CN115099118A - NSGA III-based high-dimensional multi-target 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 NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method. 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 objective; generating a consistency reference point; creating a file to be optimized according to the resource condition; creating a sentinel file; initializing a population; calculating an ideal point; returning the offspring generated by the genetic operation; non-dominant ordering; selecting a front-end solution; and judging the termination condition and outputting the optimal solution. The method utilizes finite element simulation to calculate the sound absorption coefficient of the sound absorber in a specific frequency band, and adopts a population segmentation means to search the optimal configuration of the acoustic element in parallel, thereby getting rid of the constraint of the traditional empirical design, making up the current situations that the optimization target of a single-target optimization genetic algorithm and a rapid non-dominated sorting genetic algorithm with an elite strategy is less, the optimization effect is poor, and solving the problem of low efficiency of the existing optimization algorithm.
Description
Technical Field
The invention belongs to the field of structural and acoustic calculation optimization design, and particularly relates to a NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method.
Background
Through the development of the vibration-damping and noise-reducing engineering technology for decades, submarines of all countries make great progress in the field of sound radiation control, and gradually step into a quiet submarine line, 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 send out sound waves outwards, detects a target by receiving an echo signal, has the advantage of detecting a low-noise and even completely quiet target, and is paid attention to. Therefore, considering the corresponding sound stealth technology from the aspect of active sonar detection technology has practical and important significance for modern anti-diving operation. From the viewpoint of reducing the target strength, the problems of stealth of the shape sound, laying of a sound absorbing cover, use of an underwater acoustic composite material, and the like are mainly employed at present, without circumventing the optimization. How to adjust the shape (linear shape) of the submarine, how to plan the internal structure of the sound absorption covering layer, how to select the layers and angles of the composite materials and the like are the hot problems of the current research. However, the existing acoustic optimization means is single, taking an acoustic covering layer/metamaterial development tool as an example, the existing commonly adopted parametric scanning, genetic algorithm, gradient/non-gradient topological optimization and the like have the problems of low optimization efficiency and poor optimization effect.
Disclosure of Invention
The invention aims to provide a method for solving the problems of low efficiency of the existing optimization algorithm and realizing the aim of actively designing a configuration according to a sound absorption target by getting rid of the constraint of the traditional empirical design and solving the problem of low efficiency of the existing optimization algorithm aiming at the current situations of low optimization efficiency and poor optimization effect in the optimization design process of the existing acoustic elements, and the invention adopts the following technical scheme in order to achieve the aim:
a NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method comprises the following steps:
determining an initial structure and an optimized 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;
step two, obtaining a reflection coefficient and a 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: evolution times, population scale, maximum stopping algebra, cross probability and variation 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 the sound absorption structures in different frequency bands as an optimization target;
step five, generating a consistency reference point according to the number of the self-defined population and the number of the targets in the initial stage;
creating a file to be optimized according to the resource condition, 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 segmentation command, a parameter modification command, an execution command, a data extraction command, a writing file command and a data deletion command;
the initial configuration file contains initial configuration data of the sound absorption structure to be optimized;
step seven, establishing a sentinel file and executing a monitoring function; the number of the sentinel documents is two, and the sentinel documents consist of fault detection documents and initial configuration documents;
the fault detection file in the first sentinel file is formed by adding a monitoring command to a command file and is used for replacing the command file to execute an optimization process when a certain initial configuration file runs abnormally and cannot output a result; the fault detection file in the second sentinel file is used for detecting the running state of the first sentinel file, and if the first sentinel file is found to start to execute the optimization function, the file starts to execute the monitoring function consistent with the first sentinel file;
step eight, initializing a population; in particular to
Generating a first batch of population variables by using a main function according to parameter setting, and storing the batch of variables; reading variable data, calling the corresponding COMSOL to start running, and storing a result value according to a corresponding rule after the running is finished; returning to the main function after all result values in the population are read;
ninthly, solving an ideal point; the method specifically comprises the following steps: extracting a population fitness minimum value, constructing an ideal point, and converting the target function into a self-adaptive normalization function through the ideal point;
step ten, returning offspring generated through genetic operation;
step eleven, using a constraint domination principle as a criterion for judging nonlinear inequality constraint to perform non-domination sequencing to form front-end solutions of different layers;
selecting the last front-end solution, and sequentially carrying out operations of regularization, reference line calculation, individual and reference point association and living environment selection;
step thirteen, judging a termination condition, and if the termination condition is met, outputting a Pareto optimal solution; otherwise, repeating the step eight to the step 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: determining parameters to be optimized of the gradual change type cavity structure, wherein the parameters to be optimized comprise the thickness of a cavity, the thickness of an acoustic covering layer, the size of a unit cell, the distance between each interpolation point of the cavity and the cavity wall, the radius from each interpolation point of the cavity to a central axis and the vertical distance between adjacent interpolation points.
