Introduction to Imprecise Probabilities

Chapter 13Engineering

Michael Oberguggenberger

Unit of Engineering Mathematics, University of Innsbruck, Austria

13.1 Introduction

From small gadgets of daily use, houses, cars, ships, aerospace transport to large scale structures such as nuclear power plants, the public requires usability, safety and reliability. The designing engineer is expected to guarantee these functions or at least make every reasonable effort to achieve these goals (we leave aside the trade-off between affordable performance and available resources). In the design process, models of the prospective structures are set up, at the hand of which their expected behaviour can be investigated, understood and predicted. It is here that the major issue of uncertainty enters the scene, and with it uncertainty analysis.

Scientific modelling in engineering has to deal with three facets. First, there is reality (with materials, soils etc.). Second, there is the model of reality (formulated in mathematical terms and containing physical laws and constitutive equations). Third, correspondence rules (prescribing how to translate one into the other) are needed. The physical model establishes what are the state variables and what are the material constants, the parameters to be observed. Once this has been decided, the values of the parameters have to be determined from information extracted from the real world and will serve as input in the physical model. This plus the design of the structure enters in numerical computations ...