Skip to main content
Erschienen in: Neural Processing Letters 2/2017

10.03.2017

Normalised Spline Adaptive Filtering Algorithm for Nonlinear System Identification

verfasst von: Sihai Guan, Zhi Li

Erschienen in: Neural Processing Letters | Ausgabe 2/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper proposed a normalised spline adaptive filtering algorithm to improve the stability of spline adaptive filtering (SAF) algorithm against the eigenvalue spread of the autocorrelation matrix of the input signal. The new adaptive filtering algorithm is based on the normalised least mean square (NLMS) approach and the value range of the learning rate in this algorithm is specified. This algorithm is called SAF-NLMS. In this work, first the derivation of the SAF-NLMS algorithm is given. Second, detailed convergence and the computational complexity analyses are carried out. Finally, the performance of the proposed algorithm is tested according to artificial datasets and real datasets. The achieved results present actually good performance. So, in practical engineering, the algorithm can be used to solve the problem of modeling or identification of nonlinear systems.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Nerrand O, Roussel-Ragot P, Personnaz L, Dreyfus G (1993) Neural networks and nonlinear adaptive filtering: unifying concepts and new algorithms. Neural Comput 5(5):165–199CrossRef Nerrand O, Roussel-Ragot P, Personnaz L, Dreyfus G (1993) Neural networks and nonlinear adaptive filtering: unifying concepts and new algorithms. Neural Comput 5(5):165–199CrossRef
2.
Zurück zum Zitat Barreto GA, Souza LG (2006) Adaptive filtering with the self-organizing map: a performance comparison. Neural Netw 19(6–7):785–798CrossRefMATH Barreto GA, Souza LG (2006) Adaptive filtering with the self-organizing map: a performance comparison. Neural Netw 19(6–7):785–798CrossRefMATH
3.
Zurück zum Zitat Barreto GA, Barros ALBP (2014) On the design of robust linear pattern classifiers based on M-estimators. Neural Process Lett 42(1):1–19 Barreto GA, Barros ALBP (2014) On the design of robust linear pattern classifiers based on M-estimators. Neural Process Lett 42(1):1–19
4.
Zurück zum Zitat Kong XY, Hu CH, Han CZ (2009) A self-stabilizing neural algorithm for total least squares filtering. Neural Process Lett 30(3):257–271CrossRef Kong XY, Hu CH, Han CZ (2009) A self-stabilizing neural algorithm for total least squares filtering. Neural Process Lett 30(3):257–271CrossRef
5.
Zurück zum Zitat Widrow B, Lehr MA (1990) 30 years of adaptive neural network, perceptron, madaline, and back propagation. Proc IEEE 78(9):1415–1442CrossRef Widrow B, Lehr MA (1990) 30 years of adaptive neural network, perceptron, madaline, and back propagation. Proc IEEE 78(9):1415–1442CrossRef
6.
Zurück zum Zitat Kim JH, Zhang W, Ryu SK, Oh YS (2012) An ADALINE neural network with truncated momentum for system identification of linear time varying systems. IEEE Int Conf Ind Technol 2012:292–297 Kim JH, Zhang W, Ryu SK, Oh YS (2012) An ADALINE neural network with truncated momentum for system identification of linear time varying systems. IEEE Int Conf Ind Technol 2012:292–297
7.
Zurück zum Zitat Aouiti C, M’Hamdi MS, Touati A (2016) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140CrossRef Aouiti C, M’Hamdi MS, Touati A (2016) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140CrossRef
8.
