Structure Identification Based On ARMA Model

The theory of system identification originates from cybernetics, but now it hasbeen formulated in the fields of aerospace, hydrological, mechanical and civilengineering. Structure identification belongs to system identification, whoseparticularity is that it accounts for some assumptions, such as: the classical structuraldynamics, some simple assumption of engineering application, and the actualmeasurement factors.Although the methods of system identification are various, the time-domain basedon Auto-Regressive Moving Average (ARMA) model method is selected in this thesisbecause of the under mentioned reasons: the first one is that the relationship betweenARMA model and linear second-order system results that the identification process ofstructural parameters is equivalent to the estimation process of ARMA modelparameters, the second one is that time-variant ARMAV model makes it possible toidentifying the time-variant parameters of multi-degree-of-freedom structure, the last isthat structure identification can be done and the structural characteristic can not bedropped out when the input is unknown or unmeasured.In this thesis, the ARMA model based time-domain method is discussed andapplied to structure identification. The main points are as follows:The relationship between structure and ARMA model is the precondition ofARMA model for structure identification. There are two different models equivalent tostructural system: scalar ARMA model and ARMAV model. ARMA modeling ofstructure is realized through the transition of three mathematical models describingsystem, which are differential equation, state-space equation and difference equation.Identification of ARMA model parameters is the key component. It consists ofjudging the model order obtained by the transition of three models mentioned above,estimating the model parameters yielded through the Least Square method, examiningthe estimated model got by the comparison between simulated outputs and actuallymeasured ones.In this thesis, several cases are considered about ARMA model for parameteridentification. The identification results of four different parameter-variant processes ofa single-degree-of-freedom structure have preliminarily proved the feasibility of themethod, based on this, the ARMA models of different structures, such as scalartime-invariant ARMA model, time-invariant ARMAV model and time-variant ARMAVmodel, are applied to the parameter identification of a three-story plane frame structure.The computation results have proved its problem-solving ability to identify theparameters of multi-degree-of-freedom structure and structural time-variant properties,but also displayed the advantages of ARMAV model for parameter identificationcompared with scalar ARMA model.