Piezoelectric fast tip / tilt mirror hysteresis loop parameter identification method based on tent chaotic mapping and gnu leap strategy particle swarm optimization algorithm
The particle swarm optimization algorithm improved by Tent chaotic mapping and gazelle jumping strategy solves the problems of random initialization, local optima and parameter sensitivity in the identification of hysteresis loop parameters of piezoelectric fast reflector by the traditional PSO algorithm, and achieves higher identification accuracy and precision.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHANGCHUN INST OF OPTICS FINE MECHANICS & PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-04-10
- Publication Date
- 2026-06-12
AI Technical Summary
Traditional particle swarm optimization algorithms suffer from problems such as uneven random initialization distribution, local optimum traps, unbalanced convergence performance, and parameter sensitivity in the identification of hysteresis loops in piezoelectric fast reflectors, resulting in insufficient identification accuracy and precision.
An improved particle swarm optimization algorithm (CG-PSO) based on Tent chaotic mapping and gazelle jumping strategy is adopted. The initial distribution of particles is improved by Tent chaotic mapping, and the global search capability and local exploitation capability are enhanced by combining gazelle jumping strategy. The learning factor and inertia weight are dynamically adjusted to achieve adaptive parameter adjustment.
It improves the search space coverage, enhances the global search capability, reduces the risk of local optimum traps, reduces parameter sensitivity, and improves the accuracy and precision of hysteresis loop parameter identification.
Smart Images
Figure CN122197947A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of servo control technology, and in particular to a method for identifying the hysteresis loop parameters of a piezoelectric fast mirror based on a particle swarm optimization algorithm using Tent chaotic mapping and a gazelle jump strategy. Background Technology
[0002] In the field of nonlinear system modeling and control research, the accurate description of hysteresis characteristics and parameter identification is a challenging issue. In recent years, swarm intelligence optimization algorithms have shown significant advantages in this field. Among them, the Gazelle Optimization Algorithm (GOA), as an emerging biomimetic optimization algorithm, mainly divides its optimization process into exploration, development, and hopping phases. It is used to solve complex nonlinear optimization problems and features a wide global search range, fast convergence speed, and strong ability to maintain population diversity. Meanwhile, Particle Swarm Optimization (PSO), as a classic swarm intelligence optimization method, simulates the information sharing mechanism in a flock of birds foraging. Due to its ease of implementation and efficient convergence, it is widely used in many fields such as engineering optimization, machine learning and artificial intelligence, control systems, signal processing and image processing, and bioinformatics. Although the PSO algorithm has strong optimization capabilities, it still faces key technical problems such as the problem of random initialization distribution, local optimum traps, balancing convergence performance, and parameter sensitivity. Specifically, the main technical bottlenecks of the PSO algorithm are:
[0003] 1. Random Initialization Distribution Problem: In the PSO algorithm, particles are distributed in the search space using a random initialization strategy. However, if the initial distribution of particles is uneven, it may lead to insufficient coverage of the search space, leaving some areas unexplored and thus reducing the algorithm's global search capability.
[0004] 2. Local Optimality Trap: The PSO algorithm relies on individual optimal and global optimal information for searching. However, in complex multimodal optimization problems, particles are prone to converge to suboptimal solutions too early, leading to global search failure.
[0005] 3. Balancing Convergence Performance: The algorithm needs to dynamically adjust the balance between global exploration and local exploration at different search stages. Global search is required in the early stages, while local convergence is needed in the later stages. Therefore, finding a balance between global and local exploration is one of the key problems that the PSO algorithm needs to solve.
[0006] 4. Parameter sensitivity: The performance of the PSO algorithm depends on multiple hyperparameters (such as inertia weight w, individual learning factor C1, and group learning factor C2). Different combinations of parameters have a significant impact on the optimization results, which greatly increases the difficulty of practical applications.
