Underdetermined mixed matrix estimation method based on quantum poison beetle blasting mechanism

Abstract

The application provides an underdetermined mixed matrix estimation method based on a quantum toxic beetle blasting mechanism, is an underdetermined mixed matrix robust estimation method based on the quantum toxic beetle blasting mechanism, has better effectiveness and robustness, and solves the engineering problems that existing mixed matrix estimation methods are too sensitive to initial clustering center selection, noise and outliers. The application designs a single source point detection signal preprocessing model, constructs an initial population generation strategy, combines quantum calculation and the toxic beetle blasting mechanism, designs the quantum toxic beetle blasting mechanism, then takes the optimal solution obtained by optimizing the mixed objective function by the quantum toxic beetle blasting mechanism as the mean clustering initial clustering center, and constructs the underdetermined mixed matrix estimation method combined with the quantum toxic beetle blasting mechanism and the K-means clustering method.

Description

Technical Field

[0001] This invention relates to a robust underdetermined mixing matrix estimation method based on the quantum blasting insect explosion mechanism, belonging to the field of blind source separation. Background Technology

[0002] Underdetermined blind source separation refers to estimating the source signal when the number of observed signals is less than the number of source signals and the parameters of the mixing system and filtering process are lacking. A common approach to solving the underdetermined blind source separation problem is a "two-step method" based on sparse component analysis, using the sparsity of the signal to extract the source signal. When sparsifying the signal, short-time Fourier transform and wavelet transform are commonly used to transform the signal to the transform domain, making the signal exhibit sparsity in the transform domain. The "two-step method" involves first estimating the mixing matrix, and then using the estimated mixing matrix to recover the source signal. Therefore, research on mixing matrix estimation methods is crucial. Currently, commonly used algorithms for estimating the mixing matrix include clustering algorithms or potential function-based methods. Clustering-based mixing matrix estimation requires less prior knowledge and is computationally simple, gradually becoming the mainstream method for underdetermined mixing matrix estimation. For the selection of initial cluster centers, many researchers have introduced swarm intelligence optimization algorithms. This invention selects the initial cluster centers based on the quantum poison bug explosion mechanism, and then uses the clustering method to estimate the mixing matrix.

[0003] A review of existing literature revealed that Fu Ning et al., in their paper "A Blind Estimation Algorithm for Sparse Source Mixing Matrix Based on Improved K-means Clustering and Hough Transform" published in *Journal of Electronics* (2009, Vol. 37, No. z1, pp. 92-96), addressed the issue of clustering algorithms relying on initial value selection by introducing the idea of ​​differential evolution into the mean clustering algorithm. They then used the Hough transform to correct the cluster centers of each data class. However, this method suffers from high algorithmic complexity, slow convergence, and susceptibility to noise and outliers. VGReju et al., in their paper "An algorithm for mixing matrix estimation in instantaneous blind sourceseparation" published in *Signal Processing* (2009, Vol. 89, No. 9, pp. 1762-1773), proposed single-source detection. This method first performs a Fourier transform on the signal, then compares the directions of the real and imaginary parts of the time-frequency coefficient vector to identify single-source points. Finally, a hierarchical clustering method is introduced to perform cluster analysis on the selected single-source point set. Regarding the selection of initial cluster centers, Bi Xiaojun et al., in their paper "Underdetermined Blind Matrix Estimation Based on Hybrid Clustering and Grid Density" published in *Systems Engineering and Electronics Technology* (2012, Vol. 34, No. 3, pp. 614-618), proposed introducing a bee colony algorithm into matrix estimation and then using the grid density method to correct the cluster centers, thus improving the robustness of the clustering method. Yu Jinping et al., in their paper "Mean Clustering Algorithm Based on Improved Artificial Bee Colony Algorithm" published in *Computer Applications* (2014, Vol. 34, No. 34, pp. 1001-9081), proposed an improved artificial bee colony algorithm and designed an initial population generation strategy, improving the accuracy and convergence performance of the clustering method. The performance of the above methods is sensitive to the selection of initial cluster centers, particularly outliers, and the convergence performance of existing initial cluster center selection methods needs improvement, as they are prone to getting trapped in local optima.

[0004] Existing literature shows that clustering algorithms are widely used in the field of underdetermined mixture matrix estimation. However, they suffer from high computational complexity, slow convergence, and susceptibility to the number of single source points and noise. Furthermore, the clustering effect is dependent on the selection of initial cluster centers. To address this, many researchers have introduced swarm intelligence (SCI) to select initial cluster centers. This method requires less prior knowledge and reduces the randomness of initial center selection. However, the algorithm's performance is overly sensitive to the initial center selection, noise, and outliers. Existing initial center selection strategies also have limitations and shortcomings, and their convergence performance needs improvement. Moreover, the fitness function selection in existing joint optimization methods combining SCI and clustering algorithms is singular, meaning that obtaining the globally optimal solution for the objective function using SCI does not necessarily represent the best clustering effect, thus affecting blind source separation. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention provides a robust underdetermined mixture matrix estimation method based on a quantum explosive insect blasting mechanism, offering improved effectiveness and robustness. This method overcomes the engineering challenge of existing mixture matrix estimation methods being overly sensitive to initial cluster center selection, noise, and outliers. The invention incorporates a single-source detection signal preprocessing model to construct an initial population generation strategy. It combines quantum computing with the explosive insect blasting mechanism to design a quantum explosive insect blasting mechanism. The optimal solution obtained by the quantum explosive insect blasting mechanism for optimizing the mixture objective function is then used as the initial cluster centers for mean-based clustering. This constructs an underdetermined mixture matrix estimation method that combines the quantum explosive insect blasting mechanism and the K-means clustering method.

