Mathematical models are core technologies for improving production efficiency, lowering operating costs and reducing environmental impacts of modern manufacturing processes. While more powerful computers have enabled additional details to be incorporated into individual models a more serious problem has emerged. What is now limiting how fast a solution can be obtained is not the computer capability but the time needed to build and analyze the models themselves. Indeed, one of the inevitable consequences of using models is that approximations and uncertainties are involved. The issue is not that there are uncertainties, they are always present, the real challenge is to identify those inputs that have the most influence on the predictions. This information is vital for deciding how to allocate resources for additional experiments, prototypes or building better models. When the models are large, or when there are many parameters, even the best Monte Carlo, or importance based sampling methods for uncertainty analysis can be prohibitively expensive. One consequence is that systematic uncertainty analyses are often never carried out. This presentation will describe a set of practical tools for performing systematic uncertainty analysis of complex models and their use in decision making. The methodology is based on a new computational efficient method for uncertainty analysis called the Deterministically Equivalent Modeling Method (DEMM) that is based on transforming the stochastic model into an equivalent deterministic form. A key output from the algorithm is the probability distribution of the output responses given the descriptions of the uncertain input parameters. The method is two to four orders of magnitude faster than traditional Monte Carlo methods and it can also determine the contributions of individual parameters to the variance in the model predictions. The seminar will also describe how the uncertainty analysis methods can be used to develop model-based approaches to experimental design, hypothesis testing and decision making.

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1999-2000 Reactive Flow and Transport Phenomena