Spherical-Dynamic Time Warping - A New Method for Similarity-Based Remaining Useful Life Prediction




Journal Title

Journal ISSN



Volume Title





Peer reviewed



Machinery prognostics and health management (PHM) plays a key role in the reliable and efficient operation of industrial processes. With the emerging big data era, data-driven prognostic methods which avoid considering complicated system models have attracted growing research interest. Among many data-driven models, similarity-based prediction methods have been popular due to their strong interpretability and relatively simple implementation process. Nevertheless, when quantifying the similarity between two trajectories, most existing similarity measures neglect the nonlinearity of the distance measurement at different degradation stages and degradation alignments with timing difference, which may not be sufficient to retrieve the most suitable trajectories for remaining useful life (RUL) prediction. To overcome these limitations, a spherical-Dynamic Time Warping (spherical-DTW) algorithm is put forward to find an optimal match between the test and training trajectories at the retrieval step. Dynamic Time Warping allows degradation alignments with timing difference through stretching or compressing the trajectories with regard to time, thereby the data in similar degradation levels can be well aligned across different units. Moreover, a newly defined nonlinear spherical distance method is introduced and incorporated into the retrieval process to account for the nonlinearity of the damage propagation process. The significance of this study is that the newly proposed spherical-DTW algorithm goes one step further to consider the nonlinearity of fault evolutions and allow degradation pattern alignments with timing difference when performing similarity-based prognostics. Two run-to-failure cases, involving a real-world industrial compressor failure case and a gas turbine engine failure dataset, are investigated to demonstrate the effectiveness and superiority of the proposed algorithm.


The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.


Condition monitoring, Prognosis, Dynamic time warping, Spherical distance


Li, X., X, S., Yang, Y., Lin, T., Mba, D., L., C. (2024) Spherical-Dynamic Time Warping - A New Method for Similarity-Based Remaining Useful Life Prediction. Expert Systems with Applications. 238, Part B, 121913


Attribution-NonCommercial-NoDerivs 2.0 UK: England & Wales

Research Institute

Institute of Artificial Intelligence (IAI)