CN115796046A - Optimized design method of terahertz metamaterial sensor - Google Patents
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Abstract
The invention belongs to the technical field of terahertz metamaterial sensors, and particularly relates to an optimized design method of a terahertz metamaterial sensor, which comprises the following steps: s1: determining a performance index concerned by the terahertz metamaterial sensor, analyzing the influence of geometric structure parameters of a sensor structure unit on the performance index of the sensor by using electromagnetic simulation software, and selecting proper geometric structure parameters as variables to be optimized; s2: after the geometric structure parameters to be optimized are selected, carrying out coarse optimization on the terahertz metamaterial sensor; s3: and (3) carrying out fine optimization on the geometric parameters of the sensor by adopting an improved multi-objective optimization algorithm NSGA-II. The method can solve the problems of low optimization speed and difficulty in obtaining an optimal solution when a parameter scanning method is adopted to optimally design the terahertz metamaterial sensor, and has a good market application prospect.
Description
Technical Field
The invention belongs to the technical field of terahertz metamaterial sensors, and particularly relates to an optimized design method of a terahertz metamaterial sensor.
Background
Currently, the optimized design of the terahertz metamaterial sensor is mainly completed by means of electromagnetic simulation software. The process comprises the following steps: firstly, simulating a unit structure of the sensor by using electromagnetic simulation software, and analyzing the influence of geometric structure parameters in the unit structure on the performance of the sensor; and then, optimizing the geometric structure parameters by a parameter scanning method so as to enable the sensor to obtain expected performance indexes. However, for the optimized design of the terahertz metamaterial sensor, more than one performance index needs to be concerned, and the performance indexes have a mutual constraint relationship. By using a parameter scanning method, geometric structure parameters with a plurality of performance indexes meeting requirements at the same time are difficult to find; the geometric structure parameters influencing the performance parameters of the terahertz metamaterial sensor are numerous, and different performance indexes can be obtained by combining the geometric structure parameters with different sizes. When the parameter scanning method is used for optimization, the combination of various geometric structure parameters needs to be traversed one by one, and the time consumption is huge.
Based on the problems, in order to meet the requirement of design optimization of the terahertz metamaterial sensor, the multi-objective optimization algorithm NSGA-II is improved and combined with a parameter scanning method to form the design optimization method of the terahertz metamaterial sensor.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention aims to provide an optimized design method of a terahertz metamaterial sensor, and aims to solve the problems that when a parameter scanning method is adopted to optimize the design of the terahertz metamaterial sensor, the optimization speed is low, and an optimal solution is difficult to obtain.
In order to achieve the purpose, the invention provides the following technical scheme:
an optimized design method of a terahertz metamaterial sensor is shown in the attached figure 1 and comprises the following steps:
s1: determining a performance index concerned by the terahertz metamaterial sensor, analyzing the influence of geometric structure parameters of a sensor structure unit on the performance index of the sensor by using electromagnetic simulation software, and selecting proper geometric structure parameters as variables to be optimized;
s2: after the geometric structure parameters to be optimized are selected, carrying out coarse optimization on the terahertz metamaterial sensor;
s3: and (3) carrying out fine optimization on the geometric parameters of the sensor by adopting an improved multi-objective optimization algorithm NSGA-II.
In the non-dominant sorting in the traditional NSGA-II, only one individual is selected to be compared with other individuals, and the dominant individual and the dominated individual are calculated to realize layering. However, as the number of individuals increases, the number of comparisons increases, which greatly affects the speed of the algorithm. Therefore, the invention achieves the purposes of reducing the total comparison times and improving the calculation speed of the algorithm by increasing the number of the individuals participating in comparison. Preferably, the specific method for roughly optimizing the terahertz metamaterial sensor in step S2 is as follows: and scanning the geometric structure parameters to be optimized one by using electromagnetic simulation software, and determining the value range of the geometric parameters to be optimized in the next fine optimization.
Preferably, the traditional NSGA-II is improved from four key steps of non-dominated sorting, congestion degree calculation, operator selection, crossover and mutation probability in the step S3. A flow chart of the modified NSGA-II algorithm is shown in fig. 2.
In the non-dominant sorting in the traditional NSGA-II, only one individual is selected to be compared with other individuals, and the dominant individual and the dominated individual are calculated to realize layering. However, as the number of individuals increases, the number of comparisons increases, which greatly affects the speed of the algorithm. Therefore, the invention achieves the purposes of reducing the total comparison times and improving the calculation speed of the algorithm by increasing the number of the individuals participating in comparison. The specific method for improving the non-dominated sorting comprises the following steps: the number of individuals compared in conventional NSGA-II was increased from 1 to 4. The steps of the improved non-dominated sorting method are shown in figure 3.
