Production
https://prod.org.br/article/doi/10.1590/0103-6513.20220064
Production
Research Article

A nonlinear time-series prediction methodology based on neural networks and tracking signals

Natália Maria Puggina Bianchesi; Cláudia Eliane da Matta; Simone Carneiro Streitenberger; Estevão Luiz Romão; Pedro Paulo Balestrassi; Antônio Fernando Branco Costa

Downloads: 0
Views: 70

Abstract

Paper aims: This paper presents a nonlinear time series prediction methodology using Neural Networks and Tracking Signals method to detect bias and their responsiveness to non-random changes in the time series.

Originality: This study contributes with an innovative approach of nonlinear time series prediction methodology. Furthermore, the Design of Experiments was applied to simulate datasets and to analyze the results of Average Run Length, identifying in which conditions the methodology is efficient.

Research method: Datasets were generated to simulate different nonlinear time series by changing the error of the series. The methodology was applied to the datasets and the Design of Experiments was implemented to evaluate the results. Lastly, a case study based on total oil and grease was performed.

Main findings: The results showed that the proposed prediction methodology is an effective way to detect bias in the process when an error is introduced in the nonlinear time series because the mean and the standard deviation of the error have a significant impact on the Average Run Length.

Implications for theory and practice: This study contributes to a discussion about time series prediction methodology since this new technique could be widely used in several areas to improve forecast accuracy.

Keywords

Nonlinear time series, Time series forecasting, Neural networks, Tracking signals, Design of Experiments

References

Aizenberg, I., Sheremetov, L., Villa-Vargas, L., & Martinez-Muñoz, J. (2016). Multilayer Neural Network with Multi-Valued Neurons in time series forecasting of oil production. Neurocomputing, 175, 980-989. http://dx.doi.org/10.1016/j.neucom.2015.06.092.

Amdoun, R., Khelifi, L., Khelifi-Slaoui, M., Amroune, S., Asch, M., Assaf-Ducrocq, C., & Gontier, E. (2018). The Desirability optimization methodology;a tool to predict two antagonist responses in biotechnological systems: case of biomass growth and hyoscyamine content in elicited datura starmonium hairy roots. Iranian Journal of Biotechnology, 16(1), e1339. http://dx.doi.org/10.21859/ijb.1339. PMid:30555836.

Amiri, E. (2015). Forecasting daily river flows using nonlinear time series models. Journal of Hydrology (Amsterdam), 527, 1054-1072. http://dx.doi.org/10.1016/j.jhydrol.2015.05.048.

Armstrong, J. (2001). Principles of forecasting: a handbook for researchers and practitioners, New York: Springer Science. http://dx.doi.org/10.1007/978-0-306-47630-3.

Balestrassi, P., Popova, E., Paiva, A., & Lima, J. (2009). Design of experiments on neural network’s training for nonlinear time series forecasting. Neurocomputing, 72(4-6), 1160-1178. http://dx.doi.org/10.1016/j.neucom.2008.02.002.

Bandeira, S. G., Alcalá, S. G. S., Vita, R. O., & Barbosa, T. A. (2020). Comparison of selection and combination strategies for demand forecasting methods. Production, 30, e20200009. http://dx.doi.org/10.1590/0103-6513.20200009.

Berry, M., & Linoff, G. (1997). Data mining techniques. New York: John Wiley & Sons.

Bianchesi, N., Romão, E., Lopes, M., Balestrassi, P., & Paiva, A. (2019). A design of experiments comparative study on clustering methods. IEEE Access: Practical Innovations, Open Solutions, 7, 167726-167738. http://dx.doi.org/10.1109/ACCESS.2019.2953528.

Bischak, D. P., & Trietsch, D. (2007). The rate of false signals in X̅ control charts with estimated limits. Journal of Quality Technology, 39(1), 55-65. http://dx.doi.org/10.1080/00224065.2007.11917673.

Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: forecasting and control. San Francisco. Holden Day.

Brasil, Conselho Nacional do Meio Ambiente – CONAMA. (2007, August 9). Resolution nº 393/2007. Diário Oficial da União. Retrieved in 2022, May 13, from http://www.braziliannr.com/brazilian-environmentallegislation/conama-resolution-39307/

Brence, J., & Mastrangelo, C. (2006). Parameter selection for a robust tracking signal. Quality and Reliability Engineering International, 22(4), 493-502. http://dx.doi.org/10.1002/qre.724.

