Grey wolf optimizer modeling method based on multi-strategy combination

Abstract

The invention discloses a grey wolf optimizer modeling method based on multi-strategy combination. The grey wolf optimizer modeling method comprises the following steps: 1) building a target parameter prediction model; 2) optimizing the target parameter prediction model by using a grey wolf optimizer based on multi-strategy combination; and 3) realizing prediction of target parameters by using the optimized target parameter prediction model. The invention provides a multi-strategy optimized grey wolf optimizer MGWO, and the algorithm adopts multi-strategy optimization of chaotic mapping, double nonlinear convergence factors, adaptive weight coefficients, elitist retention and introduction of AO and WOA search prey mechanisms at the same time, and achieves effective balance of the algorithm in global exploration and local mining and utilization.

Description

Technical Field

[0001] The present invention relates to the field of optimization, and specifically to a modeling method of a gray wolf optimizer based on multi-strategy combination. Background Technique

[0002] Optimization problems are widely applied in many fields such as operations research, information science, engineering design, and function optimization. Generally speaking, there are two major categories of methods to solve such problems: traditional optimization methods and meta-heuristic methods. Traditional optimization methods are easy to implement, but time-consuming, and require the optimization problem to be differentiable. Meta-heuristic algorithms (Chu et al., 2011) can not only effectively solve optimization problems, but also have advantages such as flexibility, easy implementation, global search ability, and the ability to get rid of local optima.

[0003] The gray wolf algorithm GWO is a swarm intelligence optimization algorithm inspired by the social behavior and hunting strategies of gray wolves in nature, and solves complex optimization problems by simulating the leadership hierarchy and cooperative hunting mechanism in the gray wolf swarm. It has the advantages of easy implementation, few control parameters to be adjusted, and high search accuracy, and has been widely applied.

[0004] However, the no free lunch theorem states that no single optimization algorithm can be used or developed to be suitable for all optimization problems, and there is still room to enhance the development and exploration capabilities of the performance of the traditional gray wolf algorithm. Summary of the Invention

[0005] The purpose of the present invention is to provide a modeling method of a gray wolf optimizer based on multi-strategy combination, including the following steps:

[0006] 1) Build a target parameter prediction model;

[0007] 2) Optimize the target parameter prediction model by using a gray wolf optimizer based on multi-strategy combination, and the steps include:

[0008] 2.1) Generate the initial distribution of the gray wolf population by using Tent mapping;

[0009] 2.2) Set the fitness function of the gray wolf population;

[0010] 2.3) Calculate the fitness values of the gray wolf population, and determine the positions of α, β, and δ wolves according to the fitness values;

[0011] 2.4) Update the positions of the remaining gray wolf individuals according to the positions of α, β, and δ wolves;

[0012] 2.5) Execute the search action to determine the optimal solution;

[0013] 2.6) Update the gray wolf population through the elite retention strategy;

[0014] 2.7) Determine whether the iteration termination condition is reached. If so, output the optimal solution and proceed to step 3); otherwise, return to step 2.3).

[0015] 3) Use the optimized target parameter prediction model to implement the prediction of the target parameter.

[0016] Furthermore, the Tent mapping is as follows:

[0017]

[0018] where x i and x i+1 are the positions of the i-th gray wolf before and after the mapping.

[0019] Furthermore, the gray wolf population includes wolves of four ranks: α, β, δ, and ω; among them, α, β, and δ wolves are the three gray wolf individuals with the strongest capabilities.

[0020] Furthermore, the search tendency of the gray wolf population is determined by the coefficient vectors A1 and A2;

[0021] When the coefficient vector |A1| > 1 or |A2| > 1, the search tendency of the gray wolf population is global search; when the coefficient vectors |A1| ≤ 1 and |A2| ≤ 1, the search tendency of the gray wolf population is local search;

[0022] where the coefficient vectors A1 and A2 are as follows:

[0023]

[0024] where r1 represents a random number between [0, 1]; α1 and α2 are non-linear convergence factors; t is the current iteration number; and Max_iter is the maximum number of iterations.

[0025] Furthermore, the fitness function of the gray wolf population is the training error of the target parameter prediction model.

[0026] Furthermore, in step 2.4), the positions X i (t + 1) of the remaining gray wolf individuals are as follows:

[0027]

[0028] where w1(t), w2(t), and w3(t) are weights. X α (t), X β (t), and X δ (t) are the positions of α, β, and δ wolves.

[0029] Furthermore, in step 2.5), when performing the search action, ω wolves are divided into three groups according to the set probability. The first group of ω wolves follows the α, β, and δ wolves to search for prey. The second group of ω wolves uses the eagle exploration mechanism to search for prey. The third group of ω wolves uses the whale search mechanism to search for prey;

[0030] Among them, the eagle exploration mechanism is as follows:

[0031] X i (t + 1) = X α (t) + (X i (t) - X α (t)) × Levy(D) (9)

[0032]

[0033] Among them, t represents the current iteration number, X i (t + 1) is the solution of the next iteration, X α (t) is the current optimal solution, D is the dimensional space, Levy(D) is the flight distribution function, s and β are constants; X i (t) is the solution of the current iteration; v is a random number between 0 and 1, and u follows a normal distribution with a mean of 0 and a variance of σ;

[0034] The whale search mechanism is as follows:

[0035] X i (t + 1) = D × e bl × cos(2πl) + X α (t) (12)

[0036] D = |X a (t) - X i (t)| (13)

[0037] Among them, b is a constant coefficient defining the spiral hunting; l is a random number in [-1, 1].

[0038] Furthermore, the elitist retention strategy is as follows:

[0039]

[0040] Among them, X new (t) is the solution that enters the next iteration with the population after comparison and selection, X worst (t) is the solution with the worst fitness value at the end of the t-th iteration, X tent (t) is the solution newly generated by the Tent mapping. F(X worst (t)), F(X tent (t)) are the fitness values of the solutions X worst (t), Xtent (t) corresponding fitness value.

[0041] Furthermore, the target parameter prediction model is a device fault detection model;

[0042] The device fault detection model is a convolutional neural network based on maximum correlation kurtosis deconvolution. The optimization parameters during training include the length, period, and shift number of the filter;

[0043] The input of the device fault detection model is the impact signal of the inner ring of the fan bearing, and the output is the device state, including normal device and device fault.

[0044] Furthermore, the target parameter prediction model is a wind speed sequence prediction model;

[0045] The wind speed sequence prediction model is a bidirectional long short-term memory network. The optimization parameters include the number of bilstm_layers hidden layers and the number of bilstm_neurons neurons of the bidirectional long short-term memory network;

[0046] The input of the wind speed sequence prediction model is the wind speed sequence in the past t1 time period, and the output is the wind speed sequence in the future t2 time period.

