A-Posteriori Identifiability of the Maxwell Slip Model of Hysteresis

Abstract

The a-posteriori identifiability of the Maxwell Slip model of hysteresis is addressed. The necessary and sufficient conditions that guarantee that the available data are informative enough are provided. An Output Error type estimator is subsequently postulated and its consistency is established. It is specifically shown that the estimates converge in probability to their actual counterparts under easily verifiable conditions on the Maxwell Slip model structure, the excitation, and mild assumptions on the additive measurement noise. The analytical results are verified through Monte Carlo simulations.

On forward and inverse uncertainty quantification for models involving hysteresis operators

“…The probability measure µ 0,u,t for the random variable P R [0, u](t) is the sum of a Dirac measure at 0 weighted by max{|u(τ )|:τ ∈[0,t]} ρ R (r) dr and of a measure with a density, denoted by φ t . For t ∈ {0, 0.5, 1, 2, 3, 3 13 32 , 4}, the values of u(t), of the output P 2 [0, u](t) of the play operator with yield limit 2, of the expected value E (P R [0, u](t)) 1. it holds that the function increases linearly on [0, 1.625] from 0.25 to 1.875, decreases linearly on [1.625, 1.75] to 1.75, increases linearly on [1.75, 2] to 2 and decreases linearly on [2,4] to 0 and is equal to 0 on [4, ∞), see also Figure 6. For computing the corresponding density φ 109 32 , shown in the top, right-hand side of Figure 5 by using (17), we have to sum up several values for ρ R (r).…”

“…Inverse UQ for a Prandtl-Ishlinskiȋ operator of stop type can be found in [13]. The plan of the paper is the following: In Section 2, the play operator with deterministic data is recalled and a method to efficiently compute the values of the play operators for all possible yield limits is introduced.…”

“…Values for r 0,u,3 13 32 ,k , s 0,u,313 32 ,k , z 0,u,3 13 32 ,k and the interval I 0,u,3 13 32 ,k for the considered input function. It holds K 0,u,3 13 32 = 3 and p 0,u,3 13 32 = −1.…”