Brown, G. (1959). Statistical forecasting for inventory control. New York: McGraw-Hill.

Candioti, L. V., De Zan, M., Cámara, M., & Goicoechea, H. (2014). Experimental design and multiple response optimization: using the desirability function in analytical methods development. Talanta, 124, 123-138. http://dx.doi.org/10.1016/j.talanta.2014.01.034. PMid:24767454.

Chan, K. S., & Tong, H. (1986). On estimating thresholds in autoregressive models. Journal of Time Series Analysis, 7(3), 179-190. http://dx.doi.org/10.1111/j.1467-9892.1986.tb00501.x.

Chang, J., & Tseng, C. (2017). Analysis of correlation between secondary PM2.5 and factory pollution sources by using ANN and the correlation coefficient. IEEE Access: Practical Innovations, Open Solutions, 5, 22812-22822. http://dx.doi.org/10.1109/ACCESS.2017.2765337.

Chen, T., & Chen, H. (1995). Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Transactions on Neural Networks, 6(4), 911-917. http://dx.doi.org/10.1109/72.392253. PMid:18263379.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale: Lawrence Erlbaum Associates.

Corzo, G., & Solomatine, D. (2007). Knowledge-based modularization and global optimization of artificial neural network models in hydrological forecasting. Neural Networks, 20(4), 528-536. http://dx.doi.org/10.1016/j.neunet.2007.04.019. PMid:17532609.

Cui, L., Wang, Z., & Zhou, X. (2012). Optimization of elicitors and precursors to enhance valtrate production in adventitious roots of Valeriana amurensis Smir. ex Kom. Plant Cell, Tissue and Organ Culture, 108(3), 411-420. http://dx.doi.org/10.1007/s11240-011-0052-2.

Dascalescu, L., Medles, K., Das, S., Younes, M., Caliap, L., & Mihalcioiu, A. (2008). Using design of experiments and virtual instrumentation to evaluate the tribocharging of pulverulent materials in compressedair devices. IEEE Transactions on Industry Applications, 44(1), 3-8. http://dx.doi.org/10.1109/TIA.2007.912801.

De Gooijer, J. G., & Hyndman, R. J. (2006). 25 years of time series forecasting. International Journal of Forecasting, 22(3), 443-473. http://dx.doi.org/10.1016/j.ijforecast.2006.01.001.

Deboeck, G. J. (1994). Trading on the edge: neural, genetic, and fuzzy systems for chaotic financial markets. New York: John Wiley & Sons.

Deng, Y., Jaraiedi, M., & Iskander, W. (2004). Tracking signal test to monitor an intelligent time series forecasting model. Intelligent Manufacturing, 5263, 149-160. http://dx.doi.org/10.1117/12.517225.

Derringer, G., & Suich, R. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology, 12(4), 214-219. http://dx.doi.org/10.1080/00224065.1980.11980968.

Gardner Junior, E. (1985). CUSUM vs. smoothed error forecast monitoring schemes: some simulation results. The Journal of the Operational Research Society, 36(1), 43-47. http://dx.doi.org/10.1057/jors.1985.6.

Granger, C. W. J., & Anderson, A. P. (1978). An introduction to bilinear time series models. Gottingen: Vandenhoeck & Ruprecht.

Hamilton, J. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica Journal of Economic Society, 57(2), 357-384. http://dx.doi.org/10.2307/1912559.

Harrington, E. (1965). The desirability function. Ind Quality Control, 21, 494-498.

Haykin, S. (2009). Neural networks and learning machines (3rd ed.). New Jersey: Prentice Hall.

Hippert, H. S., & Taylor, J. (2010). An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting. Neural Networks, 23(3), 386-395. http://dx.doi.org/10.1016/j.neunet.2009.11.016. PMid:20022462.

Hornik, K. (1993). Some new results on neural network approximation. Neural Networks, 6(8), 1069-1072. http://dx.doi.org/10.1016/S0893-6080(09)80018-X.

Hu, J., Wang, X., Zhang, Y., Zhang, D., Zhang, M., & Xue, J. (2020). Time series prediction method based on variant LSTM recurrent neural network. Neural Processing Letters, 52(2), 2. http://dx.doi.org/10.1007/s11063-020-10319-3.

Igunnu, E. T., & Chen, G. Z. (2014). Produced water treatment technologies. International Journal of Low-Carbon Technologies, 9(3), 157-177. http://dx.doi.org/10.1093/ijlct/cts049.

