all possible embodiments and may be combined with each other without conflict. Unless otherwise defined, all technical and scientific terms used in the embodiments of the invention have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the invention pertain. The terminology used in the embodiments of the invention is for the purpose of describing the embodiments of the invention only and is not intended to limit the invention.

[0056] This invention provides a method for selecting frequency bands in DEMON spectral analysis based on holographic Hilbert spectral analysis. (See also...) Figure 1 , Figure 1 This is a flowchart illustrating a DEMON spectral analysis frequency band selection method based on holographic Hilbert spectral analysis provided in an embodiment of the present invention, which will be combined with... Figure 1 The steps shown are explained.

[0057] Step S110: Perform spectrum analysis on the obtained underwater target radiated noise signal to obtain the main frequency range of the radiated noise signal, and perform downsampling processing on the radiated noise signal to obtain a simplified radiated noise signal.

[0058] In some embodiments, the underwater target radiated noise signal can be preprocessed, such as denoising and filtering, before spectral analysis, to reduce noise interference and improve signal quality.

[0059] In some embodiments, a suitable downsampling rate can be selected based on the results of spectral analysis, and the radiated noise signal can be resampled using the selected downsampling rate to ensure that the main features of the signal are preserved while reducing the amount of data, thereby simplifying subsequent calculations.

[0060] In some embodiments, when performing spectral analysis on the obtained underwater target radiated noise signal, the Fourier transform calculation formula is as follows:

[0061]

[0062] Where f(t) is the original received signal, ω is the signal frequency, t represents time, and j is the imaginary unit.

[0063] Step S120: Perform time-frequency analysis on the simplified radiated noise signal using short-time Fourier transform, and extract the signal by combining the time-domain plot to obtain the extracted radiated noise signal.

[0064] In some embodiments, the short-time Fourier transform (STFT) is a method that divides a signal into multiple segments (or "frames") in time and performs a Fourier transform on each frame. This method allows the acquisition of the signal's spectral characteristics at different points in time, i.e., the frequency components of the signal that change over time.

[0065] In some embodiments, short-time Fourier transform (STFT) is used to perform time-frequency analysis on the simplified radiated noise signal. After obtaining the STFT result, further signal analysis can be performed by combining it with the time-domain plot (i.e., the waveform of the signal changing over time). By observing the time-domain plot and the STFT result, specific time intervals in the signal can be identified, which may contain features of interest. Subsequently, based on the analysis results, the time interval to be truncated is determined on the time-domain plot, and appropriate signal processing techniques are used to truncate the signal within this interval, thus obtaining the truncated radiated noise signal.

[0066] In some embodiments, the truncated radiated noise signal is a subset of the original signal, containing only a portion of the original signal within a specific time interval. This truncated signal may be used for further analysis, processing, or comparison with other signals.

[0067] In some embodiments, when performing time-frequency analysis on the simplified radiated noise signal using short-time Fourier transform, the calculation formula for the short-time Fourier transform is as follows:

[0068]

[0069] Where x1(t) is the downsampled signal, h(x) is the window function, f is the signal frequency, t represents time, and j is the imaginary unit.

[0070] Step S130: Based on empirical mode decomposition in holographic Hilbert spectral analysis, the truncated radiated noise signal is decomposed into multiple intrinsic mode functions, and Hilbert spectral analysis is performed on each intrinsic mode function to obtain the amplitude variation function and carrier frequency variation function of each intrinsic mode function.

[0071] In this invention, the purpose of Empirical Mode Decomposition (EDM) is to decompose a complex radiated noise signal into a series of Intrinsic Mode Functions (IMFs) with specific frequency and time-frequency characteristics. Here, each IMF represents a component of the original signal at a different frequency scale. Then, a Hilbert transform is performed on each IMF to obtain its amplitude transformation function and carrier frequency transformation function.

[0072] In this invention, the amplitude of the analyzed signal is the envelope of the original signal, representing the instantaneous amplitude change of the signal. The phase of the analyzed signal contains the instantaneous frequency information of the signal. By differentiating or differentiating the phase, the carrier frequency change function of the signal can be obtained.