And step two, specifically, obtaining a reflection coefficient and a transmission coefficient of the sound absorption structure to be optimized by adopting a sound tube simulation method to obtain a sound absorption coefficient alpha of the sound absorption structure, wherein alpha is 1-R 2 -T 2
Wherein R is a reflection coefficient extracted through finite element simulation, and T is a transmission coefficient;
the acoustic tube simulation relies on COMSOL finite element simulation, an infinite sample structure is simulated by using a steel backing periodic unit containing a cavity, and a PML layer is arranged at the water area end to simulate an infinite water area; floquet periodic conditions are respectively arranged on the upper surface, the lower surface, the left surface and the right surface of the structure and the water area to simulate an infinite large sample and the water area.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective combined parallel simulation optimizing party, wherein an optimization objective model in the fourth step is as follows:
wherein f is i Representing the average sound absorption coefficient of the sound absorbing 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 means the radius from the kth interpolation point to the medial axis; r is k,min Is r k The lower limit of (d); r is a radical of hydrogen k,max Is r k The upper limit of (d);
h op refers to the vertical distance of adjacent interpolation points o and p; h is op,min Is h op The lower limit of (d); h is op,max Is h op The upper limit of (d);
h i the distance from the ith interpolation point to the cavity wall; h is max The upper limit of the sum of the interpolation points to the chamber walls.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-objective combined parallel simulation optimization method, wherein the step five specifically comprises the following steps:
5.1) generating reference points on the hyperplane space at the latitude of M-1, wherein the number of the reference points is
Wherein M represents the number of predefined objects, and H represents the number of divided parts of each single object;
5.2) for each x ij E.g. X, exists
The ij subscript indicates the jth element of the ith combination in X;
5.3) definition of S 1 For reference point set, for each S ij ∈S 1 And x ij Epsilon of X, existence
5.4) adding S 1 As a set of points on the boundary layer, S is defined 2 Is a set of inner layer points, for each S' ij ∈S 2 And S ij ∈S 1 Existence of
5.5) obtaining a reference point set S ═ S 1 ∪S 2 。
Further perfecting or supplementing the NSGA III-based high-dimensional multi-target combined parallel simulation optimization method, wherein in the sixth step, a detection command is used for detecting the file generation condition under a fixed path; the loading command carries the detection command and is used for extracting parameters; the population dividing command is used for dividing population parameters and dividing the population parameters into a plurality of sub-populations according to the number of files; modifying the structural parameters in the COMSOL by the parameter modifying command according to the population parameter variables extracted by each sub-population; the execution command carries the parameter modification command and is used for executing the operation command; the data extraction command carries out an execution command and is used for extracting a reflection coefficient in the simulation model and converting the reflection coefficient; the writing file command carries a data extraction command and is used for storing the extracted data; the data deleting command is used for deleting the population parameter variable file, so that the new population parameter variable generated after population evolution is prevented from being mixed with the previous population parameter variable;
the specific content of each operation in the step twelve is as follows:
regularization: calculating the p-norm of each sample, and then dividing elements in the samples by the norm to ensure that the p-norm of each processed sample is equal to 1; wherein, p-norm:
associating an individual with a reference point: solving the distance of each individual from the nearest reference point and calculating the number of relevant solutions except the last front end of each reference point;
selecting a living environment: and performing non-dominant sorting, selecting the last front-end solution and generating the next generation.
