Explosive JWL state equation parameter calculation method based on hybrid algorithm

Abstract

The invention provides an explosive JWL state equation parameter calculation method based on a hybrid algorithm, and relates to the technical field of explosive JWL state equation parameter acquirement.According to the explosive JWL state equation parameter calculation method based on the hybrid algorithm, the detonation velocity and the initial density of an explosive serve as known conditions, and an energy difference model is calculated by utilizing the C-J condition, the Hugoniot relational expression and the energy difference model when the explosive is detonated; and calculating explosive JWL state equation parameters based on a grey wolf particle swarm hybrid algorithm. The method is accurate and reliable, the complexity of calibrating the parameters of the JWL state equation in the cylinder test is avoided, the acquisition cost of the parameters of the JWL state equation is reduced, and a certain reference can be provided for acquiring the parameters of the JWL state equation of the explosive and calculating the detonation performance.

Description

Technical Field

[0001] The invention relates to the technical field of explosive JWL state equation parameter acquisition, and in particular to an explosive JWL state equation parameter calculation method based on a hybrid algorithm. Background Art

[0002] Explosives have been widely used in many fields such as military and civil industries, and they play an indispensable role in the weapons industry and civil technology. With the widespread use of explosives, the safety and reliability of explosives deserve attention, and the study of explosive detonation is an important part that cannot be ignored. The JWL state equation can accurately describe the relationship between the density, temperature and other parameters of the detonation products after the explosive detonates, and it is widely used in the fields of explosion damage, pyrotechnics research, etc.

[0003] The JWL state equation is a semi-empirical state equation that does not contain chemical reactions, and its parameters are mainly determined by experiments or calculations. At present, there are three main ways to determine the unknown parameters of the JWL state equation: one is to calibrate the JWL state equation parameters of explosives through cylinder tests; the second is to automatically calibrate the JWL state equation parameters of explosives by combining software and programs; the third is to calculate and fit the JWL state equation parameters through various optimization algorithms. The cylinder test calibration method has a long cycle and high test cost, and the software automatic calibration accuracy is not high. Therefore, it is very effective to obtain the JWL state equation parameters by optimizing the algorithm for explosive detonation assessment.

[0004] The current patent disclosures show that: 1) Patent (CN 108984996 A) discloses a method for calculating the JWL state equation parameters of aluminum-containing explosives based on the reactivity of aluminum powder. This method uses a combination of detonation theory calculations, underwater explosion numerical simulations, and underwater explosion tests to instantly determine the JWL state equation parameters of the detonation products of aluminum-containing explosives. This method has the advantages of high accuracy, strong pertinence, and good reliability, but the process of this method is relatively cumbersome, time-consuming, and costly. 2) Patent (CN115048853 A) discloses a method for calibrating the JWL state equation parameters of methane based on the optimization of BP neural networks. This method uses the overpressure data of the methane detonation test to replace the cylinder wall-displacement time data of the test, and then calculates the JWL state equation parameters of the methane detonation products. This method simplifies the optimization process of the state equation parameters and improves the optimization speed and accuracy, but this method requires a large amount of test data and is relatively cumbersome.

[0005] In recent years, scholars have proposed many heuristic bionic optimization algorithms, which have become effective methods for solving optimization problems due to their many characteristics such as avoiding local optimality, non-derivative mechanism, flexibility and simplicity. Due to the complexity of the JWL state equation parameter calculation problem, it is difficult to meet the requirements using a single heuristic algorithm, so it is necessary to combine multiple algorithms to make up for each other's shortcomings in solving the problem. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a method for calculating the parameters of the explosive JWL state equation based on a hybrid algorithm; the present invention integrates the Gray Wolf algorithm into the Particle Swarm Algorithm, overcomes the defect of the Particle Swarm Algorithm being prone to premature maturity, and proposes a method for quickly calculating and obtaining the parameters of the explosive JWL state equation based on the Gray Wolf Particle Swarm Hybrid Algorithm; the method is used to calculate the parameters of the JWL state equation of several typical explosives, and the calculation results are numerically simulated by cylinder tests, which has verified the validity of the calculation results. This method can obtain the unknown parameters of the JWL state equation by inputting the density and detonation velocity of the explosive, which improves the efficiency of obtaining the unknown parameters of the JWL state equation and provides convenience for the study of explosive detonation.