[0073] In some embodiments, the truncated radiated noise signal can be represented as:

[0074]

[0075] Among them, c j (t) represents the j-th intrinsic mode function, and the amplitude a of each IMF component is... j (t) and frequency ω j (t) represents a function of time, and N is the number of intrinsic moduli;

[0076] The nested expression for the amplitude change function is:

[0077]

[0078] Where Ω represents the slowly varying envelope frequency.

[0079] Step S140: Calculate the envelope of each intrinsic mode function, and perform empirical mode decomposition and Hilbert spectrum analysis on each envelope to obtain the envelope amplitude variation function and modulation frequency variation function.

[0080] In some embodiments, the envelope refers to the outer contour surrounding the IMF waveform, describing the instantaneous amplitude variation of the IMF. Calculating the envelope involves finding the local maxima and local minima of the IMF, generating an upper and lower envelope using methods such as interpolation, and then calculating the mean of these two envelopes (in some cases, either the upper or lower envelope is used directly as the envelope).

[0081] In this invention, since the envelope itself is also a signal, it can be further decomposed into multiple IMFs by EMD, which can be called envelope IMFs. Then, a Hilbert transform is performed on each envelope IMF to obtain its analytical representation. The instantaneous amplitude (i.e., the envelope amplitude change function) and instantaneous phase of the envelope IMF can be calculated from the analytical representation. The rate of change of the instantaneous phase corresponds to the instantaneous frequency, but here we focus more on the modulation frequency, i.e., the frequency change of the envelope IMF, which reflects the modulation characteristics of the envelope itself.

[0082] In some embodiments, the envelope amplitude variation function describes the change of the instantaneous amplitude of the IMF envelope over time. The modulation frequency variation function describes the change of the instantaneous frequency (or modulation frequency) of the envelope IMF over time.

[0083] It should be noted that this invention does not impose specific limitations on the method for calculating the envelope; the specific method depends on the specific characteristics of the signal and the analysis requirements. Here, the methods for calculating the envelope include, but are not limited to, the method based on local extrema mentioned above. Other methods, such as the Hilbert transform, can also be used to calculate the envelope.

[0084] Step S150: Integrate the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function to obtain the holographic Hilbert amplitude modulation spectrum.

[0085] In some embodiments, the purpose of integrating the time variables of the carrier frequency variation function, the modulation frequency variation function, and the envelope amplitude variation function is to calculate the effect of these functions on the time accumulation over a specific time period, thereby generating a holographic Hilbert amplitude modulation spectrum that can comprehensively reflect the signal characteristics.

[0086] In some embodiments, step S150 can be determined in the following manner:

[0087] Using edge expressions, the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function are integrated to obtain a frequency-only spectrum. This process is repeated multiple times until the amplitude change function no longer exhibits cyclic properties within the envelope, resulting in a pure frequency high-dimensional full-information representation of the signal amplitude, i.e., the holographic Hilbert amplitude modulation spectrum. The formula for calculating the edge spectrum is:

[0088]

[0089] Where T is the integration time range, ω is the signal frequency, and t represents time.

[0090] Step S160: Based on the holographic Hilbert amplitude modulation spectrum, obtain the correspondence between the modulation frequency and the carrier frequency of the truncated radiated noise signal, determine the frequency band range of the bandpass filter in DEMON spectrum analysis, and perform DEMON spectrum analysis on the truncated radiated noise signal to obtain the DEMON spectrum.

[0091] In some embodiments, the correspondence between the modulation frequency and the carrier frequency can be determined based on the holographic Hilbert amplitude modulation spectrum; and the frequency band range of the bandpass filter in DEMON spectrum analysis can be determined based on the correspondence; then, DEMON spectrum analysis is performed on the truncated radiated noise signal based on the frequency band range to obtain the DEMON spectrum.

