CN113807040A - Optimal design method for microwave circuit - Google Patents

Optimal design method for microwave circuit Download PDF

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CN113807040A
CN113807040A CN202111112523.1A CN202111112523A CN113807040A CN 113807040 A CN113807040 A CN 113807040A CN 202111112523 A CN202111112523 A CN 202111112523A CN 113807040 A CN113807040 A CN 113807040A
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陈远祥
胡聪
孙尚斌
付佳
林尚静
余建国
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Beijing University of Posts and Telecommunications
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Abstract

The invention discloses a microwave circuit-oriented optimization design method, which comprises the following steps: obtaining sample model design parameters by using an LHS (left-hand tool) and obtaining corresponding sample response by using a Matlab-HFSS (hybrid finite field system) joint simulation technology; calculating correlation coefficients of all sample responses and target responses, selecting a sample with the maximum correlation coefficient as an optimization sample, and using other samples as training samples; training the ELM by using a training sample, predicting design parameters for optimizing sample response, and optimizing the input weight and threshold of the ELM by adopting BSO (binary-base-output); and establishing a mapping relation between microwave circuit model design parameters and responses by using the ELM after optimizing the input weight and the threshold, training by using all training samples in the training process, and predicting the model design parameters corresponding to the target responses in the prediction process. The invention improves the training and predicting quality of the neural network, reduces the required training sample quantity and the time required by the optimal design of the microwave circuit, realizes the automation of the optimal design of the microwave circuit and improves the efficiency of the optimal design.

Description

Optimal design method for microwave circuit
Technical Field
The invention relates to the technical field of wireless communication, in particular to an optimal design method for a microwave circuit.
Background
With the rapid development of modern wireless communication technology, the requirement of a communication system on a microwave circuit is higher and higher, and in order to meet different requirements of the communication system, the microwave circuit needs to be continuously optimized and designed. In order to improve the design efficiency of microwave circuits and reduce the time cost of design, it has become a necessary trend to design them by using algorithms.
With the development of computers in recent years, the computing power of the computers is greatly improved, and an Artificial Neural Network (ANN) reenters the visual field of people, is concerned by more and more scholars, and is widely applied. An ANN is a mathematical model that models the actual neural network of the human brain, which can create a mapping between the inputs and outputs of the network, by choosing the appropriate algorithm, using an artificially given training sample, to find the weights and thresholds that minimize the error between the network output and the actual sample output at each iteration. After the neural network is trained, the input of a given network can be mapped to obtain the output of the network.
The most common microwave circuit optimization design methods at present are a space mapping algorithm, a group intelligence optimization algorithm and a machine learning algorithm.
The space mapping algorithm represents the microwave circuit by two models, one is a fine model with low simulation speed but accurate simulation result; the other is a coarse model with high simulation speed but the simulation result is not accurate enough. Firstly, optimizing in a coarse model to obtain ideal coarse model parameters, then obtaining fine model parameters through a mapping relation, and finally substituting the fine model parameters into a fine model for verification. By utilizing the space mapping algorithm, the complicated and time-consuming optimization work can be carried out in the coarse model, and the fine model only carries out simple verification work, so that the complex fine model is prevented from being directly optimized, and the optimization time is shortened. However, most of the fine models of microwave circuits cannot be represented by the coarse models, and therefore, there is a certain limitation in performing the optimal design by using the spatial mapping algorithm.
The swarm intelligence optimization algorithm generally searches a local optimal solution of a problem by using a specific algorithm, then determines a global optimal solution through multiple iterations, and generally adopts a variation idea to increase the diversity of the algorithm in the optimization process, so that the algorithm can accurately search the global optimal solution while ensuring the convergence. In the actual optimization design process of the algorithm, a large number of candidate solutions need to be provided, full-wave electromagnetic simulation is carried out for a large number of times, and the fitness value of the full-wave electromagnetic simulation is calculated, so that the time cost required by the algorithm is high, and the randomness is high.
