Abstract
Blast furnace gas is a significant energy resource in steel industry. Keeping stable of blast furnace gas flow is an important task for the furnace itself and the application of byproduct gas. However, owing to fluctuation and noisy of gas flow, echo state network is usually ill-posed in the prediction and it is very difficult to accurately predict the amount of gas. In this paper, in order to increase the accuracy of prediction in ill-posed echo state network model, L-curve method is used to compute the regularization parameter, which can alleviate the influence of ill-condition for ESN. Finally, to verify the effectiveness of the proposed method, the real data from blast furnace is employed in the experiments. Compared with two parameter regularization methods and four types of prediction methods, the results demonstrate that the proposed method exhibits a higher prediction accuracy for gas prediction.











Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Odgaard PF, Stoustrup J (2009) Estimation of uncertainty bounds for the future performance of a power plant. IEEE Trans Control Syst Technol 17(1):199–206
Akimoto K, Sannomiya N, Nishikawa Y, Tsuda T (1991) An optimal gas supply for a power plant using a mixed integer. Automatica 27(3):513–518
Kim JH, Yi H, Han C (2002) Optimal byproduct gas distribution in the iron and steel making process using mixed integer linear programming, In: Proceedings of international symposium on advanced control of industrial processes, Kumamoto, Japan, 581–586
Kim JH, Yi H, Han C (2003) A novel MILP model for plantwide multiperiod optimization of byproduct gas supply system in the iron and steel making process. Trans IChemE: Part A 81:1015–1025
Jaeger H, Haas H (2004) Harnessing nonlinearity predicting chaotic systems and saving energy in wireless communication. Science 304(5667):77–80
Haque ME, Sudhakar KV (2002) ANN back-propagation prediction model for fracture toughness in microalloy steel. Int J Fatigue 24(9):1003–1010
Han M, Xu ML (2013) Predicting multivariate time series using subspace echo state network. Neural Process Lett 1–9
Kim KJ (2003) Financial time series forecasting using support vector machines. Neurocomputing 55(1):307–319
Gil PG, Cortes JMR, Hernndez SEP, Aquino VA (2011) A neural network scheme for long-term forecasting of chaotic time series. Neural Process Lett 33(3):215–233
Wang XX, Ma LY, Wang BS, Wang T (2013) A hybrid optimization-based recurrent neural network for real-time data prediction. Neurocomputing 120(23):547–559
Roy P, Mahapatra GS, Rani P, Pandey SK, Dey KN (2014) Robust feedforward and recurrent neural network based dynamic weighted combination models for software reliability prediction. Appl Soft Comput 22:629–637
Shen W, Guo X, Wu C (2011) Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm algorithm. Knowl-Based Syst 24(3):378–385
Lukosevicius M, Jaeger H (2009) Reservoir computing approaches to recurrent neural network training. Comput Sci Rev 3(3):127–149
Jaeger H (2001) The echo state approach to analyzing and training recurrent neural networks. German National Research Center for Information Technology, Cologne
Tong MH, Bickett AD, Christiansen EM, Cottrell Garrison W (2007) Learning grammatical structure with echo state networks. Neural Netw 3(20):424–432
Georg H, Helmut H (2007) Echo state networks with filter neurons and a delay & sum readout. Neural Netw 23(2):244–256
Venayagamoorthy GK, Shishir B (2009) Effects of spectral radius and settling time in the performance of echo state networks. Neural Netw 22(7):861–863
Venayagamoorthy GK (2007) Online design of an echo state network based wide area monitor for a multimachine power system. Neural Netw 20(3):404–413
Cernansky M, Tin P (2008) Predictive modeling with echo state networks. Artificial neural networks—ICANN 2008, 778–787
Azadeh A, Ghaderi SF, Tarverdian S, Saberi M (2007) Integration of artificial neural networks and genetic algorithm to predict electrical energy consumption. Appl Math Comput 186(2):1731–1741
Shi Z, Han M (2009) Plane and robustness in static reservoir for nonlinear regression estimation. Neurocomputing 72(7):1732–1743
Liu Y, Zhao W (2009) Improved echo state network based on data-driven and its application to prediction of blast furnace gas output. Acta Automatica Sinica 35(6):731–738
Shi ZW, Han M (2007) Support vector echo-state machine for chaotic time-series prediction. IEEE Trans Neural Netw 18(2):359–372
Hansen PC (1999) The L-curve and its use in the numerical treatment of inverse problems. IMM, Department of Mathematical Modelling, Kongens Lyngby
Hansen PC (1987) The truncated SVD as a methodfor regularization. BIT 27:354–553
Paige CC, Saunders MA (1982) LSQR: an algorithm for sparse equations and sparse least squares. Assoc Comput Mach Trans Math Soft 8:43–71
Golub GH, Heath M, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2):215–223
Hofmann B (1986) Regularization of applied inverse and ill-posed problems, teubner texts in mathematics. B. G. Teubner Verlag, Leipzig
Phillips D (1962) A technique for the numerical solution of certain integral equations of the first kind. Adapt Comput Mach Learn 9:84–97
Lepskij O (1990) On a problem of adaptive estimation in Gaussian white noise. Theory Probab App 35:454–466
Wahba G (1985) A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Ann Stat 13:1378–1402
Harasse S, Yashiro W, Momose Atsushi (2012) Solving ill-posed linear systems with constraints on statistical moments. IEEE Signal Process Lett 19(2):103–106
Lawson CL, Hanson RJ (1974) Solving least squares problems. Prentice-Hall, Englewood Cliffs
Fathi V, Montazer GA (2013) An improvement in RBF learning algorithm based on PSO for real time applications. Neurocomputing 111(2):169–176
Chandra R, Zhang MJ (2012) Cooperative coevolution of Elman recurrent neural networks for chaotic time series prediction. Neurocomputing 86(1):116–123
Acknowledgments
This paper is partially supported by the Science Fund for Hundred Excellent Innovation Talents Support Program of Hebei Province, Doctoral Fund of Ministry of Education of China (20121333110008), Hebei Province Applied Basis Research Project (13961806D), Natural Science Foundation of Hebei Province (F2014203267), Hebei Province Development of Social Science Research Project (201401315) and the National Natural Science Foundation of China (61273260, 61290322, 61273222, 61322303).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, L., Hua, C., Tang, Y. et al. Ill-posed Echo State Network based on L-curve Method for Prediction of Blast Furnace Gas Flow. Neural Process Lett 43, 97–113 (2016). https://doi.org/10.1007/s11063-014-9404-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-014-9404-3