[0006] The objective of this invention is achieved as follows: The steps are as follows:

[0007] Step 1: Preprocess the received observation signal, and use the initial population generation strategy to initialize the initial position and quantum position of the quantum poison worm population.

[0008] Step 2: Map the position of each quantum poison bug before K-means processing to a cluster center matrix, and use K-means to obtain new cluster centers. Then, obtain the position and quantum position of the quantum poison bug after K-means processing.

[0009] Step 3: Identify the quantum poison worms, initialize the acid attraction of each quantum poison worm, construct a hybrid optimization objective function, calculate and sort the fitness value of each quantum poison worm in the population, and obtain the quantum positions of the best and second-best quantum individuals.

[0010] Step 4: Calculate the distance between each individual quantum poison bug and the optimal quantum poison bug individual. Based on the obtained distance, determine whether the quantum individual is within the splash range of the optimal individual. Update the quantum position and acid attraction according to the quantum poison bug update mechanism.

[0011] Step 5: Sort the updated individuals according to their fitness values ​​to obtain the optimal individual position of the updated population. Then, convert the optimal quantum poison bug position into the initial cluster center of K-means clustering and perform clustering to obtain the new cluster center as the updated global optimal position.

[0012] Step 6: Incorporate a random population generation strategy to generate quantum random candidate solutions, calculate the updated position and the fitness value of the quantum random candidate solutions, and use greedy selection to update the quantum position;

[0013] Step 7: Determine if the maximum number of iterations G has been reached. max If the iteration does not reach the target, return to step two and continue iterating; otherwise, output the cluster center matrix obtained by K-means clustering, which serves as the optimal estimate of the underdetermined mixing matrix of the underdetermined blind source separation system.

[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention combines quantum optimization theory and the blasting mechanism of the poison bug to obtain the core evolution formula for the quantum poison bug position update under the quantized blasting mechanism, thus improving the convergence and robustness of the poison bug optimization algorithm. Traditional underdetermined blind source separation algorithms often rely on a single criterion for judging clustering effects, leading to inconsistent clustering results for different criteria, and the effectiveness of the criterion also affects the blind source separation algorithm's performance. This invention combines two different clustering effect criteria, designs a novel hybrid fitness function, assigns different weights to inter-cluster dispersion and intra-cluster cohesion, and determines the optimal criterion for the intelligent computing method based on the change of the hybrid optimization objective function value with the weight coefficients, thereby improving the accuracy of blind source separation for mixed signals. The design incorporates a sparsity processing strategy with single-source detection to make the initial signal sufficiently sparse, improving clustering accuracy. This paper combines the quantum poison bug blasting mechanism with the K-means clustering algorithm, and uses the maximum value of the product of the initial signal and the maximum minimum distance within the initial signal set as the criterion to initialize the initial quantum poison bug swarm, thus solving the problem of the clustering algorithm's sensitivity to the initial cluster centers. The designed method based on the quantum poison bug algorithm has fast convergence speed and good robustness. It uses the optimal solution of the mixture fitness function obtained by the quantum poison bug optimization algorithm iteratively as the initial cluster centers of the clustering algorithm, and then performs K-means clustering to obtain the estimated matrix of the mixture matrix. This method improves the convergence performance of the clustering algorithm, resulting in a high-precision mixture estimation matrix and good separation effect. Attached Figure Description

[0015] Figure 1This is a flowchart of an underdetermined blind source separation method based on the quantum poison insect explosion mechanism.

[0016] Figure 2 This is a time-domain waveform diagram of the four-channel flute tone signals.

[0017] Figure 3 This is a scatter plot of the observed signal.

[0018] Figure 4 A comparison of convergence curves for the objective function estimation of the mixing matrix under the same signal-to-noise ratio.

[0019] Figure 5 This is a performance comparison chart of mixed matrix estimation methods. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] Combination Figures 1 to 5 The steps of this invention are as follows:

[0022] Step 1: Preprocess the received observation signal and use the initial population generation strategy to initialize the initial position and quantum position of the quantum poison worm population.

[0023] It is known that x(t)=As(t)+n(t)=[x1(t),x2(t),...,x N (t)] T Let s(t) = [s1(t), s2(t), ..., s2(t)] be the observed signals received by N sensors. M (t)] T There are M independent and unknown source signals. t represents the number of sampling points. Represents the maximum number of samples, n(t) = [n1(t), n2(t), ..., n N (t)] T There are N transmission process noises. When N < M, blind source separation is underdetermined blind source separation, and A is an N×M dimensional underdetermined mixing matrix. A short-time Fourier transform of the observed signal x(t) can be expressed in the time-frequency domain as follows: The observed signal is at a frequency of Time is The STFT coefficient at that time, and Let i be a complex number, i = 1, 2, ..., N, for Preprocessing is performed, including the removal of low-energy points, time-frequency single-source point detection, and normalization.

