Data-driven Prognostics with Predictive Uncertainty Estimation using Ensemble of Deep Ordinal Regression Models

Prognostics or Remaining Useful Life (RUL) Estimation from multi-sensor time series data is useful to enable condition-based maintenance and ensure high operational availability of equipment. We propose a novel deep learning based approach for Prognostics with Uncertainty Quantification that is useful in scenarios where: (i) access to labeled failure data is scarce due to rarity of failures (ii) inherent noise ispresent in the sensor readings. The two scenarios mentioned are unavoidable sources of uncertainty in the RUL estimation process, often resulting in unreliable RUL estimates. To address (i), we formulate RUL estimation as an Ordinal Regression (OR) problem and propose LSTM-OR: deep Long Short Term Memory (LSTM) network-based approach to learn the OR function. We show that LSTM-OR naturally allows for the incorporation of censored operational instances in training along with the failed instances, leading to more robust learning. To address (ii), we propose a simple yet effectiveapproach to quantify predictive uncertainty in the RUL estimation models by training an ensemble of LSTM-OR models. Through empirical evaluation on the publicly available turbofan engine benchmark datasets, we demonstrate that LSTMOR is at par with commonly used deep metric regressionbased approaches for RUL estimation when sufficient failed instances are available for training. Importantly, LSTM-OR outperforms these metric regression-based approaches in the practical scenario where failed training instances are scarce, but sufficient operational (censored) instances are additionally available. Furthermore, our uncertainty quantification approach yields high-quality predictive uncertainty estimateswhile also leading to improved RUL estimates compared to single best LSTM-OR models.