臺灣博碩士論文加值系統

源自於模型的不確定性與量測的不確定性，本研究提出一個希爾伯特黃轉換的信號過濾技術，透過振動測量數據作為結構系統的危險評估並且為公眾的福祉用於現代經濟之診斷。
希爾伯特黃轉換技術是一套高階的演算法對於分析非線性和非穩態信號。然而信號被濾出後，靠著從”被選擇的”內建模態函數進行重建，這一些導源於以經驗模態分解原始信號。這先進的過濾技術提供了準則，經使用內積概念或正交係數來選擇內建模態函數。藉由信號濾波方法，它是可能增加精確性對於時間變化系統的自然頻率估算-顯示結構損害度-其協助有效管理結構物修繕或替換；同樣地，致力於精確的經濟模型提升，這部分為經濟診斷提出合適的函數在於反覆識別系統上，經由希爾伯特黃轉換提升雜訊過濾的論點來診斷國民平均生產毛額趨向。

Springing from the model uncertainties and uncertainty of measurement, this paper presents a Hilbert-Huang transform based signal filtering technology for the hazard evaluation of structural systems via vibration measurements and the diagnosis of modern economy for public welfare.
The Hilbert-Huang transformation technology is a set of superior algorithms for analyzing non-linear and non-stationary signals. However, the signals are filtered by reconstruction from “selected” intrinsic mode functions (IMFs), which are derived from the original signal through the empirical mode decomposition (EMD) method. The developed filtering technique offers the criterion for selecting the IMFs using the inner dot concept or the orthogonalization coefficient. Through the signal filtering, it is possible to increase the accuracy for the evaluation of the time-varying system’s natural frequency—indicative of the degree of structural damage—which assists an effective management of structural repair or replacement; Similarly, aiming for accurate economy model updating, this part presents the adaptive function based repetitive identification system for economy diagnosis, through the proposition of an enhanced noise filtering of Hilbert-Huang transform (HHT) to diagnose the GDP per capita trend.

中文摘要 I
英文摘要 II
誌謝 IV
目錄 V
表目錄 VII
圖目錄 VIII

第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 2
1.3 研究範圍 3
第二章 文獻回顧 4
2.1 前言 4
2.2 傅立葉轉換 4
2.3 希爾伯特-黃轉換 8
2.3.1 瞬時頻率 8
2.3.2 內建模態函數 10
2.4 經驗模態分解法 13
2.5 完整性與正交性 18
2.6 希爾伯特頻譜 20
第三章 應用於結構系統的危險評估 22
3.1 非線性信號處理 22
3.2 內建模態函數分析 22
3.3 透過信號重建自然頻率的實驗和評估 23
3.4 小結 24
第四章 應用於現代經濟之診斷 26
4.1 前言 26
4.2 經濟的短期趨勢 27
4.3 小結 28
第五章 結論 29
參考文獻 30

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