Rigorous uncertainty quantification without integral testing
We describe a rigorous approach for certifying the safe operation of complex systems that bypasses the need for integral testing. We specifically consider systems that have a modular structure. These systems are composed of subsystems, or components, that interact through unidirectional interfaces. We show that, for systems that have the structure of an acyclic graph, it is possible to obtain rigorous upper bounds on the probability of failure of the entire system from an uncertainty analysis of the individual components and their interfaces and without the need for integral testing. Certification is then achieved if the probability of failure upper bound is below an acceptable failure tolerance. We demonstrate the approach by means of an example concerned with the performance of a fractal electric circuit.
© 2011 Elsevier Ltd. Received 20 February 2010; revised 16 July 2010; accepted 26 July 2010. Available online 8 April 2011. The authors gratefully acknowledge the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. UT gratefully acknowledges support from the Boeing Corporation.