Fault Identification Using Pseudomodal Energies and Modal Properties

The pseudomodal energy, dee ned as the integrals of the real and imaginary components of the frequencyresponse functions over various frequency ranges, is proposed for fault identie cation in structures. Equations that formulate pseudomodal energies in the modal domain and their respective sensitivities are derived in receptance and inertance form. When tested on a simulated cantilevered beam, pseudomodal energies are found to be more resistant to noise in the data than the mode shapes and are able to take into account the out-of-frequency-band modes and to be better indicators of faults than the modal properties. Furthermore, they are more sensitive to faults than the natural frequencies and are equally as sensitive to faults as the mode shapes. The pseudomodal energies are computationally faster to calculate than the modal properties. When tested on a population of 20 steel cylinders, the pseudomodal energies are, on average, better indicators of faults than the modal properties. Nomenclature aq = lower frequency bound for the qth pseudomodal energy bq = upper frequency bound for the qth pseudomodal energy [C] = damping matrix fFg = force input vector gp = changes in the pth structural parameter Hkl = frequency-response function due to excitation at k and measurement at l j = p i1 [K] = stiffness matrix [M] = mass matrix