[0092] In some embodiments, step S160 above can be determined in the following manner:

[0093] Based on the holographic Hilbert amplitude modulation spectrum, the correspondence between the modulation frequency and the carrier frequency of the truncated radiated noise signal is obtained; based on the correspondence, the frequency band range in which the modulation characteristics exist in the truncated radiated noise signal is determined; combined with the holographic Hilbert amplitude modulation spectrum, a suitable frequency band range is selected to perform bandpass filtering on the truncated radiated noise signal to obtain a filtered radiated noise signal; the Hilbert transform demodulation method is used to perform envelope demodulation on the filtered radiated noise signal to obtain an envelope signal; the envelope signal is then subjected to low-pass filtering and spectral analysis to obtain the DEMON spectrum.

[0094] Step S170: Extract features from the DEMON spectrum to obtain the estimated results of the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

[0095] In some embodiments, shaft frequency refers to the frequency at which the propeller rotates once, that is, the frequency at which the propeller shaft rotates. In the DEMON spectrum, shaft frequency reflects the rate of propeller rotation.

[0096] In some embodiments, the blade frequency refers to the frequency at which a single blade of a propeller passes a fixed point (such as a sonar sensor) during its rotation. Since a propeller has multiple blades, the blade frequency is typically an integer multiple of the shaft frequency. In the DEMON spectrum, the blade frequency is represented as a series of harmonic components with the shaft frequency as the fundamental frequency, and the intervals between these harmonics are equal to the shaft frequency.

[0097] In some embodiments, the number of blades refers to the number of blades on the propeller. Since the blade frequency is an integer multiple of the shaft frequency, the number of blades can be determined by analyzing the blade frequency harmonics in the DEMON spectrum. Specifically, this involves observing the intervals between the blade frequency harmonics (i.e., the shaft frequency) and calculating the ratio of the blade frequency to the shaft frequency; this ratio is the number of blades.

[0098] In this invention, by extracting features from the DEMON spectrum, the shaft frequency component and blade frequency harmonics are identified, thereby estimating the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

[0099] The DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis provided by this invention first performs empirical mode decomposition on the target radiated noise signal, decomposing the signal into multiple intrinsic mode functions (IMFs), and then performs Hilbert spectrum analysis to obtain the amplitude and frequency of each IMF component as functions of time. Next, the envelope of each IMF is calculated, and empirical mode decomposition and Hilbert spectrum analysis are performed again on each envelope to obtain the amplitude and frequency of the envelope as functions of time. Then, the time variable of each layer of Hilbert spectrum analysis results is integrated to obtain a frequency-only spectrum. Finally, multiple iterations are performed as needed until the amplitude function falls within the specified range. The network no longer exhibits cyclic properties, ultimately yielding a pure frequency high-dimensional full-information representation of the signal amplitude, namely the holographic Hilbert amplitude modulation spectrum. Holographic Hilbert spectral decomposition technology uses nested empirical mode decomposition and Hilbert-Huang transform methods to identify amplitude and frequency modulations frequently occurring in nonlinear and non-stationary systems. By adding an extra dimension to the spectral results and utilizing high-dimensional representation to establish the correspondence between modulation frequency and carrier frequency, it is possible to quantitatively study complex signal modulation mechanisms. Holographic Hilbert spectral analysis can directly obtain the bandpass filter range in DEMON spectral analysis, avoiding the difficulty in selecting the bandpass filter during DEMON spectral analysis.

[0100] The following will describe an exemplary application of the embodiments of the present invention in a practical application scenario.

[0101] This invention provides another method for selecting frequency bands in DEMON spectral analysis based on holographic Hilbert spectral decomposition technology, the specific process of which is as follows: Figure 2 As shown, the implementation steps are as follows:

[0102] S1 performs spectral analysis on the collected underwater target radiated noise signal to determine the main frequency range of the signal, and performs downsampling processing on the signal to simplify the calculation.

[0103] The formula for calculating the Fourier transform is as follows:

[0104]

[0105] S2 uses short-time Fourier transform to perform time-frequency analysis on the signal and combines it with the time-domain plot to extract a stable time-domain signal.

