Power equipment thermal fault inversion method based on gaussian body heat source and adaptive optimization

Abstract

The application provides a power equipment thermal fault inversion method based on a Gaussian body heat source and adaptive optimization, and comprises the following steps: S1, obtaining a surface temperature of a shell of a power equipment to be measured, and determining a temperature feature vector b obs ; S2, constructing a three-dimensional finite element simulation model of the power equipment to be measured; S3, constructing a three-dimensional Gaussian body heat source distribution function in the three-dimensional finite element model, and performing a steady-state heat flow coupling calculation to obtain a surface temperature distribution of a simulation shell, and determining a temperature feature vector b cal ; the feature vector b obs is the same in dimension as the feature vector b cal ; S4, constructing an optimization function based on the feature vector b obs and the feature vector b cal , solving the optimization function by using a swarm intelligence optimization algorithm for continuous variable optimization, determining heat source coordinates and a heating degree, and taking the heat source coordinates as a thermal fault position of the power equipment and taking the heating degree as a fault severity criterion.

Description

Technical Field

[0001] This invention relates to a method for determining the location of faults in power equipment, and more particularly to a method for inverting thermal faults in power equipment based on a Gaussian heat source and adaptive optimization. Background Technology

[0002] With the rapid development of smart grids, fully enclosed combined power equipment, represented by GIS and large power transformers, has occupied a core position in power transmission and transformation systems. Due to their compact structure and high operating voltage levels, the reliability of their internal conductive circuit connections is directly related to the safe and stable operation of the power grid.

[0003] However, due to factors such as long-term mechanical vibration, electrodynamic effects, material aging, and installation processes, the contact resistance at the conductor contact points inside the equipment (such as contacts and bolt connection surfaces) is very likely to increase, leading to local overheating. For transformers, eddy current heating of structural components caused by short circuits between winding turns, multiple grounding of the core, or leakage flux are also common thermal faults.

[0004] In existing technologies, the diagnosis of thermal faults mainly relies on infrared thermal imaging technology to monitor the casing of power equipment. Although infrared thermal imaging technology can effectively capture temperature anomalies on the equipment surface, GIS equipment and transformers are enclosed structures. The heat generated by the internal heat source needs to be conducted to the surface through convective heat transfer of the insulating medium (SF6 gas or transformer oil) and thermal conduction of the metal casing. This complex heat transfer process has significant diffusion and nonlinearity, causing the hot spots on the surface of the equipment casing to deviate from the actual internal thermal fault point. Moreover, the temperature rise amplitude mainly depends on the fault power and environmental heat dissipation conditions, making it difficult for existing technologies to accurately determine the precise internal fault location and the severity of the thermal fault.

[0005] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose a new technical approach. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a method for inverting thermal faults in power equipment based on a Gaussian heat source and adaptive optimization. By establishing a finite element simulation model and using the Gaussian heat source distribution function to perform steady-state heat flow coupling calculations to determine the temperature distribution on the outside of the simulated shell, and using the actual temperature distribution obtained by an infrared thermal imaging device to establish a corresponding optimization model, the method uses a swarm intelligent optimization algorithm for continuous variable optimization to perform inversion optimization, thereby determining the final true fault location and heat generation power, providing accurate data support for the accurate judgment of the fault degree and the formulation of operation and maintenance measures.

[0007] This invention provides a method for inverting thermal faults in power equipment based on a Gaussian heat source and adaptive optimization, comprising the following steps:

[0008] S1. Obtain the surface temperature of the casing of the electrical equipment under test and determine the temperature feature vector b. obs ;

[0009] S2. Construct a three-dimensional finite element simulation model of the power equipment under test;

[0010] S3. Construct a three-dimensional Gaussian heat source distribution function in a three-dimensional finite element model, perform steady-state heat flux coupling calculations to obtain the surface temperature distribution of the simulated shell, and determine the temperature eigenvector b. cal ;Eigenvector b obs With eigenvector b cal The dimensions are the same;

[0011] S4. Based on feature vector b obs With eigenvector b cal An optimization function is constructed, and a swarm intelligence optimization algorithm for continuous variable optimization is used to solve the optimization function to determine the coordinates of the heat source and the degree of heating. The coordinates of the heat source are used as the location of the thermal fault in the power equipment, and the degree of heating is used as the criterion for the severity of the fault.

