Skip to main content

2014 | OriginalPaper | Buchkapitel

2. Recursive Bayesian Estimation of Partially Observed Dynamic Systems

verfasst von : Saeed Eftekhar Azam

Erschienen in: Online Damage Detection in Structural Systems

Verlag: Springer International Publishing

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

search-config
loading …

Abstract

In the current Chapter, recursive Bayesian inference of partially observed dynamical systems is reviewed. As a tool for structural system identification, nonlinear Bayesian filters are applied to dual estimation problem of linear and nonlinear dynamical systems. In so doing, dual estimation of state and parameters of structural state space models is considered; EKF, SPKF, PF and EK-PF are used for parameter identification and state estimation. Dealing with a SDOF structure, it is shown that the hybrid EK-PF filter is able to furnish a reasonable estimation of parameters of nonlinear constitutive models. Assessment of SDOF systems is followed by identification of multi storey buildings. In this regard, performances of the EK-PF and EKF algorithms are compared, and it is concluded that they are nearly the same, and by an increase in the number of storeys of the building, both of the algorithms fail to provide an unbiased estimate of the parameters (stiffness of the storeys). Therefore, they are not reliable tools to monitor state and parameters of multi storey 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
Zurück zum Zitat Adelino R, da Silva Ferreira (2009) Bayesian mixture models of variable dimension for image segmentation. Comput Methods Programs Biomed 94:1–14CrossRef Adelino R, da Silva Ferreira (2009) Bayesian mixture models of variable dimension for image segmentation. Comput Methods Programs Biomed 94:1–14CrossRef
Zurück zum Zitat Allen D, Darwiche A (2008) RC_Link: genetic linkage analysis using Bayesian networks. Int J Approximate Reasoning 48:499–525CrossRef Allen D, Darwiche A (2008) RC_Link: genetic linkage analysis using Bayesian networks. Int J Approximate Reasoning 48:499–525CrossRef
Zurück zum Zitat Alvarado Mora MV, Romano CM, Gomes-Gouvêa MS, Gutierrez MF, Botelho L, Carrilho FJ, Pinho JRR (2011) Molecular characterization of the Hepatitis B virus genotypes in Colombia: a Bayesian inference on the genotype F. Infect, Genet Evol 11:103–108CrossRef Alvarado Mora MV, Romano CM, Gomes-Gouvêa MS, Gutierrez MF, Botelho L, Carrilho FJ, Pinho JRR (2011) Molecular characterization of the Hepatitis B virus genotypes in Colombia: a Bayesian inference on the genotype F. Infect, Genet Evol 11:103–108CrossRef
Zurück zum Zitat Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Sig Process 50:174–188CrossRef Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Sig Process 50:174–188CrossRef
Zurück zum Zitat Bathe K (1996) Finite element procedures. Prentice-Hall Inc, Upper Saddle River Bathe K (1996) Finite element procedures. Prentice-Hall Inc, Upper Saddle River
Zurück zum Zitat Bellman RE (1957) Dynamic programming. Princeton University Press, PrincetonMATH Bellman RE (1957) Dynamic programming. Princeton University Press, PrincetonMATH
Zurück zum Zitat Biedermann A, Taroni F (2012) Bayesian networks for evaluating forensic DNA profiling evidence: a review and guide to literature. Forensic Sci Int: Genet 6(2):147–157 Biedermann A, Taroni F (2012) Bayesian networks for evaluating forensic DNA profiling evidence: a review and guide to literature. Forensic Sci Int: Genet 6(2):147–157
Zurück zum Zitat Bittanti S, Savaresi SM (2000) On the parameterization and design of an extended Kalman filter frequency tracker. IEEE Trans Autom Control 45:1718–1724CrossRefMATHMathSciNet Bittanti S, Savaresi SM (2000) On the parameterization and design of an extended Kalman filter frequency tracker. IEEE Trans Autom Control 45:1718–1724CrossRefMATHMathSciNet
