A Stochastic Programming Approach To The Estimation Of Shell Fragmentation Distributions

Abstract

Upon detonation, a shell shatters into a large number of fragments. The characteristics of the fragmentation can be expressed using a joint distribution of three properties of the fragments, i.e. velocity, mass and the polar angle of projection. The conventional method of estimating this distribution was to build a thick plywood wall in a half-circle. This “arena” was taken down and dissected after each series of experiments. In addition to being expensive, the technique gave rather imprecise results. In this article, we present a new experimental method of estimation using test equipment consisting of metal containers called “collectors” and Doppler type radars which are not destroyed by the analysis. The data obtained from this equipment allows us to write the estimation problem in the form of a stochastic program with simple recourse into which the entropy related to this random experiment is introduced. With a validation technique based on simulation, we are able to show that this new method of estimating fragment distributions is both reliable and effective.

Résumé:

Sous la force d’un impact, un obus se fragmente en un grand nombre de particules. Les caractéristiques de cette fragmentation peuvent être résumées à l’aide d’une distribution jointe à trois dimensions soit la “vitesse”, la “masse” et “I’angle polaite d’éjection” des fragments. La méthode traditionnelle d’estimation de cette distribution consistait à construire un mur épais de contreplaqué en forme de demi-cercle appelé “arène” qui était détruit après chaque explosion: en plus de son coût trés élevé, cette méthode donnait des résultats dont la précision était discutable. Dans cet article, nous préseritons une nouvelle méthode expérimentale d’estimation qui utilise des dispositifs physiques qui ne sont pas détruits par les explosions: il s’agit de réceptacles métalliques appelés “collecteurs” et de radars de type Doppler. A partir des données obtenues de ces dispositifs, on écrit le problème d’estimation en question sous la forme d’un problème de programmation stochastique avec recours simple dans lequel on peut faire intervenir l’ehtropie attachée à cette expérience aléatoire. Grâce à une méthode de validation basée sur la simulation, on peut démontrer que cette nouvelle méthode d’estimation de la distribution des fragments constitue un outil fiable et efficace.

Additional information

Notes on contributors

Alain Martel

Alain Martel is the chairman of the Operations and Decision Systems Department at Laval University in Québec City, and he is the outgoing President of the Canadian Operational Research Society. He holds a Ph.D. in Engineering Production and an M.Sc. in OR from the University of Birmingham in England, and a B.Eng. from the Royal Military College of Canada. His current research concerns the analysis and design of logistic systems with special interests in physical distribution and in information systems design. His research articles appeared in JORS, INFOR, OMEGA, IEEE Transactions on Engineering and Management and the Revue francaise d’automatique, informatique et recherche opérationnelle. He is the author of a book on OR and he has provided consulting seivices to several public and private organizations.

Raymond Nadeau

Raymond Nadeau is an associate professor of quantitative methods at Laval University in Québec City. He received a B.Sc. in mathematics from the University of Montréal and a M.Sc. and a Ph.D. in probability and statistics from Laval University. His research interests include stochastic programming, multiple criteria decision aids and decision analysis. He is the author or co-author of two textbooks in probability and statistics and of sa

Wilson L. Price

Wilson Price is a professor at the Faculte des Sciences de l’Administration de l’Université Laval, a member (and past president) of CORS, ORSA, TIMS, and I’Ordre des ingénieurs du Québec. His current research interests include Japanese production management techniques and corporate strategy for information technology.