Single-channel blind source separation method based on euclidean distance and variational modal decomposition algorithm

Abstract

This invention discloses a single-channel blind source separation method based on Euclidean distance and variational mode decomposition (VMD) algorithm, belonging to the field of signal processing technology. This method utilizes VMD to decompose a mixed observed signal into two modes; calculates the Euclidean distance between the mode and the observed signal and takes the average; calculates the energy of the mode with the smaller Euclidean distance as a reference value; constructs a loop based on the Euclidean distance and energy value; within the loop, the number of source signals is determined, and noise in the observed signal is removed to a certain extent. The advantages of this invention are that it automatically determines the number of source signals, solving the problem that VMD algorithms require pre-determining mode values, and addressing the source number estimation failure of feedback-based VMD-based single-channel blind source separation algorithms for mixed signals with more than three single-frequency source signals. Furthermore, this algorithm can effectively achieve single-channel blind source separation even under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a single-channel blind source separation method based on Euclidean distance and variational mode decomposition algorithm. Background Technology

[0002] Blind Source Separation (BSS) is a signal processing technique that separates multiple mixed signals based solely on acquired observation data, without any prior knowledge of the source signals or the transmission channel. How to effectively detect and accurately estimate targets when multiple acoustic target signals are mixed together is a pressing problem that needs to be solved.

[0003] Blind source separation technology can be classified in various ways according to different standards. Based on the number of signal sources and observation channels, it can be divided into overdetermined blind source separation, positive definite blind source separation, and underdetermined blind source separation. Real-world sound field environments are complex, making it difficult to determine the exact number of sound sources. Therefore, it cannot be guaranteed that the number of observation channels is greater than the number of signal sources, thus limiting the practical value of overdetermined or positive definite blind source separation algorithms. Single-channel blind source separation algorithms are a type of underdetermined blind source separation algorithm. They are a processing method that estimates multiple different source signals by extracting observation data from a single receiving channel. Compared to positive definite and overdetermined blind source separation, solving single-channel blind source separation algorithms is more complex. Furthermore, single-channel blind source separation (SCBSS) technology requires fewer receiving devices, enhancing equipment flexibility and practical operability in complex environments, and reducing costs. Therefore, single-channel blind source separation algorithms have gained increasing popularity in recent years.

[0004] The single-channel blind source separation algorithm based on wavelet packet decomposition (WPT-ICA) requires that the frequencies of different source signals in the mixed signal be at different decomposition levels. Therefore, selecting an appropriate decomposition level is crucial to the performance of blind source separation. In addition, the WPT-ICA algorithm is also sensitive to the number of source signals and noise. When the number of source signals is greater than two, the performance degrades. When the signal-to-noise ratio is low, a large amount of information is lost in the separation result. The single-channel blind source separation algorithm based on empirical mode decomposition (EMD-ICA) will exhibit mode aliasing. When the signal-to-noise ratio is low, the performance deteriorates rapidly. When the signal-to-noise ratio is high, the algorithm performs well. Although the EEMD-ICA algorithm can improve the mode aliasing phenomenon to some extent, it cannot completely eliminate it and is too time-consuming, so it is not suitable for processing real-time signals. Because the EMD algorithm is sensitive to noise, these limitations can only be partially addressed by conducting more mathematical experiments on the decomposition problem. To address this, Konstantin Dragomiretskiy proposed a fully non-recursive Variational Mode Decomposition (VMD) model in 2014. This model uses an alternating direction multiplier method for optimization to find a set of modes that can reproduce the input signal, identify the center frequency of each mode, and tune each mode to its corresponding fundamental frequency band. Compared to EMD, VMD is supported by theoretical knowledge and has a certain tolerance for noise. However, the VMD algorithm has very strict requirements on the selection of the number of modes to be decomposed; improper selection can lead to over-decomposition or incomplete decomposition.

