<

f

m
+
1

;

- the center frequency f_mis defined as:

$f_{m} = F_{m e l}^{- 1} (F_{m e l} (f_{l}) + m \frac{F_{m e l} (f_{h}) - F_{m e l} (f_{l})}{M + 1});$

- where f_land f_hare respectively a lower limit frequency and an upper limit frequency of the filter H_m(k), and F_mel⁻¹is defined as F_mel⁻¹(b)=700(10^b/2595−1)=700(e^b/1127−1)
- based on the Mel filter bank, the MFCCs for 1 frame are obtained by:

${mfcc}_{i} (n) = \sqrt{\frac{2}{M}} \sum_{m = 0}^{M - 1} \log [S_{i} (m)] \cos [\frac{π n (2 m - 1)}{2 M}];$

- where n=1, 2 . . . M,

$S_{i} (m) = \sum_{k = 0}^{N - 1} {❘ X_{i} (k) ❘}^{2} H_{m} (k)$

is an mth Mel filter energy of an ith frame signal; in order to compare the bionic signal with the original signal, the Mel distance di of the ith frame of each sound signal is defined as:

$d_{i} = \sqrt{\sum_{n = 1}^{M} {({mfcc}_{synthetic}^{i} (n) - {mfcc}_{whistle}^{i} (n))}^{2}};$

- a mean Mel distance of all frames of each signal is defined as:

$D_{M e l} = \frac{\sum_{i = 1}^{k} d_{i}}{k};$

- where i=1, 2 . . . k;
- the smaller the Mel distance, the smaller the difference between the bionic signal and the original signal, and the bionic signal is more likely to be ignored as a marine mammal sound signal, that is, the better the covertness.

Preferably, step S3.5 is specifically as follows:

- assuming that a time-frequency diagram of the noise-reduced sound signal is X_m[ω,m], where ω represents frequency, m represents a time period divided by a window function w[ω], and X_m[ω] represents a Fourier transform result of a mth time period; and f(m) represents a fundamental frequency of the mth time period, and an expression using a maximum value extraction method is as follows:

$f (m) = \arg \max ❘ X_{m} [ω] ❘;$

- the fundamental frequency of each time period of the sound signal without and with the information embedded is calculated respectively, and the minimum error of the fundamental frequency of all time periods is taken, and a calculation formula is as follows:

$Δ v = \frac{\sum_{m = 1}^{n} ❘ (f_{T} (m) - f_{L} (m)) ❘}{n};$

- where n represents the number of time periods taken, f_T(m) represents the fundamental frequency of the mth time period of the original sound signal, and f_L(m) represents the fundamental frequency of the mth time period of the sound signal with the information embedded;
- an energy er(m) of a mth data block of a rth harmonic is obtained using a short-time Fourier transform with a window length L, and a formula thereof is as follows:

$e_{r} (m) = X_{m} [f_{r} (m)];$

- let amplitude of a first sampling point of each data block be ar[m1], and a formula thereof is as follows:

$a_{r} [m_{1}] = 2 \sqrt{e_{r} [m]} / L;$

- a value of each sampling point of the data block is obtained using an interpolation method, and finally an amplitude value a_r[n] of the rth harmonic at each sampling point is obtained; and a mean amplitude error of all sampling points in each harmonic of the sound signal without and with the information embedded is calculated as follows:

$Δ a_{r} = \frac{\sum_{i = 1}^{n} ❘ a_{r}^{T} [i] - a_{r}^{L} [i] ❘}{n};$

- where a_r^T[i] represents an amplitude value of an ith sampling point of the rth harmonic of the original sound signal, a_r^L[i] represents the amplitude value of the ith sampling point of the rth harmonic of the sound signal with the information embedded, n represents the number of sampling points, and finally the minimum error of the signal amplitude is calculated, which is defined as the minimum error of the mean amplitude error of all harmonics, and a calculation formula thereof is as follows:

$Δ x = \frac{\sum_{r = 1}^{m} Δ a_{r}}{m};$

- where m represents the number of harmonics, and Δa_rrepresents the mean amplitude error of the rth harmonic.

