Hysteretic benchmark with a dynamic nonlinearity

Hysteresis is a phenomenology commonly encountered in very diverse engineering and science disciplines, ranging from solid mechanics, electromagnetism and aerodynamics [1, 2, 3] to biology, ecology and psychology [4, 5, 6]. The defining property of a hysteretic system is the persistence of an input-output loop as the input frequency approaches
zero [7]. Hysteretic systems are inherently nonlinear, as the quasi-static existence of a loop requires an input-output phase shift different from and 180 degrees, which are the only two options offered by linear theory. The root cause of hysteresis is multistability [8].
A hysteretic system possesses multiple stable equilibria, attracting the output depending on the input history. In this sense, it is appropriate to refer hysteresis as system nonlinear memory.
This document describes the synthesis of noisy data exhibiting hysteresis behaviour carried out by combining the Bouc-Wen differential equations (Section 2) and the Newmark integration rules (Section 3). User guidelines to an accurate simulation are provided in Section 4. The test signals and the figures of merit that are used in this benchmark are presented in Section 5. Anticipated nonlinear system identification challenges associated with the present benchmark are listed in Section 6.