CN115099118B - NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method - Google Patents
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Abstract
The invention belongs to the field of structural and acoustic calculation optimization design, and relates to a high-dimensional multi-objective joint parallel simulation optimization method based on NSGA III. The method comprises the steps of determining an initial structure and an optimized direction of the sound absorption structure; obtaining a structural acoustic coefficient and a sound absorption coefficient; determining a main parameter; determining an optimization target; generating a consistency reference point; creating a file to be optimized according to resource conditions; creating a sentinel file; initializing a population; solving an ideal point; returning the offspring generated by the genetic operation; non-dominant ordering; selecting a front-end solution; and judging the termination condition to output an optimal solution. According to the invention, the sound absorption coefficient of the sound absorber in a specific frequency band is calculated by utilizing finite element simulation, and the optimal configuration of the acoustic original is searched in parallel by adopting a population segmentation means, so that the constraint of the traditional empirical design is eliminated, the situation that the optimization targets of a single-target optimized genetic algorithm and a rapid non-dominant ordering genetic algorithm with elite strategy are fewer is overcome, the optimization effect is poor, and the problem of low efficiency of the existing optimization algorithm is solved.
Description
Technical Field
The invention belongs to the field of structural and acoustic calculation optimization design, and particularly relates to a high-dimensional multi-objective joint parallel simulation optimization method based on NSGA III.
Background
Through the development of engineering technology of vibration reduction and noise reduction for decades, submarines in various countries have made great progress in the field of acoustic radiation control, and gradually enter a quiet submarines array, so that the detected distance is greatly shortened, and the detection performance of the traditional passive sonar is seriously weakened. The active sonar can actively emit sound waves outwards, and the object is detected by receiving the echo signals, so that the active sonar has the advantage of detecting low noise and even completely quiet objects, and is paid attention to. Therefore, the sound stealth technology corresponding to the active sonar detection technology has practical and important significance for modern anti-diving combat. From the viewpoint of reducing the target strength, the problems of outline sound hiding, applying a sound absorbing cover layer, using an underwater sound composite material and the like are mainly adopted at present, and the optimization problem is not avoided. How to adjust the submarine shape (line shape), how to plan the internal structure of the sound absorption covering layer, how to select the layering and the angle of the composite material, and the like are all hot problems in the current research. However, the current acoustic optimization means is single, and the current commonly adopted parametric scanning, genetic algorithm, gradient/non-gradient topology optimization and the like have the problems of low optimization efficiency and poor optimization effect by taking an acoustic coating/metamaterial development work as an example.
Disclosure of Invention
The invention aims to solve the problems of low efficiency of the traditional optimization algorithm and low efficiency of the traditional optimization algorithm by solving the problems of low optimization efficiency existing in the existing optimization design process of the acoustic original, and aims to realize the aim of actively designing the configuration according to the sound absorption aim, and the invention adopts the following technical scheme to achieve the aim:
a NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method comprises the following steps:
step one, determining an initial structure and an optimization direction of a sound absorption structure, specifically, improving the overall sound absorption performance by optimizing the shape and the relative position of a cavity based on a gradual change type cavity structure;
obtaining the reflection coefficient and the transmission coefficient of the sound absorption structure to be optimized by adopting a sound tube simulation method, and solving the sound absorption coefficient;
step three, determining material parameters and NSGA III algorithm parameters; the material parameters include: young's modulus, poisson's ratio, loss factor, density sound velocity; the NSGA III algorithm parameters comprise: the evolution times, population scale, maximum stop algebra, crossover probability and mutation probability;
step four, constructing an optimization target model; the method specifically comprises the following steps: establishing an optimization target model by taking the minimum average sound absorption coefficient of sound absorption structures in different frequency bands as an optimization target;
step five, generating consistency reference points according to the number of the self-defined population and the number of the targets in the starting stage;
step six, creating a file to be optimized according to resource conditions, wherein the file to be optimized comprises a command file and an initial configuration file;
the command file contains a detection command, a loading command, a population division command, a parameter modification command, an execution command, a data extraction command, a writing file command and a deleting data command;
the initial configuration file contains initial configuration data of the sound absorption structure to be optimized;
step seven, creating a sentinel file and executing a monitoring function; the number of the guard files is two, and the guard files consist of fault detection files and initial configuration files;
the fault detection file in the first sentinel file is composed of a command file added with a monitoring command and is used for replacing a certain initial configuration file to execute an optimization process when the file is abnormal in operation and cannot output a result; the fault detection file in the second sentinel file is used for detecting the running condition of the first sentinel file, and if the first sentinel file is found to start executing the optimization function, the file starts executing the monitoring function consistent with the first sentinel file;
step eight, initializing a population; in particular to
Generating a first group of group variables by using a main function according to parameter setting, and storing the group of variables; reading the COMSOL corresponding to the variable data call and starting operation, and storing a result value according to a corresponding rule after the operation is finished; returning to the main function after all result values in the population are read;
step nine, solving ideal points; the method specifically comprises the following steps: extracting a population fitness minimum value, constructing ideal points, and converting an objective function into a self-adaptive normalization function through the ideal points;
step ten, returning the offspring generated by genetic operation;
step eleven, utilizing constraint dominance principle as criterion for judging nonlinear inequality constraint to make non-dominance sorting to form front end solutions of different layers;
step twelve, selecting the last front-end solution, and sequentially carrying out regularization, reference line calculation, individual and reference point association and living environment selection;
thirteenth, judging termination conditions, and if the termination conditions are met, outputting Pareto optimal solutions; otherwise, repeating the steps eight to twelve.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein the first step comprises the following steps: and determining parameters to be optimized of the gradual change type cavity structure, wherein the parameters to be optimized comprise cavity thickness, acoustic cover layer thickness, unit cell size, distance between each interpolation point of the cavity and a cavity wall, radius from each interpolation point of the cavity to a center axis and vertical distance between adjacent interpolation points.
