Skip to main content
Springer Nature Link
Log in

Time Series Prediction Using Radial Basis Function Network with Transformation of Training Data and Its Applications

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.

Similar content being viewed by others

REFERENCES

  1. Casdagli, M., Nonlinear prediction if chaotic time series, Phys. D (Amsterdam, Neth.), 1998, vol. 35, no. 3, pp. 335–356.  https://doi.org/10.1016/0167-2789(89)90074-2

  2. Zhang, W. and Wei, D., Prediction for network traffic of radial basis function neural network model based on improved particle swarm optimization algorithm, Neural Comput. Appl., 2018, vol. 29, pp. 1143–1152. https://doi.org/10.1007/s00521-016-2483-5

    Article  Google Scholar 

  3. Cao, L., Support vector machines experts for time series forecasting, Neurocomputing, 2003, vol. 51, pp. 321–339. https://doi.org/10.1016/S0925-2312(02)00577-5

    Article  Google Scholar 

  4. Luo, C., Huang, C., Cao, J., Lu, J., Huang, W., Guo, J., and Wei, Y., Short-term traffic flow prediction based on least square support vector machine with hybrid optimization algorithm, Neural Process. Lett., 2019, vol. 50, pp. 2305–2322.  https://doi.org/10.1007/s11063-019-09994-8

    Article  Google Scholar 

  5. Cowper, M.R., Mulgrew, B., and Unsworth, C.P., Nonlinear prediction of chaotic signals using a normalised radial basis function network, Signal Process., 2002, vol. 82, pp. 775–789.  https://doi.org/10.1016/S0165-1684(02)00155-X

    Article  MATH  Google Scholar 

  6. Harpham, C. and Dawson, C.W., The effect of different basis functions on a radial basis function network for time series prediction: A comparative study, Neurocomputing, 2006, vol. 69, nos. 16–18, pp. 2161–2170.  https://doi.org/10.1016/j.neucom.2005.07.010

    Article  Google Scholar 

  7. Du, H. and Zhang, N., Time series prediction using evolving radial basis function networks with new encoding scheme, Neurocomputing, 2008, vol. 71, pp. 1388–1400.  https://doi.org/10.1016/j.neucom.2007.06.004

    Article  Google Scholar 

  8. Gan, M., Peng, H., and Dong, X., A hybrid algorithm to optimize RBF network architecture and parameters for nonlinear time series prediction, Appl. Math. Modell., 2012, vol. 36, no. 7, pp. 2911–2919.  https://doi.org/10.1016/j.apm.2011.09.066

    Article  MathSciNet  MATH  Google Scholar 

  9. Markopoulos, A.P., Georgiopoulos, S., and Manolakos, D.E., On the use of back propagation and radial basis function neural networks in surface roughness prediction, J. Ind. Eng. Int., 2016, vol. 12, pp. 389–400.  https://doi.org/10.1007/s40092-016-0146-x

    Article  Google Scholar 

  10. Manjunatha, R., Narayana, P.B., Reddy, K.H., and Reddy, V.K., Radial basis function neural networks in prediction and modeling of diesel engine emissions operated for biodiesel blends under varying operating conditions, Indian J. Sci. Technol., 2012, vol. 5, no. 3, pp. 2307–2312.  https://doi.org/10.17485/ijst/2012/v5i3.14

    Article  Google Scholar 

  11. He, X. and Lapedes, A., Nonlinear modeling and prediction by successive approximation using radial basis functions, Phys. D (Amsterdam, Neth.), 1994, vol. 70, no. 3, pp. 289–301.  https://doi.org/10.1016/0167-2789(94)90018-3

  12. Hong, W.-C., Dong, Y., Zheng, F., and Wei, S.Y., Hybrid evolutionary algorithms in a SVR traffic flow forecasting model, Appl. Math. Comput., 2011, vol. 217, no. 15, pp. 6733–6747.  https://doi.org/10.1016/j.amc.2011.01.073

    Article  MathSciNet  MATH  Google Scholar 

  13. Hu, W., Yan, L., Liu, K., and Wang, H., A short-term traffic flow forecasting method based on the hybrid PSO-SVR, Neural Process. Lett., 2016, vol. 43, pp. 155–172.  https://doi.org/10.1007/s11063-015-9409-6

    Article  Google Scholar 

  14. Luo, C., Huang, C., Cao, J., Lu, J., Huang, W., Guo, J., and Wei, Y., Short-term traffic flow prediction based on least square support vector machine with hybrid optimization algorithm, Neural Process. Lett., 2019, vol. 50, pp. 2305–2322.  https://doi.org/10.1007/s11063-019-09994-8

    Article  Google Scholar 

  15. Nakayama, H., Arakawa, M., and Sasaki, R., Simulation-based optimization using computational intelligence, Optim. Eng., 2002, vol. 3, pp. 201–214.  https://doi.org/10.1023/A:1020971504868

    Article  MathSciNet  MATH  Google Scholar 

  16. Kitayama, S. and Yamazaki, K., Simple estimate of the width in Gaussian kernel with adaptive scaling technique, Appl. Soft Comput., 2011, vol. 11, pp. 4726–4737.  https://doi.org/10.1016/j.asoc.2011.07.011

    Article  Google Scholar 

  17. Kitayama, S., Yokoyama, M., Kawamoto, K., Noda, T., Miyasaka, T., and Echigo, Y., Practical approach of simultaneous optimization of variable blank holder force and variable slide velocity trajectory in sheet metal forming, Int. J. Adv. Manuf. Technol., 2018, vol. 98, pp. 2693–2703.  https://doi.org/10.1007/s00170-018-2411-1

    Article  Google Scholar 

  18. Kitayama, S., Ishizuki, R., Takano, M., Kubo, Y., and Aiba, S., Optimization of mold temperature profile and process parameters for weld line reduction and short cycle time in rapid heat cycle molding, Int. J. Adv. Manuf. Technol., 2019, vol. 103, pp. 1735–1744.  https://doi.org/10.1007/s00170-019-03685-3

    Article  Google Scholar 

  19. Kitayama, S., Saikyo, M., Nishio, Y., and Tsutsumi, K., Torque control strategy and optimization for fuel consumption and emission reduction in parallel hybrid electric vehicles, Struct. Multidiscip. Optim., 2015, vol. 52, pp. 595–611.  https://doi.org/10.1007/s00158-015-1254-8

    Article  Google Scholar 

  20. András, P., The equivalence of support vector machine and regularization neural networks, Neural Process. Lett., 2002, vol. 15, pp. 97–104.  https://doi.org/10.1023/A:1015292818897

    Article  MATH  Google Scholar 

  21. Kitayama, S. and Yamazaki, K., Simple estimate of the width in Gaussian kernel with adaptive scaling technique, Appl. Soft. Comput., 2011, vol. 11, no. 8, pp. 4726–4737.  https://doi.org/10.1016/j.asoc.2011.07.011

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan

    Satoshi Kitayama

  2. Graduate School of Natural Science & Technology, Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan

    Kohei Saito

Authors
  1. Satoshi Kitayama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kohei Saito
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Satoshi Kitayama or Kohei Saito.

Ethics declarations

The authors declare that they have no conflicts of interest.

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.

Table A1. Driving cycle characteristics of WLTC and LA4
Full size table

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.

Table A2. Comparison of RMSE
Full size table
Fig. A1.
figure 12

Driving cycle.

Full size image
Fig. A2.
figure 13

Comparison of time series prediction between proposed and conventional RBF.

Full size image

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411622030026

Keywords: