Self-adaptive Dynamic Differential Evolution Research Articles

Electromagnetic Imaging for Buried Conductors Using Deep Convolutional Neural Networks

In the past, many conventional algorithms, such as self-adaptive dynamic differential evolution and asynchronous particle swarm optimization, were used to reconstruct buried objects in the frequency domain; these were unfortunately time-consuming during the iterative, repeated computing process of the scattered field. Consequently, we propose an innovative deep convolutional neural network approach to solve the electromagnetic inverse scattering problem for buried conductors in this paper. Different shapes of conductors are buried in one half-space and the electromagnetic wave from the other half-space is incident. The shape of the conductor can be reconstructed promptly by inputting the received scattered fields measured from the upper half-space into the deep convolutional neural network module, which avoids the computational complexity of Green’s function for training. Numerical results show that the root mean square error for differently shaped—circular, elliptical, arrow, peanut, four-petal, and three-petal—reconstructed images are, respectively, 2.95%, 3.11%, 17.81%, 15.10%, 14.14%, and 15.24%. Briefly speaking, not only can circular and elliptical buried conductors be reconstructed; some irregular shapes can be reconstructed well. On the contrary, the reconstruction result by U-Net for buried objects is worse since it is not able to obtain a good preliminary image by processing only the upper scattered field—that is, rather than the full space. In other words, our proposed deep convolutional neural network can efficiently solve the electromagnetic inverse scattering problem of buried conductors and provide a novel method for the microwave imaging of the buried conductors. This is the first successful attempt at using deep convolutional neural networks for buried conductors in the frequency domain, which may be useful for practical applications in various fields such as the medical, military, or industrial fields, including magnetic resonance imaging, mine detection and clearance, non-destructive testing, gas or wire pipeline detection, etc.

Optimization for an Indoor 6G Simultaneous Wireless Information and Power Transfer System

Antenna beamforming for Simultaneous Wireless Information and Power Transfer (SWIPT) and Wireless Power Transfer (WPT) in an indoor 6G communication system is presented in this paper. The objective function is to maximize the total harvesting power for the SWIPT and WPT nodes with the constraints of the bit error rate and minimum harvesting power. In the study, the power-splitting ratio between harvesting power and decoding information can be adjusted for the SWIPT node. Due to the non-convex problem, we use Self-Adaptive Dynamic Differential Evolution (SADDE) to optimize the designed multi-objective function. We use a symmetric antenna array to study three situations of distance—closer, farther, and similar—between the transmitting antenna and the individual SWIPT and WPT nodes in this paper. Experimental results show that the overall harvesting efficiency is improved, especially in the case of SWIPT nodes closer to the transmitter. The total harvesting power can be improved by 86.7% in the total short-distance case, and by 7.87% in the total long-distance case.

Optimization of Different Deployments and Resolution of Antenna Arrays in SWIPT

In this paper, three different deployment antenna arrays with circular, triangular and rectangular shapes were used to optimize the simultaneous wireless information and power transfer (SWIPT) system for the Internet of Things (IoT). Ray-tracing was employed to channel the model for a real environment. Self-adaptive dynamic differential evolution (SADDE) was used to optimize the harvesting power ratio with bit error rate constrained by the two different resolutions of feed length (high resolution and low resolution). Numerical results show that those three antenna arrays can achieve the goal for information quality in both resolutions. The harvesting power ratio for the circular array is the best and the harvesting power ratio for the rectangular array is the worst. The harvesting power ratio for the low-resolution case is 25% lower than the high-resolution case. However, the circular antenna array is the best deployment in those three different arrays for both high and low resolutions.

Inverse scattering of a periodic inhomogeneous dielectric scatterer

ABSTRACT This paper is to reconstruct the periodic inhomogeneous dielectric distribution of the scatterer buried in the rough surface. In order to explore the dielectric coefficient distribution of the unknown dielectric object under the rough surface, we emit electromagnetic wave to the object and measure the scattered electromagnetic wave above the rough surface. Base on Green's identity and the induced current concepts, the nonlinear integral equation can be derived and solved by the method of moments. Next, the inverse scattering problem is converted into an optimization problem. We use Self-Adaptive Dynamic Differential Evolution (SADDE) and Asynchronous Particle Swarm Optimization (APSO) to find the extreme value of the problem. With the regularization technique, the reconstruction is good. When the noise is less than 1%, the dielectric constant can also be achieved successfully. Numerical results show that SADDE can reduce the error for the permittivities of the object better than the APSO.

