A fast high-order solver for problems of scattering by heterogeneous bodies

A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(Nlog(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds.     

塑封双极型功率晶体管的失效与案例分析

由于其自身的结构与封装形式,塑封双极型功率管存在很多可靠性问题.介绍了塑封双极型功率晶体管可靠性问题及失效机理,包括封装缺陷、粘结失效以及由于温度变化而引起的热应力失效和由于吸入潮气而导致的腐蚀失效.通过剖析一晶体管的失效机理,给出了对此类晶体管失效分析的方法和思路.讨论了晶体管存在异物、芯片粘结失效和热应力失效等失效模式.     

Numerical Solution and Inference for Interval-Reliability of Repairable Components

The renewal and interval-reliability functions for repairable components are solved for given general probability distribution of renewal interarrival times. Two powerful numerical methods are 1) A finite difference approach wherein the renewal equation is written in discrete form and then the resulting system of algebraic equations is solved recursively. 2) Transforms of the renewal equation are treated and Fourier series expansions are used. The Fourier series approach has a wider range of applicability than finite difference in that it can be used to solve the complete renewal problem. A new equivalent form of the interval-reliability integral equation leads to a computationally faster scheme (by a factor of 10) and a simplified approximate solution for high reliability components. A numerical solution for confidence intervals has also been generated for the average interval-reliability of a component within a system, given component failure data, using a pseudo-Bayesian approach. The goal is to choose priors that lead to classical limits and not the usual Bayesian limits. The intervals yield close-to-exact frequency limits depending on sample size, Weibull shape parameter and the true reliability.     

Approximate Confidence Intervals for Reliability of a Series System

Two solutions are proposed for estimating s-confidence intervals for reliability of a repairable series system comprised of non-constant failure rate components: 1) the system is treated as a sum of renewal processes with the mean and variance of total number of system failures being computed from the moments of failure times of the components; and 2) a pseudo-Bayesian solution is derived for the mean and variance of the log-reliability of a system of Weibull components. In both solution approaches, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities. s-Confidence limits are then approximated using Gaussian probability tables. The intervals derived yield close-to-exact frequency limits, depending on such variables as number of test failures, number of components, and component parameters.     

A fast high-order solver for EM scattering from complex penetrablebodies: TE case

We present a new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies under TE radiation. Here, a scatterer is represented by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2-D) bounded region. Solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(N log(N)) operations, where N is the number of discretization points. Our method provides highly accurate solutions in short computing times, even for problems in which the scattering bodies contain complex geometric singularities     

The Use of Accelerated Full-Wave Modeling to Analyze Power Island Coupling in a HyperBGA SCM

Presented here are results and recommendations for reducing coupling between adjacent power islands based on full-wave simulations of a HyperBGA SCM (single-chip module). These simulations highlight the use of IBM's internally developed accelerated full-wave solver based on the precorrected fast Fourier transform approach. Speedups of 100times and memory reductions of 12times are shown for real engineering problems, as compared to direct integral equation solutions     

Asymptotic results for maximum likelihood estimation with an arrayof sensors

In many cases, the maximum likelihood (ML) estimator is consistent and asymptotically normal with covariance equal to the inverse of the Fisher's information matrix. It does not follow, though, that the covariance of the ML estimator approaches the Cramer-Rao lower bound as the sample size increases. However, it is possible to draw such a conclusion for the adaptive array problem in which direction of arrival and signal magnitude are being estimated. Proofs of w-asymptotic efficiency, which comes with a convergence-of-moments condition, and strong consistency (almost-sure convergence) of the ML estimator are given. Strong consistency is also proved for a popular quasi-ML estimator     

Redistribution of dopant impurities in a semiconductor using the series method of Chen and Chen

The series method of Chen and Chen is re-examined and applied to a variety of redistribution problems. It is seen that this analysis can play an important role in deriving closed-form solutions of the diffusion equation useful in semiconductor technology. In particular, series solutions are formulated for two alternative Si/SiO₂ interface boundary conditions. Moreover, taken in conjunction with the Euler transformation it is shown to provide exact solutions to several redistribution problems for a wide class of initial dopant profiles and for realistic diffusion times. All solutions have been compared where ever possible with existing analytical techniques, and in all other cases reference has been made to results obtained from the numerical Crank-Nicolson technique.     

