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Polynomial chaos in evaluating failure probability: A comparative study

Eliška Janouchová, Jan Sýkora, Anna Kučerová (2018)

Applications of Mathematics

Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial...

Rejection of nonharmonic disturbances in nonlinear systems

Shutang Liu, Yuan Jiang, Ping Liu (2010)

Kybernetika

This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm...

Reversible jump MCMC for two-state multivariate Poisson mixtures

Jani Lahtinen, Jouko Lampinen (2003)

Kybernetika

The problem of identifying the source from observations from a Poisson process can be encountered in fault diagnostics systems based on event counters. The identification of the inner state of the system must be made based on observations of counters which entail only information on the total sum of some events from a dual process which has made a transition from an intact to a broken state at some unknown time. Here we demonstrate the general identifiability of this problem in presence of multiple...

Shape factor extremes for prolate spheroids

Daniel Hlubinka (2006)

Kybernetika

Microscopic prolate spheroids in a given volume of an opaque material are considered. The extremes of the shape factor of the spheroids are studied. The profiles of the spheroids are observed on a random planar section and based on these observations we want to estimate the distribution of the extremal shape factor of the spheroids. We show that under a tail uniformity condition the Maximum domain of attraction is stable. We discuss the normalising constants (n.c.) for the extremes of the spheroid...

Stereology of extremes; size of spheroids

Daniel Hlubinka (2003)

Mathematica Bohemica

The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate...

Tables for a statistical quality control test

František Rublík, Marta Bognárová (1992)

Applications of Mathematics

Critical constants for a test of the hypothesis that the mean μ and the standard deviation σ of the normal N ( μ , σ 2 ) population satisfy the constrains μ + c σ M , μ - c σ m , are presented. In this setup m < M are prescribed tolerance limits and c > 0 in a chosen constant.

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