Damage localization in geometrically complex aeronautic structures using canonical polyadic decomposition of Lamb wave difference signal tensors

Monitoring in real time and autonomously the health state of aeronautic structures is referred to as structural health monitoring and is a process decomposed in four steps: damage detection, localization, classification, and quantification. In this work, the structures under study are aeronautic geometrically complex structures equipped with a bonded piezoelectric network. When interrogating such a structure, the resulting data lie along three dimensions (namely, the “actuator,”“sensor,” and “time” dimensions) and can thus be interpreted as three-way tensors. The fact that Lamb wave structural health monitoring–based data are naturally three-way tensors is here investigated for damage localization purpose. In this article, it is demonstrated that under classical assumptions regarding wave propagation, the canonical polyadic decomposition of rank 2 of the tensors build from the phase and amplitude of the difference signals between a healthy and damaged states provides direct access to the distances between the piezoelectric elements and damage. This property is used here to propose an original tensor-based damage localization algorithm. This algorithm is successfully validated on experimental data coming from a scale one part of an airplane nacelle (1.5 m in height for a semi circumference of 4 m) equipped with 30 piezoelectric elements and many stiffeners. Obtained results demonstrate that the tensor-based localization algorithm can locate a damage within this structure with an average precision of 10 cm and with a precision lower than 1 cm at best. In comparison with standard damage localization algorithms (delay-and-sum, reconstruction algorithm for probabilistic inspection of defects, and ellipse- or hyperbola-based algorithms), the proposed algorithm appears as more precise and robust on the investigated cases. Furthermore, it is important to notice that this algorithm only takes the raw signals as inputs and that no specific pre-processing steps or finely tuned external parameters are needed. This algorithm is thus very appealing as reliable and easy to settle damage localization timeliness with low false alarm rates are one of the key successes to shorten the gap between research and industrial deployment of structural health monitoring processes.