In this study, a novel approach for nonlinear process identification via neural fuzzy-based Hammerstein-Wiener model with process disturbance by means of multi-signal processing is presented. The Hammerstein-Wiener model consists of three blocks where a dynamic linear block is sandwiched between two static nonlinear blocks. Multi-signal sources are designed for achieving identification separation of the Hammerstein-Wiener process. The correlation analysis theory is utilized for estimating unknown parameters of output nonlinearity and linear block using separable signals, thus the interference of process disturbance is solved. Furthermore, the immeasurable intermediate variable and immeasurable noise term in identification model is taken over by auxiliary model output and estimate residuals, and then auxiliary model-based recursive extended least squares parameter estimation algorithm is derived to calculate parameters of the input nonlinearity and noise model. Finally, convergence analysis of the suggested identification scheme is derived using stochastic process theory. The simulation results indicate that proposed identification approach yields high identification accuracy and has good robustness.
The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00426-w
Feng Li
,
Li Jia
,
Ya Gu
. Identification of nonlinear process described by neural fuzzy Hammerstein-Wiener model using multi-signal processing[J]. Advances in Manufacturing, 2023
, 11(4)
: 694
-707
.
DOI: 10.1007/s40436-022-00426-w
1 Gou J, Liu H (2017) Hammerstein system identification with quantised inputs and quantised output observations. IET Control Theory A 11(4):593-599
2 Zhang J, Chin KS, Lawrynczuk M (2018) Nonlinear model predictive control based on piecewise linear Hammerstein models. Nonlinear Dyn 92(3):1001-1021
3 Mu B, Chen HF, Wang LY et al (2017) Recursive identification of Hammerstein systems: convergence rate and asymptotic normality. IEEE Trans Autom Control 62(7):3277-3292
4 Jia L, Li X, Chiu MS (2016) Correlation analysis based MIMO neuro-fuzzy Hammerstein model with noises. J Process Contr 41:76-91
5 Cheng CM, Peng ZK, Zhang WM (2016) A novel approach for identification of cascade of Hammerstein model. Nonlinear Dyn 86(1):513-522
6 Li F, Chen L, Wo S et al (2020) Modeling and parameter learning for the Hammerstein-Wiener model with disturbance. Meas Control 53(5/6):971-982
7 Zhang B, Mao Z (2017) Bias compensation principle based recursive least squares identification method for Hammerstein nonlinear models. J Franklin Inst 354(3):1340-1355
8 Hagenblad A, Ljung J, Wills A (2008) Maximum likelihood identification of Wiener models. Automatica 44(11):2697-2705
9 Kazemi M, Arefi MM (2017) A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems. ISA T 67:382-388
10 Schoukens M, Rolain Y (2012) Parametric identification of parallel Wiener models. IEEE Trans Instrum Meas 61(10):2825-2832
11 Li J, Hua C, Tang Y et al (2014) Stochastic gradient with changing forgetting factor-based parameter identification for Wiener systems. Appl Math Lett 33:40-45
12 Zhou L, Li X, Pan F (2015) Gradient-based iterative identification for Wiener nonlinear models with non-uniform sampling. Nonlinear Dyn 76(1):627-634
13 Quachio R, Garcia C (2019) MPC relevant identification method for Hammerstein and Wiener models. J Process Contr 80:78-88
14 Bloemen HHJ, Chou CT, van den Boom TJJ et al (2001) Wiener model identification and predictive control for dual composition control of a distillation column. J Process Contr 11(6):601-620
15 Al-Dhaifallah M, Nisar KS, Agarwal P et al (2017) Modeling and identification of heat exchanger process using least squares support vector machines. Therm Sci 21(6):2859-2869
16 George SJ, Kamat S, Madhavan KP (2007) Modeling of pH process using wave net based Hammerstein model. J Process Contr 17(6):551-561
17 Li F, Jia L, Peng D et al (2017) Neuro-fuzzy based identification method for Hammerstein output error model with colored noise. Neurocomputing 244:90-101
18 Luo SX, Song YD (2018) Data-driven predictive control of Hammerstein-Wiener models based on subspace identification. Inform Sciences 422:447-461
19 Yu F, Mao Z, Jia M et al (2014) Recursive parameter identification of Hammerstein-Wiener systems with measurement noise. Signal Process 105:137-147
20 Jeng JC, Lin YW (2018) Data-driven nonlinear control design using virtual reference feedback tuning based on block-oriented modeling of nonlinear models. Ind Eng Chem Res 57(22):7583-7599
21 Li G, Wen C, Zheng WX et al (2011) Identification of a class of nonlinear autoregressive models with exogenous inputs based on kernel machines. IEEE T Signal Process 59(5):2146-2159
22 Ding B, Ping X (2012) Dynamic output feedback model predictive control for nonlinear models represented by Hammerstein-Wiener model. J Process Contr 22(9):1773-1784
23 Wills A, Schon TB, Ljung L et al (2013) Identification of Hammerstein-Wiener models. Automatica 49(1):70-81
