A comparative study is performed to show the efficiency and limitations of the various experimental designs in uncertainty quantification of engineered systems with varying input dimensionality and computational complexity. advectionpde, a MATLAB code which solves the advection partial differential equation (PDE) dudt + c dudx 0 in one spatial dimension, with a constant velocity c, and periodic boundary conditions, using the FTCS method, forward time difference, centered space difference.
A modified IEEE 33-node distribution system is used to conduct the numerical experiments for the accuracy and efficiency verification of the proposed PLF method, under the MatlabR2016a platform. This chapter will introduce some state-of-the-art DoEs used for uncertainty quantification problems. An improved Latin hypercube sampling based Monte Carlo simulation method is utilised to solve PLF problems. The accuracy level of the metamodel depends on the DoE over the input design space. To build a PCE metamodel, design of experiments (DoEs) are carried out, i.e., determining the design points (in the input space) where the original (high-fidelity) computational model needs to be evaluated. Latin hypercube sampling can be implemented using the following. It is widely used to generate samples that are known as controlled random samples and is often applied in Monte Carlo analysis because it can dramatically reduce the number of simulations needed to achieve accurate results. Polynomial chaos expansion (PCE) has been considered as one of the promising metamodeling methods. ways to sample integers or real numbers from a uniform distribution (such as the core. Latin hypercube sampling is a method that can be used to sample random numbers in which samples are distributed evenly over a sample space. Metamodels or surrogate models are often used as substitutes to those high-fidelity numerical models to overcome this issue. In the context of UQ, one of the major challenges is the computational demand of the numerical (finite element) model that is used to analyze the large-scale engineering systems under consideration. In the past decade, uncertainty quantification (UQ) has received much attention, particularly in the research areas of reliability and risk analysis, sensitivity analysis, and optimization under uncertainty, to mention a few.