Preferably, step S4 is specifically as follows:

A mean and a standard deviation of all data of each feature are calculated, and then the data is normalized; normalization is a data preprocessing technique that subtracts the mean from each data point and then divides a result by the standard deviation to map the data to a normalized distribution with a mean of 0 and a standard deviation of 1, and a normalization formula is as follows:

normalized_data=(data−means)/stds;

- step S5 is specifically as follows:
- the importance of the six features obtained above is calculated through the random forest, and the obtained feature importance score is normalized in the random forest to ensure that the sum of the scores of all the features is 1;
- the correlation of the six features obtained above is calculated using a Pearson correlation coefficient formula, and a calculation formula of the Pearson correlation coefficient is as follows:

$r = \frac{\sum_{i = 1}^{n} (x_{i} - \overline{x}) (y_{i} - \overline{y})}{\sqrt{\sum_{i = 1}^{n} {(x_{i} - \overline{x})}^{2} \sum_{i = 1}^{n} {(y_{i} - \overline{y})}^{2}}};$

- when the correlation coefficient r>0, the feature is positively correlated with a similarity score, and when the correlation coefficient r<0, the feature is negatively correlated with the similarity score.

Preferably, step S6 is specifically as follows:

S6.1. calculating a weight coefficient formula using a linear regression method

A regression algorithm for a prediction model is established using linear regression to find a linear function suitable for the data, and a calculation formula of the weight coefficient of the linear regression is:

ω=(X^TX)⁻¹X^Ty;

- where X is an m×n matrix, each row represents a sample, each column represents a feature, and y is an m-dimensional vector representing a target variable;
- The weight coefficient formula obtained by the linear regression is as follows:
  
  y=79.2544+0.7234*x₁+0.2803*x₃+(−3.3106)*x₄+0.6653−*x₄+(−10.0353)*x₅+7.6626*x₆;
- S6.2. calculating a weight coefficient formula using a ridge regression method

A regression algorithm for the prediction model is established using ridge regression to find a linear function suitable for the data, and a calculation formula of the weight coefficient of the ridge regression is:

ω_ridge=(X^TX+λI)⁻¹X^Ty;

- where ω_ridgeis a weight vector of the ridge regression, λ is a regularization parameter, I is an identity matrix, and the regularization parameter λ controls the intensity of regularization.

The weight coefficient formulas obtained by the ridge regression is as follows:

y=79.2544+0.7138*x₁+0.2723*x₃+(−3.3078)*x₄+0.6675*x+(−9.4801)*x₅±7.0694*x₆.

The present invention has the following beneficial effects:

The computerized scoring method of feature extraction-based for covertness of imitated marine mammal sound signal of the present invention extracts six universal features of multiple marine mammal sound signals from the perspective of human hearing and signal processing, and uses these features to obtain a second bionic signal covertness score through the weight coefficient formulas to more accurately evaluate the difference between the bionic signal and the real signal, and the score value can intuitively describe the quality of the bionic signal covertness.

The computerized scoring method extracts six universal features of multiple marine mammal sound signals from the perspective of human hearing and the signal processing, and uses these features to characterize intrinsic information of the bionic signal in more detail from more perspectives of the signal with high calculation accuracy and precision, thus more accurately evaluating the difference between the bionic signal and the real signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an overall flowchart of the present invention;

FIG. 2 is a PCA correlation heatmap of the present invention;

FIG. 3 is a cross-correlation heatmap of the present invention;

FIG. 4 is a detailed description of six features of the present invention;

FIG. 5 is a flowchart of an ODG test algorithm of audio quality evaluation software of the present invention;

FIG. 6 shows importance of six features obtained in an embodiment of the present invention;

FIG. 7 shows correlation of six features obtained in an embodiment of the present invention; and

FIG. 8 is a graph of distribution of audio signal score values in an embodiment of the present invention.

DESCRIPTION OF THE EMBODIMENTS

In order to make the technical means, creative features, and achieved effects of the present invention easy to understand, the technical solutions in the embodiments of the present invention will be further described clearly and completely in conjunction with the accompanying drawings. It is obvious that the embodiments described are only some, instead of all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention.

As shown in FIG. 1, the computerized scoring method of feature extraction-based for covertness of imitated marine mammal sound signal provided by the present invention includes the following steps:

S1. Audio preprocessing:

In the scoring method, audio preprocessing is performed on an audio data set of an input original marine mammal sound signal and an audio data set of an imitated marine mammal sound signal from the perspective of human hearing and a signal waveform to obtain preprocessed audio data sets.

A specific method of the audio preprocessing is as follows: performing noise reduction, sound enhancement, echo cancellation, de-clicking and other operations on the audio data set of the original marine mammal sound and the audio data set of the imitated marine mammal sound, and then the audio signals are digitally processed to improve quality, accuracy and applicability of the audio signals.

