Selecting appropriate feature extraction method is absolutely one of the most important factors to archive high classification performance in pattern recognition systems. Among different feature extraction methods proposed for pattern recognition, statistical moments seem to be so promising. Whereas theoretical comparison of the moments is too complicated, in this paper, an experimental evaluat...

We solve Burgers’ equation with random Riemann initial conditions. The closed solution allows simple expressions for its statistical moments. Using these ideas we design an efficient algorithm to calculate the statistical moments of the solution. Our methodology is an alternative to the Monte Carlo method. The present approach does not demand a random numbers generator as does the Monte Carlo m...

An integrated method is proposed for structural nonlinear damage detection based on time series analysis and the higher statistical moments of structural responses in this study. It combines the time series analysis, the higher statistical moments of AR model residual errors and the fuzzy c-means (FCM) clustering techniques. A few comprehensive damage indexes are developed in the arithmetic and...

In the first part of this presentation, recent advances in reliability-based robust design optimization (RBRDO) will be presented. The objective of RBRDO is to minimize the product quality loss function subject to probabilistic constraints. Since the quality loss function is usually expressed in terms of the first two statistical moments, mean and variance, many methods have been proposed to ac...

We develop a complete convergence theory for the Maximum Entropy method based on moment matching for a sequence of approximate statistical moments estimated by the Multilevel Monte Carlo method. Under appropriate regularity assumptions on the target probability density function, the proposed method is superior to the Maximum Entropy method with moments estimated by the Monte Carlo method. New t...

This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of the polynomial dimensional decomposition (PDD) of a multivariate stochastic response function and score functions. Applied to the statistical moments, the me...