[0106] The formula for calculating the short-time Fourier transform is as follows:

[0107]

[0108] S3. Perform holographic Hilbert spectrum analysis on the signal intercepted in step S2. Based on empirical mode decomposition, decompose the signal into several intrinsic mode functions and perform Hilbert spectrum analysis to obtain the amplitude and frequency of each IMF component as a function of time. Calculate the envelope of each IMF and perform empirical mode decomposition and Hilbert spectrum analysis on each envelope again. Repeat the above process to clearly describe the addition or multiplication process in the signal.

[0109] Here, empirical mode decomposition adaptively decomposes any complex signal into several intrinsic mode functions based on the characteristics of the signal itself. Each decomposed IMF component represents a simple oscillation mode and contains local feature information of the original signal.

[0110] The first step is to identify all local extrema, obtain the local maxima and local minima of the signal, and fit the upper and lower envelopes. The upper and lower envelopes should cover all data. The mean of the upper and lower envelopes is defined as m1, and the difference between the data x(t) and m1 is the first component h1, i.e.

[0111] h1=x(t)-m1 (3);

[0112] Step 2: Determine if h1 is an eigenfunction. If not, continue the decimation process. In subsequent decimation, h1 is treated as a signal. Local maxima and minima of h1 are obtained, and the upper and lower envelopes are fitted. The mean of the upper and lower envelopes is defined as m. 11 h1 and m 11 The difference between them is the second component h 11 ,Right now

[0113] h 11 =h1-m 11 (4);

[0114] Following this method, the extraction process is repeated k times until the characteristics of the intrinsic modulus function are satisfied, thus obtaining h. 1k h 1k It is called the first IMF, that is

[0115] h 1k =h 1(k-1) -m 1k (5);

[0116] Designate the first IMF as c1, that is

[0117] c1 = h 1k (6);

[0118] Step 3: Separate c1 from the original signal, that is...

[0119] r1 = x(t) - c1 (7);

[0120] Treat r1 as the new signal and repeat the above steps. This process can be applied to the sequentially obtained r... i Repeating this process, we can obtain c1, c2, ..., c in sequence. n When component c n Or the remaining term r n Small enough, or when the remaining term r n The decomposition process ends when the function becomes monotonic.

[0121] Through empirical mode decomposition, the signal is decomposed into n empirical modes and a residue term. The original signal x(t) can be represented as...

[0122]

[0123] Among them, c j (t) is the j-th eigenmode function, r n It is either the trend term of the original signal or a constant value.

[0124] Through empirical mode decomposition, the original data is decomposed into n intrinsic mode functions (IMFs). Hilbert spectral analysis of each IMF yields...

[0125]

[0126] In this context, the amplitude and frequency of each IMF component are expressed as functions of time.

[0127] Calculate the envelope of each IMF, and perform empirical mode decomposition and Hilbert spectrum analysis on each envelope to obtain the amplitude and frequency of the envelope as functions of time. Repeat the above process to clearly describe the addition or multiplication process in the signal.

[0128] In mathematics, the data analysis process can be summarized as follows:

[0129]

[0130] For the second and higher layers, the nested expression of the amplitude function can be represented as:

[0131]

[0132] In equations (10) and (11), ω represents the rapidly changing instantaneous carrier frequency; Ω represents the slowly changing envelope frequency. For each additional layer of decomposition, additional dimensions Ω1, Ω2, ... must be added to accommodate the amplitude modulation frequency.

[0133] S4. In each step of S3, the time variable is integrated to obtain a frequency-only spectrum. This process can be iterated multiple times as needed until the amplitude function no longer has cyclic properties in the envelope, and finally a pure frequency high-dimensional full information representation of the signal amplitude is obtained, namely the holographic Hilbert amplitude modulation spectrum.

[0134] Integrating the time variable of each Hilbert spectral analysis result in step S3 yields a frequency-only spectrum, which is a marginal expression. The formula for calculating the marginal spectrum is:

[0135]

[0136] S5. Combining the holographic Hilbert amplitude modulation spectrum calculated in step S4, the correspondence between the signal modulation frequency and the carrier frequency is obtained. Based on this, the frequency band range of the bandpass filter in DEMON spectrum analysis is determined, and DEMON spectrum analysis is performed on the signal.

