Iterated square root unscented Kalman filter for nonlinear states and parameters estimation: three DOF damped system

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18 Citations (Scopus)

Abstract

Structural health monitoring of civil engineering infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, serviceability, performance based engineering, life-cycle performance, risk management, decision making and so on. For incorporating such uncertainties, several filtering techniques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of freedom spring-mass-dashpot system to predict the displacements and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advantages over other methods in terms of the estimation accuracy and convergence.

Original languageEnglish
Pages (from-to)493-508
Number of pages16
JournalJournal of Civil Structural Health Monitoring
Volume5
Issue number4
DOIs
Publication statusPublished - 23 Sep 2015

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State estimation
Kalman filters
Parameter estimation

Keywords

  • Civil engineering infrastructure
  • Iterated square root
  • State Estimations
  • Structural health monitoring
  • Unscented Kalman filter

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Safety, Risk, Reliability and Quality

Cite this

@article{61c6e6efbea7482b813a4d0b2ef67439,
title = "Iterated square root unscented Kalman filter for nonlinear states and parameters estimation: three DOF damped system",
abstract = "Structural health monitoring of civil engineering infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, serviceability, performance based engineering, life-cycle performance, risk management, decision making and so on. For incorporating such uncertainties, several filtering techniques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of freedom spring-mass-dashpot system to predict the displacements and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advantages over other methods in terms of the estimation accuracy and convergence.",
keywords = "Civil engineering infrastructure, Iterated square root, State Estimations, Structural health monitoring, Unscented Kalman filter",
author = "Majdi Mansouri and Onur Avci and Hazem Nounou and Mohamed Nounou",
year = "2015",
month = "9",
day = "23",
doi = "10.1007/s13349-015-0134-7",
language = "English",
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pages = "493--508",
journal = "Journal of Civil Structural Health Monitoring",
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publisher = "Springer Science + Business Media",
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T1 - Iterated square root unscented Kalman filter for nonlinear states and parameters estimation

T2 - three DOF damped system

AU - Mansouri, Majdi

AU - Avci, Onur

AU - Nounou, Hazem

AU - Nounou, Mohamed

PY - 2015/9/23

Y1 - 2015/9/23

N2 - Structural health monitoring of civil engineering infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, serviceability, performance based engineering, life-cycle performance, risk management, decision making and so on. For incorporating such uncertainties, several filtering techniques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of freedom spring-mass-dashpot system to predict the displacements and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advantages over other methods in terms of the estimation accuracy and convergence.

AB - Structural health monitoring of civil engineering infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, serviceability, performance based engineering, life-cycle performance, risk management, decision making and so on. For incorporating such uncertainties, several filtering techniques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of freedom spring-mass-dashpot system to predict the displacements and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advantages over other methods in terms of the estimation accuracy and convergence.

KW - Civil engineering infrastructure

KW - Iterated square root

KW - State Estimations

KW - Structural health monitoring

KW - Unscented Kalman filter

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