ISSN 1063-7842, Technical Physics, 2010, Vol. 55, No. 3, pp. 347–356. © Pleiades Publishing, Ltd., 2010. Original Russian Text © Yu.V. Zaika, E.P. Bormatova, 2010, published in Zhurnal Tekhnicheskoі Fiziki, 2010, Vol. 80, No. 3, pp. 31–39. 347 INTRODUCTION Modeling in the field of hydrogen material science is inspired by the prospects of hydrogen power engi- neering and the problem of protecting construction materials from hydrogen corrosion [1]. The experi- mental method of permeability is classic [2]. At the same time, experimental data processing is compli- cated by a spread in the estimates of model parame- ters. One of the main reasons is that inverse problems of mathematical physics are highly sensitive to experi- mental and computational errors. In addition, the tra- ditional “cut-and-try approach” does not usually guarantee the uniqueness of the set of parameters that fairly approximate experimental curves. Therefore, first, it is necessary to determine the data level suffi- cient for one-valued parametrical model identifica- tion. Second, the algorithm for estimating the param- eters must be correct (in particular, without differenti- ation of noisy measurements). We will use the following alternative experiment. A plate of thickness l made of the investigated material (a metal or alloy) serves as a partition in a vacuum cham- ber. At a fixed temperature T = of the sample, a pressure = const of molecular hydrogen is created spasmodically from the inlet side. From the outlet side, evacuation is performed and desorption flux J = J(t) (t is the time) is determined with the help of a mass spectrometer. The fluxes are implied to correspond to a unit of area, i.e., we speak about flux densities. Actu- ally, the pressure is measured at the outlet: T p0 p l t () θ 1 τ t – ( )θ 0 1 – { } J τ () exp τ , d 0 t ∫ = where θ i are the characteristics of the vacuum setup. Calculation of J from p l is the inverse problem, which will not be considered here (see, for example, [3]). After attaining the stationary state J(t) ≈ = const, t ≥ t ∗ , we sharply increase the pressure at the inlet up to a value > and wait until the subsequent desorption stabilizes at t ≥ t* > t ∗ . Such a version is more prefera- ble than two classic experiments, since the repeated degassing is not necessary and the second stage “starts” not from zero initial distribution of atomic hydrogen in the plate, but from the preceding station- ary state (diversity increases the information value). The stationary state is approached asymptotically. However, t ∗ and t* should not be selected too large in order that transient processes not to be “lost” against the background of stationary processes. We believe that the parameters are related to temper- ature T by Arrhenius law. For example, for the diffusion coefficient, we assume that D = D 0 exp{–E D /[RT]}. If necessary, other dependences on T are permissible (this is not essential for further analysis because the temperature remains constant during the experiment). The values of pressure and concentration c(t, x) of dis- solved hydrogen are considered to be small: D ≠ D(c). Since we discuss inverse problems and experimental errors are estimated, at the best, at 10–20%, we tried to minimize a set of parameters to be determined. MATHEMATICAL MODEL Let us consider the following model with surface desorption [4]: Jt () p · l t () p l t ( )θ 0 1 – + [ ]θ 1 1 – , = J p0 + p0 Time Lag Parametric Identification of a Hydrogen Permeability Model Yu. V. Zaika and E. P. Bormatova Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, ul. Pushkinskaya 11, Petrozavodsk, 185910 Russia e-mail: zaika@krc.karelia.ru Received April 7, 2009 Abstract—An inverse problem with dynamic boundary conditions for determining the parameters of a hydrogen permeability nonlinear model is considered. Algorithms are proposed for estimating transport parameters of adsorption, desorption, dissolution, and diffusion depending on the body of experimental information. DOI: 10.1134/S1063784210030047 THEORETICAL AND MATHEMATICAL PHYSICS