Comparison studies between two wavelet based crack detection methods of a beam subjected to a moving load

In this paper, the performances of two wavelet based damage detection approaches to find the location and the size of a crack in a beam subjected to a moving load are compared. In the first approach, designated as ‘Fixed Sensor Approach’, a sensor is assumed to be located at the mid span of the beam. Thus in this approach, Continuous Wavelet Transform (CWT) coefficient of the time varying deflection attributed to the beam at mid span is used. In the second approach, the sensor is attached to the moving load and CWT coefficient of moving sensor is analyzed. The crack is modeled as a rotational spring which its stiffness is obtained from fracture mechanics, and modal expansion theory is used to find the deflection of cracked beam. The two approaches are compared for several cases of moving load speeds, crack sizes and crack locations, and also several scales of CWT. In the both approaches, wavelet Gaussian 4 is employed. It is shown that, the highest magnitude of CWT coefficient occurs at the exact location of crack and its value depends on damage size. As a result, it can be considered as a damage index. It is found that the moving sensor approach is more effective than the fixed sensor. Thereafter, the effect of beam parameters such as length, width, modulus of elasticity and density and also, crack size and location on the damage index were investigated based on the moving sensor approach. The obtained damage index has two significant features: (a) it has an explicit expression and shows the effects of all parameters clearly, (b) it is not dependent upon the response of the undamaged beam. From the obtained explicit relation for damage index, it is illustrated that the damage index does not depend on material properties of a homogeneous beam. Moreover in a rectangular cross section beam, the damage index is independent of width and has a linear relationship with the height to length ratio. It is shown that using this damage index, small cracks with a depth more than 10% of the beam height can be detected.