A Comparison of Surrogate Modeling Techniques for Global Sensitivity Analysis in Hybrid Simulation

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation is extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation are conceived as being deterministic. However, associated uncertainties are present, whilst simulation deviation, due to their presence, could be significant. In this regard, global sensitivity analysis based on Sobol’ indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol’ sensitivity indices requires an unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques using machine learning data-driven regression are utilized to alleviate this burden. This study extends the current global sensitivity analysis practices in hybrid simulation by employing various different surrogate modeling methodologies as well as providing comparative results. In particular, polynomial chaos expansion, Kriging and polynomial chaos Kriging are used. A case study encompassing a virtual hybrid model is employed, and hybrid model response quantities of interest are selected. Their respective surrogates are developed, using all three aforementioned techniques. The Sobol’ indices obtained utilizing each examined surrogate are compared with each other, and the results highlight potential deviations when different surrogates are used.

How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model? Application to the PESHMELBA model

Pesticide transfers in agricultural catchments are responsible for diffuse but major risks to water quality. Spatialized pesticide transfer models are useful tools to assess the impact of the structure of the landscape on water quality. Before considering using these tools in operational contexts, quantifying their uncertainties is a preliminary necessary step. In this study, we explored how global sensitivity analysis can be applied to the recent PESHMELBA pesticide transfer model to quantify uncertainties on transfer simulations. We set up a virtual catchment based on a real one and we compared different approaches for sensitivity analysis that could handle the specificities of the model: high number of input parameters, limited size of sample due to computational cost and spatialized output. We compared Sobol' indices obtained from Polynomial Chaos Expansion, HSIC dependence measures and feature importance measures obtained from Random Forest surrogate model. Results showed the consistency of the different methods and they highlighted the relevance of Sobol' indices to capture interactions between parameters. Sensitivity indices were first computed for each landscape element (site sensitivity indices). Second, we proposed to aggregate them at the hillslope and the catchment scale in order to get a summary of the model sensitivity and a valuable insight into the model hydrodynamical behaviour. The methodology proposed in this paper may be extended to other modular and distributed hydrological models as there has been a growing interest in these methods in recent years.

lca_algebraic: a library bringing symbolic calculus to LCA for comprehensive sensitivity analysis

Purpose In this paper, we present new tools to ease the analysis of the effect of variability and uncertainty on life cycle assessment (LCA) results. Methods The tools consist of a standard protocol and an open-source library: lca_algebraic. This library, written in Python and based on the framework Brightway2 (Mutel in J Open Source Softw 2(12):236, 2017) provides functions to support sensitivity analysis by bringing symbolic calculus to LCA. The use of symbolic calculus eases the definition of parametric inventories and enables a very fast evaluation of impacts by factorizing the background activities. Thanks to this processing speed, a large number of Monte Carlo simulations can be generated to evaluate the variation of the impacts and apply advanced statistic tools such as Sobol indices to quantify the contribution of each parameter to the final variance (Sobol in Math Comput Simul 55(1–3):271–280, 2001). An additional algorithm uses the key parameters, identified from their high Sobol indices, to generate simplified arithmetic models for fast estimates of LCA results. Results and discussion The protocol and library were validated through their application to the assessment of impacts of mono crystalline photovoltaic (PV) systems. A comprehensive sensitivity analysis was performed based on the protocol and the complementary functions provided by lca_algebraic. The proposed tools helped building a detailed parametric reference LCA model of the PV system to identify the range of variation of multi-criterion LCA results and the key foreground-related parameters explaining these variations. Based on these key parameters, we generated simplified arithmetic models for quick and simple multi-criteria environmental assessments to be used by non-expert LCA users. The resulting models are both compact and aligned with the reference parametric LCA model of crystalline silicon PV systems. Conclusion This work brings powerful and practical tools to the LCA community to better understand, identify, and quantify the sources of variation of environmental impacts and produce simplified models to spread the use of LCA among non-experts. The library mainly explores the uncertainties of the foreground activities. Further work could also integrate the uncertainty of background activities, described, for example, by pedigree matrices.

