A 3D finite element analysis of large‐scale nonlinear dynamic electromagnetic problems by harmonic balancing and domain decomposition

The dual–primal finite element tearing and interconnecting (FETI‐DP) method is applied together with the harmonic balance method and the fixed‐point (FP) method to improve the efficiency of three‐dimensional finite element analysis of large‐scale nonlinear dynamic electromagnetic problems. The FETI‐DP method decomposes the original problem into smaller subdomains problems. Combined with parallel computing techniques, the total computation time can be reduced significantly. To account for nonlinear B‐H characteristics, the FP method is applied together with the polarization formulation. Because the FP method assumes a constant reluctivity, it decouples the systems of different harmonics. The FETI‐DP method can then be applied to speed up the simulation of each harmonic in each FP iteration. Two benchmark problems and a three‐phase inductor are simulated by the proposed method to validate the formulation and demonstrate its performance. Copyright © 2015 John Wiley & Sons, Ltd.     

A dual‐primal finite‐element tearing and interconnecting method combined with tree‐cotree splitting for modeling electromechanical devices

The dual‐primal finite‐element tearing and interconnecting (FETI‐DP) method is combined with the tree‐cotree splitting (TCS) method to expand the capability and improve the efficiency of the finite‐element analysis of electromechanical devices. With the FETI‐DP method, an original large‐scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. The TCS method is adopted to deal with the low‐frequency breakdown problem, which often accompanies the finite‐element analysis of electromechanical problems. On the basis of the computed magnetic field values, the force is computed with the use of the Maxwell stress tensor method. The proposed technique is applied to solve both high‐contrast magnetostatic problems and eddy‐current problems. Results are compared with both measurement data and brute‐force finite‐element calculations without domain decomposition. Comprehensive tests are conducted to investigate the parallel efficiency and numerical scalability. The results show that the proposed method can achieve a good parallel efficiency and an excellent numerical scalability with respect to the number of subdomains and the size of the problem. Copyright © 2012 John Wiley & Sons, Ltd.     

A non‐conformal FETI‐like domain decomposition approach of FE‐BI‐MLFMA for 3‐D electromagnetic scattering/radiation problems

A non‐conformal finite element tearing and interconnecting‐like (FETI‐like) domain decomposition approach (DDA) of the hybrid finite element–boundary integral–multilevel fast multipole algorithm (FE‐BI‐MLFMA) is presented by integrating a series efficient techniques for computing electromagnetic scattering/radiation problems. The Robin transmission condition is employed to cement the non‐conformal meshes on the interconnected surfaces between the interior and exterior regions and between sub‐domains in the interior region. The FETI‐like technique is applied to reduce the FE‐BI matrix equation. Furthermore, a preconditioner is constructed to accelerate the convergent speed of this non‐conformal FETI‐like DDA. The numerical performance of the presented non‐conformal FETI‐like DDA‐FE‐BI‐MLFMA is studied for scattering/radiation problems. Copyright © 2015 John Wiley & Sons, Ltd.     

改进量子进化混合优化算法在溪洛渡电站机组组合中的应用研究

传统方法求解水电站机组组合问题时存在易陷入局部最优、易出现"维数灾"、收敛性差等缺陷,因此提出了一种改进量子进化混合优化算法用以解决这一问题。通过将量子进化算法与基于经济运行总表的动态规划法嵌套,分别对外层机组组合和内层负荷分配问题进行迭代优化;同时,引入最短开、停机时间修补策略和备用容量修补策略,有效处理多重复杂约束,在保证计算精度的前提下,显著提高收敛速度。以溪洛渡电站经济运行中的机组组合问题为工程背景进行了实例研究,并与已有DP和IBPSO方法进行对比分析,结果显示所提算法简单高效,优化效果好,具有较强的工程实用性。     

The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space

The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large‐scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross‐approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Extending the enlarged cell and uniformly stable conformal techniques to modeling curved conductors in two‐dimensional high‐order finite‐difference time‐domain algorithms