The congestion degree calculation of the traditional NSGA-II algorithm only considersThe distance between adjacent individuals. For the terahertz metamaterial sensor, sub-targets needing to be optimized are different performance indexes. However, the units of these performance indexes are different and the numerical values are different greatly, which results in a great difference in crowdedness among different sub-targets. If the crowding degree only considers the distance between adjacent individuals, the space uniform distribution of the individuals is not facilitated, the probability that the optimized sub-targets enter the next population is reduced, and a better genetic chance cannot be obtained. Therefore, when the congestion degree is calculated, the variance of the adjacent objective function values is introduced, and the calculation formula is as follows:
wherein n is CR Indicates the degree of crowding of an individual N, N indicates the number of objective functions, F (N) d Calculating a value for the conventional congestion of individual n, F (n + 1) i And F (n-1) i Respectively are the ith target functions of two adjacent individuals of the individual n.
In the traditional NSGA-II algorithm, the selection strategy is to use an elite retention strategy. This selection strategy can ensure that the best individuals can be retained while rejecting those with poor efficacy. However, the elite retention strategy reduces the diversity of the population to a certain extent, and the optimization result is easy to fall into local optimization. Therefore, the invention improves the selection strategy in NSGA-II, uses the tournament selection strategy and improves the global searching capability. The tournament selection strategy used by the present invention is illustrated in FIG. 4.
Crossover probability P in classical NSGA-II c And the mutation probability P m The selection of the two probability values plays a key role in effectively finding the optimal solution by the genetic algorithm. In the optimization process, the cross probability P is fixed c And probability of mutation P m The value of (a) is not favorable for finding the optimal solution. Therefore, the present invention employs adaptive cross probabilities and adaptive mutation probabilities. The fitness is taken as a basis for self-adaptation of the cross probability and the mutation probability, and the method comprises the following specific steps:
(1) When the individual fitness f' approaches the average fitness f avg The cross probability and the variation probability are moderate values;
(2) When the individual fitness f' approaches the minimum fitness f min In time, the cross probability and the mutation probability both take smaller values, and the cross probability and the mutation probability are reduced;
(3) When the individual fitness f' approaches the maximum fitness f max In time, the cross probability and the mutation probability take larger values, and the probability of the cross and the mutation is increased.
The adaptive crossover probability values are:
the adaptive mutation probability value is:
compared with the prior art, the invention has the following beneficial effects:
(1) According to the optimized design method of the terahertz metamaterial sensor, the traditional NSGA-II is improved from four key steps of non-dominated sorting, congestion degree calculation, operator selection, intersection and variation probability, and the problems that when a parameter scanning method is adopted to optimally design the terahertz metamaterial sensor, the optimization speed is low and the optimal solution is difficult to obtain can be solved.
(2) According to the optimized design method of the terahertz metamaterial sensor, when non-dominated sorting is improved, the number of compared individuals in the traditional NSGA-II is increased from 1 to 4, and the total comparison times can be reduced and the algorithm calculation speed can be improved by increasing the number of the individuals participating in comparison.
(3) According to the optimized design method of the terahertz metamaterial sensor, disclosed by the invention, when the crowding degree is calculated, the variance of adjacent objective function values is introduced, so that the individuals are uniformly distributed in space, the probability that the optimized sub-targets enter the next population is improved, and a better genetic opportunity is obtained.
(4) According to the optimized design method of the terahertz metamaterial sensor, the selection strategy in NSGA-II is improved, and the global search capability can be improved by using the tournament selection strategy.
(5) According to the optimization design method of the terahertz metamaterial sensor, the self-adaptive cross probability and the self-adaptive variation probability are adopted, and the fitness serves as the self-adaptive basis of the cross probability and the variation probability, so that the optimal solution can be found in the optimization process.
Drawings
FIG. 1 is a schematic diagram of a design optimization process of a terahertz metamaterial sensor according to the present invention;
FIG. 2 is a flow chart of the improved NSGA-II algorithm of the present invention;
FIG. 3 is a flow chart of the improved non-dominated sorting method steps of the invention;
FIG. 4 is a flow diagram of the tournament selection policy of the present invention;
FIG. 5 is a schematic diagram of an optimized implementation process of a terahertz metamaterial design of a dual-opening resonant ring structure in embodiment 1 of the present invention;
FIG. 6 is a schematic diagram of a dual-open-loop terahertz metamaterial sensor according to embodiment 1 of the present invention;
fig. 7 is a schematic diagram of a resonance curve of an optimized double-open-loop terahertz metamaterial sensor in embodiment 1 of the present invention.
Detailed Description
The following is a clear and complete description of the technical solutions of the present invention, and it is obvious that the described embodiments are some, not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the orientations or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., are orientations or positional relationships indicated on the basis of the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the devices or elements referred to must have specific orientations, be constructed and operated in specific orientations, and thus, should not be construed as limiting the invention.
In the description of the present invention, it should be noted that, unless otherwise explicitly stated or limited, the terms "mounted," "connected," and "connected" should be interpreted broadly, e.g., as being fixed or detachable or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be connected internally between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 5, a terahertz metamaterial optimal design method is explained by taking a terahertz metamaterial sensor with a double-opening resonant ring structure as an example. Firstly, a resonance curve of the sensor is obtained by using electromagnetic simulation software, so as to obtain a performance index of the sensor, and the opening width w and the opening off-center pair displacement d of the opening resonance ring are determined as variables to be optimized through analysis, as shown in fig. 6. Secondly, after the optimization variables are determined, a parameter scanning method in electromagnetic simulation software is utilized to perform rough optimization on w and d one by one, and the value ranges of the next fine optimization of w and d are determined to be [0,10]. And finally, carrying out fine optimization on the values of w and d by adopting an improved multi-objective optimization algorithm NSGA-II to obtain an optimal solution.
