An Explainable Decision Analytics Framework for Multi Objective Design of Porous Al7075 B4C Functionally Graded Rotating Annular Disk

Abstract

This study develops an explainable decision-analytics framework for the coupled thermo-centrifugal and vibrational design of porous functionally graded Al7075-B4C rotating annular disks. Radial ceramic gradation, temperature-dependent properties, and symmetric, inner-rich, outer-rich, and uniform porosity patterns are incorporated into nonlinear heat-conduction, axisymmetric thermoelastic, and prestressed vibration models. A Latin hypercube design comprising 240 successful governing-equation solutions is used to train and test four surrogate model families. Gaussian-process regression provides the highest mean test coefficient of determination (R² = 0.968) across eight reliable static and dynamic responses. KernelSHAP is applied directly to the selected Gaussian-process surrogate to quantify the global influence of the input variables. To prevent surrogate extrapolation from affecting the design decision, Pareto filtering and equal-weight TOPSIS are applied to the physics-based database rather than to unevaluated surrogate candidates. The resulting 43-member Pareto set yields a compromise design with ΔT = 56.48 K, Ω = 1488.81 rad/s, n = 1.066, φ₀ = 0.014, rᵢ/rₒ = 0.500, h/rₒ = 0.037, and a symmetric porosity pattern. Its synchronous critical speed is subsequently evaluated using only the governing physics solver, yielding 37,373.93 rad/s and a safety ratio of 25.10. The framework therefore combines interpretable surrogate screening with physics-based multi-objective selection and independent critical-speed verification.