A method for optimizing micro-plane coil structure parameters of MCR-WPT system based on agap bird optimization algorithm

Abstract

The application provides an MCR-WPT system micro-plane coil structure parameter optimization method based on a kingfisher optimization algorithm, which comprises the following steps: analyzing a compensation structure network, deducing an energy transmission efficiency form of the MCR-WPT system; analyzing physical structure parameters in the micro-plane coil, calculating self-induction, mutual induction and alternating current resistance; calculating a theoretical self-induction value of the micro-plane coil; calculating a mutual induction coefficient value between the coupling coils; winding the coupling coils with Litz wires; calculating the alternating current resistance of the Litz wires under high-frequency alternating current; making the coils at the transmitting end and the receiving end have the same specifications and parameters; establishing a coupling coil structure optimization model; setting the upper and lower limits of the parameter variables; adding constraint conditions; taking the energy transmission efficiency as an optimization target of the objective function; and performing optimization calculation on the coupling coil structure optimization model by using the kingfisher optimization algorithm. The method has shorter average running time and faster operation speed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of portable electronic technology, in particular to a micro planar coil structure parameter optimization method based on a spotbill optimization algorithm for an MCR-WPT system. BACKGROUND

[0002] The MCR-WPT system is a technology that uses high-frequency electromagnetic fields to achieve wireless energy transmission through resonance coupling principle. At present, there are the following problems in the optimization of the structure parameters of the micro planar coupling coil in the MCR-WPT system: the design of the coupling coil mainly relies on a large number of simulations and experiments, gradually analyzing the parameters of the coil, or first calculating the Q value of the coil, and then designing the corresponding coil. The existing problems exist in the low design efficiency and the inability to directly obtain the physical structure parameters of the coupling coil.

[0003] Traditional optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, often face problems such as low search efficiency, easy to fall into local optimum, and sensitive to parameter settings when dealing with the optimization of the coupling coil in the MCR-WPT system. These algorithms are difficult to quickly and accurately find the optimal solution in a complex electromagnetic field environment.

[0004] Therefore, it is necessary to invent a new coupling coil structure optimization method to solve the shortcomings in the existing design using a new swarm intelligence algorithm, improve the design efficiency and directly obtain the optimized physical structure parameters, in order to solve the parameter optimization problem in the existing coupling coil design. SUMMARY

[0005] The present application provides a micro planar coil structure parameter optimization method based on a spotbill optimization algorithm for an MCR-WPT system, which can be used to solve the technical problem of the optimization efficiency of the coupling coil design in the MCR-WPT system.

[0006] The present application provides a micro planar coil structure parameter optimization method based on a spotbill optimization algorithm for an MCR-WPT system, which comprises the following steps:

[0007] Step S1: Derive the form of the energy transmission efficiency of the MCR-WPT system by analyzing the compensation structure network;

[0008] Step S2: Analyze the physical structure parameters in the micro planar coil, calculate the self-inductance, mutual inductance and AC resistance through the coupling coil structure parameters;

[0009] Step S3: Calculate the theoretical self-inductance value of the micro planar coil;

[0010] Step S4: Calculate the mutual inductance coefficient value between the coupling coils;

[0011] Step S5: winding the coupling coil with Litz wire; calculating the AC resistance of the Litz wire under high-frequency AC;

[0012] Step S6: making the coils of the transmitting end and the receiving end have the same specifications and parameters, and ensuring the numerical consistency of the resonance capacitance;

[0013] Step S7: establishing a coupling coil structure optimization model through calculation and analysis of the parameters of the coupling coil;

[0014] Step S8: setting the upper and lower limits of the parameter variables, taking the power frequency, the wire diameter of the planar coil, the pitch and the distance between the two coils as the optimization variables; adding the constraint condition k s ; taking the energy transmission efficiency as the optimization target of the objective function;

[0015] Step S9: using the peacock optimization algorithm to perform optimization calculation on the coupling coil structure optimization model, introducing Kent chaotic mapping to the initialization stage for head chaotic variation, and introducing alpha-stable distribution for the foraging strategy of the PKO algorithm, enhancing the search ability of the algorithm for the global optimal solution, avoiding the algorithm from falling into a local optimal solution, and accelerating the convergence speed.

