Robust optimization of chemical processes using a MADS algorithm (original) (raw)

A Polynomial-Chaos Based Algorithm for Robust Optimization in the Presence of Bayesian Uncertainty

2012

The paper presents a computationally efficient approach for solving a robust optimization problem in the presence of parametric uncertainties, where the uncertainty description is obtained using the Bayes' Theorem. The approach is based on Polynomial Chaos Expansions (PCE) that are used to propagate the uncertainty into the objective function for each function evaluation, resulting in significant reduction in the computational time when compared to Monte Carlo sampling. A fed-batch process for penicillin production is used as a case study to illustrate the strength of the methodology both in terms of computational efficiency as well as in terms of accuracy when compared to results obtained with more simplistic (e.g. normal) representations of parametric uncertainty.

Uncertainty quantification and global sensitivity analysis of complex chemical processes with a large number of input parameters using compressive polynomial chaos

Chemical Engineering Research and Design, 2016

Uncertainties are ubiquitous and unavoidable in process design and modeling while they can significantly affect safety, reliability, and economic decisions. The large number of uncertainties in complex chemical processes make the well-known Monte-Carlo and polynomial chaos approaches for uncertainty quantification computationally expensive and even infeasible. This study focused on the uncertainty quantification and sensitivity analysis of complex chemical processes with a large number of uncertainties. An efficient method was proposed using a compressed sensing technique to overcome the computational limitations for complex and large scale systems. In the proposed method, compressive sparse polynomial chaos surrogates were constructed and applied to quantify the uncertainties and reflect their propagation effect on process design. Rigorous case studies were provided by the interface between MATLAB TM and Aspen HYSYS TM for a propylene glycol production process and lean dry gas processing plant. The proposed methodology was compared with traditional Monte-Carlo/Quasi Monte-Carlo sampling-based and standard polynomial chaos approaches to highlight its advantages in terms of computational efficiency. The proposed approach could mitigate the simulation costs significantly using an accurate, efficient-to-evaluate polynomial chaos that can be used in place of expensive simulations. In addition, the global sensitivity indices, which show the relative importance of uncertain inputs on the process output, could be derived analytically from the obtained polynomial chaos surrogate model.

Sparse Bayesian learning for data driven polynomial chaos expansion with application to chemical processes

Chemical Engineering Research and Design, 2018

Uncertainties are ubiquitous in process system engineering. Hence, to develop a safe and profitable process, uncertainty quantification (UQ) is necessary in a reliability, availability, and maintainability (RAM) analysis. Generalized polynomial chaos expansions can be used as an efficient approach to UQ and work efficiently under the assumption of perfect knowledge with regard to the probability density distribution function of uncertainties. However, this assumption can hardly be satisfied in a real process scenario, mainly because of the limited knowledge regarding the probability density distribution function of uncertainties. To solve these issues, this study investigates the performance of orthogonal polynomial chaos in the UQ of chemical processes, including synthesis gas production and natural gas dehydration. Simultaneously, the limitations of orthogonal polynomial chaos were also investigated by an overwhelming sparse Bayesian learning approach considering a complicated nonlinear crude oil distillation unit with moderate uncertainty numbers. We found that the application of orthogonal polynomial chaos was limited to a small number of uncertainties, mainly because of using the polynomial's tensor product. Finally, the orthogonal polynomial chaos and sparse Bayesian learning approach were rendered computationally effective in comparison with the conventional Monte Carlo method (approximately 96.5% improvement).

Quantifying uncertainty in chemical systems modeling

International Journal of Chemical Kinetics, 2005

This study compares two techniques for uncertainty quantification in chemistry computations, one based on sensitivity analysis and error-propagation, and the other on stochastic analysis using polynomial chaos techniques. The two constructions are studied in the context of H 2 -O 2 ignition under supercritical-water conditions. They are compared in terms of their prediction of uncertainty in species concentrations and the sensitivity of selected species concentrations to given parameters. The formulation is extended to 1-D reacting-flow simulations. The computations are used to study sensitivities to both reaction rate preexponentials and enthalpies, and to examine how this information must be evaluated in light of known, inherent parametric uncertainties in simulation parameters. The results indicate that polynomial chaos methods provide similar firstorder information to conventional sensitivity analysis, while preserving higher-order information that is needed for accurate uncertainty quantification and for assigning confidence intervals on sensitivity coefficients. These higher-order effects can be significant, as the analysis reveals substantial uncertainties in the sensitivity coefficients themselves.

Uncertainty quantification in chemical systems

International Journal for Numerical Methods in Engineering, 2009

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.

Uncertainty in chemical process systems engineering: a critical review

Reviews in Chemical Engineering, 2019

Uncertainty or error occurs as a result of a lack or misuse of knowledge about specific topics or situations. In this review, we recall the differences between error and uncertainty briefly, first, and then their probable sources. Then, their identifications and management in chemical process design, optimization, control, and fault detection and diagnosis are illustrated. Furthermore, because of the large amount of information that can be obtained in modern plants, accurate analysis and evaluation of those pieces of information have undeniable effects on the uncertainty in the system. Moreover, the origins of uncertainty and error in simulation and modeling are also presented. We show that in a multidisciplinary modeling approach, every single step can be a potential source of uncertainty, which can merge into each other and generate unreliable results. In addition, some uncertainty analysis and evaluation methods are briefly presented. Finally, guidelines for future research are proposed based on existing research gaps, which we believe will pave the way to innovative process designs based on more reliable, efficient, and feasible optimum planning.

Bayesian Sensitivity Analysis and Uncertainty Integration for Robust Optimization

This paper presents a comprehensive methodology that combines uncertainty quantification, uncertainty propagation and design optimization using a Bayesian framework. The epistemic uncertainty due to input data uncertainty is considered. Two types of uncertainty models for input variables and/or their distribution parameters are addressed: (1) uncertainty modeled as family of distributions, and (2) uncertainty modeled as interval data. A Bayesian approach is adopted to update the uncertainty models, where the likelihood functions are constructed using limited experimental data. Global sensitivity analysis (GSA), which previously only considered aleatory inputs in the context of probabilistic representation, is extended in this paper to quantify the contributions of both aleatory and epistemic uncertainty sources for multi-output problems, using an auxiliary variable approach. Gaussian Process (GP) surrogate modeling is employed to replace the expensive physics models and improve the computational efficiency. A previously developed bias minimization technique, which only dealt with single output functions, is extended to reduce the surrogate model error for a multi-output function. A decoupled robustness-based design optimization framework is developed to include both aleatory and epistemic uncertainty. The proposed methodology is illustrated using the NASA Langley multidisciplinary uncertainty quantification challenge problem.

Erratum: Uncertainty quantification in chemical systems

International Journal for Numerical Methods in Engineering, 2011

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.