Online distributed fuzzy modeling of nonlinear PDE systems: Computation based on adaptive algorithms

Mohammad Mehdi Mardani, Mokhtar ShaSadeghi, Behrouz Safarinejadian, Tomislav Dragicevic

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

With the emergence of novel model-based controllers for partial differential equation (PDE) systems, identifying the mathematical model of PDE systems has become a promising and complicated research topic. This paper suggests a new method to identify an adaptive Takagi–Sugeno (TS) fuzzy PDE model for nonlinear multi-input multi-output (MIMO) first-order PDE systems. The proposed approach is performed online based on the measured input and output data of the nonlinear PDE systems. Furthermore, the identification process will be obtained for the cases that the noise is either white or colored. For the case of white noise, a nonlinear recursive least square (NRLS) approach is applied to identify the nonlinear system. On the other hand, when the colored noise is exerted to the nonlinear PDE system, the fuzzy PDE model of the nonlinear PDE system and also nonlinear colored noise are identified based on the nonlinear extended matrix methods (NEMM). Moreover, the problem of identification for both colored and white noise cases is investigated when premise variables of membership functions are known or unknown. Finally, in order to illustrate the effectiveness and merits of the proposed methods, the identification method is applied to a practical nonisothermal Plug-Flow reactor (PFR) and a hyperbolic PDE system with Lotka–Volterra type applications. As it is expected, the evolutions of the error between the state variables for the obtained TS fuzzy PDE model and the output data converge to the zero in the steady-state conditions. Thus one concludes, the proposed identification algorithm can accurately adjust both consequents and antecedents parameters of TS fuzzy PDE model.
OriginalsprogEngelsk
TidsskriftApplied Soft Computing
Vol/bind77
Sider (fra-til)76-87
Antal sider12
ISSN1568-4946
DOI
StatusUdgivet - apr. 2019

Fingeraftryk

Adaptive algorithms
Partial differential equations
White noise
Membership functions
Nonlinear systems
Mathematical models
Controllers

Emneord

    Citer dette

    Mardani, Mohammad Mehdi ; ShaSadeghi, Mokhtar ; Safarinejadian, Behrouz ; Dragicevic, Tomislav. / Online distributed fuzzy modeling of nonlinear PDE systems : Computation based on adaptive algorithms. I: Applied Soft Computing. 2019 ; Bind 77. s. 76-87.
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    abstract = "With the emergence of novel model-based controllers for partial differential equation (PDE) systems, identifying the mathematical model of PDE systems has become a promising and complicated research topic. This paper suggests a new method to identify an adaptive Takagi–Sugeno (TS) fuzzy PDE model for nonlinear multi-input multi-output (MIMO) first-order PDE systems. The proposed approach is performed online based on the measured input and output data of the nonlinear PDE systems. Furthermore, the identification process will be obtained for the cases that the noise is either white or colored. For the case of white noise, a nonlinear recursive least square (NRLS) approach is applied to identify the nonlinear system. On the other hand, when the colored noise is exerted to the nonlinear PDE system, the fuzzy PDE model of the nonlinear PDE system and also nonlinear colored noise are identified based on the nonlinear extended matrix methods (NEMM). Moreover, the problem of identification for both colored and white noise cases is investigated when premise variables of membership functions are known or unknown. Finally, in order to illustrate the effectiveness and merits of the proposed methods, the identification method is applied to a practical nonisothermal Plug-Flow reactor (PFR) and a hyperbolic PDE system with Lotka–Volterra type applications. As it is expected, the evolutions of the error between the state variables for the obtained TS fuzzy PDE model and the output data converge to the zero in the steady-state conditions. Thus one concludes, the proposed identification algorithm can accurately adjust both consequents and antecedents parameters of TS fuzzy PDE model.",
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    Online distributed fuzzy modeling of nonlinear PDE systems : Computation based on adaptive algorithms. / Mardani, Mohammad Mehdi; ShaSadeghi, Mokhtar; Safarinejadian, Behrouz; Dragicevic, Tomislav.