The method comprises the following steps of further improving or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method, wherein the second step specifically comprises the steps of obtaining the reflection coefficient and the transmission coefficient of a sound absorption structure to be optimized by adopting a sound tube simulation method to obtain the sound absorption coefficient alpha of the sound absorption structure, wherein alpha=1-R 2 -T 2
Wherein R is a reflection coefficient extracted through finite element simulation, and T is a transmission coefficient;
the sound tube simulation relies on COMSOL finite element simulation, and utilizes a steel backing periodic unit containing a cavity to simulate an infinite sample structure, and a PML layer is arranged at the water area end to simulate an infinite water area; the periodic conditions of Floquet are set on the upper and lower surfaces and the left and right surfaces of the structure and the water area respectively to simulate the infinite large sample and the water area.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein an optimizing objective model in the fourth step is as follows:
wherein f i Mean sound absorption coefficient representing sound absorption structure in the frequency range;
α j refers to the sound absorption performance measured in the corresponding frequency range;
k is the number of interpolation points;
r k the radius from the kth interpolation point to the center axis; r is (r) k,min Is r k Lower limit of (2); r is (r) k,max Is r k Upper limit of (2);
h op refers to the vertical distance between adjacent interpolation points o and p; h is a op,min Is h op Lower limit of (2); h is a op,max Is h op Upper limit of (2);
h i distance from the ith interpolation point to the cavity wall; h is a max Is the upper limit of the sum of the interpolation point to the cavity wall.
The method is characterized in that the NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method is further perfected or supplemented, and the fifth step specifically comprises the following steps:
5.1 Generating reference points on the hyperplane space of M-1 latitude, wherein the number of the reference points is that
Wherein M represents the predefined number of targets, and H represents the number of divided parts of each single target;
5.2 For each x) ij E X, exist
The ij index indicates the j-th element of the i-th combination in X;
5.3 Definition S 1 For each S as a set of reference points ij ∈S 1 And x ij E X, exist
5.4 S) will S 1 As a set of points on the boundary layer, define S 2 For each S 'for the inner point set' ij ∈S 2 And S is ij ∈S 1 Exists in the presence of
5.5 Obtaining a reference point set s=s) 1 ∪S 2 。
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein in the step six, a detection command is used for detecting file generation conditions under a fixed path; the loading command accepts a detection command for extracting parameters; the population segmentation command is used for segmenting population parameters and dividing the population parameters into a plurality of sub-populations according to the number of files; the parameter modification command modifies the structural parameters in the COMSOL according to the population parameter variables extracted by each subspecies; the execution command accepts parameter modification commands for executing the operation commands; the data extraction command accepts an execution command and is used for extracting the reflection coefficient in the simulation model and converting the reflection coefficient; the writing file command accepts a data extraction command for storing the extracted data; the data deleting command is used for deleting the population parameter variable file, so that the confusion between new population parameter variables generated after the population evolves and the previous population parameter variables is avoided;
the specific content of each operation in the step twelve is as follows:
regularization: obtaining the p-norm of each sample, dividing the elements in the samples by the norm, and enabling the p-norm of each processed sample to be equal to 1; wherein, p-norm:
associating an individual with a reference point: solving the distance between each individual and the nearest reference point, and calculating the number of related solutions except the last front end of each reference point;
selecting a living environment: non-dominant ordering is performed, the last front-end solution is selected, and the next generation is generated.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein in the eighth step, the main function generates a first group of group variables according to parameter setting, and stores the group of variables into a variable file; and reading the variable files in sequence by using the command files created before, calling the corresponding COMSOL to start operation, storing the result values into the corresponding files according to the corresponding rules after the operation is finished, and returning to the main function after all the result values in the population are read.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein the specific steps of the step nine comprise:
9.1 Group S) t Is defined asMinimum value->Ideal point of structureThe optimization objective function is transformed as follows:
9.2 Find additional points for each coordinate axis:
9.3 Using the extra points to construct a hyperplane and determining the intercept a of the hyperplane to the coordinate axis i ；
9.4 Normalized objective function
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing party, wherein the criterion for judging the nonlinear inequality constraint in the step eleven comprises the following steps:
if the variables of the two individuals are in the constraint range, determining a dominance relation by comparing the fitness values of the two individuals, wherein individuals with small fitness values dominate individuals with large fitness values;
if one of the two individual variables is in the constraint range and the other is out of the constraint range, the individual in the constraint range governs the individual out of the constraint range;
if the variables of the two individuals are outside the constraint range, the individual with small violation of the constraint range dominates the individual with large violation of the constraint range;
if the whole population is in the constraint range, adopting a non-dominant sorting method; if one part of the whole population is in the constraint range and the other part is out of the constraint range, the former part executes a conventional non-dominant sorting method, and the latter part is sequentially arranged on the next layers of the last layer of the feasible solution according to the size of the violation constraint range from small to large; if the whole population is outside the constraint range, the whole population is orderly sequenced from small to large according to the size of the violation constraint range.
In the sixth step, a try-catch function is added to prevent that the thread is crowded in the running process and parameter data cannot be loaded, an initial configuration file cannot be opened, and the NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method is further perfected or supplemented; the operation rule of the try-catch function is as follows: firstly, executing codes in try, and if the codes are abnormal, capturing and executing the codes in the catch by the catch; if no exception occurs, the catch capture function is ignored.
The beneficial effects of the invention are as follows:
according to the NSGA III-based high-dimensional multi-target combined parallel simulation optimization method, the sound absorption coefficient of the sound absorber in a specific frequency band is calculated through finite element simulation, then the specific frequency band is divided into a plurality of small frequency bands based on an NSGA III algorithm without a source, the average sound absorption coefficient of each frequency band is used as a target, and meanwhile an optimal configuration of an acoustic original is searched in parallel through a population segmentation means. According to the requirement of wide frequency band and high sound absorption of the current acoustic material, the invention automatically searches for a new configuration with each frequency band reaching the optimum; the scheme gets rid of the constraint of the traditional experience design, makes up the situation that the optimization targets of a single target optimization Genetic Algorithm (GA) algorithm and a rapid non-dominant ordering genetic algorithm with elite strategy (NSGA-II) are fewer, the optimization effect is poor, solves the problem of low efficiency of the existing optimization algorithm, and realizes the target of the active design configuration according to the sound absorption target; in addition, the invention is not only suitable for the problem of optimizing sound absorption structures, but also suitable for the problem of optimizing other sound vibrations, and can be expanded to all the problems of finite element optimization.
Drawings
FIG. 1 is a schematic flow diagram of a NSGA III-based high-dimensional multi-objective joint parallel simulation optimization scheme;
FIG. 2 is a schematic diagram of the gradual change type cavity sound absorption structure in one embodiment;
FIG. 3 is a schematic diagram of a graded cavity sound absorption structure II in an embodiment;
FIG. 4 is a COMSOL finite element simulation cavity cell model;
FIG. 5 is a schematic diagram of a structure optimization process of joint parallel simulation optimization;
FIG. 6 is a schematic diagram of a structural summary of simulation optimization based on scheme one;
FIG. 7 is a schematic diagram II of a structural summary of simulation optimization based on scheme II;
FIG. 8 is a structural summary schematic diagram III of joint parallel simulation optimization;
FIG. 9 is a result of joint parallel simulation optimization based on scheme one in an embodiment;
FIG. 10 is a result of joint parallel simulation optimization based on scheme two in an embodiment;
FIG. 11 is a result of joint parallel simulation optimization based on the present application in an embodiment.
