Application Lattice Constrained Optimization Method (LCOM) to Inverse Problems in Engineering

摘要

In this paper lattice constrained optimization method (LCOM) is applied to inverse problems in engineering. For solving inverse problems, it is important to use a priori information effectively. This method enables to use the a priori information which estimates take only certain discrete valuables. In example of nondestructive inspection of defect, it is seen that the density of material can be treated as 0 or 1. These class of information has not been used in conventional methods. An objective function for a LCOM is derived from the observation equation which describes an engineering system by using the maximum likelihood estimation (MLE) theory. The MLE gives a conditional probability density function which provides probability state for certain observation. This study deals with the case that the conditional probability density function is represented as the Gaussian distribution. The solution space can be represented as lattice-like located points when considering a priori information which estimates take discrete valuables. This can be treaded as the constraint condition in LCOM. A numerical example of solving inverse problem for heat source identification demonstrates the effectivity of the proposed method.