[0007] A method for calculating parameters of explosive JWL state equation based on a hybrid algorithm comprises the following steps:

[0008] Step S1: obtaining the detonation velocity and density of the explosive;

[0009] Step S2: Incorporating the CJ condition, Hugoniot relation and energy difference model during explosive detonation into the Grey Wolf Particle Swarm Hybrid Algorithm program;

[0010] Step S2.1: Establish the JWL state equation of explosive in standard form and isentropic form, which are:

[0011]

[0012]

[0013] Where: R1, R2, A, B, C, ω are 6 unknown parameters, V is the relative volume of the detonation product of the explosive, E is the internal energy per unit volume of the detonation product, P s is the pressure of the explosive detonation product in isentropic form. P is the pressure of the explosive detonation product in standard form;

[0014] Step S2.2: When the explosive detonates, the CJ condition and Hugoniot relation are used to know that the six unknown parameters of the JWL state equation satisfy the following equations:

[0015]

[0016] Where: P CJ ,V CJ ,ρ0,D and E0 are the pressure at the CJ point of the explosive, the relative volume at the CJ point, the initial density, the detonation velocity and the initial volume energy respectively; for the explosive at the CJ point P CJ and V CJ Calculated by the following formula:

[0017]

[0018]

[0019] Where: r is the adiabatic index of the detonation product, and the calculation formula is as follows:

[0020]

[0021] The initial volume energy E0 of the explosive is calculated as follows:

[0022] E0=(0.204-0.0734ρ0)ρ0D 2 (7)

[0023] Step S2.3: Conduct an explosive-driven cylinder wall test to convert the internal energy of the explosive into the kinetic energy of the wall and the explosion products. The energy difference is calculated as follows:

[0024]

[0025] Where: m and u V is the material density of the cylinder and the radial velocity of the outer wall at the characteristic position, r i0 and r e0 are the initial inner and outer diameters of the cylinder.

[0026] For the radial movement speed of the outer wall at the characteristic position of the cylinder, the calculation formula is as follows:

[0027]

[0028]

[0029] where u V＝2.4 and u V＝7.0 It represents the velocity value at the characteristic position of the cylinder when the relative volume of the detonation product is 2.4 and 7.0, 0.9 and 0.8 are exponential powers;

[0030] Step S2.4: Combine formulas (3) to (7) to obtain the relationship between the initial density ρ0 and detonation velocity D of the explosive and the six unknown parameters R1, R2, A, B, C, ω; the value ranges of ω, R1, and R2 are [0.2, 0.4], [4, 6], and [0, 2], respectively. Select the values ​​of ω, R1, and R2 in the corresponding ranges and then calculate the values ​​of A, B, and C; after obtaining a set of solutions for the six unknown parameters of the JWL state equation, calculate the energy difference when the relative volumes of the detonation products are 2.4 and 7.0 by formula (8). If f(2.4) and f(7.0) are close to 0, it means that this set of solutions is applicable to the explosive;

[0031] Step S3: Input the detonation velocity and density of the explosive into the Grey Wolf Particle Swarm Hybrid Algorithm, add limiting conditions, perform optimization calculations on ω, R1, and R2 within the upper and lower bounds, output the global optimal solution of A, B, and C, obtain the JWL state equation parameter combination with the minimum energy difference, and realize the calculation of the JWL state equation parameters of the explosive;

[0032] The gray wolf particle swarm hybrid algorithm is to nest the PSO algorithm and the GWO algorithm, with the PSO algorithm as the main cycle algorithm and the GWO algorithm as the secondary cycle algorithm. The global extreme value g of the obtained population is obtained after the main cycle of the PSO algorithm is completed once. b The alpha wolf in the secondary cycle of the GWO algorithm is guided to prey; the particle dimension is set to 3, the population size is 80, the number of main loop iterations is 300, the maximum and minimum values ​​of the inertia factor are set to 1.2 and 0.8, and the learning factors c1, c2 and c3 are set to 0.8; the number of gray wolves is set to 20, and the number of secondary loop runs is set to 20. The fitness function of the gray wolf particle swarm hybrid algorithm is set to: δ f =|f(2.4)|+|f(7.0)|;