Further perfecting or supplementing the NSGA III-based high-dimensional multi-target combined parallel simulation optimization method, wherein in the step eight, a main function specifically generates a first batch of population variables according to parameter setting, and stores the batch of population variables into a variable file; and reading the variable files in sequence by utilizing the command files created before, calling the corresponding COMSOL to start running, storing the result values into the corresponding files according to the corresponding rules after the running 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 combined parallel simulation optimizing party, wherein the ninth step comprises the following specific steps:
9.1) grouping S t Is defined as
The minimum value of (a) is determined,
ideal point of structure
And converting the optimization objective function according to the following modes:
9.2) finding additional points of each coordinate axis:
9.3) constructing a hyperplane with additional points and solvingIntercept a of the plane with the coordinate axis i ；
9.4) normalization of the objective function
Further improving or supplementing the NSGA III-based high-dimensional multi-objective joint parallel simulation optimizing method, the criterion for judging the nonlinear inequality constraint in the eleventh step comprises the following steps:
if the variables of the two individuals are in the constraint range, determining a dominance relationship by comparing the fitness values of the two individuals, wherein the individual with a small fitness value dominates the individual with a large fitness value;
if one of the variables of the two individuals is in the constraint range and the other is out of the constraint range, the individual in the constraint range dominates the individual out of the constraint range;
if the variables of the two individuals are out of the constraint range, the individual with the smaller violation constraint range dominates the individual with the larger violation constraint range;
if the whole population is in the constraint range, adopting a non-dominated sorting method; if one part of the whole population is in the constraint range and the other part of the whole population is outside the constraint range, the former executes a conventional non-dominated sorting method, and the latter is sequentially placed in the next layers of the last layer of the feasible solution from small to large according to the size of the violated constraint range; and if the whole population is outside the constraint range, sequencing the population from small to large according to the size of the violated constraint range.
Further improving or supplementing the NSGA III-based high-dimensional multi-target combined parallel simulation optimizing party, in the sixth step, in order to prevent the situation that parameter data cannot be loaded due to thread congestion in the running process and an initial configuration file cannot be started, adding a try-catch function; the running rule of the try-catch function is as follows: executing the code in try, if the execution is abnormal, the catch can capture and execute the code in the catch; if no exception occurs, the catch capture function is ignored.
The invention has the beneficial effects that:
the invention discloses a high-dimensional multi-target combined parallel simulation optimization method based on NSGA III, which utilizes finite element simulation to calculate the sound absorption coefficient of a sound absorber in a specific frequency band, then divides the specific frequency band into a plurality of small frequency bands based on an unopened NSGA III algorithm, takes the average sound absorption coefficient of each frequency band as a target, and simultaneously adopts a group division means to search the optimal configuration of an acoustic element in parallel. According to the requirement of wide-band high sound absorption of the existing acoustic material, a new configuration with each frequency band reaching the optimum is automatically searched; the scheme gets rid of the constraint of the traditional empirical design, makes up the current situations that the optimization target of a single-target optimization Genetic Algorithm (GA) and a fast non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy is less and the optimization effect is poor, solves the problem that the efficiency of the existing optimization algorithm is low, and realizes the target of actively designing the configuration according to the sound absorption target; in addition, the method is not only suitable for the optimization problem of the sound absorption structure, but also suitable for other sound vibration optimization problems, and can be expanded to all finite element optimization problems.
Drawings
FIG. 1 is a schematic flow diagram of a NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method;
FIG. 2 is a first schematic view of the sound absorbing structure of the gradient cavity in the embodiment;
FIG. 3 is a schematic view of a sound absorbing structure with a gradually changing cavity in an embodiment II;
FIG. 4 is a COMSOL finite element simulation cavity element model;
FIG. 5 is a schematic diagram of a structure optimization process for joint parallel simulation optimization;
FIG. 6 is a first schematic diagram of a simulation optimization based on a first scheme;
FIG. 7 is a schematic diagram II of a simulation optimization based on scheme II;
FIG. 8 is a schematic diagram of a structural summary of the joint parallel simulation optimization;
FIG. 9 is the result of the embodiment of the solution one based joint parallel simulation optimization;
FIG. 10 is the result of the optimization of the joint parallel simulation based on the second scheme in the embodiment;
FIG. 11 is the result of the joint parallel simulation optimization based on the present application in the embodiment.
