Multiple Quantities Of Interest Research Articles

An all-encompassing study on the joint effect of powder feedstock characteristics and manufacturing process parameters on the densification and mechanical properties of additively manufactured nickel alloy 718

Laser-powder bed fusion (L-PBF) is a commonly employed additive manufacturing (AM) technique in manufacturing 3D metallic parts with complex geometries from powder materials. It is a complex process with more than 100 process parameters affecting the properties of fabricated parts. Studies on AM of nickel alloy 718 are currently focusing on investigating the effect of the process parameters and heat treatment on final part properties. Nevertheless, the effect of different powder characteristics such as particle size distribution (PSD), the presence of fine particles, powder reuse, and moisture content has not been studied comprehensively in the literature. In this study, two types of powder: virgin and recycled, as well as four parameters: PSD, which is represented by the median particle size and the particle size range, moisture content, and volumetric energy density (VED), were studied. To reduce experimental cost and burden, statistical design of experiment (DOE) techniques were utilized. Then, the measured results were analyzed using analysis of variance (ANOVA) to ascertain the effect of the different powder characteristics on multiple quantities of interest (QoIs). Different densification and mechanical tests were performed, and their outputs were studied as the QoIs. This study revealed that VED, powder type, PSD range, and median are the most common significant factors for most QoIs. Meanwhile, moisture content had a significant effect only on the Charpy impact energy. Besides, the study showed that the presence of fine particles <20μm improved the densification of the fabricated parts but reduced the mechanical properties.

UNCERTAINTY QUANTIFICATION OF WATERFLOODING IN OIL RESERVOIRS COMPUTATIONAL SIMULATIONS USING A PROBABILISTIC LEARNING APPROACH

In the present paper, we propose an approach based on probabilistic learning for uncertainty quantification of the water-flooding processes in oil reservoir simulations, considering geological and economic uncertainties and multiple quantities of interest (QoIs). We employ the probabilistic learning on manifolds (PLoM) method, which has achieved success in many different applications. This methodology enables the construction of surrogate models to cope with expensive computational costs using high-fidelity simulators. It also allows the incorporation of unavoidable uncertainties, like in the porosity and permeability fields, resulting from difficulties in the characterization of the heterogenous subsurface media, or arising from economic instabilities. We are particularly interested in computing high-order statistics of the system response, which combines oil operational production and economic aspects, to evaluate risk losses. In this paper, we assess the efficacy of the PLoM stochastic surrogate through two numerical examples contemplating the above uncertainties and typical reservoir configurations.

The maximum entropy method for data fusion and uncertainty quantification in multifunctional materials and structures

The quantification of uncertainty in intelligent material systems and structures requires methods to objectively compare complex models to measurements, where the majority of cases include multiple model outputs and quantities of interests given multiphysics coupling. This creates questions about constructing appropriate measures of uncertainty during fusion of data and comparisons between data and models. Novel materials with complex or poorly understood coupling can benefit from advanced statistical analysis to judge models in light of multiphysics data. Here, we apply the Maximum Entropy (ME) method to more complicated ferroelectric single crystals containing domain structures and soft electrostrictive membranes under both mechanical and electrical loading. Multiple quantities of interest are considered, which requires fusing heterogeneous information together when quantifying the uncertainty of lower fidelity models. We find that parameters, which were initially unidentifiable using a single quantity of interest, become identifiable using multiple quantities of interest. We also show that posterior densities may broaden or narrow when multiple data sets are fused together. This is likely due to conflict or agreement, respectively, between the different quantities of interest and the multiple model outputs. Such information is important to advance our predictions of intelligent materials and structures from multi-model inputs and heterogeneous data.

Multifidelity framework for uncertainty quantification with multiple quantities of interest

A systematic framework, involving flow simulation and model selection at many fidelity (resolution) levels, is introduced to accurately quantify the impact of geological uncertainty on multiple output quantities of interest (QoIs). The methodology considers large numbers of realizations (O(1000) in the case presented), though very few (O(10)) simulations are performed at the highest resolutions. We proceed from coarser to finer resolution levels, and at each stage simulation results are used to select a subset of realizations to simulate at the next (higher) fidelity level. Models are constructed at all resolution levels through upscaling of the underlying fine-scale realizations. A global transmissibility upscaling procedure is applied for this purpose. Approximate cumulative distribution functions (CDFs) are constructed for all QoIs considered. The QoI values themselves are always computed at the finest scale, but corresponding percentile values are determined using results at a “rank-preserving” (coarser) fidelity level. Detailed results are presented for oil-water flow in a channelized system. Simulations at seven different fidelity levels are used, and eight QoIs are evaluated. Results for the example considered demonstrate accurate reconstruction of fine-scale CDFs for all QoIs, with a speedup factor of about 18 relative to performing all simulations on the fine scale.

Exploration of efficient reduced‐order modeling and a posteriori error estimation

SummaryEfficient algorithms are considered for the computation of a reduced‐order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced‐order model solutions, for a single and multiple quantities of interest. Various numerical results indicate the efficacy of the approach. Copyright © 2016 John Wiley &amp; Sons, Ltd.