Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

Global sensitivity analysis and uncertainty quantification of soot formation in an n-dodecane spray flame

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Uncertainty and sensitivity analysis of cooling and heating loads for building energy planning

Physiologically based pharmacokinetic (PBPK) models describe the absorption, distribution, metabolism, and excretion of chemicals. Probabilistic PBPK models can be used to produce distributional estimates of human equivalent doses (HEDs), which are external measures of human exposure predicted to result in a target internal dose, generated with Monte Carlo sampling and reverse dosimetry calculations. Very low HED percentiles represent individuals that are more sensitive to possible adverse effects of chemical exposures and are therefore frequently used in risk evaluation. Details of the parameter distributions used in probabilistic PBPK models impact HED distributions, but obtaining precise distributional estimates for all the parameters would be challenging. Therefore, we sought to determine methods that can identify the extent of model parameter influence on extreme HED percentiles. We first analyzed published PBPK models for dichloromethane and chloroform (for inhalation and oral exposures given 3 internal target levels each) by identifying the overall relative importance of parameters using global sensitivity analysis (GSA) methods. Then, we used a novel yet computationally expensive method to analyze the stability and sensitivity of extreme HED percentiles to input parameter distributions. Applying the traditional GSA methods allowed us to identify subsets of parameters most influential for accurately determining 1st and 99th percentiles, but the specific parameters included in those subsets varied for different models and exposure scenarios. Our results demonstrate that better characterizing PBPK model uncertainty by using precise distributional details for influential parameters informed by GSA methods may improve confidence in estimates of extreme percentiles of HEDs.

Quantifying kinetic uncertainty in turbulent combustion simulations using active subspaces

Simulation of fate and transport mechanisms in the porous systems from contaminant transport models are affected by uncertainty associated with input model parameters. Sensitivity analysis (SA) provides tools to quantify the sources of uncertainty to the variations in the model output metrics. To quantify the uncertainty associated with physical non-equilibrium contaminant transport model, global SA was conducted for the problem mimicking reactive transport in the saturated soil column conditions. Five global SA methods, namely Morris, RSA (Regionalized Sensitivity Analysis), Sobol, FAST (Fourier Amplitude Sensitivity Test), and PAWN, were tested based on the temporal moments of contaminant concentrations for two output metrics: zeroth temporal moment (ZTM) and mean residence time (MRT). The ranking order of ten input model parameters from global SA methods for two output metrics was compared. Morris SA implied that the ZTM at outlet of the soil column is highly sensitive to sorption distribution coefficient in the mobile and immobile regions and less sensitive to dispersion coefficient and degradation rate constant in the immobile region. The mass-transfer coefficient showed highest non-linear interactions with other flow and transport parameters based on the highest value of standard deviation of elementary effects (EEs) for ZTM output metric. The sorption distribution coefficient in the mobile region and mass-transfer coefficient showed highest sensitivity and non-linear effect toward MRT based on the Morris method. The comparison of global SA methods revealed that the top two sensitive parameters affecting ZTM and MRT were the same from all the considered methods. However, large difference in the ranking order of bottom three sensitive parameters was observed. The sorption distribution coefficient of mobile region and mass-transfer coefficient were observed as the most sensitive parameters affecting ZTM and MRT based on the comparison of all five global SA methods. Overall results suggest that the non-linear contaminant transport model should be examined based on multiple sensitivity output metrics via a multi-model approach. The multi-model global SA approach implemented in this study highlighted its significance in quantifying the interplay of non-linear model parameters.

The large number of input factors involved in a sophisticated geotechnical computational model is a challenge in the concept of probabilistic analysis. In the context of model calibration and validation, conducting a sensitivity analysis is substantial as a first step. Sensitivity analysis techniques can determine the key factors which govern the system responses. In this paper, three commonly used sensitivity analysis methods are implemented on a sophisticated geotechnical problem. The computational model of a compressed air energy storage, mined in a rock salt formation, includes many input parameters, each with large amount of uncertainties. Sensitivity measures of different variables involved in the mechanical response of the cavern are computed by different global sensitivity methods, namely, Sobol/Saltelli, Random Balance Design, and Elementary Effect method. Since performing sensitivity analysis requires a large number of model evaluations, the concept of surrogate modelling is utilised to decrease the computational burden. In the following, the accuracy levels of various surrogate techniques are compared. In addition, a comparative study on the applied sensitivity analysis methods shows that the applied sensitivity analysis techniques provide identical parameter importance rankings, although some may also give more information about the system behaviour.

Constrained Global Sensitivity Analysis: Sobol’ indices for problems in non-rectangular domains

Intelligent sensitivity analysis framework based on machine learning for spacecraft thermal design

Local and global sensitivity analysis (SA) methods were compared to demonstrate how the choice of SA method leads to differences in the quantification of the relative importance of model parameters in driving canopy reflectance variability. The global SA method used was the Extended Fourier Amplitude Sensitivity Test (EFAST), while a series of basecase simulations were defined for the local SA, and model parameters were perturbed sequentially. Canopy reflectance was simulated using the ProGOSAIL model. Some pronounced differences were found between the two methods in terms of the magnitude of the importance, the rank importance, and the wavelengths at which model parameters are most important in explaining reflectance variability.

Quantifying uncertainty and sensitivity in climate risk assessments: Varying hazard, exposure and vulnerability modelling choices

BackgroundMathematical modeling is being applied to increasingly complex biological systems and datasets; however, the process of analyzing and calibrating against experimental data is often challenging and a rate limiting step in model development. To address this problem, we developed a systematic methodology for calibrating quantitative models of dynamic biological processes and illustrate its utility by validating a model of TRAIL (Tumor necrosis factor Related Apoptosis-Inducing Ligand)-induced cell death.ResultsWe propose a serial framework integrating analysis and calibration modules and we compare various methods for global sensitivity analysis and global parameter estimation. First, adequacy of the network structure is checked by global sensitivity analysis to changes in concentrations of molecular species, validating that the model can reproduce qualitative features of the system behavior derived from experiments or literature surveys. Second, rate parameters are ranked by importance using gradient-based and variance-based sensitivity indices, and we systematically determine the optimal number of parameters to include in model calibration. Third, deterministic, stochastic and hybrid algorithms for global optimization are applied to estimate the values of the most important parameters by fitting to time series data. We compare the performance of these three optimization algorithms.ConclusionsOur proposed framework covers the entire process from validating a proto-model to establishing a realistic model for in silico experiments and thereby provides a generalized workflow for the construction of predictive models of complex network systems.

EASI RBD-FAST: An efficient method of global sensitivity analysis for present and future challenges in building performance simulation

Four methods for global sensitivity analysis are studied with respect to their applicability in the finite element analysis of composite structures: (1) sensitivities based on the variance conditional expectation involving experimental design, (2) Morris' elementary effects method (including recent improvements to effective trajectory selection), (3) Sobol's main and total sensitivity indices, and (4) the root mean square of approximate derivatives at sampled points. The sensitivities of the first ten natural frequencies to the composite material properties as well as to the ply stack are determined. The methods are compared and an assessment of their applicability is made in the case of a fairly large number (d > 25) of uncertain parameters.