ABSTRACT
This paper proposes a method for characterizing a system’s response given data. This response might prescribe the failure domain needed to assess the reliability of such a system. We focus on the case in which not all uncertain parameters affecting the response are observable and the measurements are corrupted by noise. In this setting, the system response is not given by a function but instead by a random process. In this paper we use a staircase random predictor model to characterize such a process. Consequently, the resulting failure probability is not a scalar but a random variable. This variable accounts for the aleatory contributions of the model-form uncertainty and the measurement noise affecting the system’s response. Furthermore, we propose a framework that enables trading off the system’s performance, measured by the extension of an acceptable range of operating conditions, against the system’s reliability, measured by an admissible range of failure probabilities. The risk incurred by such a practice is ignoring a (small) percentage of the predicted worst-case system responses. These ideas are illustrated by performing the reliability analysis of an aeroelastic structure subject to flutter instability. Furthermore, this paper puts forth a means to quantify the error resulting from having a dataset of limited size when performing the above analysis.