Zurück zum Zitat Egrioglu E, Yolcu U, Aladag CH, Bas E (2015) Recurrent multiplicative neuron model artificial neural network for non-linear time series forecasting. Neural Process Lett 41(2):249–258CrossRef Egrioglu E, Yolcu U, Aladag CH, Bas E (2015) Recurrent multiplicative neuron model artificial neural network for non-linear time series forecasting. Neural Process Lett 41(2):249–258CrossRef
9.
Zurück zum Zitat Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice Hall, Englewood CliffsMATH Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice Hall, Englewood CliffsMATH
10.
Zurück zum Zitat Prawin J, Rao ARM (2017) Nonlinear identification of MDOF systems using Volterra series approximation. Mech Syst Signal Process 84:58–77CrossRef Prawin J, Rao ARM (2017) Nonlinear identification of MDOF systems using Volterra series approximation. Mech Syst Signal Process 84:58–77CrossRef
11.
Zurück zum Zitat LeCaillec J-M (2011) Spectral inversion of second order Volterra models based on the blind identification of Wiener models. Signal Process 91(11):2541–2555CrossRefMATH LeCaillec J-M (2011) Spectral inversion of second order Volterra models based on the blind identification of Wiener models. Signal Process 91(11):2541–2555CrossRefMATH
12.
Zurück zum Zitat Sicuranza GL, Carini A (2011) A generalized FLANN filter for nonlinear active noise control. IEEE Trans Audio Speech Lang Process 19(8):2412–2417CrossRef Sicuranza GL, Carini A (2011) A generalized FLANN filter for nonlinear active noise control. IEEE Trans Audio Speech Lang Process 19(8):2412–2417CrossRef
13.
Zurück zum Zitat Richard C, Bermudez J, Honeine P (2009) Online prediction of time series data with kernels. IEEE Trans Signal Process 57(3):1058–1067MathSciNetCrossRef Richard C, Bermudez J, Honeine P (2009) Online prediction of time series data with kernels. IEEE Trans Signal Process 57(3):1058–1067MathSciNetCrossRef
14.
Zurück zum Zitat Engel Y, Mannor S, Meir R (2012) Kernel recursive least squares. IEEE Trans Signal Process 52(5):2275–2285MathSciNetMATH Engel Y, Mannor S, Meir R (2012) Kernel recursive least squares. IEEE Trans Signal Process 52(5):2275–2285MathSciNetMATH
15.
Zurück zum Zitat Liu W, Príncipe JC, Haykin S (2009) Extended kernel recursive least squares algorithm. IEEE Trans Signal Process 57(10):3801–3814MathSciNetCrossRef Liu W, Príncipe JC, Haykin S (2009) Extended kernel recursive least squares algorithm. IEEE Trans Signal Process 57(10):3801–3814MathSciNetCrossRef
16.
Zurück zum Zitat Liu W, Príncipe JC, Simon H (2008) Kernel affine projection algorithms. EURASIP J Adv Signal Process 2008(1):1–12CrossRefMATH Liu W, Príncipe JC, Simon H (2008) Kernel affine projection algorithms. EURASIP J Adv Signal Process 2008(1):1–12CrossRefMATH
17.
Zurück zum Zitat Chen B, Zhao S, Zhu P, Principe JC (2012) Quantized kernel least mean square algorithm. IEEE Trans Neural Netw Learn Syst 23(1):22–32CrossRef Chen B, Zhao S, Zhu P, Principe JC (2012) Quantized kernel least mean square algorithm. IEEE Trans Neural Netw Learn Syst 23(1):22–32CrossRef
18.
Zurück zum Zitat Parreira WD, Bermudez JCM, Richard C, Tourneret J-Y (2012) Stochastic behavior analysis of the Gaussian kernel least-mean-square algorithm. IEEE Trans Signal Process 60(5):2208–2222MathSciNetCrossRef Parreira WD, Bermudez JCM, Richard C, Tourneret J-Y (2012) Stochastic behavior analysis of the Gaussian kernel least-mean-square algorithm. IEEE Trans Signal Process 60(5):2208–2222MathSciNetCrossRef
19.
Zurück zum Zitat Scarpiniti M, Comminiello D, Parisi R, Uncini A (2013) Nonlinear spline adaptive filtering. Signal Process 93(4):772–783CrossRef Scarpiniti M, Comminiello D, Parisi R, Uncini A (2013) Nonlinear spline adaptive filtering. Signal Process 93(4):772–783CrossRef