The critical tool of modeling irregularly shaped perfect conductors is developed for the extended‐stencil high‐order two‐dimensional M24 variant of the finite‐difference time‐domain (FDTD) method. Two standard FDTD conformal approaches are analyzed and successfully extended to work accurately with M24. They both afford higher order convergence with respect to mesh density than a previously developed technique, which better matches M24's characteristics. Both approaches rely on borrowing weighted electromotive forces from nearby extended‐stencil cells to ensure accuracy and numerical stability while the overall algorithm is efficiently operated at the maximum allowable time steps by FDTD and M24 theories. Validation examples demonstrate that M24's amplitude and phase accuracies using coarse numerical meshes were not compromised. Copyright © 2012 John Wiley & Sons, Ltd.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Sparse approximate inverse preconditioning of deflated block‐GMRES algorithm for the fast monostatic RCS calculation

A sparse approximate inverse (SAI) preconditioning of deflated block‐generalized minimal residual (GMRES) algorithm is proposed to solve large dense linear systems with multiple right‐hand sides arising from monostatic radar cross section (RCS) calculations. The multilevel fast multipole method (MLFMM) is used to accelerate the matrix–vector product operations, and the SAI preconditioning technique is employed to speed up the convergence rate of block‐GMRES (BGMRES) iterations. The main purpose of this study is to show that the convergence rate of the SAI preconditioned BGMRES method can be significantly improved by deflating a few smallest eigenvalues. Numerical experiments indicate that the combined effect of the SAI preconditioning technique that clusters most of eigenvalues to one, coupled with the deflation technique that shifts the rest of the smallest eigenvalues in the spectrum, can be very beneficial in the MLFMM, thus reducing the overall simulation time substantially. Copyright © 2008 John Wiley & Sons, Ltd.     

Parallelization of the Scale‐Changing Technique in Grid Computing environment for the electronmagnetic simulation of multi‐scale structures

A parallel computing approach to run fast and full‐wave electromagnetic simulation of complex structures in Grid Computing environment is presented. In this study, we show how Grid Computing improves speed and/or reliability over that provided by a single computer, while typically being much more cost‐effective than single computers of comparable speed or reliability. An efficient monolithic (unique) formulation for the electromagnetic modelling of complex (multi‐scale) structures, i.e. structures that exhibit multiple metallic patterns whose sizes cover a large range of scales, is used here. This approach, named the Scale‐Changing Technique, is based on the cascade of multi‐modal Scale‐Changing Networks, each network modelling the electromagnetic coupling between two successive scale levels. These networks can be first computed separately, in an adaptive use of Grid Computing architecture nature, and then cascaded for the global electromagnetic simulation. Based on this technique, a fast computer algorithm was developed and tested in the Grid‐Computing environment. For illustration purposes, the electromagnetic analysis of multi‐scale structures, applied to phase‐shifter elements and an example of infinite passive reflectarray, was carried out. The obtained results have confirmed the effectiveness of such an approach compared with sequential computing. This approach shows very good computation performance while keeping the same accuracy. Besides, this method is very promising for optimizing circuit with multiple design parameters to handle and for the global electromagnetic simulation of multi‐scale and/or oer‐sized structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Stochastic H∞ control problem with state‐dependent noise for weakly coupled large‐scale systems

In this paper, stochastic H_∞ state feedback control with state‐dependent noise for weakly coupled large‐scale systems is discussed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), a new iterative algorithm that combines the Newton's method with the fixed‐point algorithm is derived for the first time. As a result, both the quadratic convergence and the reduced‐order computation in the same dimension of the subsystems are attained. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Modeling of ultra‐wideband indoor channels with the modified leapfrog ADI‐FDTD method

Full‐wave time‐domain electromagnetic methods are usually effective in rigorously modeling and evaluating ultra‐wideband (UWB) wireless channels. However, their computational expenditures are expensive, when they are used to deal with electrically large‐size problems consisting of fine structures. In order to reduce computational time, the unconditionally stable leapfrog alternating‐direction implicit finite‐difference time‐domain (leapfrog ADI‐FDTD) method has been proposed recently. In this paper, the leapfrog ADI‐FDTD algorithm is developed for simulating lossy objects, such as office walls, floors, and ceilings, for UWB communication channel characterization. It leads to effective UWB channel characterization with power‐decay time constant, path loss exponent, and probability distribution of power gain. In comparison with the conventional FDTD, the proposed method can achieve 60% saving in computational time while retaining good accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Free‐weighting matrices‐based robust wide‐area FACTS control design with considering signal time delay for stability enhancement of power systems

