Structural Damage Detection from Transient Responses using Square-Root Unscented Filtering

Paper number

IAC-07-C2.1.06

Author

Dr. Paul Williams, Australia

Year

2007

Abstract

Health monitoring of large structures is inherently difficult due to the relatively small number of available sensors/measurements that can be made within the budgetary constraints.  To accurately detect the presence of damage in a structure requires a reliable model, or at least a good representation of the structure prior to damage.  Approaches to detecting and localizing damage are predominantly based on either frequency changes or transient responses.  The use of frequency changes requires techniques for extracting the natural frequencies of the structure, which can be difficult at higher frequencies.  Furthermore, these approaches are difficult to apply regularly during the structure’s life cycle.  On the other hand, transient responses or closed-loop responses are available much more readily during operation and would appear to be more suitable for online damage detection.

In order to detect damage in a large structure, the structural characteristics such as mass matrices and stiffness matrices need to be estimated.  One of the associated difficulties of estimating the mass matrix from transient/forced responses is that the parameters do not appear linearly in the output.  This necessitates the use of nonlinear filtering – the most popular implementation of which is the extended Kalman filter.  The extended Kalman filter has two major drawbacks: 1) it requires Jacobians of the state transition and output functions, 2) it must be initialized close to the true solution in order for the linearization of the statistical properties to be valid.

In this paper, a robust filter for detecting damage based on measured responses is employed that does not require linearization and does not require Jacobian calculations.  Instead, the state estimates are propagated directly through the nonlinear functions, which allows preservation of the statistical properties to second order.  Higher order preservations are also possible.  The filter is based on the unscented filter introduced by Julier and Uhlmann.  A square-root version is implemented to ensure that the covariance estimates remain positive definite.

The damage detection problem is solved online by updating the structural parameter estimates using a limited amount of measurement data.  Example results are presented for large-scale truss structures, where the only measurements are accelerometer data from a limited number of nodes.  The numerical results show that the approach is capable of detecting changes in the structure from the outputs online.

Abstract document

IAC-07-C2.1.06.pdf

Manuscript document

IAC-07-C2.1.06.pdf (🔒 authorized access only).

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