In machine learning algorithms, ANN is one of the most common methods for establishing mapping relationships, and mainly includes two processes. In the training process, a mapping relation between microwave circuit model design parameters and responses thereof can be established by using a certain number of samples; in the prediction process, the target response is used as input, and ideal model design parameters can be obtained through network output.
However, when the traditional ANN method is used for optimization design, a gradient descent method needs to be used for a large number of iterations to optimize network parameters, and the problems of poor learning capability, slow training speed, low prediction accuracy and the like generally exist, so that the time complexity is high in practical application, and a large amount of time and labor cost are wasted.
Disclosure of Invention
Aiming at the technical problems, the invention provides a novel and general optimal design method for a microwave circuit, and model design parameters of target response are obtained with lower time and labor cost.
In order to achieve the above purpose, the invention provides the following technical scheme:
an optimal design method for a microwave circuit comprises the following steps:
s1, designing an ideal target response according to the design index;
s2, obtaining a certain number of sample model design parameters by Latin Hypercube Sampling (LHS), and obtaining corresponding sample response by using a Matlab-HFSS joint simulation technology;
s3, calculating correlation coefficients of all sample responses and target responses, selecting the response with the maximum correlation coefficient and design parameters thereof as an optimization sample, and using other responses and design parameters as training samples;
s4, training an Extreme Learning Machine (ELM) by using training samples, predicting design parameters of optimized sample response, and optimizing input weights and thresholds of the ELM by adopting a Brain Storm Optimization Algorithm (BSO);
s5, establishing a mapping relation between microwave circuit model design parameters and responses by using the ELM after optimizing the input weight and the threshold value, training by using all training samples including the optimized samples in the training process, and predicting the model design parameters corresponding to the target responses in the prediction process;
and S6, substituting the predicted design parameters into the microwave circuit for simulation verification, if the response does not meet the design index, adding the design parameters and the response into the original training sample set, and turning to the step S3 until the response and the design parameters meeting the design index are obtained.
Further, the ELM network structure comprises an input layer, a hidden layer and an output layer, wherein the input layer, the hidden layer and the output layer are all provided with a plurality of neurons.
Further, the training process of the ELM in step S4 is:
provided with N arbitrary training samples (X)i,Yi) Wherein X is inputtediIs n-dimension, i.e. Xi＝[xi1,xi2,…,xin]TOutput YiIs m dimension, i.e. Yi＝[yi1,yi2,…,yim]TThe output of the extreme learning machine with the hidden layer of L neurons is expressed as:
Figure BDA0003274367740000031
wherein g (x) is an activation function, Wj＝[wj1,wj2,…,wjn]TTo input the weight, θjThreshold for the jth neuron of the hidden layer, βj＝[βj1,βj2,…,βjm]TFor output weights, "·" denotes inner products;
the goal of the net learning is to minimize the output error of the net from the sample, expressed as:
Figure BDA0003274367740000032
i.e. existence of Wj、θjAnd betajSo that
Figure BDA0003274367740000033
The above equation is represented by a matrix:
Hβ＝Y (4)
where H is the output of the hidden layer neurons, β is the output weight, Y is the sample output, and
Figure BDA0003274367740000034
Figure BDA0003274367740000035
Figure BDA0003274367740000041
by inputting X through a given network, obtaining
Figure BDA0003274367740000042
And
Figure BDA0003274367740000043
so that
Figure BDA0003274367740000044
Equivalent to the minimization loss function:
Figure BDA0003274367740000045
further, if the weight W is inputtedjAnd a threshold value thetajRandomly or artificially set, the output weight β is calculated by the following formula:
β＝H+Y (10)
wherein H+Is the generalized inverse of matrix H.
Further, the prediction process of the ELM in step S4 is: given an input weight ω, a threshold value θ and an output weight β, a prediction sample input X is given, and a prediction sample output Y is obtained according to equations (4) to (7).