[0047] The technical effect of the present invention is beyond doubt. The present invention proposes a multi-strategy optimized grey wolf optimizer MGWO. This algorithm uses multi-strategy optimization of chaotic mapping, double nonlinear convergence factor, adaptive weight coefficient, elite retention, and simultaneously introduces the AO and WOA search prey mechanisms to achieve an effective balance of the algorithm in global exploration, local exploitation, and utilization. Description of the Drawings

[0048] Figure 1 (a) is the grey wolf rank and grey wolf position update mechanism; Figure 1 (b) is the grey wolf predation hunting process;

[0049] Figure 2 is the algorithm flow chart of the multi-strategy combined grey wolf optimizer;

[0050] Figure 3 is the parameter value of the convergence factor under 1000 iterations;

[0051] Figure 4 is the comparison of three common chaotic mappings;

[0052] Figure 5 is the convergence curve of each algorithm on different functions;

[0053] Figure 6 is the Friedman test result;

[0054] Figure 7For the classification results of the standard ELM model and the MGWO-ELM model;

[0055] Figure 8 For the fitness curve of the algorithm;

[0056] Figure 9 For the time-domain waveform of the fault simulation signal;

[0057] Figure 10 (a)- Figure 10 (b) For the envelope spectrum of the fault simulation signal and the envelope spectrum of the best IMF component without parameter optimization;

[0058] Figure 11 For the fitness curve of the improved algorithm MCKD and the envelope spectrum after deconvolution of the optimized best IMF component;

[0059] Figure 12 For the fitting curve of the original signal and the predicted signal. Specific implementation manner

[0060] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above-mentioned technical idea of the present invention, various substitutions and changes made according to ordinary technical knowledge and customary means in the art shall be included within the protection scope of the present invention.

[0061] Embodiment 1:

[0062] See Figures 1 to 12 , the gray wolf optimizer modeling method based on multi-strategy combination, includes the following steps:

[0063] 1) Build a target parameter prediction model;

[0064] 2) Optimize the target parameter prediction model by using the gray wolf optimizer based on multi-strategy combination, and the steps include:

[0065] 2.1) Generate the initial distribution of the gray wolf population by using Tent mapping;

[0066] 2.2) Set the fitness function of the gray wolf population;

[0067] 2.3) Calculate the fitness values of the gray wolf population, and determine the positions of α, β, and δ wolves according to the fitness values;

[0068] 2.4) Update the positions of the remaining gray wolf individuals according to the positions of α, β, and δ wolves;

[0069] 2.5) Perform search actions to determine the optimal solution;

[0070] 2.6) Update the gray wolf population through the elite retention strategy;

[0071] 2.7) Determine whether the iteration termination condition is reached. If so, output the optimal solution and proceed to step 3); otherwise, return to step 2.3).

[0072] 3) Use the optimized target parameter prediction model to predict the target parameters.

[0073] The Tent mapping is as follows:

[0074]

[0075] where x i and x i+1 are the positions of the i-th gray wolf before and after the mapping, respectively.

[0076] The gray wolf population includes wolves of four ranks: α, β, δ, and ω. Among them, α, β, and δ wolves are the three gray wolf individuals with the strongest capabilities.

[0077] The search tendency of the gray wolf population is determined by the coefficient vectors A1 and A2;

[0078] When the coefficient vector |A1| > 1 or |A2| > 1, the search tendency of the gray wolf population is global search; when the coefficient vector |A1| ≤ 1 and |A2| ≤ 1, the search tendency of the gray wolf population is local search;

[0079] Among them, the coefficient vectors A1 and A2 are as follows:

[0080]

[0081] where r1 represents a random number between [0, 1]; α1 and α2 are non-linear convergence factors; t is the current iteration number; and Max_iter is the maximum iteration number.

[0082] The fitness function of the gray wolf population is the training error of the target parameter prediction model.

[0083] In step 2.4), the positions X i (t + 1) of the remaining gray wolf individuals are as follows:

[0084]

[0085] where w1(t), w2(t), and w3(t) are weights. X α (t), X β (t), and X δ (t) are the positions of α, β, and δ wolves.

[0086] In step 2.5), when performing the search action, ω wolves are divided into three groups according to the set probability. The first group of ω wolves follows the α, β, and δ wolves to search for prey. The second group of ω wolves uses the eagle exploration mechanism to search for prey. The third group of ω wolves uses the whale search mechanism to search for prey. The division method is as follows: the wolf pack is divided into the first group of wolves with a probability of 0.2, and the unassigned wolves are then divided into the second and third groups of wolves with a probability of 0.5.

[0087] Among them, the eagle exploration mechanism is as follows:

[0088] X i (t + 1) = X α (t) + (X i (t) - X α (t)) × Levy(D) (9)

[0089]

[0090] Among them, t represents the current iteration number, X i (t + 1) is the solution for the next iteration, X α (t) is the current optimal solution, D is the dimensional space, Levy(D) is the flight distribution function, s and β are constants; X i (t) is the solution for the current iteration; v is a random number between 0 and 1, and u follows a normal distribution with a mean of 0 and a variance of σ;

[0091] The whale search mechanism is as follows:

[0092] X i (t + 1) = D × e bl × cos(2πl) + X α (t) (12)

[0093] D = |X a (t) - X i (t)| (13)

[0094] Among them, b is a constant coefficient defining spiral hunting; l is a random number in [-1, 1].

[0095] The elite retention strategy is as follows:

[0096]

[0097] Among them, X new (t) is the solution that enters the next iteration with the population after comparison and selection, X worst (t) is the solution with the worst fitness value at the end of the t-th iteration, X tent (t) is the solution newly generated by the Tent mapping. F(X worst (t)), F(Xtent (t)) is the solution X worst (t), X tent (t) corresponding fitness value.

[0098] The target parameter prediction model is a device fault detection model;

[0099] The device fault detection model is a convolutional neural network based on maximum correlation kurtosis deconvolution, and the optimization parameters during training include the length, period, and shift number of the filter;

[0100] The input of the device fault detection model is the impact signal of the inner ring of the fan bearing, and the output is the device state, including normal device and device fault.

[0101] Specifically, taking the impact signal generated by the inner ring fault of the fan bearing as the input, and using a multi-strategy algorithm to optimize the three parameters of [L (length of the filter), T (period), M (shift number)] to ensure finding the best MCKD parameters.

[0102] Or, the target parameter prediction model is a wind speed sequence prediction model;

[0103] The wind speed sequence prediction model is a bidirectional long short-term memory network, and the optimization parameters include the number of bilstm_layers hidden layers and the number of bilstm_neurons neurons of the bidirectional long short-term memory network;

[0104] The input of the wind speed sequence prediction model is the wind speed sequence in the past t1 time period, and the output is the wind speed sequence in the future t2 time period.

[0105] Example 2:

[0106] A modeling method of a grey wolf optimizer based on multi-strategy combination includes the following steps:

[0107] 1) Build a target parameter prediction model;

[0108] 2) Use a grey wolf optimizer based on multi-strategy combination to optimize the target parameter prediction model, and the steps include:

[0109] 2.1) Generate the initial distribution of the grey wolf population using Tent mapping;

[0110] 2.2) Set the fitness function of the grey wolf population;

[0111] 2.3) Calculate the fitness values of the grey wolf population, and determine the positions of α, β, δ wolves according to the fitness values;

[0112] 2.4) Update the positions of the remaining grey wolf individuals according to the positions of α, β, δ wolves;

[0113] 2.5) Perform a search action to determine the optimal solution;

[0114] 2.6) Update the gray wolf population through the elitist retention strategy;

[0115] 2.7) Determine whether the iteration termination condition is reached. If so, output the optimal solution and proceed to step 3). Otherwise, return to step 2.3);

[0116] 3) Use the optimized target parameter prediction model to achieve the prediction of the target parameter.

[0117] Example 3:

[0118] A gray wolf optimizer modeling method based on a multi-strategy combination, the technical content is the same as that of Example 2. Further, the Tent mapping is as follows:

[0119]

[0120] In the formula, x i , x i+1 are the positions of the i-th gray wolf before and after the mapping.

[0121] Example 4:

[0122] A gray wolf optimizer modeling method based on a multi-strategy combination, the technical content is the same as any one of Examples 2-3. Further, the gray wolf population includes four levels of wolves: α, β, δ, and ω; among them, the α, β, and δ wolves are the three gray wolf individuals with the strongest capabilities.

[0123] Example 5:

[0124] A gray wolf optimizer modeling method based on a multi-strategy combination, the technical content is the same as any one of Examples 2-4. Further, the search tendency of the gray wolf population is determined by the coefficient vectors A1 and A2;

[0125] When the coefficient vector |A1| > 1 or |A2| > 1, the search tendency of the gray wolf population is global search; when the coefficient vector |A1| ≤ 1 and |A2| ≤ 1, the search tendency of the gray wolf population is local search;

[0126] Among them, the coefficient vectors A1 and A2 are as follows:

[0127]

[0128] In the formula, r1 represents a random number between [0,1]; α1, α2 are non-linear convergence factors; t is the current iteration number; Max_iter is the maximum iteration number.

[0129] Example 6:

[0130] Grey Wolf Optimizer Modeling Method Based on Multi-Strategy Combination, the technical content is the same as any one of Embodiments 2-5. Further, the fitness function of the grey wolf population is the training error of the target parameter prediction model.

[0131] Embodiment 7:

[0132] Grey Wolf Optimizer Modeling Method Based on Multi-Strategy Combination, the technical content is the same as any one of Embodiments 2-6. Further, in step 2.4), the positions of the remaining grey wolf individuals are as follows:

[0133]

[0134] In the formula, w1(t), w2(t), and w3(t) are weights.

[0135] Embodiment 8:

[0136] Grey Wolf Optimizer Modeling Method Based on Multi-Strategy Combination, the technical content is the same as any one of Embodiments 2-7. Further, in step 2.5), when performing the search action, the ω wolves are divided into three groups according to a set probability. The first group of ω wolves follows the α, β, and δ wolves to search for prey. The second group of ω wolves uses the eagle exploration mechanism to search for prey. The third group of ω wolves uses the whale search mechanism to search for prey;

[0137] Among them, the eagle exploration mechanism is as follows:

[0138] X i (t + 1) = X α (t) + (X i (t) - X α (t)) × Levy(D) (9)

[0139]

[0140]

[0141] Among them, t represents the current iteration number, X i (t + 1) is the solution of the next iteration, X α (t) is the current optimal solution, D is the dimensional space, Levy(D) is the flight distribution function, s and β are constants;

[0142] v is a random number between 0 and 1, and u follows a normal distribution with a mean of 0 and a variance of σ;

[0143] The whale search mechanism is as follows:

[0144] X i (t + 1) = D × e bl × cos(2πl) + X α (t) (12)

[0145] D = |X α (t) - X i (t)| (13)

[0146] Among them, b is a constant coefficient defining spiral hunting; l is a random number in [-1, 1].

[0147] Example 9:

[0148] A modeling method of a gray wolf optimizer based on multi-strategy combination, the technical content is the same as any one of Examples 2 - 8. Further, the elite retention strategy is as follows:

[0149]

[0150] Among them, X new (t) is the solution that enters the next iteration with the population after comparison and selection, and X worst (t) is the solution with the worst fitness value at the end of the t-th iteration, and X tent (t) is the solution newly generated by Tent mapping.

[0151] Example 10:

[0152] A modeling method of a gray wolf optimizer based on multi-strategy combination, the technical content is the same as any one of Examples 2 - 9. Further, the target parameter prediction model is a device fault detection model;

[0153] The device fault detection model is a convolutional neural network based on maximum correlated kurtosis deconvolution. The optimization parameters during training include the length, period, and shift number of the filter;

[0154] The input of the device fault detection model is the impact signal of the inner ring of the fan bearing, and the output is the device state, including normal device and device fault.

[0155] Specifically, taking the impact signal generated by the inner ring fault of the fan bearing as the input, and using the multi-strategy algorithm to optimize the three parameters of [L (length of the filter), T (period), M (shift number)] to ensure finding the best MCKD parameters.

[0156] Example 11:

[0157] A modeling method of a gray wolf optimizer based on multi-strategy combination, the technical content is the same as any one of Examples 2 - 9. Further, the target parameter prediction model is a wind speed sequence prediction model;

[0158] The wind speed sequence prediction model is a bidirectional long short-term memory network. The optimization parameters include the number of bilstm_layers hidden layers and the number of bilstm_neurons neurons of the bidirectional long short-term memory network;

[0159] The input of the wind speed sequence prediction model is the wind speed sequence in the past t1 time period, and the output is the wind speed sequence in the future t2 time period.

[0160] Example 11:

[0161] The grey wolf optimizer modeling method based on multi-strategy combination is as follows:

[0162] 1. Grey wolf algorithm

[0163] The grey wolf algorithm that simulates the wolf pack divides the population into four social ranks, including four ranks of wolves: α, β, δ, and ω. As shown in Figure 1 (a), where the α wolf is the leader, mainly responsible for major decisions such as leading, hunting, and food distribution. The β wolf assists the α wolf in management. The δ wolf is a subordinate grey wolf of the α and β wolves, responsible for scouting and hunting, etc. The ω wolf has the lowest status.

