The extended Bouc-Wen differential model is one of the most widely accepted phenomenological models of hysteresis in mechanics. It is routinely used in the characterization of nonlinear damping and in system identification. In this paper, the differential model of hysteresis is carefully reexamined and two significant issues are uncovered. First, it is shown that the unspecified parameters of the model are functionally redundant. One of the parameters can be eliminated through suitable transformations in the parameter space. Second, local and global sensitivity analyses are conducted to assess the relative sensitivity of each model parameter. Through extensive Monte Carlo simulations, it is found that some parameters of the hysteretic model are rather insensitive. If the values of these insensitive parameters are fixed, a greatly simplified model is obtained.

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the five THEMIS spacecraft recorded a total of 3701 instances of bipolar magnetic variations in the magnetopause normal direction associated with enhancements of field magnitude that are interpreted as flux transfer events (FTEs) on the magnetopause and/or associated perturbations in the background magnetosphere and magnetosheath. When spacecraft traversed the FTE structures, the velocity components tangential to the magnetopause were generally antisunward, consistent with the sheath flow direction. On the other hand, when the spacecraft were located within the low-latitude boundary layer (LLBL) in the magnetosphere and remotely sensed the perturbations related to FTEs on the magnetopause, the velocity tangential to the magnetopause was found to be antisunward near the magnetopause but sunward further in from the magnetopause. The normal component variations for both groups had the same bipolar structure with inward flows followed by outward flows. This pattern has the form of a flow vortex just inside the magnetopause associated with an FTE moving in an antisunward direction at or outside of the magnetopause. A 2-dimensional magnetohydrodynamic (MHD) simulation code has been developed to understand the flow perturbations outside an FTE. Our simulation starts from an explicit solution, in which it is assumed that the plasma is inviscid and incompressible and no flow vortex is present. Only when we impose finite viscosity near the FTEs do flow vortices develop. However, the origin of this viscosity remains unknown. (2011), Flow vortices associated with flux transfer events moving along the magnetopause: Observations and an MHD simulation,

Three different time-domain system identification algorithms are presented in this paper to estimate the parameters of an extended Bouc-Wen hysteretic model. These algorithms include the simplex, extended Kalman filter, and generalized reduced gradient methods. The effectiveness of the proposed algorithms is demonstrated through simulations of nonlinear systems with pinching and degradation characteristics. Due to very modest computing requirements, the proposed identification algorithms can be acceptable as a basic tool for estimating hysteretic parameters in e~gineering design.