Global sensitivity analysis for multivariate outputs using generalized RBF-PCE metamodel enhanced by variance-based sequential sampling

In this study, a hybrid metamodel using the orthogonal constraints of radial basis function and sparse polynomial chaos expansions is proposed for the global sensitivity analysis of time-consuming models. Firstly, the orthogonal conditions of radial basis functions (RBF) and polynomial chaos expansions (PCE) were derived to construct the hybrid metamodel. Then, the variance of the metamodel was decoupled into the variances of the RBF and PCE independently by using the orthogonal condition. Furthermore, the analytical formulations of Sobol indices for the hybrid metamodel were derived according to the orthogonal decomposition. Thus, the interaction items of radial basis function and polynomial chaos expansions were eliminated, which significantly simplifies the Sobol indices. Two analytical cases were employed to investigate the influence of the number of the polynomial chaos expansions items, and several analytical and engineering cases were tested to demonstrate the accuracy and efficiency of the proposed method. In the engineering cases, the proposed method yielded significant improvements in terms of both accuracy and efficiency comparing with the existing global sensitivity analysis approaches, which indicates that the proposed method is more appropriate to the global sensitivity analysis of time-consuming engineering problems.

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

The main focus of this thesis is the uncertainty propagation (UP) and global sensitivity analysis (GSA) in complex hydrogeological numerical models. Various methods are presented with applications on numerical models for the groundwater flow and mean lifetime expectancy (MLE) in the scope of Andra's (French National Radioactive Waste Management Agency) project for the geological disposal of high-level and intermediate-level long-lived radioactive wastes in a highly impermeable layer from Callovo-Oxfordian age (COX) in France. <br> A state of the art is provided for the theory of uncertainty propagation and for the methodologies of sensitivity analyses in a broad sense. Methods for UP are provided from 2-levels Factorial Designs to quasi-random samplings. GSA techniques encompass screening methods such as the Morris Measures and the Derivative-based Global Sensitivity Measures (DGSM), and also the so-called Sobol' indices based upon the variance decomposition of the response of interest. Meta-modelling techniques such as polynomial regression and Polynomial Chaos Expansions (PCE) meta-models are employed as surrogate models for UP and GSA purpose at negligible computational-costs. A comparison of GSA techniques upon various complex analytical test-functions was undertaken with the purpose of determining a relevant method to be employed in the context of “screening” out unimportant variables in computer-intensive, high-dimensional models. <br> A numerical model of groundwater flow and lifetime expectancy is employed for assessing the effect of uncertain advection-dispersion parameters and their spatial distributions upon the MLE from a target zone inside the domain. The model is a 2-dimensions synthetic cross-section of the eastern region of the Paris Basin (Meuse/Haute-Marne sector). This model was used as an exploratory tool for sensitivity analysis methods applied upon numerous sets of uncertain hydrodynamic and dispersion parameters in 15 layers. The uncertainty characterizing the permeability-porosity values in aquifer formations encompassing the COX have proved to add much of variability to the MLE calculated from the target zone. The model also served at exploring the effect of the spatial variability of permeability-porosity parameters in two main aquifer sequences on the groundwater flow rates and MLE in the model. The variabilities of the output responses are mainly due to the uncertainty upon the means and variances of the permeability-porosity distributions, as well as the longitudinal correlation lengths, in each sequence. <br> Then, a 3-dimensions high-definition hydrogeological model representing the Meuse/Haute-Marne sector in the eastern region of the Paris Basin is a more comprehensive numerical model incorporating realistic geometries, fractures, heterogeneities and discontinuities encountered on field. A sensitivity analysis of the MLE from a given zone located in the middle of the COX layer was performed by perturbing the hydraulic conductivities and porosities values in fourteen hydrogeological formations. The uncertain permeability-porosity parameters in the aquifer formations from Bathonian in the Dogger sequence, and Rauracian-Sequanian in the Oxfordian sequence, have strong and rather non-linear effects on the variability of the output response of interest. <br> The methodologies for UP and GSA employed in the present thesis have proved to be very efficient when applied to large hydrogeological models of groundwater flow and MLE. In particular, quasi-random sampling methods offer a flexible frame for providing the uncertainty distribution of the output response of interest at low computational costs. Screening techniques provide a fast estimation for the overall contribution of each input variable to the variability of the output. Meta-modelling techniques such as PCE proved highly accurate in individualising the low- and high-order effects of each input variable upon the output response of interest.