[0005] The literature “[1] Zhao Zhijin, Huang Yanbo, Qiang Fangfang, Yang Anfeng. Single-channel blind source separation algorithm based on feedback variational mode decomposition[J]. Vibration and Shock, 2019, 38(13):268-273.DOI:10.13465 / j.cnki.jvs.2019.13.038” proposes a feedback system based on similarity coefficient to determine the number of signal sources. However, when there are more than three multi-source single-frequency mixed signals, the algorithm cannot effectively estimate the number of source signals. In response to this phenomenon, this invention constructs a cyclic decision mechanism based on Euclidean distance and variational mode decomposition, which can effectively solve the multi-source mixing problem, accurately estimate the number of source signals, separate each source signal, and has good noise resistance performance. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the aforementioned variational mode decomposition algorithm for estimating the number of modes by providing a single-channel blind source separation method (VMD-ED) based on Euclidean distance and variational mode decomposition algorithm. The smaller the Euclidean distance between a mode and the mixed signal, the higher the matching degree between the mode and the mixed signal. By utilizing this characteristic and combining it with the decision system of this invention, the individual source signals of a single-channel multi-source mixed signal can be effectively separated, and it has good noise resistance performance.

[0007] The specific technical solution for implementing the present invention includes the following steps:

[0008] (1) Establish a single-channel data reception model

[0009] Y(t) = AS(t) + N(t);

[0010] Where Y(t) represents the 1×m dimensional received signal, A is a 1×n mixing matrix, and S(t) = [s1(t), s2(t), ..., s n (t)] T It is an n×m dimensional source signal vector, and N(t) is a 1×m dimensional noise signal;

[0011] (2) Initialize the parameters

[0012] Initialize the number of calculations num = 0, the number of source signals signal_num = 0, and the number of modes K = 2; let the variable signal_mix = Y(t) as the input signal for each VMD decomposition; initialize... λ 1 Let (ω), l←0 set each vector to zero, where This represents the frequency domain representation of the k-th modal component. λ represents the center frequency of the k-th modal component. 1 (ω) represents the Lagrange multiplier, and l represents the number of iterations; when the convergence condition of the VMD algorithm is met, K modal components are obtained, denoted as U. num+1 The Euclidean distance between each mode and the signal Y(t) is denoted as... Take their mean and denote it as Will and The relative difference is recorded as The relative Euclidean distance between modes is denoted as . Calculate the energy of K modes The energy of the mode with the smallest Euclidean distance is denoted as...

[0013] (3) Determine if the decomposition is excessive. If the decomposition is excessive, interrupt the loop directly.

[0014] Let num = num + 1, K = K + 1, and repeat step (2) on the signal_mix signal to select modes with relative energy greater than 0.3 as the initial screening signal modes. The number of modes is recorded as K. num Calculate this K num The center frequency f of each mode num If f num If the relative difference between any two values ​​is less than the set value Δf, then the loop terminates and f = [f] is calculated. num-1 ,f num The number K' of any pairs of relative differences between them that are less than the set value Δf num The estimated number of source signals is signal_num = signal_num + K. num -K' num Otherwise, proceed to step (4);

[0015] (4) Determine whether there is a signal mode in the decomposed modes.

[0016] To ensure that the decomposed modes include both noise and signal modes, condition ① must be met. The maximum value is greater than 1.1 times its mean. To further ensure that there are signal modes in the decomposed modes, condition ② is required. The minimum value is less than 0.9 times its mean; when both conditions ① and ② above are met, extract K from step (3). num The condition is satisfied in each mode. The signal mode whose minimum value is less than 0.85 of its mean is denoted as Signal_sig. The frequency Signal_f corresponding to the Signal_sig signal is extracted using the peak detection method. num If Signal_f num The number of K_Signal_f num If the number of signals is much greater than Signal_f1, it is determined to be a noise signal, and the output Y(t) = Y(t) - signal_mix is ​​executed, terminating the loop; otherwise, Signal_sig is determined to be a signal mode, and the input signal is updated: signal_mix = signal_mix - Signal_sig, and Signal_f is calculated. num =[Signal_f num-1 ,Signal_f num The number of K1_Signal_f whose relative differences between any two elements are less than the set value Δf num Update frequency f num =[f num ,Signal_f numUpdate the number of source signals: signal_num = signal_num + K_Signal_f num -K1_Signal_f num Repeat steps (3)-(4);

[0017] (5) If conditions ① and ② are not satisfied, then when If the maximum value of signal_mix is ​​greater than 0.2 and the energy of the observed signal Y(t) is greater than the energy of the decomposed input signal_mix, then signal_mix is ​​determined to be noise, the loop is terminated, and the output is Y(t) = Y(t) - signal_mix. Otherwise, continue to execute steps (3) to (5).