[0024] Let Δ be the set of time-frequency points that have not undergone preprocessing. For any single time-frequency point labeled z... Because low-energy points contain a large amount of noise, they need to be removed to improve the accuracy of the estimation. Where ||·|| represents the l2 norm of taking the ·, and ζ is the threshold value, then removing Otherwise, keep Define the set of high-energy points as Ω, and arbitrarily select a time-frequency point labeled τ. To further improve the sparsity of the signal, based on the definition of a single source point, the discrimination condition is set as follows: Where |·| represents the absolute value or modulus of the ·, and ||·|| represents the l2 norm of the ·. represent The real part vector, represent The imaginary part of the vector, θ, represents the threshold angle for single-source point detection, satisfying the discrimination condition. Keep the original data, otherwise remove it; this yields the preprocessed time-frequency point set U and the observation signal sample point set. The preprocessed observation signal at a frequency of Time is The STFT coefficient at that time.

[0025] To overcome the randomness of population initialization in swarm intelligence algorithms, an initial population generation strategy is used to improve the accuracy of cluster analysis and increase the dimensionality of the search space. The population has D individuals, and the cluster center vector has a dimension of 1×N. First, D×M cluster center vectors are generated, and then they are transformed into... The initial population within the dimensional search space is determined through the following steps:

[0026] (1) Select a single time-frequency point from the preprocessed time-frequency point set U. The observation signal corresponding to this time frequency point from Take it out from the set of cluster center vectors Φ, and then randomly select a time-frequency point from the remaining time-frequency points of U. Calculate the observed signal and The Euclidean distance between them, i.e.

[0027] (2) Find and The observation signal sample point with the largest Euclidean distance between them;

[0028] (3) This sample point from Extract the data from the set of cluster center vectors and place it into the cluster center vector set Φ.

[0029] (4) Calculate separately The Euclidean distance between each remaining sample point and the cluster center vectors in Φ is calculated. The maximum and minimum Euclidean distances between each sample point and the cluster center vectors in Φ are multiplied together, so that each sample point corresponds to a product. The sample point with the largest product is found.

[0030] (5) Determine whether the number of cluster center vectors in Φ is less than D×M. If yes, return to step (3) and continue the loop; if no, output the cluster center vector set Φ, which should contain D×M 1×N-dimensional cluster center vectors.

[0031] (6) Starting with the first cluster center vector in set Φ, every D cluster center vectors form an M×N dimensional cluster center matrix. Therefore, D cluster center matrices can be obtained from set Φ. The d-th cluster center matrix is ​​defined as...

[0032]

[0033] Transform the d-th cluster center matrix into dimensional vector for As the initial position of the quantum poison blast population, that is, when ε=1, the position of the d-th quantum poison blast before K-means treatment is: ε represents the number of iterations.

[0034] The population size of the quantum poison blaster in the εth iteration is D. ε The maximum number of iterations for the entire population is G. max The quantum position of the d-th quantum poison bug before K-means treatment in the ε-th iteration is: The k-dimensional quantum position of the d-th quantum poison bug in the ε-th iteration With corresponding position The mapping rule is This is the lower bound of the position variable of the k-th dimension quantum poison bug. It is the upper bound of the position variable of the k-th dimension quantum poison bug.

[0035] Step 2: Map the position of each quantum poison bug before K-means processing to a cluster center matrix, and use K-means to obtain new cluster centers. Then, obtain the position and quantum position of the quantum poison bug after K-means processing.

[0036] Set the number of K-means clusters to M, and the maximum number of iterations to... For the d-th quantum poison insect, the cluster center of the t-th cluster before K-means processing is... Clustering is performed initially at t=0; the specific process is as follows:

[0037] (1) Convert the positions of individual quantum poison bugs into an initial cluster center matrix. The initial cluster centers are in Clustering cluster is M r r = 1, 2, ..., M, initially the r-th cluster is an empty set, i.e.

[0038] (2) Select a time-frequency point from the preprocessed audio signal sampling point set U. Calculate time and frequency points To the cluster center The square of the Euclidean distance when When the value is at its minimum, it indicates Belonging to Corresponding cluster M r Update the cluster

[0039] (3) Continue to calculate the squared Euclidean distance between the remaining time-frequency points in U and the cluster centers to obtain the new cluster centers. The vector representing the cluster center within set U. The number of time-frequency points;

[0040] (4) Determine whether the newly obtained cluster centers are consistent with the previous clustering or whether the maximum number of iterations has been reached. like and Then let t = t + 1, return to (2) and continue the loop; if or Then the clustering process ends.

[0041] The cluster center matrix is ​​obtained after K-means processing. Cluster center matrix Transform into The position formed by the dimensional vector The position of the d-th quantum poison bug after the ε-th iteration of K-means processing is obtained. Mapping the quantum poison bug's position to a quantum position Mapping rules are This is the lower bound of the k-th dimension position variable of the quantum poison bug. It is the upper limit of the k-th dimension position variable of the quantum poison bug.

[0042] Step 3: Identify the quantum poison worms, initialize the acid attraction of each quantum poison worm, construct a hybrid optimization objective function, calculate and sort the fitness value of each quantum poison worm in the population, and obtain the quantum positions of the best and second-best quantum individuals.