[0012] Furthermore, in step S1, determining the temperature feature vector specifically includes:

[0013] The four sides of the power equipment are labeled A, B, C, and D, respectively, and the surface temperature of the power equipment casing is obtained using an infrared imaging device; among them, sides A and C face each other, and sides B and D face each other.

[0014] Define an m×m square sliding window on each surface, and move through each side using this sliding window. Calculate the average temperature within the area covered by the window, and filter out the maximum sliding window temperature for each side, denoted as T_Amax, T_Bmax, T_Cmax, and T_Dmax respectively.

[0015] Calculate the average temperature of each side and denote it as T_Aavr, T_Bavr, T_Cavr, and T_Davr, respectively.

[0016] Divide surfaces A and C into i×j grids, and surfaces B and D into n×n grids, and calculate the average temperature of each grid.

[0017] The feature vector is composed of the maximum temperature of the sliding window on each side, the average temperature of the side, and the average temperature of the grid on each side.

[0018] Furthermore, in step S3, the three-dimensional Gaussian heat source distribution function is specifically as follows:

[0019] ;

[0020] Where: Q(x,y,z) represents the heat generation rate per unit volume of a three-dimensional Gaussian body, Q max σ represents the peak power density at the center of the heat source, σ represents the standard deviation of the Gaussian distribution, (x0,y0,z0) represents the coordinates of the fault center, and (x,y,z) represents the coordinates of the solution domain.

[0021] in: ;P total This represents the total power generated by the Gaussian heat source;

[0022] Where: vector X is taken as the vector to be solved, where:

[0023] .

[0024] Furthermore, in step S4, based on the feature vector b obs With eigenvector b cal The optimization function is constructed as follows:

[0025] .

[0026] Furthermore, the swarm intelligence optimization algorithm for continuous variable optimization employs four parallel candidate strategies, specifically including the AOO update strategy based on the behavior of wheat seeds, the differential evolution random mutation strategy, the differential evolution optimal guidance strategy, and the quadratic difference strategy.

[0027] In swarm intelligence optimization algorithms for continuous variables, one of four strategies is selected in each update through a roulette wheel mechanism.

[0028] The beneficial effects of this invention are as follows: By establishing a finite element simulation model and using the Gaussian heat source distribution function to perform steady-state heat flow coupling calculations to determine the temperature distribution on the outside of the simulated shell, and using the actual temperature distribution obtained by the infrared thermal imaging device to establish a corresponding optimization model, the invention utilizes a swarm intelligent optimization algorithm for continuous variable optimization to perform inversion optimization, thereby determining the final true fault location and heat generation power, providing accurate data support for the accurate judgment of the subsequent fault degree and the formulation of operation and maintenance measures.

[0029] Moreover, the Gaussian heat source model effectively overcomes the shortcomings of existing technologies that are easily affected by environmental reflection and random noise interference. It can keenly capture the subtle surface temperature rise texture induced by internal faults, avoid the singularity problem in numerical calculations, and determine the center coordinates, heating power and affected range of the fault. It is more consistent with the real physical form of contact resistance overheating or local eddy current heating, providing an accurate basis for equipment condition assessment. Attached Figure Description

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0031] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0032] The present invention will be further described in detail below:

[0033] This invention provides a method for inverting thermal faults in power equipment based on a Gaussian heat source and adaptive optimization, characterized by the following steps:

[0034] S1. Obtain the surface temperature of the casing of the electrical equipment under test and determine the temperature feature vector b. obs ;

[0035] S2. Construct a three-dimensional finite element simulation model of the power equipment under test;

[0036] S3. Construct a three-dimensional Gaussian heat source distribution function in a three-dimensional finite element model, perform steady-state heat flux coupling calculations to obtain the surface temperature distribution of the simulated shell, and determine the temperature eigenvector b. cal ;Eigenvector b obs With eigenvector b cal The dimensions are the same, meaning the number of temperature features in the two feature vectors is the same. Specifically, a Gaussian heat source distribution function is embedded in the three-dimensional finite element simulation model, followed by steady-state heat flux coupling calculations to determine the surface temperature distribution of the power equipment under test and thus the corresponding feature vector b. cal ;

