Stefano Marelli

Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes

Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol’ indices is based on Monte Carlo simulation, which is not af- fordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Then the surrogate can be used to compute the sensitivity indices in negligible time. In this chapter an introduction to each technique is given, with an emphasis on their strengths and limitations in the context of global sensitivity analysis. In particular, Sobol’ (resp. total Sobol’) indices can be computed analytically from the PCE coefficients. In contrast, confidence intervals on sensitivity indices can be derived straightforwardly from the properties of GPs. The performance of the two techniques is finally compared on three well-known analytical benchmarks (Ishigami, G-Sobol and Morris functions) as well as on a realistic engineering application (deflection of a truss structure).

Determining Rice Growth Stage with X-Band SAR: A Metamodel Based Inversion

Rice crops are important in the global food economy, and new techniques are being implemented for their effective management. These techniques rely mainly on the changes in the phenological cycle, which can be investigated by remote sensing systems. High frequency and high spatial resolution Synthetic Aperture Radar (SAR) sensors have great potential in all-weather conditions for detecting temporal phenological changes. This study focuses on a novel approach for growth stage determination of rice fields from SAR data using a parameter space search algorithm. The method employs an inversion scheme for a morphology-based electromagnetic backscattering model. Since such a morphology-based model is complicated and computationally expensive, a surrogate metamodel-based inversion algorithm is proposed for the growth stage estimation. The approach is designed to provide estimates of crop morphology and corresponding growth stage from a continuous growth scale. The accuracy of the proposed method is tested with ground measurements from Turkey and Spain using the images acquired by the TerraSAR-X (TSX) sensor during a full growth cycle of rice crops. The analysis shows good agreement for both datasets. The results of the proposed method emphasize the effectiveness of X-band PolSAR data for morphology-based growth stage determination of rice crops.

Non-intrusive monitoring using seismic tomography at the Mont Terri rock laboratory

Summary In the framework of a nuclear waste disposal program, we have conducted seismic experiments at the Mont Terri underground rock laboratory in Switzerland. The objective was to explore the possibilities and limitations of seismic tomography for remotely monitoring the changing properties of material filling a small (1 m diameter) tunnel embedded in a highly anisotropic clay formation. Crosshole traveltime tomography allowed the gross properties of the host rock to be determined, but it failed to identify the microtunnel. By comparison, recordings with verticalcomponent geophones attached to the inside of the microtunnel walls revealed significant traveltime and waveform variations for different fill materials (air and sand) and experimental conditions (dry versus saturated). Data from these geophones were not only diagnostic of the fill, but also of the excavation damage zone (EDZ) surrounding the microtunnel.

An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the model response and due to the lack of local metamodel error estimates. We propose a new method to provide local metamodel error estimates based on bootstrap resampling and sparse PCE. An initial experimental design is iteratively updated based on the current estimation of the limit-state surface in an active learning algorithm. The greedy algorithm uses the bootstrap-based local error estimates for the polynomial chaos predictor to identify the best candidate set of points to enrich the experimental design. We demonstrate the effectiveness of this approach on a well-known analytical benchmark representing a series system, on a truss structure and on a complex realistic frame structure problem.

Sequential Design of Experiment for Sparse Polynomial Chaos Expansions

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, sparse polynomial chaos expansions (PCEs) have been shown to be among the most promising methods because of their ability to model highly complex models at relatively low computational costs. A least-square minimization technique may be used to determine the coefficients of the sparse PCE by relying on the so-called experimental design (ED), i.e., the sample points where the original computational model is evaluated. An efficient sampling strategy is then needed to generate an accurate PCE at low computational cost. This paper is concerned with the problem of identifying an optimal ED that maximizes the accuracy of the surrogate model over the whole input space within a given computational budget. A novel sequential adaptive strategy where the ED is enriched sequentially by capitalizing on the sparsity of the underlying metamodel is introduced. A comparative study between several state-of-the...

UQLab: Une plate-forme pour la quantification des incertitudes sous Matlab: une plate-forme pour la quantification des incertitudes sous Matlab

A new computational platform for uncertainty quantification (UQ) in engineering is presented. It aims at disseminating the good practices of UQ towards students, field engineers and researchers by offering different levels of usage from the beginner to the advanced developer. It gathers in a single, consistent frame many state-of-the-art UQ techniques including reliability methods, polynomial chaos expansions, kriging and global sensitivity analysis while being natively developed for high performance computing. It is conceived as an open source software which shall be open to contributions from the community. MOTS-CLÉS : quantification des incertitudes, logiciel, MATLAB, fiabilité, chaos polynomial.