Efficient computation of updated lower expectations for imprecise continuous-time hidden Markov chains

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix `imprecise' refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables; in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables

Horsetail Matching for Optimization Under Probabilistic, Interval and Mixed Uncertainties

The importance of including uncertainties in the design process of aerospace systems is becoming increasingly recognized, leading to the recent development of many techniques for optimization under uncertainty. Most existing methods represent uncertainties in the problem probabilistically; however, in many real life design applications it is often difficult to assign probability distributions to uncertainties without making strong assumptions. Existing approaches for optimization under different types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Horsetail matching is a flexible approach to optimization under any mix of probabilistic and interval uncertainties that overcomes some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems and the design of a flying wing using a coupled aero-structural analysis code.Engineering and Physical Sciences Research CouncilUnited States. Office of Naval Research. Multidisciplinary University Research Initiative (Award Number FA9550-15-1-0038

Calibration Probe Uncertainty and Validation for the Hypersonic Material Environmental Test System

This paper presents an uncertainty analysis of the stagnation-point calibration probe surface predictions for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System facility located at NASA Langley Research Center. A second-order stochastic expansion was constructed over 47 uncertain parameters to evaluate the sensitivities, identify the most significant uncertain variables, and quantify the uncertainty in the stagnation-point heat flux and pressure predictions of the calibration probe for a low- and high-enthalpy test condition. A sensitivity analysis showed that measurement bias uncertainty is the most significant contributor to the stagnation-point pressure and heat flux variance for the low-enthalpy condition. For the high-enthalpy condition, a paradigm shift in sensitivities revealed the computational fluid dynamics model input uncertainty as the main contributor. A comparison between the prediction and measurement of the stagnation-point conditions under uncertainty showed that there was evidence of statistical disagreement. A validation metric was proposed and applied to the prediction uncertainty to account for the statistical disagreement when compared to the possible stagnation-point heat flux and pressure measurements