Abstract
This paper presents a time series prediction using radial basis function (RBF) network with the affine transformation of training data. Conventionally, the training data for time series prediction is considered in the absolute coordinate system, and these results in the poor prediction. For highly accurate time series prediction, in this paper, the affine transformation is applied to the training data. Therefore, the training data are transformed into the rotated coordinate system using the affine transformation, and the time series prediction using the RBF network is made in this coordinate system. The proposed approach is simple and easy to implement. Several benchmarks are selected to examine the proposed approach, and the root mean square error (RMSE) is used to numerically evaluate the prediction accuracy. It is found from the numerical results that the highly accurate prediction can be made by the proposed approach, in comparison with the conventional RBF network.
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APPENDIX
APPENDIX
The proposed approach is applied to the following two driving cycles, and the results are summarized. Like Section 4.2, the vehicle speed is predicted by using the torque and the engine speed, and the RMSE is used to evaluate the accuracy of prediction.
Worldwide harmonized Light duty driving Test Cycle (WLTC), which is a current standard driving cycle for fuel consumption.
Los Angeles number 4 mode (LA4), in which the driving in urban area is assumed.
Each driving cycle is shown in Fig. A1, and the characteristics are summarized in Table A1.
It is difficult to compare the prediction result through the driving cycle, and two parts are selected for the comparison. The results are then shown in Fig. A2 with the enlarged view and the RMSE is also listed in Table A2. Note that the white dots in Fig. A2 denote the predicted points. It is found from Fig. A2 and Table A2 that highly accurate time series prediction can be made by the proposed RBF.
Driving cycle.
Comparison of time series prediction between proposed and conventional RBF.
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Satoshi Kitayama, Kohei Saito Time Series Prediction Using Radial Basis Function Network with Transformation of Training Data and Its Applications. Aut. Control Comp. Sci. 56, 239–252 (2022). https://doi.org/10.3103/S0146411622030026
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DOI: https://doi.org/10.3103/S0146411622030026