NASA Langley’s approach to the Sandia’s structural dynamics challenge problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the acceleration response of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although deterministic analyses of this type are routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing the uncertainties of interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on the target configurations. Also, while multiple data sets from experiments conducted at the subsystem level are provided, samples sizes are not sufficient to compute high confidence statistics. Moreover, in this challenge problem, additional constraints, in the form of ground rules, have been added. One such constraint is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these subsystem models and the multiple data sets to make predictions about the target system response under completely different forcing functions.Initially, our approach involved the screening of several different methods to arrive at the three presented herein. The first one is based on a transformation of the structural dynamic data in the modal domain to an orthogonal space where the mean and covariance of the data are matched. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnessess, and damping coefficients; one matches the confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on the approaches, lessons learned, validation metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach.