Variational mode decomposition method based on multi-target crayfish algorithm

Abstract

The invention discloses a variational mode decomposition method based on a multi-objective crayfish algorithm, and the method comprises the following steps: S1, constructing an original variational mode decomposition model, determining a parameter design space, and optimizing an objective function; s2, improving a multi-target crayfish algorithm, wherein the multi-target crayfish algorithm comprises the steps of introducing non-dominated sorting to carry out comprehensive evaluation on a plurality of optimization targets; introducing a Pareto optimal frontier based on crowding degree calculation to determine a population updating strategy; s3, establishing a multi-target crayfish algorithm mathematical model, and performing iterative calculation to obtain an optimal parameter combination; and S4, inputting the optimal parameter combination into the variational mode decomposition model to obtain an optimal variational mode decomposition result, and verifying the superiority of variational mode decomposition based on the multi-target crayfish algorithm. The invention discloses a variational mode decomposition method based on a multi-target crayfish algorithm, which overcomes the defects of the existing algorithm, and in variational mode decomposition, an optimal mode number K and a penalty factor alpha are selected to realize optimal variational mode decomposition of signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing and optimization, and specifically relates to a variational mode decomposition method based on a multi-objective crayfish algorithm. Background Technique

[0002] Signal decomposition is an important technique in the field of signal processing. It involves decomposing complex signals into a series of simpler components or intrinsic mode functions (IMFs), and is widely used in scenarios such as signal denoising, compression, feature extraction, and fault detection. Common signal decomposition methods include Fourier transform (FT), wavelet transform (WT), empirical mode decomposition (EMD) and its variants, etc. Empirical mode decomposition is an adaptive signal processing technique that does not require preset basis functions. By iteratively extracting intrinsic mode functions until the conditions of the IMF are met. EMD has the advantages of self-adaptability and simple calculation, but may be affected by mode mixing and end effects. Variational mode decomposition (VMD) is a non-recursive signal decomposition method based on variational problems. It decomposes signals into modal components with different center frequencies by optimizing problems, thereby achieving effective decomposition components of a given signal and finally obtaining the optimal solution of the variational problem. Compared with the EMD method and its variants, VMD has a more solid mathematical theory foundation, can effectively separate the intrinsic mode components (IMFs), overcomes the mode mixing problem in EMD, and thus has advantages in processing non-stationary sequences.

[0003] In VMD, the parameters K and α are key control parameters that directly affect the decomposition effect. The parameter K represents the number of modal components to be decomposed. If K is set too small, it may lead to under-decomposition. If K is set too large, some meaningless spurious components may be generated. The parameter α is the penalty factor used to control the bandwidth of the modal components. A smaller α value will result in a wider bandwidth of the modal components, which may cause mode mixing; a larger α value will narrow the bandwidth, but may cause useful signal components to be ignored. Appropriate K and α can significantly improve the decomposition effect of VMD. Usually, the initial values need to be determined according to the physical characteristics of the signal and prior knowledge, and then the optimal K and α values are gradually determined through experiments and observations.

[0004] A variety of optimization algorithms are also used to optimize VMD parameters, such as the sparrow search algorithm and the gray wolf optimization algorithm. These algorithms evaluate the decomposition effect under different parameter combinations by defining fitness functions, and find the optimal solution in the design space. However, the fitness functions of these algorithms are often single objectives. In order to achieve multi-objective optimization, the method of introducing weight factors is used to calculate the mean of multiple fitness functions, and the selection criteria of fitness functions are complex and diverse. The crayfish optimization algorithm C0A was proposed in 2023. It is a meta-heuristic optimization algorithm inspired by the behavior of crayfish. It simulates the summer heat escape, competition and foraging behavior of crayfish. It performs well in tests and provides a new tool for solving complex optimization problems. The traditional crayfish algorithm only targets single-objective optimization problems, which greatly limits its scope of application. In practical applications, multi-objective optimization problems are very common in fields such as engineering and economics, so there is an increasing demand for COA variants that can handle multi-objective problems.

