Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

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

10.5194/gmd-2021-425 ◽

2021 ◽

Author(s):

Emilie Rouzies ◽

Claire Lauvernet ◽

Bruno Sudret ◽

Arthur Vidard

Keyword(s):

Water Quality ◽

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Transfer Model ◽

Valuable Insight ◽

Catchment Scale ◽

Sobol Indices ◽

Global Sensitivity ◽

Sensitivity Indices ◽

The Impact

Abstract. 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.

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Considerations and Caveats when Applying Global Sensitivity Analysis Methods to Physiologically Based Pharmacokinetic Models

The AAPS Journal ◽

10.1208/s12248-020-00480-x ◽

2020 ◽

Vol 22 (5) ◽

Author(s):

Dan Liu ◽

Linzhong Li ◽

Amin Rostami-Hodjegan ◽

Frederic Y. Bois ◽

Masoud Jamei

Keyword(s):

Sensitivity Analysis ◽

Plasma Concentration ◽

Global Sensitivity Analysis ◽

Model Parameters ◽

Model Parameter ◽

Global Sensitivity ◽

Physiologically Based ◽

The Impact ◽

Influential Parameters

Abstract Three global sensitivity analysis (GSA) methods (Morris, Sobol and extended Sobol) are applied to a minimal physiologically based PK (mPBPK) model using three model drugs given orally, namely quinidine, alprazolam, and midazolam. We investigated how correlations among input parameters affect the determination of the key parameters influencing pharmacokinetic (PK) properties of general interest, i.e., the maximal plasma concentration (Cmax) time at which Cmax is reached (Tmax), and area under plasma concentration (AUC). The influential parameters determined by the Morris and Sobol methods (suitable for independent model parameters) were compared to those determined by the extended Sobol method (which considers model parameter correlations). For the three drugs investigated, the Morris method was as informative as the Sobol method. The extended Sobol method identified different sets of influential parameters to Morris and Sobol. These methods overestimated the influence of volume of distribution at steady state (Vss) on AUC24h for quinidine and alprazolam. They also underestimated the effect of volume of liver (Vliver) for all three drugs, the impact of enzyme intrinsic clearance of CYP2C9 and CYP2E1 for quinidine, and that of UGT1A4 abundance for midazolam. Our investigation showed that the interpretation of GSA results is not straightforward. Dismissing existing model parameter correlations, GSA methods such as Morris and Sobol can lead to biased determination of the key parameters for the selected outputs of interest. Decisions regarding parameters’ influence (or otherwise) should be made in light of available knowledge including the model assumptions, GSA method limitations, and inter-correlations between model parameters, particularly in complex models.

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Probabilistic Analysis of a Metamorphic Mechanism Based on a Global Sensitivity Analysis: A Preliminary Study

Volume 5A: 41st Mechanisms and Robotics Conference ◽

10.1115/detc2017-67322 ◽

2017 ◽

Author(s):

Sarah C. Baxter ◽

Philip A. Voglewede

Keyword(s):

Sensitivity Analysis ◽

Probabilistic Analysis ◽

Global Sensitivity Analysis ◽

Kinematic Model ◽

Mathematical Structure ◽

Motion Path ◽

Model Parameters ◽

Global Sensitivity ◽

Sensitivity Indices ◽

The Impact

Mathematical modeling is an important part of the engineering design cycle. Most models require application specific input parameters that are established by calculation or experiment. The accuracy of model predictions depends on underlying model assumptions as well as how uncertainty in knowledge of the parameters is transmitted through the mathematical structure of the model. Knowledge about the relative impact of individual parameters can help establish priorities in developing/choosing specific parameters and provide insight into a range of parameters that produce ‘equally good’ designs. In this work Global Sensitivity Analysis (GSA) is examined as a technique that can contribute to this insight by developing Sensitivity Indices, a measure of the relative importance, for each parameter. The approach is illustrated on a kinematic model of a metamorphic 4-bar mechanism. The model parameters are the lengths of the four links. The results of this probabilistic analysis highlight the synergy that must exist between all four link lengths to create a design that can follow the desired motion path. The impact of individual link lengths, however, rises and falls depending on where the mechanism is along its motion path.

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On the consistency of Sobol indices with respect to stochastic ordering of model parameters

ESAIM Probability and Statistics ◽

10.1051/ps/2018001 ◽

2019 ◽

Vol 23 ◽

pp. 387-408 ◽

Cited By ~ 2

Author(s):

A. Cousin ◽

A. Janon ◽

V. Maume-Deschamps ◽

I. Niang

Keyword(s):

Sensitivity Analysis ◽

Uncertainty Quantification ◽

Global Sensitivity Analysis ◽

Stochastic Ordering ◽

Variance Decomposition ◽

Stochastic Orders ◽

Model Parameters ◽

Sobol Indices ◽

Global Sensitivity ◽

The Past

In the past decade, Sobol’s variance decomposition has been used as a tool to assess how the output of a model is affected by the uncertainty on its input parameters. We show some links between global sensitivity analysis and stochastic ordering theory. More specifically, we study the influence of inputs’ distributions on Sobol indices in relation with stochastic orders. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others.

