J-A model parameter identification method based on hybrid intelligent algorithm

Abstract

The invention provides a J-A model parameter identification method based on a hybrid intelligent algorithm. The method comprises the following steps: setting a plurality of initialization parameters of an improved artificial fish school IAFSA algorithm and a plurality of initialization parameters of a fast simulated annealing VFSAA algorithm; based on a plurality of initialization parameters of an IAFSA algorithm, performing iterative optimization on each to-be-identified parameter of the J-A model through the IAFSA algorithm in the early stage of a parameter identification process, and determining an optimal solution after the artificial fish executes different behaviors by comparing fitness function values in each iteration process; and taking an optimal solution obtained by iteration of the IAFSA algorithm as an iteration initial value of a VFSAA algorithm, and carrying out iterative optimization on the iteration initial value through the VFSAA algorithm based on a plurality of initialization parameters of the VFSAA algorithm so as to determine a final solution of each to-be-identified parameter. According to the method, multiple improved randomness optimization algorithms are mixed for parameter identification, and the precision, speed and stability of J-A model parameter identification are improved by utilizing the advantages of the multiple algorithms.

Description

Technical Field

[0001] The present application relates to the technical field of data analysis of electromagnetic mutual inductors, and in particular to a JA model parameter identification method based on a hybrid intelligent algorithm. Background Art

[0002] At present, the core of electromagnetic transformers is usually made of ferromagnetic materials such as silicon steel sheets. The magnetization process of such materials has characteristics such as nonlinearity and hysteresis. Under certain special conditions, such as DC bias conditions, the nonlinear phenomenon will be aggravated. In addition, as the power frequency increases, the eddy current loss will increase, and in severe cases, the transformer may be damaged. Therefore, accurate modeling of the nonlinear hysteresis characteristics of ferromagnetic materials and simulation of the hysteresis loop will help to further study the transmission characteristics of electromagnetic transformers.

[0003] Among them, the theoretical models for simulating hysteresis loops are mainly the Jiles-Atherton (JA) model and the Preisach model. Since the Preisach model ignores the microscopic principles of ferromagnetic materials, the modeling process is relatively complicated, and the experiment requires a lot of measured data, and the simulation is time-consuming, so it is not convenient for practical application. In contrast, the JA model can combine the microscopic and macroscopic characterizations of ferromagnetic materials, has clear physical meanings, and is relatively simple to identify parameters. Therefore, it has been widely used in the hysteresis modeling of ferromagnetic materials. The fitting effect of the JA model is determined by the saturation magnetization intensity M. s The five parameters of JA model are directly determined by the shape parameter a, mean field coefficient α, hysteresis loss coefficient k and domain wall bending constant c, so how to accurately identify the five parameters of JA model becomes an important link in the application of JA model.

[0004] In the related art, the parameters of the JA model are usually identified by two methods: formula method and fitting method. However, in practical applications, the identification results of the parameter identification methods in the above related art are prone to deviation, low solution accuracy and long calculation time. Summary of the invention

[0005] The present application aims to solve one of the technical problems in the related art at least to some extent.

[0006] To this end, the first purpose of this application is to propose a JA model parameter identification method based on a hybrid intelligent algorithm. This method mixes multiple improved random optimization algorithms for parameter identification, and utilizes the advantages of multiple algorithms to improve the accuracy, speed and stability of JA model parameter identification, and solves the problem of how to balance the accuracy, speed and stability of model parameter identification when the known data is the basic magnetization curve.

[0007] The second objective of this application is to propose a JA model parameter identification system based on a hybrid intelligent algorithm.

[0008] A third object of the present application is to provide a non-transitory computer-readable storage medium.

[0009] To achieve the above-mentioned object, the first aspect of the present application is to propose a JA model parameter identification method based on a hybrid intelligent algorithm, comprising the following steps: setting multiple initialization parameters of an improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of a fast simulated annealing VFSAA algorithm;

[0010] Based on multiple initialization parameters of the IAFSA algorithm, each parameter to be identified of the JA model is iteratively optimized by the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration;

[0011] The optimal solution obtained by iterating the IAFSA algorithm is used as the iterative initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, the iterative initial value is iteratively optimized by the VFSAA algorithm to determine the final solution of each parameter to be identified.

[0012] Optionally, in one embodiment of the present application, the multiple initialization parameters of the IAFSA algorithm include: the size of the artificial fish school, the crowding factor, the visual range of the artificial fish, the maximum number of trials for each movement, and the maximum number of iterations. The iterative optimization of each parameter to be identified of the JA model by the IAFSA algorithm includes: taking the solution of the parameter to be identified as the artificial fish, determining the position of the target artificial fish in this round of iteration, the number of other artificial fish in the visual range of the artificial fish, and the positions of each other artificial fish; calculating the population center according to the number of other artificial fish and the positions of each other artificial fish; respectively calculating the fitness function corresponding to the position of the target artificial fish and the population center; and determining whether to perform flocking behavior or foraging behavior based on the fitness function corresponding to the position of the target artificial fish and the population center, the number of other artificial fish, and the crowding factor.

[0013] Optionally, in one embodiment of the present application, the iterative optimization of each parameter to be identified of the JA model by the IAFSA algorithm also includes: determining the individual with the highest fitness within the visual range of the artificial fish, and respectively calculating the fitness functions corresponding to the position of the target artificial fish and the position of the individual; based on the fitness functions corresponding to the position of the target artificial fish and the position of the individual, the number of other artificial fish and the crowding factor, determining whether to perform the tail-chasing behavior or the foraging behavior.

