Dynamic Error Correction for Fine-Wire Thermocouples Based on CRBM-DBN with PINN Constraint

Abstract

In high-temperature testing scenarios that rely on contact, fine-wire thermocouples demonstrate commendable dynamic performance. Nonetheless, their thermal inertia leads to notable dynamic nonlinear inaccuracies, including response delays and amplitude reduction. To mitigate these challenges, a novel dynamic error correction approach is introduced, which combines a Continuous Restricted Boltzmann Machine, Deep Belief Network, and Physics-Informed Neural Network (CDBN-PINN). The unique heat transfer properties of the thermocouple’s bimetallic structure are represented through an Inverse Heat Conduction Equation (IHCP). An analysis is conducted to explore the connection between the analytical solution’s ill-posed nature and the thermocouple’s dynamic errors. The transient temperature response’s nonlinear characteristics are captured using CRBM-DBN. To maintain physical validity and minimize noise amplification, filtered kernel regularization is applied as a constraint within the PINN framework. This approach was tested and confirmed through laser pulse calibration on thermocouples with butt-welded and ball-welded configurations of 0.25 mm and 0.38 mm. Findings reveal that the proposed method achieved a peak relative error of merely 0.83%, superior to Tikhonov regularization by −2.2%, Wiener deconvolution by 20.40%, FBPINNs by 1.40%, and the ablation technique by 2.05%. In detonation tests, the corrected temperature peak reached 1045.7 °C, with the relative error decreasing from 77.7% to 5.1%. Additionally, this method improves response times, with the rise time in laser calibration enhanced by up to 31 ms and in explosion testing by 26 ms. By merging physical constraints with data-driven methodologies, this technique successfully corrected dynamic errors even with limited sample sizes.