The improved NSGA-II mainly improves four key steps of non-dominated sorting, crowdedness calculation, operator selection, crossover and mutation probability. During initialization, the population number is set to 15, the number of optimization variables is 2, and the number of objective functions is 2.
For the improvement of non-dominant sequencing, 4 individuals are selected as comparison individuals, so that the total comparison times are reduced, and the calculation speed of the algorithm is improved.
For the improvement of the congestion degree calculation, the variance of adjacent objective function values is introduced. In this embodiment, two indexes, namely, the resonance amplitude and the Q value of the sensor, are used as optimization targets, so that a specific calculation formula of the crowdedness is as follows:
for the improvement of the selection operator, a tournament selection strategy is adopted, and the number of the selected individuals is set to be 3.
For the improvement of cross and mutation, in order to achieve the purpose of self-adaptation, the self-adaptation cross mutation probability is calculated as follows:
wherein Pc3 is 0.1, pc2 is 0.5.
The adaptive mutation probability is calculated as follows:
wherein Pm3 is 0.1, pm2 is 0.5.
After improved NSGA-II optimization, an optimal solution can be obtained: d =4.7um, w =8.4um, and its resonance curve is shown in fig. 7.
The optimization design method of the terahertz metamaterial sensor solves the problems that when a parameter scanning method is adopted to optimize the terahertz metamaterial sensor, the optimization speed is low and an optimal solution is difficult to obtain, is very practical and has a good market application prospect.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.
Claims (8)
1. The optimized design method of the terahertz metamaterial sensor is characterized by comprising the following steps of:
s1: determining a performance index concerned by the terahertz metamaterial sensor, analyzing the influence of geometric structure parameters of a sensor structure unit on the performance index of the sensor by using electromagnetic simulation software, and selecting proper geometric structure parameters as variables to be optimized;
s2: after the geometric structure parameters to be optimized are selected, carrying out coarse optimization on the terahertz metamaterial sensor;
s3: and (3) carrying out fine optimization on the geometric parameters of the sensor by adopting an improved multi-objective optimization algorithm NSGA-II.
2. The optimized design method of the terahertz metamaterial sensor as claimed in claim 1, wherein the step S2 of roughly optimizing the terahertz metamaterial sensor comprises the following specific steps: and scanning the geometric structure parameters to be optimized one by using electromagnetic simulation software, and determining the value range of the geometric parameters to be optimized in the next fine optimization.
3. The optimized design method of the terahertz metamaterial sensor as claimed in claim 1, wherein in step S3, the traditional NSGA-II is improved through four key steps of non-dominated sorting, crowdedness calculation, operator selection, crossover and mutation probability.
4. The optimized design method of the terahertz metamaterial sensor as claimed in claim 3, wherein the specific way of improving the non-dominated sorting is to: the number of individuals compared in conventional NSGA-II was increased from 1 to 4.
5. The optimized design method of the terahertz metamaterial sensor as claimed in claim 3, wherein the variance of adjacent objective function values is introduced when the calculation of the crowdedness is improved,the calculation formula is as follows:
wherein n is CR Indicates the degree of crowding of an individual N, N indicates the number of objective functions, F (N) d Calculating a value for the conventional congestion of individual n, F (n + 1) i And F (n-1) i Respectively are the ith target functions of two adjacent individuals of the individual n.
6. The optimized design method of the terahertz metamaterial sensor as claimed in claim 3, wherein when a selection operator is improved, an elite retention strategy of a traditional NSGA-II algorithm is changed into a tournament selection strategy.
7. The optimized design method of the terahertz metamaterial sensor as claimed in claim 3, wherein when the crossover and mutation probabilities are improved, the adaptive crossover probability and the adaptive mutation probability are adopted, and the fitness serves as the basis for the self-adaptation of the crossover probability and the mutation probability, and the specific method comprises the following steps: when the individual fitness f' approaches the average fitness f avg The cross probability and the variation probability are moderate values; when the individual fitness f' approaches the minimum fitness f min In time, the cross probability and the mutation probability both take smaller values, and the cross probability and the mutation probability are reduced; when the individual fitness f' approaches the maximum fitness f max And in time, the cross probability and the mutation probability take larger values, and the cross probability and the mutation probability are increased.
8. The optimized design method of the terahertz metamaterial sensor as claimed in claim 7, wherein the adaptive cross probability value is as follows:
the adaptive mutation probability value is as follows:
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| CN117524372B (en) * | 2023-11-16 | 2024-05-17 | 浙江大学 | Micro-channel metamaterial design method based on genetic algorithm, electronic equipment and medium |
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