S2. Feature screening for universal audio features:

Feature screening is performed on the preprocessed audio data sets of the original marine mammal sound signal and the imitated marine mammal sound signal to select universal features therein, including a first audio feature evaluated and analyzed from the perspective of human hearing and a second audio feature evaluated and analyzed from the perspective of signal processing; and the first audio feature includes an ODG, a SWR and a DMel, and the second audio feature includes a signal waveform similarity (ρ), a minimum error of a fundamental frequency (Ef) and a minimum error of a signal amplitude (Ea).

The feature screening is performed by calculating PCA linear correlation and cross-correlation degree between the selected features, and for each pair of features with a correlation coefficient greater than 2, one of the features is deleted, and the specific method is as follows:

S2.1. Designing and implementing PCA correlation analysis to calculate the linear correlation between the features, and a PCA formula for calculating the correlation between two features is:

$cov (x, y) = \frac{1}{m - 1} \sum_{i - 1}^{m} (x_{i} - \overline{x}) (y_{i} - \overline{y}),$

- where x and y respectively represent different features, x is a mean of a feature x, y is a mean of a feature y, and m represents the number of feature samples; and a resulting correlation heatmap is shown in FIG. 2.

S2.2. Designing and implementing mutual information correlation analysis to calculate a non-linear correlation between the features, and for two discrete random variables X and Y, a calculation formula of mutual information MI (X, Y) is:

$MI (X, Y) = \sum_{x \in X} \sum_{y \in Y} p (x, y) \log \frac{p (x, y)}{p (x) \cdot p (y)},$

- where p(x,y) is a joint probability distribution, and p(x) and p(y) are respective marginal probability distributions; and a resulting correlation heatmap is shown in FIG. 3.

S2.3. Carrying out feature selection, mainly selecting the universal features of various marine mammal sound signals rather than strong correlation features specific to a certain type of marine mammal sound signals, and deleting one of each pair of features with the correlation coefficient greater than 2 according to the calculated PCA linear correlation and the mutual information non-linear correlation, and finally obtaining six features: first audio feature data and second audio feature data, the first audio feature data includes the ODG, the SWR and the DMel, and the second audio feature data includes the signal waveform similarity (ρ), the minimum error of the fundamental frequency (Ef) and the minimum error of the signal amplitude (Ea). A detailed description of the six features is shown in FIG. 4.

S3. Extracting screened six marine mammal sound audio signal features through calculation, specifically including:

S3.1. Designing and implementing an extraction algorithm of an ODG of a feature 1

Performing an ODG test on the sound signal embedded with hidden information to obtain the objective difference grade of the sound signal; the software takes the original sound signal as a reference signal and the bionic signal with the hidden information as a test signal, and the two signals enter a psychoacoustic model simultaneously for calculation, results are subject to feature extraction and synthesis by a perception model to obtain a series of output parameters MOV, and finally, the parameters are mapped as an ODG output by a neural network; when the ODG value is greater than 0 or less than 0, the larger the absolute value, the smaller the difference between the original signal and the bionic signal with the hidden information, the better the imperceptibility and the better the covertness of the bionic signal. A flowchart of an algorithm of the audio quality evaluation software is shown in FIG. 5.

S3.2. Designing and implementing an extraction algorithm of a SWR of a feature 2

The hidden information embedded in the sound signal is regarded as noise, and a numerical value thereof is taken as a degree of influence on the original sound signal, that is, the SWR; the larger the SWR value, the smaller the distortion, and the lower the embedding strength, which indicates that the bionic signal has better covertness. A calculation formula of the signal watermark-energy ratio is:

$SWR = 10 \cdot \log_{10} (\frac{\sum_{n = 0}^{L - 1} x^{2} (n)}{\sum_{n = 0}^{L - 1} {(y (n) - x (n))}^{2}});$

- where x(n) represents the original sound signal, y(n) represents the sound signal with the hidden information embedded, L represents a length of the sound signal, and the SWR is in dB.

S3.3. Designing and implementing an extraction algorithm of a signal waveform similarity (ρ) of a feature 3

The signal waveform similarity refers to the difficulty in distinguishing the original signal from the bionic signal with the embedded information in the signal form, that is, the similarity of the two signals in time domain and frequency domain is high, and the similarity of the signals in the time domain and the frequency domain is measured by a correlation coefficient ρ, and a calculation formula is:

$ρ = \frac{\sum_{n} s (n) s^{'} (n)}{\sqrt{\sum_{n} {s (n)}^{2} \cdot \sum_{n} {s^{'} (n)}^{2}}};$

- where s(n) represents an original sound signal segment, s′(n) represents a bionic signal segment with the information embedded, and s′(n)-s(n) is regarded as a desired signal. The closer the ρ value is to 1, the closer the bionic signal is to the original sound signal, and the better the covertness.