20.
Zurück zum Zitat Scarpiniti M, Comminiello D, Parisi R, Uncini A (2015) Nonlinear system identification using IIR spline adaptive filters. Signal Process 108(108):30–35CrossRef Scarpiniti M, Comminiello D, Parisi R, Uncini A (2015) Nonlinear system identification using IIR spline adaptive filters. Signal Process 108(108):30–35CrossRef
21.
Zurück zum Zitat Scarpiniti M, Comminiello D, Parisi R, Uncini A (2014) Hammerstein uniform cubic spline adaptive filters: learning and convergence properties. Signal Process 100(7):112–123CrossRef Scarpiniti M, Comminiello D, Parisi R, Uncini A (2014) Hammerstein uniform cubic spline adaptive filters: learning and convergence properties. Signal Process 100(7):112–123CrossRef
22.
Zurück zum Zitat Patel V, George NV (2016) Compensating acoustic feedback in feed-forward active noise control systems using spline adaptive filters. Signal Process 120:448–455CrossRef Patel V, George NV (2016) Compensating acoustic feedback in feed-forward active noise control systems using spline adaptive filters. Signal Process 120:448–455CrossRef
23.
Zurück zum Zitat Scarpiniti M, Comminiello D, Scarano G, Parisi R (2016) Steady-state performance of spline adaptive filters. IEEE Trans Signal Process 64(4):816–828MathSciNetCrossRef Scarpiniti M, Comminiello D, Scarano G, Parisi R (2016) Steady-state performance of spline adaptive filters. IEEE Trans Signal Process 64(4):816–828MathSciNetCrossRef
24.
Zurück zum Zitat Scarpiniti M, Comminiello D, Parisi R, Uncini A (2015) Novel cascade spline architectures for the identification of nonlinear systems. IEEE Trans Circuits Syst I 62(7):1825–1835MathSciNetCrossRef Scarpiniti M, Comminiello D, Parisi R, Uncini A (2015) Novel cascade spline architectures for the identification of nonlinear systems. IEEE Trans Circuits Syst I 62(7):1825–1835MathSciNetCrossRef
25.
Zurück zum Zitat Yin L, Astola J, Neuvo Y (1993) A new class of nonlinear filters-neural filters. IEEE Trans Signal Process 41(3):1201–1222CrossRefMATH Yin L, Astola J, Neuvo Y (1993) A new class of nonlinear filters-neural filters. IEEE Trans Signal Process 41(3):1201–1222CrossRefMATH
26.
Zurück zum Zitat Widrow B (2005) Thinking about thinking: the discovery of the LMS algorithm. IEEE Signal Process Mag 22(1):100–106CrossRef Widrow B (2005) Thinking about thinking: the discovery of the LMS algorithm. IEEE Signal Process Mag 22(1):100–106CrossRef
27.
Zurück zum Zitat Sayin MO, Vanli ND, Kozat SS (2013) A novel family of adaptive filtering algorithms based on the logarithmic cost. IEEE Trans Signal Process 62(17):4411–4424MathSciNetCrossRef Sayin MO, Vanli ND, Kozat SS (2013) A novel family of adaptive filtering algorithms based on the logarithmic cost. IEEE Trans Signal Process 62(17):4411–4424MathSciNetCrossRef
28.
Zurück zum Zitat Bershad NJ (1986) Analysis of the normalized LMS algorithm with Gaussian inputs. IEEE Trans Acoust Speech Signal Process 34(4):793–806CrossRef Bershad NJ (1986) Analysis of the normalized LMS algorithm with Gaussian inputs. IEEE Trans Acoust Speech Signal Process 34(4):793–806CrossRef
Metadaten
Titel
Normalised Spline Adaptive Filtering Algorithm for Nonlinear System Identification
verfasst von
Sihai Guan
Zhi Li
Publikationsdatum
10.03.2017
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 2/2017
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-017-9606-6

Weitere Artikel der Ausgabe 2/2017

Neural Processing Letters 2/2017 Zur Ausgabe

Neuer Inhalt