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Capsule network (CapsNet) acts as a promising alternative to the typicalconvolutional neural network, which is the dominant network to develop theremaining useful life (RUL) estimation models for mechanical equipment.Although CapsNet comes with an impressive ability to represent the entities'hierarchical relationships through a high-dimensional vector embedding, itfails to capture the long-term temporal correlation of run-to-failure timeseries measured from degraded mechanical equipment. On the other hand, theslow-varying dynamics, which reveals the low-frequency information hidden inmechanical dynamical behaviour, is overlooked in the existing RUL estimationmodels, limiting the utmost ability of advanced networks. To address theaforementioned concerns, we propose a Slow-varying Dynamics assisted TemporalCapsNet (SD-TemCapsNet) to simultaneously learn the slow-varying dynamics andtemporal dynamics from measurements for accurate RUL estimation. First, inlight of the sensitivity of fault evolution, slow-varying features aredecomposed from normal raw data to convey the low-frequency componentscorresponding to the system dynamics. Next, the long short-term memory (LSTM)mechanism is introduced into CapsNet to capture the temporal correlation oftime series. To this end, experiments conducted on an aircraft engine and amilling machine verify that the proposed SD-TemCapsNet outperforms themainstream methods. In comparison with CapsNet, the estimation accuracy of theaircraft engine with four different scenarios has been improved by 10.17%,24.97%, 3.25%, and 13.03% concerning the index root mean squared error,respectively. Similarly, the estimation accuracy of the milling machine hasbeen improved by 23.57% compared to LSTM and 19.54% compared to CapsNet.

Slow-varying Dynamics Assisted Temporal Capsule Network for Machinery Remaining Useful Life Estimation