[0164] In the algorithm, each grey wolf in the wolf pack represents a potential solution. Among them, the α wolf is the best solution, the β wolf and the δ wolf are the best and sub-optimal solutions respectively, and other candidate solutions are the positions of the ω wolves. The process of grey wolves hunting can be divided into three stages. The specific process is as shown in Figure 1 (b):

[0165] In the first stage, the wolf pack tracks the prey through information and gradually approaches it.

[0166] In the second stage, after determining the position of the prey, the wolf pack surrounds the prey and gradually shrinks the encirclement.

[0167] In the third stage, an attack is launched on the prey and it is captured.

[0168] In the D-dimensional search space, assuming that the population consists of n grey wolves, the position of the i-th grey wolf is where is the position of the i-th grey wolf in the D dimension. In GWO, the initial population of the wolf pack is randomly generated.

[0169] For the position of the i-th grey wolf in the d dimension, the behavior of the grey wolf gradually approaching and surrounding the prey is described by the following formula:

[0170]

[0171] where t is the current iteration number, is the current position of the prey, is the step length for the wolf pack to surround the prey, and:

[0172]

[0173] α = 2 - 2 × t / t max (5)

[0174] Among them, both A and C are coefficient vectors, and t max is the maximum number of iterations, r1 and r2 represent random numbers between [0, 1], and α is the convergence factor.

[0175] When |A| > 1 or |C| > 1, the gray wolf population will expand the encirclement, and the gray wolves will be as scattered as possible in each area to search for prey, preventing the population from stagnating at the local optimum. At this time, the algorithm is mainly for breadth exploration. When |A| < 1 or |C| < 1, the gray wolf population will shrink the encirclement, and the gray wolves will concentrate on searching for prey in a certain or certain areas, corresponding to the local development ability of the algorithm. At this time, the algorithm is mainly for depth development. For the convergence factor α, after T / 2 iterations, the coefficient A will start to explore the solution space.

[0176] Each wolf in the population updates its individual position according to the positions of the α wolf, β wolf, and δ wolf, that is, the sum and X α 、X β and X δ distance:

[0177]

[0178] 2. The proposed multi-strategy combination optimizer

[0179] In this embodiment, the multi-strategy combination optimizer will be systematically elaborated from three parts: the algorithm improvement based on Tent chaotic mapping, arctangent convergence factor, and adaptive weight, the search mechanism introducing the whale and eagle intelligent optimization algorithms, and the adoption of the elite retention strategy.

[0180] The multi-strategy combination optimizer proposed in this embodiment includes the following three parts.

[0181] The first part is the algorithm improvement based on Tent chaotic mapping, arctangent convergence factor, and adaptive weight. First, Tent chaotic mapping is used to initialize the population to increase the diversity of the wolf population and enhance the global optimization ability of the algorithm; second, a double non-linear convergence factor is proposed to promote the correct balance between algorithm exploration and development; finally, an adaptive weight coefficient is used to improve the exploration and development ability of the algorithm.

[0182] The second part is to introduce the search mechanisms of the whale and eagle intelligent optimization algorithms. In this part, the gray wolves are divided into three layers. The gray wolves in the first layer follow three wolf leaders to search for prey. The gray wolves in the second layer are given the flying ability of the eagle and follow the optimal wolf to quickly search for prey. The gray wolves in the third layer learn the way of the whale to search for prey in a spiral manner within a local range when following the optimal wolf, so as to enhance the information interaction between the wolves and improve the utilization ability of the algorithm, and finally achieve an effective balance between global exploration and local development of the algorithm.

[0183] The third part adopts the elitist retention strategy. After all individual positions are updated and each iteration ends, the elitist retention is used to replace the individuals with lower fitness to maintain the excellent characteristics in the population, keep the diversity of the population, and enhance the optimization performance of the algorithm. The visualization of the multi-strategy optimizer is as shown in Figure 2 as follows.

[0184] 2.1 Multi-strategy algorithm

[0185] This embodiment will elaborate on the algorithm improvement based on Tent chaotic mapping, arctangent convergence factor, and adaptive weight. First, an arctangent convergence factor is proposed, and the double nonlinear convergence factor is applied to different leading wolves to improve the algorithm convergence ability. Secondly, Tent chaotic mapping is used to initialize the population to increase the diversity of the wolf pack and enhance the global optimization ability of the algorithm. Finally, an adaptive weight coefficient is used to improve the exploration and exploitation ability of the algorithm.

[0186] 2.1.1 Double nonlinear convergence factor

[0187] Traditional GWO uses a convergence factor that linearly decreases from 2 to 0. This strategy cannot fully balance the global search and local development capabilities when dealing with complex problems, and it is easy to fall into local optima or have a too slow convergence speed. To establish a balance between development and exploration in the algorithm, this embodiment divides the wolf pack into two parts. One part only follows the alpha wolf to quickly explore the global space and develop and utilize the local space. The other part follows the beta and delta leading wolves to carefully explore the global space and quickly develop the local space. And a nonlinear function is used to replace the linear function, which is called the double nonlinear convergence factor strategy. The function expression is:

[0188]

[0189] Figure 3 The images of the GWO linear convergence factor alpha and the nonlinear convergence factors alpha1 and alpha2 proposed in this embodiment changing with the number of iterations are given. The nonlinear convergence factor a1 in this embodiment slowly decreases in the early wolf pack exploration stage to expand the search range of the wolf pack and maximize the global search. In the middle and late transition period from exploration to development of the wolf pack, the convergence factor rapidly decreases to prompt the wolf pack to concentrate on the target, enhancing the optimization accuracy of the wolf pack in the development stage while accelerating the algorithm convergence speed. The nonlinear convergence factor a2 rapidly decreases in the early wolf pack exploration stage. At this time, the learning ability of individuals is strong, enabling the algorithm to quickly converge to the optimal solution in the early and middle stages. In the later development stage, it searches near the leading wolves, and the value of the convergence factor a2 slowly drops to 0 to avoid premature maturity and strengthen the information exchange among the population, thereby enhancing the global search ability of the algorithm and jumping out of the local optimal solution.

[0190] 2.1.2 Tent mapping

[0191] In the GWO algorithm, the initial position of the wolf pack has a great restrictive effect on solving the optimal value of the target. The more uniformly the initial population is distributed in the solution space, the greater the probability that the algorithm will find the optimal value. The initial populations generated by three commonly used chaotic mappings, namely Tent, Logistic, and Chebyshev mappings, are analyzed and compared as follows Figure 4 shown.