[0014] Optionally, in one embodiment of the present application, executing the foraging behavior includes: randomly generating an update state for the target artificial fish within the visual field of the artificial fish, and respectively calculating the position of the target artificial fish and the fitness function corresponding to the update state; when the fitness function corresponding to the update state is less than the fitness function corresponding to the position of the target artificial fish, repeatedly executing the foraging behavior, and when the number of repeated executions of the foraging behavior reaches the maximum number of trials for each movement, executing random behavior.

[0015] Optionally, in one embodiment of the present application, after determining whether to perform the tail-chasing behavior or the foraging behavior, it also includes: calculating a first fitness function corresponding to the individual of the target artificial fish after performing the clustering behavior, and calculating a second fitness function corresponding to the individual of the target artificial fish after performing the tail-chasing behavior; determining an updated individual corresponding to the target artificial fish by comparing the first fitness function with the second fitness function; comparing the updated individual with the current optimal individual in the artificial fish school to determine the optimal individual after this round of iteration.

[0016] Optionally, in one embodiment of the present application, the multiple initialization parameters of the VFSAA algorithm include: an initial temperature, a termination temperature, a Markov chain length and a temperature cooling coefficient, and the iterative optimization of the iteration initial value by the VFSAA algorithm includes: calculating the current temperature in each round of iteration according to the initial temperature and the temperature cooling coefficient, and updating the current solution in each round of iteration based on the current temperature and the Cauchy distribution, wherein the current solution in the initial iteration round is the iteration initial value; determining the number of updates to be repeated in each round of iteration according to the Markov chain length, for each update, respectively calculating the fitness function corresponding to the current solution and the updated solution, and determining the optimal solution for this update by comparing the fitness function corresponding to the current solution and the updated solution; determining the optimal solution corresponding to each round of iteration by comparing the optimal solutions corresponding to each update in each round of iteration; terminating the iterative optimization when the current temperature in any round of iteration is less than the termination temperature, and taking the optimal solution corresponding to any round of iteration as the final solution.

[0017] Optionally, in one embodiment of the present application, after setting multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of the fast simulated annealing VFSAA algorithm, it also includes: setting a value range and encoding method for each parameter to be identified of the JA model, wherein the value range is used to limit the parameter value generated during the iterative optimization process, and the encoding method is used for decoding when calculating the fitness function.

[0018] To achieve the above objectives, the second aspect of the present application further proposes a JA model parameter identification system based on a hybrid intelligent algorithm, comprising the following modules:

[0019] An initialization module is used to set multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of the fast simulated annealing VFSAA algorithm;

[0020] A first identification module is used for iteratively optimizing each parameter to be identified of the JA model by the IAFSA algorithm based on multiple initialization parameters of the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration;

[0021] The second identification module is used to use the optimal solution obtained by iterating the IAFSA algorithm as the iteration initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, iteratively optimize the iteration initial value through the VFSAA algorithm to determine the final solution of each parameter to be identified.

[0022] In order to implement the above-mentioned embodiments, the third aspect embodiment of the present application also proposes a non-temporary computer-readable storage medium, on which a computer program is stored. When the computer program is executed by the processor, the JA model parameter identification method based on the hybrid intelligent algorithm in the above-mentioned first aspect is implemented.

[0023] The technical solution provided by the embodiment of the present application brings at least the following beneficial effects: the present application combines the VFSAA algorithm with the IAFSA algorithm, and uses the strong global search capability of the IAFSA algorithm to determine the area where the optimal solution is located in the early stage of model parameter optimization, and uses the strong local search capability of the VFSAA algorithm to perform precise search in the area where the optimal solution is located in the later stage of optimization. Thus, the present application can not only obtain a high-precision approximate optimal solution, but also quickly enter the most promising search area for the optimal solution in the early stage of optimization, and can take into account the accuracy and speed of JA model parameter identification. In addition, the hybrid process of multiple intelligent algorithms of the present application is relatively simple, easy to implement in practical applications, and further improves the computational efficiency of model parameter identification. Therefore, the present application performs model parameter identification by mixing multiple improved random optimization algorithms, and the identification results can draw a complete hysteresis loop, and the advantages of multiple algorithms are used to improve the accuracy, speed and stability of JA model parameter identification.

[0024] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0026] Figure 1 A flow chart of a JA model parameter identification method based on a hybrid intelligent algorithm proposed in an embodiment of the present application;

[0027] Figure 2 A flowchart of an iterative optimization method based on the IAFSA algorithm proposed in an embodiment of the present application;

[0028] Figure 3 A flowchart of an iterative optimization method based on the VFSAA algorithm proposed in an embodiment of the present application;

[0029] Figure 4 A schematic diagram of a fitting effect diagram of an ASFA algorithm proposed in an embodiment of the present application;

[0030] Figure 5 A schematic diagram of a fitting effect diagram of a SAA algorithm proposed in an embodiment of the present application;

[0031] Figure 6 A schematic diagram of a fitting effect diagram of an IASFA-VFSAA algorithm proposed in an embodiment of the present application;

[0032] Figure 7 A schematic diagram of the fitness trend of an ASFA algorithm proposed in an embodiment of the present application;

[0033] Figure 8 A schematic diagram of the fitness trend of a SAA algorithm proposed in an embodiment of the present application;

[0034] Fig. 9 A schematic diagram of the fitness trend of an IASFA-VFSAA algorithm proposed in an embodiment of the present application;

[0035] Fig.10 A schematic diagram of a hysteresis loop drawn based on the identification result of the ASFA algorithm proposed in an embodiment of the present application;

[0036] Fig.11 A schematic diagram of a hysteresis loop drawn based on the SAA algorithm identification result proposed in an embodiment of the present application;

