Higher-order transmissibility and its linear approximation for in-service crack identification in train wheelset axles

In-service structural health monitoring is a so far rarely exploited, yet potent option for early-stage crack detection and identification in train wheelset axles. This procedure is non-trivial to enforce on the basis of a purely data-driven approach and typically requires the adoption of numerical, e.g. finite element-based simulation schemes of the dynamic behavior of these axles. Damage in this particular case can be formulated as a breathing crack problem, which further complicates simulation by introducing response-dependent nonlinearities into the picture. In this study, first, a new crack detection feature based on higher-order harmonics of the breathing crack is proposed, termed Higher-Order Transmissibility (HOTr). Next, a reduced-order model is developed by introducing a first-order perturbation-based approximation of the essentially nonlinear crack contact forces. This yields a sequence of linear frequency-domain problems that approximate the higher-order harmonic response with substantial computational speedup, while retaining the damage-sensitive nonlinear features required for crack identification. The accuracy of the proposed method in reproducing the delivered HOTr is compared against the nonlinear simulation model. The obtained results suggest that the approximation of the HOTr can significantly reduce the computational burden by eliminating the need for an iterative solution of the governing nonlinear equation of motion while maintaining a high level of accuracy when compared to the reference model. Finally, the robustness and effectiveness of the proposed indicators are systematically demonstrated through noise-contaminated simulations. Results advocate the great potential of the proposed method for adoption in in-service damage identification for wheelset axles, feasibly within a near real-time context.