Detailed Description
The NSGA III-based high-dimensional multi-objective combined parallel simulation optimization method is based on an NSGA III framework, is suitable for small-scale sound vibration optimization problems, and can be expanded to all small-scale finite element optimization problems. According to the method, a multi-target MATLAB with COMSOL combined parallel simulation optimization method is established by a self-established MATLAB with COMSOL combined parallel simulation method and by means of the NSGA III algorithm concept, so that the efficiency of acoustic optimization is greatly improved, and the current situation that the optimization effect of the problems is poor is solved. The method comprises the following steps of actually optimizing an XX sound absorption structure of certain X-type equipment, and specifically describing the specific steps of the method in detail by combining a specific implementation process, wherein the specific steps are as follows:
the method comprises the following steps: the initial structure and the optimized direction of the sound absorption structure are determined. As shown in fig. 2, a gradual change type cavity structure is selected to improve the overall sound absorption performance by optimizing the shape and relative position of the cavity. In this embodiment, the thickness of the steel plate of the XX sound absorption structure of a certain X-type device is 10mm, the thickness of the acoustic covering layer is 40mm, the length and the width of the whole single cell element are 40mm, and h is 1 Represents the distance from the first interpolation point of the cavity to the steel plate, r 1 Represents the radius from the first interpolation point to the medial axis, h 2 Represents the vertical distance, r, from the second interpolation point to the first interpolation point of the cavity 2 Represents the radius of the second interpolation point to the medial 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 1 、h 2 、h 3 、r 1 、r 2 And r 3 All parameters 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, with varying parameters, may also form several structures as shown in fig. 3.
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 acoustic tube simulation relies on a COMSOL finite element simulation platform, and utilizes a steel backing period 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. In addition, because the medium on the transmission side is air, the transmission coefficient amplitude is small, and the back side of the steel plate can be approximate to a free boundary. Floquet periodic conditions are respectively arranged on the upper surface, the lower surface, the left surface and the right surface of the structure and the water area to simulate an infinite large sample and the water area. Meanwhile, the plane wave is normally incident to one side of the covering layer, the incident frequency is 1 kHz-3 kHz, and the step length is 100 Hz; and α ═ 1-R 2 -T 2 (ii) a Wherein, R is a reflection coefficient extracted by finite element simulation, and T is a transmission coefficient.
Since T < 0, formula (1) can be directly expressed as α ═ 1-R 2 ；
Step three: determining material parameters and NSGA III algorithm main parameters, wherein the material parameters are shown in Table 2, and the NAGA III algorithm main parameters are set as follows: evolution times-20, population size-30, maximum stopping algebra-20, cross probability-0.8, variation probability-0.2, and simultaneously paralleling 7 acoustic-frequency domain modules of COMSOL.
The evolution times are formulated according to the size of the initial configuration file, and if the convergence is better in order to optimize the result, the evolution times can be increased; the population scale is generally 30-200; the maximum stopping algebra benchmarking evolution times can be kept consistent with the evolution times when the evolution times are less; and the cross probability and the mutation probability are default parameter settings of the genetic algorithm.
Furthermore, to compare the advantages of the present invention horizontally, scheme one (genetic algorithm toolkit (GA) in combination with MATLAB with COMSOL) and scheme two (genetic algorithm toolkit (NSGA-ii) in combination with MATLAB with COMSOL) were created synchronously, with parameter settings consistent with the example schemes.
TABLE 2 Material parameters
| Material | Young's modulus (Pa) | Poisson ratio | Loss factor | Density (kg/m) 3 ) | Speed of sound (m/s) |
| Base body | 1.4e8 | 0.49 | 0.48 | 1100 | - |
| Steel | 2.1e11 | 0.3 | 0 | 7800 | - |
| Water (W) | - | - | - | 1000 | 1500 |
Step four: constructing an optimization target model, and establishing the optimization target model by taking the minimum average sound absorption coefficient of sound absorption structures in different frequency bands as an optimization target; in order to improve the sound absorption performance of the sound absorption structure at 1000-3000 Hz and achieve the best integral sound absorption performance, the adopted optimization target model is as follows:
wherein, f i Denotes the average sound absorption coefficient per 300Hz structure, i is 1,2,3 ….
