Uncertainty appears in many aspects of chemical and process engineering including stochastic design parameters, variable inputs, and unknown forcing functions derived from both internal and external factors. Uncertainty Quantification (UQ) has emerged as the science of quantitative characterization and reduction of uncertainties in both simulation and testing. Stretching across applied mathematics, statistics, and engineering, UQ is a multidisciplinary field with a broad base of methods including sensitivity analysis, statistical calibration, uncertainty propagation, and inverse analysis. Many of these methods treat simulations as black boxes, enabling widespread use across disparate industries and application to both individual component and system level design. Because of their ability to determine degrees of confidence in simulation results in the face of uncertain inputs, UQ methods are playing an ever larger role in decision making, robust design, design for variation, and risk reduction.
The paper introduces Uncertainty Quantification (UQ) techniques from applied mathematics and statistics and outlines UQ work flows in design. The techniques introduced include sparse grids, generalized polynomial chaos, and statistical emulation. Many UQ techniques require large numbers of input/output points and emulators (aka surrogate models or meta-models) are often used as proxies in order to save computational cost. The larger and more complex the simulation, the more advantage is gained from the use of emulation. However, common emulation techniques encounter serious numerical issues for complex large scale problems. A theoretical framework for understanding and solving these difficulties is presented. Further UQ methods for handling problems with functional responses and qualitative factors will also be discussed. The application of these methods, as well as uncertainty propagation, sensitivity analysis, and statistical calibration, are illustrated using examples from Chemical Reaction engineering, mixer and heat exchanger design, and process and plant engineering.
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