Generalized polynomial chaos paradigms to model uncertainty in wireless links

Discretization of a random field by the generalized polynomial chaos (GPC) begins with selecting a specific type of orthogonal polynomial (e.g. Legendre and Hermite polynomials) (e.g. Ghanem and Spanos, 1991). This selection of a type of orthogonal polynomial can be performed based on the reported experiences (e.g. Xiu and Karniadakis, 2003) or data revealing the distribution of a random field to be discretized. If such data or reported experiences are unavailable, a third way may be generating some pilot tests to study the performance of a specific type of orthogonal polynomial in discretizing this random field. This study tries to develop an evolutionary algorithm-based auxiliary tool for the implementation of such pilot tests. A similar tool (Allaix and Carbone, 2009), which is based on the singleobjective evolutionary algorithm, had been developed for constructing the Karhunen-Loeve (KL) representation of a random field. Both KL and GPC expansions are two of the popular random field discretization methods (Ghanem and Spanos, 1991). But, the KL expansion should be applied under a prerequisite of knowing the covariance matrix of a random field to be discretized (e.g. Ghanem and Spanos, 1991); while, the GPC expansions can be applied without similar prerequisites (e.g. Xiu and Karniadakis, 2003). Therefore, the development of an auxiliary tool for constructing a GPC representation of a random field would be necessary. The succeeding research considers the derivation of an GPC representation of a random field as a multi-objective (MO) problem having two goals: (a) limiting the computational efforts spent in applying the resulting GPC representation; and (b) keeping the resulting GPC representation satisfying all accuracy standards (e.g. getting the sufficiently accurate prediction of statistical parameters of a random field). The former goal will be attained by limiting the highest order of polynomial term and total number of uncorrelated random variables used to construct a GPC representation; while the latter goal will be attained by minimizing multiple error estimators. Since there are multiple goals to be attained, a multiple objective evolutionary algorithm (MOEA) is required. Among all available MOEAs, the strength Pareto evolutionary algorithm II (SPEA 2) (Zitzler, et al., 2001) is chosen. The highest order of polynomial term and total number of uncorrelated random variables used to construct an GPC representation are considered as two parameters to be identified. The remainder of this study is organized into four sections. In Sec. 2, the theoretical backgrounds of GPC expansions (e.g. Xiu and Karniadakis, 2003) are briefly reviewed. In Sec. 3, the SPEA 2 (Zitzler, et al., 2001) is used to construct a parameter identification procedure to identify the aforementioned highest order of orthogonal polynomial and total

Robustness of stochastic expansions for the stability of uncertain nonlinear dynamical systems – Application to brake squeal

This paper reports the experimental results of IEEE 802.11b wireless link performance in ad hoc mode. The throughput and packet loss rate are measured for user datagram protocol (UDP) and transmission control protocol (TCP) traffic in both indoor and outdoor environments. Various factors that affect the performance of the wireless link, such as the packet size, the transmission rate, the distance between stations, the retry limit and the network topology are considered. Experimental measurements are also compared against theoretical calculations.

This paper considers the model predictive control of dynamic systems subject to stochastic uncertainties due to parametric uncertainties and exogenous disturbance. The effects of uncertainties are quantified using generalised polynomial chaos expansions with an additive Gaussian random process as the exogenous disturbance. With Gaussian approximation of the resulting solution trajectory of a stochastic differential equation using generalised polynomial chaos expansion, convex finite-horizon model predictive control problems are solved that are amenable to online computation of a stochastically robust control policy over the time horizon. Using generalised polynomial chaos expansions combined with convex relaxation methods, the probabilistic constraints are replaced by convex deterministic constraints that approximate the probabilistic violations. This approach to chance-constrained model predictive control provides an explicit way to handle a stochastic system model in the presence of both model uncertainty and exogenous disturbances.

The radio link performance of short range but high data rate UWB systems is affected by both the antennas and the channel. Both aspects have been widely investigated in related literature. With respect to the antenna it is often the goal to minimize the ringing to affect less the impulse radiation. Unfortunately, in most studies the antenna integration into the chassis of the specific application is not taken into account. Investigations in this paper show that the integration significantly affects e.g. the ringing of the antenna. In order to investigate the impact of this degradation on the radio link between different applications like DVD player and PDA in a typical indoor environment propagation modeling is performed. The results show that the delay spread of the channel dominates the performance of the entire radio link. The increased ringing due to the antenna integration adds only minor to the overall performance.

This paper reviews progress in developing a mathematical framework to evaluate the performance of mobile radio links. It takes into account multi-ray multipath fading with Rician or Nakagami probability density, lognormal shadowing and path loss of wanted and interfering transmitters, additive white Gaussian noise, man-made burst noise and discontinuous transmission. The method uses Laplace transforms of the PDF of the power of each interfering signal. This method is computationally efficient and allows inclusion of a wide range of link aspects. We also show that, in contrast to common belief, it is not realistic to approximate the Rician fading of the wanted signal by a Nakagami model. New results are given for microcells along highways.

