Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models

Makrygiorgos, Georgios; Maggioni, Giovanni Maria; Mesbah, Ali

doi:10.1016/j.compchemeng.2020.106814

Cited by 16 publications

(17 citation statements)

References 63 publications

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“…A sensitivity analysis that quantifies the combined effect of all the uncertain parameters on the performance of simulated systems was performed [41,59,60].…”

Section: Global Sensitivity Analysismentioning

confidence: 99%

“…The partial and total variance are traditionally derived by evaluating the computational model M with an MCS. For a non-intrusive UQ analysis of static deterministic models, MCS takes 10 4 to 10 6 evaluations to get accurate statistics on the moments (mean and standard deviation) [35,37,39,41,44,59,61,62].…”

Section: Global Sensitivity Analysismentioning

confidence: 99%

“…We refer to Example 3.3.3 of Wu et al on combining different orthogonal polynomials when constructing the metamodel [59]. This static UQ analysis can then be extended to the so-called time-frozen PCE, where the PCE algorithm creates a metamodel at each timestep [41,68]. To analytically determine the mean and standard deviation of the NH 3 production at a time t in a computationally efficient way, we refer to the work of [41,43,[68][69][70][71].…”

Section: Global Sensitivity Analysismentioning

confidence: 99%

“…To quantify the effect of uncertainties on the performance, we need to minimize the computational cost while attaining a high accuracy. The study of Bhonsale et al [39] and Makrygiorgos et al [41] show the advantages of using non-intrusive Polynomial Chaos Expansion-based (PCE) algorithms over brute-force Monte Carlo Simulations (MCS) for uncertainty quantification in dynamic models. This PCE algorithm can be enhanced by implementing advanced sampling methods to increase the precision of the UQ analysis [42].…”

Section: Introductionmentioning

confidence: 99%

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How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)

Verleysen

Parente

Contino

2021

Energy

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The transition towards a sustainable energy sector depends on how we safely manage the transport and storage of energy to keep up with the demand. Large storage (TWh) of renewable energy can be accomplished by producing an energy carrier like ammonia. This power-to-ammonia production process overly depends on the stability of the ammonia reactor where any variations induced by uncertainties could have a large impact on the performance during its dynamic operations. To determine the effect of these variations, we need to identify which of the uncertainties have to be scrutinized during model design. The current work carries out the development of a dynamic Haber-Bosch process, implementing uncertainties in the model and performing an uncertainty quantification analysis on the process. Subsequently, the sensitivity indices quantify the impact of these uncertainties on the design during ramp-up. The global sensitivity analysis indicated that the reactor inlet temperature has the most considerable impact on the performance during ramp-up, where the hydrogen/nitrogen ratio has the second most significant impact. We see that the uncertainty on the

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“…A sensitivity analysis that quantifies the combined effect of all the uncertain parameters on the performance of simulated systems was performed [41,59,60].…”

Section: Global Sensitivity Analysismentioning

confidence: 99%

Section: Global Sensitivity Analysismentioning

confidence: 99%

Section: Global Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)

Verleysen

Parente

Contino

2021

Energy

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“…A sample-based approach is then utilized for the computation of the expected utility for a given design via an optimal stochastic collocation scheme for numerical integration over the domain of uncertain parameters. The quadrature rule is built upon the notion of orthogonal polynomials, which has been extensively used in the approximation of functions of random variables [20]. It is known that the complexity of optimization problems in a nonconvex and global optimization framework scales exponentially with the number of decision variables.…”

Section: Introductionmentioning

confidence: 99%

Tractable Global Solutions to Bayesian Optimal Experiment Design

Rodrigues

Makrygiorgos

Mesbah

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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Optimal experiment design (OED) aims to optimize the information content of experimental observations for various types of applications by designing the experimental conditions. In Bayesian OED for parameter estimation, the design selection is based on an expected utility metric that accounts for the joint probability distribution of the uncertain parameters and the observations. This work presents an approximation of the Bayesian OED problem based on Kullback-Leibler divergence that is amenable to global optimization. The experiment design adopts a parsimonious input parametrization that reduces the number of design variables. This leads to a tractable polynomial optimization problem that can be solved to global optimality via the concept of sum-of-squares polynomials.

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Adversarially robust Bayesian optimization for efficient auto‐tuning of generic control structures under uncertainty

2022

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The performance of optimization‐ and learning‐based controllers critically depends on the selection of several tuning parameters that can affect the closed‐loop control performance and constraint satisfaction in highly nonlinear and nonconvex ways. Due to the black‐box nature of the relationship between tuning parameters and general closed‐loop performance measures, there has been a significant interest in automatic calibration (i.e., auto‐tuning) of complex control structures using derivative‐free optimization methods, including Bayesian optimization (BO) that can handle expensive unknown cost functions. Nevertheless, an open challenge when applying BO to auto‐tuning is how to effectively deal with uncertainties in the closed‐loop system that cannot be attributed to a lumped, small‐scale noise term. This article addresses this challenge by developing an adversarially robust BO (ARBO) method that is particularly suited to auto‐tuning problems with significant time‐invariant uncertainties in an expensive system model used for closed‐loop simulations. ARBO relies on a Gaussian process model that jointly describes the effect of the tuning parameters and uncertainties on the closed‐loop performance. From this joint Gaussian process model, ARBO uses an alternating confidence‐bound procedure to simultaneously select the next candidate tuning and uncertainty realizations, implying only one expensive closed‐loop simulation is needed at each iteration. The advantages of ARBO are demonstrated on two case studies, including an illustrative problem and auto‐tuning of a nonlinear model predictive controller using a benchmark bioreactor problem.

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Surrogate modeling for fast uncertainty quantification: Application to 2D population balance models

Cited by 16 publications

References 63 publications

How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)

How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)

Tractable Global Solutions to Bayesian Optimal Experiment Design

Adversarially robust Bayesian optimization for efficient auto‐tuning of generic control structures under uncertainty

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