[0016] Compared with other mainstream high-performance algorithms, the optimization method based on the peacock optimization algorithm has shorter average running time, faster operation speed and higher calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flowchart of the present application.

[0018] Figure 2 is an S-S topology structure diagram in step S1 of the present application.

[0019] Figure 3 is a coaxial planar circular coil structure diagram of the present application.

[0020] Figure 4 is a PKO optimization algorithm flowchart in step S9 of the present application.

[0021] Figure 5 is a coupling coil transient model diagram of the present application. DETAILED DESCRIPTION

[0022] To make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0023] Firstly, the embodiments of the present application will be introduced below with reference to the drawings.

[0024] The application discloses a micro-plane coil structure optimization method for an MCR-WPT system based on a spotbill optimization algorithm.

[0025] Step S1: deducing an energy transmission efficiency form of the MCR-WPT system by analyzing a compensation structure network.

[0026] The energy transmission efficiency is as follows:

[0027]

[0028] In formula (1), η represents the energy transmission efficiency of the system, ω is the resonance angular frequency of the system, M is the mutual inductance value of the coupling coil, R1 and R2 respectively represent the internal resistances of the primary and secondary side coils, R L represents the load size of the system.

[0029] Step S2: analyzing the physical structure parameters of the micro-plane coil, and calculating the self-inductance, mutual inductance and AC resistance through the coupling coil structure parameters.

[0030] The input coupling coil parameter range is calculated as follows: an outer diameter of 8 mm, an inner diameter of 2 mm, a wire diameter range of 0.1 mm-1 mm, a pitch range of 0.01 mm-1 mm, a distance range of 3 mm-5 mm, and a power frequency range of 50 KHz-150 KHz.

[0031] Step S3: calculating the theoretical self-inductance value of the micro-plane coil.

[0032] The theoretical self-inductance value of the coil is determined as follows:

[0033]

[0034] Wherein, L is the theoretical self-inductance value of the coil, μ0 is the vacuum permeability, r max is the outer radius of the coil, r min is the inner radius of the coil, C1=2.46 and C2=0.2.

[0035] Step S4: calculating the mutual inductance coefficient value between the coupling coils.

[0036] The mutual inductance coefficient value between the coupling coils is determined as follows:

[0037]

[0038] Wherein, M is the theoretical mutual inductance coefficient value of the coil, N r is the number of turns of the primary side coil, N t is the number of turns of the secondary side coil, r r is the average radius of the primary side coil, r t is the average radius of the secondary side coil, and h is the distance between the coils.

[0039] Step S5: To reduce the loss caused by the increase of the AC resistance of the coil under high frequency conditions and improve the energy transmission efficiency of the MCR-WPT system, the Litz wire is used to wind the coupling coil; and the AC resistance of the Litz wire under high frequency AC is calculated.

[0040] The AC resistance value is determined as follows:

[0041]

[0042] wherein R ac is the AC resistance value, k is the number of Litz wire strands, d str is the diameter of a single strand.

[0043] Step S6: The coils of the transmitting end and the receiving end have the same specifications and parameters, and the numerical consistency of the resonance capacitance is ensured. For the S-S topology compensation network, the coupling coefficient calculation formula is:

[0044]

[0045] The critical coupling coefficient calculation formula is:

[0046]

[0047] The quality factor Q calculation formula is:

[0048]

[0049] wherein f is the frequency.

[0050] Step S7: Through the calculation and analysis of the parameters of the coupling coil, the coupling coil structure optimization model is established.

[0051] The coupling coil structure optimization model is shown in formula (8); wherein f is the frequency, R is the coil resistance, M is the theoretical mutual inductance value of the coil; N is the number of turns of the coil, r is the average radius of the coil, h is the distance between the coils; d str is the diameter of a single strand, k is the coupling coefficient, k s is the critical coupling coefficient; these parameters jointly affect the energy transmission efficiency of the system.

[0052]

[0053] Step S8: The upper and lower limits of the parameter variables are set, the frequency of the power supply, the wire diameter of the planar coil, the pitch and the distance between the two coils are taken as the optimization variables; the upper and lower limits of the parameter variables are set. To prevent the phenomenon of frequency splitting, the constraint condition k≤k s is added; and the energy transmission efficiency is taken as the optimization target of the objective function.