At the LKAB Kiruna Iron Ore Mine in Sweden, reliability and maintainability analysis techniques have been gradually accepted as standard tools for planning and operation of automatic and complex mining systems since the mid-1980s. The reliability analysis and modeling of the production system at the Kiruna mine are discussed. Since a large number of random variables (phenomena) are involved in the analysis, a simulation program SIMURES was developed to model the reliability characteristics of the production process and analyze the criticality of the various units and operations. This program has helped in evaluating the gain in production volume with improvement in reliability of the various units, and thus forms a basis for future investment for increasing the production system efficiency and capability. >

Parametric uncertainty assessment in hydrological modeling using the generalized polynomial chaos expansion

A polynomial chaos expansion in dependent random variables

Based on the generalized spectral model for non-Kolmogorov atmospheric turbulence, analytic expressions of the scintillation index (SI) are derived for plane, spherical optical waves and a partially coherent Gaussian beam propagating through non-Kolmogorov turbulence horizontally in the weak fluctuation regime. The new expressions relate the SI to the finite turbulence inner and outer scales, spatial coherence of the source and spectral power-law and then used to analyze the effects of atmospheric condition and link length on the performance of wireless optical communication links.

A technique is presented to calculate the probability density function (pdf) for a sum of random variables that have pdf's on a logarithmic scale. In mobile radio it is often necessary to calculate the pdf of the total received signal power, which is the “power sum” of a number of simultaneously received signal powers. When the signal powers are given on a linear scale (e.g. Watts) probability density functions (pdf's) of the individual signals can be convolved to give the pdf for the received power of all the signals together. When, as is usual, the signal powers are given on a logarithmic scale (e.g. dBs) this is not possible. The simple convolution for the linear domain must now be replaced by a convolution for the logarithmic domain, which is not straightforward to compute. In this paper, a method is presented to compute the pdf of a power sum of two random variables, the logarithmic convolution. The results are not in closed form, numerical integration is necessary to find the resulting pdf. The method can be applied recursively to give results for power sums of more than two random variables. Although methods exist that give solutions in a closed form, they mainly use approximations and are valid only for specific distributions. The method presented in this paper yields exact results for arbitrary distributions. The results of the logarithmic convolution are verified by Monte-Carlo simulations. Even for large numbers of random variables the power sum results are shown to be correct.

In this paper, an efficient method for the reliability analysis of systems with nonlinear limit states is described. It combines optimization-based and simulation-based approaches and is particularly applicable for problems with highly nonlinear and implicit limit state functions, which are difficult to solve by conventional reliability methods. The proposed method consists of two major parts. In the first part, an optimization-based method is used to search for the most probable point (MPP) on the limit state. This is achieved by using adaptive response surface approximations. In the second part, a multi-modal adaptive importance sampling method is proposed using the MPP information from the first part as the starting point. The proposed method is applied to the reliability estimation of a vehicle body-door subsystem with respect to one of the important quality issues -- the door closing effort. The superiority of the proposed method, in terms of efficiency and accuracy, is demonstrated with a numerical example of highly nonlinear limit state problem, as well as an automotive door closing effort application. A generalized framework for reliability estimation is also proposed for problems with large numbers of random variables and complicated limit states.

As CMOS technology enters the nanometer regime, the increasing process variation is bringing manifest impact on circuit performance. To accurately consider both global and local process variations, a large number of random variables (or parameters) have to be incorporated into circuit models. This in turn raises the complexity of the circuit models. In this paper, we propose a principle Hessian direction-based parameter-reduction approach. This new approach relies on the impact of each parameter on circuit performance to decide whether keeping or reducing the parameter. Compared with the existing principle component analysis method, this performance based property provides us a significantly smaller set of parameters after reduction. The experimental results also support our conclusions. In interconnect cases, the proposed method reduces 70% of parameters. In some cases, for example, the mesh circuit in the current paper, the new approach leads to an 85% reduction. We also tested ISCAS benchmarks. In all cases, an average of 53% of reduction is observed with less than 3% error in the mean value and less than 8% error in the variation.

This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

Modelling of the cooperative spectrum sensing in cognitive radio networks in presence of correlated multipath-fading is an important issue. It deals with complex dependencies of large number of random variables. Earlier developments on decision fusion consider correlated local decisions, correlated shadowing, spatial correlation and independent fading channels. This paper presents likelihood ratio test (LRT) based new fusion rule using normal factor graph (NFG) and Sum-Product-Algorithm (SPA) model for cooperative spectrum sensing in presence of correlated multipath-fading channels. The proposed approach requires exact channel statistics instead of instantaneous channel state information (CSI). It leads to Neyman-Pearson (N-P) criteria based optimal sensing. We assume SUs are aligned in a linear fashion and each channel is correlated only with its adjacent channels with identical fading correlation coefficients. In this respect, we derive a new tri-variate Rayleigh probability density function using Miller's [1] approach. Moreover, closed form solutions for local probabilities of detection and false alarm are also derived by assuming that all secondary users employ energy detection. The decision fusion is performed using SPA as message passing strategy over the NFG. Simulation results are provided to validate the performance of the proposed approach.