This paper presents a free‐weighting matrix (FWM) method based on linear control design approach for the wide‐area robust damping (WARD) controller associated with flexible AC transmission system (FACTS) device to improve the dynamical performance of the large‐scale power systems. First, the linearized reduced‐order plant model is established, which efficiently considers the time delay of the remote feedback signals transmitted by wide‐area measurement systems. Then, based on the robust control theory, the design of the FACTS‐WARD controller is formulated as the standard control problem on delay‐dependent state‐feedback robust control, which is described by a set of linear matrix inequality constraints. Furthermore, in order to obtain the optimal control parameters that can endure the maximum time delay, a FWM approach is proposed to solve the time‐dependent problem of the time‐delay system. Meanwhile, an iterative algorithm based on cone complementary linearization is presented to search out the optimal control parameters. Finally, the nonlinear simulations on the 2‐area 4‐machine and the 5‐area 16‐machine test systems are performed, to evaluate the control performance of the proposed robust wide‐area time‐delay control approach. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Analysis of quadruple corner‐cut ridged elliptical waveguide by scaled boundary finite element method

The scaled boundary FEM (SBFEM) is a novel semi‐analytical approach, which combines the advantages of the FEM and BEM with appealing features of its own. In this paper, the method is applied to analyse the quadruple corner‐cut ridged elliptical waveguide. A quarter of the waveguide is adopted and divided into a few subdomains. SBFEM only discretizes the surface boundaries of the subdomains in the sense of FEM, and no discretization of side‐face boundaries is needed, leading to great flexibility in mesh generation with very few nodes. It transforms the governing PDEs to ODEs of the radial parameter by the variational principle. The radial differential equation is then solved fully analytically without adoption of any numerical scheme, which brings out the inherent advantage for solving a singularity problem. Based on the SBFEM governing equation and introducing the dynamic stiffness of waveguide, a generalised eigenvalue equation with respect to cut‐off wave number is formulated by a continued fraction solution without introducing an internal mesh. The numerical example demonstrates the simplicity, excellent computation accuracy and efficiency of the present SBFEM approach. Influences of corner‐cut ridge dimensions on the cut‐off wave numbers of modes are examined in detail. Therefore, these results provide an extension to the existing design data for ridged waveguides and are considered helpful in practical applications. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of quadruple corner‐cut ridged square waveguide by hybrid mode‐matching boundary‐element method

In this paper, the square waveguide with quadruple corner‐cut ridges is analyzed using the hybrid mode‐matching boundary‐element method. Because of its symmetry, only a quarter of its cross‐section needs to be considered and it is then divided into three regions. The electromagnetic field components in two regular regions can be obtained using the mode‐matching method and the third irregular region is discretized using the boundary‐element method. The combination of two methods produces one matrix equation, from whose determinant the cutoff wavenumbers of waveguide modes can then be computed. This hybrid technique takes advantage of the mode‐matching method's high efficiency and the boundary‐element method's versatility. The convergence of this hybrid method is studied, and numerical results are compared with the conventional boundary‐element method and commercial finite‐element software package, which shows that our hybrid method can achieve the same accuracy with much less time. The influence of the cut‐corners on the cutoff wavenumbers of the dominant and higher‐order modes is then examined. A simple approximate equation is found to accurately predict the cutoff wavenumber of TE₂₀ mode. The single‐mode bandwidth of a quadruple ridged square waveguide is calculated thereafter, which shows that this corner‐cut structure can provide a broader bandwidth compared to the one without cut‐corners. Copyright © 2010 John Wiley & Sons, Ltd.     

A modified finite‐difference time‐domain method for analysing field‐to‐transmission line coupling of telecommunication system signals

A modified finite‐difference time‐domain (FDTD) code is presented for the line response characterization of a transmission line illuminated by a Gaussian pulse‐modulated electromagnetic signal. The final expressions are transformed according to the complex‐envelope representation in order to omit the high‐frequency carrier contribution and thus provide an accurate solution of the coupling phenomenon by avoiding the computational burden of the conventional FDTD algorithm. Comparison results between the conventional FDTD method and the modified one are presented, showing the advantages of the novel method. Copyright © 2002 John Wiley & Sons, Ltd.     

