Modeling of multicomponent diffraction structures based on optimization approaches and numerical methods

The paper proposes a methodological approach in which the representation of objects in the form of a set of diffraction structures is their Association into groups. Using neural network modeling, expert evaluation and application of optimization based on genetic algorithm, there is a formation of the object with the desired scattering properties. An example of modeling an object presented as a set of two-dimensional cylinders is given.


Introduction
The problems of creating electrodynamic objects with specified scattering properties have long been considered by various researchers [1,2]. Objects have, as a rule, a complex form [3] and it is impossible to say that there are universal methods of calculation and optimization of scattering properties.
In this paper, it is proposed to provide the required scattering characteristics based on the representation of objects as groups of diffraction structures and the use of a combination of optimization approaches [4].

Objects of research
Objects having a complex shape are represented as a set of diffraction structures (DS) i D , (i=1,..,I) each of them characterized by a vector of indices of the scattering properties (the radar cross section (RCS))  i . In this case 1 ( ,..., ,..., ) DS are combined into groups (m=1,..,M) to provide the required scattering levels for the entire object. Objects are grouped into groups so that the scattering level in the ( 1) m  -th group is greater than in the m -th. We consider optimization models and numerical methods for creating optimal objects with respect to two components: structural and scattered field levels. The structure is improved by the transformation of i D (i=1,..,I) to another set , and the level of the scattered field due to the displacement DS of the groups are more integrated RCS in the group with less its value. Different approaches are used to estimate the integral RCS of estimation. For example, this model can be used: (2) It will correspond to the value of the lowest value of the scattered electromagnetic field on the DS i D .

Neural network modeling of DS group creation
In order to solve the problem of grouping DS characterized by RCS  i , we will consider two specific neural networks that belong to the ART family. In obtaining a set of groups that consist of DS having similar sets of performance indicators, we proposed a combination of such networks: ART-2A Network [5] and Furry ART Network [6]. If the prototype of the group satisfies the similarity condition, we train such a prototype by changing its weights so that it is more similar to the input vector. Normalize the initial vectors ( 1, ) i iI  . We apply the cosine function of the angle between the corresponding vectors, it is characterized by their scalar product here T k shows the value of the selection function for the k-th group, and M k -the value of the matching function, k wis the current prototype vector for the k-th group. If the prototype of the group satisfies the similarity condition, we train such a prototype by changing its weights so that it is more similar to the input vector: here  is a parameter showing the speed during training. For the grouping process to be switched to the Fuzzy ART network, it is necessary for the data to scale within [0,1]. The network is controlled by the parameters , , ,, here  and  are used by analogy with the ART-2a network, and  is an ultra-small number (its order is 10-6 ), which prevents the prototypes from completely degenerating. Selection function: .
We select the group when the condition M s >=, is fulfilled, where  -is an integral criterion for similarity. If the condition is violated, the group is marked as inactive and the selection function is called again. For the training function: the modification of the weights of the tested prototypes goes like this That is, when divided into groups, the space of input vectors will be covered with ndimensional parallelepipeds, as a prototype in each cluster there will be a parallelepiped that is closest to its center in the sense of Euclidean.

Expert-optimization modeling of partitioning into groups of DS
We suppose that based on the results of the evaluation, the DS was ranked relative to the integral RCS Y, which is normalized to the numerical interval where  m-1,m -is the proportionality coefficient, which is introduced by experts to separate the ( 1) m  -th and m -th groups, 0< m-1,m <1. In order to verify the normative separation of many diffraction structures into m groups, we propose to form an optimization model.
Suppose that when we divide by condition (7), the DS 1, 1 It is possible to solve problem (10) using a directed randomized search using probability estimates i x of variables (8): In the optimization model, the choice of DS with lower values of the integral RCS is based on optimization criteria, and the problem is solved by using directional randomized search using probabilistic estimates of variables.
The separation of objects between the ( 1) m  -th m -th groups does not coincide with the normative separation of experts from the managing center, and a compromise solution is required. To this end, it is proposed to use the mechanism of visual-figurative intuition of an expert [8].
In this case, a visual-figurative model of the set of objects  The coherence of the decision and assessment for objects, the expert characterizes the values of probabilities, Fig. 1. The scheme of scattering of electromagnetic waves on an object consisting of many DS.

Conclusion
A combined approach is proposed on the basis of which it is possible to optimize the scattering characteristics of objects of complex shape. The results of calculations during a test numerical experiment are presented.