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A Review of Research Progress and Application of Wavelet Neural Networks

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New Technologies, Development and Application VI (NT 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 687))

Abstract

Artificial Neural Network (ANN) has been used extensively and constantly developed. The combination of wavelet transform theory and the neural network has become an important branch to explore the optimization of neural network structure, and Wavelet Neural Network (WNN), a special network structure, was born. This paper reviews WNN’s development and summarizes the system structure and algorithm implementation and presents derivative models and cutting-edge applications with obvious characteristics. The sorting and analysis of the above contents show that the combination of wavelet theory and neural network algorithm can make the network model have the advantages of fast convergence speed and high model accuracy, and has a rapid development trend in many fields such as audio signal and image processing. The work of this paper is intended to provide a reference for potential applications based on WNN and new network model design ideas.

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References

  1. Das, R., Sen, S., Maulik, U.: A survey on fuzzy deep neural networks. ACM Comput. Surv. (CSUR) 53, 1–25 (2021)

    Article  Google Scholar 

  2. De Simone, M.C., Veneziano, S., Guida, D.: Design of a non-back-drivable screw jack mechanism for the hitch lifting arms of electric-powered tractors. Actuators 11(12), 358 (2022)

    Article  Google Scholar 

  3. Sehgal, A., La, H., Louis, S., Nguyen, H.: Deep reinforcement learning using genetic algorithm for parameter optimization (2019)

    Google Scholar 

  4. Pappalardo, C.M., Guida, D.: Dynamic analysis and control design of kinematically-driven multibody mechanical systems. Eng. Lett. 28(4), 1125–1144 (2020)

    Google Scholar 

  5. Hassan, Y.: Deep learning architecture using rough sets and rough neural networks. Kybernetes 46, 693–705 (2017). https://doi.org/10.1108/K-09-2016-0228

    Article  Google Scholar 

  6. De Simone, M.C., Ventura, G., Lorusso, A., Guida, D.: Attitude controller design for micro-satellites. In: Karabegović, I. (ed.) NT 2021. LNNS, vol. 233, pp. 21–31. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-75275-0_2

    Chapter  Google Scholar 

  7. Chen, J.-H., Chang, T.-T., Ho, C.R., Diaz, J.F.: Grey relational analysis and neural network forecasting of REIT returns. Quant. Financ. 14, 2033–2044 (2014). https://doi.org/10.1080/14697688.2013.816765

    Article  MathSciNet  MATH  Google Scholar 

  8. Pappalardo, C.M., Lettieri, A., Guida, D.: A general multibody approach for the linear and nonlinear stability analysis of bicycle systems. Part I: methods of constrained dynamics. J. Appl. Comput. Mech. 7(2), 655–670 (2021)

    Google Scholar 

  9. Pati, Y.C., Krishnaprasad, P.S.: Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations. IEEE Trans. Neural Netw. 4, 73–85 (1993). https://doi.org/10.1109/72.182697

    Article  Google Scholar 

  10. Colucci, F., De Simone, M.C., Guida, D.: TLD design and development for vibration mitigation in structures. In: Karabegović, I. (ed.) NT 2019. LNNS, vol. 76, pp. 59–72. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-18072-0_7

    Chapter  Google Scholar 

  11. Zhang, Q., Benveniste, A.: A wavelet networks. IEEE Trans. Neural Netw. 3, 889–898 (1992). https://doi.org/10.1109/72.165591

    Article  Google Scholar 

  12. Guida, R., De Simone, M.C., Dašić, P., Guida, D.: Modeling techniques for kinematic analysis of a six-axis robotic arm. In: IOP Conference Series: Materials Science and Engineering, vol. 568, no. 1, p. 012115 (2019). https://doi.org/10.1088/1757-899X/568/1/012115

  13. Szu, H.H., Telfer, B.A., Kadambe, S.L.: Neural network adaptive wavelets for signal representation and classification. Opt. Eng. 31, 1907–1916 (1992). https://doi.org/10.1117/12.59918

    Article  Google Scholar 

  14. De Simone, M.C., Guida, D.: Modal coupling in presence of dry friction. Machines 6(1), 8 (2018). https://doi.org/10.3390/machines6010008

    Article  Google Scholar 

  15. Kugarajah, T., Zhang, Q.: Multidimensional wavelet frames. IEEE Trans. Neural Netw. 6, 1552–1556 (1995)

    Article  Google Scholar 

  16. Manrique-Escobar, C.A., Pappalardo, C.M., Guida, D.: A multibody system approach for the systematic development of a closed-chain kinematic model for two-wheeled vehicles. Machines 9(11), 245 (2021)