Detailed Description
The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method is based on an NSGA III framework, is suitable for the problem of small-scale sound vibration optimization, and can be expanded to all the problems of small-scale finite element optimization. According to the method, a multi-objective MATLAB with COMSOL joint parallel simulation optimization method is established by means of an NSGA III algorithm concept through a MATLAB with COMSOL joint parallel simulation method established by self, so that the efficiency of acoustic optimization is greatly improved, and the current situation that the optimization effect of the existing problems is poor is solved. The following is a practical optimization of the XX sound absorption structure of an X-type device, and the specific steps of the application are described in detail in connection with the specific implementation process, and are as follows:
step one: the initial structure and the optimized direction of the sound absorbing structure are determined. As shown in fig. 2, a gradual change type cavity structure is selected, and the overall sound absorption performance is improved by optimizing the cavity shape and the relative position. In the embodiment, the thickness of the steel plate of the XX sound absorption structure of certain X-shaped equipment is 10mm, the thickness of the acoustic coating is 40mm, the length and width of the whole unit cell are 40mm, and h 1 Representing the distance between the first interpolation point of the cavity and the steel plate, r 1 Represents the radius from the first interpolation point to the central axis, h 2 Representing the vertical distance r from the second interpolation point to the first interpolation point of the cavity 2 Represents the radius from the second interpolation point to the central axis, h 3 Represents the vertical distance r from the third interpolation point to the second interpolation point of the cavity 3 Representing the radius of the third interpolation point to the medial axis. h is a 1 、h 2 、h 3 、r 1 、r 2 And r 3 All are parameters to be optimized, and the parameter ranges are shown in table 1. Furthermore, fig. 2 shows only one form of this type of structure, which may also form several structures as shown in fig. 3 as the parameters change.
TABLE 1 parameter ranges to be optimized
Step two: and obtaining the reflection coefficient and the transmission coefficient of the sound absorption structure to be optimized by adopting a sound tube simulation method, and obtaining the sound absorption coefficient alpha of the sound absorption structure by utilizing the formula (1). As shown in fig. 4, the sound tube simulation relies on a COMSOL finite element simulation platform, and utilizes a steel backing periodic unit with a cavity to simulate an infinite sample structure, and a PML layer is arranged at the water area end to simulate an infinite water area. In addition, due to the transmission sideThe medium of (2) is air, and the amplitude of the transmission coefficient is small, so that the back side of the steel plate can be approximated as a free boundary. The periodic conditions of Floquet are set on the upper and lower surfaces and the left and right surfaces of the structure and the water area respectively to simulate the infinite large sample and the water area. Meanwhile, plane waves are normally incident to one side of the covering layer, the incident frequency is 1 kHz-3 kHz, and the step length is 100Hz; and α=1 to R 2 -T 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein R is a reflection coefficient extracted through finite element simulation, and T is a transmission coefficient.
Since T < 0, formula (1) can be directly expressed as α=1 to R 2 ；
Step three: determining material parameters and NSGA III algorithm main parameters, wherein the material parameters are shown in table 2, and NAGA III algorithm main parameters are set as follows: the number of evolutions, 20, population scale, 30, maximum stop algebra, 20, crossover probability, 0.8, mutation probability, 0.2, and 7 acoustic-frequency domain modules of COMSOL in parallel.
The evolution times are formulated according to the initial configuration file size, and the evolution times can be increased if convergence is better for optimizing the result; the population size is generally 30-200; the maximum stop algebra standard evolution times can be kept consistent with the evolution times when the evolution times are less; the crossover probability and the mutation probability are default parameter settings of the genetic algorithm.
Furthermore, to laterally compare the advantages of the present invention, a scheme one (genetic algorithm toolbox (GA) union MATLAB with COMSOL) and a scheme two (genetic algorithm toolbox (NSGA-ii) union MATLAB with COMSOL) were created in synchronization, and the parameter settings were consistent with the example scheme.
TABLE 2 Material parameters
| Material | Young's modulus (Pa) | Poisson's ratio | Loss factor | Density (kg/m) 3 ) | Sound velocity (m/s) |
| Matrix body | 1.4e8 | 0.49 | 0.48 | 1100 | - |
| Steel and method for producing same | 2.1e11 | 0.3 | 0 | 7800 | - |
| Water and its preparation method | - | - | - | 1000 | 1500 |
Step four: an optimization target model is built, and the minimum average sound absorption coefficient of sound absorption structures in different frequency bands is used as an optimization target to build the optimization target model; in order to improve the sound absorption performance of the sound absorption structure at 1000-3000 Hz and achieve the best overall sound absorption performance, an optimized target model is adopted as follows:
wherein f i The average sound absorption coefficient per 300Hz structure is expressed, i=1, 2,3 ….
