A frogman signal feature extraction method and system based on VMD algorithm and permutation entropy

Abstract

The present application relates to the field of frogman and frogman detection, and particularly relates to a frogman signal feature extraction method and system based on VMD algorithm and permutation entropy. The method comprises: using a variational mode decomposition method to iteratively decompose a frogman signal to obtain a fixed mode function; selecting the highest energy fixed mode function to calculate permutation entropy to obtain a frogman time series envelope; calculating a Fourier transform of the permutation entropy to obtain an envelope spectrum; and performing feature extraction on the frogman signal according to the spectrum. The system comprises: a fixed mode function acquisition module, a permutation entropy calculation module, a spectrum acquisition module and a feature extraction module. The present application can adaptively extract features of frogman radiation signals under low signal-to-noise ratio conditions. Moreover, high-frequency wide bands are not required, and the sampling rate of the device can be relatively low.

Description

Technical Field

[0001] This invention relates to the field of frogmen and frogman detection, specifically to a method and system for extracting frogman signal features based on VMD algorithm and permutation entropy. Background Technology

[0002] Frogmen are a unit responsible for underwater reconnaissance, demolition, and special operations. They are called "frogmen" because their equipment includes swimming gear shaped like frog feet. They are amphibious troops who spend long periods underwater wearing masks, equipped with flippers, rubber suits, and oxygen tanks for special missions.

[0003] The radiated sound of a light-weight diving frogman mainly comes from its breathing equipment. During inhalation, the energy is mainly concentrated at high frequencies; during exhalation, the energy is mainly at low frequencies, and the cycle of breathing is clearly regular. Its identifiable characteristic is the periodic transient spectrum of breathing, thus distinguishing it from other small targets.

[0004] Currently, frogman detection methods are divided into active and passive detection. While active sonar has a long detection range, it suffers from severe reverberation in near-shore environments such as around ports, and its high power supply requirements limit its development. In contrast, passive sonar technology offers superior stealth and does not require a power source for signal transmission, making it environmentally friendly and thus significant for frogman detection. However, frogman-radiated signals have low noise, resulting in a low signal-to-noise ratio for passive detection. Therefore, improving the signal-to-noise ratio is crucial for frogman detection.

[0005] Previous research methods were typically based on the spectral energy of frogmen, requiring certain prior knowledge. Furthermore, they could only select a fixed frequency band and calculate the envelope to extract features. However, different respirators generate noise in different frequency bands, and the selected frequency band cannot be suitable for every respirator, leading to poor extraction results. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing methods and propose a frogman feature extraction method based on Variational Mode Decomposition (VMD) and permutation entropy. This method can adaptively extract the frogman respiratory envelope spectrum under low signal-to-noise ratio conditions. Specifically, a frogman signal feature extraction method and system based on VMD algorithm and permutation entropy are proposed.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution.

[0008] This invention proposes a method for extracting frogman signal features based on the VMD algorithm and permutation entropy, the method comprising:

[0009] Step 1) Preprocess the collected frogman signals, and use variational mode decomposition to iteratively decompose the preprocessed frogman signals to obtain fixed mode functions;

[0010] Step 2) Select the solid-state mode function with the highest energy to calculate the permutation entropy;

[0011] Step 3) Calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum;

[0012] Step 4) Based on the spectrum, extract features from the frogman's signal.

[0013] As an improvement to the above technical solution, the preprocessing includes: taking the mean and normalization.

[0014] As an improvement to the above technical solution, in step 1), variational mode decomposition is used to iteratively decompose the preprocessed frogman signal to obtain a fixed mode function, specifically including:

[0015] Step 1-1) Construct a variational problem, defining each intrinsic mode function as a frequency-modulated amplitude-modulated signal;

[0016] Step 1-2) Set constraints and construct a variational mode decomposition constrained variational model; the constraints include: the decomposition sequence is a modal component with a center frequency and a finite bandwidth, the minimum sum of the estimated bandwidths of each mode, and the constraint that the sum of all modes is equal to the preprocessed frogman signal.

[0017] Steps 1-3) introduce the penalty factor and the Lagrange operator to transform the variational mode decomposition constrained variational model into an unconstrained variational problem, resulting in the extended Lagrange expression;

[0018] Steps 1-4) use the alternating direction multiplier algorithm to iterate over the extended Lagrange expression;

[0019] Steps 1-5) Repeat steps 1-4) until the iterative constraint conditions are met and the fixed mode function is obtained.

