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In order to solve the hysteretic character of the piezoelectric material for application, the initial weight factors of the hysteretic units are calculated by the Preisach theory and the first-order reversal curves test data, a hysteretic Preisach model based on the improved fuzzy least square support vector machine (improved FLS-SVM) is established. In the established model, the fuzzy least square support vector machine is introduced to calculate more weight factors of the hysteretic units and the adaptive variable chaos immune algorithm is introduced to optimize the penalty factor and the kernel parameter of the FLS-SVM (the penalty factor c = 35 and the kernel parameter σ = 1.35 are obtained). Moreover, the quadratic polynomial interpolation method is used to eliminate the sawtooth phenomenon. The validity of established model reveals that fuzzy least square support vector machine method based on adaptive variable chaos immune algorithm (FLS-SVMAVCIA) is more accurate than FLS-SVM method according to application results of the real actuators (the absolute mean error of the FLS-SVMAVCIA model is less than 1 µm and its maximum error is less than 2 µm). As a result, the hysteretic phenomenon can be effectively eliminated by the hysteretic Preisach model based on the FLS-SVMAVCIA method.

journal of low frequency noise, vibration and active control

Parameter-identification investigations on the hysteretic Preisach model improved by the fuzzy least square support vector machine based on adaptive variable chaos immune algorithm