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Global sensitivity analysis for a stochastic flow problem

Monte Carlo Methods and Applications ◽

10.1515/mcma-2018-2022 ◽

2018 ◽

Vol 24 (4) ◽

pp. 263-270

Author(s):

Dmitriy Kolyukhin

Keyword(s):

Sensitivity Analysis ◽

Single Phase ◽

Global Sensitivity Analysis ◽

Numerical Procedure ◽

Model Parameters ◽

Saturated Porous Media ◽

Global Sensitivity ◽

Flow Through ◽

The Impact ◽

Total Model

Abstract The paper is devoted to the modeling of a single-phase flow through saturated porous media. A statistical approach where permeability is considered as a lognormal random field is applied. The impact of permeability, random boundary conditions and wells pressure on the flow in a production well is studied. A numerical procedure to generate an ensemble of realizations of the numerical solution of the problem is developed. A global sensitivity analysis is performed using Sobol indices. The impact of different model parameters on the total model uncertainty is studied.

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Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework

Hydrology and Earth System Sciences ◽

10.5194/hess-19-3153-2015 ◽

2015 ◽

Vol 19 (7) ◽

pp. 3153-3179 ◽

Cited By ~ 68

Author(s):

M. S. Raleigh ◽

J. D. Lundquist ◽

M. P. Clark

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Snow Water Equivalent ◽

Model Parameters ◽

Random Errors ◽

Global Sensitivity ◽

Error Characteristics ◽

Physically Based ◽

Snow Water ◽

The Impact

Abstract. Physically based models provide insights into key hydrologic processes but are associated with uncertainties due to deficiencies in forcing data, model parameters, and model structure. Forcing uncertainty is enhanced in snow-affected catchments, where weather stations are scarce and prone to measurement errors, and meteorological variables exhibit high variability. Hence, there is limited understanding of how forcing error characteristics affect simulations of cold region hydrology and which error characteristics are most important. Here we employ global sensitivity analysis to explore how (1) different error types (i.e., bias, random errors), (2) different error probability distributions, and (3) different error magnitudes influence physically based simulations of four snow variables (snow water equivalent, ablation rates, snow disappearance, and sublimation). We use the Sobol' global sensitivity analysis, which is typically used for model parameters but adapted here for testing model sensitivity to coexisting errors in all forcings. We quantify the Utah Energy Balance model's sensitivity to forcing errors with 1 840 000 Monte Carlo simulations across four sites and five different scenarios. Model outputs were (1) consistently more sensitive to forcing biases than random errors, (2) generally less sensitive to forcing error distributions, and (3) critically sensitive to different forcings depending on the relative magnitude of errors. For typical error magnitudes found in areas with drifting snow, precipitation bias was the most important factor for snow water equivalent, ablation rates, and snow disappearance timing, but other forcings had a more dominant impact when precipitation uncertainty was due solely to gauge undercatch. Additionally, the relative importance of forcing errors depended on the model output of interest. Sensitivity analysis can reveal which forcing error characteristics matter most for hydrologic modeling.

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Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

Journal of Elasticity ◽

10.1007/s10659-021-09833-9 ◽

2021 ◽

Author(s):

Sebastian Brandstaeter ◽

Sebastian L. Fuchs ◽

Jonas Biehler ◽

Roland C. Aydin ◽

Wolfgang A. Wall ◽

...

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Model Parameters ◽

Computational Studies ◽

Growth And Remodeling ◽

Global Sensitivity ◽

Output Variability ◽

Constrained Mixture ◽

The One ◽

Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

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

The International Journal of Life Cycle Assessment ◽

10.1007/s11367-021-01921-1 ◽

2021 ◽

Author(s):

Marc Jaxa-Rozen ◽

Astu Sam Pratiwi ◽

Evelina Trutnevyte

Keyword(s):

Sensitivity Analysis ◽

Life Cycle Assessment ◽

Environmental Impacts ◽

Spectral Clustering ◽

Global Sensitivity Analysis ◽

Sobol Indices ◽

Global Sensitivity ◽

Geothermal Heating ◽

Trade Offs ◽

Heating Networks

Abstract 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.

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Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

10.5194/egusphere-egu21-6131 ◽

2021 ◽

Author(s):

Sabine M. Spiessl ◽

Dirk-A. Becker ◽

Sergei Kucherenko

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Higher Order ◽

Model Parameters ◽

High Dimensional Model Representation ◽

Model Output ◽

Global Sensitivity ◽

Sparse Polynomial ◽

Sensitivity Indices ◽

Highly Nonlinear

Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.

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