[0020] As one improvement to the above technical solution, in step 1-1), the frequency-modulated amplitude-modulated signal u corresponding to the k-th intrinsic mode function... k The expression for t is:

[0021] u k (t)=A k (t)cos(φ k (t))

[0022] Among them, A k (t) represents the instantaneous amplitude; φ k (t) represents the instantaneous phase;

[0023] In steps 1-2), the expression for the variational mode decomposition constrained variational model is:

[0024]

[0025] Where f is the preprocessed frogman signal input, {u k} = {u1, u2, u3, ..., u K} represents the k intrinsic mode function components with finite bandwidth obtained from the decomposition, {w k} = {w1, w2, ..., w K} represents the center frequency of each intrinsic mode function; K represents the number of intrinsic mode functions;

[0026] In steps 1-3), the expanded Lagrange expression is:

[0027]

[0028] Where α represents the penalty factor; λ(t) represents the Lagrange operator; Let δt denote the derivative, ft denote the impulse function, t denote the original signal, t denote time, and j denote the imaginary unit.

[0029] As one improvement to the above technical solution, the iterative process in steps 1-4) specifically includes:

[0030] In the first iteration, the spectrum is iterated as follows:

[0031]

[0032] in, This is the frequency domain representation of the intrinsic mode functions. This is the frequency domain representation of the input signal, where ω represents the frequency. k Let represent the center frequency of the model function, n represent the nth iteration, and i represent the i-th intrinsic mode function. For the frequency domain representation of the Lagrange operator;

[0033] In the next iteration, the center frequency of the modal function is solved iteratively to obtain:

[0034]

[0035] Finally, iterate over λ:

[0036]

[0037] Where γ represents the update parameter of the Lagrange operator. The frequency domain representation of the input signal;

[0038] The iterative constraint expressions in steps 1-5) are as follows:

[0039]

[0040] Where || represents the norm, and ε is the set iteration stopping condition.

[0041] As one improvement to the above technical solution, the process of calculating the permutation entropy in step 2) specifically includes:

[0042] Step 2-1) Select the intrinsic mode function with the highest energy as the time series {x(i), i = 1, 2, ..., N}, and reconstruct its phase space into a matrix Y, where N is the length of the time series;

[0043] Step 2-2) Treat each row of matrix Y as a reconstruction component, and rearrange each reconstruction component in ascending order into a vector S(l). The column indices of each element in vector S(l) form a symbol sequence.

[0044] Steps 2-3) Calculate the permutation entropy based on the probability of each symbol sequence appearing in the m-dimensional mapping phase space;

[0045] Steps 2-4) Normalize the permutation entropy values.

[0046] As one improvement to the above technical solution, the expression for the matrix Y is:

[0047]

[0048] Where m is the embedding dimension, t is the delay time, and the variable g = N - (m - 1)t.

[0049] In step 2-2), the expression for vector S(l) is:

[0050] S(l)={j1j2...j m},l=1,2,...,k

[0051] In steps 2-3), the permutation entropy H pe The formula for calculation is:

[0052]

[0053] Among them, P j This represents the probability of the j-th symbol sequence appearing;

[0054] In steps 2-4), the permutation entropy value is normalized, and the expression is:

[0055]

[0056] Where ln(m!) is the maximum value of the permutation entropy.

[0057] As an improvement to the above technical solution, in step 4), the extracted features of the frogman signal specifically include: a first energy feature, a second energy feature, and a frequency feature; wherein,

[0058] The first energy characteristic quantity is defined as: the energy corresponding to the breathing frequency band Ω, divided by the energy in the lower frequency band Ψ, while removing the DC energy;

[0059] The second energy characteristic is defined as: the energy at the maximum peak point within the breathing frequency band Ω, divided by the energy within the lower frequency band Ψ, while removing DC and peak point energy;

[0060] The frequency characteristic quantity is defined as follows: find the maximum peak frequency point in the low frequency band Ψ and see if it is within the range of the frogman's breathing frequency band Ω.

[0061] As one of the improvements to the above technical solution, the first energy characteristic quantity F diver1 The expression is:

[0062]

[0063] Among them, Z k Z1 represents the amplitude at the k-th frequency domain point, and Z2 represents the mean amplitude.

[0064] The second energy characteristic quantity F diver2 The expression is:

[0065]

[0066] This invention also proposes a frogman signal feature extraction system based on the VMD algorithm and permutation entropy. The system includes: a fixed mode function acquisition module, a permutation entropy calculation module, a spectrum acquisition module, and a feature extraction module; wherein,

[0067] The fixed mode function acquisition module is used to preprocess the collected frogman signals and iteratively decompose the preprocessed frogman signals using variational mode decomposition to obtain fixed mode functions.