[0007] Due to the aforementioned technical bottlenecks in traditional particle swarm optimization algorithms, their accuracy and identification error in identifying hysteresis loop parameters of piezoelectric fast-reflecting mirrors are insufficient, requiring further improvement and enhancement. Summary of the Invention
[0008] This invention aims to address the technical problem that the limitations of the existing PSO algorithm severely restrict its application in parameter identification of complex nonlinear systems. It provides a piezoelectric fast-reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jump strategy particle swarm optimization algorithm, which effectively balances global search and local exploitation and has strong robustness.
[0009] In the piezoelectric fast-reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy, the particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy (Chaos-Gazelle PSO, CG-PSO) is an improved particle swarm optimization algorithm for solving hysteresis model parameter identification. This algorithm improves the initial distribution of particles through Tent chaotic mapping, making the search space coverage more uniform, thereby improving the global search capability of the algorithm. At the same time, the gazelle jumping strategy draws on the nonlinear transition behavior of gazelles when avoiding predators, which can effectively enhance the ability of particles to jump out of local optima, improve the global exploration capability and convergence accuracy of the algorithm.
[0010] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:
[0011] A method for identifying the hysteresis loop parameters of a piezoelectric fast reflecting mirror based on a particle swarm optimization algorithm using Tent chaotic mapping and a gazelle jumping strategy includes the following steps:
[0012] Step (1), Population initialization;
[0013] The particle position is initialized using Tent chaotic mapping, the velocity range and the number of identification parameters are preset according to the stroke of the piezoelectric fast reflector, and the particle velocity is randomly initialized.
[0014] Step (2): Fitness evaluation and optimal solution initialization;
[0015] Calculate the fitness value of each particle under hysteresis fitting, initialize the individual optimal solution, and determine the global optimal solution of the hysteresis parameters;
[0016] Step (3), iterative update and diversity detection;
[0017] Based on the termination condition, the velocity and position of each particle are updated with reference to the dynamically changing learning factor and inertia weight, and the fitting error of the hysteresis parameter is used as the fitness value for calculation.
[0018] Step (4): Continuously update the individual optimal and global optimal;
[0019] Step (5): Implementation of the gazelle jumping strategy;
[0020] When the trigger condition is met, such as the number of iterations reaching a set number of algebras or the fitting error of the hysteresis model parameters falling below a threshold, the local optimum is exited.
[0021] Step (6): Terminate the judgment;
[0022] If the maximum number of iterations is reached or the accuracy requirement is met, output the optimal solution for the hysteresis model parameters; otherwise, return to step (3) to continue iterating.
[0023] In the above technical solution, step (1) specifically includes:
[0024] Determine the dimensions of optimization parameters based on the number of identified parameters. Particle swarm size and maximum number of iterations Then determine the maximum value of the inertia weight. and minimum value The maximum particle velocity and minimum value Upper and lower limits of the particle search space , Finally, the gazelle jump rate was determined. Gazelle's jumping range .
[0025] In the above technical solution, in step (1), the initial particle position is obtained using Tent chaotic mapping. The Tent mapping parameters are Tent mapping initial value for Random numbers are generated using the following formula:
[0026]
[0027]
[0028] in, For the first The chaotic value of the next iteration; For Tent chaotic mapping functions; For the first The chaotic value of the next iteration; This represents the upper limit of the particle search space; This is the lower bound of the particle search space; The size of the particle swarm;
[0029] The formula for random initialization speed is as follows:
[0030] ;
[0031] in, Initialize speed; This represents the minimum particle velocity. This represents the maximum particle velocity. To generate a size of A random matrix; The size of the particle swarm. To optimize parameter dimensions.
[0032] In the above technical solution, step (2) specifically involves: calculating the fitness value of each particle, setting the initial individual optimality of each particle as the current solution of that particle, selecting the one with the best fitness from the individual optimalities of all particles as the global optimality, which is the optimal solution obtained by each hysteresis parameter in the current iteration.
[0033] In the above technical solution, step (3) specifically includes:
[0034] Based on the termination condition, while updating the velocity and position of each particle with reference to the dynamically changing learning factor and inertia weight, the following population diversity indicators are calculated:
[0035] At the current iteration number In the middle, local learning factor and global learning factor The update strategy is as follows:
[0036]
[0037]
[0038] in, This represents the current iteration number; This represents the maximum number of iterations.
