Xiaojun Wang

Bio: Xiaojun Wang is an academic researcher from Beihang University. The author has contributed to research in topics: Interval (mathematics) & Interval arithmetic. The author has an hindex of 27, co-authored 109 publications receiving 2426 citations. Previous affiliations of Xiaojun Wang include Hong Kong Polytechnic University.

Non-probabilistic set-theoretic model for structural safety measure

Abstract: In this paper, a new non-probabilistic set-theoretic safety measure for structures is proposed. Based on the non-probabilistic set-theoretic stress–strength interference model, the ratio of the volume of the safe region to the total volume of the region associated with the variation of the basic interval variables is suggested as the measure of structural non-probabilistic safety. The compatibility between the presented non-probabilistic set-theoretic safety measure and the probabilistic reliability is demonstrated. Numerical examples are used to shed a light on the validity of the presented measure.

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Global optimization and simulated annealing

Abstract: In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.