On Failure-Time Distributions for Systems of Dissimilar Units

Certain reliability problems of systems of dissimilar units with repair are described. The mean time to system failure is based on the relation of mean first passage times between states of the system. The failure-time distribution is obtained from an integral equation of the renewal type. The two approaches can be also applied to a system of dissimilar units under an overload. Finally, it is shown that these results include many earlier results as special cases.     

Interception of frequency-hopped spread-spectrum signals

A frequency-hopped spread-spectrum signal is modeled as a sinusoid that has one of N random frequencies. Coherent and noncoherent interception receiver structures based on Neyman-Pearson detection theory are determined. Under the assumption that there is a single hop per detection period, the optimum receiver structure is shown to consist of a bank of matched filters called the average likelihood (AL) receiver. A suboptimum structure called the maximum likelihood (ML) receiver is also analyzed. It is shown that AL and ML receivers have essentially the same performance. Simple formulas that relate the probability of detection, P_D, to the probability of false alarm, P_F, and the signal-to-noise ratio (SNR) for large N are derived. Receiver structures are also derived and analyzed for the case where the signal hops a number of times in one detection interval. This may correspond to the detection of a multihop signal in one symbol interval or to detection based on integration over a number of symbol intervals. The relationships of P_D to P_F, for both coherent and noncoherent multiple-hop receivers, are examined     

Absorbing and antireflecting continuously inhomogeneous coatings for electromagnetic waves

It is shown that two linearly independent solutions to the wave equation written for magnetodielectric structures that are inhomogeneous in one direction can be represented as a forward and a backward wave with the help of one function g(z). All basic characteristics describing a wave propagating in an inhomogeneous medium can be expressed in terms of this auxiliary function. Boundary conditions for this function are found that generate distributions ensuring total transmission (at a given frequency) of the wave incident onto the coating layer. Correct mathematical formulation of optimization problems for various coatings is given as the problem of the search for the introduced function with additional constraints.     

Electromagnetic Wave Propagating in Uniform Waveguides Containing Inhomogeneous Dielectric

Uniform waveguides filled with inhomogeneous dielectric whose permittivity varies along one dimension are studied. Emphasis is given to the modes of propagation and to the calculation of the propagation constants. Exact solutions are given for some special cases. In some of these only asymptotic or polynomial solutions have been available previously. No restriction is placed on the waveguide dimensions so that results developed here apply to the transmission of optical frequency waves as well as to microwaves and millimeter waves. In the waveguide problems of this paper, results obtained cannot be directly found in the existing literature and have been worked out from fundamental theory of differential equations. The theory of the confluent hypergeometric function has been of great help in our treatment of these problems.     

Reliability analysis of accelerated life-test data from arepairable system

This paper analyzes accelerating testing of a repairable item modeled by a nonhomogeneous Poisson process with covariates. We extensively analyze a single accelerating variable with two stress levels, and derive closed-form maximum likelihood (ML) solutions. These closed-form solutions provide: (1) an easier way to obtain point estimates of the unknown parameters under usual operating conditions, and (2) a way to obtain confidence intervals on the process parameters and function thereof which are more accurate than those based on asymptotic normality of ML estimates. We analyze the circumstances in which a drawback to closed-form estimation arises, and guides the extent that our procedures may equally apply. An example application drawn from a real situation of accelerated testing is presented, and numerical estimates based on our procedures are derived and discussed. Theoretical and simulation results show that estimation procedures based on the power-law process and regression methods can be a flexible, useful tool for reliability analysis of a repairable item     

Comparing of system reliabilities of repairable coherent systems in a changing environment

In this paper multicomponent reliability systems are considered where component failure rate and repair completion rate depend on the environment state and, ages and current repair durations of the other components. this is a generalization of the model of Shaked M. and Shanthikumar J.G.[3]. Sufficient conditions on the set of the rates which imply stochastic ordering between first failure times of two such systems are found. Sufficient conditions on rates which imply that the first failure time of such a system is new better than used(NBU) are given. Some results of [3] may be regarded as the special cases of our assertions.     