[0039] The update strategy for inertia weights is as follows:
[0040]
[0041] in, This represents the maximum value of the inertia weight. This represents the minimum value of the inertia weight. The inertia weighting function;
[0042] In each iteration, the particle updates its velocity and position as follows:
[0043]
[0044]
[0045] in, This represents the current iteration number; Let the velocity of the j-th particle in the D-th dimension at generation t+1 be denoted as . Let the velocity of the j-th particle in the D-th dimension be denoted by t. The inertia weighting function; and for Random numbers between; The component of the historical best position of the j-th particle in the D-dimensional dimension (individual best position). The component of the historical best position of all particles in the D-dimensional dimension (global best position). Let be the position of the j-th particle in the D-th dimension of the t-th generation; Let be the position of the particle in generation t+1; Let be the velocity of the particle in generation t+1; Let be the position of the particle in generation t.
[0046] In the above technical solution, step (4) specifically involves comparing and updating the current generation's individual optimal and global optimal solutions based on the latest particle velocity and position obtained in step (3).
[0047] In the above technical solution, step (5) specifically includes:
[0048] Randomly select the particles that need to jump. Generate jump step size Then, a jump is performed, and the jump formula is:
[0049]
[0050]
[0051] in, For chaotic jumps; For random perturbations; Let be the position of the particle that needs to jump, where It is an index for jumping ions; This is the globally optimal solution;
[0052] Restricting particle position at Within the range, the formula at its boundary is:
[0053] ;
[0054] in, and These are the upper and lower bounds of the particle's position.
[0055] The present invention has the following beneficial effects:
[0056] The piezoelectric fast mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy of particle swarm optimization algorithm has three core innovations: population initialization mechanism based on Tent chaotic mapping, adaptive parameter adjustment mechanism and gazelle jumping strategy.
[0057] First, this invention utilizes Tent chaotic mapping for particle position initialization, overcoming the problem of uneven distribution of random initialization, improving the search space coverage, enhancing population diversity, reducing the possibility of particles clustering to local extrema, and improving global search capabilities.
[0058] Secondly, this invention employs dynamically changing learning factors and inertia weights to reduce parameter sensitivity, improve algorithm robustness, and adapt to different optimization problems (such as high-dimensional optimization and dynamic optimization), thereby expanding its applicability.
[0059] Finally, this invention employs a gazelle-jump strategy, appropriately adjusting the positions of some particles during the search process to move them away from local optima and into new search areas. By using this strategy, this invention enhances global search capabilities while balancing local exploitation, increasing convergence speed while avoiding getting trapped in local optima, ensuring that a better solution is found rather than a local extremum. Attached Figure Description
[0060] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0061] Figure 1 This is a schematic diagram of the CG-PSO process.
[0062] Figure 2 This is a diagram illustrating the initialization of the population comparison.
[0063] Figure 3 This diagram illustrates the optimization process for four standard test functions.
[0064] Figure 4 Figure showing the fitting results of parameter identification for traditional PSO and CG-PSO.
[0065] Figure 5 This is a schematic diagram of experimental data comparing the accuracy of the traditional PSO algorithm (Particle Swarm Optimization) and the improved PSO algorithm of this invention in identifying the hysteresis loop parameters of a piezoelectric fast-reflecting mirror.
[0066] Figure 6 This is a schematic diagram showing the comparison of identification errors between the traditional PSO algorithm (Particle Swarm Optimization) and the improved PSO algorithm of this invention in the identification of hysteresis loop parameters of piezoelectric fast-reflecting mirrors. Detailed Implementation
[0067] The inventive concept of this invention is as follows:
[0068] In the piezoelectric fast-reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy, the particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy is an improved particle swarm optimization algorithm (CG-PSO) for hysteresis model parameter identification. By innovatively integrating the Tent chaotic mapping mechanism and gazelle jumping strategy, it effectively solves the inherent defects of traditional PSO algorithm in parameter optimization.