In addition, since the GA algorithm can only deal with the single objective problem, the objective function is simplified to
min f＝-1/21(α 1000Hz +…+α 3000Hz )
Wherein f represents the average sound absorption coefficient of the structure in the frequency range of 1000-3000 Hz.
Step five: in the initial stage of optimization, generating consistent reference points according to the number of the self-defined population and the number of the target, wherein the point distribution scheme is as follows:
5.1 Generating reference points on a hyperplane space (hyperplane is a linear subspace with the latitude equal to one in an n-dimensional European space) with the latitude of (M-1), wherein the number of the reference points isWherein M represents the predefined number of targets, and H represents the number of divided parts of each single target;
5.2 For each x) ij E X, subscript ij denotes the j-th element of the i-th combination in X, all exist
5.3 Definition S 1 For each S as a set of reference points ij ∈S 1 And x ij E X, all exist
5.4 S) will S 1 As a set of points on the boundary layer, define S 2 For each S 'for the inner point set' ij ∈S 2 And S is ij ∈S 1 All present:
5.5 Defining a reference point set as s=s 1 ∪S 2 ；
Step six: testing the lowest running core number x of the simulation model according to the size of the simulation model (the time for completing one running of the simulation model under the core number is almost the same as the time for completing one running under the highest core number), and then creating n folders to be optimized in batches according to the actual available core number t of the computer (wherein n is less than or equal to t/x), wherein each file comprises an initial configuration file (optimization. Mph) file and a command file (mat_com solx.m);
wherein the initial profile is a sound absorbing profile to be optimized. The command file sequentially comprises a detection command, a loading command, a population division command, a parameter modification command, a MATLAB with COMSOL execution command, a data extraction command, a writing text file command and a deleting data command, and the specific operation is as follows:
6.1 A detection command: the command is used for detecting the file generation condition under the fixed path, and when the NSGA III main function generates population parameter variables and stores the population parameter variables into corresponding text files, the detection command detects the file generation and carries out the next step;
6.2 Load command): the command is used for receiving the detection command of the last step and extracting parameters in the text file;
6.3 Group partition command): the command divides the population into n sub-populations according to the number n of folders;
6.4 Parameter modification command): the command modifies the structural parameters in COMSOL according to the population parameter variables extracted from each subspecies;
6.5 MATLAB with COMSOL execute command: the command receives the parameter modification command in the last step, and when the parameter modification command is executed, the initial configuration file operation command is executed continuously;
6.6 Data extraction command): the command is received to execute the command in the last step, the reflection coefficient in the simulation model is extracted after the initial configuration file is run, and the reflection coefficient is converted according to the objective function setting in the optimization objective model;
6.7 Writing text file command): the command receives the data extraction command of the previous step, and the extracted data is stored in a preset folder in the form of a text file;
6.8 A delete data command: the command is continuously executed after the execution of the steps (6.1) - (6.7) is finished, and is used for deleting the population parameter variable file, so that the confusion between new population parameter variables generated after the population evolution and the previous population parameter variables is avoided.
In addition, in order to prevent the situation that the thread is crowded in the running process and parameter data cannot be loaded and the initial configuration file cannot be opened, a (try-catch) function is added so that the file can run completely. the operation rule of the try-catch function is as follows: firstly, executing codes in try, and if the codes are abnormal, capturing and executing the codes in the catch by the catch; if no exception occurs, the catch capture function is ignored.
Step seven: two sentinel files are created, each file comprising a monitoring file and an initial configuration file. The first by1.M file is used for detecting faults, and a layer of monitoring command is added on the basis of the sixth command file, so that the first by1.M file is used for replacing a certain initial configuration file to execute an optimization process when the file is abnormal in operation and cannot output results. The second monitoring file is used for detecting the running condition of the first sentinel file, if the first sentinel file is found to start executing the optimizing function, the file starts executing the monitoring function consistent with the first sentinel file, and the running flow of the sentinel is shown in fig. 5.
Step eight: and initializing a population. Generating a first group of group variables by the main function according to parameter setting, and storing the group of variables into n text files; the n command files created before sequentially read the text files, call the corresponding COMSOL to start running, and store the result value into the corresponding text files according to the corresponding rules after the running is finished; the scheme I is a single-target optimization method, the result value is stored according to the form of an objective function model, and the scheme II are multi-target optimization methods, and the result value is stored according to the setting form of an objective function in an optimization objective model. And finally, reading the result values in the text file by the fitness function in NSGA-III, and returning to the main function after all the result values in the population are read.