[0005] The variational mode decomposition VMD method based on the multi-objective crayfish algorithm MOPSO is used to select the best problem:

[0006] High computational complexity: The MOPSO algorithm itself involves the optimization of multiple objectives and needs to consider multiple fitness functions at the same time, which increases the computational complexity and running time. The VMD algorithm is already a computationally intensive process. When combined with MOPSO, the overall computational workload will increase significantly, which may lead to inefficiency when processing large-scale data.

[0007] Large parameter space: The range of K and α is wide, resulting in a very large search space. For each possible k value, multiple iterations are required to find the optimal α value, which further increases the computational burden. Global search in high-dimensional parameter space is prone to the "curse of dimensionality", that is, as the dimension increases, the difficulty of search increases exponentially.

[0008] Slow convergence: Due to the large and complex parameter space, the MOPSO algorithm may require more iterations when searching for the optimal solution, resulting in a slow convergence. Especially in practical applications, it may take a long time to get a satisfactory result, which may be a problem for application scenarios with high real-time requirements.

[0009] Stability issue: The MOPSO algorithm depends on the selection of the initial population. Different initial populations may lead to different optimization results, and there is a certain degree of randomness and instability. In some cases, the algorithm may fall into a local optimum and fail to find the global optimal solution.

[0010] The design of the fitness function is complex: To accurately evaluate the effects of different combinations of K and α, a reasonable fitness function needs to be designed. These functions usually need to consider multiple metrics, such as modal mutual information, modal edge density, modal energy concentration, etc.

[0011] The design and implementation of the fitness function are relatively complex and require comprehensive consideration of the characteristics of the signal and the objectives of decomposition. Otherwise, it may not accurately reflect the advantages and disadvantages of the parameter combinations.

[0012] Difficulty in parameter tuning: The MOPSO algorithm itself involves the setting of multiple parameters, such as population size, number of iterations, crossover probability, mutation probability, etc. The selection of these parameters has an important impact on the performance of the algorithm, but there is currently no general rule to follow, and usually, it needs to be tuned through experiments.

[0013] The parameter tuning process is time-consuming and complex, and it may require multiple attempts and adjustments to find the optimal configuration.

[0014] In summary, the variational mode decomposition method based on the multi-objective crayfish algorithm faces problems such as high computational complexity, large parameter space, slow convergence speed, stability issues, complex fitness function design, and difficulty in parameter tuning when selecting the optimal number of modes K and penalty factor α. And providing a solution is a technical problem that those skilled in the art urgently need to solve. Summary of the Invention

[0015] The purpose of the present invention is to provide a variational mode decomposition method based on the multi-objective crayfish algorithm for the problems in the prior art.

[0016] To achieve the above object, the present invention adopts the following technical solutions:

[0017] A variational mode decomposition method based on the multi-objective crayfish algorithm, characterized by comprising the following steps:

[0018] S1. Construct an original variational mode decomposition model, determine the parameter design space and the optimization objective function;

[0019] S2. Improve the multi-objective crayfish algorithm, including: S2.1. Introduce non-dominated sorting to comprehensively evaluate multiple optimization objectives; S2.2. Introduce a Pareto optimal front based on crowding degree calculation to determine the population update strategy;

[0020] S3. Establish a mathematical model of the multi-objective crayfish algorithm and iteratively calculate to obtain the optimal parameter combination;

[0021] S4. Input the optimal parameter combination into the variational mode decomposition model to obtain the optimal variational mode decomposition result and verify the superiority of the variational mode decomposition based on the multi-objective crayfish algorithm:

[0022] In step S1, the input is the acquisition of cardiac electrical signals, and the design parameters of variational mode decomposition are selected as the number of modes K and the penalty factor α. The design space of the number of modes is determined as K ∈ [3, 8] ∩ Z, and the design space of the penalty factor is α ∈ [500, 5000] ∩ R.

[0023] While adopting the above technical solution, the present invention can also adopt or combine the following technical solutions:

[0024] As a preferred technical solution of the present invention: in the step S1, the optimization objective function is calculated according to the decomposed modal components and is selected as the spectral kurtosis SK and the KL divergence. The calculation formula of the spectral kurtosis is as follows:

[0025]

[0026] Where X f is the Fourier transform of the signal at frequency f, <|X(f)| 4 > refers to the expected value of the fourth power of the modulus of the Fourier transform of the signal at frequency f, <|X(f)| 2 > refers to the expected value of the square of the modulus of the Fourier transform of the signal at frequency f. The KL divergence formula is introduced and calculated as follows:

[0027]

[0028] Where p(x) and q(x) respectively represent the modulus of the Hilbert-Huang transform of the original signal and the characteristic modal signal at point x, p and q are two discrete probability distributions, xi represents the i-th event, and p(x i ) and q(xi) are the probabilities of the event xi in the distributions p and q respectively.

[0029] As a preferred technical solution of the present invention: in the S2, the specific steps of the improved multi-objective crayfish algorithm are as follows:

[0030] S2.1, comprehensively evaluate each optimization objective function based on non-dominated sorting: if each individual in the set P has r objective functions f i (x) (i = 1, 2,..., r), r ≥ 2, where the dominance relationship between individuals is defined as: If f i (x1) ≤ f i (x2), and make f l (x1) < f l (x2), it is said that x1 dominates x2;

[0031] The non-correlation relationship between individuals is defined as: If there is no domination relationship between x1 and x2, then x1 and x2 are not relevant. If x1 ∈ P, x2 ∈ P, and x1 ≠ x2, then x1 is said to dominate in P, and the set composed of such x2 is called the maximum non-dominated set;

[0032] Based on the optimization function SK f (x) and D KL (x) continuously searches for individuals with domination relationships within the population, continuously constructs non-dominated sets, and finally finds the Pareto optimal solution set, that is, each solution in it cannot be dominated by other solutions;

[0033] S2.2, sort the obtained Pareto solution set based on the crowding degree calculation. The crowding degree is defined as:

[0034]

[0035] where f(x j_i+1 ) and f(x j_i-1 ) respectively represent two fitness values adjacent to the i-th point in the j-th level, f j_max and f j_min respectively represent the maximum and minimum fitness values in the j-th level. After sorting the Pareto solution set from largest to smallest according to the crowding degree value, the population update strategy is to take the first N individuals as the next iteration object.

[0036] As a preferred technical solution of the present invention: the specific steps in S3 include:

[0037] S3.1, given parameters such as the maximum number of iterations T, population size N, individual dimension dim, and upper and lower bounds ub, lb, etc., for the optimization objective F, initialize the population X = [X1, X2,... X N , where the individual X i，j is initialized as follows:

[0038] X i,j = lb j +(ub j -lb j )×rand

[0039] where lb j , ub j respectively represent the upper and lower bounds of the j-th dimension, rand represents a random number between (0, 1], and if the j-th dimension is an integer, then the result is rounded;

[0040] According to the initial position parameters of the crayfish, perform variational mode decomposition on the original signal S, calculate the initial positions of the crayfish population individuals and the fitness values under different objective functions based on the decomposed result IMF signals, and record the individual with the smallest fitness function as the best individual;

[0041] S3.2. According to the living habits of crayfish, change the environmental temperature to control the algorithm to enter different stages, such as

[0042] shown below:

[0043] temp = rand × 15 + 20

[0044] where temp is the temperature value of the environment where the crayfish is located, and rand represents a random number between (0, 1]. For different fitness functions, repeat steps S3.3 - S3.5 respectively;

[0045] S3.3. When temp > 30 and rand < 0.5, the multi - objective crayfish algorithm enters the summer - avoidance stage, and the update strategy of the individual position in the (t + 1) - th generation is as follows:

[0046]

[0047] X shade = (X G + X L ) / 2

[0048] where C2 is a decreasing coefficient, X shade is the cave position, X G is the value of the best position of the crayfish individual since the algorithm iteration, and X L is the value of the best individual position of the crayfish population in the current population;

[0049] S3.4. When temp > 30 and rand ≥ 0.5, the multi - objective crayfish algorithm enters the competition stage, and the update strategy of the individual position in the (t + 1) - th generation is as follows:

[0050]

[0051] where represents a random individual in the j - th dimension population in the t - th generation, and the meaning of X shade is the same as above; S3.5. When temp ≤ 30, the multi - objective crayfish algorithm enters the foraging stage, and the food intake p of the crayfish is calculated as follows:

