Probabilistic Robust Design For Dynamic Systems Using Metamodelling

Abstract

Designers use simulations to observe the behaviour of a system and to make design decisions to improve dynamic performance. However, for complex dynamic systems, these simulations are often time-consuming and, for robust design purposes, numerous simulations are required as a range of design variables is investigated. Furthermore, the optimum set is desired to meet specifications at particular instances in time. In this thesis, the dynamic response of a system is broken into discrete time instances and recorded into a matrix. Each column of this matrix corresponds to a discrete time instance and each row corresponds to the response at a particular design variable set. Singular Value Decomposition (SVD) is then used to separate this matrix into two matrices: one that consists of information in parameter-space and the other containing information in time-space. Metamodels are then used to efficiently and accurately calculate the response at some arbitrary set of design variables at any time. This efficiency is especially useful in Monte Carlo simulation where the responses are required at a very large sample of design variable sets. This work is then extended where the normalized sensitivities along with the first and second moments of the response are required at specific times. Later, the procedure of calculating the metamodel at specific times and how this metamodel is used in parameter design or integrated design for finding the optimum parameters given specifications at specific time steps is shown. In conclusion, this research shows that SVD and metamodelling can be used to apply probabilistic robust design tools where specifications at certain times are required for the optimum performance of a system.