Further, in step S4, the parameter optimization process is performed by using a BSO algorithm based on a reverse learning initialization strategy, where the reverse learning process is as follows: and randomly generating an initial population, generating a reverse population according to the initial population, calculating the fitness values of the initial population and the reverse population, and finally selecting the optimal solution of the fitness values in all the populations as a final initial population.
Further, the process of optimizing the input weight and the threshold of the ELM by using the BSO in step S4 includes: calculating correlation coefficients of all sample responses and target responses, selecting the sample response with the maximum correlation coefficient with the target response and design parameters thereof as an optimization sample, and using other responses and design parameters thereof as training samples; and training the ELM by using the training sample, and obtaining the input weight and the threshold value of the extreme learning machine which minimizes the fitness function through BSO optimization.
Further, the optimization objective of BSO is:
min e (11)
where e is a fitness function, the expression is as follows:
Figure BDA0003274367740000046
wherein
Figure BDA0003274367740000047
Design parameters, X, for optimized samples predicted by extreme learning machinesOptimizing samplesThe design parameters of the sample are optimized for what is actually known.
The BSO optimization variables are the input weight omega and the threshold value theta of the ELM, namely the values of omega and theta when the optimization target is met.
Compared with the prior art, the invention has the beneficial effects that:
compared with the traditional optimization design method, the optimization design method for the microwave circuit can realize automatic operation of all processes, effectively reduce the time and labor cost of optimization design and improve the efficiency of optimization design; compared with a space mapping method, the method is more universal; compared with the group intelligent optimization algorithm, the method does not need to perform full-wave electromagnetic simulation for a large number of times, so that the required time cost is reduced; compared with a general machine learning method, the method adopts BSO to optimize ELM network parameters, so that the ELM learning capability is stronger and the prediction precision is higher.
In conclusion, the optimal design method for the microwave circuit is inspired from the ANN, selects the appropriate neural network, and optimizes the network parameters by matching with a certain algorithm, so that the training and predicting quality of the neural network can be improved, the required training sample number is reduced, and the time cost required by the optimal design of the microwave circuit is reduced; meanwhile, the automatic operation of the microwave circuit optimization design process is realized by utilizing an algorithm and a joint simulation technology, the practical problem is solved, and the optimization design efficiency is improved.
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In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
Fig. 1 is a flowchart of an optimal design method for a microwave circuit according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of an ELM network structure according to an embodiment of the present invention.
Fig. 3 is a flowchart of reverse learning according to an embodiment of the present invention.
Fig. 4 is a flowchart of input weights and thresholds of BSO-optimized ELM according to an embodiment of the present invention.
Detailed Description
For a better understanding of the present solution, the method of the present invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides an optimized design method for microwave circuits, which includes the following steps:
(1) designing an ideal target response according to the design index;
(2) obtaining a certain number of sample model design parameters by using LHS, and obtaining corresponding sample response by using Matlab-HFSS joint simulation technology;
(3) calculating correlation coefficients of all sample responses and target responses, selecting the response with the maximum correlation coefficient and design parameters thereof as an optimization sample, and using other responses and design parameters as training samples;
(4) training the ELM by using a training sample, predicting design parameters for optimizing sample response, and optimizing the input weight and threshold of the ELM by adopting BSO (binary-base-output);
(5) establishing a mapping relation between microwave circuit model design parameters and responses by using the ELM after optimizing the input weight and the threshold, training by using all training samples including the optimized samples in the training process, and predicting model design parameters corresponding to target responses in the prediction process;
(6) and (3) substituting the predicted design parameters into the microwave circuit for simulation verification, if the response does not meet the design index, adding the design parameters and the response into the original training sample set, and turning to the step (3) until the response and the design parameters meeting the design index are obtained.
The technical scheme of the invention is based on an Extreme Learning Machine (ELM), and adopts a brain storm optimization algorithm (BSO) to improve the ELM, and simultaneously adopts Latin Hypercube Sampling (LHS) and a joint simulation technology to obtain training samples. The method mainly comprises three parts of obtaining training samples, training prediction and optimizing network parameters.