[0037] Fig.12 A schematic diagram of a hysteresis loop drawn based on the identification result of the IASFA-VFSAA algorithm proposed in an embodiment of the present application;

[0038] Fig.13 A structural diagram of a JA model parameter identification system based on a hybrid intelligent algorithm proposed in an embodiment of the present application. DETAILED DESCRIPTION

[0039] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0040] It should be noted that in the identification method of the JA model parameters of the relevant embodiments, the formula method is sensitive to the selection of the initial value of the parameter and the iteration order of the model equation. In many cases, problems such as non-convergence and falling into local minimum values ​​will occur, thus limiting the application of the formula method in practical engineering. The fitting method aims to minimize the error between the measured and calculated hysteresis loops, and identifies the parameters of the static JA model through a deterministic optimization algorithm or a random optimization algorithm.

[0041] Among them, the deterministic optimization algorithm has poor global search capability and is more sensitive to the selection of initial parameter values. On the contrary, the stochastic optimization algorithm is suitable for solving different nonlinear complex problems and has strong robustness, convergence, implicit parallelism and wide adaptability. However, various stochastic optimization algorithms in the relevant embodiments still have corresponding problems in identifying JA model parameters.

[0042] For example, the random optimization algorithms used more frequently in the relevant embodiments include Particle Swarm Optimization (PSO), Artificial Fish Swarm Algorithm (AFSA) and Simulated Annealing Algorithm (SAA). In practical applications, when the known data is the basic magnetization curve, when these three algorithms are used to identify the key parameters of the JA model, the PSO algorithm is prone to fall into the local optimal solution, the AFSA algorithm has a long running time, and the SAA algorithm has a low fitting accuracy.

[0043] To this end, the present application proposes a JA model parameter identification method based on a hybrid intelligent algorithm. When the known data is a basic magnetization curve, the method can take into account the accuracy, speed and stability of the model parameter solution.

[0044] The following describes a JA model parameter identification method and system based on a hybrid intelligent algorithm proposed in an embodiment of the present application with reference to the accompanying drawings.

[0045] Figure 1 A flow chart of a JA model parameter identification method based on a hybrid intelligent algorithm proposed in an embodiment of the present application, such as Figure 1As shown, the method comprises the following steps:

[0046] Step S101, setting a plurality of initialization parameters of an improved artificial fish swarm IAFSA algorithm and a plurality of initialization parameters of a fast simulated annealing VFSAA algorithm.

[0047] Specifically, since the AFSA algorithm has good global convergence, the algorithm can converge quickly in the early stage of optimization, but when approaching the optimal solution, the step size and field of view may restrict the action of the artificial fish, causing the solution result to fluctuate around the optimal solution. On the contrary, the SAA algorithm has a strong local search capability and has high convergence accuracy within a smaller range, but the solution result is greatly affected by the initial solution. Based on the above characteristics, the present application first improves the AFSA algorithm and the SAA algorithm respectively to obtain the Improved Artificial Fish Swarm Algorithm (IAFSA) algorithm and the Very Fast Simulated Annealing Algorithm (VFSAA) algorithm.

[0048] Then, the IAFSA algorithm is combined with the VFSAA algorithm. In the early stage of the entire JA model parameter identification process, the strong global search capability of the IAFSA algorithm is used to determine the area where the optimal solution is located. Then, in the later stage, the strong local search capability of the VFSAA algorithm is used to perform a "fine search" in the area where the optimal solution has been determined to obtain the final solution of JA model parameter identification.

[0049] In specific implementation, the present application first initializes the relevant parameters in the mixed multiple intelligent algorithms, so as to subsequently execute the corresponding algorithms using the initialized algorithm parameters to achieve optimization of the five parameters of the JA model.

[0050] In one embodiment of the present application, the initialization process includes the following three aspects:

[0051] First, multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm are set, wherein the multiple initialization parameters of the IAFSA algorithm include: setting the size N of the artificial fish swarm, the crowding factor delta, the visual range visual of the artificial fish, the maximum number of attempts try_number for each move, and the maximum number of iterations max_iteration.

[0052] Among them, in each round of iteration, the visual field visual of the artificial fish can be calculated by the following formula:

[0053] visual k+1 =visual k ×a+visualmin

[0054] Among them, a is a fixed constant, k represents the iteration round, and visual min Indicates the minimum visible area.

[0055] Second, multiple initialization parameters of the fast simulated annealing VFSAA algorithm are set. The multiple initialization parameters of the VFSAA algorithm include: setting the initial temperature T0, the termination temperature T end , Markov chain length L k and the temperature cooling coefficient alfa.

[0056] Third, after setting multiple initialization parameters of the IAFSA algorithm and the VFSAA algorithm, it also includes: setting the value range and encoding method of each parameter to be identified of the JA model, wherein the value range is used to limit the parameter value generated during the iterative optimization process, and the encoding method is used for decoding when calculating the fitness function.

[0057] Specifically, the upper and lower limits of the value ranges of the five parameters of the JA model are set, as well as the corresponding encoding methods of each parameter. In the subsequent optimization process through various algorithms, each new solution generated needs to be tested to see if it meets the preset value range of the corresponding parameter. If it is within the value range, the test passes. If it exceeds a certain limit of the value range, the new solution is replaced with the exceeded limit.

[0058] The encoding methods include linear encoding and exponential encoding. In the subsequent optimization process through various algorithms, after a new solution that meets the requirements is obtained, in the process of calculating the fitness function corresponding to the new solution, it is necessary to decode according to the encoding method preset by the corresponding parameters of the new solution.