[0052]

[0053] where C1 and σ are parameters to control the food intake of the crayfish, and μ is the environmental temperature most suitable for the crayfish to eat;

[0054] The food size Q is expressed as:

[0055] Q = C3 × rand × (fitness i / fitness food )

[0056] Among them, C3 is the food factor, representing the largest food, set as the constant 3, fitness i represents the fitness value of the i-th crayfish, fitness food represents the fitness value of the food position. At this time, the expression of the food position is:

[0057] X food = X G

[0058] When Q > (C3 + 1) / 2, that is, the food is too large, indicating that the gap between the crayfish position and the optimal solution is obvious. At this time, the crayfish will tear the food, and the food position is updated as:

[0059]

[0060] The crayfish position update formula is as follows:

[0061]

[0062] When Q ≤ (C3 + 1) / 2, that is, the food size is appropriate, the crayfish will directly forage, and the position is updated as follows:

[0063]

[0064] S3.6. Merge the populations of the t + 1 generation obtained by updating different fitness functions, calculate the fitness function values of individuals, obtain the Pareto solution set by non-dominated sorting, and finally calculate the crowding degree to sort the population individuals, and take the top N individuals as the population of the t + 1 generation;

[0065] S3.7. Judge whether the current iteration times have reached the maximum iteration times T. If so, the algorithm stops iterating and outputs the optimal parameter combination calculated based on the crowding degree. Otherwise, return to S3.2 to continue the optimization.

[0066] As a preferred technical solution of the present invention: in the step S4, after the algorithm iteration terminates, the optimal parameter combination obtained is used as parameters to input into the variational mode decomposition model, and the optimal variational mode decomposition result IMF signal is obtained by taking the number of modes K and the penalty factor α of the output optimal parameter combination.

[0067] Compared with the prior art, a variational mode decomposition method based on a multi-objective crayfish algorithm of the present invention improves the original single-objective crayfish algorithm, introduces non-dominated sorting to comprehensively evaluate multiple optimization objectives, and introduces a Pareto optimal front based on crowding degree calculation to determine the population update strategy, solving the limitation that the original algorithm cannot be applied to multi-objective optimization problems, greatly expanding the applicable scope of the original algorithm. The improved multi-objective crayfish algorithm is used to optimize the parameter decomposition number K and penalty factor α of variational mode decomposition, introduces spectral kurtosis and KL divergence as fitness functions for evaluating the results of variational mode decomposition, achieves good results, solves the problem that the parameters of variational mode decomposition need to be repeatedly adjusted relying on experience, and improves the effect and operability of the variational mode decomposition algorithm.

[0068] The present invention discloses a variational mode decomposition method based on a multi-objective crayfish algorithm, which overcomes the deficiencies of existing algorithms. In variational mode decomposition (VMD), the optimal mode number K and penalty factor α are selected to achieve the optimal variational mode decomposition of signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is the algorithm flowchart of a variational mode decomposition method based on a multi-objective crayfish algorithm of the present invention;

[0070] Figure 2 is the Pareto optimal front of the optimization result of the multi-objective crayfish algorithm provided by the present invention;

[0071] Figure 3 is the comparison of the variational mode decomposition effects before and after optimization provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] The present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.

[0073] Embodiment 1

[0074] As Figure 1 shown, a variational mode decomposition method based on a multi-objective crayfish algorithm of the present invention includes the following specific steps:

[0075] S1: Construct an original variational mode decomposition model, and determine the parameter design space and optimization objective function.

[0076] Further, in the S1, the cardiac electrical signal is obtained as the input, and the variational mode decomposition design parameters are selected as the mode number K and the penalty factor α. In this example, the mode number design space is determined as K ∈ [3, 8] ∩ Z, and the penalty factor design space is α ∈ [500, 5000] ∩ R.

