Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

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>

Parameter Screening in Statistical Dynamic Computer Model Calibration Using Global Sensitivities

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Dorin Drignei ◽  
Zissimos P. Mourelatos
Keyword(s):  
Sensitivity Analysis ◽  
Computer Model ◽  
Model Calibration ◽  
Simulation Models ◽  
Computer Models ◽  
Automotive Application ◽  
Transient Signals ◽  
Sensitivity Indices ◽  
Calibration Algorithm ◽  
Computationally Intensive

Computer, or simulation, models are ubiquitous in science and engineering. Two research topics in building computer models, generally treated separately, are sensitivity analysis and computer model calibration. In sensitivity analysis, one quantifies the effect of each input factor on outputs, whereas in calibration, one finds the values of input factors that provide the best match to a set of test data. In this article, we show a connection between these two seemingly separate concepts for problems with transient signals. We use global sensitivity analysis for computer models with transient signals to screen out inactive input factors, thus making the calibration algorithm numerically more stable. We show that the computer model does not vary with respect to parameters having zero total sensitivity indices, indicating that such parameters are impossible to calibrate and must be screened out. Because the computer model can be computationally intensive, we construct a fast statistical surrogate of the computer model which is used for both sensitivity analysis and computer model calibration. We illustrate our approach with both a simple example and an automotive application involving a road load data acquisition (RLDA) computer model.

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 New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Binary Outcome ◽  
Global Sensitivity ◽  
First Order ◽  
Sensitivity Measure ◽  
Sensitivity Indices ◽  
Alternative Measures ◽  
Input Variables ◽  
Dome Shape

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

scholarly journals PROBABILISTIC ANALYSIS OP SEAFLOOR LIQUEFACTION

1988 ◽  
Vol 1 (21) ◽  
pp. 101 ◽  
Author(s):  
Rafael Blazquez ◽  
Felipe M. Martinez
Keyword(s):  
Soil Layer ◽  
Water System ◽  
Deterministic Models ◽  
Risk Models ◽  
First Order ◽  
Sensitivity Indices ◽  
Reliability Method ◽  
Input Variables ◽  
Relationship Of ◽  
The Relationship

To investigate the reliability of a sandy soil layer in an ocean wave environment a liquefaction model is used in conjunction with a first order reliability method. Thus, sensitivity indices of the soil-water system with respect to the uncertain strength and input variables are computed, and the relative importance of the various factors defining the problem can be determined. The relationship of this approach with more conventional design methods (deterministic models, risk models) is discussed along with the range of applicability of the different safety measurements.

scholarly journals APPLICATION OF METAMODELLING TECHNIQUES FOR MECHANIZED TUNNEL SIMULATION

2014 ◽  
Vol 44 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Kavan Khaledi ◽  
Tom Schanz ◽  
Shorash Miro
Keyword(s):  
Sensitivity Analysis ◽  
Sampling Methods ◽  
Numerical Study ◽  
Simulation Models ◽  
Moving Least Squares ◽  
Optimization Parameter ◽  
Engineering Problems ◽  
Routine Tasks ◽  
Long Time ◽  
Complex Engineering

Abstract Complex engineering problems require using computation- ally expensive simulations which take relatively long time. In such cases, routine tasks such as design optimization, parameter identification, or sensitivity analysis become impractical since they require thousands or even millions of simulations. A common practice for engineers to solve this problem is to use metamodels in place of actual simulation models. In this paper, we investigate the performance of four metamodelling approaches, namely, Response Surface Methodology, Moving Least Squares, POD-RBF, and Neighborhood Approximation considering the effect of sample size and sampling methods. Our main goal in this work is to find a reliable and robust metamodel technique in order to construct an approximated function for mechanized tunnel simulation. For this reason, a numerical study is carried out on a 3D tunnel modeled in Plaxis3D and the accuracy and robustness of the aforementioned metamodelling techniques are discussed

Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty

2004 ◽  
Author(s):  
Wei Chen ◽  
Ruichen Jin ◽  
Agus Sudjianto
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Simulation Models ◽  
Design Under Uncertainty ◽  
Global Sensitivity ◽  
Functional Relationships ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Input Variables ◽  
The Impact

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels of engineering simulation models. We examine the types of GSA needed for design under uncertainty and derive generalized analytical formulations of GSA based on a variety of metamodels commonly used in engineering applications. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

scholarly journals BEPU robustness analysis via perturbed law-based sensitivity indices

2021 ◽  
pp. 1748006X2110365
Author(s):  
Bertrand Iooss ◽  
Vanessa Vergès ◽  
Vincent Larget
Keyword(s):  
Nuclear Reactor ◽  
Probability Distributions ◽  
Safety Margin ◽  
Robustness Analysis ◽  
Computer Experiments ◽  
Simulation Models ◽  
Pressurized Water ◽  
Sensitivity Indices ◽  
Input Variables ◽  
The Impact

The “best-estimate plus uncertainty” (BEPU) methodology is the term used in the nuclear engineering community when dealing with uncertainty quantification issues in realistic numerical simulation models. One of the most critical hypothesis in these studies is the choice of the probability distributions of uncertain input variables which are propagated through the model. Bringing stringent justifications to the BEPU approach, especially in a safety study, requires quantifying the impact of potential uncertainty on the input variable distribution. To solve this problem, this paper deepens the robustness analysis based on the “Perturbed Law-based sensitivity Indices” (PLI). The PLI quantifies the impact of a perturbation of an input distribution on the quantity of interest (as a quantile of a model output or a safety margin) in the BEPU study. The mathematical formalism of the PLI is applied to two particular quantities of interest: the quantile and the superquantile. For both quantities, the PLI can be easily computed using a unique Monte-Carlo sample containing model inputs and output. Numerical tests are developed in order to define validity criteria of a PLI-based robustness analysis. The practical use of the method is illustrated on thermal-hydraulic computer experiments, simulating a cold leg Intermediate Break Loss Of Coolant Accident (IBLOCA) in a pressurized water nuclear reactor.

scholarly journals A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2489
Author(s):  
Zhiwei Bai ◽  
Hongkui Wei ◽  
Yingying Xiao ◽  
Shufang Song ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Joint Probability ◽  
Copula Functions ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Input Variables ◽  
Vine Copula ◽  
Bivariate Copula

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

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