A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.

Numerical Analysis and Transformative Predictions of Fractional Order Epidemic Model during COVID-19 Pandemic: A Critical Study from Bangladesh

The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (R0) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.

Identification of fractional order Hammerstein models based on mixed signals

An algorithm based on mixed signals is proposed,to solve the issues of low accuracy of identification algorithm,immeasurable intermediate variables of fractional order Hammerstein model,and how to determine the magnitude of fractional order.In this paper,a special mixed input signal is designed to separate the nonlinear and linear parts of the fractional order Hammerstein model so that each part can be identified independently.The nonlinear part is fitted by the neural fuzzy network model,which avoids the limitation of polynomial fitting and broadens the application range of nonlinear models.In addition,the multi-innovation Levenberg-Marquardt(MILM)algorithm and auxiliary recursive least square algorithm are innovatively integrated into the parameter identification algorithm of the fractional order Hammerstein model to obtain more accurate identification results.A simulation example is given to verify the accuracy and effectiveness of the proposed method.

Modeling mechanism of a novel fractional grey mode based on matrix analysis

To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.

Model Identification and Control of Electromagnetic Actuation in Continuous Casting Process With Improved Quality

This paper presents an original theoretical framework to model steel material properties in continuous casting line process. Specific properties arising from non-Newtonian dynamics are herein used to indicate the natural convergence of distributed parameter systems to fractional order transfer function models. Data driven identification from a real continuous casting line is used to identify model of the electromagnetic actuator device to control flow velocity of liquid steel. To ensure product specifications, a fractional order control is designed and validated on the system. A projection of the closed loop performance onto the quality assessment at end production line is also given in this paper.

Fractional description of mechanical property evolution of soft soils during creep

The motion of pore water directly influences mechanical properties of soils, which are variable during creep. Accurate description of the evolution of mechanical properties of soils can help to reveal the internal behavior of pore water. Based on the idea of using the fractional order to reflect mechanical properties of soils, a fractional creep model is proposed by introducing a variable-order fractional operator, and realized on a series of creep responses in soft soils. A comparative analysis illustrates that the evolution of mechanical properties, shown through the simulated results, exactly corresponds to the motion of pore water and the solid skeleton. This demonstrates that the proposed variable-order fractional model can be employed to characterize the evolution of mechanical properties of and the pore water motion in soft soils during creep. It is observed that the fractional order from the proposed model is related to the dissipation rate of pore water pressure.

Fractional order battery modelling methodologies for electric vehicle applications:Recent advances and perspectives

Accurate modelling of lithium ion batteries is crucial for battery management in electric vehicles.Recent studies have revealed the fractional order nature of lithium ion batteries,leading to fractional order modelling techniques.In this paper,a comprehensive review of the fractional order battery models and their applications in battery management of electric vehicles is provided from the perspectives of frequency and time domains.In the frequency domain,the fractional order models to fit electrochemical impedance spectroscopy data are investigated,followed by their applications in health diagnosis,battery heating and charging strategies.In the time domain,the fractional order models adopted for voltage simulation are discussed,followed by their applications in battery state estimation and fault diagnosis.Finally,from the perspectives of time domain and frequency domain applications,critical challenges and research trends for future work in terms of fractional order modelling are highlighted to advance the development of next-generation battery management.