[0137] In this embodiment, based on the holographic Hilbert amplitude modulation spectrum analysis results, a suitable frequency band is selected to perform bandpass filtering on the target radiated noise signal; the Hilbert transform demodulation method is used to perform envelope demodulation on the filtered radiated noise signal to obtain the envelope signal; the envelope signal is then subjected to low-pass filtering and spectral analysis to obtain the DEMON spectrum.

[0138] Based on the above, Figure 3 This is a schematic diagram of the holographic Hilbert spectral analysis process provided by the present invention, as shown below. Figure 3 As shown.

[0139] S6 extracts features from the DEMON spectrum to accurately estimate parameters such as shaft frequency, blade frequency, and number of blades of the underwater target propeller.

[0140] In addition, the present invention provides an experimental example, the specific details of which are as follows.

[0141] Radiated noise data from a specific AUV performing a particular task is selected, downsampled, and a time-domain plot is generated, as shown below. Figure 4 As shown, the sampling frequency after downsampling is 20480Hz. Short-time Fourier transform is used to perform time-frequency analysis on the signal, and the time-frequency graph is shown below. Figure 5 As shown. A stable time-domain signal segment with a duration of 30 seconds is extracted from the time-domain plot, and the time-domain plot is shown below. Figure 6 As shown.

[0142] Given that the propeller of this aircraft has three blades, the shaft frequency of the propeller within the intercepted time range can be calculated to be approximately 8.24 Hz based on the propeller PWM frequency.

[0143] Holographic Hilbert spectral analysis is performed on the intercepted signal. Based on empirical mode decomposition (EMD), the signal is decomposed into several intrinsic mode functions (IMFs), and Hilbert spectral analysis is performed to obtain the amplitude and frequency of each IMF component as functions of time. The envelope of each IMF is calculated, and EMD and Hilbert spectral analysis are performed again on each envelope. This process is repeated to clearly describe the addition or multiplication processes in the signal. The time variable of the Hilbert spectrum obtained in each step is integrated to obtain a frequency-only spectrum. This process can be iterated multiple times as needed until the amplitude function no longer has cyclic properties in the envelope. Finally, a high-dimensional full-information representation of the signal amplitude in pure frequency form is obtained, i.e., the holographic Hilbert amplitude modulation spectrum, as shown below. Figure 7 As shown.

[0144] By combining the holographic Hilbert amplitude modulation spectrum, the correspondence between the signal modulation frequency and the carrier frequency is obtained. Integrating over the amplitude modulation frequency, such as... Figure 8 As shown in the figure, the modulation is mainly concentrated in the 400-800Hz frequency band. Based on this, the frequency band range of the bandpass filter in the DEMON spectral analysis was determined.

[0145] The envelope signal is obtained by envelope demodulation of the filtered radiated noise signal using the Hilbert transform demodulation method. The envelope signal is then low-pass filtered and subjected to spectral analysis to obtain the DEMON spectrum. Figure 9 As shown, line spectra exist at 8.3Hz, 16.6Hz, and 24.9Hz in the DEMON spectrum, indicating harmonic relationships, with a fundamental frequency of 8.3Hz.

[0146] Based on the above analysis, the propeller is estimated to be a three-bladed propeller with a shaft frequency of 8.3 Hz, which is approximately equal to the actual value.

[0147] In summary, this invention proposes a DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectral decomposition technology. By utilizing holographic Hilbert spectral decomposition technology, the correspondence between the modulation frequency and the carrier frequency can be directly obtained, solving the problem of difficult bandpass filter selection in traditional DEMON spectrum analysis.

