Structure reduction and robust experimental design for distributed parameter identification
Ne‐Zheng Sun · Inverse Problems · 2005
Designing an experiment for identifying a distributed parameter is a very challenging problem when the spatial variability of the parameter is unknown. First, we need to determine an appropriate structure complexity for the unknown parameter. A more complicated structure needs more data for identification. Second, we need to evaluate the sufficiency of an experiment design before it is actually conducted. In this paper, the complexity of parameter structure is determined by the accuracy requirement of model application, and the sufficiency of data is evaluated by solving a generalized inverse problem. The worst-case parameter (WCP) defined in this paper is the one that causes the maximum deviation in model application when its structure is simplified. The WCP of a structure can be found by solving a discrete optimization problem with the genetic algorithm. Quantitative relationships between structure complexity, parameter identifiability, data sufficiency and model reliability are derived. For example, it has been proven that if an experimental design is sufficient for identifying the WCP then it must be sufficient for identifying all other parameters with the same structure or simplified structures in the admissible region, and thus, it is a robust design. Based on the theoretical results and algorithms presented in this paper, we may develop a cost-effective methodology for constructing reliable distributed parameter models.