Physics-informed virtual sensor design for inter-turbine temperature in turbofan engines under component degradation

Monitoring the inter-turbine temperature T43 of turbofan engines is critical for performance assessment and safety margin management. Traditional physical sensors become unreliable under extreme operating conditions, while virtual sensor methods are prone to failure when faced with model mismatch and component degradation. This paper proposes a virtual sensor for T43 by integrating rotor inertia power balance (RPB) with a physics-informed neural network (PINN). First, based on engine thermodynamics and rotor dynamics, we extract rotor inertia power as a characteristic quantity and derive an RPB-based constraint that links measurable variables to T43. The derived constraint is then embedded into the PINN training objective. Automatic differentiation is used to compute the required derivatives, and an explicit constraint form is adopted to improve numerical stability and facilitate loss balancing between the data term and the physics term. Simulations under multiple turbine degradation scenarios show that the proposed method maintains stable accuracy compared with gas-path-based and purely data-driven baselines. In our setup, an intermediate physics weight provides a favorable trade-off between physical consistency and overall loss reduction. The proposed model also achieves shorter per-step prediction time while delivering robust T43 predictions across the operating envelope.