Study on stealth characteristics of metamaterials based on simulated annealing algorithm

ScienceDirect ProcediaScienceDirect Computer Science 00 (2019) 000–000

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Procedia Computer Science 147 (2019) 221–227

2018 International Conference on Identification, Information and Knowledge in the Internet of Things, IIKI 2018 2018 International Conference on Identification, Information and Knowledge in the Internet of Things, IIKI 2018

Study on stealth characteristics of metamaterials based on simulated annealing algorithm Study on stealth characteristics of metamaterials based on simulated 1

1

1 1 annealing algorithm Feiliang Liu *, Yan Wang , Yang Bai 1, Jie Yu 1

Science and Technology on Electromagnetic Scattering Laboratory，Box No. 207,P.O. Box142,Beijing, 100854，P.R. China

Feiliang Liu 1*, Yan Wang1, Yang Bai 1, Jie Yu 1

Science and Technology on Electromagnetic Scattering Laboratory，Box No. 207,P.O. Box142,Beijing, 100854，P.R. China

Abstract

Auxiliary differential equation finite-difference time domain (ADE-FDTD) expressions of drude dispersive Abstract medium model are applied to simulate stealth characteristics of metamaterials coating. Then, simulated annealing Auxiliary differential equation finite-difference time domain (ADE-FDTD) expressions ofcoating, drude dispersive algorithm is used to optimize electromagnetic parameters considered include metamaterials collision simulatedcovering annealing medium appliedand to coating simulatethickness. stealth characteristics of that metamaterials Then,cylinder frequencymodel drude are frequency The results show monostatic coating. RCS of metal algorithm is used to optimize electromagnetic includecovering metamaterials coating, collision with metamaterial coating can reduce 6.3dB and parameters bistatic RCSconsidered of metal cylinder with metamaterial coating frequency frequency andbefore. coating Simulated thickness. The results algorithm show that monostatic RCS of metal cylinder can shrinkdrude 0.1dB less than annealing can play an important effect oncovering stealth with metamaterial coating can reduce 6.3dB and bistatic RCS of metal cylinder covering with metamaterial coating characteristics of metamaterials. can shrink 0.1dB less than before. Simulated annealing algorithm can play an important effect on stealth characteristics of metamaterials.

© 2019 The Author(s). Published by Elsevier B.V. © 2019 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility ofElsevier the scientific © 2019 The Author(s). Published by B.V. committee of the 2018 International Conference on Identification, Peer-review under responsibility of the scientific committee of the 2018 International Conference on Identification, Information and Information Knowledge in the of Things This is an open access article under theInternet CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Knowledge in and the Internet of Things. Peer-review under responsibility of the scientific committee of the 2018 International Conference on Identification, Keywords: metamaterials; stealth characteristics; simulated annealing algorithm Information and Knowledge in the Internet of Things Keywords: metamaterials; stealth characteristics; simulated annealing algorithm

1. Introduction

1. Introduction In recent years, due to the good global searching ability and high convergence speed of intelligence algorithm, it is widely used in engineering. The so-called intelligence optimization algorithm is a process of continuously In recent years, due to the good global searching ability and high convergence speed of intelligence algorithm, it is widely used in engineering. The so-called intelligence optimization algorithm is a process of continuously * Corresponding author. Tel.: 010-88526923; fax: 010-88527207. E-mail address: [email protected] * Corresponding author. Tel.: 010-88526923; fax: 010-88527207. 1877-0509 © 2019 The Author(s). Published by Elsevier B.V. E-mail address: [email protected] This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review of Published the scientific committee of the 2018 International Conference on Identification, Information and 1877-0509 ©under 2019 responsibility The Author(s). by Elsevier B.V. Knowledge in theaccess Internet of Things This is an open article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 2018 International Conference on Identification, Information and Knowledge in the Internet of Things

1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 2018 International Conference on Identification, Information and Knowledge in the Internet of Things. 10.1016/j.procs.2019.01.230

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Feiliang Liu et al. / Procedia Computer Science 147 (2019) 221–227 Feiliang Liu / Procedia Computer Science 00 (2019) 000–000

searching for global optimal solution, according to some certain rules or ideas in a given area to obtain a solution of the problem. In this paper, ADE-FDTD method is applied to simulate the electromagnetic scattering characteristics of metamaterials, but the stealth characteristics of metamaterials are directly related to Drude frequency, collision frequency and coating thickness of metamaterials coatings. In fact, we usually need an optimal solution to cover the target with metamaterials. And considering that simulated annealing optimization algorithm is quietly differently from the traditional random search strategy, and the above algorithm features are easy to program, so this paper will use simulated annealing algorithm optimize the design of metal cylinder covered with metamaterial coating. 2. Simulated annealing algorithm According to Metropolis criterion, the solid annealing process can be used to simulate the combinatorial optimization problem. In the combinatorial optimization problem, assuming that one solution i of it corresponds to a microscopic state i in the solid annealing process, also the objective function f (i) of it corresponds to energy

E(i) of above i and let the evolution of temperature T during the solid annealing process be a control parameter t of cooling schedule, thus, the simulated annealing algorithm for solving the combinatorial optimization problem is started by the initial solution i and control initial value t, let current solution repeat following iterative process: “generating a new solution calculating the difference of objective function –accepting | discarding”, which corresponds to a process tending to thermal equilibrium of the solid in the some temperature and makes the value of control parameter t gradually attenuate. The current solution at the end of this algorithm is approximation of the optimal solution. Figure 1 is the flow chart of entire simulated annealing algorithm.