    Article  Google Scholar 

  17. Zhang, Q.: Using wavelet network in nonparametric estimation. IEEE Trans. Neural Netw. 8, 227–236 (1997). https://doi.org/10.1109/72.557660

    Article  Google Scholar 

  18. Pappalardo, C.M., Lettieri, A., Guida, D.: Identification of a dynamical model of the latching mechanism of an aircraft hatch door using the numerical algorithms for subspace state-space system identification. IAENG Int. J. Appl. Math. 51(2), 346–359 (2021)

    Google Scholar 

  19. Oussar, Y.: Training wavelet networks for nonlinear dynamic input-output modeling. Neurocomputing 20, 173–188 (1998)

    Article  MATH  Google Scholar 

  20. Rivera, Z.B., De Simone, M.C., Guida, D.: Unmanned ground vehicle modelling in Gazebo/ROS-based environments. Machines 7(2), 42 (2019). https://doi.org/10.3390/machines7020042

    Article  Google Scholar 

  21. Guo, T., Zhang, T., Lim, E., López-Benítez, M., Ma, F., Yu, L.: A review of wavelet analysis and its applications: challenges and opportunities. IEEE Access 10, 58869–58903 (2022). https://doi.org/10.1109/ACCESS.2022.3179517

    Article  Google Scholar 

  22. Pappalardo, C.M., Manca, A., Guida, D.: A combined use of the multibody system approach and the finite element analysis for the structural redesign and the topology optimization of the latching component of an aircraft hatch door. IAENG Int. J. Appl. Math. 51(1), 175–191 (2021)

    Google Scholar 

  23. Junling, R., Guo, J.: Construction of neural network model on wavelet theoretic. Computer Development & Applications (2004)

    Google Scholar 

  24. De Simone, M.C., Rivera, Z.B., Guida, D.: Obstacle avoidance system for unmanned ground vehicles by using ultrasonic sensors. Machines 6(2), 18 (2018). https://doi.org/10.3390/machines6020018

    Article  Google Scholar 

  25. Daubechies, I.: Ten Lectures on Wavelets. Computers in Physics, p. 697 (1992)

    Google Scholar 

  26. Pappalardo, C.M., Vece, A., Galdi, D., Guida, D.: Developing a reciprocating mechanism for the emergency implementation of a mechanical pulmonary ventilator using an integrated CAD-MBD procedure. FME Trans. 50(2), 238–247 (2022)

    Article  Google Scholar 

  27. Gao, R., Tsoukalas, L.: Neural-wavelet methodology for load forecasting. J. Intell. Rob. Syst. 31, 149–157 (2001). https://doi.org/10.1023/A:1012205313137

    Article  MATH  Google Scholar 

  28. Xu, J., Ho, D.W.C.: A constructive algorithm for wavelet neural networks. In: Wang, L., Chen, K., Ong, Y.S. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 730–739. Springer, Heidelberg (2005). https://doi.org/10.1007/11539087_97

    Chapter  Google Scholar 

  29. Cannon, M., Slotine, J.-J.E.: Space-frequency localized basis function networks for nonlinear system estimation and control. Neurocomputing 9, 293–342 (1995). https://doi.org/10.1016/0925-2312(95)00036-1

    Article  MATH  Google Scholar 

  30. Zhao, J., Chen, B., Shen, J.: Multidimensional non-orthogonal wavelet-sigmoid basis function neural network for dynamic process fault diagnosis. Comput. Chem. Eng. 23, 83–92 (1998). https://doi.org/10.1016/S0098-1354(98)00258-0

    Article  Google Scholar 

  31. Becerikli, Y.: On three intelligent systems: dynamic neural, fuzzy, and wavelet networks for training trajectory. Neural Comput. Appl. 13, 339–351 (2004). https://doi.org/10.1007/s00521-004-0429-9

    Article  Google Scholar 

  32. Deng, R., Li, Z.-X., Fan, Y.-H.: Discussion of stability in a class of models on recurrent wavelet neural networks. Appl. Math. Mech. 28, 471–476 (2007). https://doi.org/10.1007/s10483-007-0407-z

    Article  MathSciNet  MATH  Google Scholar 

  33. Alarcon-Aquino, V., Ramirez-Cortes, J.M., Gomez-Gil, P., Starostenko, O., Garcia-Gonzalez, Y.: Network intrusion detection using self-recurrent wavelet neural network with multidimensional radial wavelons. Inf. Technol. Control 43, 347–358 (2014). https://doi.org/10.5755/j01.itc.43.4.4626