[0148] Figure 10 This is a schematic diagram of the composition structure of the DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis provided in an embodiment of the present invention, as shown below. Figure 10 As shown, the DEMON spectrum analysis frequency band selection device 1000 based on holographic Hilbert spectrum analysis includes: a downsampling module 1001, used to perform spectrum analysis on the obtained underwater target radiated noise signal to obtain the main frequency range of the radiated noise signal, and to perform downsampling processing on the radiated noise signal to obtain a simplified radiated noise signal; a signal truncation module 1002, used to perform time-frequency analysis on the simplified radiated noise signal through short-time Fourier transform, and to perform signal truncation in combination with the time domain diagram to obtain the truncated radiated noise signal; a first analysis module 1003, used to decompose the truncated radiated noise signal into multiple intrinsic mode functions based on empirical mode decomposition in holographic Hilbert spectrum analysis, and to perform Hilbert spectrum analysis on each intrinsic mode function to obtain the amplitude change function and carrier frequency change function of each intrinsic mode function; and a second analysis module 1. 004 is used to calculate the envelope of each intrinsic mode function, and perform empirical mode decomposition and Hilbert spectrum analysis on each envelope to obtain the envelope amplitude variation function and modulation frequency variation function; integration module 1005 is used to integrate the time variables of the carrier frequency variation function, the modulation frequency variation function and the envelope amplitude variation function to obtain the holographic Hilbert amplitude modulation spectrum; third analysis module 1006 is used to obtain the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum, determine the frequency band range of the bandpass filter in DEMON spectrum analysis, perform DEMON spectrum analysis on the truncated radiated noise signal to obtain the DEMON spectrum; feature extraction module 1007 is used to extract features from the DEMON spectrum to obtain the estimation results of the shaft frequency, blade frequency and number of blades of the underwater target propeller.

[0149] In some embodiments, when performing spectral analysis on the obtained underwater target radiated noise signal, the Fourier transform calculation formula is as follows:

[0150]

[0151] Where f(t) is the original received signal, ω is the signal frequency, t represents time, and j is the imaginary unit.

[0152] In some embodiments, when performing time-frequency analysis on the simplified radiated noise signal using short-time Fourier transform, the calculation formula for the short-time Fourier transform is as follows:

[0153]

[0154] Where x1(t) is the downsampled signal, h(t) is the window function, f is the signal frequency, t represents time, and j is the imaginary unit.

[0155] In some embodiments, the empirical mode decomposition based on holographic Hilbert spectral analysis decomposes the truncated radiated noise signal into multiple eigenmode functions, wherein the truncated radiated noise signal is represented as follows:

[0156]

[0157] Among them, c j (t) represents the j-th intrinsic mode function, and the amplitude a of each IMF component is... j (t) and frequency ω j (t) represents a function of time, and N is the number of intrinsic moduli;

[0158] The nested expression for the amplitude change function is:

[0159]

[0160] Where Ω represents the slowly varying envelope frequency.

[0161] In some embodiments, the integration module is further configured to integrate the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function using edge expressions to obtain a frequency-only spectrum, and perform multiple iterations until the amplitude change function no longer has cyclic characteristics in the envelope, thereby obtaining a pure frequency high-dimensional full-information representation of the signal amplitude, i.e., the holographic Hilbert amplitude modulation spectrum; wherein, the formula for calculating the edge spectrum is:

[0162]

[0163] Where T is the integration time range, ω is the signal frequency, and t represents time.

[0164] In some embodiments, the third analysis module is further configured to: obtain the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum; determine the frequency band range in which modulation characteristics exist in the truncated radiated noise signal based on the correspondence; select a suitable frequency band range to perform bandpass filtering on the truncated radiated noise signal in conjunction with the holographic Hilbert amplitude modulation spectrum to obtain a filtered radiated noise signal; perform envelope demodulation on the filtered radiated noise signal using the Hilbert transform demodulation method to obtain an envelope signal; and perform low-pass filtering and spectral analysis on the envelope signal to obtain a DEMON spectrum.

[0165] In some embodiments, it should be noted that the description of the apparatus of the present invention is similar to the description of the method embodiments described above, and has similar beneficial effects to the same method embodiments, therefore, it will not be repeated. For technical details not disclosed in the embodiments of this apparatus, please refer to the description of the method embodiments of the present invention for understanding.

[0166] It should be noted that, in the embodiments of the present invention, if the above-described DEMON spectrum analysis frequency band selection method based on holographic Hilbert spectrum analysis is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of the present invention, or the part that contributes to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a terminal to execute all or part of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of the present invention are not limited to any specific hardware and software combination.