Multi-Objective Function for SWIPT System by SADDE

Simultaneous wireless information and power transfer (SWIPT) optimization with multiple objective function optimization is presented in the millimeter band in this paper. Three different objective functions that are used for harvest power (HP), capacity, and bit error rate (BER) were studied. There are three different nodes in real environment for wireless power transfer (WPT) and SWIPT. The channel estimation calculated by shooting and bouncing ray/image techniques includes multi-path, fading effect, and path-loss in the real environment. We applied beamforming techniques at the transmitter to focus the transmitter energy in order to reduce the multi-path effect and adjust the length of the feed line on each array element in order to find the extremum of the objective functions by the self-adaptive dynamic differential evolution (SADDE) method. Numerical results showed that SWIPT node cannot achieve good performance by single objective function, but wireless power transfer (WPT) can. Nevertheless, both WPT and SWIPT nodes can meet the criteria by the multiple objective function. The harvesting power ratio as well as the BER and capacity can be improved by the multiple objective function to an acceptable level by only reducing a little harvesting energy compared to the best harvesting energy for the single objective function. Finally, the multiple optimization function cannot merely provide good information quality for SWIPT node but achieve good total harvesting power for WPT and SWIPT node as well.

Microwave imaging of a periodic homogeneous dielectric object buried in rough surfaces

ABSTRACTThis paper presents the reconstruction of a periodic homogeneous dielectric object buried in rough surfaces. First, a TM (Transverse Magnetic) polarized wave is transmitted through the surface to a buried object. Integral equations are derived by using the Maxwell equation, the two-dimensional periodic Green function, Green identity and the boundary condition. The integral equations are solved numerically by the method of moment (MOM) to obtain the scattering field. The problem of inverse scattering is transformed into an optimization problem. Next, the Self-Adaptive Dynamic Differential Evolution (SADDE) method is used for object reconstruction. Numerical results show that the SADDE converges to the overall extreme value (global extreme) regardless of the initial guess. We have found that the convergence speed of the periodic length is always better than the shape function and dielectric constant. Moreover, we can still obtain good reconstruction results even if the noise is added in the scattered field.

Comparison of self‐adaptive dynamic differential evolution and particle swarm optimization for smart antennas in wireless communication

SummaryIn this paper, ultrawide band (UWB) communication systems with eight transmitting and receiving ring antenna arrays are implemented to test the bit error rate and capacity performance. By using the ray‐tracing technique to compute any given indoor wireless environment, the impulse response of the system can be calculated. The synthesized beamforming problem can be reformulated into a multiobjective optimization problem. Self‐adaptive dynamic differential evolution (SADDE) and particle swarm optimization (PSO) are used to find the excitation current and the feed line length of each antenna to form the appropriate beam pattern. This pattern can then reduce the bit error rate and increase the channel capacity and receiving energy. Numerical results show that the fitness value and the convergence speed by the SADDE are better than those by the PSO. Moreover, the SADDE had better results for both line‐of‐sight and nonline‐of‐sight cases. In other words, compared with PSO, SADDE has improved more effectively the main beam radiation energy and reduced the multipath interference.

Capacity optimization of multi-input/multi-output relay channel by SADDE algorithm

In this paper, we use self-adaptive dynamic differential evolution (SADDE) to search for multi-input/multi-output (MIMO) relay locations and transmitter locations to reduce the outage probability in the indoor ultra-wideband (UWB) environment. Amplify-and-forward (AF) MIMO relay is chosen to improve the performance of the environment. We use the shooting and bouncing ray/image (SBR/image) method to compute the frequency response, which is used to compute capacity. The channel capacities for the linear antenna with 1 × 1 antenna, 3 3 spaced linear antennas, and 3 × 3 tri-polarized antennas are compared. First, we deploy the relay and transmitter at the equipartition area. It is found that there are some outage receiving points. Thus, the SADDE is employed to optimize the position of the relay and transmitter in order to reduce the outage probability. Numerical results show that the outage probability for the relay and transmitter location is reduced by SADDE. Moreover, it is found that the channel capacity for the tri-polarized antennas has increased when comparing to 3 × 3 spaced linear antennas. For the zero outage probability requirement, the signal to noise for the tri-polarized antennas is lower 6 dB than that for 3 × 3 spaced linear antennas.