In addition, in the first scheme, because the GA algorithm can only process a single target problem, the target function is simplified into
min f＝-1/21(α 1000Hz +…+α 3000Hz )
Wherein f represents the average sound absorption coefficient of the structure in the frequency band of 1000-3000 Hz.
Step five: generating a consistency reference point according to the number of the self-defined population and the number of the targets at the initial stage of optimization, wherein the point distribution scheme is as follows:
5.1) generating reference points on the hyperplane space (hyperplane is a linear subspace with the remaining latitude equal to one in the n-dimensional Euclidean space) at the latitude (M-1), wherein the number of the reference points is
Wherein M represents the number of predefined objects, and H represents the number of divided parts of each single object;
5.2) for each x ij E.g. X, the subscript ij indicates that the ith combination jth element in X is present
5.3) definition of S 1 For reference point set, for each S ij ∈S 1 And x ij ∈X，All exist
5.4) adding S 1 Defining S as a set of points on the boundary layer 2 Is a set of inner layer points, for each S' ij ∈S 2 And S ij ∈S 1 There are, both:
5.5) defining the set of reference points as S ═ S 1 ∪S 2 ；
Step six: testing the minimum core number x of the simulation model according to the size of the simulation model (the time of completing one operation of the simulation model under the core number is required to be ensured to be almost the same as the time of completing one operation under the maximum 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) and a command file (mat _ communication. m);
wherein the initial configuration file is a sound absorption structure file to be optimized. The command file sequentially comprises a detection command, a loading command, a population division command, a parameter modification command, an MATLAB with COMSOL execution command, a data extraction command, a text file writing command and a data deletion command, and the specific operations are as follows:
6.1) detection command: the command is used for detecting the file generation condition under the fixed path, when the NSGA III main function generates the population parameter variable and stores the population parameter variable into a corresponding text file, the detection command can detect the generation of the file, and the next step is carried out;
6.2) load command: the command carries the last step of detection command and is used for extracting parameters in the text file;
6.3) group division 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 sub-population;
6.5) MATLAB with COMSOL execute command: the command receives the parameter modification command of 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 carries the execution command of the previous step, the reflection coefficient in the simulation model is extracted after the initial configuration file is completely operated, and the reflection coefficient is converted according to the target function setting in the optimization target model;
6.7) write 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 a text file form;
6.8) delete data Command: and (4) the command is executed continuously after the execution of the steps (6.1) to (6.7) is finished, and the command is used for deleting the population parameter variable file, so that the new population parameter variable generated after population evolution is prevented from being mixed with the previous population parameter variable.
In addition, in order to prevent the situations that parameter data cannot be loaded due to thread congestion and an initial configuration file cannot be opened in the running process, a (try-catch) function is added to enable the file to run completely. the running rule of the try-catch function is as follows: executing the code in the try, if the execution is abnormal, the catch can capture and execute the code in the catch; if no exception occurs, the catch capture function is ignored.
Step seven: two sentinel files are created, each file including a monitoring file and an initial configuration file. The first by1.m file is used for detecting faults, a layer of monitoring command is added on the basis of the six-step command file, and the monitoring command is used for replacing a certain initial configuration file to execute an optimization process when the file runs abnormally and a result cannot be output. The second monitoring file is used to detect the operating status 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, and the "sentinel" operation flow is shown in fig. 5.
Step eight: and (5) initializing a population. The main function generates a first batch of population variables according to parameter setting, and stores the batch of variables into n text files; sequentially reading the text files by the n command files created before, calling the corresponding COMSOL to start running, and storing result values into the corresponding text files according to corresponding rules after the running is finished; the scheme I is a single-target optimization method, and the result value is stored according to the form of an objective function model, and the scheme II and the invention are multi-target optimization methods, and the result value is stored according to the setting form of the objective function in the optimization objective model. And finally, reading the result values in the text file by the fitness function in the NSGA-III, and returning to the main function after all the result values in the population are read.