Zurück zum Zitat Bittanti S, Maier G, Nappi A (1984) Inverse problems in structural elastoplasticity: a Kalman filter approach. In: Sawczukand A, Bianchi G (eds) Plasticity today. Applied Science Publications, London, pp 311–329 Bittanti S, Maier G, Nappi A (1984) Inverse problems in structural elastoplasticity: a Kalman filter approach. In: Sawczukand A, Bianchi G (eds) Plasticity today. Applied Science Publications, London, pp 311–329
Zurück zum Zitat Cadini F, Zio E, Avram D (2009) Monte Carlo-based filtering for fatigue crack growth estimation. Probab Eng Mech 24:367–373CrossRef Cadini F, Zio E, Avram D (2009) Monte Carlo-based filtering for fatigue crack growth estimation. Probab Eng Mech 24:367–373CrossRef
Zurück zum Zitat Caron F, Doucet A, Gottardo R (2012) On-line change point detection and parameter estimation with application to genomic data. Stat Comput 22:579–595CrossRefMathSciNet Caron F, Doucet A, Gottardo R (2012) On-line change point detection and parameter estimation with application to genomic data. Stat Comput 22:579–595CrossRefMathSciNet
Zurück zum Zitat Chatzi EN, Smyth AW, Masri SF (2010) Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty. Struct Saf 32:326–337CrossRef Chatzi EN, Smyth AW, Masri SF (2010) Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty. Struct Saf 32:326–337CrossRef
Zurück zum Zitat Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30:2779–2811CrossRefMATH Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30:2779–2811CrossRefMATH
Zurück zum Zitat Corigliano A, Mariani S (2001a) Parameter identification of a time-dependent elastic-damage interface model for the simulation of debonding in composites. Compos Sci Technol 61:191–203CrossRef Corigliano A, Mariani S (2001a) Parameter identification of a time-dependent elastic-damage interface model for the simulation of debonding in composites. Compos Sci Technol 61:191–203CrossRef
Zurück zum Zitat Corigliano A, Mariani S (2001b) Simulation of damage in composites by means of interface models: parameter identification. Compos Sci Technol 61:2299–2315CrossRef Corigliano A, Mariani S (2001b) Simulation of damage in composites by means of interface models: parameter identification. Compos Sci Technol 61:2299–2315CrossRef
Zurück zum Zitat Corigliano A, Mariani S (2004) Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Comput Methods Appl Mech Eng 193:3807–3835CrossRefMATH Corigliano A, Mariani S (2004) Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Comput Methods Appl Mech Eng 193:3807–3835CrossRefMATH
Zurück zum Zitat Corigliano A, Mariani S, Pandolfi A (2006) Numerical analysis of rate-dependent dynamic composite delamination. Compos Sci Technol 66:766–775CrossRef Corigliano A, Mariani S, Pandolfi A (2006) Numerical analysis of rate-dependent dynamic composite delamination. Compos Sci Technol 66:766–775CrossRef
Zurück zum Zitat Creal D (2012) A survey of sequential Monte Carlo methods for economics and finance. Econ Rev 31(3):245–296 Creal D (2012) A survey of sequential Monte Carlo methods for economics and finance. Econ Rev 31(3):245–296
Zurück zum Zitat de Freitas JFG, Niranjan MA, Gee AH, Doucet A (2000) Sequential Monte Carlo methods to train neural network models. Neural Comput 12:955–993CrossRef de Freitas JFG, Niranjan MA, Gee AH, Doucet A (2000) Sequential Monte Carlo methods to train neural network models. Neural Comput 12:955–993CrossRef
Zurück zum Zitat Doucet A (1997) Monte Carlo methods for Bayesian estimation of hidden Markov models: application to radiation signals. (unpublished) doctoral dissertation, University Paris-Sud Orsay Doucet A (1997) Monte Carlo methods for Bayesian estimation of hidden Markov models: application to radiation signals. (unpublished) doctoral dissertation, University Paris-Sud Orsay
Zurück zum Zitat Doucet A, Johansen AM (2009) A tutorial on particle filtering and smoothing: fifteen years later. Handbook of Nonlinear Filtering 12:656–704 Doucet A, Johansen AM (2009) A tutorial on particle filtering and smoothing: fifteen years later. Handbook of Nonlinear Filtering 12:656–704