Noncausal 2-D spectrum estimation for direction finding

A two-dimensional noncausal autoregressive (NCAR) plus additive noise model-based spectrum estimation method is presented for planar array data typical of signals encountered in array processing applications. Since the likelihood function for NCAR plus noise data is nonlinear in the model parameters and is further complicated by the unknown variance of the additive noise, computationally intensive gradient search algorithms are required for computing the estimates. If a doubly periodic lattice is assumed, the complexity of the approximate maximum likelihood (ML) equation is significantly reduced without destroying the theoretical asymptotic properties of the estimates and degrading the observed accuracy of the estimated spectra. Initial conditions for starting the approximate ML computation are suggested. Experimental results that can be used to evaluate the signal-plus-noise approach and compare its performance to those of signal-only methods are presented for Gaussian and simulated planar array data. Statistics of estimated spectrum parameters are given, and estimated spectra for signals with close spatial frequencies are shown. The approximate ML parameter estimate's asymptotic properties, such as consistency and normality, are established, and lower bounds for the estimate's errors are derived, assuming that the data are Gaussian     

Discrete multiloop, modified multiloop, and plate-loopantennas-multifrequency and wideband VSWR characteristics

Three types of loop antennas are presented: discrete multiloop (ML), modified ML and plate-loop (PL) antennas. The discrete ML and modified ML antennas are composed of N square loops. The N square loops of the modified ML antenna are connected by wires at the loop corners. The PL antenna is regarded as a modified ML antenna with infinite loops (N=∞). The analysis of the discrete ML antenna shows that one of the N loops resonates when its circumference is approximately one wavelength. It follows that the discrete ML antenna has N minima in the frequency response curve of the VSWR. In contrast to the discrete ML antenna, the modified ML has a VSWR with a wide-band frequency response: approximately 16% with N=7, which is more than 2.5 times as wide as that for a single-loop antenna (N=1). Further analysis reveals that the PL antenna has a VSWR bandwidth similar to that of the modified ML antenna. The maximum gain of the PL antenna is approximately 9 dB, which is very close to those of the discrete and modified ML antennas     

Analyzing Reliability Data and Designing Acceptance Tests

Persons designing testing programs to specify reliability functions and failure rates need theoretical means of assigning confidence intervals to the quantities obtained. Also, persons designing acceptance tests for items with unknown reliability functions need simple, general methods of test design which do not rely on the myriad specialized tables for specific mathematical models available in the literature. The two problems are really opposite ways of looking at the same theoretical structure. The theoretical structure is examined here and solutions to the problems are posed.     

Estimation and choice of neighbors in spatial-interaction models of images

Some aspects of statistical inference for a class of spatial-interaction models for finite images are presented: primarily the simultaneous autoregressive (SAR) models and conditional Markov (CM) models. Each of these models is characterized by a set of neighbors, a set of coefficients, and a noise sequence of specified characteristics. We are concerned with two problems: the estimation of the unknown parameters in both SAR and CM models and the choice of an appropriate model from a class of such competing models. Assuming Gaussian-distributed variables, we discuss maximum likelihood (ML) estimation methods. In general, the ML scheme leads to nonlinear optimization problems. To avoid excessive computation, an iterative scheme is given for SAR models, which gives approximate ML estimates in the Gaussian case and reasonably good estimates in some non-Gaussian situations as well. Likewise, for CM models, an easily computable consistent estimate is given. The asymptotic mean-squared error (mse) of this estimate for a four-neighbor CM model is shown tn be substantially less than the mse of the popular coding estimate. Asymptotically consistent decision rules are given for choosing an appropriate SAR or CM model. The usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns. Synthetic patterns obeying known SAR and CM models are generated, and the models corresponding to true and several competing neighbor sets are fitted. The estimation scheme yields estimates close to the parameters of the true models, and the decision rule for the choice of neighbors picks up the true model from the class of competing models.     

A Unified Formula for Analysis of Some Network Reliability Problems

A topological formula is derived for solving a variety of network reliability problems such as vertex-to-vertex communication from a source to a terminal; from a source to some specified subset of the vertices or else all vertices; between any given vertex-pair; between all vertex-pairs within a given subset of the vertices; or else between all vertex-pairs. The formula applies to networks consisting of imperfect (unreliable) vertices and/or links, and with failure events s-independent or not. The formula explicitly characterizes the structure of both cancelling and noncancelling terms in the reliability expression obtained by Inclusion-Exclusion, and involves only noncancelling terms. Earlier topological formulas for the source-to-terminal problem and the source-to-all-vertices problem are shown to be special cases of this new one.