Probabilistic Fault Identification Using a Committee of Neural Networks and Vibration Data

Abstract

Bayesian-formulated neural network architecture is implemented using a hybrid Monte Carlo method for probabilistic fault identification in a population of ten nominally identical cylindrical shells using vibration data. Each cylinder is divided into three substructures. Holes of 12 mm in diameter are introduced in each of the substructures. Vibration data are measured by impacting the cylinders at selected positions using a modal hammer and measuring the acceleration responses at a fixed position. Modal energies, defined as the integrals of the real and imaginary components of the frequency response function over 12-Hz frequency bandwidths, are extracted and transformed into the coordinate modal energy assurance criterion. This criterion and the identity of faults are used to train the frequency response function (FRF) neural network. Modal analysis is then employed to identify modal properties. Mode shapes are transformed into the coordinate modal assurance criterion. The natural frequencies and the coordinate modal assurance criterion, as well as the identities of faults, are utilized to train the modal-property neural network. The weighted average of the modal-property network and the FRF network form a committee of two networks. The committee approach is observed to give lower mean square errors and standard deviations (thus, a higher probability of giving the correct solution) than the individual methods. This approach gives accurate identities of damage and their respective confidence intervals while requiring affordable computational resources.