# Data-Driven Remaining Useful Life Prediction for Pt–Rh Thermocouples Using an Extended Kalman Filter

## TL;DR

This paper introduces a hybrid algorithm combining an extended Kalman filter and a neural network to improve the accuracy of predicting the remaining useful life of Pt–Rh thermocouples used in high-temperature industrial environments.

## Contribution

The novel contribution is the integration of a back-propagation neural network with an extended Kalman filter to enhance RUL prediction accuracy for Pt–Rh thermocouples.

## Key findings

- The hybrid EKF–BPNN algorithm achieves high prediction accuracy with MAE 0.0016%, RMSE 0.0019%, MAPE 0.039%, and R2 0.9833.
- The degradation model based on the Seebeck effect and vapor-transport theory aligns with laboratory test data.
- Strongly nonlinear algorithms are less suitable for RUL prediction of Pt–Rh thermocouples due to larger errors.

## Abstract

Platinum (Pt)–Rhodium (Rh) thermocouples are widely used in industrial processes such as chemical and nuclear power production, serving as one of the most common temperature measuring instruments and playing a vital role in real-time condition monitoring. However, the measurement accuracy can be affected by harsh high-temperature operating environments, which may cause measurement drift or even functional failure. To address this challenge, and considering the very slow drift of Pt–Rh thermocouples over long time scales, a back-propagation neural network (BPNN) is introduced to compensate for the nonlinear error introduced by the linearization step of the extended Kalman filter (EKF). This combined algorithm enhances the accuracy of remaining useful life (RUL) prediction for Pt–Rh thermocouples. First, based on the Seebeck effect and vapor-transport theory, a degradation model for Pt–Rh thermocouples operating at high temperatures was developed. The simulation results of the degradation model align with laboratory degradation test data, confirming the validity of the model. Subsequently, the improved RUL prediction algorithm was compared with other methods. The results show that the EKF–BPNN hybrid approach provides better prediction accuracy for objects with slow degradation and weak nonlinearity, with MAE 0.0016%, RMSE 0.0019%, MAPE 0.039%, R2 0.9833, respectively. Algorithms with strong nonlinear estimation capability introduce larger errors and are not suited for RUL prediction of Pt–Rh thermocouples. Therefore, the proposed hybrid EKF–BPNN algorithm is optimal for RUL prediction of Pt–Rh thermocouples degrading under high temperature conditions.