[0059] Therefore, this step performs the initialization setting of the algorithm parameters and the value ranges of the five parameters of the JA model. The set initialization parameters are used for various operations in the subsequent iterative optimization process.

[0060] Step S102, based on multiple initialization parameters of the IAFSA algorithm, each parameter to be identified of the JA model is iteratively optimized by the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration.

[0061] Specifically, the present application can optimize the five parameters of the JA model respectively. The principles of solving the optimal solutions for various parameters are the same. The present application will exemplify the process of solving the optimal solution for one of the parameters in the following. Among them, the IAFSA algorithm is first executed in the early stage of the model parameter identification process. In the IAFSA algorithm, each possible solution corresponding to a JA model parameter is called an "artificial fish". The optimal solution is searched iteratively. In each iteration, the artificial fish updates itself by performing four behaviors, namely, clustering, tail chasing, foraging, and randomization, so as to achieve optimization. In each round of iteration, the present application determines the optimal solution after the artificial fish performs different behaviors by comparing the fitness function values ​​of each new solution.

[0062] As a possible implementation method, the present application introduces the speed v, inertia weight ω and information sharing mechanism of the PSO algorithm into the AFSA algorithm in advance to obtain the IAFSA algorithm adopted by the present application. Before executing the IAFSA algorithm, the linearly decreasing inertia weight required for executing the IAFSA algorithm is calculated using the introduced inertia weight. The linearly decreasing inertia weight is calculated by the following formula:

[0063] ω k =ω ini -(ω ini -ω end )·t / T max

[0064] Among them, ω ini is the starting value of the inertia weight, which can be determined according to the introduced inertia weight, ω end is the inertia weight termination value, t is the current iteration number, T max is the maximum number of iterations.

[0065] In order to more clearly illustrate the specific implementation process of iteratively optimizing each parameter to be identified of the JA model through the IAFSA algorithm in the present application, an optimization method proposed in an embodiment of the present application is exemplified below. Figure 2 Flow chart of an iterative optimization method based on the IAFSA algorithm proposed in the embodiment of the present application, which is used to determine the clustering behavior or foraging behavior among the above four behaviors, such as Figure 2 As shown, the method comprises the following steps:

[0066] Step S201, taking the solution of the parameters to be identified as the artificial fish, determining the position of the target artificial fish in this round of iteration, the number of other artificial fish in the visual field of the artificial fish, and the position of each other artificial fish.

[0067] Specifically, suppose that the position of the target artificial fish i in the kth iteration of this round is In this iteration, the visual domain of the artificial fish isk Other artificial fish arrive The distance is d ij , in d ij <visual k The number of other artificial fish in the range is n f .

[0068] Step S202, calculating the population center according to the number of all other artificial fish and the position of each other artificial fish.

[0069] Specifically, based on the above settings, the average state X of other artificial fish is calculated by the following formula: c As a center for small populations:

[0070]

[0071] Among them, the meaning of each parameter is as described above and will not be elaborated in this application.

[0072] Step S203, respectively calculating the fitness function corresponding to the position of the target artificial fish and the population center.

[0073] Specifically, calculate the position of the target artificial fish The corresponding fitness function Y i k , and calculate the population center X c The corresponding fitness function Y c .

[0074] Step S204, determining whether to perform a flocking behavior or a foraging behavior based on the position of the target artificial fish and the fitness function corresponding to the population center, the number of other artificial fish and the crowding factor.

[0075] Specifically, the obtained parameters are subjected to relevant calculations and then the following judgment is made: c / n f >delta·Y i k , then the flocking behavior is executed, if it does not meet the judgment condition, then the foraging behavior is executed. In this embodiment, the expression of the flocking behavior is as follows:

[0076]

[0077] Among them, V i k is the step size of the target artificial fish i in the kth iteration, V ini is the initial step size, X best is the optimal solution for the group, c1 and c2 are different learning factors, and rand1 and rand2 are random numbers between (0,1).

[0078] Therefore, in this round of iterative optimization, if the above clustering behavior is performed, the new solution obtained will be the position of the artificial fish in the next round.

[0079] Based on the above embodiment, each parameter to be identified in the JA model is iteratively optimized through the IAFSA algorithm, and also includes: determining the individual with the highest fitness in the visual field of the artificial fish, and calculating the fitness functions corresponding to the position of the target artificial fish and the position of the individual respectively; based on the fitness functions corresponding to the position of the target artificial fish and the position of the individual, the number of other artificial fish and the crowding factor, determining whether to perform tail-chasing behavior or foraging behavior.

[0080] Specifically, in this embodiment, for the position The target artificial fish is still in d ij <visual k Find the individual X with the highest fitness within the range max Among them, visual k The fitness function values ​​of each artificial fish in the range are calculated, and the individual with the highest fitness is obtained by determining the maximum value. Then, calculate and X max The corresponding fitness function and Y max , if Y max / n f >delta·Y i k , then the tail-chasing behavior is executed, otherwise the foraging behavior is executed.

[0081] The expression of the rear-end behavior is as follows:

[0082]

[0083] Furthermore, in the above two embodiments, if it is determined that a foraging behavior needs to be performed, an updated state is first randomly generated for the target artificial fish within the visual range of the artificial fish, and then the foraging behavior is performed based on the updated state.