    Article  Google Scholar 

  34. Mallat, S.G.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989). https://doi.org/10.1109/34.192463

    Article  MATH  Google Scholar 

  35. Pappalardo, C.M., Lettieri, A., Guida, D.: A general multibody approach for the linear and nonlinear stability analysis of bicycle systems. Part II: application to the Whipple-Carvallo bicycle model. J. Appl. Comput. Mech. 7(2), 671–700 (2021)

    Google Scholar 

  36. Li, T., et al.: WaveletKernelNet: an interpretable deep neural network for industrial intelligent diagnosis. IEEE Trans. Syst. Man Cybern.: Syst. 52, 2302–2312 (2022)

    Article  Google Scholar 

  37. Ray, S., Ganguly, B., Dey, D.: Identification and classification of stator inter-turn faults in induction motor using wavelet kernel based convolutional neural network. Electr. Power Compon. Syst. 48, 1421–1432 (2020). https://doi.org/10.1080/15325008.2020.1854384

    Article  Google Scholar 

  38. Ganguly, B., et al.: Wavelet kernel-based convolutional neural network for localization of partial discharge sources within a power apparatus. IEEE Trans. Ind. Inform. 17, 1831–1841 (2021). https://doi.org/10.1109/TII.2020.2991686

    Article  Google Scholar 

  39. Recoskie, D., Mann, R.: Learning Sparse Wavelet Representations (2018)

    Google Scholar 

  40. Manrique Escobar, C.A., Pappalardo, C.M., Guida, D.: A parametric study of a deep reinforcement learning control system applied to the swing-up problem of the cart-pole. Appl. Sci. 10(24), 9013 (2020)

    Article  Google Scholar 

  41. Lei, L., Chen, W., Xue, Y., Liu, W.: A comprehensive evaluation method for indoor air quality of buildings based on rough sets and a wavelet neural network. Build. Environ. 162, 106296 (2019). https://doi.org/10.1016/j.buildenv.2019.106296

    Article  Google Scholar 

  42. Ghoushchi, S.J., Manjili, S., Mardani, A., Saraji, M.K.: An extended new approach for forecasting short-term wind power using modified fuzzy wavelet neural network: a case study in wind power plant. Energy 223, 120052 (2021). https://doi.org/10.1016/j.energy.2021.120052

    Article  Google Scholar 

  43. Xu, B., Shen, H., Cao, Q., Qiu, Y., Cheng, X.: Graph Wavelet Neural Network (2019)

    Google Scholar 

  44. De Simone, M.C., Laiola, V., Rivera, Z.B., Guida, D.: Dynamic analysis of a hybrid heavy-vehicle. In: Karabegović, I., Kovačević, A., Mandžuka, S. (eds.) New Technologies, Development and Application V. NT 2022. Lecture Notes in Networks and Systems, vol. 472. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-05230-9_27

  45. Liu, J., Li, P., Tang, X., Li, J., Chen, J.: Research on improved convolutional wavelet neural network. Sci. Rep. 11, 17941 (2021). https://doi.org/10.1038/s41598-021-97195-6

    Article  Google Scholar 

  46. Liu, W., Yan, Q., Zhao, Y.: Densely Self-guided Wavelet Network for Image Denoising (2020)

    Google Scholar 

  47. De Simone, M.C., Guida, D.: Experimental investigation on structural vibrations by a new shaking table. In: Carcaterra, A., Paolone, A., Graziani, G. (eds.) AIMETA 2019. LNME, pp. 819–831. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-41057-5_66

    Chapter  Google Scholar 

  48. Zhu, X., Li, Z., Lou, J., Shen, Q.: Video super-resolution based on a spatio-temporal matching network. Pattern Recognit. 110, 107619 (2021). https://doi.org/10.1016/j.patcog.2020.107619

    Article  Google Scholar 

  49. Zhao, C., et al.: Multi-scale wavelet network algorithm for pediatric echocardiographic segmentation via hierarchical feature guided fusion. Appl. Soft. Comput. 107, 107386 (2021). https://doi.org/10.1016/j.asoc.2021.107386

    Article  Google Scholar 

  50. Salvati, L., d’Amore, M., Fiorentino, A., Pellegrino, A., Sena, P., Villecco, F.: Development and testing of a methodology for the assessment of acceptability systems. Machines 8(3), 47 (2020). https://doi.org/10.3390/machines9020044