[0068] The permutation entropy calculation module is used to select the solid-state mode function with the highest energy to calculate the permutation entropy;

[0069] The spectrum acquisition module is used to calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum;

[0070] The feature extraction module is used to extract features from the frogman's signal based on the spectrum.

[0071] The advantages of this invention compared to the prior art are:

[0072] 1. The method of the present invention can extract features from frogman radiation signals under low signal-to-noise ratio conditions;

[0073] 2. The method of the present invention can adaptively decompose frogman signals to obtain features without any prior knowledge;

[0074] 3. The method of the present invention has low requirements for equipment because it does not require the use of high frequency and wide bandwidth, so the equipment sampling rate can be low. Attached Figure Description

[0075] Figure 1 This is the network structure of this article;

[0076] Figure 2 It is an iterative process of variational mode decomposition;

[0077] Figure 3 This is a spectrum diagram of frogmen;

[0078] Figure 4 It is the entropy output of a 30s signal arrangement;

[0079] Figure 5 These are the characteristic quantities of frogmen, boats, and background noise;

[0080] Figure 6 It incorporates signal-to-noise ratio (SNR) and background noise characteristics;

[0081] Figure 7 It is the detection rate under different input signal-to-noise ratios. Detailed Implementation

[0082] To achieve the above objectives, this invention provides a frogman feature extraction method based on variational mode decomposition and permutation entropy, the method comprising:

[0083] The collected frogman breathing data were processed by removing the mean and normalizing the data.

[0084] The processed data is iteratively decomposed into fixed mode functions by using variational mode decomposition.

[0085] The permutation entropy is calculated by selecting the solid-state mode function with the highest energy to obtain the envelope of the frogman time series;

[0086] Calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum;

[0087] Based on the spectrum, feature extraction is performed on the signal.

[0088] As an improvement to the above technical solution, the step of substituting the processed frogman signal into variational mode decomposition to obtain the fixed mode function with the highest energy specifically includes:

[0089] First, we construct a variational problem. Variational mode decomposition defines each intrinsic mode function as a frequency-modulated and amplitude-modulated signal, which can be expressed as:

[0090] u k (t)=A k (t)cos(φ k (t)) (1)

[0091] Among them, A k (t) represents the instantaneous amplitude, φ k (t) represents the instantaneous phase. It is necessary to ensure that the decomposed sequence consists of modal components with a finite bandwidth and a center frequency, while minimizing the sum of the estimated bandwidths of each mode. The constraint condition is that the sum of all modes is equal to the original signal. Therefore, the constraint variational model for variational mode decomposition is as follows:

[0092]

[0093] In the formula, k represents the number of intrinsic mode functions, f is the input signal, and {u k} = {u1, u2, u3, ..., u K} represents the k intrinsic mode function components with finite bandwidth obtained from the decomposition, {w k} = {w1, w2, ..., w K} represents the center frequency of each intrinsic mode function. This includes intrinsic mode functions with more stringent constraints on the signal's finite bandwidth, Hilbert transform, modulation mixing, and demodulation using Gaussian smoothing to obtain the bandwidth of each mode function.

[0094] To solve the constrained variational problem of equation (2), a penalty factor α and the Lagrange operator λ(t) are introduced, transforming the above equation into an unconstrained variational problem, resulting in the extended Lagrange expression:

[0095]

[0096] The Alternate Direction Method of Multipliers (ADMM) algorithm is used to solve the problem. This decomposes the complete optimization problem into a series of iterative sub-optimization problems. These sub-problems aim to minimize the cost function iteratively over individual parameters, rather than simultaneously optimizing the cost function over all optimization variables, thus making the problem easier to handle. In the first iteration, consider u... k The problem with (t) produces the following update in the spectrum:

[0097]

[0098] In the next step, in order to obtain the center frequency ωk The update, obtained by iteratively solving the following sub-optimization problems, yields:

[0099]

[0100] Finally, iterate over λ:

[0101]

[0102] The process continues iteratively, that is, by repeating formula (4-6), until the following iterative constraints are met.

[0103]

[0104] As an improvement to the above technical solution, the permutation entropy is calculated by selecting the mode function with the highest energy, specifically as follows:

[0105] Selecting the intrinsic mode function with the highest energy as the time series {x(i), i = 1, 2, ..., N}, its phase space can be reconstructed as matrix Y:

[0106]

[0107] Where m is the embedding dimension, t is the delay time, and g = N - (m - 1)t.