[0033] The limiting conditions are as follows:

[0034]

[0035] In the optimization calculation, the upper and lower bounds of ω, R1, and R2 are {(0.2, 0.4), (4, 6), (0, 2)};

[0036] In order to prevent the particle swarm from falling into the local optimum and adjust and optimize its speed formula, the optimal position value obtained by the GWO algorithm cycle is introduced into the update calculation of the particle flight speed. The formula is as follows:

[0037]

[0038] Where k is the number of iterations; r1, r2 and r3 are random numbers; c1, c2 and c3 are learning factors; X1(k), X2(k) and X3(k) are the positions of the three best wolves in the population; v id and x id is the speed and position of the ith particle in the dth dimension; ω is the inertia factor. A linear differential decreasing strategy is adopted. The initial ω value is large and the optimization ability is strong. When approaching the optimal solution, the ω value decreases and a small step size optimization is performed. The update calculation formula is as follows:

[0039]

[0040] In the formula, iter max is the maximum number of iterations; k is the number of iterations; ω max and ωmin are the maximum and minimum values ​​of the inertia factor, respectively.

[0041] The beneficial effects of adopting the above technical solution are:

[0042] The present invention provides a method for calculating the JWL state equation parameters of explosives based on a hybrid algorithm. The present invention integrates the Grey Wolf algorithm into the Particle Swarm Algorithm, and based on this, the method is used to quickly calculate and obtain the JWL state equation parameters of explosives. The calculation process is simple, and the calculation result is accurate and reliable. The JWL state equation parameters calculated by the hybrid algorithm can be used for explosive parameter calibration, overcoming the shortcomings of traditional test calibration such as high cost and long cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flow chart of the grey wolf particle swarm hybrid algorithm in an embodiment of the present invention.

[0044] Figure 2 It is a fitness curve diagram for calculating the JWL state equation parameters of four explosives in an embodiment of the present invention.

[0045] Figure 3 It is a numerical simulation curve diagram of the calculation results and test results of four explosive algorithms in the embodiment of the present invention;

[0046] Figures (a) to (d) are numerical fitting curves of the algorithm calculation results and the test results of explosive 1#, explosive 2#, explosive 3# and explosive 4#, respectively. DETAILED DESCRIPTION

[0047] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0048] A method for calculating parameters of explosive JWL state equation based on a hybrid algorithm comprises the following steps:

[0049] Step S1: obtaining the detonation velocity and density of the explosive;

[0050] Step S2: Incorporating the CJ condition, Hugoniot relation and energy difference model during explosive detonation into the Grey Wolf Particle Swarm Hybrid Algorithm program;

[0051] Step S2.1: Establish the JWL state equation of explosive in standard form and isentropic form, which are:

[0052]

[0053]

[0054] Where: R1, R2, A, B, C, ω are 6 unknown parameters, V is the relative volume of the detonation product of the explosive, E is the internal energy per unit volume of the detonation product, P s is the pressure of the explosive detonation product in isentropic form. P is the pressure of the explosive detonation product in standard form;

[0055] Step S2.2: When the explosive detonates, the CJ condition and Hugoniot relation are used to know that the six unknown parameters of the JWL state equation satisfy the following equations:

[0056]

[0057] Where: P CJ ,V CJ ,ρ0,D and E0 are the pressure at the CJ point of the explosive, the relative volume at the CJ point, the initial density, the detonation velocity and the initial volume energy respectively; for the explosive at the CJ point P CJ and V CJ Calculated by the following formula:

[0058]

[0059]

[0060] Where: r is the adiabatic index of the detonation product, which is related to the initial density of the explosive, detonation velocity, etc. The calculation formula is as follows:

[0061]

[0062] The initial volume energy E0 of the explosive is calculated as follows:

[0063] E0=(0.204-0.0734ρ0)ρ0D 2 (7)

[0064] Step S2.3: Conduct an explosive-driven cylinder wall test to convert the internal energy of the explosive into the kinetic energy of the wall and the explosion products. The energy difference is calculated as follows:

[0065]