[0077] The optimized objective function can be further calculated based on the decomposed modal components and is selected as the spectral kurtosis (SK) and the KL divergence. The formula for calculating the spectral kurtosis is as follows:

[0078]

[0079] where X f is the Fourier transform of the signal at frequency f, and <·> represents calculating the expected value of the sequence. The formula for introducing the KL divergence is calculated as follows:

[0080]

[0081] where p(x) and q(x) represent the moduli of the Hilbert-Huang transform of the original signal and the characteristic modal signal at point x respectively. In summary, the mathematical expression of this optimization problem is:

[0082]

[0083] s.t. x1 = K ∈ [3, 8] ∩ Z

[0084] x2 = α ∈ [500, 5000] ∩ R.

[0085] The KL divergence, also known as the Kullback-Leibler divergence, is also called relative entropy or information divergence, and is an asymmetric measure of the difference between two probability distributions.

[0086] S2: Improve the multi-objective crayfish algorithm. The improvement points include: (1) introducing non-dominated sorting to comprehensively evaluate multiple optimization objectives; (2) introducing the Pareto optimal front based on crowding degree calculation to determine the population update strategy.

[0087] Furthermore, in the step S2, the specific steps for improving the multi-objective crayfish algorithm are as follows:

[0088] S2.1, comprehensively evaluate multiple optimization objectives based on non-dominated sorting. If each individual in the set P has r (r ≥ 2) evaluation functions (objective functions) f i (x) (i = 1, 2,..., r), where the dominance relationship between individuals is defined as: If f i (x1) ≤ f i (x2), and make f l (x1) < f l (x2), it is said that x1 dominates x2; the non-correlation relationship between individuals is defined as: If there is no dominance relationship between x1 and x2, then x1 and x2 are not relevant. If x1 ∈ P, x2 ∈ P, and x1 ≠ x2, then x1 is said to dominate in, and the set composed of such x2 is called the maximum non-dominated set. Based on the optimization function SK f (x) and D KL (x) continuously searches for individuals with dominance relationships within the population, continuously constructs non-dominated sets, and finally finds the Pareto optimal solution set, that is, each solution in it cannot be dominated by other solutions, as Figure 2 shown.

[0089] S2.2, sort the obtained Pareto solution set based on crowding degree calculation. The crowding degree is defined as:

[0090]

[0091] where f(x j_i+1 ) and f(x j_i-1 ) represent two fitness values adjacent to the i-th point in the j-th rank respectively, and f j_max and f j_min represent the maximum and minimum fitness values in the j-th rank respectively. After sorting the Pareto solution set from largest to smallest according to the crowding degree value, the population update strategy is to take the first N individuals as the next iteration object.

[0092] S3: Establish a mathematical model of the multi-objective crayfish algorithm and iteratively calculate to obtain the optimal parameter combination.

[0093] Furthermore, in the above S3, the specific steps for establishing a mathematical model of the multi-objective crayfish algorithm and iteratively calculating to obtain the optimal parameter combination are as follows:

[0094] S3.1, given parameters such as the maximum number of iterations T, population size N, individual dimension dim, and upper and lower bounds ub and lb, for the optimization objective F, initialize the population X = [X1, X2,... X N , where the individual X i，j is initialized as follows:

[0095] X i，j = lb j +(ub j - lb j )×rand

[0096] where lb j , ub j represent the upper and lower bounds of the j-th dimension respectively, and rand represents a random number between (0, 1]. If the j-th dimension is an integer, then the result is rounded.

[0097] According to the initial position parameters of crayfish, the original signal S is subjected to variational mode decomposition. The initial positions of individuals in the crayfish population and the fitness values ​​under different objective functions are calculated based on the decomposition result IMF signal, and the individuals with the smallest fitness function are recorded as the best individuals.

[0098] S3.2, according to the living habits of crayfish, change the ambient temperature to control the algorithm to enter different stages, such as

[0099] As shown below:

[0100] temp=rand×15+20

[0101] Where temp is the temperature of the environment where the crayfish is located, and rand represents a random number between (0, 1]. For different fitness functions, steps S3-S5 are repeated respectively.

[0102] S3.3, when temp>30 and rand<0.5, the multi-objective crayfish algorithm enters the summer vacation stage. The update strategy of individual positions in generation t+1 is as follows:

[0103]

[0104] X shade =(X G +X L ) / 2

[0105] Where C2 is the decreasing coefficient, X shade is the cave location, X G is the value of the best position of the individual crayfish since the algorithm iteration, X L is the value of the best individual position of the crayfish population in the current population.