[0192] According to Figure 4 , the initial population generated by using the Tent mapping is the most uniformly distributed. The multi-strategy optimizer in this embodiment introduces the chaotic initialization population of the Tent mapping. The expression of Tentmap is as follows:

[0193]

[0194] 2.1.3 Adaptive weight coefficient

[0195] The traditional grey wolf algorithm updates the positions of the wolves in the pack with the average value of the current positions of the three wolf leaders, without considering the strength of the abilities of the three wolf leaders themselves. The improved algorithm takes into account the contribution of the three best wolves to the update of the positions of the wolves in the pack. The weight coefficient will be adjusted and changed during the iterative optimization process of the wolf pack. The specific formula is as follows:

[0196]

[0197] The weight w1(t) for updating the position of the wolves in the pack must be greater than w2(t) and w3(t). However, at this time, the distance between the position of the alpha wolf and the position of the current wolf individual is not necessarily the largest, and at the same time, the position of the alpha wolf is not necessarily the global optimal solution. Therefore, the adaptive weight coefficient is more conducive to global optimization.

[0198] 2.2 Search mechanism combination

[0199] A single search mechanism has limited exploration ability. The multi-strategy optimizer in this embodiment introduces the search mechanisms of the eagle and the whale. The eagle enables the wolf to have the ability to fly, and the whale enables the wolf to approach the prey along a spiral path, improving the global exploration and local development capabilities of the algorithm and effectively jumping out of the local optimum.

[0200] 2.2.1 Eagle exploration mechanism

[0201] The hunting of the eagle has four stages. In the expansion and exploration stage and the stage of narrowing the exploration range, when the eagle discovers the prey area from high altitude, the eagle will circle above the target prey, get ready to land, and then launch an attack. This method is called contour flight and short glide attack, which well demonstrates the global exploration ability of the eagle. The specific expression is as follows:

[0202] X i (t + 1) = X α(t)+(X i (t)-X α (t))×Levy(D) (17)

[0203]

[0204] where t represents the current iteration number, X i (t + 1) is the solution for the next iteration, X α (t) is the current optimal solution, reflecting the approximate position of the prey, D is the dimensional space, Levy(D) is the flight distribution function, s is a constant value fixed to 0.01, v is a random number between 0 and 1, u follows a normal distribution with mean 0 and variance σ, and β is a constant value fixed to 1.5.

[0205] 2.2.2 Whale Search Mechanism

[0206] When whales approach the global optimal solution, they search locally in a spiral manner. The strategy of the spiral behavior is to generate a spiral path between the current position and the global optimal solution position, and then the whales move along this path, which can effectively jump out of the local optimum. The specific expression is as follows:

[0207] X i (t + 1) = D × e bl × cos(2πl) + X α (t) (20)

[0208] D = |X α (t) - X i (t)| (21)

[0209] where b is a constant coefficient defining the spiral hunting, generally set to 1, and l is a random number in [-1, 1].

[0210] 2.3 Elite Retention Strategy

[0211] Execute the elite retention strategy. After all individual positions are updated and at the end of each iteration, find the wolf with the worst fitness value except for the elite, and compare it with the new wolf generated by the Tent mapping. If the fitness value of the new wolf is better than that of the worst non - elite wolf, then expel the worst non - elite wolf and introduce the new wolf; otherwise, make no changes. Update the population of each iteration through elite retention, which can improve the global convergence ability of the algorithm, accelerate the convergence speed, avoid premature convergence, and thus enhance the overall performance of the population and the robustness of the algorithm. The specific formula is as follows:

[0212]

[0213] where X new(t) is the solution that enters the next iteration with the population after contrast selection, X worst (t) is the solution with the worst fitness value at the end of the t-th iteration, X tent (t) is the newly generated solution by Tent mapping.

[0214] 3 Experiments and Discussions

[0215] In this embodiment, the algorithm performance test of the multi-strategy optimized gray wolf optimizer will be carried out, and relevant statistical analysis and sensitivity analysis will be done.

[0216] 3.1 Benchmark Functions

[0217] To further verify the exploration ability of this multi-strategy combined optimizer, variants of the gray wolf algorithm Clb_GWO(2023), AGWO(2022), GNHGWO(2021), SOGWO(2020), as well as the parent GWO algorithm, the traditional PSO algorithm, and the new algorithms SABO and DBO algorithms, etc., are selected. The performance of this algorithm and the above 8 optimization algorithms are tested using 23 typical benchmark test functions in the CEC2005 test set. To ensure fairness among algorithms and reach the convergence state, the population size and the maximum number of iterations of each algorithm are set to 50 and 500 respectively. To reduce the influence of randomness on the results, each algorithm runs independently 30 times for each function, and each comparison algorithm is set with fixed parameters according to the references. In addition, three indicators are used to evaluate the search ability, and their calculation methods are as follows:

[0218] Mean, calculate the average value of the function values obtained by each algorithm running 25 times for each benchmark test function. The calculation formula is as follows:

[0219]

[0220] where f i is the objective function value calculated by the algorithm in the i-th iteration, and n is the number of independent operations of the algorithm on the function.

[0221] Standard Deviation (Std), the calculation formula is as follows:

[0222]

[0223] Optimal Value (Best): the minimum value among the n calculation results, and the calculation formula is as follows:

[0224] Min f =min{f i , 1≤i≤n} (25)

[0225] These 23 basic test functions are divided into three categories: the first category is the unimodal benchmark test functions F1 - F7, as shown in Table 1; the second category is the multimodal benchmark test functions F8 - F13, as shown in Table 2; the third category is the fixed - dimensional multimodal benchmark test functions, as shown in Table 3.

[0226] Table 1 Unimodal Benchmark Test Functions

[0227]

[0228] Table 2 Multimodal Benchmark Test Functions

[0229]

[0230] Table 3 Fixed - Dimensional Multimodal Benchmark Functions

[0231]

[0232]

[0233] 3.2 Development and Exploration Ability Analysis

[0234] The unimodal functions (F1 - F7) have exactly one extreme solution in the given search domain and can be used to test the optimization accuracy and convergence speed of the algorithm, thereby evaluating the development performance of the algorithm. The multimodal functions (F14 - F23) contain more than one extreme solution in the given search. Once the algorithm has weak search ability, it is very likely to fall into local solutions. Such functions are used to evaluate the performance of the algorithm to avoid local optima and reach the global solution.

[0235] Table 4 contains the performance results of each algorithm in functions F1 - F13 (the best results are shown in bold). Among them, for functions F1 - F4, the MGWO algorithm reaches the theoretical minimum value of 0 in both the minimum value, standard deviation, and average value. For unimodal functions, the MGWO algorithm is stronger than the comparison algorithms in terms of both optimization accuracy and algorithm stability, that is, the MGWO algorithm has strong development ability. For the multimodal function F9, the average value of the MGWO algorithm reaches the theoretical minimum value of 0.

