Al, R.

Behera, C. R.

Gernaey, K. V.

Sin, G.

Zubov, A.

Global sensitivity analysis (GSA) provides model developers with invaluable insights into the interactions between uncertain model parameters and model output uncertainty. Among its large class of applications are identifying relevant input variables for uncertainty quantification, model quality assessment, model selection, calibration, optimization, to name a few. In the wastewater treatment modelling community, several global sensitivity analysis techniques using Monte Carlo (MC) approach has been applied. (Sin et al., 2011; Cosenza et al., 2013; Ramin et al. 2014). Although the MC approach to sensitivity analysis is relatively well established, it requires a large number of model evaluations (typically in the order 10 for variance decomposition based techniques) to estimate sensitivity indices of each parameter accurately, making its use impractical for computationally intensive models such as wastewater treatment process models. In an alternative approach, the original model behavior is approximated using computationally less costly metamodels (also referred to as surrogate models), which are then used to calculate Sobolâ€™ sensitivity indices. Two of the most efficient type of metamodels used for this purpose are polynomial chaos expansions (PCE) (Sudret, 2008) and Gaussian process (GP) models (Marrel et al., 2009).This study explores applications of these surrogate models for performing global sensitivity analysis of models used within the BSM2 framework. To this end, three different scenarios are framed. The first scenario looks into the case of uncertain influent fractionation (pollutant loads), the second into the uncertain stoichiometric and biokinetic parameters of Activated Sludge Model 1 (ASM1) whereas the third investigates sensitivity of secondary settler model to hydraulics and design related parameters. Experimental designs (i.e. learning sample) are generated using two different space-filling sampling algorithms, i.e., Latin hypercube sampling and Sobol sequence (quasi-Monte Carlo) and surrogate models of type PCA using least angle regression and GP model are constructed. Confidence intervals of the sensitivity indices are also estimated using the bootstrap method for PCE and the internal model structure of GP. Sobol sensitivity indices of metamodeling-based approach showed great similarity with those obtained from MC approach for each of the investigated scenarios, yet with much faster computation times. An experimental design size of 200 was found to be adequate to construct efficient surrogate models. Effect of using different sampling algorithms was found negligible. Further, the obtained results also suggest surrogate models can efficiently be used to replace complex mechanistic models used in wastewater treatment for complex modelling needs

