Path-Parameterized Takagi–Sugeno Fuzzy Modeling for Physics-Consistent Reconstruction of Multivalued Fretting Loops

Fretting hysteresis exhibits multivalued force–displacement behavior that challenges conventional single-valued regression. This study develops a path-parameterized Takagi–Sugeno (TS) fuzzy framework for reconstructing experimental hysteresis loops through two single-valued functions of normalized acquisition order. Four architectures were evaluated using a 600-point experimental loop: an adaptive neuro-fuzzy inference system (ANFIS–TS), fuzzy c-means clustering (FCM–TS), and nine- and sixteen-rule subtractive-clustering TS models (SC9–TS and SC16–TS). Ten repeated 70/30 train–test partitions yielded mean normalized root-mean-square errors (NRMSEs) of 0.00528, 0.00817, 0.01333, and 0.00616, respectively. ANFIS–TS and SC16–TS showed no statistically significant difference after Holm correction. Physical consistency was assessed through dissipated energy, force extrema, displacement span, loop closure, and cumulative energy evolution, supplemented by robustness analyses. A radial-basis-function support-vector regression (RBF–SVR) benchmark achieved a lower NRMSE of 0.000838, whereas the fuzzy models retained interpretable rule structures and adjustable complexity. Independent fitting across three displacement amplitudes demonstrated procedural applicability without establishing generalization to unseen conditions. These findings support reliable and interpretable reconstruction of experimental fretting loops rather than a new friction constitutive law.