[0084] Specifically, in this embodiment, for the position The target artificial fish, in d ij <visual k Randomly select a new state X in the range j , the update state can be expressed by the following formula:

[0085]

[0086] Then, the foraging behavior is performed by the following formula:

[0087]

[0088] Furthermore, in the process of executing the foraging behavior in the above embodiment, it also includes: respectively calculating the fitness function corresponding to the position of the target artificial fish and the updated state; when the fitness function corresponding to the updated state is less than the fitness function corresponding to the position of the target artificial fish, repeatedly executing the foraging behavior, and when the number of repeated executions of the foraging behavior reaches the maximum number of trials for each movement, executing random behavior.

[0089] Specifically, in this embodiment, the following are calculated: and X j The corresponding fitness function Y i k and Y j , if Y j <Y i , then the foraging behavior is repeated. And after each foraging behavior, the above fitness function Y i k and Y j Calculate and compare, and determine whether to continue foraging behavior based on the comparison result. Then, after repeating the foraging behavior for the maximum number of try_number times, the foraging behavior is determined to have failed, and random behavior is executed instead.

[0090] Among them, the expression of random behavior is shown in the following formula:

[0091] X j =X i +rand·ω k ·V ini

[0092] It should be noted that in the above embodiment, the same artificial fish performs both the swarming behavior and the tail-chasing behavior, and the process of performing the two behaviors includes respectively determining whether to perform the foraging behavior, and the foraging behavior includes determining whether to perform the random behavior, so the results of the foraging behavior or the random behavior can also be regarded as the results of the swarming and tail-chasing behaviors. Because the same artificial fish will obtain two new solutions when performing the two behaviors at the same time, that is, two new individuals, the embodiment of the present application also needs to perform fitness judgment, and finally retain the new individual with the highest fitness.

[0093] That is, in one embodiment of the present application, after determining whether to perform a tail-chasing behavior or a foraging behavior, it also includes: calculating a first fitness function corresponding to the individual of the target artificial fish after performing a clustering behavior, and calculating a second fitness function corresponding to the individual of the target artificial fish after performing a tail-chasing behavior; determining an updated individual corresponding to the target artificial fish by comparing the first fitness function and the second fitness function; comparing the updated individual with the current optimal individual in the artificial fish school to determine the optimal individual after this round of iteration.

[0094] Specifically, based on the implementation of the above embodiment, assuming that the target artificial fish The new individual obtained after executing the clustering behavior is X swarm , the corresponding first fitness function is Y swarm . Target Artificial Fish The new individual obtained after the rear-end behavior is X follow , and its corresponding second fitness function is Y follow If Y swarm >Y follow , then Update to X swarm , otherwise update to X follow The new artificial fish (i.e., the updated individual) is then compared with the current best individual, where the current best individual is the best artificial fish individual in the artificial fish group of size N, determined before executing this round of iterative optimization. If the artificial fish updated in the above manner after this round of optimization is better, the current best individual (i.e., the best individual after this round of iterative optimization) is updated to the artificial fish updated in the above manner.

[0095] It should be noted that the optimization process in the above embodiment can be repeated N times, and in each iteration, it is checked whether the iteration stop condition is met, that is, whether the maximum number of iterations max_iteration is reached. If it is met, the iteration is stopped and the optimal solution is returned, otherwise the above steps are repeated.

[0096] Therefore, the execution time of the IAFSA algorithm can be adjusted by setting the maximum number of iterations max_iteration, so that the IAFSA algorithm can be executed in the early stage of the entire JA model parameter identification process according to actual needs to obtain the optimal solution obtained by iterating the IAFSA algorithm.

[0097] Step S103, taking the optimal solution obtained by iterating the IAFSA algorithm as the iteration initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, iteratively optimizing the iteration initial value through the VFSAA algorithm to determine the final solution of each parameter to be identified.

[0098] Specifically, the VFSAA algorithm is executed, and the current optimal solution obtained based on the IAFSA algorithm in the previous step is used as the initial value of the VFSAA algorithm. The VFSAA algorithm is continued to iterate and optimize to find the optimal solution for each model parameter, and the optimal solution finally output by the VFSAA algorithm is used as the final solution of each parameter to be identified of the identified JA model parameters.

[0099] Among them, since the IAFSA algorithm performed in the early stage has found a satisfactory solution domain for the global extreme value, the initial temperature of the VFSAA algorithm in this application is no longer a high temperature, but it starts iterating from a lower temperature, thereby fully utilizing the advantage of the VFSAA algorithm's strong local search capability at low temperatures.

[0100] In order to more clearly illustrate the specific implementation process of continuing to iteratively optimize the obtained iterative initial value through the VFSAA algorithm in the present application, an optimization method proposed in an embodiment of the present application is exemplified below. Figure 3 This is a flowchart of an iterative optimization method based on the VFSAA algorithm proposed in an embodiment of the present application, such as Figure 3 As shown, the method comprises the following steps:

[0101] Step S301, calculate the current temperature in each round of iteration according to the initial temperature and the temperature cooling coefficient, and update the current solution in each round of iteration based on the current temperature and the Cauchy distribution, wherein the current solution in the initial iteration round is the iteration initial value.

[0102] Specifically, compared with the traditional SAA algorithm, the VFSAA algorithm of the present application uses a model perturbation based on the Cauchy distribution to update the current solution, and the current solution can be updated by the following formula:

[0103] β 1i =β 0i +y i (B i -A i )

[0104] y i =T·sign(r-0.5)[(1+1 / T) |2r-1| -1]

[0105] Among them, β 0i is the i-th variable of the current solution β0, r is a random number between (0,1), [A i ,B i ] is β 0i The value range of β 1i is the i-th variable of the new solution β1, and T is the current temperature.

[0106] It is understandable that during the first-round operation, the current solution β0 is the received initial iteration value, that is, the optimal solution obtained by the IAFSA algorithm.

