Impairment localization and quantification using noisy static deformation influence lines and Iterative Multi-parameter Tikhonov Regularization

Abstract Bridge structures decay throughout their lives even under nominal operating conditions. As bridge infrastructure ages and wears naturally or under extreme load, there is a need to monitor and evaluate bridge performance in an efficient way. This paper presents an impairment detection method that assesses the curvature of noisy static deformation influence lines to predict the location and severity of structural damage. In this method, a parametric approximation and two direct regularization methods i.e., Tikhonov Regularization (TR) and the proposed Iterative Multi-parameter Tikhonov Regularization (IMTR), are implemented to reduce the impact of measurement noise on flexural rigidity estimations. While the TR method assumes one regularization parameter for all unknowns of the optimization problem, the IMTR method has individual, iteratively optimized, regularization parameters for each unknown. To evaluate the performance of the presented method, four nominally identical beam structures with four different damage scenarios and multiple levels of measurement noise are studied. Combining the quadratic spline parametric approximation with either direct regularization method produces adequate curvature estimates that are subsequently used to predict the location and severity of damage. In cases of deep, sharp damage, the IMTR method improves the prediction performance by reducing percent error 4–32%, for noise levels ranging from 0% to 5%, when compared to prediction results from the conventional TR. Both regularization methods give comparable results for shallow, wide damage. A laboratory experiment is included that presents the FRE on a statically indeterminate system; both TR and IMTR provide reasonable estimations of the location and severity of damage.