[0037] S4. Based on feature vector b obs With eigenvector b cal An optimization function is constructed, and a swarm intelligent optimization algorithm for continuous variable optimization is used to solve the optimization function to determine the coordinates of the heat source and the degree of heating. The coordinates of the heat source are used as the location of the thermal fault in the power equipment, and the degree of heating is used as the criterion for the severity of the fault. Through the above method, a finite element simulation model is established, and the temperature distribution on the outside of the simulated shell is determined by steady-state heat flux coupling calculation using the Gaussian heat source distribution function. The actual temperature distribution obtained by the infrared thermal imaging equipment is used to establish a corresponding optimization model. The swarm intelligent optimization algorithm for continuous variable optimization is used for inverse optimization, thereby determining the final true fault location and heating power, providing accurate data support for the accurate judgment of the fault degree and the formulation of operation and maintenance measures.

[0038] Moreover, the Gaussian heat source model effectively overcomes the shortcomings of existing technologies that are easily affected by environmental reflection and random noise interference. It can keenly capture the subtle surface temperature rise texture induced by internal faults, avoid the singularity problem in numerical calculations, and determine the center coordinates, heating power and affected range of the fault. It is more consistent with the real physical form of contact resistance overheating or local eddy current heating, providing an accurate basis for equipment condition assessment.

[0039] In this embodiment, step S1, determining the temperature feature vector specifically includes:

[0040] The four sides of the power equipment are labeled A, B, C, and D, respectively, and the surface temperature of the power equipment casing is obtained using an infrared imaging device; among them, sides A and C face each other, and sides B and D face each other.

[0041] Define an m×m square sliding window on each surface, and move through each side using this sliding window. Calculate the average temperature within the area covered by the window, and filter out the maximum sliding window temperature for each side, denoted as T_Amax, T_Bmax, T_Cmax, and T_Dmax respectively.

[0042] Calculate the average temperature of each side and denote it as T_Aavr, T_Bavr, T_Cavr, and T_Davr, respectively.

[0043] Divide surfaces A and C into i×j grids, and surfaces B and D into n×n grids, and calculate the average temperature of each grid.

[0044] The feature vector is composed of the maximum temperature of the sliding window on each side, the average temperature of the side, and the average temperature of the grid on each side.

[0045] In practice, for two faces A and C (usually the longer faces), they are geometrically divided into 5 rows and 10 columns, resulting in 50 sub-regions. The average temperatures TA(i,j) avr and T_C(i,j) avr of each sub-region T(i,j) are calculated.

[0046] For faces B and D (usually the shorter side faces), their geometry is divided into 25 sub-regions of 5 rows and 5 columns. Calculate the average temperature TB(m,n) avr and TD(m,n) avr of T(m,n) for each sub-region.

[0047] Total number of features: 4 (extreme values) + 4 (mean values) + 50*2 (A / C regions) + 25*2 (B / D regions) = 158 features. Therefore, the number of features N in the optimized model f(X) is 158. Through the above, the temperature distribution state of the equipment casing can be fully reflected, which provides a guarantee for the accuracy of subsequent inversion.

[0048] In this embodiment, the three-dimensional Gaussian heat source distribution function in step S3 is specifically as follows:

[0049] ;

[0050] Where: Q(x,y,z) represents the heat generation rate per unit volume of a three-dimensional Gaussian body, Q max σ represents the peak power density at the center of the heat source, and σ represents the standard deviation of the Gaussian distribution. This standard deviation determines the shape of the heat source, thus reflecting the affected area. (x0,y0,z0) represents the coordinate position of the fault center, and (x,y,z) represents the coordinates of the solution domain, that is, the coordinate positions of windings, conductors, joints, busbars, etc. in reality (of course, taking the joint as an example, there is a coordinate range in the coordinate system, which is determined by the boundary of the conductor, and values ​​are taken within this coordinate range).