Optimal Location of the Access Points for MIMO-UWB Systems

A multiple-input and multiple-output ultra-wideband (MIMO-UWB) system provides a higher data rate. However, the multipath effect of the intersymbol interference (ISI) increases the bit error rate (BER) and outage probability of the MIMO-UWB system. For this paper, the authors applied the real orthogonal design (ROD) to an MIMO-UWB system to improve the efficiency of that system. A ray-tracing technique and an inverse fast Fourier transform were used to get the impulse response of the indoor environment. In addition, a rake receiver was used to increase the strength of the received signal to minimize the multipath effect. For this paper, two cases of an indoor wireless MIMO-UWB system were studied: case (A) used different antenna arrays, whereas case (B) placed antenna arrays in different locations to find the best position of the transmitter. In case (A), three different shapes of antenna arrays, namely L-shape, circular-shape, and Y-shape, were used for the transmitter and receiver. The BER performance for these arrays in the UWB frequency of 3.1–10.6 GHz was examined. Numerical results showed that the outage probability of the circular array was better than that of the other two arrays. In case (B), the transmitter used was an array with two antenna elements. The optimal location for the transmitter was found by using both asynchronous particle swarm optimization (APSO) and self-adaptive dynamic differential evolution (SADDE). The numerical results indicated that the performance of APSO was better than that of SADDE.

Microwave imaging of periodic rough surfaces

AbstractThis article presents the reconstruction of the periodic rough surface. By the Maxwell equations, the periodic Green functions and the boundary conditions, we can get the integral equations; then these equations can be converted into matrix form by the method of moment. We can reconstruct the relative permittivity and shape of periodic rough surfaces through the application of the integral equations and the measured scattered field. The inverse scattering problem is transformed into an optimization problem and solved by self‐adaptive dynamic differential evolution (SADDE) which can process a lot of unknowns for the electromagnetic imaging problems. The article tests the search ability and the resistance to noise for SADDE by different initial guesses for the periodic rough surface. By using the SADDE to reconstruct the periodic rough surface, numerical results show that the SADDE converges to the overall extreme value (global extreme) regardless of the initial guess. Even if the initial guess is far away from the actual value, SADDE can get the correct periodic length, the relative permittivity and shape of the periodic rough surface. Simulation results also show that good reconstruction can be obtained for the noise <1%.

Dielectric objects reconstruction by combining subspace-based algorithm and randomly global optimization algorithm

This paper discusses an inverse scattering problem for the reconstruction of permittivity distribution of two-dimensional dielectric objects. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equation is derived and the imaging problem is reformulated into optimization problem. We solved the problem by combining subspace-based algorithm and self-adaptive dynamic differential evolution (SADDE). SADDE can process numerous unknowns of electromagnetic imaging problems. Different scatterers and environment have used to verify the stability of subspace-based algorithm and SADDE. We also compare genetic algorithm (GA) to show the robustness and the searching speed of SADDE. Numerical results show that the permittivity distribution of the dielectric objects is well reconstructed by SADDE.

Microwave imaging for half-space imperfect conductors

This article presents an inverse scattering problem for recovering the shape and conductivity of an imperfect conductor buried in a half space by self-adaptive dynamic differential evolution (SADDE). The imperfect conductor of unknown conductivity and shapes is buried in one half-space and illuminated by the transverse magnetic plane wave from the other half-space. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equation is derived and the imaging problem is reformulated into optimisation problem. The SADDE algorithm is employed to find out the global extreme solution of the object function. Numerical results show that the conductivity and the shape of the conductor are well reconstructed. Moreover, the shape function is more sensitive to the scattered field variation than the conductivity. Accurate reconstruction of the shape function can be obtained by using the novel optimisation algorithm. As a result, the electric conductivity can be computed more accurately.

