A new, multiple model approach for detection and identi cation of structural damage in a rotating helicopter blade is presented. A full-scale rotor analysis using a detailed model of the hingeless blade elastic behavior and dynamics is carried out. Several stiffness damage levels and locations are considered, and a set of Kalman lters is constructed accordingly. The best tting model is determined in a probabilistic manner. Because the new method is model-based, the need for a training stage is eliminated, and a wide range of ight regimes can be handled. Moreover, process and measurement noises are treated inherently, contributing to the superiority of the method over previously published related methods. A Monte Carlo simulation study is used to provide a comprehensive analysis of the statistical nature of the method. Single-blade analysis results demonstrate excellent identi cation capability and good damage detection in the presence of a relatively high level of noise. The case of damage located near the blade's root combined with a sensor near the tip produces a high damage identi cation probability. In less detectable cases, such as damage located in midspan, a simple statistical procedure enables achieving a high detection probability along with a low false alarm rate.
NomenclatureA j = j th lter residual covariance matrix a = vector of unknown parameters (fault in uence) B = continuous-time control matrix F = continuous-time state transition matrix G = continuous-time process noise distribution model H = measurement matrix N = number of single-run repetitions n= number of runs where damage was detected n d = predetermined threshold P = lter error covariance matrix P D = overall detection probability P FA = overall false alarm probability p = probability p D = single-run detection probability p FA = single-run false alarm probability Q d = discrete-time process noise covariance matrix q = tness probability R = measurement noise variance matrix r = residual vector u = control vector v = measurement noise vector w = process noise vector w d = equivalent discrete-time process noise vector x = state vector x d = damage location along the blade's span (measured from root) x s = sensor location along the blade's span (measured from root) O x j = j th lter predicted state estimate Z i = measurement history from the rst sample until sample time t i z = measurement vector H = mode shape matrix » = vector of elastic mode participating factors U = state transition matrix W = control matrix
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