[0069] The core innovations of this invention's method for identifying piezoelectric fast-reflecting mirror hysteresis loop parameters in a particle swarm optimization (PSO) algorithm based on Tent chaotic mapping and a gazelle jump strategy are mainly reflected in the following three aspects: a population initialization mechanism based on Tent chaotic mapping, an adaptive parameter adjustment mechanism, and a gazelle jump strategy. First, this invention utilizes the ergodicity and pseudo-randomness of Tent chaotic mapping to ensure a uniform distribution of initial solutions in the search space. An initial population is generated through a chaotic sequence, improving the coverage of the search space and helping the PSO algorithm find better solutions more quickly in its early stages. Second, the adaptive parameter adjustment mechanism uses dynamically changing learning factors and inertia weights to optimize the algorithm, achieving adaptive adjustment of algorithm parameters, reducing reliance on manual parameter tuning, and balancing global exploration with local development capabilities. Finally, the gazelle jump strategy is triggered when the number of iterations reaches a set number of generations or when the population diversity falls below a set threshold.
[0070] The execution mechanism is as follows:
[0071] 1. Randomly select the particles that need to jump and determine their probability of jumping;
[0072] 2. Generate the jump step size and calculate the new position of the particle;
[0073] 3. Perform a jump to move the selected particles closer to the global optimum, while adding a certain amount of random perturbation to ensure that the jump does not directly converge to the global optimum, thus maintaining search diversity;
[0074] 4. Boundary constraints restrict the particle position to... Within the specified range, avoid invalid solutions.
[0075] This invention achieves a comprehensive improvement in algorithm performance through the organic combination of the three innovative modules mentioned above, providing an efficient and reliable solution for hysteresis model parameter identification.
[0076] The present invention will now be described in detail with reference to the accompanying drawings.
[0077] The present invention relates to a method for identifying hysteresis loop parameters of a piezoelectric fast-reflecting mirror based on a particle swarm optimization algorithm using Tent chaotic mapping and a gazelle jump strategy. The flowchart of the particle swarm optimization algorithm based on Tent chaotic mapping and the gazelle jump strategy is shown below. Figure 1 As shown, it mainly includes the following six key steps:
[0078] Step (1) Population initialization. The particle positions are initialized using Tent chaotic mapping, and the particle velocities are randomly initialized within a preset velocity range.
[0079] Step (2): Fitness evaluation and optimal solution initialization. Calculate the fitness value of each particle, initialize the individual optimal solution, and determine the global optimal solution.
[0080] Step (3), Iterative Update and Diversity Detection. Based on the termination condition, the velocity and position of each particle are updated with reference to the dynamically changing learning factor and inertia weight, while the population diversity index is calculated.
[0081] Step (4): Continuously update the individual optimal and global optimal.
[0082] Step (5): Implementation of the gazelle jumping strategy. When the triggering condition is met, such as the number of iterations reaching the set number of generations or the population diversity falling below the threshold, the local optimum is escaped.
[0083] Step (6): Termination judgment. If the maximum number of iterations is reached or the accuracy requirement is met, output the optimal solution of the hysteresis model parameters; otherwise, return to step (3) to continue iterating.
[0084] Specifically:
[0085] First, step (1) determines the dimension of the optimization parameters based on the number of identified parameters. Particle swarm size and maximum number of iterations Then determine the maximum value of the inertia weight. and minimum value The maximum particle velocity and minimum value Upper and lower limits of the particle search space , Finally, the gazelle jump rate was determined. Gazelle's jumping range .
[0086] This invention uses Tent chaotic mapping to obtain the initial particle position. The Tent chaotic mapping parameters are Tent chaotic mapping initial value for Random numbers. The formula is as follows:
[0087]
[0088]
[0089] in, For the first The chaotic value of the next iteration; For Tent chaotic mapping functions; For the first The chaotic value of the next iteration; This represents the upper limit of the particle search space; This is the lower bound of the particle search space; The size of the particle swarm;
[0090] The formula for random initialization speed is as follows:
[0091]
[0092] in, Initialize speed; This represents the minimum particle velocity. This represents the maximum particle velocity. To generate a size of A random matrix; The size of the particle swarm. To optimize parameter dimensions.