[0054] Step S9: the coupled coil structure optimization model is optimized by using the kingfisher optimization algorithm, Kent chaos mapping is introduced into the initialization stage for head chaos variation, and a-stable distribution is introduced for the foraging strategy of the PKO algorithm, which enhances the search ability of the algorithm for the global optimal solution, avoids the algorithm from falling into a local optimal solution, and speeds up the convergence speed. Thus, the physical structure parameters of the coupled coil of the MCR-WPT system are calculated quickly.

[0055] Step S9 includes:

[0056] Step S91, algorithm initialization stage: the initialization of the PKO algorithm adopts a random initialization method to randomly generate an initial population in the search space; assuming that the dimension space is D and the population size is N; the algorithm generates an initial population, and the solution of each individual is generated by random, ranging between the upper and lower bounds of the search space; each individual in the population will represent the current position of the kingfisher; the calculation formula is as follows:

[0057]

[0058] In the formula, X i,j represents the position of the i-th individual in the j-th dimension, rand represents a random value between 0 and 1, UB and LB represent the upper and lower bounds of the search range;

[0059] Step S92, determine the foraging strategy: the strategy simulates the behavior of the kingfisher hovering or perching to find prey in the air; the kingfisher detects potential optimal solutions in a wide search area;

[0060] The position of each individual is dynamically adjusted by using a random factor to ensure that the entire solution space is fully explored. This stage aims to avoid falling into a local optimal solution. The formula for updating the position is calculated based on the distance between individuals to ensure that the kingfisher can explore unexplored areas:

[0061]

[0062] In the iteration process, the solution of the next iteration is represented by X i (t+1), and the position of the current iteration is represented by X i (t); the parameter a is calculated as 2*randn(1,dim), where randn represents a random number in a normal distribution; N represents the total population size, and dim represents the dimension of the problem considered;

[0063] The value of the parameter T is dynamically determined according to the current strategy, including perching or hovering, to ensure the best performance in different running modes;

[0064] The T parameter in the perching strategy is calculated as follows:

[0065]

[0066] Crest_angles = 2*pi*rand(12);

[0067] The maximum number of iterations is specified by Max_Iter; the constant value BF, i.e. beat factor, is set to 8, and rand is a random value between 0 and 1.

[0068] The T parameter in the hovering strategy is calculated as follows:

[0069]

[0070] The fitness of the i-th and j-th plover is denoted by PKO_Fitness(i) and PKO_Fitness(j), respectively; similarly, the constant value BF is set to 8, and rand is a random value between 0 and 1.

[0071] Step S93, the diving strategy simulates the behavior of plover diving to catch prey; the goal is to search and develop the found good solution; the algorithm performs local search and optimization by moving individuals towards the current optimal solution; each individual will update its position according to its fitness value and the position of the optimal individual in the population to ensure that it is closer to the global optimal solution; the calculation formula is as follows:

[0072] X i (t+1) = X i (t) + HA*o*alpha*(b-X best (t)), i = 1, 2, … N (15);

[0073] where the fitness value of the i-th plover is denoted by PKO_Fitness(i), Best_Fitness represents the best fitness value obtained by all iterations, alpha is a control parameter calculated as 2*randn(1, dim)-1, o and HA represent hunting ability, which is calculated by the following two formulas:

[0074]

[0075]

[0076] b = X i (t) + o 2 *randn*X best (t) (18);

[0077] Step S94, the symbiotic strategy simulates the symbiotic relationship between the kingfisher and other animals (such as the symbiosis with the otter), and the fitness is compared and optimized by referring to the positions of other individuals; when an individual refers to other solutions, the better solution will be retained according to the comparison result, so as to avoid falling into a local optimum; the position comparison and exchange with a randomly selected individual are implemented, which is similar to cache search, and helps the algorithm to jump out of the local optimum; the calculation formula is as follows:

[0078]

[0079] α=2*randn(1,dim)-1 (21);

[0080]

[0081] In the formula, two individuals are randomly selected from the population, and the positions are represented by X m and X n ; the predation efficiency of the kingfisher is represented by PE, wherein PE max and PE min are fixed values of 0.5 and 0, respectively;

[0082] Step S95, the exploitation strategy simulates the kingfisher returning to the storage area using symbiotic partners to perform fine search; in the comparison between the new and old positions, the algorithm determines whether to adopt the new solution by judging the fitness value; this stage switches between foraging and symbiotic strategies, ensuring the balance between global search and local optimization.