[0107] Among them, the update method of the current temperature can be calculated by the following formula:

[0108] T′ = alfa·T

[0109] Among them, the initial value of T is T0, and T′ is the current temperature in the next-round iteration calculated.

[0110] Step S302: Determine the number of updates repeatedly executed in each round of iteration according to the length of the Markov chain. For each update, calculate the fitness functions corresponding to the current solution and the updated solution respectively, and determine the optimal solution of this update by comparing the fitness functions corresponding to the current solution and the updated solution.

[0111] Step S303: Determine the optimal solution corresponding to each round of iteration by comparing the optimal solutions corresponding to each update in each round of iteration.

[0112] Specifically, after each update operation using the formula in step S301, calculate the fitness functions f(β0) and f(β1) corresponding to the current solution β0 and the updated solution β1 respectively, and determine whether to accept the new solution β1 by comparing these two fitness functions. If f(β1) ≥ f(β0), then accept the new solution β1; if f(β1) < f(β0), then accept the new solution β1 with a certain probability. And, repeat the above steps of updating and comparing and judging the current solution L k times, and then select the optimal solution among the L k times as the optimal solution of this round of iteration.

[0113] Step S304: End the iterative optimization when the current temperature in any round of iteration is less than the termination temperature, and use the optimal solution corresponding to any round of iteration as the final solution.

[0114] Specifically, during each round of iteration, detect whether the iteration stop condition is satisfied, that is, whether the current temperature T is less than the termination temperature T end , if satisfied, stop the iteration and return the optimal solution, otherwise repeat to update the current temperature and perform iterative optimization according to the above steps.

[0115] Thus, this application overcomes both the defect that it is difficult for the AFSA algorithm to obtain a high-precision approximate optimal solution and the defect that the SAA algorithm cannot quickly enter the most promising search area in the early stage of optimization. The mixing process of multiple algorithms in this application is simple and easy to implement, improving the calculation efficiency.

[0116] In summary, the JA model parameter identification method based on the hybrid intelligent algorithm of the embodiment of the present application combines the VFSAA algorithm with the IAFSA algorithm, and uses the strong global search ability of the IAFSA algorithm to determine the optimal solution area in the early stage of model parameter optimization, and uses the strong local search ability of the VFSAA algorithm to perform precise search in the optimal solution area in the later stage of optimization. Thus, the method can not only obtain a high-precision approximate optimal solution, but also quickly enter the most promising search area for the optimal solution in the early stage of optimization, and can take into account the accuracy and speed of JA model parameter identification. In addition, the hybrid process of multiple intelligent algorithms in the method is relatively simple, easy to implement in practical applications, and further improves the computational efficiency of model parameter identification. Therefore, the method performs model parameter identification by mixing multiple improved random optimization algorithms, and the identification results can draw a complete hysteresis loop, which uses the advantages of multiple algorithms to improve the accuracy, speed and stability of JA model parameter identification.

[0117] Based on the above embodiments, in order to more fully illustrate the effect of the JA model parameter identification method based on the hybrid intelligent algorithm of the present application in practical applications, the fitting effect of the basic magnetization curve by comparing the AFSA algorithm, the SAA algorithm and the identification method of the present application (IAFSA-VFSAA) in a specific embodiment is exemplified below.

[0118] Among them, the fitting process of the basic magnetization curve by the three methods to be compared is the process of parameter identification of the JA model, that is, determining a set of optimal model parameters so that the simulation results of the JA model under these parameters are closest to the measured results of the basic magnetization curve. Among them, the JA model is essentially a nonlinear, multivariable differential equation, and its mathematical expression is shown in the following formula:

[0119]

[0120] Where M is the magnetization intensity, H is the magnetic field intensity, and M an is the hysteresis-free magnetization, α is the mean field parameter characterizing the internal coupling of magnetic domains, k is the loss coefficient, c is the reversible susceptibility, δ and δ M are different directional coefficients.

[0121] The five parameters to be identified in the JA model are the saturation magnetization M s , shape parameter a, mean field coefficient α, hysteresis loss coefficient k and domain wall bending constant c, where M s , a, k and c use linear coding, α uses logarithmic coding, and the value range of the encoded parameters is (0,1).

[0122] The weighted root mean square value is used to calculate the fitness function during the operation. The relevant expression is shown in the following formula:

[0123]

[0124] Among them, B mea is the measured magnetic induction intensity, B cal is the calculated magnetic induction intensity, ω is the weight, and M is the number of sampling points.

[0125] The basic magnetization curve used as known data in this embodiment is derived from the measured data of a specific type of oriented silicon steel sheet, and its characteristic is that except for the vicinity of the knee point, the rest of the curve is approximately two straight lines. The same equipment and software are used for each simulation.

[0126] In order to comprehensively evaluate the performance of the above three algorithms, this embodiment will compare and analyze from the two aspects of accuracy and speed. The evaluation index of accuracy is the root mean square error (RMSE) and the fitting effect diagram. The evaluation index of speed is the code running time and the number of iterations corresponding to the optimal solution.

[0127] In this embodiment, each of the above methods is used to perform parameter identification 10 times, the RMSE corresponding to the optimal solution of the 10 parameter identifications is calculated, and the average value, maximum value and minimum value are calculated as evaluation indicators. The relevant results are shown in the following Table 1.

[0128] Table 1 Fitting effect of different algorithms

[0129]

[0130] The unit of parameter RMSE is Tesla (T). The fitting effects of these three algorithms are as follows: Figures 4 to 6 As shown, the parameters used are the parameters corresponding to the simulation group closest to the RMSE average value.