24 Zhu Y (2002) Estimation of an N-L-N Hammerstein-Wiener model. Automatica 38(9):1607-1614
25 Voros J (2015) Iterative identification of nonlinear dynamic models with output backlash using three-block cascade models. Nonlinear Dyn 79(3):2187-2195
26 Allafi W, Zajic I, Uddin K et al (2017) Parameter identification of the fractional-order Hammerstein-Wiener model using simplified refined instrumental variable fractional-order continuous time. IET Control Theory A 11(15):2591-2598
27 Bai EW (2002) A blind approach to the Hammerstein-Wiener model identification. Automatica 38(6):967-979
28 Brouri A, Kadi L, Slassi S (2017) Frequency identification of Hammerstein-Wiener models with backlash input nonlinearity. Int J Control Autom Syst 15(5):2222-2232
29 Li F, Yao K, Li B et al (2021) A novel learning algorithm of the neuro-fuzzy based Hammerstein-Wiener model corrupted by process noise. J Frankl Inst 358(3):2115-2137
30 Sung SW, Je CH, Lee J et al (2008) Improved system identification method for Hammerstein-Wiener processes. Ind Eng Chem Res 25(4):631-636
31 Wang DQ, Ding F (2012) Hierarchical least squares estimation algorithm for Hammerstein-Wiener models. IEEE Signal Proc Lett 19(2):825-828
32 Ward MacArthur J (2012) A new approach for nonlinear process identification using orthonormal bases and ordinal splines. J Process Contr 22(2):375-389
33 Yu F, Mao Z, Yuan P et al (2017) Recursive parameter identification for Hammerstein-Wiener models using modified EKF algorithm. ISA T 70:104-115
34 Wang D, Ding F (2008) Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX models. Comput Math Appl 56:3157-3164
35 Wang J, Chen T, Wang L (2009) A blind approach to identification of Hammerstein-Wiener models corrupted by nonlinear-process noise. In: Processing of the 7th Asian control conference, Hong Kong, China, 24-29 August, pp 1340-1345
36 Ni B, Gilson M, Garnier H (2013) Refined instrumental variable method for Hammerstein-Wiener continuous-time model identification. IET Control Theory A7(9):1276-1286
37 Wang Z, Wang Y, Ji Z (2017) A novel two-stage estimation algorithm for nonlinear Hammerstein-Wiener models from noisy input and output data. J Frankl Inst 354:1937-1944
38 Lang ZQ (1994) On identification of the controlled plants described by the Hammerstein models. IEEE Trans Automat Contr 39(3):569-573
39 Navarro-Almanza R, Sanchez MA, Castro JR et al (2022) Interpretable Mamdani neuro-fuzzy model through context awareness and linguistic adaptation. Expert Syst Appl 189:116098. https://doi.org/10.1016/j.eswa.2021.116098
40 Soto J, Castillo O, Melin P et al (2019) A new approach to multiple time series prediction using MIMO fuzzy aggregation models with modular neural networks. Int J Fuzzy Syst 21(5):1629-1648
41 Soto J, Melin P, Castillo O (2018) A new approach for time series prediction using ensembles of IT2FNN models with optimization of fuzzy integrators. Int J Fuzzy Syst 20(3):701-728
42 Castillo O, Castro JR, Melin P et al (2014) Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction. Soft Comput 18(6):1213-1224
43 Li J, Zong T, Lu G (2021) Parameter identification of Hammerstein-Wiener nonlinear systems with unknown time delay based on the linear variable weight particle swarm optimization. ISA T. https://doi.org/10.1016/j.isatra.2021.03.021
44 Abouda SE, Abid DBH, Elloumi M et al (2019) Identification of nonlinear dynamic systems using fuzzy Hammerstein-Wiener systems. In: The 19th international conference on sciences and techniques of automatic control and computer engineering (STA), 24-26 March, Sousse, Tunisia, https://doi.org/10.1109/STA.2019.8717218
45 Li F, Jia L, Peng D (2017) Identification method of neuro-fuzzy-based Hammerstein model with coloured noise. IET Control Theory A 11(17):3026-3037
46 Enqvist M, Ljung L (2005) Linear approximations of nonlinear FIR models for separable input processes. Automatica 41(3):459-473
47 Ding F, Wang F, Xu L et al (2017) Parameter identification for pseudo-linear models using the auxiliary model and the decomposition technique. IET Control Theory A 11(13):390-400
48 Ljung L (1999) Model identification: theory for the user, 2nd edn. Prentice Hall, Englewood Cliffs
49 Ding F, Gu Y (2012) Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems. Int J Comput Math 89(15):2019-2028
50 Wang Y, Ding F (2016) Recursive least squares algorithm and gradient algorithm for Hammerstein-Wiener models using the data filtering. Nonlinear Dyn 84(2):1045-1053
51 Mohammadzadeh A, Rathinasamy S (2020) Energy management in photovoltaic battery hybrid systems: a novel type-2 fuzzy control. Int J Hydrogen Energ 45(41):20970-20982
52 Mosavi A, Qasem SN, Shokri M et al (2020) Fractional-order fuzzy control approach for photovoltaic/battery systems under unknown dynamics, variable irradiation and temperature. Electronics 9(9):1455. https://doi.org/10.3390/electronics9091455