Soils show inherent variability due to various physio-chemical, geological and environmental processes. It is necessary to consider soil spatial variability in evaluation and probabilistic design of foundations. However probabilistic frameworks become computationally expensive and infeasible for a complex realistic scenario. This study develops an approach to evaluate the bearing capacity factor of strip footing resting on a spatially varying clayey slope using a Sparse polynomial chaos expansion (SPCE) surrogate model. Non-stationary soil condition is adopted in this study. Initially random fields are generated using KL expansion method considering 95% energy variance terms. This helps to reduce the terms for a random field as input to the SPCE model. The combined model of SPCE with Global Sensitivity analysis (GSA) reduced computational time and cost. This approach is very efficient because the predicted bearing capacity factor is accurate and needs only a smaller number of realizations to train. This makes it computationally time efficient. Meanwhile using any traditional approach, the probabilistic analysis is computationally inefficient in terms of cost and time.

Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

Non-Linear Partial-Least-Squares-based Polynomial Chaos Expansion (NLPLS-based PCE) approach for global sensitivity analysis of a High-Q Partially Air-Filled Pedestal Resonator Integrated in a Printed Circuit Board (PCB)

This paper extends previous works related to the assessment of component degradation, through Markov multi-state physic models. The extension includes the evaluation of the effects of uncertain parameters in the model, and the definition of their importance with respect to their influence on the output of the model. Global Sensitivity Analysis (GSA) is selected as the technique because it enables us to 1) consider the simultaneous effects of parameters variations, and 2) to define importance indexes that allow a ranking of the components. GSA requires a large number of evaluations for specific points, identified by an appropriate design of experiment. To avoid the many costly evaluations, a meta-model is built based on polynomial chaos expansion (PCE). A PCE is a multi-dimensional polynomial approximation of the model with coefficients determined by evaluating the model in a reduced set of predetermined points. Importance index values are then derived directly from the PCE. Because, in the problem considered, the model provides the time-dependent behavior of the state probabilities, the importance indexes are also functions of time. An application is presented, related to the cracking process in an Alloy 82/182 dissimilar metal weld in the primary coolant system of a nuclear power plant.

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

The design optimization of acoustic metamaterials represents a critical challenge in modern noise control applications. Global sensitivity analysis (GSA) has emerged as a powerful tool for quantifying the correlation between metamaterials' design variables and corresponding sound quality metrics (loudness, sharpness, and speech intelligibility index). However, GSA's high computational intensity limits the practical application of design optimization, especially for sound quality metrics which vary with sound stimulus. This study introduces a computational framework using radial basis function (RBF) interpolation to accelerate the GSA of acoustic metamaterials, with a periodic arrangement of micro-perforated panels (MPPs) serving as an exemplary case study. The methodology employs RBF interpolation to create a surrogate model of metamaterial acoustic response, demonstrating the potential for computational cost reduction while maintaining accuracy. It is validated across three acoustic scenarios that represent common challenges in noise control: stationary signals (broad/narrowband noise), environmental sounds (mechanical noise, traffic), and dynamic signals (speech, music). The study systematically compares sensitivity indices derived from direct numerical simulation and interpolated predictions, assessing the RBF's impact on GSA accuracy. [The European Commission is gratefully acknowledged for supporting the Marie Sklodowska Curie program through the Horizon Europe DN METAVISION project (GA 101072415)]

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model

Global sensitivity analysis in high dimensions with PLS-PCE

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

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV variations plays an important role in designing optimal voltage control schemes. This paper proposes a Kriging, i.e., Gaussian process modeling enabled data-driven GSA method. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol index can be conveniently calculated to assess the global sensitivity of voltage to various power injection variations. Comparison results with other model-based GSA methods on the IEEE 37-bus feeder, such as the polynomial chaos expansion and the Monte Carlo approaches demonstrate that the proposed method can achieve accurate GSA outcomes while maintaining high computational efficiency.