Journal of Sound and < ibration (2000) 237(4), 727}732 doi:10.1006/jsvi.1999.3003, available online at http://www.idealibrary.com on LETTERS TO THE EDITOR IS DAMAGE IDENTIFICATION USING VIBRATION DATA IN A POPULATION OF CYLINDERS FEASIBLE? T. MARWALA AND H. E. M. HUNT Department of Engineering, ;niversity of Cambridge, ¹rumpington Street, Cambridge, CB21PZ, England (Received 5 May 1999, and in ,nal form 14 December 1999) 1. INTRODUCTION Fault identi"cation in mechanical and aerospace structures at the manufacturing stage o!ers substantial economic bene"ts. Vibration data have been employed with varying degrees of success to identify faults in structures [1}5]. However, in the literature there is little coverage of fault identi"cation using vibration data from a population of structures. Srinivasan and Kot [6] have studied the feasibility of using vibration data to identify faults in cylinders. These authors tested a cylinder, which had a machined notch, suspended by relatively soft springs to simulate free boundary conditions. The authors examined changes in the natural frequencies and mode shapes as a result of damage. They found that the presence of damage changes the vibration response of the cylinder. In this study, the feasibility of using vibration data to identify faults in a population of 22 seam-welded cylindrical shells made of steel is assessed. Each cylinder is excited at various locations using an impulse hammer and vibration responses are measured using an accelerometer located at "xed position. Each cylinder is measured three times under di!erent boundary conditions by changing the orientation of a rectangular sponge inserted inside the cylinder which is rested on bubble wrap, to simulate a free}free environment (see Figure 1). The number of sets of measurements taken for undamaged population is 66 (22 cylinders3 for di!erent boundary conditions). Each cylinder is divided into three equal substructures and holes of 10}15 mm are introduced at the centres of the substructures. The total number of measurements taken for cylinders with holes is 66. From the measured vibration data frequency response functions (FRFs) are calculated. Modal properties, i.e., natural frequencies and mode shapes, are then extracted from the FRFs using modal analysis. Mode shapes are transformed into the co-ordinate modal assurance criterion (COMAC) [7] by computing the correlation between mode shape matrix from each fault case and the median mode shape matrix of a population of undamaged cylinders. Modal energies are then calculated from the FRFs by determining the integrals of the real and imaginary components of the FRFs over chosen bandwidths that bracket the natural frequencies [4]. Similarly, modal energies are transformed into the co-ordinate modal energy assurance criterion (COMEAC) by calculating the correlation between each measured modal energy matrix and the median of the modal energy matrices from population of undamaged cylinders. By comparing the modal properties, modal energies, the COMAC and the COMEAC between undamaged and damaged populations the feasibility of using vibration data for fault identi"cation is assessed. The changes of these parameters as a result of faults are 0022-460X/00/440727#06 $35.00/0  2000 Academic Press