    I: Applied Soft Computing, Bind 77, 04.2019, s. 76-87.

    Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

    TY - JOUR

    T1 - Online distributed fuzzy modeling of nonlinear PDE systems

    T2 - Computation based on adaptive algorithms

    AU - Mardani, Mohammad Mehdi

    AU - ShaSadeghi, Mokhtar

    AU - Safarinejadian, Behrouz

    AU - Dragicevic, Tomislav

    PY - 2019/4

    Y1 - 2019/4

    N2 - With the emergence of novel model-based controllers for partial differential equation (PDE) systems, identifying the mathematical model of PDE systems has become a promising and complicated research topic. This paper suggests a new method to identify an adaptive Takagi–Sugeno (TS) fuzzy PDE model for nonlinear multi-input multi-output (MIMO) first-order PDE systems. The proposed approach is performed online based on the measured input and output data of the nonlinear PDE systems. Furthermore, the identification process will be obtained for the cases that the noise is either white or colored. For the case of white noise, a nonlinear recursive least square (NRLS) approach is applied to identify the nonlinear system. On the other hand, when the colored noise is exerted to the nonlinear PDE system, the fuzzy PDE model of the nonlinear PDE system and also nonlinear colored noise are identified based on the nonlinear extended matrix methods (NEMM). Moreover, the problem of identification for both colored and white noise cases is investigated when premise variables of membership functions are known or unknown. Finally, in order to illustrate the effectiveness and merits of the proposed methods, the identification method is applied to a practical nonisothermal Plug-Flow reactor (PFR) and a hyperbolic PDE system with Lotka–Volterra type applications. As it is expected, the evolutions of the error between the state variables for the obtained TS fuzzy PDE model and the output data converge to the zero in the steady-state conditions. Thus one concludes, the proposed identification algorithm can accurately adjust both consequents and antecedents parameters of TS fuzzy PDE model.

    AB - With the emergence of novel model-based controllers for partial differential equation (PDE) systems, identifying the mathematical model of PDE systems has become a promising and complicated research topic. This paper suggests a new method to identify an adaptive Takagi–Sugeno (TS) fuzzy PDE model for nonlinear multi-input multi-output (MIMO) first-order PDE systems. The proposed approach is performed online based on the measured input and output data of the nonlinear PDE systems. Furthermore, the identification process will be obtained for the cases that the noise is either white or colored. For the case of white noise, a nonlinear recursive least square (NRLS) approach is applied to identify the nonlinear system. On the other hand, when the colored noise is exerted to the nonlinear PDE system, the fuzzy PDE model of the nonlinear PDE system and also nonlinear colored noise are identified based on the nonlinear extended matrix methods (NEMM). Moreover, the problem of identification for both colored and white noise cases is investigated when premise variables of membership functions are known or unknown. Finally, in order to illustrate the effectiveness and merits of the proposed methods, the identification method is applied to a practical nonisothermal Plug-Flow reactor (PFR) and a hyperbolic PDE system with Lotka–Volterra type applications. As it is expected, the evolutions of the error between the state variables for the obtained TS fuzzy PDE model and the output data converge to the zero in the steady-state conditions. Thus one concludes, the proposed identification algorithm can accurately adjust both consequents and antecedents parameters of TS fuzzy PDE model.

    KW - Nonlinear System Identification

    KW - nonlinear first-order partial differential equation (PDE) system

    KW - Takagi-Sugeno (TS) fuzzy model

    KW - nonlinear least squares (NLS)

    KW - parameter estimation

    U2 - 10.1016/j.asoc.2018.12.035

    DO - 10.1016/j.asoc.2018.12.035

    M3 - Journal article

    VL - 77

    SP - 76

    EP - 87

    JO - Applied Soft Computing

    JF - Applied Soft Computing

    SN - 1568-4946

    ER -