[0167] Correspondingly, embodiments of the present invention provide a DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis. Figure 11 This is a schematic diagram of the composition structure of the DEMON spectrum analysis band selection device based on holographic Hilbert spectrum analysis provided in an embodiment of the present invention, as shown below. Figure 11 As shown, the DEMON spectrum analysis band selection device 1100 based on holographic Hilbert spectrum analysis includes at least: a processor 1101 and a computer-readable storage medium 1102 configured to store executable instructions, wherein the processor 1101 generally controls the overall operation of the DEMON spectrum analysis band selection device based on holographic Hilbert spectrum analysis. The computer-readable storage medium 1102 is configured to store instructions and applications executable by the processor 1101, and can also cache data to be processed or processed by various modules in the processor 1101 and the DEMON spectrum analysis band selection device 1100 based on holographic Hilbert spectrum analysis, which can be implemented by flash memory or random access memory (RAM).

[0168] This invention provides a storage medium storing executable instructions. When these executable instructions are executed by a processor, they cause the processor to perform the method provided in this invention, for example... Figure 1 The method shown.

[0169] In some embodiments, the storage medium may be a computer-readable storage medium, such as a ferromagnetic random access memory (FRAM), a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), flash memory, magnetic surface memory, optical disc, or a compact disk-read-only memory (CD-ROM); or it may be a device that includes one or any combination of the above-mentioned memories.

[0170] In some embodiments, executable instructions may take the form of a program, software, software module, script, or code, written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and may be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.

[0171] As an example, executable instructions may, but do not necessarily, correspond to files in a file system. They may be stored as part of a file containing other programs or data, for example, in one or more scripts within a Hyper Text Markup Language (HTML) document, in a single file dedicated to the program in question, or in multiple co-located files (e.g., files storing one or more modules, subroutines, or code sections). As an example, executable instructions may be deployed to execute on a single electronic device, or on multiple electronic devices located in one location, or on multiple electronic devices distributed across multiple locations and interconnected via a communication network.

[0172] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and scope of the present invention are included within the scope of protection of the present invention.

[0173] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of the invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of the invention, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the invention. The sequence numbers of the above-described embodiments of the invention are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0174] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. In the several embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components may be combined, or integrated into another system, or some features may be ignored or not performed.

[0175] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for selecting frequency bands in DEMON spectral analysis based on holographic Hilbert spectral analysis, characterized in that, The method includes: The obtained underwater target radiated noise signal is subjected to spectral analysis to obtain the main frequency range of the radiated noise signal, and the radiated noise signal is downsampled to obtain a simplified radiated noise signal; The simplified radiated noise signal is subjected to time-frequency analysis by short-time Fourier transform, and the signal is truncated by combining the time-domain plot to obtain the truncated radiated noise signal. Based on empirical mode decomposition in holographic Hilbert spectral analysis, the truncated radiated noise signal is decomposed into multiple intrinsic mode functions, and Hilbert spectral analysis is performed on each intrinsic mode function to obtain the amplitude variation function and carrier frequency variation function of each intrinsic mode function. The envelope of each intrinsic mode function is calculated, and empirical mode decomposition and Hilbert spectrum analysis are performed on each envelope to obtain the envelope amplitude variation function and the modulation frequency variation function. Integrating the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function yields the holographic Hilbert amplitude modulation spectrum. Based on the holographic Hilbert amplitude modulation spectrum, the correspondence between the modulation frequency and the carrier frequency of the truncated radiated noise signal is obtained, the frequency band range of the bandpass filter in the DEMON spectrum analysis is determined, and the DEMON spectrum analysis is performed on the truncated radiated noise signal to obtain the DEMON spectrum. Feature extraction was performed on the DEMON spectrum to obtain estimates of the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

2. The method according to claim 1, characterized in that, When performing spectral analysis on the obtained underwater target radiated noise signal, the Fourier transform calculation formula is as follows: ； Where f(t) is the original received signal, ω is the signal frequency, t represents time, and j is the imaginary unit.