Feiliang Liu et al. / Procedia Computer Science 147 (2019) 221–227 Feiliang Liu/ Procedia Computer Science 00 (2019) 000–000

start annealing

、 initial temperature cooling process iterations

initial value

select a feasible solution for the current solution

calulate the error of evalution function

E

E  0

223 3

YES

a new solution replace with the current solution

NO

exp(E/ k )  random (0....1) NO

calculate the new temperature

YES

has the cooling time been reached?

NO has the termination conditions been met?

YES End

Fig.1. The flow chart of entire simulated annealing algorithm

3. Simulation optimization of metamaterial coating

Let the Drude in the dispersive medium be a model, the dielectric constant and magnetic permeability of metamaterials can be expressed as:

（）=（ 0  -

 2pe ）  (  je )

 2pm （）=（  ）  0  (  j m )

（1）

Where  0，0 are respectively dielectric constant and magnetic permeability in vacuum,  ， are respectively infinite frequency relative dielectric constant and relative magnetic permeability,  pe ,  pm are Drude

Feiliang et al. / Computer Procedia Computer (2019) 221–227 Feiliang Liu /Liu Procedia Science 00Science (2019) 147 000–000

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  1,  1 。 frequencies, e，m are collision frequencies. if   e ,   m ， Substituting the lossless time-harmonic field Maxwell rotation equation, we get ADE-FDTD equation: p



0   1  1 n n 2 En    H  2  (k p  1) J p   t E   2  0   p   0   p    t t 2 2

1

n+1

H

n+

1 2



（2）



m 1  0  n- 1  n  1 n  2 2    E   (km  1) J m     t H 2 0   m  2 0      m 2 2 t t

1

(3)

where，

 kp

t 0 2p t 0m2 2  t 2  t 。   ,p  , km , m 2  t 2  t 2  t 2  t

In the simulation calculation, metal cylinder radius R1  0.2m , metamaterial coating thickness d  0.1m , the frequency is taken as   100GHz ,  pe   pm  0.1GHz , namely, the refractive index of metamaterials is pe pm

n(0 )  6.0361  0.0187i , TM wave is incident from below the cylinder, E z value distribution is obtained through 500 time steps iterations. 2 1.5

200

1 400 0.5 600

Ez

metamaterial coating thickness

0 -0.5

800

-1 1000 -1.5 1200 200

400

600

800

1000

1200

-2

grid number of FDTD Fig.2. The

Ez

of metal cylinder covering with metamaterial coating

It can be seen from Fig 2 that plane wave exhibits the characteristics of the backward wave, when spreading to the metamaterial coating. As time goes by, plane wave does not have much backscatter, when it encounters the target, but keeps the trend of moving forward. In order to further analyze stealth characteristics of metal cylinder, the program is further subjected to far-field extrapolation, and bistatic RCS results are compared with the bistatic RCS of the same electric-size metal cylinder. The result is shown in Fig 3.



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Fig.3 . The RCS of metal cylinder covering with metamaterial coating and metal cylinder

It can be seen from Fig3, the RCS value of metal cylinder covered with matamaterial coating is significantly reduced over a large double station angle. However, there is a slight increase in RCS when bistatic angle around 180°. When the bistatic angle is 46°，316°, the maximum reduction is 23.1dB, when the angle is 180°, the RCS is increase 4.0dB. According to above simulation analysis, ADE-FDTD can be used to determine the steath characteristics of metamaterail coating under different thickness, Drude frequency and collision frequency. But how to combine and optimize target’s monostatic RCS and bistatic RCS through using formed three-bit space by the given thickness, Drude frequency and collision frequency. In this section, the solution space selected is a three-dimensional space consisting of a metamaterial thickness of 0.2m ~ 0.5m , a collision frequency of 0.01e9 ~ 0.5e9 and Drude frequency of 40e9 ~ 200e9 . The objective selects the target monostatic RCS and bistatic RCS mean value respectively as the opitimization object, the initial temperature is 1000, the starting coordinate is X (1)  [0.2,100e9,0.1e9] , the step size is Step  [0.01,5e9,0.01e9] ,the temperature control parameter cooling strategy is selected as Tk   Tk 1 ,   0.8 . After several iterations, the point obtained of optimal monostatic RCS is X  [0.2093,88.503e9,0.11668e9] and its simulation result is shown in Fig 4.

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Fig.4 . The optimal solution of monostatic RCS

The optimal solution of monostatic mean RCS calculated is X  [0.2342,84.312e9,0.11738e9] , its bistatic RCS is shown as following figure 5.

Fig.5. the optimal solution of bistatic RCS

Due to be the simulation results of Fig 5 and Fig 6, monostatic mean RCS is reduced by 6.3dB, bistatic mean RCS is reduced by 0.1dB through optimaization of simulated annealing.

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4. Conclusions Following conclusions are reached by simulation and optimization. 1)

It is reasonable for analysis of steath characteristics of metamaterials coating based on ADE-FDTD.

2)

From the results of simulation, it can be seen that monostatic mean RCS is reduced by 6.3dB, bistatic mean RCS is reduced by 0.1dB through optimaization of simulated annealing.

3)

From the results of simulate and optimization, it shows that the optimal solution can be obtained in a given space as long as the given initial temperature is large enough and the number of iterations at each temperature is large enough. However, there are some insufficiencies in the simulated annealing algorithm. It takes more time to obtain a high-quality approximate solution. If the cooling process is too fast, it is likely that the global optimization will not be got.

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