Probabilistic load flow calculation based on sparse polynomial chaos expansion

Adaptive sparse polynomial chaos expansion based on least angle regression

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin typ...

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistic...

Classification Algorithms based on Generalized Polynomial Chaos

Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion

To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical pa...

Minimal Sparse Sampling for Fourier-polynomial Chaos in Acoustic Scattering

Single frequency acoustic scattering from an uncertain surface (with sinusoidal components) admits an efficient Fourier-polynomial chaos (FPC) expansion of the acoustic field. The expansion coefficients are computed nonintrusively, i.e., by functional sampling from existing acoustic models. The structure of the acoustic decomposition permits sparse selection of FPC orders within the framework o...