Step nine: calculating an ideal point, extracting the minimum value of population fitness, constructing an ideal point, and converting the objective function into an adaptive normalization function through the ideal point, wherein the specific operation is as follows:
9.1) grouping S t Is defined as
Minimum value of (2)
Constructing an ideal point
And transforming the objective function according to equation (10):
9.2) finding additional points of each coordinate axis:
9.3) constructing a hyperplane by using the extra points and solving the intercept a of the hyperplane and the coordinate axis i ；
9.4) normalization of the objective function:
step ten: and returning the offspring generated by genetic operation, wherein the calculation rule of the fitness value of the offspring is consistent with the population initialization process, but in order to avoid parameter confusion between the child population and the parent population, a command of clearing the parameter file and the result file in real time is added. And then, carrying out the operation of judging the constraint dominance relation and solving the ideal point on the generated sub-population.
Step eleven: non-domination sorting, which is based on constraint domination relation to perform non-domination sorting, and utilizes constraint domination principle as criterion for judging nonlinear inequality constraint, and the specific implementation process is as follows: if both the individual variables are within the constraint range, the dominance relationship is determined by comparing the fitness values of the two, and the dominance fitness value having a small fitness value is large. If two individual variables are one within the constraint range and one outside the constraint range, the former dominates the latter. If both of the individual variables are outside the constraint range, the smaller violating constraint range will dominate the larger violating constraint range. According to the principle, the level of non-dominant sorting can be determined, and if the whole population is in the constraint range, a conventional non-dominant sorting 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 executes the conventional non-dominated sorting method, and the latter sequentially puts the next layers of the last layer of the feasible solution from small to large according to the size of the violated constraint range. And if the whole population is outside the constraint range, sequencing the population from small to large according to the size of the violated constraint range.
Step twelve: and selecting the last front-end solution, wherein the front-end solution is a set, and front-edge pareto solutions of different layers formed by the individuals in a population after non-dominant sorting are recorded, and the operations of regularization, reference line calculation, association of the individuals and a reference point, living environment selection and the like are sequentially performed.
Regularization, namely, ensuring that subsequent solutions are mutually connected with a reference point in order to maintain the diversity of a population; because the target function scales of each solution are inconsistent, regularization is required to be performed to keep the learned bias consistent:
the idea of regularization is to take the p-norm of each sample and then divide the elements in the sample by this norm, which results in the p-norm of each processed sample being equal to 1; wherein, p norm:
linking individuals with reference points-solving the distance of each individual from the nearest reference point and calculating the number of relevant solutions except the last front end of each reference point.
Selecting living environment, non-dominant sorting, selecting the last front end solution and generating the next generation.
Step thirteen: judging a termination condition, namely whether the maximum evolution times is 20 or not, and if so, outputting a Pareto optimal solution; otherwise, repeating the step eight to the step twelve.
After 20 iterative cycles, the three schemes are terminated, wherein the first scheme is used for 12.84 hours, the second 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 the first scheme and 6.28 times compared with the second scheme. This is not all the advantages of the present invention, since the optimization efficiency increases in multiples as the number of concurrent COMSOLs increases, which means that the more cores the computer actually has available, the greater the improvement in 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 of partial optimization.
TABLE 4 optimized parameters
Through comparison, the scheme I is used as a single-target optimization scheme to only provide an optimal solution, and the schemes II and III adopting Pareto optimal solutions provide multiple groups of optimal solutions. It can be seen that the three schemes can be optimized to obtain a better result, the peak value of the sound absorption coefficient of the optimized result is close to 1, and the average sound absorption coefficient of the whole frequency band is about 0.78, but the second scheme and the result obtained by the first scheme have obvious advantages in diversity compared with the first scheme. In addition, the scheme is superior to the scheme, and the divided 7 frequency bands are emphasized while the integral broadband sound absorption performance is ensured; although the second scheme can also ensure the whole broadband sound absorption performance, the algorithm has the defects that only the first 3 frequency bands can be optimized in a key mode, and the last 4 frequency bands cannot be considered completely. Comprehensive efficiency and optimization effect, this application has showing the advantage.
