This study focuses on crack identification in beams from vibration measurements using principles of dynamic state estimation. The FEM is used to model the beam with cracked-beam elements that account for the presence of an edge crack under near-tip elasto-plastic conditions. The crack size and its location are treated as the variables that are identified using a particle filter algorithm. A parametric study is first carried out with synthetic measurements to numerically analyze the performance of the algorithm. Subsequently, using measurements acquired from physical experiments involving a cantilever beam subjected to arbitrary excitations, the proposed algorithm is used to identify the size and location of crack-like defects. The proposed method does not require measurements of the undamaged beam, hence, can be used for crack identification in beams for which no earlier measurements are available. antiresonance peaks in the frequency response functions have also been carried out to locate cracks [20][21][22]. Alternative methods that use modal parameters for crack detection include optimization approaches in conjunction with perturbation methods [23] and wavelet analysis [24,25].Time domain-based studies using iterative approaches for locating and estimating the severity of damage from vibration measurements have been discussed in [26][27][28][29][30]. These studies typically introduce the damage into the numerical model either through an unknown variable or a function with unknown parameters. Subsequently, these unknown quantities are estimated through an iterative procedure applied on available response measurements. Unlike modal analysis-based methods, which are primarily applicable to linear systems, these methods are applicable in nonlinear systems [28,29] as well as when measurements are noisy [30,31]. However, inverse methods using deterministic models lack robustness because of the unknown and unavoidable errors that enter the analysis due to the inevitable inaccuracies in mathematical modeling and data acquisition. These errors enter the inverse analysis in the form of noise, which need to be appropriately taken into account.The robustness of inverse methods can be improved by explicit modeling of the uncertainties (i.e., noise) using a probabilistic approach. This has led to adopting Bayesian filtering frameworks in the damage-detection algorithms. The focus in these methods is not on identifying the exact location and sizes of the damage but on defining their corresponding probability density functions (pdf) and estimating their most probable values, conditioned on the available measurements. A set of variables are defined for the system and/or damage parameters to be identified; these are modeled as random variables with an assumed pdf. A vector of realizations for these random variables is simulated in the computer having the specified probabilistic properties. Corresponding to each realization for the system parameters, a mathematical model is used to predict the structure response for a particular...

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