1. Obtaining a training sample portion
The obtaining the training sample portion includes obtaining model design parameters for the training sample and obtaining a response for the training sample.
And the model design parameter part for obtaining the training sample is realized by adopting LHS. LHS is a layered sampling technology, high sampling precision can be obtained with few sampling times, model design parameters obtained through the LHS are mutually independent and are uniformly generated in all intervals, and the quality of training samples can be effectively improved.
The response part for acquiring the training sample is realized by Matlab-HFSS joint simulation, and HFSS modeling, design parameter modification, response output, operation and other instructions are written in the script by utilizing Matlab software and an HFSS-Matlab-Api library function, so that the simulation by utilizing the Matlab software to control the HFSS electromagnetic simulation software can be realized. Matlab-HFSS joint simulation has very obvious advantages for establishing a complex structure model and repeatedly modifying specified design parameters, and by calling HFSS electromagnetic simulation software for simulation, the optimized design of a microwave circuit can be automatically completed in Matlab without bringing the design parameters into the HFSS software one by one, so that the labor cost is saved.
2. Training prediction component
The training prediction part is realized by adopting ELM, the ELM is a neural network based on forward propagation, compared with the traditional algorithm, the learning speed is higher and the generalization capability is stronger while the precision is ensured, and the network structure is shown in figure 2. Wherein ω isijInput weights, θ, for the ith neuron of the input layer to the jth neuron of the hidden layerLThreshold for the L-th neuron of the hidden layer, βjkThe output weight of the jth neuron of the hidden layer to the kth neuron of the output layer.
In actual work, the extreme learning machine can be divided into two processes of training and predicting:
(1) training process: the known extreme learning machine trains the input and the output of the sample, and the mapping relation between the input and the output is solved.
Provided with N arbitrary training samples (X)i,Yi) Wherein X is inputtediIs n-dimension, i.e. Xi＝[xi1,xi2,…,xin]TOutput YiIs m dimension, i.e. Yi＝[yi1,yi2,…,yim]TThe output of the extreme learning machine with the hidden layer of L neurons can be expressed as:
Figure BDA0003274367740000071
wherein g (x) is an activation function, Wj＝[wj1,wj2,…,wjn]TTo input the weight, θjThreshold for the jth neuron of the hidden layer, βj＝[βj1,βj2,…,βjm]TFor the output weights, "·" denotes the inner product.
The goal of the net learning is to minimize the output error of the net from the sample, expressed as:
Figure BDA0003274367740000072
i.e. existence of Wj、θjAnd betajSo that
Figure BDA0003274367740000073
The above equation is represented by a matrix:
Hβ＝Y (4)
where H is the output of the hidden layer neurons, β is the output weight, Y is the sample output, and
Figure BDA0003274367740000081
Figure BDA0003274367740000082
Figure BDA0003274367740000083
by inputting X through a given network, it is desired to obtain
Figure BDA0003274367740000084
And
Figure BDA0003274367740000085
so that
Figure BDA0003274367740000086
Equivalent to the minimization loss function:
Figure BDA0003274367740000087
the traditional learning algorithm adopts a gradient descent method to solve, but the gradient descent method needs to be adopted for multiple iterations, all parameters need to be adjusted in the iteration process, and the process is complex and time-consuming.In the extreme learning machine, if the weight W is inputtedjAnd a threshold value thetajRandomly or artificially set, the matrix H in equation (4) is uniquely determined, and the output weight β can be calculated by:
β＝H+Y (10)
wherein H+Is the generalized inverse of matrix H.
(2) And (3) prediction process: the output of the extreme learning machine is obtained by knowing the input of the extreme learning machine and the mapping relation between the input and the output.
In the prediction process, the mapping relation between the input and the output of the training sample is known, namely the input weight omega, the threshold value theta and the output weight beta of the extreme learning machine are known, and the predicted sample output Y can be obtained according to the equations (4) to (7) given the predicted sample input X.