[0131] It can be seen from Table 1 above that the fitting accuracy of the IAFSA-VFSAA hybrid algorithm is basically the same as that of the AFSA algorithm, and both are greater than that of the SAA algorithm.

[0132] In terms of the running speed in this embodiment, the average running time of 10 simulations is used to reflect the running speed, and the relevant results obtained are shown in the following Table 2.

[0133] Table 2 Running speed of different algorithms

[0134] Algorithm Type Average running time ASFA 851.0706s SAA 665.9590s IASFA-VFSAA 115.6566s

[0135] The unit of average running time is seconds (s).

[0136] As can be seen from Table 2, the running speed of the IAFSA-VFSAA hybrid algorithm of the present application is much faster than that of the AFSA algorithm and the SAA algorithm. For further analysis, the trend graphs of the fitness function of the three algorithms over time during a certain simulation are plotted, respectively, as shown in Figures 7 to 9 shown.

[0137] Among them, comparison Figures 7 to 9 It can be seen that compared to the SAA algorithm, the IAFSA-VFSAA hybrid algorithm of the present application has the global search capability of the AFSA algorithm in the early stage of optimization, and can increase the fitness function more quickly, that is, determine the area where the optimal solution is located more quickly. Similarly, compared to the AFSA algorithm, the IAFSA-VFSAA hybrid algorithm has the local search capability of the SAA algorithm in the later stage of optimization, which can further improve the accuracy of finding the optimal solution. The AFSA algorithm does a lot of "useless work" in the later stage of optimization, while the SAA algorithm does a lot of "useless work" in the early stage of optimization. This is the main reason why the two algorithms take a long time. The IAFSA-VFSAA hybrid algorithm of the present application uses the AFSA algorithm in the early stage and the SAA algorithm in the later stage, which has a higher solution efficiency and therefore takes less time.

[0138] Since the purpose of parameter identification using the basic magnetization curve is to draw a hysteresis loop, it is necessary to test whether the identification results can be used to draw a complete hysteresis loop. The stability indicator is the proportion of groups that can draw hysteresis loops in 10 identification results. The relevant results are shown in Table 3 below.

[0139] Table 3 Stability table of different algorithms

[0140] Algorithm Type The proportion of hysteresis loop ASFA 100％ SAA 100％ IASFA-VFSAA 100％

[0141] From Table 3 and compare Figures 10 to 12 It can be seen that all the identification results of the IAFSA-VFSAA hybrid algorithm of the present application can draw a complete hysteresis loop.

[0142] Therefore, through the results of this embodiment, it can be seen that the IAFSA-VFSAA hybrid algorithm of the present application not only has a higher fitting accuracy, and its identification results can draw a complete hysteresis loop, but also has a faster running speed compared to the AFSA algorithm and the SAA algorithm, and realizes the optimization of the JA model parameter identification algorithm when the known data is the basic magnetization curve.

[0143] In order to implement the above embodiment, the present application also proposes a JA model parameter identification system based on a hybrid intelligent algorithm. Fig.13 A structural diagram of a JA model parameter identification system based on a hybrid intelligent algorithm proposed in an embodiment of the present application is shown in FIG. Fig.13 As shown, the system includes:

[0144] The initialization module 100 is used to set a plurality of initialization parameters of the improved artificial fish swarm IAFSA algorithm and a plurality of initialization parameters of the fast simulated annealing VFSAA algorithm.

[0145] The first identification module 200 is used for iteratively optimizing each parameter to be identified of the JA model through the IAFSA algorithm based on multiple initialization parameters of the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration.

[0146] The second identification module 300 is used to use the optimal solution obtained by iterating the IAFSA algorithm as the iteration initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, iteratively optimize the iteration initial value through the VFSAA algorithm to determine the final solution of each parameter to be identified.

[0147] Optionally, in one embodiment of the present application, the first identification module 200 is specifically used to: use the solution of the parameters to be identified as the artificial fish, determine the position of the target artificial fish in this round of iteration, the number of other artificial fish in the visual field of the artificial fish, and the positions of each other artificial fish; calculate the population center according to the number of other artificial fish and the positions of each other artificial fish; calculate the fitness function corresponding to the position of the target artificial fish and the population center respectively; based on the fitness function corresponding to the position of the target artificial fish and the population center, the number of other artificial fish and the crowding factor, determine whether to perform flocking behavior or foraging behavior.

[0148] It should be noted that the aforementioned explanation of the embodiment of the JA model parameter identification method based on the hybrid intelligent algorithm is also applicable to the system of this embodiment and will not be repeated here.

[0149] In summary, the JA model parameter identification system based on the hybrid intelligent algorithm in the embodiment of the present application can not only obtain a high-precision approximate optimal solution, but also quickly enter the most promising search area for the optimal solution in the early stage of optimization, and can take into account the accuracy and speed of JA model parameter identification. Therefore, the system identifies model parameters by mixing a variety of improved random optimization algorithms, and the identification results can draw a complete hysteresis loop, which uses the advantages of multiple algorithms to improve the accuracy, speed and stability of JA model parameter identification.

[0150] In order to implement the above-mentioned embodiments, the present application also proposes a non-temporary computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the JA model parameter identification method based on a hybrid intelligent algorithm as described in any one of the above-mentioned first aspect embodiments.

[0151] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0152] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0153] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0154] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute the instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing in other suitable ways if necessary, and then stored in a computer memory.

