Joint Reconstruction of Lift, Pressure-Drag, and Pitching-Moment Hysteresis Using Multivalued Parametric Fuzzy Trajectories

Dynamic stall produces different loads at the same incidence during pitch-up and pitch-down. We reconstruct this hysteresis from 128 synchronized University of Glasgow NACA 0012 pressure samples using a common normalized ordered-path coordinate adapted from the authors’ IEEE fuzzy-orbit framework. Four shared-antecedent, three-output first-order Takagi–Sugeno models—FCM–TS6, SC16–TS, SC9–TS, and ANFIS–TS9—represent lift, pressure drag, and quarter-chord moment. Across ten matched 70/30 within-cycle partitions, mean pooled normalized root-mean-square errors are 0.03468, 0.02754, 0.03552, and 0.01781, respectively. ANFIS–TS9 also gives the lowest error under 5% training-output contamination (0.03833); SC16–TS better preserves pressure-drag and moment signed-contour-integral magnitudes in full-data fits. Shared rules provide a common representation, but no accuracy advantage over independently trained single-output models has been established. Separate seven-condition assessments yield mean pooled NRMSE values of 0.16871 for fixed-bandwidth fuzzy-surrogate transfer and 0.10500 for nested measured-trajectory interpolation. These unmatched protocols do not support an algorithm ranking. The findings support interpretable reconstruction of recorded hysteresis, not prediction of arbitrary motion histories. Small sample size, within-cycle dependence, and limited unseen-frequency validation bound the conclusions.