4,113 research outputs found
Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter
This paper investigates the state estimation of a high-fidelity spatially
resolved thermal- electrochemical lithium-ion battery model commonly referred
to as the pseudo two-dimensional model. The partial-differential algebraic
equations (PDAEs) constituting the model are spatially discretised using
Chebyshev orthogonal collocation enabling fast and accurate simulations up to
high C-rates. This implementation of the pseudo-2D model is then used in
combination with an extended Kalman filter algorithm for differential-algebraic
equations to estimate the states of the model. The state estimation algorithm
is able to rapidly recover the model states from current, voltage and
temperature measurements. Results show that the error on the state estimate
falls below 1 % in less than 200 s despite a 30 % error on battery initial
state-of-charge and additive measurement noise with 10 mV and 0.5 K standard
deviations.Comment: Submitted to the Journal of Power Source
An effective spectral collocation method for the direct solution of high-order ODEs
This paper reports a new Chebyshev spectral collocation method for directly solving high-order ordinary differential equations (ODEs). The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows the multiple boundary conditions to be incorporated more efficiently. Numerical results show that the
proposed formulation significantly improves the conditioning of the system and yields more accurate results and faster convergence rates than conventional formulations
A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
In this paper, the fractional order of rational Bessel functions collocation
method (FRBC) to solve Thomas-Fermi equation which is defined in the
semi-infinite domain and has singularity at and its boundary condition
occurs at infinity, have been introduced. We solve the problem on semi-infinite
domain without any domain truncation or transformation of the domain of the
problem to a finite domain. This approach at first, obtains a sequence of
linear differential equations by using the quasilinearization method (QLM),
then at each iteration solves it by FRBC method. To illustrate the reliability
of this work, we compare the numerical results of the present method with some
well-known results in other to show that the new method is accurate, efficient
and applicable
Boundary knot method: A meshless, exponential convergence, integration-free, and boundary-only RBF technique
Based on the radial basis function (RBF), non-singular general solution and
dual reciprocity principle (DRM), this paper presents an inheretnly meshless,
exponential convergence, integration-free, boundary-only collocation techniques
for numerical solution of general partial differential equation systems. The
basic ideas behind this methodology are very mathematically simple and
generally effective. The RBFs are used in this study to approximate the
inhomogeneous terms of system equations in terms of the DRM, while non-singular
general solution leads to a boundary-only RBF formulation. The present method
is named as the boundary knot method (BKM) to differentiate it from the other
numerical techniques. In particular, due to the use of non-singular general
solutions rather than singular fundamental solutions, the BKM is different from
the method of fundamental solution in that the former does no need to introduce
the artificial boundary and results in the symmetric system equations under
certain conditions. It is also found that the BKM can solve nonlinear partial
differential equations one-step without iteration if only boundary knots are
used. The efficiency and utility of this new technique are validated through
some typical numerical examples. Some promising developments of the BKM are
also discussed.Comment: 36 pages, 2 figures, Welcome to contact me on this paper: Email:
[email protected] or [email protected]
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