Phase space reconstruction features for LSTM-based fault classification in gearboxes and roller bearings

Phase space reconstruction (PSR) converts a vibration signal into a multidimensional trajectory encoding the nonlinear dynamics of rotating machinery, yet existing PSR-based deep learning approaches rasterize this trajectory into an image before classification, discarding its inherent temporal ordering. This paper proposes feeding two derivative-augmented PSR constructions—the Approximated Phase Space (APS) and the Classical Phase Space (CPS), directly as sequential inputs to a Long Short-Term Memory (LSTM) neural network, exploiting the structural compatibility between the column-sequential organization of the PSR matrix and LSTM’s temporal processing, and avoiding the image-conversion step used in CNN-based PSR approaches on the two datasets studied here. Each PSR matrix is augmented with the first and second derivatives computed via the Savitzky–Golay filter, extending the feature space to a derivative-augmented state representation that jointly encodes signal amplitude, rate of change, and curvature. Both constructions are validated through k-fold cross-validation on a 10-class spur gearbox dataset and a 7-class roller bearing dataset, both acquired under variable speed and load conditions. File-level classification via majority voting over feature pieces yields 99.7% accuracy for the gearbox and 99.7% for roller bearings using CPS features, and 94.6% and 99.0%, respectively, using APS features. CPS consistently outperforms APS by 9–14 percentage points at the piece level, attributable to its overlapping lag structure, while the majority voting substantially closes this gap at the file level. These results show that, on the two datasets evaluated, PSR matrices can be fed directly as sequential inputs to an LSTM without image conversion, yielding competitive fault classification accuracy, and that derivative-augmented phase space features provide a computationally efficient representation for fault diagnosis in rotating machinery.