Experimental investigation and design criteria extraction for wide-operating rectangular slotted casing treatment in axial compressor via interpretable machine learning

Resolving the inherent trade-off between efficiency preservation and stability enhancement remains a critical challenge for wide-operating aero-compressors. This study conducts multi-objective optimization on an axial rotor to extract robust design criteria for the rectangular slotted casing treatment (RSCT). Initially, a parameterized modeling method for RSCT is proposed. Through 24 sets of aerodynamic tests on 12 typical configurations under dual-speed conditions, the significant sensitivity of RSCT's stability expansion to geometric parameter variations was revealed. To guarantee physical reliability, the numerical solver was rigorously anchored by exact 1:1 high-fidelity simulations of the 12 physical experimental configurations, achieving exceptionally low mean absolute errors for both SMI and PEL. Relying on this highly validated solver, a high-dimensional database of approximately 500 samples was sequentially constructed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) evolutionary framework to comprehensively explore the design space. Optimization results indicate that Pareto optimal solutions can achieve an average stall margin improvement (SMI) of up to 60.40%, with an average peak efficiency loss (PEL) of merely 1.65%. Furthermore, a quantitative aerodynamic analysis of these optimal designs was conducted to decouple the internal loss sources and interpret the underlying physical mechanisms of flow control. Relying on this validated foundation, a high-fidelity Extreme Gradient Boosting (XGBoost) surrogate model was developed. The model exhibits exceptional predictive accuracy, with coefficients of determination (R²) for SMI and PEL reaching 0.9635 and 0.9586, respectively. By integrating interpretable machine learning methods, this robust model profoundly reveals the influence laws between RSCT geometric parameters and compressor aerodynamic performance, facilitating the extraction of robust design criteria. Finally, an Optimal Latin Hypercube Sampling (OLHS) scheme utilizing a "paired control" strategy was employed for rigorous statistical validation of the extracted criteria. Ultimately, this study establishes comprehensive, multi-objective geometric design criteria across wide operating conditions, dominated by slot length, open area ratio, and axial skew angle. These findings provide robust quantitative support for the advanced engineering design of high-performance casing treatments.