Zurück zum Zitat Duan L, Gao W, Zeng W, Zhao D (2005) Adaptive relevance feedback based on Bayesian inference for image retrieval. Signal Process 85:395–399CrossRefMATH Duan L, Gao W, Zeng W, Zhao D (2005) Adaptive relevance feedback based on Bayesian inference for image retrieval. Signal Process 85:395–399CrossRefMATH
Zurück zum Zitat Eftekhar Azam S, Mariani S (2012) Dual estimation of partially observed nonlinear structural systems: a particle filter approach. Mech Res Commun 46:54–61CrossRef Eftekhar Azam S, Mariani S (2012) Dual estimation of partially observed nonlinear structural systems: a particle filter approach. Mech Res Commun 46:54–61CrossRef
Zurück zum Zitat Eftekhar Azam S, Ghisi A, Mariani S (2012a) Parallelized sigma-point Kalman filtering for structural dynamics, Comp Struct 92–93, pp. 193–205 Eftekhar Azam S, Ghisi A, Mariani S (2012a) Parallelized sigma-point Kalman filtering for structural dynamics, Comp Struct 92–93, pp. 193–205
Zurück zum Zitat Eftekhar Azam S, Bagherinia M, Mariani S (2012b) Stochastic system identification via particle and sigma-point Kalman filtering, Scientia Iranica A, 19:982–991 Eftekhar Azam S, Bagherinia M, Mariani S (2012b) Stochastic system identification via particle and sigma-point Kalman filtering, Scientia Iranica A, 19:982–991
Zurück zum Zitat Gao F, Lu Y (2006) A Kalman-filter based time-domain analysis for structural damage diagnosis with noisy signals. J Sound Vib 297:916–930CrossRef Gao F, Lu Y (2006) A Kalman-filter based time-domain analysis for structural damage diagnosis with noisy signals. J Sound Vib 297:916–930CrossRef
Zurück zum Zitat Gelb A (1974) Applied optimal estimation. MIT Press, Cambridge Gelb A (1974) Applied optimal estimation. MIT Press, Cambridge
Zurück zum Zitat Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE proceedings F, vol 140. pp 107–113 Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE proceedings F, vol 140. pp 107–113
Zurück zum Zitat Hol JD, Schon TB, Gustafsson F (2006) On resampling algorithms for particle filtering. In: Proceedings of nonlinear statistical signal processing workshop 2006, pp 79–82 Hol JD, Schon TB, Gustafsson F (2006) On resampling algorithms for particle filtering. In: Proceedings of nonlinear statistical signal processing workshop 2006, pp 79–82
Zurück zum Zitat Holmes S, Klein G, Murray DW (2008) A square root unscented Kalman filter for visual monoSLAM. In: Proceedings—EEE international conference on robotics and automation, p 3710 Holmes S, Klein G, Murray DW (2008) A square root unscented Kalman filter for visual monoSLAM. In: Proceedings—EEE international conference on robotics and automation, p 3710
Zurück zum Zitat Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover, New YorkMATH Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover, New YorkMATH
Zurück zum Zitat Ishihara T, Omori Y (2012) Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors. Comput Stat Data Anal 56(11):3674–3689CrossRefMATHMathSciNet Ishihara T, Omori Y (2012) Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors. Comput Stat Data Anal 56(11):3674–3689CrossRefMATHMathSciNet
Zurück zum Zitat Jay E, Philippe Ovarlez J, Declercq D, Duvaut P (2003) BORD: Bayesian optimum radar detector. Signal Process 83:1151–1162CrossRefMATH Jay E, Philippe Ovarlez J, Declercq D, Duvaut P (2003) BORD: Bayesian optimum radar detector. Signal Process 83:1151–1162CrossRefMATH
Zurück zum Zitat Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. Proceedings of SPIE—the international society for optical engineering, pp 182–193 Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. Proceedings of SPIE—the international society for optical engineering, pp 182–193
Zurück zum Zitat Julier SJ, Uhlmann JK, Durrant-Whyte HF (1995) New approach for filtering nonlinear systems. In: Proceedings of the American control conference, pp 1628–1632 Julier SJ, Uhlmann JK, Durrant-Whyte HF (1995) New approach for filtering nonlinear systems. In: Proceedings of the American control conference, pp 1628–1632