[0236] Table 5 gives the calculation results of different algorithms on fixed - dimensional multimodal functions. The MGWO algorithm obtains the minimum value among the comparison algorithms in the optimization of most functions. At the same time, it converges to the theoretical optimal value of 3 on the fixed - dimensional multimodal function F18. Although the MGWO algorithm performs slightly less well on functions F8 - F13, overall, the improved gray wolf algorithm also has good ability on multimodal functions.

[0237] Through comparison, it is found that the proposed algorithm achieves a good balance between exploration, development, and exploitation behaviors and has good exploration and development performance.

[0238] Table 4 Experimental results of F1 - F13

[0239]

[0240]

[0241] Table 5 Fixed - dimension multimodal benchmark functions (F14 - F23)

[0242]

[0243] 3.3 Convergence analysis

[0244] To further illustrate the superiority of the MGWO algorithm, the convergence curves of 10 algorithms for different functions are as Figure 5 shown. By comparison, it is found that whether it is unimodal benchmark functions, multimodal benchmark functions or fixed - dimension multimodal benchmark functions, in most cases, compared with the other several algorithms, the MGWO algorithm has a faster convergence speed and reaches a higher search accuracy. Generally speaking, the optimization convergence performance of the MGWO algorithm is better than that of the other comparative algorithms.

[0245] 3.4 Statistical analysis

[0246] Statistical analysis is carried out to determine whether it is statistically significant that the MGWO algorithm is superior to the other 8 algorithms.

[0247] Outliers may have a greater impact on the results of parametric statistical methods, making the results of parametric statistical methods less robust. Non - parametric statistical methods usually have better robustness to outliers, can better handle abnormal situations in data, and obtain more scientific analysis results. At the same time, the Wilcoxon rank - sum test and the Friedman test are used to determine the substantial differences between algorithms. Table 6 and Figure 6 respectively give the calculation results of the Wilcoxon rank - sum test and the algorithm rankings of the Friedman test.

[0248] Table 6 Results of Wilcoxon rank - sum test

[0249]

[0250] The statistic of the Wilcoxon rank - sum test is the sum of the ranks of two independent samples, which is used to compare the median differences between two independent samples. Its null hypothesis is that the population distributions from which the two independent samples come are the same, that is, there is no significant difference between the two independent samples. The experimental results output the P - value. If it is less than 0.05, the null hypothesis is considered to be rejected, and there is a significant difference between the MGWO algorithm and the comparative algorithms.

[0251] The Friedman test is also a non-parametric statistical test method used to test whether the medians of multiple related samples are equal. In the test of the experimental results of algorithms, the Friedman test is mainly used to give an overall ranking of the algorithms. Since the objective is to find the minimum value of the objective function, the smaller the algorithm ranking in the experimental results, the better the performance.

[0252] Based on the rank sum test results in Table 6 and combined with the previous analysis, the optimization performance of the MGWO algorithm on the unimodal functions F1 - F4 is significantly better than the other 8 comparison algorithms, and the optimization performance on the multimodal functions F9 and F10 is significantly better than the other 7 comparison algorithms except the DBO algorithm. According to Figure 6 the Friedman test results, the MGWO algorithm has the smallest ranking and shows better algorithm stability in the experiments of 23 benchmark test functions.

[0253] 3.5 Sensitivity Analysis

[0254] For a regression decision tree, in the MGWO algorithm, there are two key parameters (population size and number of iterations) that will significantly affect the effectiveness of the prediction. Perform parameter sensitivity analysis on the improved algorithm, analyze the influence of each tuned parameter, and determine the sensitivity of each parameter of the algorithm. In order to perform sensitivity analysis on a specific parameter, the method of controlling variables is used.

[0255] The experiment uses the Iris dataset from the UCI Machine Learning Repository. This dataset contains three types of iris flowers (Setosa, Versicolor, and Virginica), with 50 samples of each type, for a total of 150 samples. Set 5 different population sizes and 5 different numbers of iterations, and output the average error rate after multiple runs under specific combinations of population size and different numbers of iterations. Table 7 gives the corresponding results.

[0256] When the population size is 20, as the number of iterations increases from 50 to 250, the average error rate fluctuates between 0.004444 and 0.006667. When the population size is 30, as the number of iterations increases from 50 to 250, the error rate fluctuates between 0.002222 and 0.011111, and reaches a peak of 0.011111 when the number of iterations is 100. Similar trends are observed for other population sizes.

[0257] It can be concluded from this that a larger population size may bring better performance to the algorithm, but may increase the computational cost. A larger number of iterations may also bring good performance to the algorithm, but once a certain threshold is exceeded, the performance may not improve anymore.

[0258] Table 7 Combinations of Specific Population Sizes and Numbers of Iterations

[0259]

[0260] To more intuitively and scientifically analyze which parameter has a greater impact on the algorithm, multi-factor variance analysis is used, and Table 8 shows the output results.

[0261] The P-value of the number of iterations is 0.0191, which is less than 0.05, while the P-value of the population size is 0.0607, which is greater than 0.05. This indicates that the number of iterations is statistically significant, while the population size is not. That is, the number of iterations has a greater impact on the performance of the improved algorithm than the population size.

[0262] Table 8 ANOVA results

[0263]

[0264] 4 Practical applications of the algorithm

[0265] In this embodiment, the multi-strategy optimized gray wolf algorithm is applied to three practical problems: optimizing the extreme learning machine to achieve breast cancer diagnosis, optimizing the maximum correlation kurtosis deconvolution to achieve early weak fault diagnosis, and optimizing the LSTM to achieve wind speed sequence prediction, demonstrating the algorithm performance in its practical applications.

[0266] 4.1 Optimizing the extreme learning machine to achieve breast cancer diagnosis

[0267] The extreme learning machine ELM is a fast feedforward neural network for regression and classification tasks. Its characteristic lies in randomly initializing the parameters of the hidden layer and then directly determining the weights of the output layer through the least squares method.

[0268] Although the extreme learning machine ELM has significant advantages in terms of speed, its performance depends on randomly generated weight thresholds, so it may not be the best. An intelligent algorithm is used to optimize the weight thresholds of ELM to make the mapping relationship between input and output more perfect. The error of the ELM model on the test set is used as the fitness function of the improved algorithm to guide the optimization of parameters, thereby improving the accuracy of the ELM data classification model.

[0269] For the classification case of MGWO-ELM, the data used is the breast cancer classification dataset in the publicly available UCI dataset. This dataset contains the nuclear feature data of 569 patients, which are obtained from fine needle aspiration (FNA) images of breast masses. The data of each patient is used to diagnose whether their cancer is malignant or benign, that is, whether they have breast cancer or not.

