摘 要
本論文對頻譜分析技術作進一步的改進與利用。分為三部份：信號參數評估、頻譜分析的最佳化及電機狀況監視。研究結果對現今信號處理的理論與應用提出了完整的改善方法。
參數評估是動態設計、控制和監視的基礎。本論文推導一組完整的參數評估方法。以頻域的觀點分析信號參數。在電機領域中最常處理的信號都可以用複數指數型式表示。該信號的參數包含頻率、阻尼、振幅及相位。根據阻尼的存在與否可分為週期性信號及非週期性信號。每個複數指數分量在頻譜將產生所屬的頻帶。該方法利用每個頻帶中最高振幅的刻度為參考，分別求取信號精確的參數。在條件許可下，計算式亦可簡化到相當實用的程度，並維持精確分析的結果。
頻譜分析技術廣泛地應用快速傅立葉轉換(FFT)於時頻轉換的工作。然而數位信號取樣是隨機的，FFT的轉換又有特定的限制。使得信號經由FFT轉換到頻譜上將不可避免地產生誤差。本論文利用最佳化的方法解決頻譜對信號分析所產生的誤差。當頻率刻度符合信號特性時，信號在頻譜中所產生的柵欄效應及洩漏效應將會降到最低的程度。該方法由信號參數評估、最佳刻度參數選取及可調式頻譜等三種新技術所構成。不僅能將信號的參數清楚而精確地顯示在頻譜上，並可維持快速處理的能力。當分析的信號愈複雜，最佳化的結果將受到限制。在這種情況下可針對局部的信號予以明確化，則仍可維持精確的分析結果。
本論文整合監視技術於一種信號的量測上。使監測的信號取樣更簡單、方便。透過聲訊的分析來監視電機機械的運轉狀況及故障診斷。不僅能對其他無法測量的馬達依然能正常偵測，同時也擴大監測的功能。在運轉狀況監視方面，以聲訊的分析監視感應機轉速及輸入功率；在故障狀況辨識方面，辨識系統在不同負載的情況下仍可成功地辨識出不同的故障狀況。辨識系統以類神經網路建立，證實其對辨識能力的提昇。
有關本論文所提的方法，均透過實際而合理的評估，驗證其精確性及實用性。

Abstract
An improvement and more accuracy method for spectrum analysis has been achieved in this thesis. There are three major parts in this thesis: the signal parameter estimation, the optimization of spectrum analysis, and the supervision to electric machinery. All these parts suggest the improvement ways to theories and applications of signal process.
Parameter estimation is the base of dynamic designs, controls, and supervisions. This thesis infers the complete method to estimate parameters. The method estimates signal parameters in frequency domain. In electric machinery analysis, the most signals can consist of complex exponents. The component parameters include frequency, damping, amplitude, and phase. Basing on the damping existed or not, signals can be classified into two parts: periodic and non-periodic. Each complex exponent component will produce its band on spectrum. This method references the scales with highest amplitudes to estimate exact parameters. In suitable conditions, these mathematical equations can be simplified substantially to save computing time.
The developed technologies of spectrum analysis take FFT to deal with the time-frequency transform work extensively. However, the sample of discrete signal is at random, and FFT suffers specific restrictions. When FFT transforms signal into frequency domain, the signal will cause errors on spectrum inevitably. This thesis corrects the errors by the optimization method. When frequency scales can match with signal characteristics, the picket-fence effect and leakage effect that the signal caused on spectrum will decrease to minimum. This method consists of three new technologies: parameter estimation, selection for optimal scale parameters, and adjustable spectrum. The method not only displays signal parameters on spectrum exactly and clearly, but also keeps the ability of fast process. When analyzing the more complex signal, the result of optimization will be restricted. Under this condition, the method can focus on the partial components and analyze them, then the result will keep accurate.
This thesis combines supervisory technologies via a signal measurement. The signal sampling of these technologies is more convenient and simple. The system monitors operating conditions and fault conditions of the electric machinery with sound signal analysis. This signal analysis not only keeps normal measurement in the place which other signals can’t be detected, but also can expand the monitoring ability. In operation conditions, the system monitors the speed and the input power of electric machinery through sound signal analysis. In fault conditions, the system recognizes type of fault under variation loads successfully. The recognition system is established by artificial neural network. The improvement of recognition ability is also discussed in this thesis.
The methods discussed in the thesis give powerful estimation method for the signal analysis accurately and practically.

