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

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 thermocouples bimetallic structure are represented through an Inverse Heat Conduction Equation (IHCP). An analysis is conducted to explore the connection between the analytical solutions ill-posed nature and the thermocouples dynamic errors. The transient temperature responses 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 0.25mm and 0.38mm. Findings reveal that the proposed method achieved a peak relative error of merely 0.83%, surpassing the 2.05% of the ablation technique and the 2.2% of Tikhonov regularization. In detonation tests, the corrected temperature peak reached 1045.7°C, with the relative error decreasing from 77.6% to 4.9%, and the rise time enhanced by 26 milliseconds. By merging physical constraints with data-driven methodologies, this technique successfully corrected dynamic errors even with limited sample sizes.