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] This invention proposes a cyclic decision system based on Euclidean distance and variational mode decomposition, avoiding the drawback of the WPT-ICA algorithm requiring the selection of a suitable decomposition layer and corresponding wavelet function; it overcomes the mode aliasing problem of the EMD-ICA algorithm; and it solves the problem of inaccurate estimation of single-frequency multi-source (three or more sources) mixed signals by the single-channel blind source separation method based on feedback variational mode decomposition. This invention can accurately estimate the number of sources in multi-source mixed signals, effectively separate each source signal, and achieve denoising, exhibiting good noise resistance. Attached Figure Description

[0020] Figure 1 This is a flowchart of the implementation of the present invention.

[0021] Figure 2 This refers to the success rate of the method of this invention and the single-channel blind source separation method (VMDF) based on feedback variational mode decomposition for estimating the number of multi-source mixed signals under different signal-to-noise ratio conditions (100 Monte Carlo experiments were conducted at each signal-to-noise ratio). Detailed Implementation

[0022] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and implementation steps.

[0023] (1) Establish a single-channel data reception model:

[0024] Suppose there are n unknown source signals s1(t), s2(t), ... s n These n source signals (t) are statistically independent of each other. After being transmitted through the channel, they are received by a sensor. Considering environmental interference and noise, the expression for the received signal is as follows:

[0025]

[0026] In the formula: ai Let s represent the mixing coefficients i∈{1,2,…,n}, where it is assumed that the differences between the mixing coefficients are not too large. i (t) is the i-th source signal, and the above equation can be represented by a matrix and a vector:

[0027] Y(t)=AS(t)+N(t) (2)

[0028] In the formula: matrix A is a 1×n mixing matrix, and the elements in column i of A are the mixing coefficients a. i S(t) = [s1(t), s2(t), ..., s n (t)] T It is an n×1 dimensional source signal vector, and N(t) is a 1×m dimensional noise signal.

[0029] (2) Initialize the parameters

[0030] When mode K=2, let signal_mix=Y(t), and perform VMD decomposition on the mixed signal signal_mix. The specific steps of the VMD algorithm are as follows:

[0031] ① Initialization: λ 1 (ω),l←0, where This represents the frequency domain representation of the k-th modal component. λ represents the center frequency of the k-th modal component. 1 (ω) represents the Lagrange multiplier, and l represents the number of iterations;

[0032] ②Iteration: l←l+1

[0033] a) k = 1: K

[0034] For all ω≥0, update

[0035]

[0036] In the formula, α is the penalty factor;

[0037] b) k = 1: K

[0038] renew

[0039]

[0040] c) Update

[0041]

[0042] ③ For any positive number ε>0, if equation (6) is satisfied, stop the iteration; otherwise, return to step ②.

[0043]

[0044] ④ Perform an inverse Fourier transform to obtain K modal components, and the algorithm ends.

[0045] Denote the K modes as a vector form: U num+1 =[u (num+1)1 (t),…,u (num+1)K (t)] (7)

[0046] Calculate the Euclidean distance between each mode and the signal Y(t):

[0047]

[0048] Its vector form is expressed as:

[0049] right The average value is obtained as follows:

[0050]

[0051] Will and The relative difference is recorded as:

[0052]

[0053] The relative Euclidean distance between modes is:

[0054]

[0055] The energy of each mode is:

[0056]

[0057] The energy of the K modes can then be represented as a vector as follows:

[0058]

[0059] The energy of the mode with the smallest Euclidean distance is denoted as...

[0060] (3) Determine if the decomposition is excessive. If the decomposition is excessive, interrupt the loop directly.

