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

2019 ◽  
Vol 23 ◽  
pp. 387-408 ◽  
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.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

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.

Analytical global sensitivity analysis with Gaussian processes

2017 ◽  
Vol 31 (3) ◽  
pp. 235-250 ◽  
Author(s):  
Ankur Srivastava ◽  
Arun K. Subramaniyan ◽  
Liping Wang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Global Sensitivity Analysis ◽  
Decomposition Methods ◽  
Variance Decomposition ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Sobol Indices ◽  
Global Sensitivity

AbstractMethods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

Uncertainty quantification and global sensitivity analysis with dependent inputs: Application to the 2D hydraulic model of the Loire River

2020 ◽  
Author(s):  
Lucie Pheulpin ◽  
Vito Bacchi
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Large Scale ◽  
Global Sensitivity Analysis ◽  
Numerical Models ◽  
Hydraulic Model ◽  
Model Parameters ◽  
Traditional Methods ◽  
Global Sensitivity ◽  
Loire River

<p>Hydraulic models are increasingly used to assess the flooding hazard. However, all numerical models are affected by uncertainties, related to model parameters, which can be quantified through Uncertainty Quantification (UQ) and Global Sensitivity Analysis (GSA). In traditional methods of UQ and GSA, the input parameters of the numerical models are considered to be independent which is actually rarely the case. The objective of this work is to proceed with UQ and GSA methods considering dependent inputs and comparing different methodologies. At our knowledge, there is no such application in the field of 2D hydraulic modelling.</p><p>At first the uncertain parameters of the hydraulic model are classified in groups of dependent parameters. Within this aim, it is then necessary to define the copulas that better represent these groups. Finally UQ and GSA based on copulas are performed. The proposed methodology is applied to the large scale 2D hydraulic model of the Loire River. However, as the model computation is high time-consuming, we used a meta-model instead of the initial model. We compared the results coming from the traditional methods of UQ and GSA (<em>i.e.</em> without taking into account the dependencies between inputs) and the ones coming from the new methods based on copulas. The results show that the dependence between inputs should not always be neglected in UQ and GSA.</p>

Variance Based Global Sensitivity Analysis for Uncorrelated and Correlated Inputs With Gaussian Processes

2015 ◽  
Author(s):  
Ankur Srivastava ◽  
Arun K. Subramaniyan ◽  
Liping Wang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Global Sensitivity Analysis ◽  
Decomposition Methods ◽  
Variance Decomposition ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Sobol Indices ◽  
Global Sensitivity

Methods for efficient variance based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices which can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed efficiently in the Kennedy & O’Hagan framework with Gaussian Processes (GPs). These methods use the High Dimensional Model Representation (HDMR) concept for variance decomposition which presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li & Rabitz in the context of Kennedy & O’ Hagan framework with GPs. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

scholarly journals Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models

2018 ◽  
Author(s):  
Olivia Eriksson ◽  
Alexandra Jauhiainen ◽  
Sara Maad Sasane ◽  
Andrei Kramer ◽  
Anu G Nair ◽  
...  
Keyword(s):  
Experimental Data ◽  
Sensitivity Analysis ◽  
Bayesian Analysis ◽  
Uncertainty Quantification ◽  
Posterior Distribution ◽  
Global Sensitivity Analysis ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Individual Parameter ◽  
Global Sensitivity

AbstractMotivationDynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as give guidance on parameters that are essential in distinguishing different qualitative output behaviours.ResultsWe used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a global sensitivity analysis was performed on the prediction using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large and complex model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions.This approach is useful both for experimental design as well as model building.

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

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.

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

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.

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

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

<p>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.</p><p>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.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[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.</p><p>[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.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

Sign in / Sign up

Export Citation Format

Share Document