This thesis primarily discuss about the development of design analysis framework
for high-dimensional problems that includes reliability analysis (RA),
sensitivity analysis (SA), and uncertainty quantification (UQ). Monte Carlo
Simulation (MCS) is commonly used to perform the analysis, but instead of
using MCS solely, a metamodel called Kriging was used to assist the design
analysis process. Usually UQ, SA, and RA need numerous function evaluation,
however the implementation of metamodel could help alleviate this problem
by substituting the function evaluation with the metamodel prediction. For
very high-dimensional problem e.g. 20 design variables or more, the use of
Kriging is computationally expensive. Therefore, a dimensionality reduction
method is further employed to modify the Kriging kernel function resulting in
significant speed gain while maintaining the accuracy performance of the ordinary
Kriging. Later, the framework was tested on a various functions ranging
from 10 dimensions to 100 dimensions in three applications, UQ, SA, and RA.
The result shows that when the dimensionality of the function is insufficiently
high Kriging with Partial Least Square (KPLS) only slightly worse to ordinary
Kriging (OK) in terms of accuracy of the applications. However, when
the dimensionality is high and the number of sampling points is low KPLS
outperforms OK in terms of accuracy and the execution time of those three
applications.