Quantifying Component Importance for Disaster Resilience of Communities with Interdependent Civil Infrastructure Systems

Communities and their supporting civil infrastructure systems can be viewed as an assembly of, often numerous, interacting components. Tools that can identify components relevant for community disaster resilience can help to efficiently allocate limited resources to reach community resilience goals. We use Sobol’ indices to measure the importance of vulnerability and recoverability of components for disaster resilience of communities with interdependent civil infrastructure systems. The initial component importance analysis requires no prior knowledge regarding component’s vulnerability and recoverability. We first rank components based on their importance, using their Sobol’ indices. Secondly, we illustrate how the results of the component importance analysis can be used to improve community disaster resilience. Finally, we use component importance to show how model complexity can be reduced by abstracting less important components.

A survey of surrogate modeling techniques for global sensitivity analysis in hybrid simulation

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual loading-rate-sensitive substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation has been extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation is conceived as deterministic. However, associated uncertainties are present whilst simulation deviation due to their presence could be significant. To this regard, global sensitivity analysis based on Sobol' indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol' sensitivity indices requires unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques are used to alleviate this burden. In this paper, three different surrogate modeling methods are examined, namely polynomial chaos expansion, Kriging and polynomial chaos Kriging. A case study encompassing a virtual hybrid model is employed and hybrid model response quantities of interest are selected. Their respective surrogates are developed using all three aforementioned techniques. The Sobol' indices obtained utilizing each examined surrogate are compared with each other and results highlight potential deviations.

Variance-based global sensitivity analysis and beyond in life cycle assessment: an application to geothermal heating networks

Purpose Global sensitivity analysis increasingly replaces manual sensitivity analysis in life cycle assessment (LCA). Variance-based global sensitivity analysis identifies influential uncertain model input parameters by estimating so-called Sobol indices that represent each parameter’s contribution to the variance in model output. However, this technique can potentially be unreliable when analyzing non-normal model outputs, and it does not inform analysts about specific values of the model input or output that may be decision-relevant. We demonstrate three emerging methods that build on variance-based global sensitivity analysis and that can provide new insights on uncertainty in typical LCA applications that present non-normal output distributions, trade-offs between environmental impacts, and interactions between model inputs. Methods To identify influential model inputs, trade-offs, and decision-relevant interactions, we implement techniques for distribution-based global sensitivity analysis (PAWN technique), spectral clustering, and scenario discovery (patient rule induction method: PRIM). We choose these techniques because they are applicable with generic Monte Carlo sampling and common LCA software. We compare these techniques with variance-based Sobol indices, using a previously published LCA case study of geothermal heating networks. We assess eight environmental impacts under uncertainty for three design alternatives, spanning different geothermal production temperatures and heating network configurations. Results In the application case on geothermal heating networks, PAWN distribution-based sensitivity indices generally identify influential model parameters consistently with Sobol indices. However, some discrepancies highlight the potentially misleading interpretation of Sobol indices on the non-normal distributions obtained in our analysis, where variance may not meaningfully describe uncertainty. Spectral clustering highlights groups of model results that present different trade-offs between environmental impacts. Compared to second-order Sobol interaction indices, PRIM then provides more precise information regarding the combinations of input values associated with these different groups of calculated impacts. PAWN indices, spectral clustering, and PRIM have a computational advantage because they yield stable results at relatively small sample sizes (n = 12,000), unlike Sobol indices (n = 100,000 for second-order indices). Conclusions We recommend adding these new techniques to global sensitivity analysis in LCA as they give more precise as well as additional insights on uncertainty regardless of the distribution of the model outputs. PAWN distribution-based global sensitivity analysis provides a computationally efficient assessment of input sensitivities as compared to variance-based global sensitivity analysis. The combination of clustering and scenario discovery enables analysts to precisely identify combinations of input parameters or uncertainties associated with different outcomes of environmental impacts.