Model-based Uncertainty Quantification, Propagation, and Analysis using Generalized Polynomial Chaos

Abstract

This article introduces a probabilistic model-based programming language called AURA-Sim that enables the quantification, propagation, and analysis of arbitrary random distributions through nonlinear systems. Probabilistic programming languages are a relatively recent innovation that are intended to automate much of the low-level programming required to implement common statistical computations. Model-based programming languages are designed to simplify the specification of complex dynamical systems, having many separate components that interact over time, and are widely used for developing complex systems in numerous disciplines. This articles explains the harmonious combination of these two programming concepts into a unified programming language that enables system designers to directly solve many of the most important problems of uncertainty management for dynamical systems. The resulting language is developed as a set of C++ libraries and exposed to the user in the model-based language of SIMULINK and MATLAB. AURA-Sim allows system designers to model essentially arbitrary random processes and to propagate them through a wide variety of nonlinear dynamical systems. This capability is not currently available in any model-based programming language. The AURA-Sim library is based on generalized polynomial chaos (gPC) theory which is reviewed in the following. Traditionally, uncertainty quantification, propagation, and analysis has been conducted using Monte Carlo simulation; however, Monte Carlo simulations often incur a high computational cost, are time consuming, and slow to converge. Even after dedicating the time and computational resources to perform exhaustive Monte Carlo analysis, comprehensive coverage of the uncertainty space is not assured and reasoning over the simulation results requires additional cost. The AURA-Sim approach offers the potential to provide comprehensive coverage with a single simulation run, drastically reducing the required cost. Reasoning and calculating inferential statistics from the results does not required large data sets because the simulation signals are represented as random quantities.