Physics-Informed Predictive Diagnostics for Industrial Steam Turbine Generators Start-Ups: Connecting Rotor Kinematics and Energy Market Economics

Safe and efficient operation of large-scale steam turbines is too significant for grid stability, yet frequent transient start-ups cause severe rotor displacements/vibrations and thermal bowing, delaying grid connection. Operators face this by enforcing conservative "heat-soak" pauses, increasing substantial financial costs through wasted fuel and missed dispatch windows. One way to predict the optimal duration of the “heat-soak” pauses is by using data-driven Long Short-Term Memory (LSTM) networks, which however operate as unsafe low-pass filters and "black boxes" ignorant of mechanical realities. This study proposes a novel "Gray-Box" Physics-Informed Machine Learning (PIML) framework, combining kinematic gradient regularization, asymmetric risk penalties, and thermodynamic boundary conditions directly into the LSTM's objective function. Using a low-frequency (0.2 Hz) industrial SCADA dataset from generator journal bearings, the optimized architecture maps multivariate rotor dynamics, reducing predictive error to an exceptional median Mean Absolute Percentage Error (MAPE) of 6.09% and Normalized Mean Absolute Error (NMAE) of 4.72%. Crucially, the framework operates as an autonomous actuator, dynamically evaluating thermal memory to safely compress start-up timelines. It eliminates unnecessary runtime while mandating extensions during critical excursions, guaranteeing physical integrity. Finally, an economic layer quantifies optimized time differentials into financial returns within the European market, delivering a reliable decision-support system.