應用含外變數的非線性自我迴歸模型估算結構系統之線性及非線性特徵參數之研究

Abstract

過去十年來，雖然線性的結構物系統識別發展得相當蓬勃；但往往將非線性因子的響應視作雜訊干擾或忽略不計。因此，本文即是要應用含外變數的非線性自我迴歸模型，推導出非線性特徵參數識別公式，再配合狀態空間系統識別理論，成功地識別出非線性結構物系統之線性與非線性特徵參數。本文也將探討線性與非線性之異同，以及透過伏爾泰拉級數推導廣義頻率響應函數，並建立在廣義頻率響應函數的基礎上，分析非線性結構物系統特性等。 最後以本文所提出之非線性系統識別流程，透過電腦分別模擬單自由度與三自由度之自由振動及強迫振動系統識別；另外，兩個實際結構物系統識別例子，其中之一為直立式懸臂鋼樑結構之衝擊測試，另一個為由國家地震工程研究中心提供之地震波測試五層樓縮尺鋼架結構。以上將一併完整地呈現數值模擬與實際識別之結果。

During the past decade, although the linear structural system identification had been well developed, the nonlinear response was often taken as noise or neglected throughout the linear system identification procedure. Therefore, in this thesis, using the NARX (Nonlinear AutoRegressive with eXogenous input) model, a nonlinear characteristic parameters identification formula was derived. And combining with state-space system identification theorem, the linear and nonlinear characteristic parameters were estimated successfully. Furthermore, the differences between linear and nonlinear characteristics were discussed. Using Volterra series, the GFRF (generalized frequency response function) was derived; and basing on the GFRF, the nonlinear characteristics of nonlinear structural systems were examined. In the end, the nonlinear system identification procedure was applied on computer simulations, including free and forced vibrations in single-degree-of-freedom and three-degree-of-freedom structural systems. The procedure was then further applied on two real structural system identification cases, one is the impact test of a vertical cantilever steel beam structure, and the other one is the earthquake shaking test of a Bench-Mark-Model, which was conducted by National Center for Research on Earthquake Engineering of R.O.C. All the results of identifications are represented completely.