Sensitivity Analysis Of Computer Models Research Articles

Sensitivity Analysis of Computational Models for solving Paradox

Sensitivity Analysis of Computational Models for solving Paradox

VARIANCE-BASED SENSITIVITY INDICES OF COMPUTER MODELS WITH DEPENDENT INPUTS: THE FOURIER AMPLITUDE SENSITIVITY TEST

Several methods are proposed in the literature to perform the global sensitivity analysis of computer models with independent inputs. Only a few allow for treating the case of dependent inputs. In the present work, we investigate how to compute variance-based sensitivity indices with the Fourier amplitude sensitivity test. This can be achieved with the help of the inverse Rosenblatt transformation or the inverse Nataf transformation. We illustrate so on two distinct benchmarks. As compared to the recent Monte Carlo based approaches recently proposed by the same authors in Mara et al. (2015), the new approaches allow to divide by two the computational effort to assess the entire set of first-order and total-order variance-based sensitivity indices.

Variational inference of cluster-weighted models for local and global sensitivity analysis

Variational inference is employed to infer cluster-weighted models from input-output data. Variational relations are derived for hyperparameters of the joint probability density of the model's parameters and latent variables. The result is an alternative to inferring the parameters through expectation maximisation. Surrogate models derived from the resulting predictive distributions have high data fidelity, good regularity between the data, and are quickly evaluated. These traits make them well-suited to sampling-based global sensitivity analyses through variance decomposition. Moreover, analytical local derivatives of the regression functions are readily computed to support sampling of the derivatives throughout the factor space. Results are presented for local and global sensitivities of two examples based on cluster-weighted surrogate models inferred from limited samples. The first example is analytical; the second builds on previous work by the authors in global, full-field sensitivity analysis of computational models of near-ground sound propagation.

Evaluation of MARS modeling technique for sensitivity analysis of model output

Sensitivity analysis of computer models can typically require a large number of model runs. When these models are computationally expensive to run, it may be advantageous to invest in computationally cheaper surrogate models (emulators or meta-models) that can provide almost the same output as the original model and estimate the sensitivity indices for each input. In this abstract the MARS method is used to mimic the behavior of a nonlinear and non-additive test function. The results show that, overall, MARS provides acceptable estimates of total sensitivity indices at a much lower cost than using only runs of the original model.

Automation of primal and sensitivity analysis of transient coupled problems

The paper describes a hybrid symbolic–numeric approach to automation of primal and sensitivity analysis of computational models formulated and solved by finite element method. The necessary apparatus for the automation of steady-state, steady-state coupled, transient and transient coupled problems is introduced as combination of a symbolic system, an automatic differentiation (AD) technique and an automatic code generation. For this purpose the paper extends the classical formulation of AD by additional operators necessary for a high abstract description of primal and sensitivity analysis of the typical computational models. An appropriate abstract description for the fully implicit primal and sensitivity analysis of hyperelastic and elasto-plastic problems and a symbolic input for the generation of necessary user subroutines for the two-dimensional, hyperelastic finite element are presented at the end.

Global sensitivity analysis of computer models with functional inputs

Global sensitivity analysis is used to quantify the influence of uncertain model inputs on the response variability of a numerical model. The common quantitative methods are appropriate with computer codes having scalar model inputs. This paper aims at illustrating different variance-based sensitivity analysis techniques, based on the so-called Sobol's indices, when some model inputs are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary metamodeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked generalized linear models (GLMs) or generalized additive models (GAMs). The “mean model” allows to estimate the sensitivity indices of each scalar model inputs, while the “dispersion model” allows to derive the total sensitivity index of the functional model inputs. The proposed approach is compared to some classical sensitivity analysis methodologies on an analytical function. Lastly, the new methodology is applied to an industrial computer code that simulates the nuclear fuel irradiation.

Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models

We consider a class of input sampling plans, called permuted column sampling plans, that are popular in sensitivity analysis of computer models. Permuted column plans, including replicated Latin hypercube sampling, support estimation of first-order sensitivity coefficients, but these estimates are biased when the usual practice of random column permutation is used to construct the sampling arrays. Deterministic column permutations may be used to eliminate this estimation bias. We prove that any permuted column sampling plan that eliminates estimation bias, using the smallest possible number of runs in each array and containing the largest possible number of arrays, can be characterized by an orthogonal array of strength 2. We derive approximate standard errors of the first-order sensitivityindices for this sampling plan. We give two examples demonstrating the sampling plan, behavior of the estimates, and standard errors, along with comparative results based on other approaches.

A review of techniques for parameter sensitivity analysis of environmental models

Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.

An Approach to Sensitivity Analysis of Computer Models: Part II—Ranking of Input Variables, Response Surface Validation, Distribution Effect and Technique Synopsis

This is the second part of a two-part paper presenting a statistical approach to the sensitivity analysis of computer models. In this part consideration is given to response surface construction techniques including identification of possible overfit an..

An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment

This is the first part of a two-part article presenting a statistical approach to the sensitivity analysis of computer models. Part I defines the objectives of sensitivity analysis and presents a computer model that is used for purposes for illustration..