Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Soft Computing
Erschienen in: Soft Computing 13/2019

13.03.2018 | Methodologies and Application

Cost function based on hidden Markov models for parameter estimation of chaotic systems

verfasst von: Yasser Shekofteh, Sajad Jafari, Karthikeyan Rajagopal

Erschienen in: Soft Computing | Ausgabe 13/2019

Einloggen

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

search-config
loading …

Abstract

In this note, we deal with parameter estimation methods of chaotic systems. The parameter estimation of the chaotic systems has some significant issues due to their butterfly effects. It can be formulated as an optimization problem and needs a suitable cost function. In this paper, we propose a new cost function based on a hidden Markov model which is a statistical tool for modeling of time series data. It can model dynamical characteristics of the chaotic systems. Moreover, the use of dynamical features of their strange attractors is investigated to achieve a better cost function in the procedure of parameter estimation. Our experimental results indicate the success of the proposed cost function in the one-dimensional parameter estimation of a new four-dimensional chaotic system and Lorenz system as a well-known three-dimensional chaotic system.
Vorheriger Artikel Weibull statistical modeling for textured image retrieval using nonsubsampled contourlet transform
Nächster Artikel A novel approach for protein structure prediction based on an estimation of distribution algorithm

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren
Literatur
Bao B, Jiang T, Xu Q, Chen M, Wu H, Hu Y (2016) Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonlinear Dyn 86:1711–1723CrossRef
Barati K, Jafari S, Sprott JC, Pham V-T (2016) Simple chaotic flows with a curve of equilibria. Int J Bifurcat Chaos 26:1630034MathSciNetCrossRefMATH
Baum LE, Petrie T (1966) Statistical inference for probabilistic functions of finite state Markov chains. Ann Math Stat 37:1554–1563MathSciNetCrossRefMATH
Bird S (2006) NLTK: the natural language toolkit. In: Proceedings of the COLING/ACL on interactive presentation sessions. Association for computational linguistics, pp 69–72
Bishop CM (2006) Pattern recognition and machine learning. Springer, New YorkMATH
Breslin C (2008) Generation and combination of complementary systems for automatic speech recognition. Dissertation, University of Cambridge
Chaudhuri U, Prasad A (2014) Complicated basins and the phenomenon of amplitude death in coupled hidden attractors. Phys Lett A 378:713–718MathSciNetCrossRefMATH
Ethier SN, Kurtz TG (2009) Markov processes: characterization and convergence. Wiley, New YorkMATH
Furui S (1986) Speaker-independent isolated word recognition using dynamic features of speech spectrum. IEEE Trans Acoust Speech Signal Process 34:52–59CrossRef
Gotmare A, Patidar R, George NV (2015) Nonlinear system identification using a cuckoo search optimized adaptive Hammerstein model. Expert Syst Appl 42:2538–2546CrossRef
Hilborn RC (2000) Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford, New YorkCrossRefMATH
Holmes WJ, Russell MJ (1999) Probabilistic-trajectory segmental HMMs. Comput Speech Lang 13:3–37CrossRef
Jafari S, Hashemi Golpayegani SMR, Jafari AH, Gharibzadeh S (2012) Some remarks on chaotic systems. Int J Gen Syst 41:329–330CrossRefMATH
Jafari S, Hashemi Golpayegani SMR, Daliri A (2013a) Comment on ‘Parameters identification of chaotic systems by quantum-behaved particle swarm optimization’ [Int. J. Comput. Math. 86 (12)(2009), pp. 2225–2235]. Int J Comput Math 90:903–905MathSciNetCrossRef
Jafari S, Sprott JC, Hashemi Golpayegani SMR (2013c) Elementary quadratic chaotic flows with no equilibria. Phys Lett A 377:699–702MathSciNetCrossRef
Jafari S, Sprott JC, Pham V-T, Golpayegani SMRH, Jafari AH (2014) A new cost function for parameter estimation of chaotic systems using return maps as fingerprints. Int J Bifurcat Chaos 24:1450134MathSciNetCrossRefMATH
Jafari S, Sprott JC, Pham V-T, Volos C, Li C (2016b) Simple chaotic 3D flows with surfaces of equilibria. Nonlinear Dyn 86:1349–1358CrossRef
Jafari S, Hashemi Golpayegani SMR, Rasoulzadeh Darabad M (2013b) Comment on “Parameter identification and synchronization of fractional-order chaotic systems” [Commun Nonlinear Sci Numer Simulat 2012; 17: 305–16]. Commun Nonlinear Sci Numer Simul 18:811–814
Kantz H, Schreiber T (2004) Nonlinear time series analysis. Cambridge University Press, CambridgeMATH
Kennedy J (2011) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, MA
Khoubrouy SA, Hansen JH (2016) Microphone array processing strategies for distant-based automatic speech recognition. IEEE Signal Process Lett 23:1344–1348CrossRef
