Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach

Abstract

a b s t r a c tUncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol's sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.

A two-stage approach of multiplicative dimensional reduction and polynomial chaos for global sensitivity analysis and uncertainty quantification with a large number of process uncertainties

“…Assume that n<N important inputs are detected from SA in the previous step. The following polynomial chaos based method 8 can be used for UQ. The unimportant inputs are fixed to their nominal value.…”

“…Probabilistic approaches, such as Monte-Carlo (MC) and Quasi Monte-Carlo (QMC) methods, provide a common framework for the uncertainty quantification (UQ) and uncertainty propagation (UP) in the model input to its output [4][5][6][7] . MC/QMC methods generate an ensemble of random realizations from its uncertainty distribution to evaluate the model for each element of a sample set and estimate the relevant statistical properties, such as the mean, standard deviation, and quantile of output 8 . Furthermore, it can examine the different parameter values one by one and combinations using a more comprehensive approach, performing a global sensitivity analysis 9 .…”

“…Currently, there is growing demand for computationally efficient surrogate models 14 that can ensure an acceptable degree of accuracy 15 . Similarly, quantifying the dependence on the uncertain parameters using a surrogate model for generalized polynomial chaos (gPC) expansion achieved faster convergence rate in various areas, such as modeling, control, robust optimal design, and fault detection problems 8 . The gPC method, which was first proposed by Wiener 16 , is a spectral expansion of a random process based on the orthonormal polynomials in terms of the random variables.…”

“…A current limitation of the standard full gPC approach, where the coefficients are estimated using the tensor cubature, is that the number of model evaluations grows exponentially and may not be applicable to systems with a moderate/large number of uncertainties. In this paper, to overcome this computational limitation in the conventional approaches, a two-stage approach was proposed using the multiplicative dimensional reduction method (M-DRM) 24 and the standard gPC method 8 . In the proposed approach, the M-DRM was first used to detect important inputs by approximating a complicated function of random variables as a derivation of the univariate functions.…”

A robust feeding strategy to maintain set‐point glucose in mammalian fed‐batch cultures when input parameters have a large error

“…Examples are found in the aviation industry (flight trajectories), 7 financial technologies (price bidding on the energy market from renewable but unstable energy sources), 8 to classical chemical processes (syngas production). 9 Often, uncertainty is addressed using Monte-Carlo sampling from a probability distribution 10 ; in more advanced cases polynomial chaos expansion is applied when dealing with computationally intense problems. 11,12 Adding uncertainty to simulations allows to make better statements about its output and adds a layer of confidence to its results.…”