[0043] The cluster center matrix of the d-th quantum poison insect in the ε-th iteration is obtained after K-means processing. Corresponding cluster center vector Choose any time frequency point from set U. Calculate the Euclidean distance from the point to each cluster center vector. Where ||·|| represents the l2 norm of the · group, which yields the cluster center vector. With time and frequency points The distance, when When the minimum value is taken, it indicates Belonging to For clusters, repeat the above calculation process to obtain the reciprocal of the inter-class scatter. For cluster center vectors Indicates the distribution center of the internal time-frequency point set. The vector representing the cluster center within set U. The number of time-frequency points is used to calculate the second moment of the corresponding time-frequency points within the cluster, thus obtaining the reciprocal of the intra-cluster cohesion. Constructing a hybrid optimization objective function

[0044] Calculate the fitness value of the position of the d-th quantum poison bug in the swarm. A higher fitness value indicates a better clustering effect; the quantum poison bug individuals are ranked according to their fitness values. The quantum position of the optimal quantum individual up to the εth generation. Let R be the quantum position of the suboptimal quantum individual up to the εth generation; set the sputtering radius R. Let be the minimum value of the individual position of the Quantum Poison Bug across all dimensions. The maximum value of the quantum poison blaster's individual position across all dimensions; initialize the quantum poison blaster identity i within the population. d i of ordinary quantum poison bugs d =1, the ordinary quantum poison bug evolves with probability α, and the probabilities of evolving into a quantum splitter and a quantum hunter bug are α1 and α2, respectively. d =2 represents the evolution of the Quantum Venomous Bug into the Quantum Splitter, i d =3 represents the evolution of the Quantum Poison Bug into the Quantum Hunter Bug, and the offspring individuals i formed by the splitting of the Quantum Splitter Bug. d =4; Calculate the acid attraction of the d-th quantum poison worm. Initialize the acidic attraction of the d-th quantum poison blaster in the k-th dimension. It is a random number that follows a uniform distribution between [0,1].

[0045] Step 4: Calculate the distance between each individual quantum poison worm and the optimal quantum poison worm individual. Based on the obtained distance, determine whether the quantum individual is within the splash range of the optimal individual. Update the quantum position and acid attraction according to the quantum poison worm update mechanism.

[0046] For the quantum position of the d-th quantum poison bug in the ε-th iteration Update the acidity of the k-th dimension of the acidic attraction of the d-th quantum poison blaster. and It represents the acidic attraction of the best and second-best quantum individuals in the k-th dimension before the (ε+1)-th iteration update. and It represents the acidic attraction of the best and second-best quantum individuals in the k-th dimension after the (ε+1)-th iteration update. and The updated acidic attraction is normalized using random numbers that follow a uniform distribution between [0,1]. and It is the acidic attraction of the d-th quantum poisonous insect in the ε-th iteration. The maximum and minimum values ​​across all dimensions, ι1 and ι2, are the normalization constants for acidic attraction.

[0047] The quantum position of the d-th quantum individual with discovery probability If selected for updating, a random number will be generated between [0,1] following a uniform distribution. when At that time, by The distance between the d-th quantum poison bug and the optimal quantum poison bug is obtained. Compare with the sputtering radius R. If... show To determine the identity of a quantum individual, i is located outside the sputtering range of the optimal quantum individual. d =3 represents quantum insect hunting, where the quantum rotation angle of the k-th dimension of the d-th quantum individual in the ε+1th iteration is defined as... Among the parameters It is a random number uniformly distributed between [0.5, 1]; if the quantum individual is not a quantum hunter, its k-th dimension quantum rotation angle is updated to It is a random number that follows a uniform distribution between [-1, 1], i.e., the identity of the individual i. d When ≠3, the k-th quantum position of the d-th quantum poison bug is updated using a simulated quantum rotation gate. like Then the d-th quantum poison bug is located within the self-destruct splash range of the optimal quantum individual, if i d =2, then the quantum poison bug is identified as a quantum splitting bug. In the ε-th iteration, the d-th quantum poison bug splits into two quantum positions respectively. and When a quantum splitting offspring is added to the population, the quantum rotation angles of the k-th dimension of the two quantum splitting offspring are updated to... and and All are random numbers that follow a uniform distribution between [0,1]. and Each represents all The maximum and minimum values ​​of the k-th dimension, and the k-th dimension quantum positions generated using a simulated quantum rotation gate, are respectively... and The acidic attraction of the k-th dimension is respectively and and It is a random number that follows a uniform distribution between [0,1], a quantum splitting insect. The quantum rotation angle of the k-th quantum position is updated as follows in Random numbers that are uniformly distributed between [0,1]. and These are the maximum and minimum values ​​of the k-th dimension quantum poison bug in the ε-th generation. A simulated quantum rotation gate is introduced, and the quantum position is updated as follows: When the d-th quantum individual in the ε-th iteration is not a quantum splitting worm, that is, the identity of that individual is i d When ≠2, the k-th dimension quantum rotation angle is updated to The k-th dimension quantum position is updated using a simulated quantum rotation gate.