[0083] Step S96, the end stage: the algorithm continues to cycle in each stage until the stop condition is met, for example, the maximum number of iterations is reached or a satisfactory solution is found; in each iteration, the individual finds the global optimal solution through the foraging exploration and exploitation strategies;

[0084] Step S97, the Kent chaotic mapping is introduced into the initialization stage to perform head chaotic mutation; the chaotic mapping uniformly distributes the initialized population in the entire solution space, enhances the search ability of the algorithm for the global optimal solution, avoids the algorithm falling into a local optimal solution, and speeds up the convergence speed. Realize fast calculation.

[0085] The expression of the Kent chaotic mapping initialized population is as follows:

[0086]

[0087] The control parameter a ∈ (0, 1); the chaotic orbit state value range is (0, 1); the Kent chaotic mapping strategy is used to initialize the population distribution, and the generated population is more uniform, which is more conducive to the global traversal of the particle in the optimization space, and can enhance the global optimization ability of the algorithm.

[0088] Step S98, introduce alpha-stable distribution for PKO algorithm foraging strategy in the speed update formula, with alpha stable distribution generated random number instead of the traditional pseudo-random number rand, thereby increasing the ability of the algorithm to jump out of local optimum.

[0089] The PKO optimization algorithm framework is used to build an optimization model for verification. In the operation, the iteration number is set to 1000. In order to ensure the accuracy of the results and the inherent randomness of the search algorithm, 50 independent operations are performed. Finally, a representative output is obtained by comprehensively analyzing the operation results. Through the analysis of the obtained data results, the average solving time of the PKO algorithm is 0.14s, and it can stably converge to the optimal solution in about 150 iterations. Compared with the whale optimization algorithm (WOA), Harris hawk algorithm (HHO), and sine cosine optimization algorithm (SCA), the PKO has significant advantages in convergence speed and calculation accuracy. Compared with the traditional coupled coil design optimization method, the MCR-WPT system micro plane coil structure optimization method has the following advantages: the optimization method based on the PKO algorithm has shorter average running time, faster operation speed and higher calculation efficiency compared with other mainstream high-performance algorithms.

[0090] When the outer diameter is 8mm and the inner diameter is 2mm, the optimal coupling coil parameter configuration is determined by optimization calculation in the given parameter range: the power frequency is 150KHz, the wire diameter is 0.18mm, the distance between the primary coil and the secondary coil is 3mm, and the number of turns is 15.7 turns, achieving an energy transmission efficiency of up to 13.88%. The result data of the coupling coil under different parameter specifications is shown in Table 1.

[0091] Table 1 Comparison of different parameter performance

[0092]

[0093] Through the obtained result data, the energy transmission efficiency of the optimized coupling coil structure parameters is the highest compared with other parameters, which verifies the effectiveness and feasibility of the optimization method adopted.

[0094] The application optimizes the physical structure parameters of the coil by the plover optimization algorithm to improve the energy transmission efficiency of the system; calculates the self-inductance and mutual inductance of the coil, and the alternating current resistance considering the skin effect and proximity effect under high-frequency alternating current; verifies the optimized coil structure by electromagnetic simulation software to ensure the effectiveness of the optimized parameters; deduces the calculation formula of the energy transmission efficiency of the system by analyzing the S-S topology compensation structure network; the calculation formula includes parameters such as resonant angular frequency, mutual inductance value, primary and secondary coil resistance and system load size; the electrical characteristics of the coil are optimized by calculating the theoretical self-inductance value of the microplane coil; the calculation of the self-inductance value considers the outer diameter, inner diameter, wire diameter and coil spacing of the coil; the coupling effect between the coils is optimized by calculating the mutual inductance coefficient value between the coupled coils; the calculation of the mutual inductance coefficient value considers the number of turns, average radius of the primary and secondary coils and the distance between the coils; the resistance characteristics of the coil are optimized by calculating the alternating current resistance of the Litz wire under high-frequency alternating current; the calculation of the alternating current resistance considers the number of strands and the single strand diameter of the Litz wire; the frequency splitting phenomenon of the MCR-WPT system is considered to establish a constraint condition to prevent overcoupling; the optimization model of the coupled coil structure is established by simultaneously solving the energy transmission efficiency calculation formula; the optimization model considers the influence of the physical structure parameters of the coil on the energy transmission efficiency; the upper and lower limits of the optimization variables and the constraint conditions are set, and the energy transmission efficiency is taken as the optimization target; the optimization variables include the power frequency, the wire diameter, the pitch and the coil spacing; the chaos mapping and the alpha-stable distribution are used for the initialization and foraging strategy of the optimization algorithm to speed up the convergence speed of the algorithm and avoid falling into local optimal solution.