Set‐theoretic adaptive filtering based on data‐driven sparsification

In this article, we propose a fast and efficient algorithm named the adaptive parallel Krylov‐metric projection algorithm. The proposed algorithm is derived from the variable‐metric adaptive projected subgradient method, which has recently been presented as a unified analytic tool for various adaptive filtering algorithms. The proposed algorithm features parallel projection—in a variable‐metric sense—onto multiple closed convex sets containing the optimal filter with high probability. The metric is designed based on (i) sparsification by means of a certain data‐dependent Krylov subspace and (ii) maximal use of the obtained sparse structure for fast convergence. The numerical examples show the advantages of the proposed algorithm over the existing ones in stationary/nonstationary environments. Copyright © 2011 John Wiley & Sons, Ltd.     

The application of the generalized product‐type method based on Bi‐CG to accelerate the sparse‐matrix/canonical grid method

When the sparse‐matrix/canonical grid (SMCG) method is applied to analyse scattering of randomly positioned dielectric spheroids, the impedance matrix is decomposed into a strong interaction matrix and a weak interaction matrix. The strong interaction portion of the matrix–vector multiplication is computed directly as the moment method (MOM). The far‐interaction portion of matrix–vector multiplication is computed indirectly using fast Fourier transforms by a Taylor series expansion of impedance matrix elements about the canonical grid point. However, the condition number of the impedance matrix obtained from the SMCG method becomes large compared to the one from MOM. As a result, the conjugate gradient (CG) method converges slowly. To attack such a trouble, the generalized product‐type method based on Bi‐CG (GPBi‐CG) is used as an iterative solver in this paper. The numerical results show that the GPBi‐CG method can achieve good convergence improvement compared to the other iterative methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Large‐scale super‐Gaussian sources separation using Fast‐ICA with rational nonlinearities

Independent component analysis (ICA) is one of the most powerful methods for solving blind source separation problem. In various ICA methods, the Fast‐ICA is an excellent algorithm, and it finds the demixing matrix that optimizes the nonlinear contrast function. There are three original contrast functions in the Fast‐ICA to separate super‐Gaussian and sub‐Gaussian sources, and their respective derivatives are similar to nonlinearities used in neural networks. For the separation of large‐scale super‐Gaussian sources, however, the contrast functions and the nonlinearities are not optimal owing to high computational cost. To solve this potential problem, this paper proposes four rational polynomial functions to replace the original nonlinearities. Because the rational polynomials can be quickly evaluated, when they are used in the Fast‐ICA, the computational load of the algorithms can be effectively reduced. The proposed rational functions are derived by the Pade approximant from Taylor series expansion of the original nonlinearities. To reduce the error of approximation, we make the behaviors of rational functions approach that of the original ones within an effective range as well as possible. The simulation results show that the Fast‐ICA algorithms with rational nonlinearities not only can speed up the convergence but also improve the separation performance of super‐Gaussian blind source separation. Copyright © 2016 John Wiley & Sons, Ltd.     

Semi‐blind fast equalization of QAM channels using concurrent gradient‐Newton CMA and soft decision‐directed scheme

This contribution considers semi‐blind adaptive equalization for communication systems that employ high‐throughput quadrature amplitude modulation signalling. A minimum number of training symbols, approximately equal to the dimension of the equalizer, are first utilized to provide a rough initial least‐squares estimate of the equalizer's weight vector. A novel gradient‐Newton concurrent constant modulus algorithm and soft decision‐directed scheme are then applied to adapt the equalizer. The proposed semi‐blind adaptive algorithm is capable of converging fast and accurately to the optimal minimum mean‐square error equalization solution. Simulation results obtained demonstrate that the convergence speed of this semi‐blind adaptive algorithm is close to that of the training‐based recursive least‐square algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Convergence properties of bias‐eliminating algorithms for errors‐in‐variables identification

This paper considers the problem of dynamic errors‐in‐variables identification. Convergence properties of the previously proposed bias‐eliminating algorithms are investigated. An error dynamic equation for the bias‐eliminating parameter estimates is derived. It is shown that the convergence of the bias‐eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias‐eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration‐type bias‐eliminating algorithms in the case of high noise, the bias‐eliminating problem is re‐formulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis. Copyright © 2005 John Wiley & Sons, Ltd.