Experimental comparison of probabilistic methods and fuzzy sets for designing under uncertainty

Abstract

Recently, probabilistic methods have been used extensively to model uncertainty in many design optimization problems. An alternative approach for modeling uncertainties is fuzzy sets. Fuzzy sets usually require much less information than probabilistic methods and they rely on expert opinion. In principle, probability theory should work better in problems involving only random uncertainties, if sufficient information is available to model these uncertainties accurately. However, because such information is rarely available, probabilistic models rely on a number of assumptions regarding the magnitude of the uncertainties and their distributions and correlations. Moreover, modeling errors can introduce uncertainty in the predicted reliability of the system. Because of these assumptions and inaccuracies it is not clear if a design obtained from probabilistic optimization will actually be more reliable than a design obtained using fuzzy set optimization. Therefore, it is important to compare probabilistic methods and fuzzy sets and determine the conditions under which each method provides more reliable designs. This research work aims to be a first step in that direction. The first objective is to understand how each approach maximizes reliability. The second objective is to experimentally compare designs obtained using each method. A cantilevered truss structure is used as a test case. The truss is equipped with passive viscoelastic tuned dampers for vibration control. The structure is optimized by selecting locations for tuning masses added to the truss. The design requirement is that the acceleration at given points on the truss for a specified excitation be less than some upper limit. The properties of the dampers are the primary sources of uncertainty. They are described by their probability density functions in the probabilistic analysis. In the fuzzy set analysis, they are represented as fuzzy numbers. Two pairs of alternate optimal designs are obtained from the probabilistic and the fuzzy set optimizations, respectively. The optimizations are performed using genetic algorithms. The probabilistic optimization minimizes the system probability of failure. Fuzzy set optimization minimizes the system possibility of failure. Problem parameters (e.g., upper limits on the acceleration) are selected in a way that the probabilities of failure of the alternate designs differ significantly, so that the difference can be measured with a relatively small number of experiments in the lab. The main difference in the way each method maximizes safety is the following. Probabilistic optimization tries to reduce more the probabilities of failure of the modes that are easier to control. On the other hand, fuzzy set optimization tries to equalize the possibilities of failure of all failure modes. These optimum probabilistic and fuzzy set designs are then compared in the laboratory. Twenty-nine realizations of each optimum design are tested and the failure rates are measured. The results confirm that, for the selected problems, probabilistic methods can provide designs that are significantly more reliable than designs obtained using fuzzy set methods.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 7 citations exist upstream.