臺灣博碩士論文加值系統

雖然，電腦蓬勃發展而大幅提升了工程師的分析和設計能力，但是工程師仍然完全受限於處理龐大且複雜的系統行為。如土木工程之結構。根據量測所得之反應資料，藉由正確分析系統之模型可識別出系統之特性。此外，識別所得的資料，可用來評估系統之損害。
在本研究中，分別以時間序列模型─ARX、ARMAX及狀態空間模式來描述輸入與輸出間之關係。當量測反應資料含有雜訊時，以傳統最小平方法及迭代工具變數法配合ARX模型皆無法準確地識別系統之動態特性。為了改進前述之問題，提出一平穩估算程序。平穩估算程序配合ARX與ARMAX模型，可有效求解AR部分之係數矩陣。再藉由Ibrahim時間域識別法之觀念估算結構之動態特性。本文亦應用現代控制學所發展之次空間法於土木工程，並利用狀態空間模式識別結構之動態特性。
藉由兩組數值模擬來驗證本文所提出的方法。其一是六層樓剪力建築物受一地震輸入；其二是三跨連續橋樑受多支承運動。在這些數值模擬中，並探討雜訊、量測自由度之數目與不完整之量測輸入源對識別動態特性之影響。最後，將以研究所提出之方法來識別三種不同形式之五層樓鋼構於振動台試驗的動態特性。

In this research, time series models such as the ARX and ARMAX models and state-space model were applied to describe the relationship between input and output. The traditional least-square approach and iterative instrumental variable approach do not provide accurate results of dynamic characteristics of structural system from the ARX model when the measured responses are contaminated by noises. A stationary approach was developed to remedy such problem. This procedure cooperates with the ARX and ARMAX models to effectively evaluate the coefficient matrices of the AR part, then estimates the structural dynamic characteristics by adopting the concept behind the Ibrahim’s time domain identification technique. A subspace method developed by researchers in control field was also adopted and modified to estimate the structural dynamic characteristics by using state space model.
To verify the capacity of the proposed procedures, two groups of numerical simulations were made. One considered a six-floor shear building subjected to base excitation generated by a real earthquake record. The other considered a three-span continuous bridge subjected to multiple support motion. In these case studies, the effects of noise, number of measured degrees of freedom, and incompleteness of input on identifying the dynamic characteristics were investigated. Finally, the proposed procedures were applied to identify the dynamic characteristics of three five-story steel frames from the responses of shaking table tests.

第一章 緒論 1
1.1 前言 1
1.2 研究動機與內容 1
1.3 文獻回顧 3
第二章 多變數ARX模式系統識別 6
2.1 ARX數學模式 6
2.2 ARX模式與結構系統運動方程式之對應 7
2.2.1 單自由度系統 7
2.2.2 多自由度系統 8
2.3 建模 10
2.3.1 傳統最小平方差法 10
2.3.2 工具變數法(Instrumental Variables Method) 11
2.3.3 平穩最小平方差法 14
2.4 結構系統動態特性之估算 16
2.5 數值模擬 19
2.5.1 傳統最小平方差法之識別結果 20
2.5.2 工具變數法之識別結果 21
2.5.3 平穩最小平方差法之識別結果 22
2.5.4 雜訊之影響 22
2.5.5 量測自由度之影響 23
第三章 多變數ARMAX模式系統識別 43
3.1 ARMAX數學模式 43
3.2 ARMAX模式與結構系統運動方程式之對應 44
3.3 建模 45
3.3.1 迭代法 45
3.3.2 兩階段最小平方差法 47
3.3.3 平穩最小平方差法 51
3.4 結構系統動態特性之估算 53
3.5 數值模擬 53
3.5.1 迭代法之識別結果 54
3.5.2 兩階段最小平方差法之識別結果 54
3.5.3 識別動態特性之平穩最小平方差法 55
3.5.4 雜訊之影響 55
3.5.5 量測自由度之影響 56
第四章 狀態空間模式 67
4.1 狀態空間數學模式 67
4.2 狀態空間模式與結構系統運動方程式之對應 68
4.3 狀態空間模式與時間序列模式之關係 71
4.4 建模 75
4.5 結構系統特性之估算 86
4.6 數值模擬 89
4.6.1 自由度縮減之影響 89
4.6.2 雜訊之影響 90
第五章 實測資料分析 94
5.1 待測結構物 94
5.2 輸入之地震力 95
5.3 識別動態特性 95
5.3.1 識別同一構架不同地震形式之動態特性 96
5.3.2 不同構架之識別結果 97
第六章 多重輸入╱多重輸出數值模擬與識別 130
6.1 橋樑受多支承運動反應之數值模擬 130
6.1.1 多支承運動反應之解 130
6.1.1.1 擬靜力反應解 131
6.1.1.2 動力反應解 132
6.2 多支承輸入地震歷時之模擬 135
6.3 識別結果 139
第七章 結論及建議 163

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