[0048] if To determine the identity of the d-th quantum poison bug individual, if the individual is a offspring of a quantum split bug, i.e., i... d =4, then the k-th dimension quantum rotation angle of the d-th quantum poison bug is updated to... ν ε Represents the inertia weighting coefficient. and All are random numbers that follow a uniform distribution between [0,1]. It is a randomly selected location. The label, the k-th dimension quantum position of the d-th quantum poison bug is updated to If we need to determine the identity of the quantum poison explosives... d If ≠4, meaning any individual other than the offspring of the quantum splitting insect, then the quantum rotation angle is updated to... It is a random number that follows a standard Gaussian distribution. The k-th dimension quantum position of the d-th quantum individual is updated to...

[0049] Step 5: Sort the updated individuals according to their fitness values ​​to obtain the optimal individual position of the updated population. Then, convert the position of the optimal quantum poison bug into the initial cluster center of K-means clustering and perform clustering to obtain the new cluster center as the updated global optimal position.

[0050] After updating the quantum positions of all Quantum Poison Bugs in the swarm, the updated quantum positions will be displayed. Mapped to the location of the quantum poison bug Calculate the fitness value function Sort the updated individuals according to their fitness values ​​to obtain the position of the best individual in the updated population.

[0051] Position of the optimal individual As the initial cluster centers for K-means clustering, the cluster centers of the t-th cluster at position t before K-means processing are: Perform clustering; the clustering process is the same as the K-means clustering process in step two.

[0052] After K-means processing, a new cluster center matrix is ​​obtained. Cluster center matrix Transform into dimensional vector Obtain the global optimal position after K-means processing. Mapped to the globally optimal quantum position according to the mapping rules. k-dimensional quantum position With corresponding position The mapping rule is

[0053] Step 6: Incorporate a random population generation strategy to generate quantum random candidate solutions, calculate the updated position and the fitness value of the quantum random candidate solutions, and use greedy selection to update the quantum position.

[0054] Introducing a random generation strategy increases the diversity of solutions, according to the formula. Generating the k-th dimension of the quantum random candidate position for the optimal individual quantum position in the population These are candidate quantum random solutions for the optimal individual generated by the time-of-flight mechanism. It is a random number that follows a uniform distribution on [0,1]. because so The position mapping of quantum random candidate solutions is as follows Based on the fitness function The fitness value of the optimal individual random candidate solution is calculated, and the fitness value is used to evaluate whether to replace the updated optimal individual quantum position with the quantum random candidate solution. Update the quantum position using greedy selection, calculate the fitness value of the d-th quantum poison bug after the ε-th iteration, and compare it with the fitness value before the update. If... If the previous quantum position of an individual is replaced with the new quantum position, then no update is performed. The acidity is updated based on the fitness value. The quantum poison worm population after the ε-th iteration is re-identified. Based on the biological characteristics of the quantum poison worm, ordinary quantum poison worms have an α1 probability of evolving into quantum splitters and quantum hunters. Offspring of quantum splitters cannot evolve. The population size D after the ε-th iteration is determined. ε+1 Compared with the population size D before the update ε The size of D, if ε+1 >D ε Then, the individual identities of the quantum poison blast bugs that are greater than a certain number i d =4, which is the offspring of the quantum splitting insect, and the updated population is used as the initial population for the ε+1th iteration.

[0055] Step 7: Determine if the maximum number of iterations G has been reached. max If the iteration does not reach the target, return to step two and continue iterating; otherwise, output the cluster center matrix obtained by K-means clustering, which serves as the optimal estimate of the underdetermined mixing matrix of the underdetermined blind source separation system.

[0056] Determine if the maximum number of iterations G has been reached. max If the number of iterations has not been reached, let ε = ε + 1 and return to step two to continue iterating; if the number of iterations has been reached, output the cluster center matrix obtained by K-means clustering. r = 1, 2, ..., M, is the optimal estimation matrix of the underdetermined mixing matrix of the underdetermined blind source separation system.

[0057] For ease of description, the robust underdetermined blind source separation method based on the quantum poison bug blasting mechanism is abbreviated as QBOA-BSS, and the underdetermined blind source separation method based on the particle swarm optimization algorithm is abbreviated as PSO-BSS.

[0058] The parameters for QBOA-BSS are as follows: population size D = 20, mutation probability of ordinary poison blast bug α = 0.2, probability of mutation into splitting bug α1 = 0.5, probability of mutation into predator bug α2 = 0.5, and detection probability... The acidity normalization parameters for individuals in the population were set to ι1 = 0.9 and ι2 = 0.1, the mixed fitness function was set to γ ​​= 0, and the maximum number of iterations for K-means clustering was set to...

[0059] For relevant parameters of PSO-BSS, please refer to "Blind Source Separation Algorithm Based on Particle Swarm Optimization" published by Zhang Wenai et al. in the Journal of Taiyuan University of Technology (2006, Vol.37, No.2, pp.169-172). The population size and number of iterations are the same as those of QBOA-BSS.

[0060] Set the blending matrix to That is, N=3, M=4, performing mixture matrix estimation for four flute tone signals. Additive white Gaussian noise is selected, with a signal-to-noise ratio (SNR) of 15dB. Additive Gaussian noise is also selected for the short-time Fourier transform (SFT), with an SNR of 15dB. Since mixture matrix estimation and source signal recovery are performed in the time-frequency domain, the Hanning window length for the SFT is set to 1024, the number of overlapping sampling points between windows is set to 512, and the number of sampling points for the discrete Fourier transform is 1024. The time-domain waveforms of the four flute tone signals are as follows: Figure 2 As shown.