[0051] in: ;P total This represents the total power generated by the Gaussian heat source;

[0052] Where: vector X is taken as the vector to be solved, where:

[0053] In this vector, all variables are unknowns to be solved. Initially, they are assigned initial values ​​based on the actual working conditions. Then, a swarm intelligence optimization algorithm for continuous variable optimization is used to gradually optimize the function f(X) until the value is minimized or the set convergence condition is met, thus outputting the final solution. In other words, each time a value of X is updated, it is substituted into the Gaussian heat source distribution function, and then the eigenvector b is calculated. cal Then, the values ​​are substituted into the optimization function f(X) for calculation, and this process is repeated iteratively. In the final output solution, (x0, y0, z0) represents the coordinates of the fault center, i.e., the actual location of the thermal fault point inside the power equipment; σ reflects the affected area of ​​the fault point; and P... total This represents the total power generated by the Gaussian heat source, reflecting the current degree of failure.

[0054] In this embodiment, in step S4, based on feature vector b obs With eigenvector b cal The optimization function is constructed as follows:

[0055] During optimization, the optimization function terminates when it reaches its minimum value or meets the set convergence condition, and the final vector X to be calculated is output.

[0056] In this embodiment, the swarm intelligence optimization algorithm for continuous variable optimization adopts four parallel candidate strategies, specifically including the AOO update strategy based on the behavior of wheat seeds, the differential evolution random mutation strategy, the differential evolution optimal guidance strategy, and the quadratic difference strategy.

[0057] In swarm intelligence optimization algorithms for continuous variables, one of four strategies is selected in each update through a roulette wheel mechanism.

[0058] Among them, the swarm intelligence optimization algorithm Ms-AOO-sd (Multi-strategy Self-adaptive Differential Animated Oat Optimization) for continuous variable optimization and its four strategies are all existing technologies. The core of it is to introduce the DE (Differential Evolution) operator and the analytical quadratic interpolation development strategy on the original AOO (Animated Oat Optimization) framework, and achieve a dynamic balance between exploration and development through the adaptive strategy selection mechanism driven by the "improvement quantity".

[0059] The following is a brief description of swarm intelligence optimization algorithms for continuous variable optimization and their four strategies:

[0060] In the inversion calculation, each particle X in the algorithm population represents a set of thermal fault parameter vectors of the power equipment to be solved, defined as follows:

[0061]

[0062] Where (x0, y0, z0) are the three-dimensional center coordinates of the Gaussian heat source to be determined, P is the total heating power of the heat source to be calculated, and σ is the standard deviation of the Gaussian distribution. The goal of the algorithm is to continuously evolve X to make the temperature eigenvector b obtained from the finite element simulation more consistent. cal Compared with the measured infrared feature vector b obs The dimensionless objective function f(X) is minimized between these points.

[0063] During the iteration process, the algorithm dynamically adjusts the probability of each strategy being selected based on its actual contribution to fitness improvement (i.e., the success rate ck), thereby achieving an adaptive balance of search weights. The specific mechanisms of each candidate strategy are defined as follows:

[0064] Strategy 1: AOO update strategy for dynamic seed behavior:

[0065] A search mechanism based on the behavior of wheat seed is employed. This strategy simulates the displacement behavior of wheat seed awns driven by environmental humidity, mimicking the random diffusion and hygroscopic crawling of wheat seeds to achieve global exploration and local development of the solution space. In the t-th iteration, the position vector of the i-th individual is updated.

[0066] During the movement of oat seeds, their distribution characteristics are related to seed length, mass, and eccentricity coefficient during rolling. The relevant parameters are shown in the following formula:

[0067]

[0068] Where χ i m is the deformation coefficient. i For quality parameters, L i The main awn length parameter, e i is the eccentricity coefficient, and dim is the parameter dimension.

[0069] Define a decay factor c(t) to control the gradual convergence of the step size with respect to the iteration:

[0070]

[0071] Where T is the maximum number of iterations.

[0072] Meanwhile, to enhance the ability to escape local optima, a Levy flight random vector Levy(dim) is generated for each individual to update the position of the new individual:

[0073] Wind diffusion search phase:

[0074] If the random number rand > 0.5, perform global diffusion and calculate the wind disturbance vector:

[0075]

[0076] Where r∈(0,1), and ub is the upper bound of the parameter.

[0077] To balance group information with optimal guidance, diffusion centers are selected in segments based on individual IDs, resulting in candidate locations:

[0078]

[0079] Among them, X best It is the optimal position for the group, X t It is the center of the group.