[0093] For fitness evaluation and optimal solution initialization in step (2), the fitness value of each particle is calculated according to step (1) above. The initial individual optimal of each particle is set as the current solution of that particle. The particle with the best fitness is selected from the individual optimal of all particles as the global optimal.
[0094] Step (3) involves iterative updates and diversity detection. Based on the termination condition, the velocity and position of each particle are updated with reference to the dynamically changing learning factor and inertia weights, and population diversity is detected. At the current iteration number... In the middle, local learning factor and global learning factor The update strategy is as follows:
[0095]
[0096]
[0097] in, This represents the current iteration number; This represents the maximum number of iterations.
[0098] The update strategy for inertia weights is as follows:
[0099]
[0100] in, This represents the maximum value of the inertia weight. This represents the minimum value of the inertia weight. This is the inertia weighting function.
[0101] In each iteration, the particle updates its velocity and position as follows:
[0102]
[0103]
[0104] in, This represents the current iteration number; Let the velocity of the j-th particle in the D-th dimension at generation t+1 be denoted as . Let the velocity of the j-th particle in the D-th dimension be denoted by t. The inertia weighting function; and for Random numbers between; The component of the historical best position of the j-th particle in the D-dimensional dimension (individual best position). The component of the historical best position of all particles in the D-dimensional dimension (global best position). Let be the position of the j-th particle in the D-th dimension of the t-th generation; Let be the position of the particle in generation t+1; Let be the velocity of the particle in generation t+1; Let be the position of the particle in generation t.
[0105] Step (4) Based on the latest particle velocity and position obtained in step (3) above, compare and update the current generation's individual optimal and global optimal solutions.
[0106] Step (5) employs the gazelle jumping strategy. To prevent premature convergence of the PSO algorithm, maintain population activity, and enhance global search capabilities while also considering local search, this invention utilizes the experience of individual gazelles during the escape process to help them escape local optima. The gazelle jumping strategy is implemented every 50 generations or when population diversity falls below a threshold. First, particles to be jumped are randomly selected. Generate jump step size Then, a jump is performed, and the jump formula is as follows:
[0107]
[0108]
[0109] in, For chaotic jumps; For random perturbations; Let be the position of the particle that needs to jump, where It is an index for jumping ions; This is the globally optimal solution.
[0110] Adjust the position of the selected particle to be near the global optimum gbest. At the same time, it adds a certain amount of random disturbance. This ensures that after a jump, the particle doesn't directly converge to gbest, but rather maintains a certain level of exploration capability. Finally, the particle position is restricted to... Within the range, to avoid invalid solutions, the formula at its boundary is as follows:
[0111]
[0112] in, and These are the upper and lower bounds of the particle's position.
[0113] Finally, step (6) outputs the optimal solution of the hysteresis model parameters according to the termination condition; otherwise, iteration continues.
[0114] The particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy of the present invention achieves a comprehensive improvement in algorithm performance through the coordinated work of the above modules, and provides an efficient and reliable solution for hysteresis model parameter identification.
[0115] The particle swarm optimization algorithm (CG-PSO) based on Tent chaotic mapping and gazelle jumping strategy in this invention has been experimentally proven to be feasible.
[0116] First, to verify the advantages of the Tent-based chaotic mapping of this invention over traditional random initialization in terms of population distribution, a visual comparison can be made using a frequency distribution histogram. (Setting parameters...) =0.50, =1.0, =0, Divide the interval into ten equal steps. The frequency of population distribution was calculated for each interval, and the results were compared as follows: Figure 2 As shown.
[0117] Secondly, in order to verify the superiority of the CG-PSO optimization algorithm, this invention will use four test functions to compare it with PSO and TGPSO. Figure 3 The performance of each algorithm in the objective function optimization process is demonstrated.
