Modified trajectory piecewise linear approximation for nonlinear model order reduction

  • Toheed Aizad

    Student thesis: Doctoral ThesisDoctor of Philosophy


    Reduced order modelling is a recognised and effective technique to reduce the intensive burden in heavily complex numerical simulations. Model order reduction (MOR) has been successfully implemented in linear and nonlinear areas. This thesis deals with the challenging nonlinear MOR. Trajectory piece-wise linear (TPWL) approximation has produced substantial results to simplify the high order nonlinear systems. TPWL approach contains the idea of suitably selecting multiple linearisation points along the state trajectory of the nonlinear system. The carefully chosen linearisation points are reduced to lower order models using a linear MOR approach before obtaining the weighted combination of the bank of linearised models.

    This thesis presents and demonstrates the benefits of improved approaches in the area of linearisation point selection and reduced order basis. There are many advantages of these improvements, such as; smaller number of linearisation points resulting in reduced computational cost, capable of reducing very high order models while retaining the stability of reduced order models, producing lower order model yet retaining the simulation accuracy. This thesis also proposes a combination of data based and TPWL approximation approaches in order to expand the applications of TPWL for various nonlinear systems available in different structures.

    The comparison of the new approaches with the original work done in this area is illustrated using different examples and case studies.
    Date of AwardApr 2020
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorDina Laila (Supervisor) & Olivier Haas (Supervisor)

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