[0270] Figure 7The classification results of the standard ELM model and the MGWO-ELM model are shown. The results consist of the confusion matrix and the fitting effect of the true value - predicted value. There are 69 data in the test set belonging to the first category. According to the shown results, among the predictions of the standard ELM for the first category, 65 are predicted correctly, and the classification accuracy is only 85.9649%. For the prediction of the entire test set by the optimized ELM, the MGWO-ELM model, the accuracy reaches 100%. Therefore, the improved algorithm MGWO significantly improves the prediction accuracy of the ELM model, reduces the instability caused by random initialization in the ELM model, improves the stability of the model, and at the same time enhances the generalization ability for unknown data.

[0271] Figure 8 The fitness curve of the MGWO algorithm is shown. Based on this, it can be seen that the MGWO algorithm not only accelerates the parameter convergence but also effectively improves the overall performance of the ELM model by using the global search ability of the algorithm.

[0272] 4.2 Optimize the maximum correlation kurtosis deconvolution to achieve early weak fault diagnosis

[0273] Since the impacts generated by the early faults of some devices are very weak and are easily interfered by system noise, how to effectively denoise the original fault signals of the devices and enhance the weak impact components in the signals is the key to the early fault diagnosis of such components.

[0274] The maximum correlation kurtosis deconvolution (MCKD) is an effective noise reduction and signal enhancement technique, especially suitable for extracting the continuous transient impact components in weak fault signals. Through deconvolution operations, this method can highlight the continuous impact pulses submerged by noise and increase the correlation kurtosis value of the original signal. MCKD uses the correlation kurtosis as the objective function to find the optimal filter parameters to maximize the correlation kurtosis value. This method has been widely used in the early fault diagnosis of rolling bearings and can effectively extract weak fault features under strong noise backgrounds. However, the performance of MCKD depends on the prior fault cycle information and may perform poorly under low signal-to-noise ratio conditions. To overcome this limitation, some scholars have proposed MCKD methods based on parameter optimization to improve its effect by optimizing the filter length and shift number. In addition, combining other technologies such as variational mode decomposition (VMD) and optimization algorithms can further enhance the performance of MCKD in weak fault feature extraction.

[0275] To verify the applicability of the improved grey wolf algorithm, in this embodiment, a rolling bearing fault model is used to simulate early fault signals, and strong Gaussian white noise is added to simulate the weak faults covered by environmental noise in actual working condition equipment. The performance of the MGWO algorithm is judged by comparing the envelope effects before and after parameter optimization. The simulation calculation formula is as follows:

[0276]

[0277] A k = A0sin(2πft r )+1 (24)

[0278] h(t) = exp(-Ct)sin(2πft n ) (25)

[0279] where A0 = 0.500, the rotation frequency f r is 25 Hz, C is the attenuation coefficient with a value of 800, the resonance frequency f n value is 4000 Hz, τ k is the small fluctuation of the k-th impact relative to the period T, the random fluctuation follows a normal distribution with a mean of 0 and a standard deviation of 0.5% of the rotation frequency, n(t) is strong Gaussian white noise, the signal-to-noise ratio is set to -16 dB, the sampling frequency is 12800 Hz, the number of analysis points is 8192, and through calculation, the inner race fault frequency is 120 Hz.

[0280] Figure 9 and Figure 10 respectively show the time-domain waveform of the fault simulation signal, the envelope spectrum of the fault simulation signal, and the envelope spectrum of the best IMF component without parameter optimization. From Figure 10 the envelope spectrum of the fault simulation signal in Figure (a), it can be seen that the periodic impact signal of the simulation signal is completely submerged by noise, it is difficult to find prominent frequencies, and it is impossible to distinguish fault characteristics. The VMD is used to decompose the fault signal to obtain the IMF component with the largest envelope spectrum peak factor, that is, the best IMF component, and then the envelope spectrum analysis is performed on the best IMF component to obtain Figure (b). According to the result display, it is found that it is still not ideal enough.

[0281] Furthermore, the improved grey wolf algorithm MGWO is used to optimize the three parameters (filter length parameter L, impact signal period T, displacement number M) of the maximum correlation kurtosis deconvolution (MCKD) to obtain the improved optimal IMF component, and then the envelope spectrum analysis is performed on the IMF component to finally obtain the fault characteristic frequency.

[0282] Figure 11 shows the fitness curve of the improved algorithm MCKD and the envelope spectrum after deconvolution of the optimized best IMF component. It can be seen from this that through the comparison of the envelope spectra of the IMF components before and after optimization, a significant enhancement is obtained after optimization. The spectral lines of the fault characteristic frequency and its 2 and 3 times frequencies are clearly visible in the envelope spectrum after deconvolution, indicating that the characteristic frequency is accurately extracted, and it is considered that the improved grey wolf algorithm MGWO has strong optimization ability.

[0283] 4.3 Optimization of LSTM for Wind Speed Sequence Prediction

[0284] To better achieve the prediction of time series and simultaneously verify the optimization performance of the improved Grey Wolf Optimizer (MGWO) for multi-variables, this embodiment adopts the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and the MGWO-BiLSTM multi-feature variable sequence prediction model based on the improved Grey Wolf Optimizer (MGWO) to improve the prediction performance of time series data.

[0285] The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise is a signal processing method based on empirical mode decomposition that improves the stability and accuracy of mode decomposition by adding adaptive noise. It is used to extract the hidden oscillation patterns from signals and is an advanced signal decomposition technology for processing non-linear and non-stationary signals. The core idea of CEEMDAN is to add white noise to the original signal to make the distribution of extreme points more balanced, thereby reducing the mode mixing phenomenon. This method not only adds noise to the original signal but also adds noise to the residuals at each step to further improve the accuracy of decomposition.

[0286] The Bidirectional Long Short-Term Memory network (BiLSTM) is an improved Recurrent Neural Network (RNN) specifically designed for processing sequence data. It captures the bidirectional context information in the sequence by combining forward and backward LSTM layers, thereby improving the prediction accuracy of the model.

[0287] This embodiment uses the public meteorological dataset of Szeged from 2006 to 2016 in the Kaggle public dataset, including data such as hourly and daily temperature, pressure, wind speed, etc. The article uses its wind speed data for prediction analysis.

[0288] First, use the CEEMDAN algorithm to decompose the wind speed sequence, then merge all components and the original dataset variables to form an enhanced feature input. Make the dataset for experiments through a sliding window and use multi-variables to predict the wind speed. Calculate two hyperparameters, the number of hidden layers and the number of neurons of the BiLSTM, through the improved Grey Wolf Optimizer (MGWO). During the training process of the model, use the Mean Squared Error (MSE) as the loss function to optimize the MGWO-BiLSTM model, extract the enhanced features, and then send them into the fully connected layer to finally achieve a higher-precision prediction model.

