臺灣博碩士論文加值系統

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.

中文摘要 I
Abstract II
謝誌 III
目錄 VI
圖目錄 IX
表目錄 XIV
簡稱術語對照 XVI
符號說明 XVII
第一章 導論 1
1.1研究動機與方向 1
1.2文獻回顧 2
1.3論文章節架構 5
第二章 非線性結構系統之特性研究 7
2.1線性與非線性結構系統 7
2.2微擾法求非線性無阻尼系統之振盪頻率 11
2.3廣義頻率響應函數 15
2.3.1伏爾泰拉級數及廣義頻率響應函數 15
2.3.2微分方程之廣義頻率響應函數 18
2.3.3差分方程之廣義頻率響應函數 19
2.4非線性系統特性分析理論 21
2.4.1諧波特性理論 23
2.4.2增益壓縮或擴張特性理論 27
2.4.3互抑特性 28
2.5非線性結構系統受雜訊干擾下之影響 30
第三章 狀態空間系統識別理論 38
3.1狀態空間系統 38
3.2 ARX模型轉換至離散狀態空間系統 39
3.3凝縮理論及連續/離散狀態空間系統 42
3.4矩陣轉換法 46
3.5狀態空間系統識別流程 50
第四章 NARX模型及非線性結構系統識別理論 51
4.1 NARMAX與NARX模型 51
4.2 NARX模型之正交參數估計 52
4.3非線性結構系統識別理論 55
4.3.1概念闡述 55
4.3.2非線性特徵參數識別公式 55
4.3.3非線性結構系統識別流程 61
第五章 非線性結構系統之數值模擬 62
5.1單自由度非線性結構系統識別模擬與分析 62
5.1.1單自由度非線性具阻尼之自由振動系統識別 63
5.1.2單自由度非線性具阻尼之強迫振動系統識別與特性分析 66
5.2三自由度非線性結構系統識別模擬 80
5.2.1三自由度非線性具阻尼之自由振動系統識別 81
5.2.2三自由度非線性具阻尼之強迫振動系統識別 84
第六章 實際結構物識別之應用分析 89
6.1直立式懸臂鋼樑結構 89
6.1.1直立式懸臂鋼樑結構理論解 90
6.1.2直立式懸臂鋼樑結構識別與結果討論 93
6.2國家地震工程研究中心之五層樓縮尺鋼架結構 99
第七章 結論探討與未來展望 108
7.1結論探討 108
7.2未來展望 110
參考資料 112

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