Zurück zum Zitat Julier S, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45:477–482CrossRefMATHMathSciNet Julier S, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45:477–482CrossRefMATHMathSciNet
Zurück zum Zitat Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45CrossRef Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45CrossRef
Zurück zum Zitat Kitagawa G (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J Comput Graphical Stat 5:1–25MathSciNet Kitagawa G (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J Comput Graphical Stat 5:1–25MathSciNet
Zurück zum Zitat Koh CG, See LM, Balendra T (1995) Determination of storey stiffness of three-dimensional frame buildings. Eng Struct 17:179–186 Koh CG, See LM, Balendra T (1995) Determination of storey stiffness of three-dimensional frame buildings. Eng Struct 17:179–186
Zurück zum Zitat Lazkano E, Sierra B, Astigarraga A, Martínez-Otzeta JM (2007) On the use of Bayesian Networks to develop behaviours for mobile robots. Rob Auton Syst 55:253–265CrossRef Lazkano E, Sierra B, Astigarraga A, Martínez-Otzeta JM (2007) On the use of Bayesian Networks to develop behaviours for mobile robots. Rob Auton Syst 55:253–265CrossRef
Zurück zum Zitat Li P, Goodall R, Kadirkamanathan V (2004) Estimation of parameters in a linear state space model using a Rao-Blackwellised particle filter. IEE proceedings: control theory and applications, vol 151. pp 727–738 Li P, Goodall R, Kadirkamanathan V (2004) Estimation of parameters in a linear state space model using a Rao-Blackwellised particle filter. IEE proceedings: control theory and applications, vol 151. pp 727–738
Zurück zum Zitat Ljung L (1999) System identification. Theory for the user, 2nd edn. Prentice Hall, Englewood Cliffs Ljung L (1999) System identification. Theory for the user, 2nd edn. Prentice Hall, Englewood Cliffs
Zurück zum Zitat Mariani S (2009a) Failure of layered composites subject to impacts: constitutive modeling and parameter identification issues. In: Mendes G, Lago B (eds) Strength of materials. Nova Science Publishers, New York, pp 97–131 Mariani S (2009a) Failure of layered composites subject to impacts: constitutive modeling and parameter identification issues. In: Mendes G, Lago B (eds) Strength of materials. Nova Science Publishers, New York, pp 97–131
Zurück zum Zitat Mariani S (2009b) Failure assessment of layered composites subject to impact loadings: a finite element, sigma-point Kalman filter approach. Algorithms 2:808–827CrossRefMathSciNet Mariani S (2009b) Failure assessment of layered composites subject to impact loadings: a finite element, sigma-point Kalman filter approach. Algorithms 2:808–827CrossRefMathSciNet
Zurück zum Zitat Mariani S, Corigliano A (2005) Impact induced composite delamination: state and parameter identification via joint and dual extended Kalman filters. Comput Methods Appl Mech Eng 194:5242–5272CrossRefMATH Mariani S, Corigliano A (2005) Impact induced composite delamination: state and parameter identification via joint and dual extended Kalman filters. Comput Methods Appl Mech Eng 194:5242–5272CrossRefMATH
Zurück zum Zitat Mariani S, Ghisi A (2007) Unscented Kalman filtering for nonlinear structural dynamics. Nonlinear Dyn 49:131–150CrossRefMATH Mariani S, Ghisi A (2007) Unscented Kalman filtering for nonlinear structural dynamics. Nonlinear Dyn 49:131–150CrossRefMATH
Zurück zum Zitat Miazhynskaia T, Frühwirth-Schnatter S, Dorffner G (2006) Bayesian testing for non-linearity in volatility modeling. Comput Stat Data Anal 51:2029–2042CrossRefMATH Miazhynskaia T, Frühwirth-Schnatter S, Dorffner G (2006) Bayesian testing for non-linearity in volatility modeling. Comput Stat Data Anal 51:2029–2042CrossRefMATH
