Weighted multi-order Viterbi algorithm (WMOVA): Instantaneous angular speed estimation under harsh conditions

Instantaneous angular speed (IAS) information is essential for vibration-based fault diagnosis of rotating machinery under non-stationary operating conditions. Possessing the advantages of being cost-effective and less intrusive, tacholess IAS estimation methods that use vibration signals have been researched and implemented in recent years. However, such methods often suffer from poor performance when subjected to the harsh operating conditions found in real-world settings, such as large speed variations, extreme noise, and poorly excited harmonics of vibration signals. To address these challenges, this paper proposes a weighted multi-order Viterbi algorithm (WMOVA) method for tacholess IAS estimation under harsh conditions. The novel harmonic weighting of WMOVA enables selective extraction of the correct IAS information, while exploiting multiple harmonics to construct an accurate ridge in the time-frequency representation (TFR). The TFR ridge is then tracked by using a modified Viterbi algorithm. The benefits of the proposed method are demonstrated in this research, first by applying the new approach to simulated vibration signals and then using the proposed approach with data in two case studies. The first case study examines public data from the 2014 international conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMNO); the second study uses data measured from a gearbox testbed. Comprehensive comparative studies show that the proposed method outperforms the conventional IAS estimation approach in real-world applications.