[0106] S3.4, when temp>30 and rand≥0.5, the multi-objective crayfish algorithm enters the competition phase. The update strategy of the individual position in the t+1 generation is as follows:

[0107]

[0108] in represents a random individual in the j-th dimension population of generation t, X shade The meaning is the same as above.

[0109] S3.5, when temp≤30, the multi-objective crayfish algorithm enters the foraging stage. The crayfish's food intake p is calculated as follows:

[0110]

[0111] Among them, C1 and σ are parameters that control the amount of food eaten by crayfish, and μ is the environmental temperature most suitable for crayfish to eat.

[0112] The food size Q is expressed as:

[0113] Q = C3 × rand × (fitness i / fitness food )

[0114] Where C3 is the food factor, representing the largest food, and is set as the constant 3. fitness i represents the fitness value of the i-th crayfish, and fitness food represents the fitness value of the food position. At this time, the expression of the food position is:

[0115] X food = X G

[0116] When Q > (d3 + 1) / 2, that is, the food is too large, indicating that the gap between the crayfish position and the optimal solution is obvious. At this time, the crayfish will tear the food, and the food position is updated as:

[0117]

[0118] The crayfish position update formula is as follows:

[0119]

[0120] When Q ≤ (C3 + 1) / 2, that is, the food size is appropriate, the crayfish will directly forage, and the position is updated as follows:

[0121]

[0122] S3.6. Merge the populations of the t+1 generation obtained by updating different fitness functions, calculate the fitness function values of individuals, obtain the Pareto solution set by non-dominated sorting, and finally calculate the crowding degree to sort the population individuals, and take the top N individuals as the population of the t+1 generation.

[0123] S3.7. Judge whether the current iteration number reaches the maximum iteration number T. If so, the algorithm stops iterating and outputs the optimal parameter combination calculated based on the crowding degree. Otherwise, return to S2 to continue the optimization.

[0124] S4: Input the optimal parameter combination into the variational mode decomposition model to obtain the optimal variational mode decomposition result, and verify the superiority of the variational mode decomposition method based on the multi-objective crayfish algorithm.

[0125] Furthermore, in the step S4, after the algorithm iteration terminates, the optimal parameter combination (K = 6, α = 1460) is obtained, as Figure 3As shown in Fig. b, the optimal parameter combination modal number K and penalty factor α of the output are used as parameters to input into the variational mode decomposition model to obtain the optimal variational mode decomposition result IMF signal. A moderate parameter combination of K and α (K = 5, α = 2000) is selected for reference and comparison. As Figure 3 shown in Fig. a, it can be seen that the optimized IMF components have more moderate frequencies and bandwidths, the residual after decomposition is smaller, and the distribution is more uniform. Calculate their fitness functions respectively as shown in Table 1. It can be seen that the optimized decomposition effect is better than that before optimization under the evaluation of the two fitness functions, verifying the superiority of the variational mode decomposition method based on the multi-objective crayfish algorithm proposed in this paper.

[0126] Table 1 Comparison of fitness values before and after optimization

[0127]

[0128] As shown in the above specific implementation methods and experimental effects, a variational mode decomposition method based on a multi-objective crayfish algorithm proposed by the present invention improves the original single-objective crayfish algorithm, introduces non-dominated sorting to comprehensively evaluate multiple optimization objectives; and introduces the Pareto optimal front based on crowding degree calculation to determine the population update strategy, solving the limitation that the original algorithm cannot be applied to multi-objective optimization problems and greatly expanding the applicable scope of the original algorithm. The improved multi-objective crayfish algorithm is used to optimize the parameter decomposition number K and penalty factor α of the variational mode decomposition, and the spectral kurtosis and KL divergence are introduced as fitness functions to evaluate the variational mode decomposition results, achieving good results, solving the problem that the parameters of the variational mode decomposition need to be repeatedly adjusted relying on experience, and improving the effect and operability of the variational mode decomposition algorithm.

