A new methodology for the estimation of total uncertainty in computational simulation

Abstract

INTRODUCTION This paper develops a general methodology for estimating the total uncertainty in computational simulations that deal with the numerical solution of a system of partial differential equations. A comprehensive, new view of the general phases of modeling and simulation is proposed, consisting of the following phases: conceptual modeling of the physical system, mathematical modeling of -the conceptual model, discretization and algorithm selection for the mathematical model, computer programming of the discrete model, numerical solution of the computer program model, and representation of the numerical solution. In each of these phases, general sources of variability, uncertainty, and error are identified. Our general methodology is applicable to any discretization procedure for solving ordinary or partial differential equations. To demonstrate this methodology, we describe a system-level analysis of an unguided, rocket-boosted, aircraft-launched missile. In the conceptual modeling phase, a wide variety of analysis options are considered, but only one branch of the analysis is computed: rigid body flight dynamics. We choose two parameters as nondeterministic elements of the system: one has variability that is treated probabilistically and one has uncertainty that is represented as a set of possible alternatives. To illustrate mathematical modeling uncertainty, we pursue two models with differing levels of physics: a six-degree-of-freedom and a three-degree-of- freedom model. We also examine numerical solution error in the analysis, which is ubiquitous in computational simulations. Historically the primary method of evaluating the performance of a proposed system design has been to build the design and then test it in the use environment. This testing process is often iterative, as design flaws are sequentially discovered and corrected. The number of design-test iterations has been reduced with the advent of computer simulation through numerical solution of the mathematical equations describing the system behavior. Computational results can identify some flaws and they avoid the difficulty or safety issues involved in conducting certain types of physical tests. Examples include the atmospheric entry of a space probe into another planet, structural failure of a full-scale containment vessel of a nuclear power plant, failure of a bridge during an earthquake, and exposure of a nuclear weapon to certain types of accident environments. Modeling and simulation are valuable tools in assessing the survivability and vulnerability of complex systems to either natural, abnormal, and hostile events. However, there still remains the need to assess the accuracy of simulations by comparing computational predictions with experimental test data through the process known as validation of computational simulations. Experimental validation, however, is continually increasing in cost and time rcquircd to conduct the test. For these reason modeling and simulation must take increasing responsibility for the safety, performance, and reliability of many high consequence systems.

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