[0061] Let num = num + 1, K = K + 1, perform VMD decomposition on the mixed signal signal_mix, and continue to execute step (2); the relative energy is defined as: Select K that satisfies equation (15).num Each mode, calculate this K num The center frequency f of each mode num If f num If the relative difference between any two values ​​is less than the set value Δf, then the loop terminates and f = [f num-1 ,f num The number of pairs of numbers whose relative differences are less than the set value Δf is denoted as K'. num The estimated number of source signals is signal_num = signal_num + K. num -K' num Otherwise, proceed to step (4);

[0062] (4) Determine whether there is a signal mode in the decomposed modes: In order to ensure that there are both noise modes and signal modes in the decomposed modes, conditions ① and ② must be satisfied at the same time.

[0063] Condition ①:

[0064] Condition 2:

[0065] Condition ③: The values ​​of 1.1, 0.9, and 0.85 here are empirical values ​​obtained through extensive simulations. The success rate will decrease when other parameters are selected. When conditions ① and ② are met simultaneously, K in step (3) is extracted. num The signal mode that satisfies condition ③ among the modes is denoted as Signal_sig, and its frequency Signal_f is extracted using the peak detection method. num If Signal_f num The number of K_Signal_f num If the number of signals is much greater than the number of Signal_f1 signals, then the model input signal signal_mix is ​​determined to be a noise signal, the loop terminates, and the output signal is:

[0066]

[0067] This step achieves the effect of noise reduction; otherwise, Signal_sig is determined to be a signal mode, and the input signal is updated.

[0068] signal_mix=signal_mix-Signal_sig (20)

[0069] Calculate Signal_f num =[Signal_f num-1 ,Signal_f num The number of K1_Signal_f whose relative difference between any two values ​​is less than the set value Δfnum Update frequency f num =[f num ,Signal_f num Update the number of source signals:

[0070] signal_num=signal_num+K_Signal_f num -K1_Signal_f num (twenty one)

[0071] Repeat steps (3)-(4);

[0072] (5) If conditions ① and ② are not satisfied, then when If the maximum value of signal_mix is ​​greater than 0.2 and the energy of the observed signal Y(t) is greater than the energy of the decomposed input signal_mix, then signal_mix is ​​determined to be noise, the loop is terminated, and the output Y(t) = Y(t) - signal_mix is ​​given. The estimated number of source signals is signal_num. Otherwise, continue to execute steps (3) to (5).

[0073] This invention discloses a single-channel blind source separation method based on Euclidean distance and variational mode decomposition (VMD) algorithm. The invention utilizes VMD to decompose a mixed observed signal into two modes; calculates the Euclidean distance between each mode and the observed signal and takes the average; calculates the energy of the mode with the smaller Euclidean distance as a reference value; constructs a loop based on the Euclidean distance and energy value; within the loop, the number of source signals is determined, and noise in the observed signal is removed to a certain extent. The advantages of this invention are that it automatically determines the number of source signals, solving the problem that VMD algorithms require pre-determining mode values, and addressing the source number estimation failure of feedback-based VMD-based single-channel blind source separation algorithms for mixed signals with more than three single-frequency source signals. Furthermore, this algorithm can effectively achieve single-channel blind source separation even under low signal-to-noise ratio conditions.

