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Mathematical Problems in Engineering
Volume 2013, Article ID 391273, 11 pages
Research Article

Selection Method for Kernel Function in Nonparametric Extrapolation Based on Multicriteria Decision-Making Technology

1College of Mechanical Science and Engineering, Jilin University, Changchun 130025, China
2College of Automotive Engineering, Jilin University, Changchun 130025, China
3Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130025, China

Received 21 May 2013; Accepted 16 August 2013

Academic Editor: Fabrizio Greco

Copyright © 2013 Jixin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Selecting the most appropriate kernel function to extrapolate a load set is the paramount step in compiling load spectrum, as it affects the results of nonparametric extrapolation largely. Aiming at this issue, this paper provides a new approach in selecting kernel function for the nonparametric extrapolation. To solve the complexity and uncertainty of nonparametric extrapolation, characteristics of four kernel functions and their effects on the results are explained in the “from-to” diagram obtained by rainflow counting. Multicriteria decision-making (MCDM) is then applied to solve the selection problem of kernel function. To evaluate the dispersion degrees of the mean and amplitude of a load set accurately, their range, standard deviation, and interquartile range are selected as the evaluation criteria. The weight of each criterion, which represents the impact degree on the selection of the kernel function, is calculated separately using the eigenvector and entropy method. The comprehensive weights are obtained by applying the optimization theory and Jaynes’ maximum entropy principle. Finally, the importance of each criterion is discussed according to their calculated comprehensive weights, and the selection method for kernel functions is obtained, which is illustrated by extrapolating the output torque of the power split device of hybrid electrical vehicles.