Step nine: solving ideal points, extracting a population fitness minimum value, constructing an ideal point, converting an objective function into a self-adaptive normalization function through the ideal point, and specifically, the method comprises the following steps of:
9.1 Group S) t Is defined asMinimum value +.>Construct an ideal point +.>And converting the objective function according to equation (10): />
9.2 Find additional points for each coordinate axis:
9.3 Using the extra points to construct a hyperplane and determining the intercept a of the hyperplane to the coordinate axis i ；
9.4 Normalized objective function):
step ten: and returning the offspring generated by genetic operation, wherein the offspring fitness value calculation rule is consistent with the population initialization process, but in order to avoid confusion between the child population and the parent population parameters, a command for clearing the parameter file and the result file in real time is added. Further, constraint dominant relationship determination and ideal point calculation operations are performed on the generated sub-population.
Step eleven: non-dominant ordering, which is performed based on constraint dominant relation, and uses constraint dominant principle as criterion for judging nonlinear inequality constraint, the specific implementation process is as follows: if both individual variables are within the constraint range, the fitness values of the two are compared to determine a dominant relationship, and a dominant fitness value with a small fitness value is large. If two individual variables are within the constraint range and one is outside the constraint range, the former dominates the latter. If both individual variables are outside the constraint range, then a small violation of the constraint range governs a large violation of the constraint range. According to the principle, the level of non-dominant ranking can be determined, and if the whole population is in the constraint range, a conventional non-dominant ranking method is adopted. If one part of the whole population is in the constraint range and the other part is out of the constraint range, the former performs a conventional non-dominant sorting method, and the latter sequentially locates at the next layers of the last layer of the feasible solution according to the size of the violation of the constraint range from small to large. If the whole population is outside the constraint range, the whole population is orderly sequenced from small to large according to the size of the violation constraint range.
Step twelve: the last front-end solution is selected, the front-end solution is a set, front-end pareto solutions of different layers formed after individuals in a population are sorted according to non-dominance are recorded, and operations such as regularization, reference line calculation, individual and reference point association, living environment selection and the like are sequentially carried out.
(1) Regularization-to maintain diversity of the population, ensuring that subsequent solutions are interrelated with the reference points; since the respective objective function scales of each solution are not uniform, regularization is required to keep the bias of knowledge uniform:
the idea of regularization is to find the p-norm of each sample and then divide the elements in the sample by the norm, such that the p-norm of each processed sample can be equal to 1; wherein, p norm:
(2) associate individuals with reference points—solve for the distance of each individual from the nearest reference point, and calculate the number of related solutions except for the last front end of each reference point.
(3) Selecting a living environment-performing non-dominant sorting, selecting the last front-end solution, and generating the next generation.
Step thirteen: judging termination conditions, namely whether the maximum evolution times are reached or not 20, and if the conditions are reached, outputting Pareto optimal solutions; otherwise, repeating the steps eight-twelve.
After 20 iterative cycles, three schemes are terminated, wherein one scheme is used for 12.84 hours, the other scheme is used for 12.66 hours, the total time of the schemes is 2.01 hours, and the efficiency is improved by 6.36 times compared with that of the scheme I and 6.28 times compared with that of the scheme II. However, this is not an all advantage of the present invention, since the optimization efficiency increases by a multiple with the number of parallel COMSOL, which means that the greater the number of actual cores available for the computer, the greater the improvement in the optimization efficiency.
In addition, table 4 shows the optimized parameters, fig. 6 to 8 show the optimized structures, and fig. 9 to 11 show the results after partial optimization.
TABLE 4 optimized parameters
Through comparison, the scheme one is used as a single-target optimization scheme to only give one optimal solution, and the schemes two and three adopting Pareto optimal solutions give a plurality of groups of optimal solutions. It can be seen that the three schemes can be optimized to obtain better results, the peak value of the sound absorption coefficient of the optimized results is close to 1, the average sound absorption coefficient of the whole frequency band is about 0.78, but the scheme II has obvious advantages in diversity compared with the scheme I. In addition, compared with the scheme II, the method has the advantages that the method ensures the sound absorption performance of the whole broadband and simultaneously has emphasis on 7 divided frequency bands; and the scheme II can ensure the whole broadband sound absorption performance, but only the first 3 frequency bands can be optimized mainly due to the defects of the algorithm, and the last 4 frequency bands cannot be considered completely. The method has the advantages of comprehensive efficiency and optimization effect.