3. The method according to claim 1, characterized in that, When performing time-frequency analysis on the simplified radiated noise signal using the short-time Fourier transform, the calculation formula for the short-time Fourier transform is as follows: ； Where x1(t) is the downsampled signal, h(t) is the window function, f is the signal frequency, t represents time, and j is the imaginary unit.

4. The method according to claim 1, characterized in that, The empirical mode decomposition based on holographic Hilbert spectral analysis decomposes the truncated radiated noise signal into multiple eigenmode functions, wherein the truncated radiated noise signal is represented as follows: ； Among them, c j (t) represents the j-th intrinsic mode function, and the amplitude a of each IMF component is... j (t) and frequency ω j (t) represents a function of time, and N is the number of intrinsic moduli; The nested expression for the amplitude change function is: ； Where Ω represents the slowly varying envelope frequency.

5. The method according to claim 1, characterized in that, The process of integrating the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function to obtain the holographic Hilbert amplitude modulation spectrum includes: Using edge expressions, the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function are integrated to obtain a frequency-only spectrum. This process is repeated multiple times until the amplitude change function no longer exhibits cyclic properties within the envelope, resulting in a pure frequency high-dimensional full-information representation of the signal amplitude, i.e., the holographic Hilbert amplitude modulation spectrum. The formula for calculating the edge spectrum is: ； Where T is the integration time range, ω is the signal frequency, and t represents time.

6. The method according to claim 1, characterized in that, The process of obtaining the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum, determining the bandpass filter range in DEMON spectral analysis, and performing DEMON spectral analysis on the truncated radiated noise signal includes: The correspondence between the modulation frequency and the carrier frequency of the truncated radiated noise signal is obtained based on the holographic Hilbert amplitude modulation spectrum. Based on the aforementioned correspondence, the frequency band range in which modulation characteristics exist in the extracted radiated noise signal is determined; By combining the holographic Hilbert amplitude modulation spectrum, a suitable frequency band is selected to perform bandpass filtering on the truncated radiated noise signal to obtain the filtered radiated noise signal; The Hilbert transform demodulation method is used to perform envelope demodulation on the filtered radiated noise signal to obtain the envelope signal. The envelope signal is low-pass filtered and spectral analyzed to obtain the DEMON spectrum.

7. A DEMON spectrum analysis frequency band selection device based on holographic Hilbert spectrum analysis, characterized in that, The device includes: The downsampling module is used to perform spectral analysis on the obtained underwater target radiated noise signal to obtain the main frequency range of the radiated noise signal, and to perform downsampling processing on the radiated noise signal to obtain a simplified radiated noise signal; The signal interception module is used to perform time-frequency analysis on the simplified radiated noise signal through short-time Fourier transform, and to intercept the signal by combining the time domain diagram to obtain the intercepted radiated noise signal. The first analysis module is used to decompose the truncated radiated noise signal into multiple intrinsic mode functions based on empirical mode decomposition in holographic Hilbert spectral analysis, and to perform Hilbert spectral analysis on each intrinsic mode function to obtain the amplitude variation function and carrier frequency variation function of each intrinsic mode function. The second analysis module is used to calculate the envelope of each intrinsic mode function, and to perform empirical mode decomposition and Hilbert spectrum analysis on each envelope to obtain the envelope amplitude variation function and the modulation frequency variation function. An integration module is used to integrate the time variables of the carrier frequency change function, the modulation frequency change function, and the envelope amplitude change function to obtain the holographic Hilbert amplitude modulation spectrum. The third analysis module is used to obtain the correspondence between the modulation frequency and carrier frequency of the truncated radiated noise signal based on the holographic Hilbert amplitude modulation spectrum, determine the frequency band range of the bandpass filter in DEMON spectrum analysis, and perform DEMON spectrum analysis on the truncated radiated noise signal to obtain the DEMON spectrum. The feature extraction module is used to extract features from the DEMON spectrum to obtain estimates of the shaft frequency, blade frequency, and number of blades of the underwater target propeller.

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