[0080] Development phase:

[0081] During the propagation stage, wheat seeds are propagated in two ways depending on whether they encounter obstacles: hygroscopic crawling and ejection renewal. In the absence of obstacles, the change in seed position is achieved through hygroscopic rolling driven by the stress gradient induced by moisture.

[0082] Assuming the probabilities of the two scenarios are equal and controlled by a random parameter r, when r > 0.5, moisture-absorbing crawling is performed, and the formula for calculating the candidate location is as follows:

[0083]

[0084]

[0085]

[0086] In the formula, r is a random vector of 0-1, A is the upper limit of the disturbance amplitude, U(-A,A) represents a random vector obtained by independent and uniform sampling in each dimension interval (-Aj,Aj), and mi, ei, and Li are the internal state parameters of AOO of the i-th individual, which are used to adjust the displacement amplitude.

[0087] When r ≤ 0.5, the propagation of wheat seeds encountering obstacles is simulated, and a projectile update is performed. When a seed encounters an obstacle during propagation, the main awn undergoes a jetting motion driven by stored energy. A simplified projectile motion model is used for position updates, and the position update formula is as follows:

[0088]

[0089]

[0090]

[0091]

[0092] Where k is the elastic coefficient of the seed awn, x is the change in the length of the awn during the energy storage period of the projectile, θ is the angle between the projectile trajectory and the ground, α is the air resistance coefficient during the projectile motion, and r is a random number between 0 and 1.

[0093] Strategy 2: Differential Evolutionary Random Mutation Strategy (DE / rand / 1)

[0094] Differential Evolution (DE) is a heuristic random search algorithm based on swarm intelligence, which evolves the solution through the vector differences between individuals. DE / rand / 1 is a classic mutation mode, where three distinct individuals are randomly selected from the population, and the vector difference between two of them is scaled and added to the third individual, thus generating a mutated vector. This method does not rely on the current optimal solution, possesses strong randomness, and allows the population to search extensively throughout the solution space, effectively preventing the inversion process from getting trapped in local minima. Its mathematical expression is as follows:

[0095]

[0096]

[0097] In the formula, V is the generated mutation vector, Xr1, Xr2, and Xr3 are the indices of randomly selected individuals in the population, F is the scaling factor of the difference algorithm, used to control the scaling ratio of the difference vector, U is the experimental vector generated by binomial crossover, and CR is the crossover probability.

[0098] Strategy 3: Differential Evolution Optimal Guidance Strategy (DE / best / 1)

[0099] DE / best / 1 is a strongly guided mutation strategy in differential evolution algorithms. Its core mechanism lies in using the globally optimal solution found by the current population as a baseline vector, and then superimposing it with the difference vectors between random individuals. This strategy significantly enhances the algorithm's local evolutionary ability, emphasizing convergence towards the current optimal solution and accelerating convergence. The relevant mathematical expressions are as follows:

[0100]

[0101] In the formula, V is the generated mutation vector, and Xbest is the optimal solution of the current population.

[0102] Strategy 4: Quadratic Interpolation

[0103] Quadratic interpolation is a local search strategy based on the principle of mathematical function approximation. This strategy uses the three currently searched locations and their corresponding fitness values ​​to fit a parabola to simulate the local shape of the real objective function, enabling fine-tuning.

[0104] This strategy uses the current population optimum Xbest and two other random points Xp and Xq in the population to construct the following interpolation formula:

[0105]

[0106] Where, Xp, Xq, and Xcurr are three different spatial position vectors. Xcurr usually selects the current optimal individual in the population. fbest, fp, and fq are the corresponding fitness function values.

[0107] To screen out the search operator that best suits the characteristics of the current solution space in real time during the iteration process, the algorithm introduces an adaptive strategy selection mechanism based on the contribution of success. This mechanism realizes the dynamic optimization of the search behavior by quantifying the contribution of each strategy to the residual reduction. The specific execution logic is as follows:

[0108] At the beginning of the algorithm, equal selection probabilities are assigned to the four strategies, that is, the initial probability vector p = [p1, p2, p3, p4] = [0.25, 0.25, 0.25, 0.25]. For each individual i, the strategy k used is obtained by roulette sampling.

