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

A novel theoretical and numerical framework for the estimation of Sobol’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low dimensionality and the MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol’ sensitivity indices. Several model test functions with constraints are considered for which analytical solutions for Sobol’ sensitivity indices were found. These solutions were used as benchmarks for verifying numerical estimates. The method is shown to be general and efficient.

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.

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

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

Efficient sampling methods for global reliability sensitivity analysis

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.

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

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.

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.

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

Improved understanding of dynamic hydrological performance of green roof (GR) design parameters towards different model responses is important for maximizing its target design goals at the unit-scale. Replication of an optimally designed GR unit at the catchment-scale significantly contributes to achieving its target design goals (i.e., surface runoff reduction, urban flood reduction, peak flow control, etc.). Moreover, adequate efforts are required to explore and provide appropriate knowledge about the categorization of influential and non-influential design parameters with their suitable design spaces to guide researchers, drainage engineers, and stormwater management practitioners for effective and efficient planning, designing and optimization of GR at catchment-scales.This study employs a robust and comprehensive global sensitivity analysis (GSA) method known as the variogram analysis of response surfaces (VARS) for sensitivity analysis of GR design parameters. Firstly, a total of 13,999 sample points for 14 GR parameters of three layers (i.e., surface, soil and drainage mat) are generated by using the latin hypercube sampling technique and their factor spaces are decided based on design guidelines in current SWMM manuals. Following that, the PySWMM is used to simulate these design samples in a Monte-Carlo-type setting on a conceptual catchment of 0.01km2 (100m2 × 100m2) with 50% treatment area of GR, and the model responses (e.g., surface infiltration, surface outflow, storage volume, and peak flow) are estimated and applied for sensitivity analysis. Finally, VARS evaluates different sensitivity analysis metrics by using different model responses corresponding to their designed samples.Overall, the senstivity analysis results demonstrate that 8 out of 14 design parameters are highly influential on different model responses, however, the parameters’ sensitivity varies towards different model responses under different perturbation scales and rainfall conditions. Moreover, the selection of an effective range of design space of design parameters is necessary as it has a higher influence on model responses, while the parameters’ rankings and contributions to total sensitivity indices change with the range of design spaces. Furthermore, this research also provides an opportunity through VARS directional variogram index (an integrated sensitivity index) to study and understand the underlying mechanisms of design parameters under different perturbation scales with no extra computational burden. Senstivity analysis results will be presented with insights and recommendations for other regions, which will be helpful for decision-makers for effective planning, designing and implementation of GR. The findings of this parametric study would be helpful for the calibration and optimization of design parameters of GR for different case studies. 

Hybrid high dimensional model representation (HHDMR) on the partitioned data

This paper presents an application of the Global Sensitivity Analysis (GSA) method in evaluating performance of impedance measurement algorithms implemented in modern Intelligent Electronic Devices (IEDs) when affected by uncertainty. To be specific, the GSA is applied in testing an algorithm for distance protection of a single transmission line in a system with two lines on the same towers. Factors contributing to uncertainty are discussed in the paper. The GSA method decomposes variance of the estimation error according to the factors and their interactions, and in this way identifies the factors that have the highest impact on the estimation error. Computation of the GSA sensitivity indices relies on the Quasi-Monte Carlo (QMC) technique with Sobol's quasi-random sampling. This is time-consuming for large number of factors therefore, fast pre-screening process based on the Morris method is implemented to remove non-influential parameters and reduce the factor space before running the QMC. The methodology is implemented using fault simulation software DIgSILENT PowerFactory to calculate fault impedance as a function of uncertain parameters (i.e. factors) as well as voltage and current signals that are inputs to an IED under test. In this simulation, factor space is sampled using Sobol's quasi-random sequence generated with the standard GSA software tool called SIMLAB. All simulations of the transmission line faults for various parameter values and calculation of the performance indices (i.e. sensitivities) is automated using the program developed in DIgSILENT Programming Language (DPL). This testing technique is applied to study the fault impedance measurement implemented in SEL-421. (6 pages)

Global sensitivity analysis (GSA) measures the variation of a model output as a function of the variations of the model inputs given their ranges. In this paper we consider variance-based GSA methods that do not rely on certain assumptions about the model structure such as linearity or monotonicity. These variance-based methods decompose the output variance into terms of increasing dimensionality called 'sensitivity indices', first introduced by Sobol' [25]. Sobol' developed a method of estimating these sensitivity indices using Monte Carlo simulations. McKay [13] proposed an efficient method using replicated Latin hypercube sampling to compute the 'correlation ratios' or 'main effects', which have been shown to be equivalent to Sobol's first-order sensitivity indices. Practical issues with using these variance estimators are how to choose adequate sample sizes and how to assess the accuracy of the results. This paper proposes a modified McKay main effect method featuring an adaptive procedure for accuracy assessment and improvement. We also extend our adaptive technique to the computation of second-order sensitivity indices. Details of the proposed adaptive procedure as wells as numerical results are included in this paper.