Two-Stage Method for Diagonal Recurrent Neural Network Identification of a High-Power Continuous Microwave Heating System


This paper proposes a diagonal recurrent neural network (DRNN) based identification scheme to handle the complexity and nonlinearity of high-power continuous microwave heating system (HPCMHS). The new DRNN design involves a two-stage training process that couples an efficient forward model selection technique with gradient-based optimization. In the first stage, an impact recurrent network structure is obtained by a fast recursive algorithm in a stepwise forward procedure. To ensure stability, update rules are further developed using Lyapunov stability criterion to tune parameters of reduced size model at the second stage. The proposed approach is tested with an experimental regression problem and a practical HPCMHS identification, and the results are compared with four typical network models. The results show that the new design demonstrates improved accuracy and model compactness with reduced computational complexity over the existing methods.

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

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


  1. 1.

    Vongpradubchai S, Rattanadecho P (2009) The microwave processing of wood using a continuous microwave belt drier. Chem Eng Process Process Intensif 48(5):997–1003

    Article  Google Scholar 

  2. 2.

    Rattanadecho P, Suwannapum N, Chatveera B, Atong D, Makul N (2008) Development of compressive strength of cement paste under accelerated curing by using a continuous microwave thermal processor. Mater Sci Eng A 472(1):299–307

    Article  Google Scholar 

  3. 3.

    Atong D, Ratanadecho P, Vongpradubchai S (2006) Drying of a slip casting for tableware product using microwave continuous belt dryer. Dry Technol 24(5):589–594

    Article  Google Scholar 

  4. 4.

    Zhao D, Wang Y, Zhu Y, Ni Y (2016) Effect of carbonic maceration pre-treatment on drying behaviour and physicochemical compositions of sweet potato dried with intermittent or continuous microwave. Dry Technol 34(13):1604–1612

    Article  Google Scholar 

  5. 5.

    Shi X, Li J, Xiong Q, Wu Y, Yuan Y (2016) Research of uniformity evaluation model based on entropy clustering in the microwave heating processes. Neurocomputing 173:562–572

    Article  Google Scholar 

  6. 6.

    Chen S, Billings SA (1991) Neural networks for nonlinear dynamic system modelling and identification. Int J Control 56(2):319–346

    MathSciNet  MATH  Article  Google Scholar 

  7. 7.

    Chen D, Zhang Y, Li S (2018) Tracking control of robot manipulators with unknown models: a Jacobian-matrix-adaption method. IEEE Trans Ind Inform 14(7):3044–3053

    Article  Google Scholar 

  8. 8.

    Chen D, Zhang Y (2018) Robust zeroing neural-dynamics and its time-varying disturbances suppression model applied to mobile robot manipulators. IEEE Trans Neural Netw Learn Syst 29(9):4385–4397

    Article  Google Scholar 

  9. 9.

    Li S, Zhou M, Luo X (2018) Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans Neural Netw Learn Syst 29(10):4791–4801

    MathSciNet  Article  Google Scholar 

  10. 10.

    Chen D, Zhang Y (2017) A hybrid multi-objective scheme applied to redundant robot manipulators. IEEE Trans Autom Sci Eng 14(3):1337–1350

    Article  Google Scholar 

  11. 11.

    Chen D, Zhang Y, Li S, Chen D, Zhang Y, Li S (2017) Zeroing neural-dynamics approach and its robust and rapid solution for parallel robot manipulators against superposition of multiple disturbances. Neurocomputing 275:845–858

    Article  Google Scholar 

  12. 12.

    Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254

    MathSciNet  Article  Google Scholar 

  13. 13.

    Momenzadeh L, Zomorodian A, Mowla D (2011) Experimental and theoretical investigation of shelled corn drying in a microwave-assisted fluidized bed dryer using artificial neural network. Food Bioprod Process 89(1):15–21

    Article  Google Scholar 

  14. 14.

    Krishna Murthy TP, Manohar B (2012) Microwave drying of mango ginger (Curcuma amada roxb): prediction of drying kinetics by mathematical modelling and artificial neural network. Int J Food Sci Technol 47(6):1229–1236

    Article  Google Scholar 

  15. 15.

    Motavali A, Najafi GH, Abbasi S, Minaei S, Ghaderi A (2013) Microwavevacuum drying of sour cherry: comparison of mathematical models and artificial neural networks. J Food Sci Technol 50(4):714

    Article  Google Scholar 

  16. 16.

    Yousefi G, Emam-Djomeh PZ, Omid M, Askari GR (2014) Prediction of physicochemical properties of raspberry dried by microwave-assisted fluidized bed dryer using artificial neural network. Dry Technol 32(1):4–12

    Article  Google Scholar 

  17. 17.

    Qin SZ, Su HT, Mcavoy TJ (1992) Comparison of four neural net learning methods for dynamic system identification. IEEE Trans Neural Netw 3(1):122–130

    Article  Google Scholar 

  18. 18.

    Coban R (2013) A context layered locally recurrent neural network for dynamic system identification. Eng Appl Artif Intell 26(1):241–250

    Article  Google Scholar 

  19. 19.

    Jin L, Li S, Luo X, Li Y, Qin B (2018) Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans Ind Inform 14(9):3812–3821

    Article  Google Scholar 

  20. 20.

    Jin L, Li S, Hu B, Liu M, Yu J (2018) A noise-suppressing neural algorithm for solving the time-varying system of linear equations: a control-based approach. IEEE Trans Ind Inform 15(1):236–246

    Article  Google Scholar 

  21. 21.

