Nonlinear spectral correlation for fatigue crack detection under noisy environments

When ultrasonic waves at two distinct frequencies are applied to a structure with a fatigue crack, crack-induced nonlinearity creates nonlinear ultrasonic modulations at the sum and difference of the two input frequencies. The amplitude of the nonlinear modulation components is typically one or two orders of magnitude smaller than that of the primary linear components. Therefore, the modulation components can be easily buried under noise levels and it becomes difficult to extract the nonlinear modulation components under noisy environments using a conventional spectral density function. In this study, nonlinear spectral correlation, which calculates the spectral correlation between nonlinear modulation components, is proposed to isolate the nonlinear modulation components from noisy environments and used for fatigue crack detection. The proposed nonlinear spectral correlation offers the following benefits: (1) Stationary noises have little effect on nonlinear spectral correlation; (2) By using a wideband high-frequency input and a single low-frequency input, the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced; and (3) The test efficiency can be also improved via reducing the data collection time. Validation tests are performed on aluminum plates and scaled steel shafts with real fatigue cracks. The experimental results demonstrate that the proposed nonlinear spectral correlation owns a higher sensitivity to fatigue crack than the classical nonlinear coefficient estimated from the spectral density function, and the usage of nonlinear spectral correlation allows the detection of fatigue crack even using noncontact air-coupled transducers with a low signal-to-noise ratio. (C) 2017 Elsevier Ltd. All rights reserved.