Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte-Carlo method for probabilistic fault identification in structures. Each of the 20 nominally identical cylindrical shells is arbitrarily divided into three substructures. Holes of 10-15 mm diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the coordinate modal assurance criterion (COMAC), with natural-frequency-vector taken as an additional mode, are utilised to train the modal-property-network and the COMAC-network. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the coordinate modal energy assurance criterion (COMEAC) are used to train the modal-energy-network and the COMEAC-network. The average of the modal-property-network and the modal-energy-network as well as the COMAC-network and the COMEAC-network form a modal-energy-modal-property-committee and COMEAC-COMAC-committee, respectively. Both committees are observed to give lower mean square errors and standard deviations than their respective individual methods. The modal-energy- and COMEAC-networks are found to give more accurate fault identification results than the modal-property-network and the COMAC-network, respectively. For classification (the presence or absence of faults) the modal-property-network is found to give the best results, followed by the COMEAC-COMAC-committee. The modal-energies and modal properties are observed to give better identification of faults than the COMEAC and the COMAC data. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective standard deviations.