    Li S, Wang H, Rafique MU (2018) A novel recurrent neural network for manipulator control with improved noise tolerance. IEEE Trans Neural Netw Learn Syst 29(5):1908–1918

    MathSciNet  Article  Google Scholar 

  22. 22.

    Tsoi AC, Back AD (1994) Locally recurrent globally feedforward networks: a critical review of architectures. IEEE Trans Neural Netw 5(2):229–39

    Article  Google Scholar 

  23. 23.

    Ku CC, Lee KY (1995) Diagonal recurrent neural networks for dynamic systems control. IEEE Trans Neural Netw 6(1):144–156

    Article  Google Scholar 

  24. 24.

    Blanco A, Delgado M, Pegalajar MC (2001) A real-coded genetic algorithm for training recurrent neural networks. Neural Netw 14(1):93–105

    Article  Google Scholar 

  25. 25.

    Luitel B, Venayagamoorthy GK (2010) Quantum inspired PSO for the optimization of simultaneous recurrent neural networks as mimo learning systems. Neural Netw 23(5):583

    Article  Google Scholar 

  26. 26.

    Seyab RKA, Cao Y (2008) Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. J Process Control 18(6):568–581

    Article  Google Scholar 

  27. 27.

    Chen CC, Shen LP (2018) Improve the accuracy of recurrent fuzzy system design using an efficient continuous ant colony optimization. Int J Fuzzy Syst 20(2):1–18

    MathSciNet  Google Scholar 

  28. 28.

    Puskorius GV, Feldkamp LA (1994) Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks. IEEE Trans Neural Netw 5(2):279–297

    Article  Google Scholar 

  29. 29.

    De Jesus Rubio J, Yu W (2005) Dead-zone Kalman filter algorithm for recurrent neural networks. In: IEEE Conference on Decision and Control, pp 2562–2567

  30. 30.

    Kumar R, Srivastava S, Gupta JRP, Mohindru A (2018) Diagonal recurrent neural network based identification of nonlinear dynamical systems with Lyapunov stability based adaptive learning rates. Neurocomputing 287(26):102–117

    Article  Google Scholar 

  31. 31.

    Kumar R, Srivastava S, Gupta JR (2017) Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion. ISA Trans 67:407

    Article  Google Scholar 

  32. 32.

    Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J Mach Learn Res 13(1):281–305

    MathSciNet  MATH  Google Scholar 

  33. 33.

    Juang CF (2004) A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans Syst Man Cybern Part B Cybern 34(2):997–1006

    Article  Google Scholar 

  34. 34.

    Subrahmanya N, Shin YC (2010) Constructive training of recurrent neural networks using hybrid optimization. Neurocomputing 73(1315):2624–2631

    Article  Google Scholar 

  35. 35.

    Wang X, Ma L, Wang B, Wang T (2013) A hybrid optimization-based recurrent neural network for real-time data prediction. Neurocomputing 120(10):547–559

    Article  Google Scholar 

  36. 36.

    Chen S, Billings SA, Luo W (1989) Orthogonal least squares methods and their application to non-linear system identification. Int J Control 50(5):1873–1896

    MATH  Article  Google Scholar 

  37. 37.

    Chen S, Cowan CFN, Grant PM (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 2(2):302–309

    Article  Google Scholar 

  38. 38.

    Chen S, Wu Y, Luk BL (1999) Combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks. IEEE Trans Neural Netw 10(5):1239–43

    Article  Google Scholar 

  39. 39.

    Bataineh M, Marler T (2017) Neural network for regression problems with reduced training sets. Neural Netw 95(11):1–9

    Article  Google Scholar 

  40. 40.

    Wei HL, Billings SA, Zhao YF, Guo LZ (2010) An adaptive wavelet neural network for spatio-temporal system identification. Neural Netw 23(10):1286–1299

    Article  Google Scholar 

  41. 41.

    Chen S, Wigger J (1995) Fast orthogonal least squares algorithm for efficient subset model selection. IEEE Trans Signal Process 43(7):1713–1715

    Article  Google Scholar 

  42. 42.

    Zhu QM, Billings SA (1994) Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks. Int J Control 64(5):871–886

    MATH  Article  Google Scholar 

  43. 43.

    Mao KZ (2002) Fast orthogonal forward selection algorithm for feature subset selection. IEEE Trans Neural Netw 13(5):1218–1224

    Article  Google Scholar 

  44. 44.

    Li K, Peng JX, Irwin GW (2005) A fast nonlinear model identification method. IEEE Trans Autom Control 50(8):1211–1216

    MathSciNet  MATH  Article  Google Scholar 

  45. 45.

    Zhang L, Li K, Bai EW, Irwin GW (2015) Two-stage orthogonal least squares methods for neural network construction. IEEE Trans Neural Netw Learn Syst 26(8):1608

    MathSciNet  Article  Google Scholar 

Download references


This work was supported by the National Natural Science Foundation of China under Grant 61771077.

Author information



Corresponding author

Correspondence to Shan Liang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, T., Liang, S., Xiong, Q. et al. Two-Stage Method for Diagonal Recurrent Neural Network Identification of a High-Power Continuous Microwave Heating System. Neural Process Lett 50, 2161–2182 (2019).

Download citation


  • Diagonal recurrent neural network
  • High-power continuous microwave heating system
  • Fast recursive algorithm
  • Lyapunov stability criterion
  • Computational complexity