[0061] The four flute tone signals were mixed using a mixing matrix and then preprocessed. During preprocessing, the relevant parameters were set as follows: ζ = 4, θ = 4.8°. The resulting scatter plot of the observed signals from the three channels is shown below. Figure 3 .

[0062] Maximum number of iterations G max =1000, signal-to-noise ratio set to 15dB, the experiment was conducted using the average of 30 independent runs, the convergence performance comparison curves of QBOA-BSS and PSO-BSS based on the objective function are shown below. Figure 4 As shown. By Figure 4 It can be seen that QBOA has better convergence performance on the objective function. Compared with PSO, QBOA has a faster convergence speed, higher convergence accuracy, and better robustness.

[0063] Normalized mean squared error (NMSE) is used to evaluate the performance of the mixture matrix estimation method. NMSE is calculated as follows: Where a' ir a represents the element in the i-th row and r-th column of the estimated mixture matrix. ir This represents the element in the i-th row and r-th column of the actual mixing matrix. The smaller the NMSE, the higher the accuracy of the method.

[0064] Under additive white Gaussian noise interference with a signal-to-noise ratio of 15 dB, QBOA-BSS is used to estimate the mixing matrix, yielding the optimal estimated matrix of the mixing matrix. At this point, NMSE = -59.31 dB.

[0065] The termination iteration count for QBOA-BSS and PSO-BSS is set to 100. The K-means clustering algorithm, denoted as KMA, also has its iteration count set to 100. Other parameters remain unchanged. Experimental results at the same signal-to-noise ratio are the average of 50 independent runs. The performance comparison curves for the three methods are shown below. Figure 5 As shown.

[0066] Depend on Figure 5 As can be seen, compared with traditional clustering methods applied to hybrid matrix estimation, QBOA-BSS can achieve higher accuracy in hybrid matrix estimation and performs well under low signal-to-noise ratio conditions. Compared with hybrid matrix estimation methods that combine swarm intelligence algorithms with clustering, this invention performs better in dealing with outliers and different signal-to-noise ratios. This is because the quantum poison bug optimization obtained by quantizing the poison bug optimization algorithm has good search performance, the initial population generation strategy reduces the sensitivity of the swarm intelligence algorithm to the initial cluster centers, and the designed hybrid fitness function improves the judgment effect of the clustering algorithm.