[0118] Table 1 Comparison of optimization results of the two algorithms
[0119]
[0120] The two algorithms were run independently 10 times each under the same parameter conditions. Table 1 shows the comparison of the results of the two algorithms.
[0121] Finally, to verify the reliability of CG-PSO in practical applications, Figure 4 By comparing the errors in parameter identification of the hysteresis model, the fitting accuracy of the present invention is significantly higher than that of existing tracking methods.
[0122] The particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy in this invention has three core innovations: a population initialization mechanism based on Tent chaotic mapping, an adaptive parameter adjustment mechanism, and a gazelle jumping strategy.
[0123] First, this invention utilizes Tent chaotic mapping for particle position initialization, overcoming the problem of uneven distribution of random initialization, improving the search space coverage, enhancing population diversity, reducing the possibility of particles clustering to local extrema, and improving global search capabilities.
[0124] Secondly, this invention employs dynamically changing learning factors and inertia weights to reduce parameter sensitivity, improve algorithm robustness, and adapt to different optimization problems (such as high-dimensional optimization and dynamic optimization), thereby expanding its applicability.
[0125] Finally, this invention employs a gazelle-jump strategy, appropriately adjusting the positions of some particles during the search process to move them away from local optima and into new search areas. By using this strategy, this invention enhances global search capabilities while balancing local exploitation, increasing convergence speed while avoiding getting trapped in local optima, ensuring that a better solution is found rather than a local extremum.
[0126] Having introduced and explained the particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy, the present invention further describes the method for identifying the hysteresis loop parameters of a piezoelectric fast-reflecting mirror based on the particle swarm optimization algorithm based on Tent chaotic mapping and gazelle jumping strategy.
[0127] The piezoelectric fast-reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy particle swarm optimization algorithm of the present invention mainly includes the following six key steps:
[0128] Step (1), Population initialization. The particle positions are initialized using Tent chaotic mapping. The velocity range and the number of identification parameters are preset according to the stroke of the piezoelectric fast reflector, and the particle velocities are randomly initialized.
[0129] Step (2), Fitness Evaluation and Optimal Solution Initialization. Calculate the fitness value of each particle under hysteresis fitting, initialize the individual optimal solution, and determine the global optimal solution for the hysteresis parameters;
[0130] Step (3), Iterative Update and Diversity Detection. Based on the termination condition, update the velocity and position of each particle with reference to the dynamically changing learning factor and inertia weight, and calculate the fitness value using the fitting error of the hysteresis parameter;
[0131] Step (4): Continuously update the individual optimal and global optimal;
[0132] Step (5) Implementation of the gazelle jump strategy. When the triggering condition is met—that is, the number of iterations reaches the set number of algebras or the fitting error of the hysteresis model parameters is lower than the threshold—the local optimum is escaped.
[0133] Step (6): Termination judgment. If the maximum number of iterations is reached or the accuracy requirement is met, output the optimal solution of the hysteresis model parameters; otherwise, return to step (3) to continue iterating.
[0134] The piezoelectric fast mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy of particle swarm optimization algorithm has three core innovations: population initialization mechanism based on Tent chaotic mapping, adaptive parameter adjustment mechanism and gazelle jumping strategy.
[0135] First, step (1) determines the dimension of the optimization parameters based on the number of identified parameters. Particle swarm size and maximum number of iterations Then determine the maximum value of the inertia weight. and minimum value The maximum particle velocity and minimum value Upper and lower limits of the particle search space , Finally, the gazelle jump rate was determined. Gazelle's jumping range This invention uses Tent chaotic mapping to obtain the initial particle position. The Tent mapping parameters are Tent mapping initial value for Random numbers. The formula is as follows:
[0136]
[0137]
[0138] The formula for random initialization speed is as follows:
[0139]
[0140] For fitness evaluation and optimal solution initialization in step (2), the fitness value of each particle is calculated according to step (1) above. The initial individual optimal of each particle is set as the current solution of that particle. The particle with the best fitness is selected from the individual optimal of all particles as the global optimal, which is the optimal solution obtained by each hysteresis parameter in the current iteration.