Zurück zum Zitat Mitra SK, Lee T, Goldbaum M (2005) A Bayesian network based sequential inference for diagnosis of diseases from retinal images. Pattern Recogn Lett 26:459–470CrossRef Mitra SK, Lee T, Goldbaum M (2005) A Bayesian network based sequential inference for diagnosis of diseases from retinal images. Pattern Recogn Lett 26:459–470CrossRef
Zurück zum Zitat Powell WB (2007) Approximate dynamic programming: solving the curse of dimensionality. Princeton University Press, PrincetonCrossRef Powell WB (2007) Approximate dynamic programming: solving the curse of dimensionality. Princeton University Press, PrincetonCrossRef
Zurück zum Zitat Rose JH, Ferrante J, Smith JR (1981) Universal binding energy curves for metals and bimetallic interfaces. Phys Rev Lett 47:675–678CrossRef Rose JH, Ferrante J, Smith JR (1981) Universal binding energy curves for metals and bimetallic interfaces. Phys Rev Lett 47:675–678CrossRef
Zurück zum Zitat Saleh GMK, Niranjan M (2001) Speech enhancement using a Bayesian evidence approach. Comput Speech Lang 15:101–125CrossRef Saleh GMK, Niranjan M (2001) Speech enhancement using a Bayesian evidence approach. Comput Speech Lang 15:101–125CrossRef
Zurück zum Zitat Ting J, D’Souza A, Schaal S (2011) Bayesian robot system identification with input and output noise. Neural Networks 63:99–108CrossRef Ting J, D’Souza A, Schaal S (2011) Bayesian robot system identification with input and output noise. Neural Networks 63:99–108CrossRef
Zurück zum Zitat Van der Merwe, R. 2004, Sigma-point Kalman filters for probabilistic inference in dynamic state-space models, Oregon Health and Science University Van der Merwe, R. 2004, Sigma-point Kalman filters for probabilistic inference in dynamic state-space models, Oregon Health and Science University
Zurück zum Zitat Velarde LGC, Migon HS, Alcoforado DA (2008) Hierarchical Bayesian models applied to air surveillance radars. Eur J Oper Res 184:1155–1162CrossRefMATH Velarde LGC, Migon HS, Alcoforado DA (2008) Hierarchical Bayesian models applied to air surveillance radars. Eur J Oper Res 184:1155–1162CrossRefMATH
Zurück zum Zitat White OL, Safaeinili A, Plaut JJ, Stofan ER, Clifford SM, Farrell WM, Heggy E, Picardi G (2009) MARSIS radar sounder observations in the vicinity of Ma’adim Vallis, Mars. Icarus 201:460–473CrossRef White OL, Safaeinili A, Plaut JJ, Stofan ER, Clifford SM, Farrell WM, Heggy E, Picardi G (2009) MARSIS radar sounder observations in the vicinity of Ma’adim Vallis, Mars. Icarus 201:460–473CrossRef
Zurück zum Zitat Xie Z, Feng J (2011) Real-time nonlinear structural system identification via iterated unscented Kalman filter. Mechanical Syst Signal Process 28:309–322CrossRef Xie Z, Feng J (2011) Real-time nonlinear structural system identification via iterated unscented Kalman filter. Mechanical Syst Signal Process 28:309–322CrossRef
Zurück zum Zitat Yahya AA, Mahmod R, Ramli AR (2010) Dynamic Bayesian networks and variable length genetic algorithm for designing cue-based model for dialogue act recognition. Comput Speech Lang 24:190–218CrossRef Yahya AA, Mahmod R, Ramli AR (2010) Dynamic Bayesian networks and variable length genetic algorithm for designing cue-based model for dialogue act recognition. Comput Speech Lang 24:190–218CrossRef
Zurück zum Zitat Yang S, Lee J (2011) Predicting a distribution of implied volatilities for option pricing. Expert Syst Appl 38:1702–1708CrossRef Yang S, Lee J (2011) Predicting a distribution of implied volatilities for option pricing. Expert Syst Appl 38:1702–1708CrossRef
Zurück zum Zitat Zhou H, Sakane S (2007) Mobile robot localization using active sensing based on Bayesian network inference. Rob Auton Syst 55:292–305CrossRef Zhou H, Sakane S (2007) Mobile robot localization using active sensing based on Bayesian network inference. Rob Auton Syst 55:292–305CrossRef
Metadaten
Titel
Recursive Bayesian Estimation of Partially Observed Dynamic Systems
verfasst von
Saeed Eftekhar Azam
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-02559-9_2

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.