A cantilever beam with a breathing crack is studied to detect the crack and evaluate the crack depth using entropy measures. During the vibration in engineering structures, fatigue cracks undergo the status from close-to-open (and open-to-close) repetitively leading to a crack breathing phenomenon. Entropy is a measure, which can quantify the complexity or irregularity in system dynamics, and hence employed to quantify the bi-linearity/irregularity of the vibration response, which is induced by the breathing phenomenon of a crack. A mathematical model of harmonically excited unit length steel cantilever beam with a breathing crack located near the fixed end is established, and an iterative numerical method is applied to generate accurate time domain vibration responses. The steady-state time domain vibration signals are pre-processed with wavelet transformation, and the bi-linearity/irregularity of the vibration signals due to breathing effect is then successfully quantified using both sample entropy and quantized approximation of sample entropy to detect and estimate the crack depth. It is observed that the method is capable of identifying crack depths even at very early stages of 3% of the beam thickness with significant increment in the entropy values (more than 200%) compared to the healthy beam. In addition, experimental studies are conducted, and the simulation results are in good agreement with the experimental results. The proposed technique can also be applied to damage identification in other types of structures, such as plates and shells.

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Breathing crack detection and evaluation on a beam under random loading is experimentally studied and realized using entropy measures. During testing, the beam is subjected to random excitations which is the most evident excitation type experienced by most of the engineering structures. Frequency response function is employed to erase the random frequency components due to the excitation from the response of the structure to pick up the vibration characteristics of the beam structure itself with/without the breathing crack. Based on experimental results, the proposed methodology can clearly discriminate a crack with 25% depth of the total thickness of the beam from the healthy case. It is also capable of distinguishing a 50% crack depth from a 25% crack depth with distinct entropy values.

During vibration of engineering structures, fatigue cracks may exhibit repetitive crack open-close breathing like phenomenon which ultimately result in a distinct crack type, breathing cracks.This breathing phenomenon generates bi-linearity and irregularities in vibration signals of the cracked structure which carry useful information about the crack occurrence. In this thesis, the concept of entropy is employed to quantify this bi-linearity/irregularity of the vibration response so as to evaluate crack severity. To increase the sensitivity of the entropy calculation to detect the damage severity, sample entropy and quantized approximation of sample entropy are merged with wavelet transformation (WT) which is capable of amplifying the weak irregularities in vibration signal caused by small and initial breathing cracks. A cantilever beam with a breathing crack is studied to asses proposed crack identification method under two vibration conditions with sinusoidal and random excitations. An iterative numerical model is established to generate accurate time domain vibration responses of the cantilever with a breathing crack. Through both numerical simulations and experimental testing, the breathing crack identification with entropy under sinusoidal excitation is studied first and proven to be effective. Then, the crack identification sensitivity under lower excitation frequencies is further improved by parametric optimization of sample entropy and WT. Finally, effective breathing crack identification under general random excitations are experimentally studied and realized using frequency response functions (FRFs) which adapts the proposed crack identification technique to the incurred extra complexity due to random nature of the excitation and structural response.iii

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