Multiple cracks detection in a beam subjected to a moving load using wavelet analysis combined with factorial design

In this paper, a new method of multiple cracks detection in a simply supported beam subjected to a moving load along the beam based on Continuous Wavelet Transform (CWT) combined with factorial design is presented. Deflection of the beam when the moving load passes the mid span of the beam is considered. Peaks in the CWT coefficient of data using Gaussian4 Wavelet show Cracksʹ location. The value of CWT coefficient at the points of cracks assumed as Damage Index (DI). A technique for defining the velocity of moving load and normalizing the deflection introduced which makes the DI independent from beam material parameters. The important parameters which affect the damage index are found using factorial design. By introducing a novel multivariable curve fitting approach, an explicit expression for the DI is developed which shows effect of all important parameters clearly. Applying factorial design, it is shown that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. The proposed damage index can detect the crack depths of more than 5% of beamʹs height and can predict the size of crack even in the case of noisy data. The effect of 10% noise level on the beam having three cracks was introduced and is shown this noise level does not affect the procedure of damage detection introduced in this paper. Each crack is modeled as a rotational spring whose stiffness is obtained from fracture mechanics. The modal expansion theory is used to obtain the response of the beam due to moving load.