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Downloaded from orbit.dtu.dk on: Mar 29, 2019Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wastewater Treatment Plant ModelingAl, Resul; Behera, Chitta Ranjan; Zubov, Alexandr; Gernaey, Krist V.; Sin, GürkanPublication date:2018Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Al, R., Behera, C. R., Zubov, A., Gernaey, K. V., & Sin, G. (2018). Improving Speed and Efficiency of GlobalSensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wastewater Treatment PlantModeling. Abstract from 2018 AIChE Annual Meeting , Pittsburgh, United States.12/12/2018 (642d) Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wast…https://www.aiche.org/conferences/aiche-annual-meeting/2018/proceeding/paper/642d-improving-speed-and-efficiency-global-sensitivity-analysis-… 1/3(642d) Improving Speed and Efficiency of GlobalSensitivity Analysis Using Metamodeling-BasedApproach: A Case Study on Wastewater Treatment PlantModelingConference: AIChE Annual MeetingYear: 2018Proceeding: 2018 AIChE Annual MeetingGroup: Environmental DivisionSession: Advanced Treatment for Water Reuse and Recycling IITime: Thursday, November 1, 2018 - 1:15pm-1:30pmAuthors: Al, R., Technical University of DenmarkBehera, C. R., Technical University of DenmarkZubov, A., Technical University of DenmarkGernaey, K. V., Technical University of DenmarkSin, G., Technical University of Denmark12/12/2018 (642d) Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wast…https://www.aiche.org/conferences/aiche-annual-meeting/2018/proceeding/paper/642d-improving-speed-and-efficiency-global-sensitivity-analysis-… 2/3Global sensitivity analysis (GSA) provides model developers with invaluable insights into the interactionsbetween uncertain model parameters and model output uncertainty. Among its large class of applicationsare identifying relevant input variables for uncertainty quantification, model quality assessment, modelselection, calibration, optimization, to name a few. In the wastewater treatment modelling community,several global sensitivity analysis techniques using Monte Carlo (MC) approach has been applied. (Sin etal., 2011; Cosenza et al., 2013; Ramin et al. 2014). Although the MC approach to sensitivity analysis isrelatively well established, it requires a large number of model evaluations (typically in the order 10  forvariance decomposition based techniques) to estimate sensitivity indices of each parameter accurately,making its use impractical for computationally intensive models such as wastewater treatment processmodels. In an alternative approach, the original model behavior is approximated using computationallyless costly metamodels (also referred to as surrogate models), which are then used to calculate Sobolâ€™sensitivity indices. Two of the most efficient type of metamodels used for this purpose are polynomialchaos expansions (PCE) (Sudret, 2008) and Gaussian process (GP) models (Marrel et al., 2009).This study explores applications of these surrogate models for performing global sensitivity analysis ofmodels used within the BSM2 framework. To this end, three different scenarios are framed. The firstscenario looks into the case of uncertain influent fractionation (pollutant loads), the second into theuncertain stoichiometric and biokinetic parameters of Activated Sludge Model 1 (ASM1) whereas thethird investigates sensitivity of secondary settler model to hydraulics and design related parameters.Experimental designs (i.e. learning sample) are generated using two different space-filling samplingalgorithms, i.e., Latin hypercube sampling and Sobol sequence (quasi-Monte Carlo) and surrogatemodels of type PCA using least angle regression and GP model are constructed. Confidence intervals ofthe sensitivity indices are also estimated using the bootstrap method for PCE and the internal modelstructure of GP. Sobol sensitivity indices of metamodeling-based approach showed great similarity withthose obtained from MC approach for each of the investigated scenarios, yet with much fastercomputation times. An experimental design size of 200 was found to be adequate to construct efficientsurrogate models. Effect of using different sampling algorithms was found negligible. Further, theobtained results also suggest surrogate models can efficiently be used to replace complex mechanisticmodels used in wastewater treatment for complex modelling needs.ReferencesSin, G., Gernaey, K. V., Neumann, M. B., van Loosdrecht, M. C. M., & Gujer, W. (2011). Global sensitivityanalysis in wastewater treatment plant model applications: Prioritizing sources of uncertainty. WaterResearch, 45(2), 639â€“651. https://doi.org/10.1016/j.watres.2010.08.025Cosenza, A., Mannina, G., Vanrolleghem, P. A., & Neumann, M. B. (2013). Global sensitivity analysis inwastewater applications: A comprehensive comparison of different methods. Environmental Modellingand Software, 49, 40â€“52. https://doi.org/10.1016/j.envsoft.2013.07.009Ramin, E., Flores-Alsina, X., Sin, G., Gernaey, K. V., Jeppsson, U., Mikkelsen, P. S., & PlÃ³sz, B. G.(2014). Influence of selecting secondary settling tank sub-models on the calibration of WWTP models â€“A global sensitivity analysis using BSM2. Chemical Engineering Journal, 241, 28â€“34.https://doi.org/10.1016/j.cej.2013.12.015Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineeringand System Safety, 93(7), 964â€“979. https://doi.org/10.1016/j.ress.2007.04.002Marrel, A., Iooss, B., Laurent, B., & Roustant, O. (2009). Calculations of Sobol indices for the Gaussianprocess metamodel. Reliability Engineering & System Safety, 94(3), 742â€“751.https://doi.org/10.1016/j.ress.2008.07.008412/12/2018 (642d) Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wast…https://www.aiche.org/conferences/aiche-annual-meeting/2018/proceeding/paper/642d-improving-speed-and-efficiency-global-sensitivity-analysis-… 3/3Topics: Water (Sustainability & Environment)

Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wastewater Treatment Plant Modeling

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Improving Speed and Efficiency of Global Sensitivity Analysis Using Metamodeling-Based Approach: A Case Study on Wastewater Treatment Plant Modeling

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