Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co

The Minimum Number of Sensors – Interpolation of Spatial Temperature Profiles in Chilled Transports

Abstract. Wireless sensor networks are an important tool for the supervision of cool chains. Previous research with a high number of measurement points revealed spatial temperature deviations of more than 5 °C in chilled transport, but the number of sensors has to be reduced to an economically useful value for use in regular transport. This paper presents a method to estimate the minimum number of sensors and to compare different sensor positioning strategies. Different methods of interpolating the temperature data of intermediate positions were applied to the experimental data from a delivery truck. The average prediction error for intermediate points was estimated as a function of the number of sensors. The Kriging method, originally developed for the interpolation of geostatistical data, produced the best results

On potentially negative space time covariances obtained as sum of products of marginal ones

Generalised product-sum model, Geostatistics, Nonseparability, Separability, Space–time covariance functions,