Surrogate Based Sensitivity Analysis of Process Equipment

The computational cost associated with the use of highfidelity Computational Fluid Dynamics (CFD) models poses a serious impediment to the successful application of formal sensitivity analysis in engineering design. Even though advances in computing hardware and parallel processing have reduced costs by orders of magnitude over the last few decades, the fidelity with which engineers desire to model engineering systems has also increased considerably. Evaluation of such high-fidelity models may take significant computational time for complex geometries. In many engineering design problems, thousands of function evaluations may be required to undertake a sensitivity analysis. As a result, CFD models are often impractical to use for design sensitivity analyses. In contrast, surrogate models are compact and cheap to evaluate (order of seconds or less) and can therefore be easily used for such tasks. This paper discusses and demonstrates the application of several common surrogate modelling techniques to a CFD model of flocculant adsorption in an industrial thickener. Results from conducting sensitivity analyses on the surrogates are also presented. NOMENCLATURE A radial angle between flocculant sparge and feed pipe j A Fourier coefficients b LS-SVM model parameter l j b neuron bias B vertical location of flocculant sparge j B Fourier coefficients C distance from feedwell wall to flocculant sparge D variance k e acceptable error ( ) E y expectation of y F ANN activation function i G transformation functions K RBF kernel function N number of sample points or number of neurons in ANN p integer number s real number S main effect ST total effect u input to neuron ( ) V y variance of y w LS-SVM model parameter