Claims

1. An underdetermined mixed matrix estimation method based on the quantum poison beetle explosion mechanism, characterized in that, The steps are as follows: Step one: pre-process the received observation signal, and initialize the initial position and quantum position of the quantum bionic mayfly population using the initial population generation strategy for the pre-processed signal; Step 1.1: randomly take a single time-frequency point from the time-frequency point set U obtained after pre-processing The observation signal corresponding to the time-frequency point is taken out From and put into the clustering center vector set Φ, and then randomly take a time-frequency point from the remaining time-frequency points in U The Euclidean distance between the observation signals and is calculated, that is Step 1.2: Find the observation signal sample point with the largest Euclidean distance between and Step 1.3: This sample point is taken out from the set of cluster center vectors Φ; Step 1.4: Calculate separately The Euclidean distance between each remaining sample point and the cluster center vectors in Φ is calculated. The maximum and minimum Euclidean distances between each sample point and the cluster center vectors in Φ are multiplied together, so that each sample point corresponds to a product. The sample point with the largest product is found. Step 1.5: determine whether the number of cluster center vectors in Φ is less than D x M, if yes, return to step 1.3 to continue the loop; if no, output the cluster center vector set Φ, which should contain D x M cluster center vectors of 1 x N dimensions; Step 1.6: starting from the first cluster center vector in set Φ, every D cluster center vectors form a cluster center matrix of M x N dimensions, then D cluster center matrices can be obtained from set Φ, and the dth cluster center matrix is defined as: The dth cluster center matrix is converted into The dth cluster center matrix is converted into The dth cluster center matrix is converted into d = 1, 2, …, D, as the initial position of the quantum toxic explosion bug population, that is, when ε = 1, the position of the dth quantum toxic explosion bug before K-means processing is ε represents the number of iterations; The population size of the quantum toxic explosion bug in the εth iteration is D ε The maximum iteration number of the entire population is G max The quantum position of the quantum toxic explosion bug before K-means processing in the dth quantum toxic explosion bug in the εth iteration is d=1,2,...,D ε , The k-dimensional quantum position of the quantum toxic explosion bug in the dth quantum toxic explosion bug in the εth iteration The mapping rule of the corresponding position is is the lower limit of the position variable of the k-dimensional quantum toxic explosion bug, and is the upper limit of the position variable of the k-dimensional quantum toxic explosion bug.​ Step two: map the position of each quantum bionic mayfly before K-means processing to the cluster center matrix, and use K-means to obtain new cluster centers, then obtain the position and quantum position of the quantum bionic mayfly after K-means processing; Step three: identity identification of quantum bionic mayfly, initialization of acid attraction degree of each quantum bionic mayfly, construction of mixed optimization objective function, calculation of fitness value of each quantum bionic mayfly in population and sorting, and obtaining of quantum position of optimal and suboptimal quantum individuals; Step four: calculate the distance between each quantum bionic mayfly individual and the optimal quantum bionic mayfly individual, and determine whether the quantum individual is within the sputtering range of the optimal individual according to the obtained distance, and update the quantum position and acid attraction degree according to the quantum bionic mayfly update mechanism; Step five: sort the updated individuals according to the fitness value, obtain the optimal individual position of the updated population, and convert the position of the optimal quantum bionic mayfly to the initial cluster center of K-means clustering to obtain new cluster centers as the updated global optimal position; Step six, add a random population generation strategy to generate a quantum random candidate solution, calculate the fitness value of the updated position and the quantum random candidate solution, and update the quantum position using greedy selection; Step seven, determine if the maximum number of iterations G has been reached max If not, return to step two and continue iteration. Otherwise output the matrix of cluster centers obtained by K-means clustering as the optimal estimation matrix of the underdetermined mixing matrix of the underdetermined blind source separation system 2. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, The step two specifically comprises: setting the K-means clustering cluster number as M and the maximum iteration number as The cluster center of the K-means processing before the dth quantum toxic explosion of the beetle for the tth clustering is r=1,2,...,M, clustering, initially t=0; the specific process is as follows: (1) converting the positions of the quantum-toxic explosion bug individuals into an initial clustering center matrix The initial clustering center is wherein The clustering class cluster is M r , r = 1, 2, …, M, the initial rth class cluster is an empty set, that is, (2) Select a time-frequency point from the preprocessed audio signal sampling point set U. Calculate time and frequency points To the cluster center The square of the Euclidean distance when When the value is at its minimum, it indicates Belonging to Corresponding cluster M r Update the cluster (3) Continue to calculate the squared Euclidean distance between the time-frequency points remaining in U and the cluster center, and obtain a new cluster center p = 1, 2,..., N, denotes the number of time-frequency points belonging to the cluster center vector in the set U; (4) judging whether the new clustering center obtained is consistent with the clustering center before clustering or whether the maximum iteration number is reached If and then let t=t+1, return to (2) to continue the loop; if or then end the clustering; After K-means processing, the cluster center matrix is obtained The cluster center matrix is converted to The position composed of the D-dimensional vector is obtained The position of the dth quantum toxic explosion bug after the kth iteration of K-means processing is obtained The quantum toxic explosion bug position is mapped to the quantum position d = 1, 2,..., D ε The mapping rule is is the lower limit of the kth-dimensional position variable of the quantum toxic explosion bug, is the upper limit of the kth-dimensional position variable of the quantum toxic explosion bug.​ 3. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, Step three specifically includes: obtaining the cluster center matrix of the d-th quantum poison bug in the ε-th iteration through K-means processing. Corresponding cluster center vector r = 1, 2, ..., M, arbitrarily select a time-frequency point from set U. Calculate the Euclidean distance from the point to each cluster center vector. Where ||·|| represents the l2 norm of the · group, which yields the cluster center vector. With time and frequency points The distance, when When the minimum value is taken, it indicates Belonging to For clusters, repeat the above calculation process to obtain the reciprocal of the inter-class scatter. For cluster center vectors Indicates the distribution center of the internal time-frequency point set. r = 1, 2, ..., M p = 1, 2, ..., N The vector representing the cluster center within set U. The number of time-frequency points is used to calculate the second moment of the corresponding time-frequency points within the cluster, thus obtaining the reciprocal of the intra-cluster cohesion. Constructing a hybrid optimization objective function γ∈{0,1}; Calculate the fitness value of the dth quantum toxic blast position in the population The quantum position of the optimal quantum individual until the εth generation, The quantum position of the suboptimal quantum individual until the εth generation; set the sputtering radius R, The minimum value of the quantum toxic blast individual position in all dimensions, The maximum value of the quantum toxic blast individual position in all dimensions; initialize the identity i of the quantum toxic blast in the population d i of the ordinary quantum toxic blast d = 1, the ordinary quantum toxic blast evolves with a probability of α, and the probabilities of evolving into quantum fissioners and quantum hunters are α1 and α2, i d = 2 represents the evolution of the quantum toxic blast into a quantum fissioner, i d = 3 represents the evolution of the quantum toxic blast into a quantum hunter, and the offspring individuals formed by the quantum fissioner splitting i d = 4; calculate the acid attraction degree of the dth quantum toxic blast Initialize the acid attraction degree of the dth quantum toxic blast in the kth dimension is a random number uniformly distributed between [0, 1], 4. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, Step four specifically includes: updating the quantum position of the dth quantum bollworm in the e th iteration updating the kth dimensional acidic attraction degree of the dth quantum bollworm to and is the kth dimensional acidic attraction degree of the optimal quantum individual and the suboptimal quantum individual before the update in the e+1 th iteration, and is the kth dimensional acidic attraction degree of the optimal quantum individual and the suboptimal quantum individual after the update in the e+1 th iteration, and is a random number between 0 and 1 subject to uniform distribution, and the normalized acidic attraction degree after the update and is the acidic attraction degree of the dth quantum bollworm in the e th iteration the maximum and minimum values in all dimensions, ι1 and ι2 are acidic attraction degree normalization constants; The quantum position of the dth quantum individual is updated with the discovery probability If the dth quantum individual is selected for updating, a random number uniformly distributed in [0, 1] is generated When The distance between the dth quantum individual and the optimal quantum individual is obtained The distance between the dth quantum individual and the optimal quantum individual is obtained Compared with the sputtering radius R; if Indicates Outside the sputtering range of the optimal quantum individual, the identity of the quantum individual i is determined d = 3 is a quantum predator, and the kth-dimensional quantum rotation angle of the dth quantum individual in the ε+1th iteration is defined as Where the parameter is a random number uniformly distributed in [0.5, 1]; if the quantum individual is not a quantum predator, the kth-dimensional quantum rotation angle is updated as is a random number uniformly distributed in [-1, 1], i.e. the identity of the individual i d ≠ 3, the kth-dimensional quantum position of the dth quantum individual is updated using the simulated quantum rotation gate If The dth quantum individual is located within the self-sputtering range of the optimal quantum individual, and if i d = 2, the identity of the quantum individual is determined as a quantum split worm, and the dth quantum individual is split into two quantum positions in the εth iteration And The quantum split worm offspring are added to the population, and the kth-dimensional quantum rotation angles of the two quantum split worm offspring are updated as And And are random numbers uniformly distributed in [0, 1], And represent the maximum and minimum values of the kth dimension among all The kth-dimensional quantum position generated using the simulated quantum rotation gate is And The kth-dimensional acidic attraction degree is And And are random numbers uniformly distributed in [0, 1], and the kth-dimensional quantum position of the quantum split worm The kth-dimensional quantum rotation angle of the quantum split worm Where is a random number uniformly distributed in [0, 1], And are the maximum and minimum values of the th ε-dimensional quantum explosive termite, respectively, the simulated quantum rotation gate is introduced, and the quantum position update is When the th d quantum individual is not a quantum explosive termite in the th ε iteration, that is, the identity i of the individual d ≠ 2, the th k-dimensional quantum rotation angle is updated as The th k-dimensional quantum position is updated using the simulated quantum rotation gate as If the identity of the dth quantum individual is determined, and if the individual is the quantum splitworm offspring, i d = 4, the kth dimensional quantum rotation angle of the dth quantum individual is updated as ν ε represents the inertia weight coefficient, and are random numbers uniformly distributed in [0, 1], is a randomly selected position with index d, the kth dimensional quantum position of the dth quantum individual is updated as If the identity of the quantum individual is determined, i d ≠ 4, i.e., the individual is other than the quantum splitworm offspring, the quantum rotation angle is updated as is a random number following a standard Gaussian distribution, and the kth dimensional quantum position of the dth quantum individual is updated as 5. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, Step five specifically includes: after updating the quantum position of all quantum poison beetles in the population mapping the updated quantum position as the position of the quantum poison beetle calculating the fitness value function sorting the updated individuals according to the fitness value to obtain the position of the optimal individual in the updated population the position of the optimal individual As the initial clustering center of K-means clustering, the clustering center of the t-th clustering before K-means processing is r = 1, 2,..., M, clustering; the clustering process is consistent with the K-means clustering process in step two. After K-means processing, a new clustering center matrix is obtained The clustering center matrix is converted to a dimension vector The global optimal position after K-means processing is obtained According to the mapping rule, it is mapped to the global optimal quantum position The k-dimensional quantum position The mapping rule of the corresponding position is 6. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, Step six specifically includes: introducing random generation strategy to increase the diversity of solutions, according to the formula The k-dimensional quantum random candidate position of the optimal individual of the population The quantum random solution candidate solution of the optimal individual generated by the anytime mechanism, is a random number on [0,1] obeying uniform distribution, Since Therefore The position mapping of the quantum random candidate solution is According to the fitness function The fitness value of the optimal individual random candidate solution is calculated, and whether the quantum random candidate solution is used to replace the updated optimal individual quantum position is evaluated by the fitness value The quantum position is updated using greedy selection, the fitness value of the dth quantum mutillidae after the εth iteration is calculated and compared with the fitness value before updating, if The quantum position after iteration is used to replace the quantum position of the individual before iteration, otherwise it is not updated; according to the size of the fitness value, it is judged whether to update the acidity; the quantum mutillidae population after the εth iteration is re-identified, according to the biological characteristics of the quantum mutillidae, the ordinary quantum mutillidae have a probability of α1 to evolve into quantum splitting insects and quantum hunting insects, the offspring of the quantum splitting insects cannot evolve, and the size of the population D after the εth iteration is judged ε+1 And the size of the population D ε Before updating, if D ε+1 >D ε , the identity i d =4 of the quantum mutillidae individuals in the greater part is the offspring of the quantum splitting insects, and the updated population is taken as the initial population of the (ε+1) th iteration.

7. The underdetermined mixing matrix estimation method based on quantum poison beetle explosion mechanism according to claim 1, characterized in that, Step seven specifically includes: judging whether the maximum iteration number G is reached max , if not, setting ε = ε + 1, returning to step two to continue iteration; if yes, outputting the clustering center matrix obtained by K-means clustering r = 1, 2,..., M as the optimal estimation matrix of the underdetermined mixing matrix of the underdetermined blind source separation system

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