Review of uncertainty quantification, associated parables, and Raphael Tuvia Haftka’s contributions

Abstract

Two quotes, although unusual for the abstract, immediately appear to be called for in a way of describing what this paper is about; the first one is by Alfred Freudenthal (1968) in his classic paper: "… it seems absurd to strive for more and more refinement of methods of stress-analysis of the structural elements if, in order to determine the dimensions of the structural elements, its results are subsequently compared with so-called 'working stresses,' derived in a rather crude manner by dividing the values of somewhat dubious material parameters obtained in conventional material tests by still more dubious empirical numbers called 'safety factors'." His equally classic paper by Giuseppe Grandori in Meccanica 26:17-21 (1990) resonates, as it were, with the above quote, stressing: "The probabilistic approach to structural safety is today a well-established paradigm. As to the current state of this paradigm, one can notice a dissymmetry similar to that observed by Freudenthal in the traditional approach. An overwhelming part of the research effort, in fact, has been and still is devoted to estimating failure probabilities. By contrast, only sporadic research deals with the problem of choosing an acceptable risk of failure. It is true that the adoration of the probabilistic approach is in any case a progress, even in the case when acceptable risk levels are conveniently defined, because it allows us to treat different structures with homogeneous criteria. However, the concept of structural safety will not leave the 'realm of metaphysics' unless we devise a method for justifying the choice of risk acceptability levels." As we see, the first quote criticizes the deterministic approach in engineering; the other one questions the validity of a probabilistic approach. Here we are concerned with the "mother of all problems," namely how to deal with uncertainty, which methodology to choose and why and how. Hereinafter, the author's musings on uncertainty quantification are presented, via some parables. Finally, connection will be made with the philosophy adopted by late Professor Raphael Tuvia Haftka in his researches on uncertainty.