Vibration-based damage identification with enhanced frequency dataset and a cracked beam element model
Damage identification is an important topic in structural assessment and structural health monitoring (SHM). Vibration-based identification techniques use modal data to identify the existence, location and severity of possible damages in structures, often via a numerical model updating procedure. Among other factors influencing the practicality and reliability of a damage identification approach, two are of primary interest to this study. The first one concerns the amount and quality of modal data that can be used as ‘response’ data for the model updating. It is generally recognised that natural frequencies can be measured with relatively high accuracy; however, their number is limited. Mode shapes, on the other hand, are susceptible to larger measurement errors. Seeking additional modal frequency data is therefore of significant value. The second one concerns the errors at the numerical (finite element) model level, particularly in the representation of the effect of damage on the dynamic properties of the structure. An inadequate damage model can lead to inaccurate and even false damage identification. The first part of the thesis is devoted to enhancing the modal dataset by extracting the so called ‘artificial boundary condition’ (ABC) frequencies in a real measurement environment. The ABC frequencies correspond to the natural frequencies of the structure with a perturbed boundary condition, but can be generated without the need of actually altering the physical support condition. A comprehensive experimental study on the extraction of such frequencies has been conducted. The test specimens included steel beams of relatively flexible nature, as well as thick and stiffer beams made from metal material and reinforced concrete, to cover the typical variation of the dynamic characteristics of real-life structures in a laboratory condition. The extracted ABC frequencies are subsequently applied in the damage identification in beams. Results demonstrate that it is possible to extract the first few ABC frequencies from the modal testing in different beam settings for a variety of ABC incorporating one or two virtual pin supports. The inclusion of ABC frequencies enables the identification of structural damages satisfactorily without the necessity to involve the mode shape information. The second part of the thesis is devoted to developing a robust model updating and damage identification approach for beam cracks, with a special focus on thick beams which present a more challenging problem in terms of the effect of a crack than slender beams. The priority task has been to establish a crack model which comprehensively describes the effect of a crack to reduce the modelling errors. A cracked Timoshenko beam element model is introduced for explicit beam crack identification. The cracked beam element model is formulated by incorporating an additional flexibility due to a crack using the fracture mechanics principles. Complex effects in cracked thick beams, including shear deformation and coupling between transverse and longitudinal vibrations, are represented in the model. The accuracy of the cracked beam element model for predicting modal data of cracked thick beams is first verified against numerically simulated examples. The consistency of predictions across different modes is examined in comparison with the conventional stiffness reduction approach. Upon satisfactory verification, a tailored model updating procedure incorporating an adaptive discretisation approach is developed for the implementation of the cracked beam element model for crack identification. The updating procedure is robust in that it has no restriction on the location, severity and number of cracks to be identified. Example updating results demonstrate that satisfactory identification can be achieved for practically any configurations of cracks in a beam. Experimental study with five solid beam specimens is then carried out to further verify the developed cracked beam element model. Both forward verification and crack damage identification with the tested beams show similar level of accuracy to that with the numerically simulated examples. The cracked beam element model can be extended to crack identification of beams with complex cross sections. To do so the additional flexibility matrix for a specific cross-section type needs to be re-formulated. In the present study this is done for box sections. The stress intensity factors (SIF) for a box section as required for the establishment of the additional flexibility matrix are formulated with an empirical approach combining FE simulation, parametric analysis and regression analysis. The extended cracked beam element model is verified against both FE simulated and experimentally measured modal data. The model is subsequently incorporated in the crack identification for box beams. The successful extension of the cracked beam element model to the box beams paves the way for similar extension to the crack identification of other types of sections in real-life engineering applications.