[0289] Figure 12The fitting curves of the original signal and the predicted signal are shown. By optimizing the hyperparameter tuning of the algorithm, the number of hidden layers and the number of neurons of the BiLSTM are set to 1 and 100 respectively. After calculation, the R^2 value of the CEEMDAN+MGWO-BiLSTM model is 0.8995, and the values of the mean square error MSE, root mean square error RMSE, and mean absolute error MAE are 0.1481, 0.3849, and 0.2915 respectively. The fitting degree between the model prediction result and the original model is relatively high, indicating that the improved grey wolf algorithm MGWO has good hyperparameter tuning performance, that is, the MGWO algorithm achieves an effective balance between global exploration and local exploitation.

[0290] 5 Summary

[0291] This embodiment proposes a multi-strategy optimized grey wolf optimizer (MGWO). By using a multi-strategy combination of chaotic mapping, double non-linear convergence factor, adaptive weight coefficient, elite retention, and simultaneously introducing the prey search mechanisms of AO and WOA, the cooperation ability of the wolf pack is enhanced, so as to achieve an effective balance between global exploration and local development. The performance of MGWO is tested using 23 benchmark test functions in the CEC2005 conference, and statistical analysis, convergence analysis, and sensitivity analysis are carried out on the results. The experimental results show that compared with a variety of swarm intelligence optimization algorithms, the solutions obtained by MGWO have higher quality, proving that it has a faster convergence speed and higher convergence accuracy, indicating that the algorithm has strong search ability and competitiveness.

[0292] In addition, based on the good performance of MGWO, the algorithm is also applied to three practical application problems: (1) optimizing the extreme learning machine to realize breast cancer diagnosis, (2) optimizing the maximum correlation kurtosis deconvolution to realize early weak fault diagnosis, and (3) optimizing LSTM to realize wind speed sequence prediction. According to the experimental results, using the MGWO proposed in this embodiment has significantly improved it.

[0293] The improvement strategies proposed in this embodiment also further provide some ideas for future research. First, the MGWO optimizer proposed in this embodiment has good optimization performance and can be used as a challenge standard for future meta-heuristic algorithms; and in the future, the proposed MGWO algorithm can be applied to solve various real-world problems, such as image processing, path planning, etc.; because the MGWO proposed in this embodiment is only used to solve single-objective optimization problems, this method can be extended to solve multi-objective optimization and binary optimization problems.

Claims

1. The gray wolf optimizer modeling method based on multi-strategy combination is characterized by: The following steps are involved: 1) Build a target parameter prediction model. 2) Optimize the target parameter prediction model using the Gray Wolf Optimizer based on multi-strategy combination, the steps include: 2.1) Generate the initial distribution of the gray wolf population using Tent mapping; 2.2) Set the fitness function of the gray wolf population; 2.3) Calculate the fitness value of the gray wolf population and determine the positions of α, β, and δ wolves based on the fitness value; 2.4) Update the positions of the remaining gray wolves based on the positions of α, β, and δ wolves; 2.5) Perform search actions to determine the optimal solution; 2.6) Renewing the gray wolf population through an elite retention strategy; 2.7) Determine whether the iteration termination condition is met. If so, output the optimal solution and proceed to step 3). Otherwise, return to step 2.3); 3) Use the optimized target parameter prediction model to predict the target parameters.

2. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The Tent mapping looks like this: In the formula, x i 、x i+1 is the position of the i-th gray wolf before and after mapping.

3. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The gray wolf population includes four levels of wolves: α, β, δ, and ω; among them, α, β, and δ wolves are the three most capable gray wolf individuals.

4. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The search tendency of the gray wolf population is determined by the coefficient vectors A1 and A2; When the coefficient vector |A1|>1 or |A2|>1, the search tendency of the gray wolf population is global search; when the coefficient vector |A1|≤1, |A2|≤1, the search tendency of the gray wolf population is local search; Among them, the coefficient vectors A1 and A2 are as follows: Where r1 represents a random number between [0,1]; α1 and α2 are nonlinear convergence factors; t is the current number of iterations; Max_iter is the maximum number of iterations.

5. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The fitness function of the gray wolf population is the training error of the target parameter prediction model.

6. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: In step 2.4), the positions of the remaining gray wolves are i (t+1) is as follows: Where w1(t), w2(t), w3(t) are weights; X α (t), X β (t), X δ (t) is the position of α, β, and δ wolves.

7. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: In step 2.5), when performing the search action, the ω wolves are divided into three groups according to the set probability. The first group of ω wolves follows the α, β, and δ wolves to search for prey. The second group of ω wolves uses the eagle exploration mechanism to search for prey. The third group of ω wolves uses the whale search mechanism to search for prey. Among them, the Sky Eagle exploration mechanism is as follows: X i (t+1)=X α (t)+(X i (t)-X α (t))×Levy(D) (9) Among them, t represents the current iteration number, X i (t+1) is the solution of the next iteration, X α (t) is the current optimal solution, D is the dimension space, Levy (D) is the flight distribution function, s and β are constants; X i (t) is the solution of the current iteration; v is a random number between 0 and 1, and u follows a normal distribution with a mean of 0 and a variance of σ; The whale search mechanism is as follows: X i (t+1)=D×e bl ×cos(2πl)+X α (t) (12)D=|X a (t)-X i (t)| (13) Among them, b is the constant coefficient that defines spiral hunting; l is a random number in [-1,1].

8. The gray wolf optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The elite retention strategy is as follows: Among them, X new (t) is the solution that follows the population into the next iteration after the comparison selection, X worst (t) is the solution with the worst fitness value at the end of the tth iteration, X tent (t) is the solution newly generated by Tent mapping; F(X worst (t))、F(X tent (t)) is the solution worst (t), X tent (t) The corresponding fitness value.

9. The Grey Wolf Optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The target parameter prediction model is an equipment fault detection model; The equipment fault detection model is a convolutional neural network based on maximum correlation kurtosis deconvolution, and the optimization parameters during training include the length, period and shift number of the filter; The input of the equipment fault detection model is the impact signal of the inner ring of the fan bearing, and the output is the equipment status, including normal equipment and equipment fault.

10. The Grey Wolf Optimizer modeling method based on multi-strategy combination according to claim 1 is characterized in that: The target parameter prediction model is a wind speed sequence prediction model; The wind speed sequence prediction model is a bidirectional long short-term memory network, and the optimization parameters include the number of bilstm_layers hidden layers and the number of bilstm_neurons neurons of the bidirectional long short-term memory network; The input of the wind speed sequence prediction model is the wind speed sequence of the past time period t1, and the output is the wind speed sequence of the future time period t2.

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