[0066] Where: m and u V is the material density of the cylinder and the radial movement speed of the outer wall at the characteristic position; r i0 and r e0 is the initial inner diameter and initial outer diameter of the cylinder. m =8.93g / cm 3 , r i0 =12.7mm, r e0 =15.2mm;

[0067] For the radial movement speed of the outer wall at the characteristic position of the cylinder, the calculation formula is as follows:

[0068]

[0069]

[0070] where u V＝2.4 and u V＝7.0 It represents the velocity value at the characteristic position of the cylinder when the relative volume of the detonation product is 2.4 and 7.0, 0.9 and 0.8 are exponential powers;

[0071] Step S2.4: Combine formulas (3) to (7) to obtain the relationship between the initial density ρ0 and detonation velocity D of the explosive and the six unknown parameters R1, R2, A, B, C, ω; the value ranges of ω, R1, and R2 are [0.2, 0.4], [4, 6], and [0, 2], respectively. Select the values ​​of ω, R1, and R2 in the corresponding ranges and then calculate the values ​​of A, B, and C; after obtaining a set of solutions for the six unknown parameters of the JWL state equation, calculate the energy difference when the relative volumes of the detonation products are 2.4 and 7.0 by formula (8). If f(2.4) and f(7.0) are close to 0, it means that this set of solutions is applicable to the explosive;

[0072] Step S3: Input the detonation velocity and density of the explosive into the Grey Wolf Particle Swarm Hybrid Algorithm, add limiting conditions, perform optimization calculations on ω, R1, and R2 within the upper and lower bounds, output the global optimal solution of A, B, and C, obtain the JWL state equation parameter combination with the minimum energy difference, and realize the calculation of the JWL state equation parameters of the explosive;

[0073] Combining the PSO algorithm with the GWO algorithm can improve the performance of the PSO algorithm in local and global search. Figure 1 shown.

[0074] The gray wolf particle swarm hybrid algorithm is to nest the PSO algorithm and the GWO algorithm, with the PSO algorithm as the main cycle algorithm and the GWO algorithm as the secondary cycle algorithm. The global extreme value g of the obtained population is obtained after the main cycle of the PSO algorithm is completed once. b The alpha wolf in the secondary cycle of the GWO algorithm is guided to prey; the particle dimension is set to 3, the population size is 80, the number of main loop iterations is 300, the maximum and minimum values ​​of the inertia factor are set to 1.2 and 0.8, and the learning factors c1, c2 and c3 are set to 0.8; the number of gray wolves is set to 20, and the number of secondary loop runs is set to 20. The fitness function of the gray wolf particle swarm hybrid algorithm is set to: δ f =|f(2.4)|+|f(7.0)|;

[0075] The limiting conditions are as follows:

[0076]

[0077] In the optimization calculation, the upper and lower bounds of ω, R1, and R2 are {(0.2, 0.4), (4, 6), (0, 2)};

[0078] In order to prevent the particle swarm from falling into the local optimum and adjust and optimize its speed formula, the optimal position value obtained by the GWO algorithm cycle is introduced into the update calculation of the particle flight speed. The formula is as follows:

[0079]

[0080] Where k is the number of iterations; r1, r2 and r3 are random numbers; c1, c2 and c3 are learning factors; X1(k), X2(k) and X3(k) are the positions of the three best wolves in the population; v id and x id is the speed and position of the ith particle in the dth dimension; ω is the inertia factor. A linear differential decreasing strategy is adopted. The initial ω value is large and the optimization ability is strong. When approaching the optimal solution, the ω value decreases and a small step size optimization is performed. The update calculation formula is as follows:

[0081]

[0082] In the formula, iter max is the maximum number of iterations; k is the number of iterations; ω max and ω min are the maximum and minimum values ​​of the inertia factor, respectively.

[0083] When the detonation velocity and density of explosives are known, the Grey Wolf Particle Swarm Hybrid Algorithm is used to calculate the JWL state equation parameters of four kinds of explosives. Figure 2 is the fitness function value change curve of the four kinds of explosives, Figure 2 It can be seen that the fitness function values ​​of the four explosives are finally close to 0, which means that the energy difference between the relative volumes of the detonation products of the four explosive cylinder tests is very small when they are 2.4 and 7.0.