Claims (10)
1. A NSGA III-based high-dimensional multi-target joint parallel simulation optimization method is characterized by comprising the following steps:
determining an initial structure and an optimized 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;
step two, obtaining a reflection coefficient and a transmission coefficient of the sound absorption structure to be optimized by adopting a sound tube simulation method, and solving a sound absorption coefficient;
step three, determining material parameters and NSGA III algorithm parameters; the material parameters include: young modulus, Poisson's ratio, loss factor, density acoustic velocity; the NSGA III algorithm parameters comprise: evolution times, population scale, maximum stopping algebra, cross 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 the sound absorption structures in different frequency bands as an optimization target;
step five, generating a consistency reference point according to the number of the self-defined population and the number of the targets in the initial stage;
creating a file to be optimized according to the resource condition, 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 segmentation command, a parameter modification command, an execution command, a data extraction command, a writing file command and data of a data deletion 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 sentinel documents is two, and the sentinel documents consist of fault detection documents and initial configuration documents;
the fault detection file in the first sentinel file is formed by adding a monitoring command layer to a command file and is used for replacing the file to execute an optimization process when a certain initial configuration file runs abnormally and cannot output a result; the fault detection file in the second sentinel file is used for detecting the running state of the first sentinel file, and if the first sentinel file is found to start to execute the optimization function, the file starts to execute the monitoring function consistent with the first sentinel file;
step eight, initializing a population; the method specifically comprises the following steps:
generating a first batch of population variables by using a main function according to parameter setting, and storing the batch of variables; reading variable data, calling the corresponding COMSOL to start running, and storing a result value according to a corresponding rule after the running is finished; returning to the main function after all result values in the population are read;
step nine, solving an ideal point; the method specifically comprises the following steps: extracting the minimum value of population fitness, constructing an ideal point, and converting the target function into a self-adaptive normalization function through the ideal point;
step ten, returning the filial generation generated by genetic operation;
step eleven, using a constraint domination principle as a criterion for judging nonlinear inequality constraint to perform non-domination sequencing to form front-end solutions of different layers;
selecting the last front-end solution, and sequentially carrying out operations of regularization, reference line calculation, individual and reference point association and living environment selection;
step thirteen, judging and judging a termination condition, and if the termination condition is met, outputting a Pareto optimal solution; otherwise, repeating the step eight to the step twelve.
2. The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein the first step comprises the following steps: determining parameters to be optimized of the gradual change type cavity structure, wherein the parameters to be optimized comprise the thickness of a cavity, the thickness of an acoustic covering layer, the size of a unit cell, the distance between each interpolation point of the cavity and the cavity wall, the radius from each interpolation point of the cavity to a central axis and the vertical distance between adjacent interpolation points.
3. The NSGA III-based high-dimensional multi-objective combined parallel simulation optimization method according to claim 1, wherein the second step specifically includes obtaining a reflection coefficient and a transmission coefficient of the sound absorption structure to be optimized by using a sound tube simulation method to obtain a sound absorption coefficient alpha of the sound absorption structure, wherein alpha is 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, an infinite sample structure is simulated by using a steel backing period unit containing a cavity, and a PML layer is arranged at the water area end and used for simulating an infinite water area; floquet periodic conditions are respectively arranged on the upper surface, the lower surface, the left surface and the right surface of the structure and the water area to simulate an infinite large sample and the water area.
4. The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein the optimization objective model in the fourth step is as follows:
wherein f is i Representing the average sound absorption coefficient of the sound absorbing 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 means the radius from the kth interpolation point to the medial axis; r is k,min Is r k The lower limit of (d); r is k,max Is r k The upper limit of (d);
h op refers to the vertical distance of adjacent interpolation points o and p; h is op,min Is h op The lower limit of (d); h is op,max Is h op The upper limit of (d);
h i the distance from the ith interpolation point to the cavity wall; h is max The upper limit of the sum of the interpolation points to the chamber walls.
