Neural Networks for Inverse Problems Using Principal Component Analysis and Orthogonal Arrays

An obstacle in applying artificial neural networks (NNs) to system identification problems is that the dimension and the size of the training set for NNs can be too large to use them effectively in solving a problem with available computational resources. To overcome this obstacle, principal component analysis (PCA) can be used to reduce the dimension of the inputs for the NNs without impairing the integrity of data and orthogonal arrays (OAs) can be used to select a smaller number of training sets that can efficiently represent the given behavior system. NNs with PCA and OAs are used here in solving two parameter identification problems in two different fields. The first problem is identifying the location of damage in cantilever plates using the free vibration response of the structure. The free vibration response is simulated using the finite element method. The second problem is identifying an anomaly in an illuminated opaque homogeneous tissue using near-infrared light based on the simulation of the photon intensity and the photon mean time of flight in perfect and imperfect tissues using the finite element method.