Kialashaki, A., & Reisel, J. (2013). Modeling of the energy demand of the residential sector in the United States using regression models and artificial neural networks. Applied Energy, 108, 271-280. http://dx.doi.org/10.1016/j.apenergy.2013.03.034.

Krishnamurthy, B. (2006). A comparison of the relative efficiency of tracking signals in forecast control (Thesis). West Virginia University, West Virginia.

Kumar, D., & Murugan, S. (2017). A novel fuzzy time series model for stock market index analysis using neural network with tracking signal approach. Indian Journal of Science and Technology, 10(16), 10. http://dx.doi.org/10.17485/ijst/2017/v10i16/104994.

Lee, J. Y., Chang, J. H., Kang, D. H., Kim, S. I., & Hong, J. P. (2007). Tooth shape optimization for cogging torque reduction of transverse flux rotary motor using design of experiment and response surface methodology. IEEE Transactions on Magnetics, 43(4), 1817-1820. http://dx.doi.org/10.1109/TMAG.2007.892611.

Liu, Z., Zhu, Z., Gao, J., & Xu, C. (2021). Forecast methods for time series data: a survey. IEEE Access: Practical Innovations, Open Solutions, 9, 91896-91912. http://dx.doi.org/10.1109/ACCESS.2021.3091162.

Lorscheid, I., Heine, B. O., & Meyer, M. (2012). Opening the ‘black box’ of simulations: Increased transparency and effective communication through the systematic design of experiments. Computational & Mathematical Organization Theory, 18(1), 22-62. http://dx.doi.org/10.1007/s10588-011-9097-3.

Makridakis, S., & Wheelwright, S. (1989). Forecasting methods for management (5th ed.) New York: John Wiley.

Mao, S., & Xiao, F. (2019). Time series forecasting based on complex network analysis. IEEE Access: Practical Innovations, Open Solutions, 7, 40220-40229. http://dx.doi.org/10.1109/ACCESS.2019.2906268.

Matta, C., Bianchesi, N., Oliveira, M., Balestrassi, P., & Leal, F. (2021). A comparative study of forecasting methods using real-life econometric series data. Production, 31, e20210043. http://dx.doi.org/10.1590/0103-6513.20210043.

McClain, J. (1988). Dominant tracking signals. International Journal of Forecasting, 4(4), 563-572. http://dx.doi.org/10.1016/0169-2070(88)90133-1.

Mircetic, D., Rostami-Tabar, B., Nikolicic, S., & Maslaric, M. (2022). Forecasting hierarchical time series in supply chains: an empirical investigation. International Journal of Production Research, 60(8), 2514-2533. http://dx.doi.org/10.1080/00207543.2021.1896817.

Mo, F., Shen, C., Zhou, J., & Khonsari, M. (2017). Statistical analysis of the influence of imperfect texture shape and dimensional uncertainty on surface texture performance. IEEE Access: Practical Innovations, Open Solutions, 5, 27023-27035. http://dx.doi.org/10.1109/ACCESS.2017.2769880.

Montgomery, C. D. (2009). Introduction to statistical quality control (6th ed.). New York: John Wiley & Sons.

Olson, O., Delen, D., & Meng, Y. (2012). Comparative analysis of data mining methods for bankruptcy prediction. Decision Support Systems, 52(2), 464-473. http://dx.doi.org/10.1016/j.dss.2011.10.007.

Pant, M., & Kumar, S. (2022). Particle swarm optimization and intuitionistic fuzzy set-based novel method for fuzzy time series forecasting. Granular Computing, 7(2), 285-303. http://dx.doi.org/10.1007/s41066-021-00265-3.

Priestley, M. (1980). State-dependent models: a general approach to nonlinear time series analysis. Journal of Time Series Analysis, 1(1), 47-71. http://dx.doi.org/10.1111/j.1467-9892.1980.tb00300.x.

Qian, B., Xiao, Y., Zheng, Z., Zhou, M., Zhuang, W., Li, S., & Ma, Q. (2020). Dynamic multi-scale convolutional neural network for time series classification. IEEE Access: Practical Innovations, Open Solutions, 8, 8. http://dx.doi.org/10.1109/ACCESS.2020.3002095.

Ravi, P. (2014). An analysis of a widely used version of the CUSUM tracking signal. The Journal of the Operational Research Society, 65(8), 1189-1192. http://dx.doi.org/10.1057/jors.2013.50.

