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 cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. 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 two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Parameters identification by a single point free response measurement

When a thin rectangular plate is restrained on the two long edges and free on the remaining edges, the equivalent stiffness of the restraining joints can be identified by the order of the natural frequencies obtained using the free response of the plate at a single location. This work presents a method to identify the equivalent stiffness of the restraining joints, being represented as simply supporting the plate but elastically restraining it in rotation. An integral transform is used to map the autospectrum of the free response from the frequency domain to the stiffness domain in order to identify the equivalent torsional stiffness of the restrained edges of the plate and also the order of natural frequencies. The kernel of the integral transform is built interpolating data from a finite element model of the plate. The method introduced in this paper can also be applied to plates or shells with different shapes and boundary conditions. © 2011 Elsevier Ltd. All rights reserved.