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1

Iterative methods for efficient sampling-based optimal motion planning of nonlinear systems

Ha J. S., Choi H. L., Jeon J. H.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

155--168

EN

This paper extends the RRT* algorithm, a recently developed but widely used sampling based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often leads to difficulties in choosing an appropriate distance metric and in computing optimized trajectory segments in tree construction. To tackle these two difficulties, this work adopts the affine quadratic regulator-based pseudo-metric as the distance measure and utilizes iterative two-point boundary value problem solvers to compute the optimized segments. The proposed extension then preserves the inherent asymptotic optimality of the RRT* framework, while efficiently handling a variety of kinodynamic constraints. Three numerical case studies validate the applicability of the proposed method.

2

A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion

Tagade P. M., Choi H. L.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 2

229--243

EN

This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

3

Solvent Extraction of Co, Ni and Mn from NCM Sulfate Leaching Solution of Li(NCM)O2 Secondary Battery Scraps

Hong H. S., Kim D. W., Choi H. L., Ryu S.-S.

Archives of Metallurgy and Materials

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2017

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Vol. 62, iss. 2B

1011--1014

EN

As a part of the study on recycling Li(NCM)O2 lithium-ion battery scraps, solvent extraction experiments were performed using different extraction agents such as PC88A, Cyanex272 and D2EHPA to separate Co, Ni and Mn from the leaching solution. When the ratio of Mn to Ni was about 0.4 in the leaching solution, the separation factor for Co and Mn was found to be less than 10 so that the separation of Co and Ni was insufficient. When solvent extraction was done using the solution with the lower Mn/Ni ratio of 0.05 where Mn was removed by potassium permanganate and chlorine dioxide, more than 99% of Mn could be extracted through five courses of extraction using 30vol% D2EHPA while the extraction rates of Co and Ni were around 17% and 11%, respectively. In the case that Mn was removed from the solution, the extraction rate of Co was higher than 99% whereas less than 7% Ni was extracted using Cyanex272 suggesting that Co and Ni elements were effectively separated.