[0108] Each row in matrix Y represents a reconstructed component, and there are k reconstructed components in total. Rearranging each reconstructed component in ascending order yields a sequence of symbols formed by the column indices of each element in the vector.

[0109] S(l)={j1j2...j m},l=1,2,...,k (9)

[0110] There are a total of m! different symbol sequences mapped to an m-dimensional phase space. The probability of such a symbol sequence occurring is:

[0111] {P1,P2,...,P k} (10)

[0112] The formula for calculating the permutation entropy of the time series {x(i)} is:

[0113]

[0114] The maximum value of the permutation entropy is ln(m!). Normalizing the permutation entropy value results in:

[0115]

[0116] H PE Permutation entropy represents the degree of randomness in a time series.

[0117] As an improvement to the above technical solution, the target's characteristic quantities include: energy characteristic quantities and frequency characteristic quantities, specifically:

[0118] Feature quantities are extracted from the spectrum of the permutation entropy output signal. Assume the signal output by this method is y. PEn , in y PEn By selecting continuous L-point data and calculating the FFT of L points, we can obtain... Calculate two energy characteristics and one frequency characteristic on the spectrum.

[0119] (1) Energy characteristic quantity: defined as the energy corresponding to the breathing frequency band Ω, divided by the energy in the lower frequency band Ψ, while removing the DC energy, we have:

[0120]

[0121] Where Ψ∈[0,4], Ω∈[0.1,0.4].

[0122] (2) Energy characteristic quantity: defined as the energy at the maximum peak point within the respiratory frequency band Ω, divided by the energy within the lower frequency band Ψ, while removing DC and peak point energy, we have:

[0123]

[0124] (3) Frequency characteristics: Find the maximum peak frequency point in the low frequency band Ψ and see if it is within the range of the frogman's breathing rhythm frequency band Ω.

[0125] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0126] Example 1

[0127] like Figure 1 As shown, this invention proposes a method for extracting frogman signal features based on variational mode decomposition and permutation entropy. This method includes:

[0128] Step 1) Perform data processing on the collected frogman breathing data, including demeaning and normalization.

[0129] Step 2) Use variational mode decomposition to iteratively decompose the frogman signal using the processed data to obtain a series of fixed mode functions.

[0130] The variational mode decomposition iterative steps are as follows:

[0131] 1. Initialization and n, where Λ is the frequency domain transformed using Fourier transform.

[0132] 2. Update According to the following formula:

[0133]

[0134]

[0135]

[0136] 3. Repeat step 2 until the iteration stopping condition is met.

[0137]

[0138] Where ε > 0.

[0139] 4. The inverse Fourier transform is used to obtain u k (t), thus obtaining K intrinsic mode functions.

[0140] The specific iterative steps are as follows: Figure 2 As shown.

[0141] Step 3) Select the solid mode function with the highest energy to calculate the permutation entropy and obtain the envelope of the frogman time series.

[0142] The permutation entropy is calculated by reconstructing the phase space of the time series {x(i), i = 1, 2, ..., N} into a matrix Y:

[0143]

[0144] Where m is the embedding dimension, t is the delay time, and g = N - (m - 1)t.

[0145] Each row in matrix Y represents a reconstructed component, and there are k reconstructed components in total. Rearranging each reconstructed component in ascending order yields a sequence of symbols formed by the column indices of each element in the vector.

[0146] S(l)={j1 j2 ... j m},l=1,2,...,k

[0147] There are a total of m! different symbol sequences mapped to an m-dimensional phase space. The probability of such a symbol sequence occurring is:

[0148] {P1,P2,...,P k}

[0149] The formula for calculating the permutation entropy of the time series {x(i)} is:

[0150]

[0151] The maximum value of the permutation entropy is ln(m!). Normalizing the permutation entropy value results in:

[0152]

[0153] H PE Let be the permutation entropy.

[0154] Step 4) Select the permutation entropy sequence of 30s, perform a fast Fourier transform on it, and obtain the envelope spectrum.

[0155] Assume the signal output by the entropy arrangement method is y. PEn , in y PEn By selecting continuous L-point data and calculating the FFT of L points, we can obtain...

[0156] Step 5) Extract features from the signal based on the spectrum.

[0157] Calculate two energy characteristics and one frequency characteristic:

[0158] (1) Energy characteristic quantity: defined as the energy corresponding to the breathing frequency band Ω, divided by the energy in the lower frequency band Ψ, while removing the DC energy, we have:

[0159]

[0160] Where Ψ∈[0,4], Ω∈[0.1,0.4].

