Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Robust topology optimization for multi-material structures considering material uncertainties

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

The strong growth of Electrical Vehicles (EVs) necessities the fast EV charging infrastructure. The variation of charging demand from commercial fast charging stations may significantly impact power system stability. To fast assess this impact, this paper proposes an uncertainty quantification algorithm based on polynomial chaos expansion (PCE). A stochastic transportation model is first introduced to project the regional Level 3 EV charging demand and the predicted profiles are then utilized to construct the orthogonal polynomials for PCE. The correlation among commercial Level 3 EV charging stations is also considered. Simulation results show that the proposed PCE method is able to solve the computational complexity issues from the uncertainties of random variables and to save computing resources without compromising the result accuracy when compared with Monte Carlo simulation (MCS). The high efficacy and accuracy of the proposed approach make it potential for fast uncertainty quantification in power system dynamic analysis.

In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the va...

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

In engineering systems with uncertain parameters, it is crucial for system analysis and control to analyze the relationship between these uncertain parameters and system outputs (or states). Nevertheless, the acquisition of this parameter-output function, termed parametric problem in this article, is not easy because it is usually a complicated implicit nonlinear function. Polynomial chaos expansion (PCE), based on the generalized Fourier expansion, is a state-of-the-art method for both parametric problems and uncertainty quantification. Its basic idea is to approximate the implicit parameter-output function with a globally optimal explicit polynomial function, which remains accurate in the case of strong nonlinearity compared with the local Taylor expansion. This article provides a review of PCE and its applications in parametric problems. In terms of PCE theory, a rigorous and complete framework of PCE is established and a detailed review of typical PCE methods is presented. In terms of applications, two kinds of general parametric problems, namely parametric nonlinear algebraic equations and parametric differential equations, as well as their examples in some engineering fields, are introduced. Furthermore, some worthwhile future works are presented at the end of this article, which may facilitate the development of PCE.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation

Equations governing flow and transport in randomly heterogeneous porous media are stochastic and scale dependent. In the moment equation (ME) method, exact deterministic equations for the leading moments of state variables are obtained at the same support scale as the governing equations. Computable approximations of the MEs can be derived via perturbation expansion in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for standard deviation smaller than one. Here, we consider steady‐state saturated flow in a porous medium with random second‐order stationary conductivity field. We show it is possible to identify a support scale , where the typically employed approximate formulations of MEs yield accurate (statistical) moments of a target state variable. Therefore, at support scale and larger, MEs present an attractive alternative to slowly convergent Monte Carlo (MC) methods whenever lead‐order statistical moments of a target state variable are needed. We also demonstrate that a surrogate model for statistical moments can be constructed from MC simulations at larger support scales and be used to accurately estimate moments at smaller scales, where MC simulations are expensive and the ME method is not applicable.

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

This study focuses on the development of efficient surrogate models by polynomial chaos expansion (PCE) for the prediction of the long-term extreme surge motion of a moored floating offshore structure. The structure is subjected to first-order and second-order (difference-frequency) wave loading. Uncertainty in the long-term response arises from contrasting sea state conditions, characterized by significant wave height, Hs, and spectral peak period, Tp, and their relative likelihood of occurrence; these two variables are explicitly included in the PCE-based uncertainty quantification (UQ). In a given sea state, however, response simulations must be run for the associated Hs and Tp; in such simulations, typically, a set of random amplitudes and phases define an irregular wave train consistent with that sea state. These random amplitudes and phases for all the frequency components in the wave train introduce additional uncertainty in the simulated waves and in the response. The UQ framework treats these two sources of uncertainty—from Hs and Tp on the one hand, and the amplitude and phase vectors on the other—in a manner that efficiently yields long-term surge motion extreme predictions consistent with more expensive Monte Carlo simulations (MCS) that serve as the “truth” system. To reduce uncertainty in response extremes that result from sea states with a low likelihood of occurrence, importance sampling is employed with both MCS- and PCE-based extreme response predictions. Satisfactory performance with such efficient surrogate models can help in assessing the long-term response of various offshore structures.

A cell-based smoothed finite element method with discrete shear gap technique is used to study the stochastic free vibration behavior of functionally graded plates with material uncertainty. The plate kinematics is based on the first-order shear deformation theory and the effective material properties are estimated by simple rule of mixtures. The input random field is represented by the Karhunen–Loéve expansion and the polynomial chaos expansion is used to represent the stochastic output response. The accuracy of the proposed approach in terms of the first- and the second-order statistical moments are demonstrated by comparing the results with the Monte Carlo Simulations. A systematic parametric study is carried out to bring out the influence of the material gradient index, the plate aspect ratio and the skewness of the plate on the stochastic global response of functionally graded plates. It is inferred that all the considered parameters significantly influence the statistical moments of the first fundamental mode.

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

Rapid design centering of multi-band antennas using knowledge-based inverse models and response features

In this article, uncertainty quantification is applied to molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. We consider a silica pore model connecting two reservoirs containing a solution of sodium (Na(+)) and chloride (Cl(-)) ions in water. An ad hoc concentration control algorithm is developed to simulate a concentration driven counter flow of ions through the pore, with the ionic flux being the main observable extracted from the MD system. We explore the sensitivity of the system to two physical parameters of the pore, namely, the pore diameter and the gating charge. First we conduct a quantitative analysis of the impact of the pore diameter on the ionic flux, and interpret the results in terms of the interplay between size effects and ion mobility. Second, we analyze the effect of gating charge by treating the charge density over the pore surface as an uncertain parameter in a forward propagation study. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of intrinsic noise and quantify the impact of parametric uncertainty on the MD predictions. We highlight the challenges arising from the heterogeneous nature of the system, given the several components involved, and from the substantial effect of the intrinsic thermal noise.