Neural Networks for Inverse Problems in Damage Identification and Optical Imaging Using Principal Component Analysis and Orthogonal Arrays

An obstacle in applying artificial neural networks (NNs) in solving inverse problems is that the dimension and the size of the training sets required for the NNs can be too large to use NNs effectively with the 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 excessively 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 system. Here, we try to use NNs with PCA and OAs in solving two parameter identification problems in two different fields. The first problem is identifying the location of damage in cantilever plates using the vibration response of the structure. The 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, using the simulation of the photon intensity and the photon mean time of flight in perfect and imperfect tissues using the finite element method. *†