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

• Published in: Chemical engineering research & design Vol. 137; pp. 553 - 565
• Main Authors: Luu Trung Duong, Pham, Quang Minh, Le, Abdul Qyyum, Muhammad, Lee, Moonyong
• Format: Journal Article
• Language: English
• Published: Rugby Elsevier B.V 01-09-2018; Elsevier Science Ltd
• Subjects: Bayesian analysis; Chemical reactions; Crude oil; Crude oil distillation unit; Data driven; Dehydration; Density distribution; Distillation; Distribution functions; Machine learning; Maintainability; Monte Carlo simulation; Natural gas; Natural gas dehydration; Natural gas industry; Organic chemistry; Polynomial chaos; Polynomials; Reliability analysis; Synthesis gas; Synthesis gas production; Tensors; Uncertainty; Uncertainty quantification; Uncertainty quantification; Data driven; Polynomial chaos; Natural gas dehydration; Synthesis gas production; Crude oil distillation unit
• ISSN: 0263-8762; 1744-3563
• DOI: 10.1016/j.cherd.2018.08.006

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•Uncertainty quantification is studied for processes with small/moderate number of uncertainties.•A data driven polynomial chaos approach (DD-gPC) is examined for small number of uncertainties.•A sparse DD-gPC from sparse Bayesian learning is applied for moderate number of uncertainties.•The proposed methods provide well-matched results with the conventional Monte-Carlo (MC) approach.•The proposed methods improve computational efficiency significantly over the MC method.
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).