Lao S-K, Shekofteh Y, Jafari S, Sprott JC (2014) Cost function based on gaussian mixture model for parameter estimation of a chaotic circuit with a hidden attractor. Int J Bifurcat Chaos 24:1450010MathSciNetCrossRefMATH
Lee L, Le H, Jean F (2017) Improved hidden Markov model adaptation method for reduced frame rate speech recognition. Electron Lett 53(14):962–964CrossRef
Leonov GA, Kuznetsov NV (2013) Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int J Bifurcat Chaos 23:1330002MathSciNetCrossRefMATH
Li X, Yin M (2014) Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm. Nonlinear Dyn 77:61–71MathSciNetCrossRef
Li L, Yang Y, Peng H, Wang X (2006) Parameters identification of chaotic systems via chaotic ant swarm. Chaos Solitons Fractals 28:1204–1211CrossRefMATH
Molaie M, Jafari S, Sprott JC, Hashemi Golpayegani SMR (2013) Simple chaotic flows with one stable equilibrium. Int J Bifurcat Chaos 23:1350188MathSciNetCrossRefMATH
Panahi S, Jafari S, Pham V-T, Kingni ST, Zahedi A, Sedighy SH (2016) Parameter identification of a chaotic circuit with a hidden attractor using Krill herd optimization. Int J Bifurcat Chaos 26:1650221MathSciNetCrossRefMATH
Pham V-T, Volos C, Jafari S, Kapitaniak T (2017) Coexistence of hidden chaotic attractors in a novel no-equilibrium system. Nonlinear Dyn 87:2001–2010CrossRef
Povinelli RJ, Johnson MT, Lindgren AC, Roberts FM, Ye J (2006) Statistical models of reconstructed phase spaces for signal classification. IEEE Trans Signal Process 54:2178–2186CrossRefMATH
Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proce IEEE 77(2):257–286CrossRef
Rahimi A, Bavafa F, Aghababaei S, Khooban MH, Naghavi SV (2016) The online parameter identification of chaotic behaviour in permanent magnet synchronous motor by self-adaptive learning bat-inspired algorithm. Int J Electric Power Energy Syst 78:285–291CrossRef
Sharma P, Shrimali M, Prasad A, Kuznetsov N, Leonov G (2015) Control of multistability in hidden attractors. Eur Phys J Spec Top 224:1485–1491CrossRef
Shekofteh Y, Almasganj F (2013) Feature extraction based on speech attractors in the reconstructed phase space for automatic speech recognition systems. ETRI J 35:100–108CrossRef
Shekofteh Y, Almasganj F, Daliri A (2015a) MLP-based isolated phoneme classification using likelihood features extracted from reconstructed phase space. Eng Appl Artif Intell 44:1–9CrossRef
Shekofteh Y, Jafari S, Sprott JC, Golpayegani SMRH, Almasganj F (2015b) A gaussian mixture model based cost function for parameter estimation of chaotic biological systems. Commun Nonlinear Sci Numer Simul 20:469–481MathSciNetCrossRef
Shekofteh Y, Almasganj F (2010) Using phase space based processing to extract proper features for ASR systems. In: 5th International symposium on telecommunications (IST), pp 596–599
Wang L (2009) 3-Scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system. Nonlinear dyn 56:453–462MathSciNetCrossRefMATH
Wei Z, Zhang W, Yao M (2015) On the periodic orbit bifurcating from one single non-hyperbolic equilibrium in a chaotic jerk system. Nonlinear Dyn 82:1251–1258MathSciNetCrossRefMATH
Xu G, Shekofteh Y, Akgul A, Li C, Panahi S (2018) A new chaotic system with a self-excited attractor: entropy measurement, signal encryption, and parameter estimation. Entropy 20:86CrossRef
Yao X, Liu Y (1996) Fast evolutionary programming. Evol Program 3:451–460
Zhang H, Li B, Zhang J, Qin Y, Feng X, Liu B (2016) Parameter estimation of nonlinear chaotic system by improved TLBO strategy. Soft Comput 20:4965–4980CrossRef
Zucchini W, MacDonald IL, Langrock R (2016) Hidden Markov models for time series: an introduction using R. CRC press, Boca RatonMATH
Metadaten
Titel
Cost function based on hidden Markov models for parameter estimation of chaotic systems
verfasst von
Yasser Shekofteh
Sajad Jafari
Karthikeyan Rajagopal
Publikationsdatum
13.03.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 13/2019
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-018-3129-6

Weitere Artikel der Ausgabe 13/2019

Soft Computing 13/2019 Zur Ausgabe

Methodologies and Application

A novel approach for protein structure prediction based on an estimation of distribution algorithm

Methodologies and Application

Multiperiod mean absolute deviation uncertain portfolio selection with real constraints

Foundations

Maximal similarity granular rough sets for mixed and incomplete information systems

Methodologies and Application

A hybrid intelligent technique for model order reduction in the delta domain: a unified approach

Methodologies and Application

Optimization of different non-traditional turning processes using soft computing methods

Methodologies and Application

Design mining microbial fuel cell cascades