[0084] Step S4: using the simulation software AUTODYN to perform numerical simulation of the cylinder test, setting the JWL state equation parameters of the explosive to the values ​​calculated by the hybrid algorithm, and then solving the change value of the radial displacement of the cylinder wall;

[0085] The parameters of the explosive JWL state equation calculated based on the Grey Wolf Particle Swarm Hybrid Algorithm were used to simulate the cylinder expansion process driven by explosive detonation using the AUTODYN software. A 1 / 2 two-dimensional model was established. The explosive in the cylinder was detonated from one end, using the surface detonation method, and 6 Gaussian points were evenly distributed on the outside of the tube wall from the detonation end to record the radial displacement of the cylinder expansion process.

[0086] Step S5: Compare the obtained simulation values ​​with the test values, and draw a conclusion that the JWL state equation parameters of the explosive calculated by the hybrid algorithm are feasible.

[0087] In step S5, the radial displacement variation diagram at Gauge #3 on the outer wall of the cylinder is recorded, and the determination coefficient R is taken. 2 The similarity of the quantitative analysis curves is greater than 0.99, which proves that this method is feasible.

[0088] In step S4, in order to verify the accuracy of the JWL state equation parameters calculated by the Gray Wolf Particle Swarm Algorithm, the AUTODYN software is used to simulate the expansion process of the cylinder driven by explosive detonation. The cylinder is OHFC oxygen-free copper with a length of 306 mm, an inner diameter of 25 mm, and a wall thickness of 5 mm. The Mie-Grüneisen state equation and the Streinberg-Guian strength model are used in the simulation, and the parameter values ​​are taken from the AUTODYN material library. The cylinder simulation model is symmetrical, and a 1 / 2 two-dimensional model is established. The explosive in the cylinder is detonated from one end, and the surface detonation method is adopted. Six Gauss points are evenly distributed on the outside of the tube wall from the detonation end to record the radial displacement of the cylinder expansion process. During the simulation, the Euler algorithm is used for the meshes of explosives and air domains. The size of the air domain is 366mm×46mm, and the mesh size is 0.5mm×0.5mm. The cylinder is divided into Lagrangian meshes, and the mesh size is also 0.5mm×0.5mm. The fluid-solid coupling method is adopted to deal with the interaction in the simulation.

[0089] Figure 3 The radial displacement variation diagram of Gauge #3 on the outer wall of the cylinder is shown in Figure 1. The determination coefficient R 2 Similarity of quantitative analysis curves. Determination coefficient R 2 =1-SSE / SST, SSE is the sum of squares of the difference between the true value and the calculated value, SST is the sum of squares of the difference between the true value and the mean, R 2 The closer to 1, the higher the similarity of different curves. The variation curves of the simulation results of the four explosives R 2The calculated results are all greater than 0.99 and close to 1. It can be seen that the JWL state equation parameters calculated by the hybrid algorithm have a high degree of coincidence with the curves obtained by numerical simulation of the JWL state equation parameters in the material library. During the entire process of cylinder expansion, the radial displacement of the outer wall changes in a basically consistent manner, indicating that the calculation results of the Grey Wolf Particle Swarm Hybrid Algorithm have high accuracy.

[0090] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A method for calculating parameters of explosive JWL state equation based on hybrid algorithm, characterized in that: The following steps are involved: Step S1: obtaining the detonation velocity and density of the explosive; Step S2: Incorporating the CJ condition, Hugoniot relation and energy difference model during explosive detonation into the Grey Wolf Particle Swarm Hybrid Algorithm program; Step S3: Input the detonation velocity and density of the explosive into the Grey Wolf Particle Swarm Hybrid Algorithm, add limiting conditions, perform optimization calculations on the unknown parameters ω, R1, and R2 within the upper and lower bounds, output the global optimal solution of A, B, and C, obtain the JWL state equation parameter combination with the smallest energy difference, and realize the calculation of the JWL state equation parameters of the explosive.