The ELM is characterized in that the input weight from the input layer to the hidden layer and the threshold value of the hidden layer unit are set randomly or manually, updating is not needed, and meanwhile, the output weight from the hidden layer to the output layer is determined once by solving an equation set.
The ELM has the advantages of simple network structure, high convergence rate, strong generalization capability and the like, and is very suitable for solving the problem of optimal design of a microwave circuit.
3. Optimizing network parameter parts
The network parameters in the ELM mainly comprise an input weight omega, a threshold value theta and an output weight beta, and because beta is calculated according to omega and theta which are randomly or artificially set, the selection of omega and theta is very important. To improve the quality of the network, the part optimizes ω and θ with BSO.
BSO was proposed based on human elicitations at group decision time for brainstorming meetings. Firstly, initializing a certain number of ideas by adopting a random strategy, and enabling all the ideas to be uniformly distributed in a search space as much as possible; then, according to the similarity, dividing all ideas into a certain number of classes by using a K-means clustering method; secondly, calculating all thought fitness values according to a given fitness function, and selecting the idea with the optimal fitness value in each class, wherein the fitness value represents the goodness and badness of the idea; and finally, selecting the overall optimal idea through iteration.
The pure random strategy is adopted in the population initialization process of the original BSO algorithm, so that the quality of the final optimization result and the convergence rate of the population are poor. The scheme of the invention adopts an initialization strategy of reverse learning to improve the BSO algorithm, firstly, a reverse population of an initial population is searched, and finally, an optimal solution is selected to carry out a subsequent iterative optimization process through competition between a current population and the reverse population, wherein a reverse learning flow chart is shown in figure 3.
The BSO can search a global optimal solution while ensuring convergence, is very suitable for solving the optimization problem of a multimodal high-dimensional function, and is very suitable for optimizing ELM multidimensional network parameters.
A flow chart for BSO optimizing the extreme learning machine input weights and thresholds is shown in fig. 4 below. Firstly, designing an ideal target response according to design indexes; then calculating the correlation coefficient between the response of all training samples and the response of an ideal target, and selecting the training sample with the maximum correlation coefficient as an optimization sample; secondly, training the ELM by using other training samples, and predicting model design parameters corresponding to the response of the optimized samples; and finally, obtaining the input weight and the threshold value of the extreme learning machine which enables the fitness function to be minimum by utilizing a brain storm optimization algorithm.
The optimization target of the brain storm algorithm is as follows:
min e (11)
where e is a fitness function, the expression is as follows:
Figure BDA0003274367740000091
wherein
Figure BDA0003274367740000092
Design parameters, X, for optimized samples predicted by extreme learning machinesOptimizing samplesThe design parameters of the sample are optimized for what is actually known.
In summary, the invention provides an optimal design method for a microwave circuit, and the key points are as follows:
1) obtaining a specified number of model design parameters by using the LHS as training samples so as to uniformly distribute the samples in the space and improve the quality of the samples;
2) utilizing Matlab-HFSS joint simulation to obtain the response of the design parameters so as to realize full-process automatic operation;
3) improving a BSO algorithm by utilizing a population initialization strategy of reverse learning so as to improve the optimization capability of BSO;
4) the input weight and threshold of the ELM are optimized by improving the ELM by using the BSO, so that the learning ability, accuracy and precision of the ELM are improved.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, but such modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. An optimal design method for a microwave circuit is characterized by comprising the following steps:
s1, designing an ideal target response according to the design index;
s2, obtaining a certain number of sample model design parameters by using LHS, and obtaining corresponding sample response by using Matlab-HFSS joint simulation technology;
s3, calculating correlation coefficients of all sample responses and target responses, selecting the response with the maximum correlation coefficient and design parameters thereof as an optimization sample, and using other responses and design parameters as training samples;
s4, training the ELM by using the training samples, predicting design parameters for optimizing sample response, and optimizing input weight and threshold of the ELM by adopting BSO;
s5, establishing a mapping relation between microwave circuit model design parameters and responses by using the ELM after optimizing the input weight and the threshold value, training by using all training samples including the optimized samples in the training process, and predicting the model design parameters corresponding to the target responses in the prediction process;
and S6, substituting the predicted design parameters into the microwave circuit for simulation verification, if the response does not meet the design index, adding the design parameters and the response into the original training sample set, and turning to the step S3 until the response and the design parameters meeting the design index are obtained.
