Katerina Konakli

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

Abstract The study makes use of polynomial chaos expansions to compute Sobol׳ indices within the frame of a global sensitivity analysis of hydro-dispersive parameters in a simplified vertical cross-section of a segment of the subsurface of the Paris Basin. Applying conservative ranges, the uncertainty in 78 input variables is propagated upon the mean lifetime expectancy of water molecules departing from a specific location within a highly confining layer situated in the middle of the model domain. Lifetime expectancy is a hydrogeological performance measure pertinent to safety analysis with respect to subsurface contaminants, such as radionuclides. The sensitivity analysis indicates that the variability in the mean lifetime expectancy can be sufficiently explained by the uncertainty in the petrofacies, i.e. the sets of porosity and hydraulic conductivity, of only a few layers of the model. The obtained results provide guidance regarding the uncertainty modeling in future investigations employing detailed numerical models of the subsurface of the Paris Basin. Moreover, the study demonstrates the high efficiency of sparse polynomial chaos expansions in computing Sobol׳ indices for high-dimensional models.

Uncertainty quantification in high-dimensional spaces with low-rank tensor approximations

Polynomial chaos expansions have proven powerful for emulating responses of computational models with random input in a wide range of applications. However, they suffer from the curse of dimensionality, meaning the exponential growth of the number of unknown coefficients with the input dimension. By exploiting the tensor product form of the polynomial basis, low-rank approximations drastically reduce the number of unknown coefficients, thus providing a promising tool for effectively dealing with high-dimensional problems. In this paper, first, we investigate the construction of low-rank approximations with greedy approaches, where the coefficients along each dimension are sequentially updated and the rank of the decomposition is progressively increased. Furthermore, we demonstrate the efficiency of the approach in different applications, also in comparison with state-of-art methods of polynomial chaos expansions.

Numerical Investigations into the Value of Information in Lifecycle Analysis of Structural Systems

AbstractPreposterior analysis can be used to assess the potential of an experiment to enhance decision-making by providing information on parameters of the decision problem that are surrounded by epistemic uncertainties. The present paper describes a framework for preposterior analysis for support of decisions related to maintenance of structural systems. In this context, experiments may refer to inspections or structural health monitoring. The value-of-information concept comprises a powerful tool for determining whether the experimental cost is justified by the expected gained benefit during the lifecycle of a structural system and for identifying the optimal among different possible experimental schemes. This concept is herein elaborated through case studies that involve individual structural components subject to deterioration as well as systems with interdependencies. Extensive numerical investigations demonstrate how the decision problem is influenced by the assumed probabilistic models, including t...

Low-rank tensor approximations for reliability analysis

Low-rank tensor approximations have recently emerged as a promising tool for efficiently building surrogates of computational models with high-dimensional input. In this paper, we shed light on issues related to their construction with greedy approaches and demonstrate that meta-models built with small experimental designs can be used to estimate tail probabilities with high accuracy.

Value of Information Analysis in Structural Safety

Pre-posterior analysis can be used to assess the potential of an experiment to enhance decision making by providing information on parameters characterized by uncertainty. The present paper describes a framework for pre-posterior analysis for support of decisions related to maintenance of structural systems. In this context, experiments may refer to inspections or techniques of structural health monitoring. The Value of Information concept provides a powerful tool for determining whether the experimental cost is justified by the expected benefit and for identifying the optimal among different possible experimental schemes. This concept is elaborated through principal examples for structural components and system models. Sensitivity analyses are performed to investigate how the decision problem is influenced by the level of uncertainty that characterizes the structural properties, the amount and quality of information and the probabilistic dependencies between components of a system.

Seismic Response Analysis with Spatially Varying Stochastic Excitation

Assessment of the seismic vulnerability of extended structures (e.g. bridges and lifelines) as well as of systems of structures covering extended areas requires to properly account for the effects of ground-motion spatial variability. Even in cases with relatively uniform soil conditions, ground motions may exhibit significant variations due to the incoherence and wave-passage effects, respectively manifested as random differences and deterministic time delays. Differential soil conditions cause additional variations in the amplitude and frequency content of the ground motions as these propagate from the bedrock to the surface level. The present chapter describes methods for the modeling of ground-motion spatial variability, the simulation of spatially varying ground-motion arrays and the evaluation of the response of multiply-supported structures to differential support excitations. The pertinent uncertainties in the characteristics of the ground motions are accounted for by employing concepts from stochastic time-series analysis. In particular, the notion of coherency is employed to describe the spatial variability of the ground-motion arrays, which are considered as realizations of a random field at the locations of interest. The statistical properties of the ground motions at separate locations are described through the respective auto-power spectral densities. A statistical characterization of linear structural response to differential support motions is obtained by means of a response-spectrum method, rooted in random vibration theory, while the non-linear response is investigated on the basis of the ‘equal-displacement’ rule. This chapter is inspired by the doctoral research of the author under the supervision of Professor Armen Der Kiureghian.