[0109] When the individual generates a new position Xnew according to the selected strategy, the algorithm decides whether to accept this position through the "greedy criterion". Calculate the fitness value fnew at the new position Xnew. If fnew < fold, it is considered that this parameter is better and the current strategy is successful. Calculate the fitness improvement amount Δf = fold - fnew. To evaluate the ability of each strategy, a success accumulator ck is set for each strategy. If strategy k guides the algorithm to find a better solution, the improvement amount Δf is added to ck.

[0110]

[0111] At the end of each generation of iteration, according to the total contribution of each strategy in this generation, the probability of being selected in the next generation is recalculated as shown in the following formula:

[0112]

[0113] Where, is the cumulative contribution of the normalized strategy k; αp is the probability smoothing factor. In this case, α = 0.2 is taken.

[0114] By using the roulette mechanism with the above four strategies, the problem that the high-dimensional non-convex objective function is prone to falling into local optimum is effectively solved, and the rapid convergence and precise positioning of the fault parameters are achieved.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for inverting thermal faults in power equipment based on a Gaussian heat source and adaptive optimization, characterized in that: Includes the following steps: S1. Obtain the surface temperature of the casing of the electrical equipment under test, and determine the temperature feature vector b. obs ; S2. Construct a three-dimensional finite element simulation model of the power equipment under test; S3. Construct a three-dimensional Gaussian heat source distribution function in a three-dimensional finite element model, perform steady-state heat flux coupling calculations to obtain the surface temperature distribution of the simulated shell, and determine the temperature eigenvector b. cal ;Eigenvector b obs With eigenvector b cal The dimensions are the same; S4. Based on feature vector b obs With eigenvector b cal An optimization function is constructed, and a swarm intelligence optimization algorithm for continuous variable optimization is used to solve the optimization function to determine the coordinates of the heat source and the degree of heating. The coordinates of the heat source are used as the location of the thermal fault in the power equipment, and the degree of heating is used as the criterion for judging the severity of the fault.

2. The method for inverting thermal faults in power equipment based on Gaussian heat source and adaptive optimization according to claim 1, characterized in that: In step S1, determining the temperature feature vector specifically includes: The four sides of the power equipment are labeled A, B, C, and D, respectively, and the surface temperature of the power equipment casing is obtained using an infrared imaging device; among them, sides A and C face each other, and sides B and D face each other. Define an m×m square sliding window on each surface, and move through each side using this sliding window. Calculate the average temperature within the area covered by the window, and filter out the maximum sliding window temperature for each side, denoted as T_Amax, T_Bmax, T_Cmax, and T_Dmax respectively. Calculate the average temperature of each side and denote it as T_Aavr, T_Bavr, T_Cavr, and T_Davr, respectively. Divide surfaces A and C into i×j grids, and surfaces B and D into n×n grids, and calculate the average temperature of each grid. The feature vector is composed of the maximum temperature of the sliding window on each side, the average temperature of the side, and the average temperature of the grid on each side.

3. The method for inverting thermal faults in power equipment based on Gaussian heat source and adaptive optimization as described in claim 2, characterized in that: In step S3, the three-dimensional Gaussian heat source distribution function is specifically as follows: ； Where: Q(x,y,z) represents the heat generation rate per unit volume of a three-dimensional Gaussian body, Q max σ represents the peak power density at the center of the heat source, σ represents the standard deviation of the Gaussian distribution, (x0,y0,z0) represents the coordinates of the fault center, and (x,y,z) represents the coordinates of the solution domain. in: ;P total This represents the total power generated by the Gaussian heat source; Where: vector X is taken as the vector to be solved, where: 。 4. The method for inverting thermal faults in power equipment based on Gaussian heat source and adaptive optimization as described in claim 1, characterized in that: In step S4, based on feature vector b obs With eigenvector b cal The optimization function is constructed as follows: 。 5. The method for inverting thermal faults in power equipment based on Gaussian heat source and adaptive optimization according to claim 1, characterized in that: The swarm intelligence optimization algorithm for continuous variable optimization employs four parallel candidate strategies, including the AOO update strategy based on the behavior of wheat seeds, the differential evolution random mutation strategy, the differential evolution optimal guidance strategy, and the quadratic difference strategy. In swarm intelligence optimization algorithms for continuous variables, one of four strategies is selected in each update through a roulette wheel mechanism.

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