  Capsule network (CapsNet) acts as a promising alternative to the typical
convolutional neural network, which is the dominant network to develop the
remaining 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, it
fails to capture the long-term temporal correlation of run-to-failure time
series measured from degraded mechanical equipment. On the other hand, the
slow-varying dynamics, which reveals the low-frequency information hidden in
mechanical dynamical behaviour, is overlooked in the existing RUL estimation
models, limiting the utmost ability of advanced networks. To address the
aforementioned concerns, we propose a Slow-varying Dynamics assisted Temporal
CapsNet (SD-TemCapsNet) to simultaneously learn the slow-varying dynamics and
temporal dynamics from measurements for accurate RUL estimation. First, in
light of the sensitivity of fault evolution, slow-varying features are
decomposed from normal raw data to convey the low-frequency components
corresponding to the system dynamics. Next, the long short-term memory (LSTM)
mechanism is introduced into CapsNet to capture the temporal correlation of
time series. To this end, experiments conducted on an aircraft engine and a
milling machine verify that the proposed SD-TemCapsNet outperforms the
mainstream methods. In comparison with CapsNet, the estimation accuracy of the
aircraft 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 has
been improved by 23.57% compared to LSTM and 19.54% compared to CapsNet.
