Impact Parameter Inversion and Quantitative Damage Assessment of Helicopter Tail Drive Shafts Based on Stress Wave Characteristics and Physics-Guided Hierarchical Gaussian Process Regression

The helicopter tail drive shaft is vulnerable to failure from projectile impacts during low-altitude flight. Stress wave-based inversion of impact parameters and quantitative damage assessment remain insufficiently explored. To address small-sample and nonlinear challenges, a framework based on stress wave characteristics and physics-guided hierarchical Gaussian process regression is proposed. Four key features, namely first-arrival wave trough amplitude, frequency standard deviation, ratio of low-frequency to high-frequency root mean square, and wavelet energy entropy, are extracted from transient signals to construct a hierarchical progressive architecture for damage mode discrimination, parameter inversion, and quantitative assessment. Perforation is identified using a wavelet energy entropy-based adaptive threshold. Incidence angle inversion is achieved by an adaptive composite kernel and Bayesian physical prior correction. Damage degree is assessed through residual learning guided by a physical prior surface mean function. Results show an incidence angle inversion root mean square error (RMSE) of 3.02°, with entry and exit hole equivalent failure area RMSEs of 13.32 mm2 and 12.98 mm2, respectively. The 95% prediction interval maintained reliable coverage across the validation samples. This framework provides a new method with both physical interpretability and uncertainty quantification for the assessment of impact damage in thin-walled tube structures.