Topic
Polynomial chaos
About: Polynomial chaos is a research topic. Over the lifetime, 3700 publications have been published within this topic receiving 86289 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, three kinds of uncertainty factors, namely the sheath resistivity per unit length, the equivalent grounding resistance on both sides, and the length of the cable section, were taken as random input variables without interaction.
Abstract: In HV cable fault location technology, line parameter uncertainty has an impact on the location criterion and affects the fault location result. Therefore, it is of great significance to study the uncertainty quantification of line parameters. In this paper, an impedance-based fault location criterion was used for an uncertainty study. Three kinds of uncertainty factors, namely the sheath resistivity per unit length, the equivalent grounding resistance on both sides, and the length of the cable section, were taken as random input variables without interaction. They were subject to random uniform distribution within a 50% amplitude variation. The relevant statistical information, such as the mean value, standard deviation and probability distribution, of the normal operation and fault state were calculated using the Monte Carlo simulation (MCS) method, the polynomial chaos expansion (PCE) method, and the univariate dimension reduction method (UDRM), respectively. Thus, the influence of uncertain factors on fault location was analyzed, and the calculation results of the three uncertainty quantification methods compared. The results indicate that: (1) UQ methods are effective for simulation analysis of fault locations, and UDRM has certain application prospects for HV fault location in practice; (2) the quantification results of the MCS, PCE, and UDRM were very close, while the mean convergence rate was significantly higher for the UDRM; (3) compared with the MCS, PCE, and UDRM, the PCE and UDRM had higher accuracy, and MCS and UDRM required less running time.
TL;DR: In this paper , the authors proposed a method for the reliability analysis of bridge under different types of loads by combining Polynomial Chaos (PC) and subset simulation techniques, in which the PC coefficients are obtained from the least-squares method.
Abstract: Reliability analysis of bridges is essential for the design of civil engineering structures. The classical methods, such as Monte Carlo Simulation (MCS) and subset simulation techniques, may provide accurate results. However, since the finite element model of the large-scale civil engineering structures usually consists of a large number of degrees of freedom, structural reliability analysis of such structures is time-consuming and computational intensive, which may restrict the use of these methods. This paper proposes a novel method for the reliability analysis of bridge under different types of loads by combining Polynomial Chaos (PC) and subset simulation techniques. The surrogate model of the limit state function is approximated by using the PC expansion, in which the PC coefficients are obtained from the least-squares method. The subset simulation with a PC-based surrogate model is then used to estimate the rare failure probability. Reliability analyses of bridge structures under different loading types, that is, static load, dynamic moving load, and seismic load are performed. Studies by using the MCS method and the classical subset simulation are also conducted, and the results from the proposed approach are compared with those from MCS and subset simulation to demonstrate the accuracy and efficiency of the proposed method.
TL;DR: In this article , wavelet collocation approach has been united with the polynomial chaos expansion for numerically solving the stochastic partial differential equations, which is associated with the concept of autocorrelation functions of compactly supported Daubechies scaling functions.
TL;DR: In this paper , a polynomial chaos expansion-based method for uncertain power flow calculation with parametric probability boxes (p-boxes) is proposed, and the interval-valued Borgonovo index is proposed for global sensitivity analysis and identifying the input variables that have critical impacts on systems.
24 Nov 2022
TL;DR: In this paper , the authors combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data.
Abstract: The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the ``interesting'' projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and is thus subject to the same physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.