scholarly journals Moment-based Metrics for Global Sensitivity Analysis of Hydrological Systems

2017 ◽  
Author(s):  
Aronne Dell'Oca ◽  
Monica Riva ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Original System ◽  
Model Complexity ◽  
Model Output ◽  
Global Sensitivity ◽  
Reduction Techniques ◽  
The Impact

Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized Polynomial Chaos Expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer, and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. Our approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.

scholarly journals Moment-based metrics for global sensitivity analysis of hydrological systems

2017 ◽  
Vol 21 (12) ◽  
pp. 6219-6234 ◽  
Author(s):  
Aronne Dell'Oca ◽  
Monica Riva ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Original System ◽  
Model Complexity ◽  
Model Output ◽  
Global Sensitivity ◽  
Reduction Techniques ◽  
The Impact

Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher-order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized polynomial chaos expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. The approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.

Efficient and Accurate Global Sensitivity Analysis for Reservoir Simulations By Use of the Probabilistic Collocation Method

SPE Journal ◽  
2013 ◽  
Vol 19 (04) ◽  
pp. 621-635 ◽  
Author(s):  
Cheng Dai ◽  
Heng Li ◽  
Dongxiao Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Collocation Method ◽  
History Matching ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Global Sensitivity ◽  
Reservoir Simulations ◽  
Probabilistic Collocation Method ◽  
The Impact ◽  
Probabilistic Collocation

Summary Reservoir simulations involve a large number of formation and fluid parameters, many of which are subject to uncertainties owing to the combination of spatial heterogeneity and insufficient measurements. Accurately quantifying the impact of varying parameters on simulation models can reveal the importance of the parameters, which helps in designing field-characterization strategies and determining parameterization for history matching. Compared with the commonly used local sensitivity analysis (SA), global SA considers the whole variation range of the parameters and can thus provide more-complete information. However, the traditional global sensitivity analysis that is derived from Monte Carlo simulation (MCS) is computationally too demanding for reservoir simulations. In this study, we propose an alternative approach that is both accurate and efficient. In the proposed approach, the model outputs such as pressure and reservoir production quantities are expressed by polynomial chaos expansions (PCEs). The probabilistic collocation method is used to determine the coefficients of the polynomial expansions by solving outputs at different sets of collocation points by means of the original partial-differential equations. Then, a proxy is constructed with such coefficients. Accurate statistical sensitivity indices of the uncertainty parameters can be obtained by running the proxy. We validate the approach with 2D examples by comparing with the MCS-based global SA. It is found that with only a small fraction of the computational cost required by the MCS approach, the new approach gives accurate global sensitivity for each parameter. The proposed approach is also demonstrated on a large-scale 3D black-oil model, for which the MCS-based global SA is found to be computationally infeasible. It is found that the developed approach possesses the following key advantages: It requires a much smaller number of reservoir simulations for accurate global SA; it is nonintrusive and can be implemented with existing codes or simulators; and it can accommodate arbitrary distributions of parameters encountered in realistic geological situations.

scholarly journals Global Sensitivity Analysis of a Spray Drying Process

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 562 ◽  
Author(s):  
Satyajeet Bhonsale ◽  
Carlos André Muñoz López ◽  
Jan Van Impe
Keyword(s):  
Sensitivity Analysis ◽  
Spray Drying ◽  
Global Sensitivity Analysis ◽  
Drug Product ◽  
Control Strategies ◽  
Computational Cost ◽  
Drying Process ◽  
Operational Parameters ◽  
Global Sensitivity ◽  
The Impact

Spray drying is a key unit operation used to achieve particulate products of required properties. Despite its widespread use, the product and process design, as well as the process control remain highly empirical and depend on trial and error experiments. Studying the effect of operational parameters experimentally is tedious, time consuming, and expensive. In this paper, we carry out a model-based global sensitivity analysis (GSA) of the process. Such an exercise allows us to quantify the impact of different process parameters, many of which interact with each other, on the product properties and conditions that have an impact on the functionality of the final drug product. Moreover, classical sensitivity analysis using the Sobol-based sensitivity indices was supplemented by a polynomial chaos-based sensitivity analysis, which proved to be an efficient method to reduce the computational cost of the GSA. The results obtained demonstrate the different response dependencies of the studied variables, which helps to identify possible control strategies that can result in major robustness for the spray drying process.

scholarly journals A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

2021 ◽  
Vol 7 ◽  
Author(s):  
Nikolaos Tsokanas ◽  
Xujia Zhu ◽  
Giuseppe Abbiati ◽  
Stefano Marelli ◽  
Bruno Sudret ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Hybrid Model ◽  
Surrogate Model ◽  
Global Sensitivity Analysis ◽  
Hybrid Simulation ◽  
Hybrid Models ◽  
Analysis Framework ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Realistic Situation

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

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.

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>

Sensitivity analysis and the challenges posed by multiple approaches: a multifaceted mess

2020 ◽  
Author(s):  
Monica Riva ◽  
Aronne Dell'Oca ◽  
Alberto Guadagnini
Keyword(s):  
Sensitivity Analysis ◽  
Model Calibration ◽  
Global Sensitivity Analysis ◽  
System Model ◽  
Model Parameters ◽  
Model Output ◽  
Multiple Model ◽  
Total Uncertainty ◽  
Global Sensitivity ◽  
Sensitivity Indices

<p>Modern models of environmental and industrial systems have reached a relatively high level of complexity. The latter aspect could hamper an unambiguous understanding of the functioning of a model, i.e., how it drives relationships and dependencies among inputs and outputs of interest. Sensitivity Analysis tools can be employed to examine this issue.</p><p>Global sensitivity analysis (GSA) approaches rest on the evaluation of sensitivity across the entire support within which system model parameters are supposed to vary. In this broad context, it is important to note that the definition of a sensitivity metric must be linked to the nature of the question(s) the GSA is meant to address. These include, for example: (i) which are the most important model parameters with respect to given model output(s)?; (ii) could we set some parameter(s) (thus assisting model calibration) at prescribed value(s) without significantly affecting model results?; (iii) at which space/time locations can one expect the highest sensitivity of model output(s) to model parameters and/or knowledge of which parameter(s) could be most beneficial for model calibration?</p><p>The variance-based Sobol’ Indices (e.g., Sobol, 2001) represent one of the most widespread GSA metrics, quantifying the average reduction in the variance of a model output stemming from knowledge of the input. Amongst other techniques, Dell’Oca et al. [2017] proposed a moment-based GSA approach which enables one to quantify the influence of uncertain model parameters on the (statistical) moments of a target model output.</p><p>Here, we embed in these sensitivity indices the effect of uncertainties both in the system model conceptualization and in the ensuing model(s) parameters. The study is grounded on the observation that physical processes and natural systems within which they take place are complex, rendering target state variables amenable to multiple interpretations and mathematical descriptions. As such, predictions and uncertainty analyses based on a single model formulation can result in statistical bias and possible misrepresentation of the total uncertainty, thus justifying the assessment of multiple model system conceptualizations. We then introduce copula-based sensitivity metrics which allow characterizing the global (with respect to the input) value of the sensitivity and the degree of variability (across the whole range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by a governing model. In this sense, such an approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. The methodology is demonstrated in the context of flow and reactive transport scenarios.</p><p> </p><p><strong>References</strong></p><p>Sobol, I. M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Sim., 55, 271-280.</p><p>Dell’Oca, A., Riva, M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydr. Earth Syst. Sci., 21, 6219-6234.</p>

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

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

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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