We give an intrinsic algebraic definition of fault detectability and isolability, parity equations, and residuals for time-invariant linear systems. The applicability and efficiency of our approach are illustrated by numerical simulations for three academic examples and a concrete case-study. Keywords— Linear system, fault diagnosis, detectability, isolation, parity equations, residuals, module...

Previous studies from PKP(AB^DF) differential travel times at large distances suggest that the central part of the inner core is very anisotropic. These differential times, however, can be affected greatly by strong heterogeneity in the lowermost mantle. Here we examine a unique data set of PKP travel times from global digital and analog stations at near antipodal distances, where the effects o...

New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a "best" error bound emerges from our comparisons as the sum of two natural residuals.

Probit residuals need not sum to zero in general. However, if explanatory variables are qualitative the sum can be shown to be zero for many models. Indeed this remains true for binary dependent variable models other than Probit and Logit. Even if some explanatory variables are quantitative, residuals can sum to almost zero more often than might at first seem plausible.

Consider a stationary, pth order autoregression fX n g satisfying whose innovation sequence fZ n g is iid with regularly varying tail probabilities of index ?. From p of the autore-gressive coeecients and then to estimate the residuals by and then to apply Hill's estimator to the estimated residuals. We show that from the point of asymptotic variance, the second procedure is superior.

Tests for change-points for location or regression models are often based on cumulative sums of recursive residuals. In the context of general estimable parameters (functionals of the underlying distributions), such recursive residuals may be defined in terms of recursive U-statistics. Along with some invariance principles for recursive U-statistics, asymptotic properties of some proposed tests...

This paper considers robust fault detection for nonlinear systems with full state information. We propose and solve a multi-objective fault detection criterion by maximizing the smallest singular value of the transformation from faults to fault detection residuals while decoupling/or minimizing the largest singular value of the transformation from disturbance to the fault detection residuals.

Relations and relational operators can be used to define the semantics of programming languages. The operations ∨ and ◦ serve to give angelic semantics by defining a program to go right when there is a possibility to go right. On the other hand, the demonic operations and do the opposite: if there is a possibility to go wrong, a program whose semantics is given by these operators will go wrong;...

Usually in multivariate regression problem it is assumed that residuals of outputs are independent of each other. In many applications a more realistic model would allow dependencies between the outputs. In this paper we show how a Bayesian treatment using Markov Chain Monte Carlo (MCMC) method can allow for a full covariance matrix with Multi Layer Perceptron (MLP) neural networks.

State-of-the-art image denoising algorithms attempt to recover natural image signals from their noisy observations, such that the statistics of the denoised image follow the statistical regularities of natural images. One aspect generally missing in these approaches is that the properties of the residual image (defined as the difference between the noisy observation and the denoised image) have...