Claims

1. A single-channel blind source separation method based on Euclidean distance and variational mode decomposition algorithm, characterized in that, Includes the following steps: Step 1: Establish a single-channel data reception model: ;in express The received signal of dimension, for The mixture matrix, yes dimensional source signal vector, for Dimensional noise signal; Step 2: Initialize parameters: Initialize the number of calculations Number of source signals Number of modes Let the variable This serves as the input signal for each VMD decomposition; initialization ,in Indicates the first Frequency domain representation of each modal component Indicates the first The center frequency of each modal component Let represent the Lagrange multiplier, and l represent the number of iterations; Perform VMD decomposition on the signal. When the convergence condition of the VMD algorithm is met, the result is obtained. There are 1 modal component, denoted as . ; associate each mode with the signal The Euclidean distance is denoted as Take their average and denote it as ,Will and The relative difference is recorded as The relative Euclidean distance between modes is calculated and denoted as . ;calculate Energy of each mode The energy of the mode with the smallest Euclidean distance is denoted as... ; The specific details of step 2 are as follows: When mode season For mixed signals Perform VMD decomposition: ① Initialization: ,in Indicates the first Frequency domain representation of each modal component Indicates the first The center frequency of each modal component Let represent the Lagrange multiplier, and l represent the number of iterations; ② Iteration: a) For all ,renew : (3) In the formula, As a penalty factor; b) renew : (4) c) Update : (5) ③ For any positive number If equation (6) is satisfied, then stop the iteration; otherwise, return to step ②. (6) ④ To Performing the inverse Fourier transform yields... The algorithm terminates when all modal components are identified. Will Each mode is denoted in vector form: (7) Calculate each mode and signal Euclidean distance: (8) Its vector form is expressed as: (9) right The average value is obtained as follows: (10) Will and The relative difference is recorded as: (11) The relative Euclidean distance between modes is: (12) The energy of each mode is: (13) but The energy of each mode is represented in vector form as follows: (14) The energy of the mode with the smallest Euclidean distance is denoted as... ; Step 3: Determine if the decomposition is excessive. If excessive, interrupt the loop directly: Let , ,right The signal undergoes step 2 again, selecting modes with relative energy greater than 0.3 as the initial screening signal modes. The number of modes is recorded as follows: Calculate this The center frequency of each mode ,like The relative difference between any two values ​​is less than the set value. Then the loop terminates and the calculation continues. The relative difference between any two values ​​is less than the set value. Number of The number of source signals estimated at the output. Otherwise, proceed to step 4. Step 4: Determine if a signal mode exists in the decomposed modes: To ensure that the decomposed modes contain both noise and signal modes, condition ① must be met. The maximum value is greater than 1.1 times its mean. To further ensure that there are signal modes in the decomposed modes, condition ② is required. The minimum value is less than 0.9 times its mean; when both conditions ① and ② above are met, extract the value from step 3. The condition is satisfied in each mode. The signal mode whose minimum value is less than 0.85 of its mean is denoted as Extracted by peak detection method The frequency corresponding to the signal ,like number Much larger If the number of such signals is not specified, it is considered a noise signal and the output is... If the loop terminates, then proceed to the next step; otherwise, determine the outcome. To update the input signal as a mode: ,calculate The relative difference between any two values ​​is less than the set value. Number of Update frequency Update the number of source signals: Repeat steps 3-4; Step 5: If conditions ① and ② are not satisfied, then when The maximum value is greater than 0.2, and the observed signal The energy is greater than the decomposed input signal Energy determination To eliminate noise, terminate the loop and output. Otherwise, continue with steps 3-5.

2. The single-channel blind source separation method based on Euclidean distance and variational mode decomposition algorithm according to claim 1, characterized in that, The specific details of step 1 are as follows: It has An unknown source signal ,this The individual source signals are statistically independent of each other. After transmission through the channel, they are received by a sensor. Considering environmental interference and noise, the expression for the received signal is as follows: (1) In the formula: Indicates the mixing coefficient Here it is assumed that the differences between the mixing coefficients are not too large. It is the first For each source signal, the above equation can be represented using matrices and vectors: (2) Where: matrix for The mixture matrix, of The elements of the column are the mixing coefficients. , yes dimensional source signal vector, for Dimensional noise signal.

3. The single-channel blind source separation method based on Euclidean distance and variational mode decomposition algorithm according to claim 1, characterized in that, The specific details of step 3 are as follows: make , For mixed signals Perform VMD decomposition and continue to step 2; Relative energy is defined as: (15) Select those that satisfy equation (15). This modality, calculate this The center frequency of each mode ,like The relative difference between any two values ​​is less than the set value. Then the loop will terminate and... The relative difference between any two pairs of values ​​is less than the set value. The number of them is denoted as The number of source signals estimated by output Otherwise, proceed to step 4.

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