Sensitivity Analysis for Uncertainty Quantification in Mathematical Models (original) (raw)
Related papers
Sensitivity analysis when model outputs are functions
Reliability Engineering & System Safety, 2006
When outputs of computational models are time series or functions of other continuous variables like distance, angle, etc., it can be that primary interest is in the general pattern or structure of the curve. In these cases, model sensitivity and uncertainty analysis focuses on the effect of model input choices and uncertainties in the overall shapes of such curves. We explore methods for characterizing a set of functions generated by a series of model runs for the purpose of exploring relationships between these functions and the model inputs.
Pygpc: A sensitivity and uncertainty analysis toolbox for Python
SoftwareX
We present a novel Python package for the uncertainty and sensitivity analysis of computational models. The mathematical background is based on the non-intrusive generalized polynomial chaos method allowing one to treat the investigated models as black box systems, without interfering with their legacy code. Pygpc is optimized to analyze models with complex and possibly discontinuous transfer functions that are computationally costly to evaluate. The toolbox determines the uncertainty of multiple quantities of interest in parallel, given the uncertainties of the system parameters and inputs. It also yields gradient-based sensitivity measures and Sobol indices to reveal the relative importance of model parameters.
Energies, 2021
This work reviews the state-of-the-art methodologies for the deterministic sensitivity analysis of nonlinear systems and deterministic quantification of uncertainties induced in model responses by uncertainties in the model parameters. The need for computing high-order sensitivities is underscored by presenting an analytically solvable model of neutron scattering in a hydrogenous medium, for which all of the response’s relative sensitivities have the same absolute value of unity. It is shown that the wider the distribution of model parameters, the higher the order of sensitivities needed to achieve a desired level of accuracy in representing the response and in computing the response’s expectation, variance, skewness and kurtosis. This work also presents new mathematical expressions that extend to the sixth-order of the current state-of-the-art fourth-order formulas for computing fourth-order correlations among computed model response and model parameters. Another novelty presented ...
Sensitivity analysis for model output
Computational Statistics & Data Analysis, 1992
The paper analyses the difficulties of performing sensitivity analysis on the output of complex models. To this purpose a number of selected non-parametric statistics techniques are applied to model outputs without assuming knowledge of the model structure, ie as to a black box. The techniques employed are mainly concerned with the analysis of the rank transiormation of both input and output variables (eg standardised rank regression coefficients, model coefficient of determination on ranks.. . ). The test models taken into consideration are three benchmarks of the Probabilistic System Assessrnent Code (PSAC) User Group, an international working party coordinated by the OECD/NEA. They describe nuclide chain transport through a multi-barrier system (near field, geosphere, biosphere) and are employed in the analysis of the safety of a nuclear waste disposal in a geological formation. Due to the large uncertainties affecting the system these models are normally run within a Monte Carlo driver in order to characterise the distribution of the model output. A crucial step in the analysis of the system is the study of the sensitivity of the model output to the value of its input parameters. This study may bc complicated by factors such as the complexity of the model, its non-linearity and non-monotcnicity and others. The problem is discussed with reference to the three test cases and model non-monotonicity is shown to be particularly difficult to handle with the employed techniques. Alternative approaches to sensitivity analysis are also touched upon.
Sensitivity analysis of model output
Computational Statistics & Data Analysis, 1993
Sensitivity Analysis (SA) of model output investigates the relationship between the predictions of a model, possibly implemented in a computer program, and its input parameters. Such an analysis is relevant for a number of practices, including quality assurance of models and codes, and the identification of crucial regions in the parameter space. This note compares established techniques with variants, such as a modified version of the Hora and Iman importance measure (SANDIA Laboratory Report SAND85-2839, 19891, or new methods, such as the iterated fractional factorial design (Andres, Hajas, Report in prep. for AECL, Pinawa, Canada, 1991). Comparison is made on the basis of method reproducibility and of method accuracy. The former is a measure of how well SA predictions are replicated when repeating the analysis on different samples taken from the same input parameters space. The latter deals with the physical correctness of the SA results. The present article is a sequel to an earlier study in this journal (Saltelli, Homma, Comp. Stat. and Data Anal. 13 (1) 1992, 73-94 of limitations in existing SA techniques, where the inadequacy of existing schemes to deal with non-monotonic relationships within the model was pointed out.
Methods for Sensitivity and Uncertainty Analysis of Computer Intensive Simulation Models
In dit rapport behandelen we methoden voor gevoeligheids-en onzekerheidsanalyses voor rekenintensieve simulatiemodellen. We geven een overzicht van de meest gebruikte methoden en technieken en recente ontwikkelingen op het gebied van gevoeligheids-en onzekerheidsanalyse, waarbij we de nadruk leggen op beperking van de benodigde rekentijd. Technieken voor lokale en globale gevoeligheidsanalyse komen aan bod, met speciale aandacht voor metamodellering, factorial designs en de adjoint vergelijking methode.