[0095] The embodiments of the application described above do not constitute a limitation on the protection scope of the application.

Claims

1. A method for optimizing the structural parameters of a microplanar coil in an MCR-WPT system based on the kingfisher optimization algorithm, characterized in that, The method includes: Step S1: Derive the form of energy transfer efficiency of the MCR-WPT system by analyzing the compensation structure network; Step S2: Analyze the physical structure parameters in the micro planar coil, and calculate the self-inductance, mutual inductance, and AC resistance by using the coupled coil structure parameters; Step S3: Calculate the theoretical self-inductance of the tiny planar coil; Step S4: Calculate the mutual inductance coefficient between the coupled coils; Step S5: Wind the coupling coil using Litz wire; calculate the AC resistance of the Litz wire under high-frequency AC conditions; Step S6: Ensure that the coils at the transmitting and receiving ends have the same specifications and parameters to guarantee the consistency of the resonant capacitance value; Step S7: Establish an optimization model for the coupled coil structure by calculating and analyzing the parameters of the coupled coil; The optimized model of the coupled coil structure is shown in equation (8); where f is the frequency, R is the coil internal resistance, M is the theoretical mutual inductance coefficient of the coil; N is the number of coil turns, r is the average radius of the coil, and h is the distance between coils; d str Where is the diameter of a single strand, and k is the coupling coefficient. s The critical coupling coefficient; η represents the energy transfer efficiency of the system; L is the theoretical self-inductance of the coil; Step S8: Set the upper and lower limits of the parameter variables, using the power supply frequency, wire diameter of the planar coil, pitch, and distance between the two coils as optimization variables; add the constraint k≤k s The optimization objective is to use energy transfer efficiency as the objective function. Step S9: Optimize the coupled coil structure optimization model using the kingfisher optimization algorithm, introduce Kent chaotic mapping to the initialization stage for head chaotic mutation, and introduce α-stable distribution for the foraging strategy of the PKO algorithm to enhance the algorithm's ability to search for the global optimum, avoid the algorithm getting stuck in local optima, and accelerate the convergence speed.

2. The method according to claim 1, characterized in that, In step S1, the energy transfer efficiency is as follows: In formula (1): η represents the energy transfer efficiency of the system; ω is the resonant angular frequency of the system; M is the mutual inductance of the coupling coils; R1 and R2 represent the internal resistances of the primary and secondary coils, respectively; R L This indicates the system load.

3. The method according to claim 1, characterized in that, In step S2, the calculated range of input coupling coil parameters is: outer diameter 8mm, inner diameter 2mm, wire diameter range 0.1mm-1mm, pitch range 0.01mm-1mm, spacing range 3mm-5mm, and power frequency range 50KHz-150KHz.

4. The method according to claim 1, characterized in that, In step S3, the theoretical self-inductance of the coil is determined as follows: Where L is the theoretical self-inductance of the coil, and μ0 is the free permeability. r max r is the outer radius of the coil. min Let C1 = 2.46 and C2 = 0.2 be the inner radius of the coil.

5. The method according to claim 1, characterized in that, In step S4, the method for determining the mutual inductance coefficient between the coupled coils is as follows: Where M is the theoretical mutual inductance of the coils, and N... r N represents the number of turns of the primary coil. t r is the number of turns of the secondary coil. r r is the average radius of the primary coil. t denoted as the average radius of the secondary coil, and h as the distance between the coils.

6. The method according to claim 1, characterized in that, In step S5, the method for determining the AC resistance value is as follows: Among them, R ac Here, k is the AC resistance value, k is the number of Litz wire strands, and d is the resistance value. str It is a single strand wire diameter.

7. The method according to claim 1, characterized in that, Step S6: Ensure that the coils at the transmitting and receiving ends have the same specifications and parameters, and ensure the consistency of the resonant capacitance value, including: For the SS topology compensation network, the coupling coefficient is calculated using the following formula: The formula for calculating the critical coupling coefficient is: The formula for calculating the quality factor Q is: Where f is the frequency.

