Journal of Sound and < ibration (2000) 230(3), 561 } 589 doi:10.1006/jsvi.1999.2630, available online at http://www.idealibrary.com on TIME DOMAIN ESTIMATION OF RESPONSE AND INTENSITY IN BEAMS USING WAVE DECOMPOSITION AND RECONSTRUCTION B. R. MACE AND C. R. HALKYARD Department of Mechanical Engineering, ¹ he ;niversity of Auckland, Private Bag 92019, Auckland, New Zealand (Received 29 June 1998, and in ,nal form 4 August 1999) A method is described by which instantaneous values of the response, the internal forces and the intensity in beams can be estimated as functions of time. The individual components of intensity which propagate in each direction and the components due to shear and moment can also be estimated. The estimates are provided in real time by digitally "ltering the outputs of an array of sensors. The digital "lters are designed in the frequency domain using a wave decomposition approach and reconstructed in the time domain as FIR "lters in this paper. The design and implementation process is described, numerical simulations of measurements in the far"eld performed and an experimental implementation presented. The method is relatively insensitive to sensor miscalibration and measurement noise compared to other approaches, and yields instantaneous estimates as well as time averages.  2000 Academic Press 1. INTRODUCTION In this paper a technique for the time domain measurement of structural response and intensity is described. The technique is based on a wave decomposition and reconstruction approach. The outputs of an array of sensors are digitally "ltered to provide estimates of any desired response quantity such as beam rotation, shear force, bending moment and so on, as well as net intensity and the components of the intensity which #ow in each direction along the beam. The sensors may be of any form, such as accelerometers or non-contact devices. While the approach described is applicable to the estimation of any response quantity, the emphasis in this paper is placed somewhat on the estimation of intensity, that is, the #ow of vibrational energy through a structure, and its components. The measurement of intensity has attracted signi"cant attention in the last few decades or so. However, practical applications are relatively few, especially - This work was carried out while the author was at Industrial Research Ltd., P.O. Box 2225, Auckland, New Zealand. 0022-460X/00/080561#29 $35.00/0  2000 Academic Press