[0129] A variational mode decomposition method based on a multi-objective crayfish algorithm of the present invention belongs to the technical field of signal processing and optimization. The specific steps are as follows: S1: Construct an original variational mode decomposition model, and determine the parameter design space and optimization objective function. S2: Improve the multi-objective crayfish algorithm. The improvement points include: S2.1, introduce non-dominated sorting to comprehensively evaluate multiple optimization objectives; S2.2, introduce the Pareto optimal front based on crowding degree calculation to determine the population update strategy. S3: Establish a mathematical model of the multi-objective crayfish algorithm, and iteratively calculate to obtain the optimal parameter combination. S4: Input the optimal parameter combination into the variational mode decomposition model to obtain the optimal variational mode decomposition result, and verify the superiority of a variational mode decomposition based on a multi-objective crayfish algorithm.

[0130] The present invention solves the limitation that the original crayfish algorithm cannot be applied to multi-objective optimization problems, greatly expands the applicable scope of the original algorithm, and applies the improved multi-objective crayfish algorithm to optimize the key parameters of variational mode decomposition, solves the problem that the parameters of variational mode decomposition need to be repeatedly adjusted depending on experience, and improves the effect and operability of the variational mode decomposition algorithm.

[0131] The above specific embodiments are used to explain the present invention, which are only the preferred embodiments of the present invention, rather than limiting the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A variational mode decomposition method based on a multi-objective crayfish algorithm, characterized in that: The following steps are involved: S1, construct the original variational mode decomposition model, determine the parameter design space and optimize the objective function; S2, improved multi-objective crayfish algorithm, including: S2.1, introducing non-dominated sorting to comprehensively evaluate multiple optimization objectives; S2.2, introducing the Pareto optimal frontier based on crowding calculation to determine the population update strategy; S3, establish a mathematical model of the multi-objective crayfish algorithm, and iterate to obtain the optimal parameter combination; S4, input the optimal parameter combination into the variational mode decomposition model to obtain the optimal variational mode decomposition result, and verify the superiority of variational mode decomposition based on the multi-objective crayfish algorithm; In step S1, a cardiac electrical signal is obtained as input, and the variational modal decomposition design parameters are selected as the modal number K and the penalty factor α. The modal number design space is determined to be K∈[3,8]∩Z, and the penalty factor design space is α∈[500,5000]∩R.

2. The variational mode decomposition method based on the multi-objective crayfish algorithm according to claim 1, characterized in that: In step S1, the optimization objective function is calculated based on the modal components obtained by decomposition, and is selected as the spectral kurtosis SK and KL divergence. The spectral kurtosis calculation formula is as follows: Where X f is the Fourier transform of the signal at frequency f, <|X(f)| 4 > refers to the expected value of the fourth power of the modulus of the Fourier transform of the signal at frequency f, <|X(f)| 2 > refers to the expected value of the square of the modulus of the Fourier transform of the signal at frequency f. The KL divergence formula is introduced and calculated as follows: Where p(x) and q(x) represent the modulus of the Hilbert-Huang transform of the original signal and the characteristic mode signal at point x, respectively. p and q are two discrete probability distributions. Xi represents the i-th event. p(x) i ) and q(xi) are the probabilities of event xi in distribution p and q respectively.

3. The variational mode decomposition method based on the multi-objective crayfish algorithm according to claim 1, characterized in that: In S2, the specific steps of improving the multi-objective crayfish algorithm are as follows: S2.1, Comprehensively evaluate each optimization objective function based on non-dominated sorting: If each individual in the set P has r evaluation functions f i (x)(i=1,2,…,r), r≥2, where the dominance relationship between individuals is defined as: like f i (x1)≤f i (x2), and Make l (x1)<f l (x2), x1 is said to dominate x2; The uncorrelated relationship between individuals is defined as: If there is no domination relationship between x1 and x2, x1 and x2 are unrelated. If x1∈P, x2∈P, x1≠x2, then x1 is said to be dominated in P, and the set consisting of such x2 is called the maximum non-dominated set; Based on the optimization function SK f (x) and D KL (x) Continuously search for individuals with dominant relationships within the population, continuously construct non-dominated sets, and eventually find the Pareto optimal solution set, that is, each solution cannot be dominated by other solutions; S2.2, sort the obtained Pareto solution set based on the crowding degree calculation, where the crowding degree is defined as: Where f(x j_i+1 ) and f(x j_i-1 ) represent the two fitness values ​​adjacent to the i-th point in the j-th level, f i_max and f i_min They represent the maximum and minimum values ​​of fitness in the jth level respectively. After sorting the Pareto solution set from large to small according to the crowding value, the population update strategy is to take the first N individuals as the next iteration object.