[0161] (2) Energy characteristic quantity: defined as the energy at the maximum peak point within the respiratory frequency band Ω, divided by the energy within the lower frequency band Ψ, while removing DC and peak point energy, we have:

[0162]

[0163] (3) Frequency characteristics: Find the maximum peak frequency point in the low frequency band Ψ and see if it is within the range of the frogman's breathing rhythm frequency band Ω.

[0164] Example 2

[0165] Embodiment 2 of this invention provides a frogman signal feature extraction system based on the VMD algorithm and permutation entropy, comprising: a fixed mode function acquisition module, a permutation entropy calculation module, a spectrum acquisition module, and a feature extraction module; wherein,

[0166] The fixed mode function acquisition module is used to preprocess the collected frogman signals and iteratively decompose the preprocessed frogman signals using variational mode decomposition to obtain fixed mode functions.

[0167] The permutation entropy calculation module is used to select the solid-state mode function with the highest energy to calculate the permutation entropy;

[0168] The spectrum acquisition module is used to calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum;

[0169] The feature extraction module is used to extract features from the frogman's signal based on the spectrum.

[0170] Example 3

[0171] In this example, the short-time Fourier transform of the radiation signal collected by frogmen at sea is as follows: Figure 3 As shown, the device sampling frequency is 16kHz. The time-spectrum graph reveals a clear periodic signal in the frogman's breathing, which is used to identify the frogman. In this experiment, the frogman's breathing intervals were relatively long and unstable, approximately once every 7 seconds, with a frequency of about 0.14Hz.

[0172] A 30-second frogman radiation signal was selected for variational mode decomposition (VMD). The VMD parameter α was set to 2000, and the number of modes K was determined by empirical mode decomposition. The center frequencies of all modes were set to a uniform distribution. The permutation entropy was calculated for the intrinsic mode function with the highest energy obtained after VMD. The parameters for entropy were chosen to be an embedding dimension of 3 and a time delay of 1. The permutation entropy output y was then calculated. out (Here referring to H) PE And calculate the FFT, such as Figure 4 As shown, the output entropy has a significant peak at low frequencies (0.13Hz), which matches the frogman's breathing rhythm. The feature extraction results are as follows... Figure 5 As shown, the three features are clearly distinct from both the ship and the background noise.

[0173] The energy characteristics of features 1 and 2 are much higher than those of the ship and background noise. The frequency characteristic of feature 3 is stable between 0.13Hz and 0.2Hz in the 0Hz-4Hz range, while that of the small boat is generally around 0.01Hz. The background noise has no fixed peak frequency.

[0174] Example 4

[0175] To verify the noise immunity of the proposed method under low signal-to-noise ratio conditions, simulations were performed by adding Gaussian white noise with a certain signal-to-noise ratio to the frogman's radiated noise, and the characteristic values ​​were obtained. These values ​​were then compared with environmental noise. Figure 6 As shown, a reasonable detection threshold is determined. The threshold is set higher than the maximum characteristic value of the environmental noise; the threshold for characteristic 1 is set to 0.4, and the threshold for characteristic 2 is set to 0.08. Decisions are made based on this threshold. Gaussian white noise with a certain signal-to-noise ratio is added to the frogman's radiated noise. 100 Monte Carlo experiments are conducted at one signal-to-noise ratio to obtain the change in decision probability with the input signal-to-noise ratio, as shown below. Figure 7 As shown. Feature 2 is the most robust decision, and this invention achieves a detection rate of approximately 85% at -5dB.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for extracting frogman signal features based on VMD algorithm and permutation entropy, the method comprising: Step 1) Preprocess the acquired frogman signals, and iteratively decompose the preprocessed frogman signals using variational mode decomposition to obtain fixed mode functions; specifically, the iterative decomposition of the preprocessed frogman signals using variational mode decomposition to obtain fixed mode functions includes: Step 1-1) Construct a variational problem, defining each intrinsic mode function as a frequency-modulated amplitude-modulated signal; Steps 1-2) Set constraints and construct a variational mode decomposition constrained variational model; the constraints include: the decomposition sequence is a modal component with a center frequency and a finite bandwidth, the sum of the estimated bandwidths of each mode is minimized, and the constraint condition is that the sum of all modes is equal to the preprocessed frogman signal; Steps 1-3) introduce the penalty factor and the Lagrange operator to transform the variational mode decomposition constrained variational model into an unconstrained variational problem, resulting in the extended Lagrange expression; Steps 1-4) use the alternating direction multiplier algorithm to iterate over the extended Lagrange expression; Steps 1-5) Repeat steps 1-4) until the iterative constraint conditions are met to obtain the fixed mode function; Step 2) Select the solid-state mode function with the highest energy to calculate the permutation entropy; specifically including: Step 2-1) Select the intrinsic mode function with the highest energy as the time series. Reconstruct its phase space into a matrix , N It is the length of the time series; Step 2-2) Convert the matrix Y Each row in the vector is treated as a reconstruction component, and each reconstruction component is rearranged into a vector in ascending order. ,vector The column indices of each element's position form a sequence of symbols; Steps 2-3) Based on each symbol sequence in m Calculate the permutation entropy based on the probability of occurrence of the phase space of the dimensional mapping. Steps 2-4) Normalize the permutation entropy values; Step 3) Calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum; Step 4) Extract features from the frogman's signal based on the spectrum.

2. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 1, characterized in that, The preprocessing includes: taking the mean and normalization.

3. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 1, characterized in that, In step 1-1), the first k Frequency-modulated and amplitude-modulated signals corresponding to each intrinsic mode function The expression is: in, Instantaneous amplitude; It is the instantaneous phase; In steps 1-2), the expression for the variational mode decomposition constrained variational model is: in, The input is the preprocessed frogman signal. The result of decomposition A finite bandwidth intrinsic mode function component, The center frequency of each intrinsic mode function is represented by K; K represents the number of intrinsic mode functions. In steps 1-3), the expanded Lagrange expression is: in, Indicates the penalty factor; Represents the Lagrange operator; To express differentiation, Represents the impulse function. Represents the original signal. t Indicates time, j It represents the imaginary unit.

4. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 3, characterized in that, The iterative process in steps 1-4) specifically includes: In the first iteration, the spectrum is iterated as follows: in, This is the frequency domain representation of the intrinsic mode functions. This is the frequency domain representation of the input signal. Indicates frequency, This represents the center frequency of the model function. n Indicates the first n iteration i Indicates the first i One intrinsic mode function, For the frequency domain representation of the Lagrange operator; In the next iteration, the center frequency of the modal function is solved iteratively to obtain: Finally, Perform iterations: in, This represents the update parameters of the Lagrange operator; The iterative constraint expressions in steps 1-5) are as follows: in, Represents the norm, This is the set iteration stopping condition.

5. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 1, characterized in that, The expression for the matrix Y is: in, t For the delay time, the variable ; In step 2-2), the vector The expression is: In steps 2-3), the permutation entropy The formula for calculation is: in, Indicates the first J The probability of a sequence of symbols appearing; In steps 2-4), the permutation entropy value is normalized, and the expression is: in, This represents the maximum value of the permutation entropy.

6. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 1, characterized in that, In step 4), the extracted features of the frogman signal specifically include: a first energy feature, a second energy feature, and a frequency feature; wherein, The first energy characteristic quantity is defined as: respiratory frequency band The corresponding energy within is lower than that in the lower frequency band. The energy inside is removed, while the energy of the direct current (DC) is eliminated. The second energy characteristic quantity is defined as: in the respiratory band The maximum peak energy is higher than that of the lower frequency band. The energy within is removed, while DC and peak point energy are also removed; The frequency characteristic quantity is defined as: in the low frequency band Search for the point of maximum peak frequency within the frogman's breathing frequency band. Within the range.

7. The frogman signal feature extraction method based on VMD algorithm and permutation entropy according to claim 6, characterized in that, The first energy characteristic quantity The expression is: in, This represents the amplitude at the k-th frequency domain point. Indicates the mean amplitude; Second energy characteristic quantity The expression is: 。 8. A system for extracting frogman signal features based on the VMD algorithm and permutation entropy as described in claim 1, characterized in that, The system includes: a fixed mode function acquisition module, a permutation entropy calculation module, a spectrum acquisition module, and a feature extraction module; wherein... The fixed mode function acquisition module is used to preprocess the collected frogman signals and iteratively decompose the preprocessed frogman signals using variational mode decomposition to obtain fixed mode functions. The permutation entropy calculation module is used to select the solid-state mode function with the highest energy to calculate the permutation entropy; The spectrum acquisition module is used to calculate the Fourier transform of the permutation entropy to obtain the envelope spectrum; The feature extraction module is used to extract features from the frogman's signal based on the spectrum.

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