Optimizing TEG Dehydration Process under Metamodel Uncertainty

Natural gas processing requires the removal of acidic gases and dehydration using absorption, mainly conducted in tri-ethylene glycol (TEG). The dehydration process is accompanied by the emission of volatile organic compounds, including BTEX. In our previous work, multi-objective optimization was undertaken to determine the optimal operating conditions in terms of the process parameters that can mitigate BTEX emission using data-driven metamodeling and metaheuristic optimization. Data obtained from a process simulation conducted using the ProMax® process simulator were used to develop a metamodel with machine learning techniques to reduce the computational time of the iterations in a robust process simulation. The metamodels were created using limited samples and some underlying phenomena must therefore be excluded. This introduces the so-called metamodeling uncertainty. Thus, the performance of the resulting optimized process variables may be compromised by the lack of adequately accounting for the uncertainty introduced by the metamodel. In the present work, the bias of the metamodel uncertainty was addressed for parameter optimization. An algorithmic framework was developed for parameter optimization, given these uncertainties. In this framework, metamodel uncertainties are quantified using real model data to generate distribution functions. We then use the novel Better Optimization of Nonlinear Uncertain Systems (BONUS) algorithm to solve the problem. BTEX mitigation is used as the objective of the optimization. Our algorithm allows the determination of the optimal process condition for BTEX emission mitigation from the TEG dehydration process under metamodel uncertainty. The BONUS algorithm determines optimal process conditions compared to those from the metaheuristic method, resulting in BTEX emission mitigation up to 405.25 ton/yr.

Uncertainty Modelling in Metamodels for Fire Risk Analysis

In risk-related research of fire safety engineering, metamodels are often applied to approximate the results of complex fire and evacuation simulations. This approximation may cause epistemic uncertainties, and the inherent uncertainties of evacuation simulations may lead to aleatory uncertainties. However, neither the epistemic ‘metamodel uncertainty’ nor the aleatory ‘inherent uncertainty’ have been included in the results of the metamodels for fire safety engineering. For this reason, this paper presents a metamodel that includes metamodel uncertainty and inherent uncertainty in the results of a risk analysis. This metamodel is based on moving least squares; the metamodel uncertainty is derived from the prediction interval. The inherent uncertainty is modelled with an original approach, directly using all replications of evacuation scenarios without the assumption of a specific probability distribution. This generic metamodel was applied on a case study risk analysis of a road tunnel and showed high accuracy. It was found that metamodel uncertainty and inherent uncertainty have clear effects on the results of the risk analysis, which makes their consideration important.

Uncertainty Quantification in Metamodel-Based Reliability Prediction

Optimization under uncertainty has been studied in two directions — (1) Reliability-based Design Optimization (RBDO), and (2) Robust Design Optimization (RDO). One of the crucial elements in an RBDO problem is reliability analysis. Reliability analysis is affected by different types of epistemic uncertainty, due to inadequate data and modeling errors, along with aleatory uncertainty in input random variables. When the original physics-based model is computationally expensive, a metamodel has often been used in reliability analysis, introducing additional uncertainty due to the metamodel. This work presents a framework to include statistical uncertainty and model uncertainty in metamodel-based reliability analysis. Inadequate data causes uncertainty regarding the statistics (distribution types and distribution parameters) of the input variables, and regarding the system model parameters. Model errors include model form errors, solution approximation errors, and metamodel uncertainty. Two types of metamodels have been considered in literature for reliability analysis: (1) metamodels that compute the system model output over the desired ranges of the input random variables; and (2) metamodels that concentrate only on modeling the limit state. This work focuses on the latter type, using Gaussian process (GP) metamodels for performing both component reliability (single limit state) and system reliability (multiple limit states) analyses. A systematic procedure for the inclusion of model discrepancy terms in the limit-state metamodel construction is developed using an auxiliary variable approach. An efficient single-loop sampling approach using the probability integral transform is used for sampling the input variables with statistical uncertainty. The variability in the GP model prediction (metamodel uncertainty) is also included in reliability analysis through correlated sampling of the model predictions at different inputs. Two mechanical systems — a cantilever beam with point-load at the free end and a two-bar supported panel with point load at its center, are used to demonstrate the proposed techniques.

Simulation-based robust design of complex product considering uncertainties of metamodel, design variables, and noise parameters

The uncertainties of design variables, noise parameters, and metamodel are important factors in simulation-based robust design optimization. Most conventional metamodel construction methods only consider one or two uncertainties. In this paper, a new surrogate modeling method simultaneously measuring all the uncertainties is proposed for simulation-based robust design optimization of complex product. The effect of metamodel uncertainty on product performance uncertainty is quantified through uncertainty propagation analysis among design variables uncertainty, noise parameters uncertainty, metamodel uncertainty, and performance uncertainty. Then, the sampling points are selected and the metamodel is constructed based on the predictive interval of product performance and mean square error of the Kriging metamodel. The constructed metamodel is applied to robust design optimization considering multiple uncertainties. Results of two mathematical examples show that the proposed metamodel considering multiple uncertainties increases the result accuracy of robust design optimization. Finally, the proposed algorithm is applied to robust design optimization of a heat exchanger, and the total heat transfer rate is enhanced under uncertainties of fin structural parameters, operation conditions parameters and simulation metamodel.

Metamodel Uncertainty Quantification by Using Bayes’ Theorem

In complex engineering systems, approximation models, also called metamodels, are extensively constructed to replace the computationally expensive simulation and analysis codes. With different sample data and metamodeling methods, different metamodels can be constructed to describe the behavior of an engineering system. Then, metamodel uncertainty will arise from selecting the best metamodel from a set of alternative ones. In this study, a method based on Bayes’ theorem is used to quantify this metamodel uncertainty. With some mathematical examples, metamodels are built by six metamodeling methods, i.e., polynomial response surface, locally weighted polynomials (LWP), k-nearest neighbors (KNN), radial basis functions (RBF), multivariate adaptive regression splines (MARS), and kriging methods, and under four sampling methods, i.e., parameter study (PS), Latin hypercube sampling (LHS), optimal LHS and full factorial design (FFD) methods. The uncertainty of metamodels created by different metamodeling methods and under different sampling methods is quantified to demonstrate the process of implementing the method.

Crashworthiness-based lightweight design problem via new robust design method considering two sources of uncertainties

Metamodel-based robust design methods are commonly used to mitigate the influence of parametric uncertainty associated in sheet gauges and material properties in crashworthiness-based vehicle lightweight design. Since the crash performances are highly nonlinear and high-dimensional responses, the prediction error of metamodels inevitably introduces the so-called metamodeling uncertainty in robust design that may mislead to a wrong solution. In this article, a new robust design method considering both parametric uncertainty and metamodeling uncertainty is proposed in the autobody lightweight design problem. Six crash responses in side impact and roof crush are defined as the constraint responses. The results demonstrate that the proposed robust design method is superior to the conservative-surrogate-based robust design method. The final confirmed robust solution achieves 14.39% weight reduction. The method provides an efficient way to reduce the risk of constraint violation and avoids an over-conservative design due to metamodel uncertainty in crashworthiness-based lightweight design problems.