Order-tracked bispectrum-based feature extraction and machine learning for structural health monitoring of turboshaft engine gearboxes under non-stationary conditions

This study presents a comprehensive fault diagnosis framework that integrates the order-tracked bispectrum (OTB) with supervised machine learning (ML) algorithms for detecting and classifying progressive gear degradation in a turboshaft engine gearbox under highly non-stationary operating conditions. The OTB framework converts angularly resampled vibration signals into a speed-invariant, noise-robust bispectral representation in the order domain, effectively eliminating frequency smearing induced by rotational speed fluctuations. A rich feature vector comprising seven higher-order spectral indices—bicoherence (BC), real bispectral component, skewness, bispectral energy, bispectral flatness (BF), bispectral magnitude index (BMI), and bispectral phase entropy—is extracted from the non-redundant triangular region of each run’s OTB. These features train and evaluate four ML classifiers: support vector machine, random forest (RF), k -nearest neighbour, and a one-dimensional convolutional neural network (CNN), across both binary (healthy/faulty) and multi-class (incipient/propagating/severe/healthy) fault severity labelling schemes. Experimental results demonstrate that the OTB + RF combination achieves 97.8% classification accuracy on the multi-class task, outperforming classical frequency-domain features across all ML models and label schemes. The CNN operating directly on the raw OTB surface achieves 98.4% accuracy, confirming the richness of the two-dimensional bispectral representation as an input modality for deep learning. A SHapley Additive exPlanations-based feature importance analysis identifies BC and BMI as the dominant diagnostic descriptors. The proposed framework is validated against existing benchmarks, confirming superior trendability, sensitivity, and fault separability for aerospace gearbox condition monitoring.