8. The method according to claim 1, characterized in that, Step S9 includes: Step S91, Algorithm Initialization Phase: The PKO algorithm uses a random initialization method, randomly generating an initial population in the search space; assuming the dimension space is D and the population size is N; the algorithm generates an initial population, and the solution for each individual is randomly generated, ranging between the upper and lower bounds of the search space; each individual in the population represents the current position of the kingfisher; the calculation formula is as follows: In the formula, X i,j This represents the position of the i-th individual in the j-th dimension, rand represents a random value between 0 and 1, and UB and LB represent the upper and lower bounds of the search range; Step S92, determine the foraging strategy: the strategy simulates the behavior of the kingfisher hovering or perching in the air to find prey; simulates the kingfisher exploring a wide search area to find potential optimal solutions; The formula for dynamically adjusting an individual's position using random factors is calculated based on the distance between individuals, ensuring that the kingfisher can explore unexplored areas: During the iteration process, the solution for the next iteration is represented by X. i (t+1) represents the position of the current iteration, denoted by X. i (t) represents; the parameter α is calculated as 2*randn(1,dim), where randn represents a random number in a normal distribution; N represents the total size, and dim represents the dimension of the problem under consideration; The value of parameter T is dynamically determined based on the current strategy, including whether to perch or hover, to ensure optimal performance in different operating modes; The T parameter in the habitat strategy is calculated as follows: Crest_angles=2*pi*rand (12); The maximum number of iterations is specified by Max_Iter; the constant value BF, i.e., the beat factor, is set to 8, and rand is a random value between 0 and 1; The T parameter in the hovering strategy is calculated as follows: The fitness of the i-th and j-th kingfishers are represented by PKO_Fitness(i) and PKO_Fitness(j), respectively; similarly, the constant value BF is set to 8, and rand is a random value between 0 and 1; Step S93: The diving strategy simulates the swooping hunting behavior of a kingfisher; the goal is to search for and develop the best solutions found; the algorithm performs local search and optimization by moving individuals toward the current optimal solution; each individual updates its position based on its fitness value and the position of the best individual in the population to ensure it gets closer to the global optimum; the calculation formula is as follows: X i (t+1)=X i (t)+HA*o*α*(b-X best (t)),i=1,2,…N (15); Wherein, the fitness value of the i-th kingfisher is denoted as PKO_Fitness(i), Best_Fitness represents the best fitness value obtained from all iterations, α is a control parameter, calculated as 2*randn(1,dim)-1, and o and HA represent hunting ability, calculated by the following two formulas: b=X i (t)+o 2 *randn*X best (t)(18); Step S94: The symbiotic strategy simulates the symbiotic relationship between the kingfisher and other animals, comparing and optimizing fitness by referencing the positions of other individuals. When an individual references other solutions, it retains the better solution based on the comparison results, thus avoiding getting trapped in local optima. This is achieved by comparing and exchanging positions with randomly selected individuals, similar to cached search, helping the algorithm escape local optima. The calculation formula is as follows: α=2*randn(1,dim)-1 (21); In the formula, two individuals are randomly selected from the population, and their positions are represented by X. m and X n The predation efficiency of the kingfisher is represented by PE, where PE = ... max and PE min The fixed values ​​are 0.5 and 0 respectively; Step S95: The algorithm simulates the kingfisher using symbiotic partners to return to the storage area; in the comparison between the old and new locations, the algorithm decides whether to adopt the new solution based on the fitness value. Step S96, Termination Phase: The algorithm continues to loop through each phase until the stopping condition is met; in each iteration, the individual seeks the global optimum through foraging, exploration, and development strategies. Step S97: Introduce the Kent chaotic map into the initialization phase for head chaotic mutation. The chaotic map evenly distributes the initial population throughout the solution space. The expression for the Kent chaotic map initialization population is as follows: The control parameter a∈(0,1); the chaotic orbit state value range is (0,1); the population distribution is initialized using the Kent chaotic mapping strategy, resulting in a more uniform population; Step S98 introduces the α-stable distribution for the foraging strategy of the PKO algorithm. In the velocity update formula, the random number generated by the α-stable distribution is used instead of the traditional pseudo-random number rand.

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