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Heating and Cooling Curves02:44

Heating and Cooling Curves

When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves.
For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...

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

Na Li1, Siyang Dai2, Yi Liu3

  • 1State Key Laboratory of Chemical Safety, College of Mechanical and Electrical Engineering, China University of Petroleum (East China), Qingdao 266580, China.

Sensors (Basel, Switzerland)
|March 14, 2026
PubMed
Summary

A new hybrid algorithm combining an extended Kalman filter (EKF) and a back-propagation neural network (BPNN) improves remaining useful life (RUL) prediction for Platinum-Rhodium (Pt-Rh) thermocouples. This method accurately forecasts degradation in high-temperature industrial settings.

Keywords:
Pt–Rh thermocoupleback-propagation neural networkextended Kalman filterremaining useful life

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Area of Science:

  • Materials Science and Engineering
  • Sensor Technology
  • Artificial Intelligence

Background:

  • Platinum-Rhodium (Pt-Rh) thermocouples are critical for high-temperature industrial monitoring.
  • Harsh environments cause degradation, affecting measurement accuracy and leading to potential failure.
  • Existing methods struggle with the slow, nonlinear drift characteristic of Pt-Rh thermocouples.

Purpose of the Study:

  • To develop an accurate Remaining Useful Life (RUL) prediction model for Pt-Rh thermocouples under high-temperature conditions.
  • To address the nonlinear errors and slow drift affecting thermocouple measurements.
  • To enhance the reliability of real-time condition monitoring in industrial processes.

Main Methods:

  • Developed a degradation model for Pt-Rh thermocouples based on the Seebeck effect and vapor-transport theory.
  • Implemented a hybrid Extended Kalman Filter (EKF) and Back-Propagation Neural Network (BPNN) algorithm.
  • Validated the degradation model with laboratory data and compared the EKF-BPNN algorithm with other prediction methods.

Main Results:

  • The developed degradation model accurately reflects laboratory test data.
  • The EKF-BPNN hybrid algorithm demonstrated superior prediction accuracy (MAE 0.0016%, RMSE 0.0019%, MAPE 0.039%, R2 0.9833).
  • Algorithms with strong nonlinear estimation capabilities were found to be less suitable for this specific application.

Conclusions:

  • The hybrid EKF-BPNN algorithm is optimal for RUL prediction of Pt-Rh thermocouples experiencing high-temperature degradation.
  • This approach effectively compensates for nonlinear errors and slow drift.
  • The findings support improved condition monitoring and predictive maintenance in industrial settings.