  51. Tiddeman, B.P., Ghahremani, M.: Principal component wavelet networks for solving linear inverse problems. Symmetry 13, 1083 (2021)

    Article  Google Scholar 

  52. Wei, Z., et al.: Sparse-view CT image restoration via multiscale wavelet residual network. Nan fang yi ke da xue xue bao = J. South. Med. Univ. 39, 1320–1328 (2019). https://doi.org/10.12122/j.issn.1673-4254.2019.11.09

  53. Ding, Z., Ma, K.: Identifying changing interspecific associations along gradients at multiple scales using wavelet correlation networks. Ecology 102, e3360 (2021). https://doi.org/10.1002/ecy.3360

    Article  Google Scholar 

  54. Manrique-Escobar, C.A., Pappalardo, C.M., Guida, D.: On the analytical and computational methodologies for modelling two-wheeled vehicles within the multibody dynamics framework: a systematic literature review. J. Appl. Comput. Mech. 8(1), 153–181 (2022)

    Google Scholar 

  55. Turkan, Y., Hong, J., Laflamme, S., Puri, N.: Adaptive wavelet neural network for terrestrial laser scanner-based crack detection. Autom. Constr. 94, 191–202 (2018). https://doi.org/10.1016/j.autcon.2018.06.017

    Article  Google Scholar 

  56. De Simone, M.C., Celenta, G., Rivera, Z.B., Guida, D.: Mechanism design for a low-cost automatic breathing applications for developing countries. In: Karabegović, I., Kovačević, A., Mandžuka, S. (eds.) New Technologies, Development and Application V. NT 2022. Lecture Notes in Networks and Systems, vol. 472. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-05230-9_40

  57. Santos, C.A., Freire, P.K., Silva, R.M.D., Akrami, S.A.: Hybrid wavelet neural network approach for daily inflow forecasting using tropical rainfall measuring mission data. J. Hydrol. Eng. 24, 04018062 (2019). https://doi.org/10.1061/(ASCE)HE.1943-5584.0001725

    Article  Google Scholar 

  58. Pappalardo, C.M., La Regina, R., Guida, D.: Multibody modeling and nonlinear control of a pantograph scissor lift mechanism. J. Appl. Comput. Mech. 9(1), 129–167 (2023)

    Google Scholar 

  59. Huang, L., Wang, J.: Forecasting energy fluctuation model by wavelet decomposition and stochastic recurrent wavelet neural network. Neurocomputing 309, 70–82 (2018). https://doi.org/10.1016/j.neucom.2018.04.071

    Article  Google Scholar 

  60. Mei, S., Liu, M., Kudreyko, A., Cattani, P., Baikov, D., Villecco, F.: Bendlet transform based adaptive denoising method for microsection images. Entropy 24, 869 (2022). https://doi.org/10.3390/e24070869

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Information and Electrical Engineering, China Agricultural University, No. 17 Tsinghua East Road, Haidian District, Beijing, 100083, China

    Tonghao Wang

  2. Engineering School, Deim University of Tuscia, Largo dell’Università, 01100, Viterbo, Italy

    Vincenzo Guercio

  3. Department of Computer, Control and Management Engineering, University of Rome “La Sapienza”, via Ariosto 25, 00185, Roma, Italy

    Piercarlo Cattani

  4. Department of Industrial Engineering, University of Salerno, via Giovanni Paolo II 132, 84084, Fisciano, Italy

    Francesco Villecco

Authors
  1. Tonghao Wang
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  2. Vincenzo Guercio
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  3. Piercarlo Cattani
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  4. Francesco Villecco
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Correspondence to Francesco Villecco .

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Editors and Affiliations

  1. Academy of Sciences and Arts of Bosnia and Herzegovina, Sarajevo, Bosnia and Herzegovina

    Isak Karabegovic

  2. City University of London, London, UK

    Ahmed Kovačević

  3. Faculty of Traffic and Transport Sciences, University of Zagreb, Zagreb, Croatia

    Sadko Mandzuka

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Wang, T., Guercio, V., Cattani, P., Villecco, F. (2023). A Review of Research Progress and Application of Wavelet Neural Networks. In: Karabegovic, I., Kovačević, A., Mandzuka, S. (eds) New Technologies, Development and Application VI. NT 2023. Lecture Notes in Networks and Systems, vol 687. Springer, Cham. https://doi.org/10.1007/978-3-031-31066-9_56

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