S3.4. Designing and implementing extraction algorithm for feature 4 DMel

The Mel-Frequency Cepstral Coefficient (MFCC) is an effective sound representation based on the human auditory system, and a human subjective auditory frequency formula is:

$F_{mel} = 2595 \log_{10} (1 + \frac{f}{700}) = 1127 \ln (1 + \frac{f}{700});$

- where F_melis a sensory frequency in Mel, and f is an actual frequency in Hz.

A transfer function of an mth bandpass filter in the human hearing frequency range is defined as H_m(k), where m is the total number of filters in a same bank in the hearing range. If each filter has a triangular filter characteristic with a center frequency f_m, and each filter has equal bandwidth on a Mel frequency scale, then the discrete transfer function H_m(k) of each filter is defined as:

$H_{m} (k) = {\begin{matrix} 0 & k < f_{m - 1}, f_{m - 1} lek \\ \frac{k - f_{m - 1}}{f_{m} - f_{m - 1}} & f_{m - 1} lek < f_{m - 1} \\ \frac{f_{m + 1} - k}{f_{m + 1} - f_{m}} & f_{m} lek < f_{m + 1} \end{matrix};$

The center frequency f_mis defined as:

$f_{m} = F_{mel}^{- 1} (F_{mel} (f_{l}) + m \frac{F_{mel} (f_{h}) - F_{mel} (f_{l})}{M + 1});$

- where f_land f_hare respectively a lower limit frequency and an upper limit frequency of the filter H_m(k). F_mel⁻¹is defined as F_mel⁻¹(b)=₇₀₀(10^b/2595−1)=700(e^b/1127−1).

Based on the Mel filter bank, the MFCCs for 1 frame are obtained by:

${mfcc}_{i} (n) = \sqrt{\frac{2}{M}} \sum_{m = 0}^{M - 1} \log [S_{i} (m)] \cos [\frac{π n (2 m - 1)}{2 M}];$

- where n=1, 2 . . . M,

$S_{i} (m) = \sum_{k = 0}^{N - 1} {❘ X_{i} (k) ❘}^{2} H_{m} (k)$

is an mth Mel filter energy of an ith frame signal. In order to compare the bionic signal with the original signal, the Mel distance di of the ith frame of each sound signal is defined as:

$d_{i} = \sqrt{\sum_{n = 1}^{M} {({mfcc}_{synthetic}^{i} (n) - {mfcc}_{whistle}^{i} (n))}^{2}};$

- a mean Mel distance of all frames of each signal is defined as:

$D_{Mel} = \frac{\sum_{i = 1}^{k} d_{i}}{k};$

- where i=1, 2 . . . k.

The smaller the Mel distance, the smaller the difference between the bionic signal and the original signal, and the bionic signal is more likely to be ignored as a marine mammal sound signal, that is, the better the covertness.

S3.5. designing and implementing an extraction algorithm of the minimum error of the fundamental frequency (Ef) of a feature 5 and the minimum error of the signal amplitude (Ea) of a feature 6. Specifically:

Assuming that a time-frequency diagram of the noise-reduced sound signal is X_m[ω,m], where ω represents frequency, m represents a time period divided by a window function w[ω], and X_m[ω] represents a Fourier transform result of a mth time period. f(m) represents a fundamental frequency of the mth time period, and an expression using a maximum value extraction method is as follows:

$f (m) = \arg \max ❘ X_{m} [ω] ❘;$

The fundamental frequency of each time period of the sound signal without and with the information embedded is calculated respectively, and the minimum error of the fundamental frequency of all time periods is taken, and a calculation formula is as follows:

$Δ v = \frac{\sum_{m = 1}^{n} ❘ (f_{T} (m) - f_{L} (m)) ❘}{n};$

- where n represents the number of time periods taken, f_T(m) represents the fundamental frequency of the mth time period of the original sound signal, and f_L(m) represents the fundamental frequency of the mth time period of the sound signal with the information embedded.

An energy e_r(m) of a mth data block of a rth harmonic is obtained using a short-time Fourier transform with a window length L, and a formula thereof is as follows:

$e_{r} (m) = X_{m} [f_{r} (m)];$

Let amplitude of a first sampling point of each data block be a_r[m1], and a formula thereof is as follows:

a
r

[

m
1

]

=

2
⁢