Ray, J., & Engelhardt, F. R. (1992). Produced water: technological environmental issues and solutions. New York: Plenum Press. http://dx.doi.org/10.1007/978-1-4615-2902-6.

Rosenthal, R. (1994). Parametric measures of effect size. In H. Cooper and L. V. Hedges (Eds.), The Handbook of research synthesis (pp. 231–244). New York: Russell Sage Foundation.

Sabeti, H., Al-Shebeeb, O., & Jaridi, M. (2016). Forecasting system monitoring under non-normal input noise distributions. Journal of Industrial Engineering and Management, 5(2), 1000194.

Santos, C. H., Lima, R. D. C., Leal, F., Queiroz, J. A., Balestrassi, P. P., & Montevechi, J. A. B. (2020). A decision support tool for operational planning: a Digital Twin using simulation and forecasting methods. Production, 30, e20200018. http://dx.doi.org/10.1590/0103-6513.20200018.

Sun, K., Huang, S., Wong, D., & Jang, S. (2017). Design and application of a variable selection method for multilayer perceptron neural network with LASSO. IEEE Transactions on Neural Networks and Learning Systems, 28(6), 1386-1396. http://dx.doi.org/10.1109/TNNLS.2016.2542866. PMid:28113826.

Superville, C. (2019). Tracking signal performance in monitoring manufacturing processes. Journal of Business and Management, 21, 23-28.

Tong, H. (1978). On a threshold model. In C. H. Chen (Ed.), Pattern recognition and signal processing. Amsterdam: Sijhoff & Noordhoff. http://dx.doi.org/10.1007/978-94-009-9941-1_24.

Trigg, W. (1964). Monitoring a forecasting system. Operational Research Quarterly, 15(3), 271-274. http://dx.doi.org/10.1057/jors.1964.48.

Tsay, R. (2005). Analysis of financial time series (2nd ed.). Hoboken: Wiley. http://dx.doi.org/10.1002/0471746193.

Verma, P., Reddy, S. V., Ragha, L., & Datta, D. (2021). Comparison of time-series forecasting models. In 2021 International Conference on Intelligent Technologies (CONIT). New York: IEEE. http://dx.doi.org/10.1109/CONIT51480.2021.9498451.

Wang, Z., & Lou, Y. (2019). Hydrological time series forecast model based on wavelet de-noising and ARIMA-LSTM. In 3rd Information Technology, Networking, Electronic and Automation Control Conference (ITNEC) (pp. 1697-1701). New York: IEEE.

Wong, W. K., Xia, M., & Chu, W. C. (2010). Adaptive neural network model for time-series forecasting. European Journal of Operational Research, 207(2), 207. http://dx.doi.org/10.1016/j.ejor.2010.05.022.

Xiao, D., Shi, H., & Wu, D. (2012). Short-term load forecasting using bayesian neural networks learned by Hybrid Monte Carlo algorithm. Applied Soft Computing, 12(6), 1822-1827. http://dx.doi.org/10.1016/j.asoc.2011.07.001.

Xiao, H., Jiang, X., Chen, C., Wang, W., Wang, C., Ali, A., Berthe, A., Moussa, R., & Diaby, V. (2020). Using time series analysis to forecast the health-related quality of life of post-menopausal women with non-metastatic ER+ breast cancer: a tutorial and case study. Research in Social & Administrative Pharmacy, 16(8), 1095-1099. http://dx.doi.org/10.1016/j.sapharm.2019.11.009. PMid:31753693.

Yang, M. (2011). Measurement of oil in Produced Water. In K. Lee & J. Neff (Eds.), Produced water (pp. 57-88). New York: Springer. http://dx.doi.org/10.1007/978-1-4614-0046-2_2.

Yu, L., & Lai, K. (2005). Adaptive smoothing neural networks in foreign exchange rate forecasting. In International Conference on Computational Science (pp. 523-530). Berlin: Springer. http://dx.doi.org/10.1007/11428862_72.

Zhai, X., Ali, A., Amira, A., & Bensaali, F. (2016). MLP neural network based gas classification system on Zynq SoC. IEEE Access: Practical Innovations, Open Solutions, 4, 8138-8146. http://dx.doi.org/10.1109/ACCESS.2016.2619181.
 


Submitted date:
05/13/2022

Accepted date:
09/09/2022

6333215ba953957afe707364 production Articles
Links & Downloads

Production

Share this page
Page Sections