5. The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein the step five specifically refers to:
5.1) generating reference points on the hyperplane space at the latitude of M-1, wherein the number of the reference points is
Wherein M represents the number of predefined objects, and H represents the number of divided parts of each single object;
5.2) for each x ij Epsilon of X, existence
The ij subscript indicates the jth element of the ith combination in X;
5.3) definition of S 1 For reference point set, for each S ij ∈S 1 And x ij E.g. X, exists
5.4) adding S 1 Defining S as a set of points on the boundary layer 2 Is a set of inner layer points, for each S' ij ∈S 2 And S ij ∈S 1 Existence 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 according to claim 1, wherein in the sixth step, the specific operation of detecting the command comprises:
6.1) detection command: the command is used for detecting the file generation condition under the fixed path, when the NSGA III main function generates the population parameter variable and stores the population parameter variable into a corresponding text file, the detection command can detect the generation of the file, and the next step is carried out;
6.2) load command: the command carries the last step of detection command and is used for extracting parameters in the text file;
6.3) population partitioning 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 sub-population;
6.5) MATLAB with COMSOL executes the command: the command receives the parameter modification command of 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 carries the last step of executing the command, and after the initial configuration file is operated, the reflection coefficient in the simulation model is extracted and converted according to the target function setting in the optimized target model;
6.7) write 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 a text file form;
6.8) delete data Command: the command is executed continuously after the execution of the steps 6.1) to 6.7) is finished, and the command is used for deleting the population parameter variable file to avoid the confusion between new population parameter variables generated after population evolution and the previous ones;
the specific content of each operation in the step twelve is as follows:
1, regularization: in order to maintain the diversity of the population, the correlation between the subsequent solutions and the reference point is ensured; because the target function scales of each solution are inconsistent, regularization is required to be performed to keep the learned bias consistent: the idea of regularization is to take the p-norm of each sample and then divide the elements in the sample by this norm, so that the norm p of each processed sample is equal to 1; wherein p is a norm:
associating the individual with a reference point: solving the distance of each individual from the nearest reference point and calculating the number of relevant solutions except the last front end of each reference point;
selecting a living environment: and performing non-dominant sorting, selecting the last front-end solution and generating the next generation.
7. The NSGA III-based high-dimensional multi-objective combined parallel simulation optimization method according to claim 1, wherein in the eighth step, the main function specifically generates a first batch of population variables according to parameter settings, and stores the batch of population variables into a variable file; and reading the variable files in sequence by utilizing the command files created before, calling the corresponding COMSOL to start running, storing the result values into the corresponding files according to the corresponding rules after the running 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 according to claim 1, wherein the concrete steps of the ninth step include:
9.1) grouping S t Is defined as
The minimum value of (a) is determined,
ideal point of structure
The optimization objective function is transformed according to the following modes:
9.2) finding additional points of each coordinate axis:
9.3) constructing a hyperplane by using the extra points and solving the intercept a of the hyperplane and the coordinate axis i ；
9.4) normalization of the objective function
9. The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method according to claim 1, wherein the criterion for judging the nonlinear inequality constraints in the eleventh step comprises:
if the variables of the two individuals are in the constraint range, determining a dominance relationship by comparing the fitness values of the two individuals, wherein the individual with a small fitness value dominates the individual with a large fitness value;
if one of the variables of the two individuals is in the constraint range and the other is out of the constraint range, the individual in the constraint range dominates the individual out of the constraint range;
if the variables of the two individuals are out of the constraint range, the individual with the smaller violation constraint range dominates the individual with the larger violation 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 executes a conventional non-dominated sorting method, and the latter is sequentially placed on the next layers of the last layer of the feasible solution from small to large according to the size of the violated constraint range; and if the whole population is outside the constraint range, sequencing the population from small to large according to the size of the violated constraint range.
10. The NSGA III-based high-dimensional multi-objective joint parallel simulation optimization method as claimed in claim 1, wherein in the sixth step, in order to prevent the situation that parameter data cannot be loaded due to thread congestion and an initial configuration file cannot be started in the running process, a try-catch function is added; the running rule of the try-catch function is as follows: executing the code in the try, if the execution is abnormal, the catch can capture and execute the code in the catch; if no exception occurs, the catch capture function is ignored.
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