4. The variational mode decomposition method based on the multi-objective crayfish algorithm according to claim 1, characterized in that: The specific steps in S3 include: S3.1, given the maximum number of iterations T, population size N, individual dimension dim and upper and lower bounds ub, lb and other parameters, for the optimization target F, initialize the population X = [X1, X2, ...X N ], where individual X i，j Initialization looks like this: X i，j =lb j +(ub j -lb j )×rand where lb j ,ub j They represent the upper and lower bounds of the j-th dimension respectively, rand represents a random number between (0, 1], and if the j-th dimension is an integer, the result is rounded; According to the initial position parameters of the crayfish, the original signal S is subjected to variational mode decomposition. Based on the decomposition result IMF signal, the initial position of the crayfish population individuals and the fitness values ​​under different objective functions are calculated, and the individuals with the smallest fitness function are recorded as the best individuals. S3.2, according to the living habits of crayfish, change the ambient temperature to control the algorithm to enter different stages, as shown below: temp=rand×15+20 Where temp is the temperature of the environment where the crayfish is located, rand represents a random number between (0, 1]. For different fitness functions, repeat steps S3.3-S3.5 respectively; S3.3, when temp>30 and rand<0.5, the multi-objective crayfish algorithm enters the summer vacation stage, and the update strategy of the individual position in the t+1 generation is as follows: X shade =(X G +X L ) / 2 Where C2 is the decreasing coefficient, X shade is the cave location, X G is the value of the best position of the individual crayfish since the algorithm iteration, X L is the value of the best individual position of the crayfish population in the current population; S3.4, when temp>30 and rand≥0.5, the multi-objective crayfish algorithm enters the competition stage, and the update strategy of the individual position in the t+1 generation is as follows: in represents a random individual in the j-th dimension population of generation t, X shade The meaning is the same as above; S3.5, when temp≤30, the multi-objective crayfish algorithm enters the foraging stage, and the crayfish's food intake p is calculated as follows: Among them, C1 and σ are parameters that control the amount of food that crayfish eat, and μ is the most suitable environmental temperature for crayfish to eat; The food size Q is expressed as: Q=C3×rand×(fitness i / fitness food ) C3 is the food factor, which represents the maximum food, and is set to a constant of 3. i Represents the fitness value of the i-th crayfish, fitness food Represents the fitness value of the food position. The expression of the food position is: X food =X G When Q>(C3+1) / 2, the food is too large, indicating that the crayfish position is significantly different from the optimal solution. At this time, the crayfish will tear the food, and the food position is updated to: The formula for updating the crayfish position is as follows: When Q≤(C3+1) / 2, that is, the food size is appropriate, the crayfish will go directly to forage, and the position update is as follows: S3.6, merge the t+1 generation populations obtained by updating different fitness functions, calculate the fitness function values ​​of the individuals, use non-dominated sorting to obtain the Pareto solution set, and finally calculate the crowding degree to sort the individuals in the population, and take the first N individuals as the t+1 generation population; S3.7, determine whether the current number of iterations reaches the maximum number of iterations T. If so, the algorithm stops iterating and outputs the optimal parameter combination based on the congestion calculation. Otherwise, return to S3.2 to continue optimizing.

5. The variational mode decomposition method based on the multi-objective crayfish algorithm according to claim 1, characterized in that: In step S4, after the algorithm iteration is terminated, the optimal parameter combination is obtained, and the output optimal parameter combination mode number K and penalty factor α are input as parameters into the variational mode decomposition model to obtain the optimal variational mode decomposition result IMF signal.

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