[0141] Step (3) involves iterative updates and diversity detection. Based on the termination condition, the velocity and position of each particle are updated with reference to the dynamically changing learning factor and inertia weights, and the errors in the hysteresis model's identification parameters are detected. At the current iteration number... In the middle, local learning factor and global learning factor The update strategy is as follows:
[0142]
[0143]
[0144] The update strategy for inertia weights is as follows:
[0145]
[0146] In each iteration, the particle updates its velocity and position as follows:
[0147]
[0148]
[0149] In the above formula, and for Random numbers between; For the individual's optimal; It is the global optimal solution.
[0150] Step (4) Based on the latest particle velocity and position obtained in step (3) above, compare and update the current generation's individual optimal and global optimal solutions.
[0151] Step (5) employs the gazelle jumping strategy. To prevent premature convergence of the PSO algorithm, maintain population activity, and enhance global search capabilities while also considering local search, this invention utilizes the experience of individual gazelles during the escape process to help them escape local optima. The gazelle jumping strategy is implemented every 50 generations or when population diversity falls below a threshold. First, particles to be jumped are randomly selected. Generate jump step size Then, a jump is performed, and the jump formula is as follows:
[0152]
[0153]
[0154] Adjust the position of the selected particle to be near the global optimum gbest. At the same time, it adds a certain amount of random disturbance. This ensures that after a jump, the particle doesn't converge directly to gbest, but rather maintains a certain level of exploration capability. Finally, the particle position is restricted to [pop]. min pop max Within the range, to avoid invalid solutions, the formula at its boundary is as follows:
[0155]
[0156] In the final step (6), the optimal solution for the hysteresis model parameters is output according to the termination condition; otherwise, the iteration continues.
[0157] This invention achieves a comprehensive improvement in algorithm performance through the coordinated operation of the above modules, providing an efficient and reliable solution for hysteresis model parameter identification.
[0158] To verify the accuracy of the piezoelectric fast reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy (PSO algorithm before and after improvement) in identifying piezoelectric fast reflecting mirror hysteresis loop parameters, the output signal of the piezoelectric fast reflecting mirror platform was collected when the input signal was 50 Hz. The piezoelectric fast reflecting mirror hysteresis loop parameter identification method based on Tent chaotic mapping and gazelle jumping strategy (PSO algorithm before and after improvement) of the present invention had 400 iterations and 40 particle swarms. The following are the hysteresis and error identification of the traditional PSO algorithm and the improved PSO algorithm. It can be seen that the improved PSO algorithm has significant application prospects in the field of piezoelectric fast reflecting mirror parameter identification.
[0159] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. A method for identifying the hysteresis loop parameters of a piezoelectric fast reflecting mirror based on a particle swarm optimization algorithm using Tent chaotic mapping and a gazelle jumping strategy, characterized in that, Includes the following steps: Step (1), Population initialization; The particle position is initialized using Tent chaotic mapping, the velocity range and the number of identification parameters are preset according to the stroke of the piezoelectric fast reflector, and the particle velocity is randomly initialized. Step (2): Fitness evaluation and optimal solution initialization; Calculate the fitness value of each particle under hysteresis fitting, initialize the individual optimal solution, and determine the global optimal solution of the hysteresis parameters; Step (3), iterative update and diversity detection; Based on the termination condition, the velocity and position of each particle are updated with reference to the dynamically changing learning factor and inertia weight, and the fitting error of the hysteresis parameter is used as the fitness value for calculation. Step (4): Continuously update the individual optimal and global optimal; Step (5): Implementation of the gazelle jumping strategy; When the trigger condition is met, such as the number of iterations reaching a set number of algebras or the fitting error of the hysteresis model parameters falling below a threshold, the local optimum is exited. Step (6): Terminate the judgment; If the maximum number of iterations is reached or the accuracy requirement is met, output the optimal solution for the hysteresis model parameters; otherwise, return to step (3) to continue iterating.
