Related papers: Efficient Polynomial Chaos Expansion for Uncertain…
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…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…
Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but…
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…
This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…
Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…
Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…
Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying…
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…
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…
Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…
Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear…
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…
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…