2. The microwave-circuit-oriented optimization design method according to claim 1, wherein the ELM network structure comprises an input layer, a hidden layer and an output layer, and the input layer, the hidden layer and the output layer are all provided with a plurality of neurons.
3. The optimal design method for microwave circuits according to claim 1, wherein the ELM training process in step S4 is as follows:
provided with N arbitrary training samples (X)i,Yi) Wherein X is inputtediIs n-dimension, i.e. Xi＝[xi1,xi2,…,xin]TOutput YiIs m dimension, i.e. Yi＝[yi1,yi2,…,yim]TThe output of the extreme learning machine with the hidden layer of L neurons is expressed as:
Figure FDA0003274367730000011
wherein g (x) is an activation function, Wj＝[wj1,wj2,…,wjn]TTo input the weight, θjThreshold for the jth neuron of the hidden layer, βj＝[βj1,βj2,…,βjm]TFor output weights, "·" denotes inner products;
the goal of the net learning is to minimize the output error of the net from the sample, expressed as:
Figure FDA0003274367730000012
i.e. existence of Wj、θjAnd betajSo that
Figure FDA0003274367730000021
The above equation is represented by a matrix:
Hβ＝Y (4)
where H is the output of the hidden layer neurons, β is the output weight, Y is the sample output, and
Figure FDA0003274367730000022
Figure FDA0003274367730000023
Figure FDA0003274367730000024
by inputting X through a given network, obtaining
Figure FDA0003274367730000025
And
Figure FDA0003274367730000026
so that
Figure FDA0003274367730000027
Equivalent to the minimization loss function:
Figure FDA0003274367730000028
4. a microwave circuit-oriented optimization design method according to claim 3, characterized in that if the weight W is inputjAnd a threshold value thetajRandomly or artificially set, the output weight β is calculated by the following formula:
β＝H+Y (10)
wherein H+Is the generalized inverse of matrix H.
5. The microwave circuit-oriented optimization design method of claim 3, wherein the ELM prediction process in step S4 is as follows: given an input weight ω, a threshold value θ and an output weight β, a prediction sample input X is given, and a prediction sample output Y is obtained according to equations (4) to (7).
6. The microwave circuit-oriented optimization design method of claim 1, wherein the parameter optimization process in step S4 is performed by using a BSO algorithm based on a reverse learning initialization strategy, and the reverse learning process is as follows: and randomly generating an initial population, generating a reverse population according to the initial population, calculating the fitness values of the initial population and the reverse population, and finally selecting the optimal solution of the fitness values in all the populations as a final initial population.
7. The microwave circuit-oriented optimization design method of claim 1, wherein the procedure of optimizing the input weight and the threshold of the ELM by using the BSO in the step S4 is as follows: calculating correlation coefficients of all sample responses and target responses, selecting the sample response with the maximum correlation coefficient with the target response and design parameters thereof as an optimization sample, and using other responses and design parameters thereof as training samples; and training the ELM by using the training sample, and obtaining the input weight and the threshold value of the extreme learning machine which minimizes the fitness function through BSO optimization.
8. A microwave circuit-oriented optimization design method as claimed in claim 7, characterized in that the optimization goal of BSO is:
min e (11)
where e is a fitness function, the expression is as follows:
Figure FDA0003274367730000031
wherein
Figure FDA0003274367730000032
Design parameters, X, for optimized samples predicted by extreme learning machinesOptimizing samplesThe design parameters of the sample are optimized for what is actually known.
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