Claims (10)
1. The high-dimensional multi-target joint parallel simulation optimization method based on NSGA III is characterized by comprising the following steps of:
step one, determining an initial structure and an optimization direction of a sound absorption structure, specifically, improving the overall sound absorption performance by optimizing the shape and the relative position of a cavity based on a gradual change type cavity structure;
obtaining the reflection coefficient and the transmission coefficient of the sound absorption structure to be optimized by adopting a sound tube simulation method, and solving the sound absorption coefficient;
step three, determining material parameters and NSGA III algorithm parameters; the material parameters include: young's modulus, poisson's ratio, loss factor, density sound velocity; the NSGA III algorithm parameters comprise: the evolution times, population scale, maximum stop algebra, crossover probability and mutation probability;
step four, constructing an optimization target model; the method specifically comprises the following steps: establishing an optimization target model by taking the minimum average sound absorption coefficient of sound absorption structures in different frequency bands as an optimization target;
step five, generating consistency reference points according to the number of the self-defined population and the number of the targets in the starting stage;
step six, creating a file to be optimized according to resource conditions, wherein the file to be optimized comprises a command file and an initial configuration file;
the command file contains the data of detection command, loading command, population division command, parameter modification command, execution command, data extraction command, writing file command and deleting data command;
the initial configuration file contains initial configuration data of the sound absorption structure to be optimized;
step seven, creating a sentinel file and executing a monitoring function; the number of the guard files is two, and the guard files consist of fault detection files and initial configuration files;
the fault detection file in the first sentinel file is composed of a command file added with a monitoring command layer and is used for replacing a certain initial configuration file to execute an optimization process when the file is abnormal in operation and cannot output a result; the fault detection file in the second sentinel file is used for detecting the running condition of the first sentinel file, and if the first sentinel file is found to start executing the optimization function, the file starts executing the monitoring function consistent with the first sentinel file;
step eight, initializing a population; the method specifically comprises the following steps:
generating a first group of group variables by using a main function according to parameter setting, and storing the group of variables; reading the COMSOL corresponding to the variable data call and starting operation, and storing a result value according to a corresponding rule after the operation is finished; returning to the main function after all result values in the population are read;
step nine, solving ideal points; the method specifically comprises the following steps: extracting a population fitness minimum value, constructing ideal points, and converting an objective function into a self-adaptive normalization function through the ideal points;
step ten, returning the offspring generated by genetic operation;
step eleven, utilizing constraint dominance principle as criterion for judging nonlinear inequality constraint to make non-dominance sorting to form front end solutions of different layers;
step twelve, selecting the last front-end solution, and sequentially carrying out regularization, reference line calculation, individual and reference point association and living environment selection;
thirteenth, judging termination conditions, and outputting Pareto optimal solutions if the termination conditions are met; otherwise, repeating the steps eight to twelve.
2. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein the step one includes: and determining parameters to be optimized of the gradual change type cavity structure, wherein the parameters to be optimized comprise cavity thickness, acoustic cover layer thickness, unit cell size, distance between each interpolation point of the cavity and a cavity wall, radius from each interpolation point of the cavity to a center axis and vertical distance between adjacent interpolation points.
3. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein the second step is specifically that a sound tube simulation method is adopted to obtain a reflection coefficient and a transmission coefficient of a sound absorption structure to be optimized, and obtain a sound absorption coefficient α of the sound absorption structure, where α=1-R 2 -T 2 ；
Wherein R is a reflection coefficient extracted through finite element simulation, and T is a transmission coefficient;
the sound tube simulation relies on COMSOL finite element simulation, and utilizes a steel backing periodic unit containing a cavity to simulate an infinite sample structure, and a PML layer is arranged at the water area end to simulate an infinite water area; the periodic conditions of Floquet are set on the upper and lower surfaces and the left and right surfaces of the structure and the water area respectively to simulate the infinite large sample and the water area.
4. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein the optimization objective model in the fourth step is as follows:
wherein f i Mean sound absorption coefficient representing sound absorption structure in the frequency range;
α j refers to the sound absorption performance measured in the corresponding frequency range;
k is the number of interpolation points;
r k the radius from the kth interpolation point to the center axis; r is (r) k,min Is r k Lower limit of (2); r is (r) k,max Is r k Upper limit of (2);
h op refers to the vertical distance between adjacent interpolation points o and p; h is a op,min Is h op Lower limit of (2); h is a op,max Is h op Upper limit of (2);
h i distance from the ith interpolation point to the cavity wall; h is a max Is the upper limit of the sum of the interpolation point to the cavity wall.
5. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein the fifth step specifically comprises:
5.1 Generating reference points on the hyperplane space of M-1 latitude, wherein the number of the reference points is that
Wherein M represents the predefined number of targets, and H represents the number of divided parts of each single target;
5.2 For each x) ij E X, exist
The ij index indicates the j-th element of the i-th combination in X;
5.3 Definition S 1 For each S as a set of reference points ij ∈S 1 And x ij E X, exist
5.4 S) will S 1 As a set of points on the boundary layer, define S 2 For each S 'for the inner point set' ij ∈S 2 And S is ij ∈S 1 Exists in the presence of
5.5 Obtaining a reference point set s=s) 1 ∪S 2 。
6. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein in the sixth step, the specific operation of detecting the command comprises:
6.1 A detection command: the command is used for detecting the file generation condition under the fixed path, and when the NSGA III main function generates population parameter variables and stores the population parameter variables into corresponding text files, the detection command detects the file generation and carries out the next step;
6.2 Load command): the command is used for receiving the detection command of the last step and extracting parameters in the text file;
6.3 Group partition command): the command divides the population into n sub-populations according to the number n of folders;
6.4 Parameter modification command): the command modifies the structural parameters in COMSOL according to the population parameter variables extracted from each subspecies;
6.5 MATLAB with COMSOL execute command: the command receives the parameter modification command in the last step, and when the parameter modification command is executed, the initial configuration file operation command is executed continuously;
6.6 Data extraction command): the command is received to execute the command in the last step, the reflection coefficient in the simulation model is extracted after the initial configuration file is run, and the reflection coefficient is converted according to the objective function setting in the optimization objective model;
6.7 Writing text file command): the command receives the data extraction command of the previous step, and the extracted data is stored in a preset folder in the form of a text file;
6.8 A delete data command: the command is continuously executed after the execution of the steps 6.1) to 6.7) is finished, and is used for deleting the population parameter variable file, so that the confusion between new population parameter variables generated after the population evolution and the previous population parameter variables is avoided;
the specific content of each operation in the step twelve is as follows:
(1) regularization: in order to maintain diversity of the population, the follow-up solution and the reference point are ensured to be mutually connected; since the respective objective function scales of each solution are not uniform, regularization is required to keep the bias of knowledge uniform: the idea of regularization is to find the p-norm of each sample and then divide the elements in the sample by the norm, such that the result of the processing can be such that the norm p of each processed sample is equal to 1; wherein p is the norm:
(2) associating an individual with a reference point: solving the distance between each individual and the nearest reference point, and calculating the number of related solutions except the last front end of each reference point;
(3) selecting a living environment: non-dominant ordering is performed, the last front-end solution is selected, and the next generation is generated.
7. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein in the eighth step, specifically, the main function generates a first group of variables according to parameter settings, and stores the first group of variables into a variable file; and reading the variable files in sequence by using the command files created before, calling the corresponding COMSOL to start operation, storing the result values into the corresponding files according to the corresponding rules after the operation is finished, and returning to the main function after all the result values in the population are read.
8. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method of claim 1, wherein the specific steps of step nine include:
9.1 Group S) t Is defined asMinimum value->Ideal point of structureThe optimization objective function is transformed as follows: />
9.2 Find additional points for each coordinate axis:
9.3 Using the extra points to construct a hyperplane and determining the intercept a of the hyperplane to the coordinate axis i ；
9.4 Normalized objective function
9. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method as claimed in claim 1, wherein the criteria for determining the nonlinear inequality constraint in step eleven include:
if the variables of the two individuals are in the constraint range, determining a dominance relation by comparing the fitness values of the two individuals, wherein individuals with small fitness values dominate individuals with large fitness values;
if one of the two individual variables is in the constraint range and the other is out of the constraint range, the individual in the constraint range governs the individual out of the constraint range;
if the variables of the two individuals are outside the constraint range, the individual with small violation of the constraint range dominates the individual with large violation of the constraint range;
if the whole population is in the constraint range, adopting a non-dominant sorting method; if one part of the whole population is in the constraint range and the other part is out of the constraint range, the former part executes a conventional non-dominant sorting method, and the latter part is sequentially arranged on the next layers of the last layer of the feasible solution according to the size of the violation constraint range from small to large; if the whole population is outside the constraint range, the whole population is orderly sequenced from small to large according to the size of the violation constraint range.
10. The NSGA iii-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein in the sixth step, in order to prevent thread congestion during operation from occurring, parameter data cannot be loaded, an initial configuration file cannot be opened, and a try-catch function is added; the operation rule of the try-catch function is as follows: firstly, executing codes in try, and if the codes are abnormal, capturing and executing the codes in the catch by the catch; if no exception occurs, the catch capture function is ignored.
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