Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion.

In this paper, the fractional-order modeling of multiple groups of lithium-ion batteries with different states is discussed referring to electrochemical impedance spectroscopy (EIS) analysis and iterative learning identification method. The structure and parameters of the presented fractional-order equivalent circuit model (FO-ECM) are determined by EIS from electrochemical test. Based on the working condition test, a P-type iterative learning algorithm is applied to optimize certain selected model parameters in FO-ECM affected by polarization effect. What's more, considering the reliability of structure and adaptiveness of parameters in FO-ECM, a pre-tested nondestructive 1 / f noise is superimposed to the input current, and the correlative information criterion (CIC) is proposed by means of multiple correlations of each parameter and confidence eigen-voltages from weighted co-expression network analysis method. The tested batteries with different state of health (SOH) can be successfully simulated by FO-ECM with rarely need of calibration when excluding polarization effect. Particularly, the small value of CIC α indicates that the fractional-order α is constant over time for the purpose of SOH estimation. Meanwhile, the time-varying ohmic resistance R 0 in FO-ECM can be regarded as a wind vane of SOH due to the large value of CIC R 0 . The above analytically found parameter-state relations are highly consistent with the existing literature and empirical conclusions, which indicates the broad application prospects of this paper.

Modelling heat transfer in heterogeneous media using fractional calculus.

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.

Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders.

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations.

Modulatory influences of ventilatory disorders on electrical stability of the rat heart.

It is a known fact that there is a relationship between some ventilatory disorders and the incidence of ventricular arrhythmias. The aim of our study was to show this relation in the circadian dependence in in-vivo rat models. The electrical stability of the heart was measured by ventricular arrhythmia threshold (VAT) at 3h intervals during a 24h period. The experiments were performed in the Wistar rats (pentobarbital anaesthesia 40mg/l kg i.p., open chest experiments, adaptation to the light regime 12:12 hours, with the dark phase from 18.00h to 06.00h). The normal artificial ventilation was used in the control group (n = 17), hypoventilation (n = 10) and hyperventilation (n = 7) in the second and third ones. The fourth group (n = 4) was subjected to 20 min. hypoventilation and subsequent 20 min. reoxygenation. The significant circadian rhythm was detected under normal ventilatory conditions. Hypoventilation significantly decreased (alpha = 0.001) the VAT and changed the 24h rhythm to the moderate biphasic compared to the control group. The biphasic character was evident only after 10 min. of hypoventilation. Hyperventilation non-significantly increased the VAT, but did not change the rhythm. Reoxygenation, after 20 minutes of hypoventilation, expressively changed the VAT circadian rhythm, inversely compared to the control group. The biphasic character was kept only after 5 min. of reoxygenation. It is concluded that myocardial vulnerability to the ventricular arrhythmias is influenced by ventilatory disorders in the circadian dependence.