相关论文: Adaptive Polynomial Chaos Expansion for Uncertaint…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike existing PCEs, whether classical or generalized, no…
In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…
The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…
Automating the design of microstrip antennas has been an active area of research for the past decade. By leveraging machine learning techniques such as Genetic Algorithms (GAs) or, more recently, Deep Neural Networks (DNNs), a number of…
In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…
Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…
We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…
A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…