Guided Wave (GW)-based crack monitoring method as a promising method has been widely studied, as this method is sensitive to small cracks and can cover a wide monitoring range. Online crack quantification is difficult as the initiation and growth of crack are affected by various uncertainties. In addition, crack-sensitive GW features are influenced by time-varying conditions which further increase the difficulty in crack quantification. Considering these uncertainties, the Gaussian mixture model (GMM) is studied to model the probability distribution of GW features. To further improve the accuracy and stability of crack quantification under uncertainties, this paper proposes a multi-dimensional uniform initialization GMM. First, the multi-channel GW features are integrated to increase the accuracy of crack quantification, as GW features from different channels have different sensitivity to cracks. Then, the uniform initialization method is adopted to provide more stable initial parameters in the expectation-maximization algorithm. In addition, the relationship between the probability migration index of GMMs and crack length is calibrated with fatigue tests on prior specimens. Finally, the proposed method is applied for online crack quantification on the notched specimen of an aircraft spar with complex fan-shaped cracks under uncertainty.

Accurate evaluation of fatigue crack by using structural health monitoring (SHM) methods is very important to the life management of aircraft structures. However, fatigue crack propagation is always a complicated process for individual aircraft structures during their long-term service. And the monitoring has to be performed under different environmental and operational conditions. These factors result in the uncertain distribution of the damage index obtained by SHM. The distribution usually changes along with the service time, which can be defined as heteroscedasticity. The heteroscedasticity characteristic of the uncertain distribution of damage index has an important negative impact on the SHM based diagnostics algorithms if not considered during the evaluation. However, till now, few researchers have considered this important aspect. To improve the evaluation accuracy under different environmental and operational conditions for individual aircraft, this paper proposes a new guided wave-based heteroscedastic Gaussian process method. Gaussian process quantile regression is adopted to estimate the conditional quantiles of the damage index distribution during the service to deal with the heteroscedasticity. The method is validated on an attachment lug fatigue test, an important aircraft structural component. The experimental results demonstrate that the proposed method can quantify the heteroscedastic uncertainty associated and obviously improve the quality of crack evaluation. For the serious heteroscedastic specimen, the maximum evaluation is only 0.7 mm reduced from the original 7.4 mm, which is an order of magnitude.

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