Comparison of particle swarm optimization and self-adaptive dynamic differential evolution for the imaging of a periodic conductor

The application of two techniques to reconstruct the shape of a two-dimensional periodic perfect conductor from mimic the measurement data is presented. A periodic conducting cylinder of unknown periodic length and shape scatters the incident wave in half-space and the scattered field is recorded outside. After an integral formulation, the microwave imaging is recast as a nonlinear optimization problem; a cost functional is defined by the norm of a difference between the measured scattered electric fields and the calculated scattered fields for an estimated shape of a conductor. Thus, the shape of conductor can be obtained by minimizing the cost function. In order to solve this inverse scattering problem, transverse magnetic (TM) waves are incident upon the objects and two techniques are employed to solve these problems. The first is based on an particle swarm optimization (PSO) and the second is a self-adaptive dynamic differential evolution (SADDE). Both techniques have been tested in the case of simulated mimic the measurement data contaminated by additive white Gaussian noise. Numerical results indicate that the SADDE algorithm is better than the PSO in reconstructed accuracy and convergence speed.

Comparative Study of Some Population-Based Optimization Algorithms on Inverse Scattering of a Two-Dimensional Perfectly Conducting Cylinder in Dielectric Slab Medium

The application of four techniques for the shape reconstruction of a 2-D metallic cylinder buried in dielectric slab medium by measured the scattered fields outside is studied in the paper. The finite-difference time-domain (FDTD) technique is employed for electromagnetic analyses for both the forward and inverse scattering problems, while the shape reconstruction problem is transformed into optimization one during the course of inverse scattering. Then, four techniques including asynchronous particle swarm optimization (APSO), PSO, dynamic differential evolution (DDE) and self-adaptive DDE (SADDE) are applied to reconstruct the location and shape of the 2-D metallic cylinder for comparative purposes. The statistical performances of these algorithms are compared. The results show that SADDE outperforms PSO, APSO and DDE in terms of the ability of exploring the optima. However, these results are considered to be indicative and do not generally apply to all optimization problems in electromagnetics.

Comparison of Dynamic Differential Evolution and Self-Adaptive Dynamic Differential Evolution for Buried Metallic Cylinder

The application of two techniques for the reconstruction of shape reconstruction of a metallic cylinder from scattered field measurements is studied in this paper. These techniques are applied to two-dimensional configurations, for which the method of moment (MoM) is applied to solve the integral equations. Considering that the microwave imaging is recast as a nonlinear optimization problem, an objective function is defined by the norm of the difference between the measured scattered electric fields and those calculated for each estimated metallic cylinder. Thus, the shape of a metallic cylinder can be obtained by minimizing the objective function. In order to solve this inverse scattering problem, two techniques are employed. The first one is based on dynamic differential evolution (DDE) algorithm, while the second one is an improved version of the DDE algorithm with self-adaptive control parameters, called SADDE. Both techniques are tested for the simulated data contaminated by additive white Gaussian noise. Numerical results indicate that SADDE algorithm outperforms DDE algorithm in terms of reconstruction accuracy and convergence speed.

Inverse scattering of dielectric cylindrical target using dynamic differential evolution and self-adaptive dynamic differential evolution

The inverse problem under consideration is to reconstruct the characteristic of scatterer from the scattering E field. Dynamic differential evolution (DDE) and self-adaptive dynamic differential evolution (SADDE) are stochastic-type optimization approach that aims to minimize a cost function between measurements and computer-simulated data. These algorithms are capable of retrieving the location, shape, and permittivity of the dielectric cylinder in a slab medium made of lossless materials. The finite-difference time-domain (FDTD) is employed for the analysis of the forward scattering. The comparison is carried out under the same conditions of initial population of candidate solutions and number of iterations. Numerical results indicate that SADDE outperforms the DDE a little in terms of reconstruction accuracy. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.