Staircase predictor models for reliability and risk analysis

This paper proposes a technique for constructing computational models describing the distribution of a continuous output variable given input-output data. These models are called Random Predictor Models (RPMs) because the predicted output corresponding to any given input is a random variable. We focus on RPMs having a bounded support set and prescribed values for the first four moments. This prescription, to be realized by staircase variables, enables modeling skewed and multimodal phenomena distributed over an input-dependent interval. Responses with such complex features often arise in structural dynamics. As an example we consider the reliability analysis of an aeroelastic airfoil subject to flutter instability whose data is corrupted by model-form uncertainty and measurement noise. Furthermore, we propose a risk analysis methodology to trade-off performance against reliability. This example demonstrates that substantial performance improvements are obtained by (taking the risk of) ignoring a small percentage of the predicted responses.