[0155] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0156] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0157] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0158] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A JA model parameter identification method based on a hybrid intelligent algorithm, characterized in that: The following steps are involved: Set multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of the fast simulated annealing VFSAA algorithm; Based on multiple initialization parameters of the IAFSA algorithm, each parameter to be identified of the JA model is iteratively optimized by the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration; The optimal solution obtained by iterating the IAFSA algorithm is used as the iterative initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, the iterative initial value is iteratively optimized by the VFSAA algorithm to determine the final solution of each parameter to be identified.

2. The identification method according to claim 1, characterized in that: The multiple initialization parameters of the IAFSA algorithm include: the size of the artificial fish school, the crowding factor, the visual range of the artificial fish, the maximum number of attempts for each movement, and the maximum number of iterations. The iterative optimization of each parameter to be identified of the JA model by the IAFSA algorithm includes: Taking the solution of the parameter to be identified as an artificial fish, determining the position of the target artificial fish, the number of other artificial fish in the visual field of the artificial fish, and the position of each other artificial fish in this round of iteration; Calculating a population center according to the number of the other artificial fish and the positions of the other artificial fish; Calculating the fitness function corresponding to the position of the target artificial fish and the population center respectively; Based on the position of the target artificial fish and the fitness function corresponding to the population center, the number of other artificial fish and the crowding factor, it is determined whether to perform a flocking behavior or a foraging behavior.

3. The identification method according to claim 2, characterized in that: The iterative optimization of each parameter to be identified of the JA model by the IAFSA algorithm also includes: Determine an individual with the highest fitness within the visual range of the artificial fish, and calculate the fitness functions corresponding to the position of the target artificial fish and the position of the individual respectively; Based on the fitness function corresponding to the position of the target artificial fish and the position of the individual, the number of the other artificial fish and the crowding factor, it is determined whether to perform the tail-chasing behavior or the foraging behavior.

4. The identification method according to claim 2, characterized in that: Performing the foraging behavior includes: Randomly generating an update state for the target artificial fish within the visual domain of the artificial fish, and respectively calculating the position of the target artificial fish and the fitness function corresponding to the update state; When the fitness function corresponding to the updated state is less than the fitness function corresponding to the position of the target artificial fish, the foraging behavior is repeatedly executed, and when the number of repeated executions of the foraging behavior reaches the maximum number of trials for each movement, a random behavior is executed.

5. The identification method according to claim 3, characterized in that: After determining whether to perform the tail-chasing behavior or the foraging behavior, the method further includes: Calculating a first fitness function corresponding to an individual of the target artificial fish after performing the grouping behavior, and calculating a second fitness function corresponding to an individual of the target artificial fish after performing the tail-chasing behavior; Determine an updated individual corresponding to the target artificial fish by comparing the first fitness function and the second fitness function; The updated individual is compared with the current best individual in the artificial fish swarm to determine the best individual after this round of iteration.

6. The identification method according to claim 1, characterized in that: The multiple initialization parameters of the VFSAA algorithm include: initial temperature, termination temperature, Markov chain length and temperature cooling coefficient. The iterative optimization of the iterative initial value by the VFSAA algorithm includes: According to the initial temperature and the temperature cooling coefficient, the current temperature in each round of iteration is calculated, and based on the current temperature and the Cauchy distribution, the current solution in each round of iteration is updated, wherein the current solution in the initial iteration round is the iteration initial value; Determine the number of updates to be repeated in each iteration according to the length of the Markov chain, calculate the fitness functions corresponding to the current solution and the updated solution for each update, and determine the optimal solution for this update by comparing the fitness functions corresponding to the current solution and the updated solution; By comparing the optimal solutions corresponding to each update in each round of iteration, the optimal solution corresponding to each round of iteration is determined; When the current temperature in any round of iteration is less than the termination temperature, the iterative optimization is terminated, and the optimal solution corresponding to any round of iteration is used as the final solution.

7. The identification method according to any one of claims 2 to 6, characterized in that: After setting multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of the fast simulated annealing VFSAA algorithm, it also includes: The value range and encoding method of each parameter to be identified of the JA model are set, wherein the value range is used to limit the parameter value generated during the iterative optimization process, and the encoding method is used for decoding when calculating the fitness function.

8. A JA model parameter identification system based on a hybrid intelligent algorithm, characterized in that: Includes the following modules: An initialization module is used to set multiple initialization parameters of the improved artificial fish swarm IAFSA algorithm and multiple initialization parameters of the fast simulated annealing VFSAA algorithm; A first identification module is used for iteratively optimizing each parameter to be identified of the JA model by the IAFSA algorithm based on multiple initialization parameters of the IAFSA algorithm in the early stage of the parameter identification process, wherein the optimal solution after the artificial fish performs different behaviors is determined by comparing the fitness function values ​​in each round of iteration; The second identification module is used to use the optimal solution obtained by iterating the IAFSA algorithm as the iteration initial value of the VFSAA algorithm, and based on multiple initialization parameters of the VFSAA algorithm, iteratively optimize the iteration initial value through the VFSAA algorithm to determine the final solution of each parameter to be identified.

9. The identification system according to claim 8, characterized in that: The first identification module is specifically used for: Taking the solution of the parameter to be identified as an artificial fish, determining the position of the target artificial fish, the number of other artificial fish in the visual field of the artificial fish, and the position of each other artificial fish in this round of iteration; Calculating a population center according to the number of the other artificial fish and the positions of the other artificial fish; Calculating the fitness function corresponding to the position of the target artificial fish and the population center respectively; Based on the position of the target artificial fish and the fitness function corresponding to the population center, the number of other artificial fish and the crowding factor, it is determined whether to perform a flocking behavior or a foraging behavior.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the JA model parameter identification method based on a hybrid intelligent algorithm as described in any one of claims 1 to 7 is implemented.

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