Abstract
In this paper, a new method is proposed to identify solid oxide fuel cell using extreme learning machine–Hammerstein model (ELM–Hammerstein). The ELM–Hammerstein model consists of a static ELM neural network followed by a linear dynamic subsystem. First, the structure of ELM–Hammerstein model is determined by Lipschitz quotient criterion from input–output data. Then, a generalized ELM algorithm is proposed to estimate the parameters of ELM–Hammerstein model, including the parameters of linear dynamic part and the output weights of ELM. The proposed method can obtain accurate identification results and its computation is more efficient. Simulation results demonstrate its effectiveness.
Similar content being viewed by others
References
Abonyi J, Babuška R, Botto MA, Szeifert F, Nagy L (2000) Identification and control of nonlinear systems using fuzzy Hammerstein models. Ind Eng Chem Res 39(11):4302–4314
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723
Arriagada J, Olausson P, Selimovic A (2002) Artificial neural network simulator for SOFC performance prediction. J Power Sources 112(1):54–60
Cui M, Liu H, Li Z, Tang Y, Guan X (2014) Identification of Hammerstein model using functional link artificial neural network. Neurocomputing 142:419–428
Deng J, Li K, Irwin GW (2011) Fast automatic two-stage nonlinear model identification based on the extreme learning machine. Neurocomputing 74(16):2422–2429
Fink A, Nelles O (2001) Nonlinear internal model control based on local linear neural networks. In: 2001 IEEE international conference on systems, man, and cybernetics, vol 1, pp 117–122
Hajimolana S, Hussain M, Daud WW (2011) Mathematical modeling of solid oxide fuel cells: a review. Renew Sustain Energy Rev 15:1893–1917
He X, Asada H (1993) A new method for identifying orders of input–output models for nonlinear dynamic systems. In: American control conference, pp 2520–2523
Hong X, Chen S (2012) The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization. Neurocomputing 82:216–223
Huang G, Huang GB, Song S, You K (2015) Trends in extreme learning machines: a review. Neural Netw 61:32–48
Huang GB (2015) What are extreme learning machines? Filling the gap between Frank Rosenblatt’s dream and John von Neumann’s puzzle. Cogn Comput 7(3):263–278
Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: 2004 IEEE international joint conference on neural networks, vol 2, pp 985–990
Huo HB, Zhu XJ, Tu HY (2007) Iterative learning control of SOFC based on ARX identification model. J Zhejiang Univ Sci A 8:1921–1927
Huo H, Kuang X, Huo H, Zhu X (2012) Dynamic modeling of SOFC stack using ARX identification algorithm. In: Proceedings of international conference on modelling, identification & control (ICMIC), 2012
Huo HB, Zhong ZD, Zhu XJ, Tu HY (2008) Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model. J. Power Sources 175(1):441–446
Iora P, Aguiar P, Adjiman C, Brandon N (2005) Comparison of two IT DIR-SOFC models: impact of variable thermodynamic, physical, and flow properties. Steady-state and dynamic analysis. Chem Eng Sci 60(11):2963–2975
Jia L, Chiu MS, Ge SS (2005) A noniterative neuro-fuzzy based identification method for Hammerstein processes. J Process Control 15(7):749–761
Jia L, Chiu MS, Ge SS (2005) Iterative identification of neuro-fuzzy-based Hammerstein model with global convergence. Ind Eng Chem Res 44(6):1823–1831
Padullés J, Ault GW, McDonald JR (2000) An integrated SOFC plant dynamic model for power system simulation. J Power Sources 86:495–500
Jurado F (2004) Modeling SOFC plants on the distribution system using identification algorithms. J Power Sources 129(2):205–215
Jurado F (2006) A method for the identification of solid oxide fuel cells using a Hammerstein model. J Power Sources 154(1):145–152
Le F, Markovsky I, Freeman CT, Rogers E (2012) Recursive identification of Hammerstein systems with application to electrically stimulated muscle. Control Eng Pract 20:386–396
Li Y, Rajakaruna S, Choi SS (2007) Control of a solid oxide fuel cell power plant in a grid-connected system. IEEE Trans Energy Convers 22:405–413
Li Y, Shen J, Lu J (2011) Constrained model predictive control of a solid oxide fuel cell based on genetic optimization. J Power Sources 196:5873–5880
Lunghi P, Ubertini U (2001) Solid oxide fuel cells and regenerated gas turbines hybrid systems: a feasible solution for future ultra high efficiency power plants. In: Proceedings of the seventh international symposium on solid oxide fuel cells (SOFC-VII)
Nehter P (2006) Two-dimensional transient model of a cascaded micro-tubular solid oxide fuel cell fed with methane. J Power Sources 157(1):325–334
Ota T, Koyama M, Ju Wen C, Yamada K, Takahashi H (2003) Object-based modeling of SOFC system: dynamic behavior of micro-tube SOFC. J Power Sources 118:430–439
Razbani O, Assadi M (2014) Artificial neural network model of a short stack solid oxide fuel cell based on experimental data. J Power Sources 246:581–586
Recknagle K, Williford R, Chick L, Rector D, Khaleel M (2003) Three-dimensional thermo-fluid electrochemical modeling of planar SOFC stacks. J Power Sources 113(1):109–114
Adachi S, Murakami H (1995) Generalized predictive control system design based on non-linear identification by using Hammerstein. Trans Inst Syst Control Inf Eng 8:115–121 (in Japanese)
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464
Shi J, XU X, Dai Y (2011) Identification of Hammerstein LSSVM–ARMA systems and its application in continuous stirred tank rector. Energy Proc 13:5359–5365
Su HT, McAvoy TJ (1993) Integration of multilayer perceptron networks and linear dynamic models: a Hammerstein modeling approach. Ind Eng Chem Res 32:1927–1936
Tang Y, Li Z, Guan X (2014) Identification of nonlinear system using extreme learning machine based Hammerstein model. Commun Nonlinear Sci Numer Simul 19(9):3171–3183
Togun N, Baysec S, Kara T (2012) Nonlinear modeling and identification of a spark ignition engine torque. Mech Syst Sig Process 26:294–304
Wang S, Wang W, Liu F, Tang Y, Guan X (2015) Identification of chaotic system using Hammerstein–ELM model. Nonlinear Dyn 81(3):1081–1095
Wu W, Jhao DW (2012) Identification and control of a fuel cell system using wavelet network-based Hammerstein models. In: the 8th IFAC symposium on advanced control of chemical processes, Singapore, pp 10–13
Wu XJ, Zhu XJ, Cao GY, Tu HY (2007) Modeling a SOFC stack based on GA-RBF neural networks identification. J Power Sources 167(1):145–150
Wu XJ, Zhu XJ, Cao GY, Tu HY (2008) Nonlinear modeling of SOFC stack based on ANFIS identificaiton. Simul Model Parct Theor 16:399–409
Yokoo M, Take T (2004) Simulation analysis of a system combining solid oxide and polymer electrolyte fuel cells. J Power Sources 137(2):206–215
Zhu QY, Qin A, Suganthan P, Huang GB (2005) Evolutionary extreme learning machine. Pattern Recognit 38:1759–1763
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (Nos. 61273260, 61471313), Natural Science Foundation of Hebei Province (No. F2014203208), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20121333120010), China Postdoctoral Science Foundation (Nos. 2013M530888, 2014T70229).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tang, Y., Bu, C., Liu, M. et al. Application of ELM–Hammerstein model to the identification of solid oxide fuel cells. Neural Comput & Applic 29, 401–411 (2018). https://doi.org/10.1007/s00521-016-2453-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-016-2453-y