2. The method for identifying the hysteresis loop parameters of a piezoelectric fast-reflecting mirror based on the particle swarm optimization algorithm using Tent chaotic mapping and gazelle jumping strategy as described in claim 1, is characterized in that... Step (1) is as follows: Determine the dimensions of optimization parameters based on the number of identified parameters. Particle swarm size and maximum number of iterations Then determine the maximum value of the inertia weight. and minimum value The maximum particle velocity and minimum value Upper and lower limits of the particle search space , Finally, the gazelle jump rate was determined. Gazelle's jumping range .
3. The method for identifying the hysteresis loop parameters of a piezoelectric fast-reflecting mirror based on the particle swarm optimization algorithm using Tent chaotic mapping and gazelle jumping strategy as described in claim 2, is characterized in that... In step (1), the initial particle positions are obtained using Tent chaotic mapping. The Tent mapping parameters are Tent mapping initial value for Random numbers are generated using the following formula: in, For the first The chaotic value of the next iteration; For Tent chaotic mapping functions; For the first The chaotic value of the next iteration; This represents the upper limit of the particle search space; This is the lower bound of the particle search space; The size of the particle swarm; The formula for random initialization speed is as follows: ； in, Initialize speed; This represents the minimum particle velocity. This represents the maximum particle velocity. To generate a size of A random matrix; The size of the particle swarm. To optimize parameter dimensions.
4. The method for identifying piezoelectric fast-reflecting mirror hysteresis loop parameters based on Tent chaotic mapping and gazelle jumping strategy particle swarm optimization algorithm according to claim 1, characterized in that, Step (2) specifically involves: calculating the fitness value of each particle, setting the initial individual optimality of each particle as the current solution of that particle, selecting the particle with the best fitness from the individual optimalities of all particles as the global optimality, which is the optimal solution obtained by each hysteresis parameter in the current iteration.
5. The method for identifying piezoelectric fast-reflecting mirror hysteresis loop parameters based on Tent chaotic mapping and gazelle jumping strategy particle swarm optimization algorithm according to claim 1, characterized in that, Step (3) is as follows: Based on the termination condition, while updating the velocity and position of each particle with reference to the dynamically changing learning factor and inertia weight, the following population diversity indicators are calculated: At the current iteration number In the middle, local learning factor and global learning factor The update strategy is as follows: in, This represents the current iteration number; This represents the maximum number of iterations. The update strategy for inertia weights is as follows: in, This represents the maximum value of the inertia weight. This represents the minimum value of the inertia weight. The inertia weighting function; In each iteration, the particle updates its velocity and position as follows: in, This represents the current iteration number; Let the velocity of the j-th particle in the D-th dimension at generation t+1 be denoted as . Let the velocity of the j-th particle in the D-th dimension be denoted by t. This is the inertia weighting function; and for Random numbers between; The component of the historical best position of the j-th particle in the D-dimensional dimension (individual best position). The component of the historical best position of all particles in the D-dimensional dimension (global best position). Let be the position of the j-th particle in the D-th dimension of the t-th generation; Let be the position of the particle in generation t+1; Let be the velocity of the particle in generation t+1; Let be the position of the particle in generation t.
6. The method for identifying the hysteresis loop parameters of a piezoelectric fast-reflecting mirror based on the particle swarm optimization algorithm using Tent chaotic mapping and gazelle jumping strategy as described in claim 1, is characterized in that... Step (4) specifically involves comparing and updating the current generation's individual optimal and global optimal solutions based on the latest particle velocity and position obtained in step (3).
7. The method for identifying piezoelectric fast-reflecting mirror hysteresis loop parameters based on Tent chaotic mapping and gazelle jumping strategy particle swarm optimization algorithm according to claim 1, characterized in that, Step (5) is as follows: Randomly select the particles that need to jump. Generate jump step size Then, a jump is performed, and the jump formula is: in, For chaotic jumps; For random perturbations; Let be the position of the particle that needs to jump, where It is an index for jumping ions; This is the globally optimal solution; Restricting particle position at Within the range, the formula at its boundary is: ； in, and These are the upper and lower bounds of the particle's position.