NONLINEAR DYNAMICS, IDENTIFICATION AND MONITORING OF STRUCTURES Steady state shift damage localization D. Bernal . A. Kunwar Received: 28 December 2015 / Accepted: 22 July 2016 / Published online: 2 August 2016 Ó Springer Science+Business Media Dordrecht 2016 Abstract The accuracy of the identified modal model is the weak link in many vibration based damage localization schemes. This paper presents a localization approach that avoids identification by operating with two frequency domain subspaces, one obtained by Fourier transformation of output mea- surements and the other from a model of the reference state and a postulated damage distribution. The approach differs from a model updating framework in that only the damage distribution, and not the extent, enters the formulation. The method operates on the premise that the loads are time limited, have an invariant distribution in space and requires that the histories be repeatable, or that the excitation be a single history, in which case repeatability is not necessary. The time histories of the excitation are not used in the technique and therefore need not be known. It is shown that multiple damages can be considered without combinatorics if e  j where e is the number of available actuators and j is the rank of the change in the transfer matrix due to damage. The constraint on the number of measurements, m, is m  j: The method, designated as the steady state shift damage localization (S3DL) is experimentally tested on an aluminum plate where damage is simulated by mass additions and by an edge cut. Keywords Damage localization  Frequency domain  Steady state response  Harmonic excitation  Thin plates 1 Introduction Damage characterization by model updating is poorly conditioned. Efforts to improve conditioning have led to a strategy where the problem is factored into: (1) detection, (2) location and (3) quantification and solved in cascade fashion. A fourth stage, prognosis, is important in some cases but it is not part of model update factorization. The detection task is usually approached in a data-driven manner by testing the hypothesis that the signals measured during monitor- ing are from the same system that generated the reference model [1, 2]. If the monitoring data is such that this (null) hypothesis cannot be accepted at some preselected level of confidence damage is announced. In cases where damage can be identified as an ‘‘unexpected reflector of high frequency waves’’ triangulation, using an appropriately designed net- work of emitters and recorders can in principle be used D. Bernal (&) Civil and Environmental Engineering Department, Center for Digital Signal Processing, Northeastern University, Boston, MA 02115, USA e-mail: bernal@neu.edu A. Kunwar Civil and Environmental Engineering Department, Northeastern University, Boston, MA, USA 123 Meccanica (2016) 51:2861–2871 DOI 10.1007/s11012-016-0501-4