結構系統具有其獨特的特性,其輸出入資料隱含著結構系統的特徵;因此將結構動態現象量測所得的輸出入資料,建立數學模型,並由此模型估算出此結構系統的特性,稱為結構系統識別。在結構系統識別程序中,結構系統除了以從運動方程式的形式來描述其結構的特性外,也可以以一階矩陣微分方程式形式來描述。一階狀態空間運動方程式組有無限多種,本文提出以描述子狀態空間系統來建立一階狀態空間運動方程式組,進而延伸出一套描述子狀態空間系統次空間運算的結構系統識別法。可以直接從量測所得的輸出入資料經由次空間演算法後得到描述子狀態空間系統的形式,並以此形式來分析結構系統的阻尼比、自然振頻及模態振型、系統矩陣(質量、阻尼及勁度矩陣)。 另外,為了驗證描述子狀態空間方程組可有效地應用於自由響應及強迫響應資料的識別,文中透過一個三自由度系統,在加速度的量測條件下及加入不同程度的雜訊以測試描述子狀態空間系統抗雜訊的能力。為了降低因未知雜訊具隨機散漫性所產生的變動性,因此實行1024次蒙地卡羅模擬來識別,並將識別後的結果來做一個綜合性的比較。最後探討三種不同的實際例,分別為懸臂鋼樑結構、衝擊槌敲擊機車車架結構、強迫振動儀激振機車車架結構來檢驗描述子狀態空間系統在真實結構上的識別能力。
Structural system has its own unique characteristics, which can be abstracted from the interdependence between its input-output information. Measuring the dynamic input and output information of a system to evaluate the associated characteristics can establish the mathematical model required to identify the system. Regarding to the structural system identification procedure, in addition to the second-order matrix differential equations to describe the characteristics of its structure, it can be a first order matrix of differential equations. A first order matrix of differential equations can be one of infinite types. This study propose descriptor systems to set up a first order matrix of differential equations, and further to extend subspace algorithms of descriptor state space systems to identify the structure of system. One type of subspace algorithms is obtained to get descriptor systems from input to output information and further to identify the damping ratio of stucture, its natural frequency, model shape and associated system matrix. In addition to verify the descriptor systems can effectively to free and force vibrations, this study is to use both the acceleration measurement for the system of three degrees of freedom and adding of different signal noise ratio to test the capacity of descriptor systems anti-noise. In order to reduce randomly scattered volatility resulting form an unknown noise, it is to perform Monte Carlo simulation for 1024 times. Finally, it is to discuss three cases, which respectively are cantilever steel beam, impact motorcycle structure and shake motorcycle structure, to test the availability of descriptor state-space system to identify real structures.