2. The method for calculating parameters of explosive JWL state equation based on hybrid algorithm according to claim 1, characterized in that: The step S2 specifically includes the following steps: Step S2.1: Establish the JWL state equation of explosive in standard form and isentropic form, which are: Where: R1, R2, A, B, C, ω are 6 unknown parameters, V is the relative volume of the detonation product of the explosive, E is the internal energy per unit volume of the detonation product, P s is the pressure of the explosive detonation product in isentropic form; P is the pressure of the explosive detonation product in standard form; Step S2.2: When the explosive detonates, the CJ condition and Hugoniot relation are used to know that the six unknown parameters of the JWL state equation satisfy the following equations: Where: P CJ ,V CJ ,ρ0,D and E0 are the pressure at the CJ point of the explosive, the relative volume at the CJ point, the initial density, the detonation velocity and the initial volume energy respectively; for the explosive at the CJ point P CJ and V CJ Calculated by the following formula: Where: r is the adiabatic index of the detonation product, and the calculation formula is as follows: The initial volume energy E0 of the explosive is calculated as follows: E0=(0.204-0.0734ρ0)ρ0D 2 (7) Step S2.3: Conduct an explosive-driven cylinder wall test to convert the internal energy of the explosive into the kinetic energy of the wall and the explosion products. The energy difference is calculated as follows: Where: m and u V is the material density of the cylinder and the radial velocity of the outer wall at the characteristic position, r i0 and r e0 are the initial inner diameter and initial outer diameter of the cylinder; For the radial movement speed of the outer wall at the characteristic position of the cylinder, the calculation formula is as follows: where u V＝2.4 and u V＝7.0 It represents the velocity value at the characteristic position of the cylinder when the relative volume of the detonation products is 2.4 and 7.0; Step S2.4: Combine formulas (3) to (7) to obtain the relationship between the initial density ρ0 and detonation velocity D of the explosive and the six unknown parameters R1, R2, A, B, C, ω; the value ranges of ω, R1, and R2 are [0.2, 0.4], [4, 6], and [0, 2], respectively. Select the values ​​of ω, R1, and R2 in the corresponding ranges and then calculate the values ​​of A, B, and C. After obtaining a set of solutions for the six unknown parameters of the JWL state equation, use formula (8) to calculate the energy difference when the relative volumes of the detonation products are 2.4 and 7.

0. If f(2.4) and f(7.0) are close to 0, it means that this set of solutions is applicable to the explosive.

3. The method for calculating parameters of explosive JWL state equation based on hybrid algorithm according to claim 1, characterized in that: In step S3, the gray wolf particle swarm hybrid algorithm is to nest the PSO algorithm and the GWO algorithm, with the PSO algorithm as the main loop algorithm and the GWO algorithm as the secondary loop algorithm. The PSO algorithm completes the main loop once, and the global extreme value g of the obtained population is b The alpha wolf in the secondary cycle of the GWO algorithm is guided to prey; the particle dimension is set to 3, the population size is 80, the number of main loop iterations is 300, the maximum and minimum values ​​of the inertia factor are set to 1.2 and 0.8, and the learning factors c1, c2 and c3 are set to 0.8; the number of gray wolves is set to 20, and the number of secondary loop runs is set to 20; the fitness function of the gray wolf particle swarm hybrid algorithm is set to: δ f =|f(2.4)|+|f(7.0)|.

4. The method for calculating parameters of explosive JWL state equation based on hybrid algorithm according to claim 1, characterized in that: In step S3, the limiting conditions are as follows: In the optimization calculation, the upper and lower bounds of ω, R1, and R2 are {(0.2, 0.4), (4, 6), (0, 2)}; In order to prevent the particle swarm from falling into the local optimum and adjust and optimize its speed formula, the optimal position value obtained by the GWO algorithm cycle is introduced into the update calculation of the particle flight speed. The formula is as follows: Where k is the number of iterations; r1, r2 and r3 are random numbers; c1, c2 and c3 are learning factors; X1(k), X2(k) and X3(k) are the positions of the three best wolves in the population; v id and x id is the speed and position of the ith particle in the dth dimension; ω is the inertia factor. A linear differential decreasing strategy is adopted. The initial ω value is large and the optimization ability is strong. When approaching the optimal solution, the ω value decreases and a small step size optimization is performed. The update calculation formula is as follows: In the formula, iter max is the maximum number of iterations; k is the number of iterations; ω max and ω min are the maximum and minimum values ​​of the inertia factor, respectively.

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