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

arXiv: https://arxiv.org/abs/2203.16373 · HTML: https://mlsanity.com/paper/2203.16373/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Time-Series Regeneration with Convolutional Recurrent Generative Adversarial Network for Remaining Useful Life Estimation](https://mlsanity.com/paper/2101.03678/) (2021)
- [A Transfer Learning-based State of Charge Estimation for Lithium-Ion Battery at Varying Ambient Temperatures](https://mlsanity.com/paper/2101.03704/) (2021)
- [Temporal Convolutional Memory Networks for Remaining Useful Life Estimation of Industrial Machinery](https://mlsanity.com/paper/1810.05644/) (2018)
- [A deep learning-based remaining useful life prediction approach for bearings](https://mlsanity.com/paper/1812.03315/) (2018)

## Built on by (most cited first, 10 of 10)

- [A Federated Learning-based Industrial Health Prognostics for Heterogeneous Edge Devices using Matched Feature Extraction](https://mlsanity.com/paper/2305.07854/) (2023)
- [Diff-MTS: Temporal-Augmented Conditional Diffusion-based AIGC for Industrial Time Series Towards the Large Model Era](https://mlsanity.com/paper/2407.11501/) (2024)
- [Transfer Learning-based State of Health Estimation for Lithium-ion Battery with Cycle Synchronization](https://mlsanity.com/paper/2208.11204/) (2022)
- [A Transferable Multi-stage Model with Cycling Discrepancy Learning for Lithium-ion Battery State of Health Estimation](https://mlsanity.com/paper/2209.00190/) (2022)
- [Spatiotemporal Capsule Neural Network for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2303.02880/) (2023)
- [A Hybrid Deep Learning Model-based Remaining Useful Life Estimation for Reed Relay with Degradation Pattern Clustering](https://mlsanity.com/paper/2209.06429/) (2022)
- [Superpixel perception graph neural network for intelligent defect detection of aero-engine blade](https://mlsanity.com/paper/2210.07539/) (2022)
- [Lithium-ion Battery Online Knee Onset Detection by Matrix Profile](https://mlsanity.com/paper/2304.00691/) (2023)
- [A Slow-Shifting Concerned Machine Learning Method for Short-term Traffic Flow Forecasting](https://mlsanity.com/paper/2303.17782/) (2023)
- [1D-CapsNet-LSTM: A Deep Learning-Based Model for Multi-Step Stock Index Forecasting](https://mlsanity.com/paper/2310.02090/) (2023)

## Abstract (arXiv)

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.