Abstract
Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.
Highlights
The play operator with deterministic dataAn important example for an hysteresis operator is the play operator, see, e.g., [3, 8, 9, 17]
Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are subject to corresponding errors
We apply the methods of Uncertainty Quantification (UQ), see, e.g., [14, 15], to deal with these uncertainties, i.e., we describe them by introducing appropriate random variables modeling the corresponding information/assumptions/beliefs and use probability theory to describe and determine the influence of the uncertainties
Summary
An important example for an hysteresis operator is the play operator, see, e.g., [3, 8, 9, 17]. Defining tKw,u,t+2 = t, rk := 0 and tk := t for all k ∈ N with k > Kw,u,t + 2 and recalling the definition of a memory sequence as in the text before Proposition II.2.5 from [9], it follows that {(tj, rj)}∞ j=1 is the memory sequence of u at the point t with respect to the initial configuration λ It holds that (−1)j = pw,u,t(−1)j−1 for all j ∈ {0, 1, 2, . Recalling II.(2.17) in Proposition II.2.5 from [9] and considering the value of pw,u,t, we see that the assertion is proved
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