目 錄

頁次

目錄 …………………………………………………………... …………………. I
圖目錄 ……………………………………………………………………………. VI
表目錄 ………………………………………………………………….………… X
摘要 ………………………………………………………………………………… XI
Abstract ……………………………………………………………………………. XII

第一章 緒論 ………………………………………………………………….. 1
1.1 研究背景與目的 …………………………………………… 1
1.2 創新與貢獻 …………………………………………………. 3
1.3 內容概述 ……………………………………………………… 4

第二章 頻譜分析技術及其限制 …………………………..……… 7
2.1 前言 ……………………………………………………….…… 7
2.2 頻譜分析的演化 …………………………..……………… 8
2.2.1 傅立葉級數 ………………………….………………… 8
2.2.2 離散傅立葉轉換 ……………………………………… 9
2.2.3 頻譜參數及其影響 …………………………………… 10
2.2.4 快速傅立葉轉換 ……………………………………… 11
2.3 FFT造成的誤差 …………………………………………… 12
2.3.1 理想的頻譜分析 ……………………………………… 13
2.3.2 柵欄效應 ……………………………….……………… 14
2.3.3 洩漏效應 ……………………………….……………… 14
2.3.4 混疊效應 ……………………………….……………… 16
2.3.5 非週期性信號 …………………….…………………… 16

第三章 信號參數評估 …………………………..……………………… 18
3.1 前言 …………………………………………….……………… 18
3.2 諧波的參數評估 ……………..…………………………… 21
3.2.1理論 ……………………………………………………… 21
3.2.1.1 諧波對頻譜刻度的影響 ………………………… 21
3.2.1.2 參數評估 ………………………………………… 23
3.2.1.3 干擾去除 ………………………………………… 25
3.2.2 程序 ………………………………………………..…… 26
3.2.2.1 處理步驟 ………………………………………… 26
3.2.2.2 特殊情況 ………………………………………… 27
3.2.3 評估 ………………………………..…………………… 27
3.2.3.1 精確度 …………………………………………… 28
3.2.3.2 處理速度 ………………………………………… 28
3.2.3.3 分析限制與解決方法 …………………………… 30
3.2.3.4 實際應用 ………………………………………… 30
3.2.4 不同分析方法的比較 …………..…………………… 31
3.2.4.1 準牛頓法 ………………………………………… 32
3.2.4.2 群集諧波法 ……………………………………… 33
3.2.4.3 FFT插值法 …………………………….………… 33
3.3 複數指數的參數評估 ……………….…………………… 36
3.3.1理論 ……………………………………………………… 36
3.3.1.1 複數指數對頻譜的影響 ………………………… 36
3.3.1.2 參數評估 ………………………………………… 38
3.3.1.3 干擾去除 ………………………………………… 40
3.3.2 程序 …………………………………………………..… 40
3.3.2.1 處理步驟 ………………………………………… 41
3.3.2.2 特殊情況 ………………………………………… 42
3.3.3 評估 …………………………………………………..… 43
3.3.3.1 精確度 …………………………………………… 43
3.3.3.2 處理速度 ………………………………………… 43
3.3.3.3 限制與解決方法 ………………………………… 44
3.3.3.4 實際應用 ………………………………………… 46
3.4 計算式的簡化 ……………………………………….……… 48
3.4.1 簡化的條件 ……………………………….…………… 48
3.4.2 諧波參數的求解 ……………………………………… 48
3.4.3 複數指數參數的求解 …………..…………………… 49
3.4.4 殘項補償 ……………………………….……………… 50
3.4.5 評估 …………………………………………..………… 52
3.4.5.1 誤差 ……………………………………………… 52
3.4.5.2 精確度的提昇 …………………………………… 57
3.5 頻帶放大技術 ………………………….…………………… 59
3.5.1 頻率解析度對頻譜分析的影響 ………….……..… 59
3.5.2 傳統的頻帶放大技術 …………………..…………… 59
3.5.3 取樣週期擴充法 ……………………………………… 60
3.5.4 能力評估 ……………………….……………………… 60


第四章 頻譜分析的最佳化 …………………………..……………… 62
4.1 前言 ……………………………………………………….…… 62
4.2 最佳刻度參數選取 ……………….……………………… 65
4.2.1 最佳化的現象 ………………………………………… 65
4.2.2 最小洩漏量 ………………………….………………… 66
4.2.3 程序 …………………………………………..………… 69
4.2.4 評估 …………………………..………………………… 69
4.3 可調式頻譜 ……………………………….………………… 72
4.3.1 理論 ……………………………………..……………… 72
4.3.1.1 刻度間隔的調整 ………………………………… 72
4.3.1.2 刻度位移的調整 ………………………………… 73
4.3.1.3 可調式頻譜的演算流程 ………………………… 74
4.3.2評估 ……………………………….……………………… 74
4.3.2.1 刻度間隔改變的影響 …………………………… 74
4.3.2.2 刻度位移改變的影響 …………………………… 76
4.3.2.3 最佳化的解 ……………………………………… 78
4.3.2.4 處理速度………………………………………… 78
4.3.2.5 不同頻率刻度對信號的解析…………………… 79
4.4 最佳化法 …………………………..………………………… 81
4.4.1 程序 ………………………………………………..…… 81
4.4.2 評估 ……………………………………..……………… 82
4.4.2.1 諧波參數評估 …………………………………… 82
4.4.2.2 最佳刻度參數選取 ……………………………… 83
4.4.2.3 可調式頻譜 ……………………………………… 84
4.4.2.4 速度 ……………………………………………… 85
4.4.2.5 限制 ……………………………………………… 85
4.4.3 不同方法的比較 ……………………………………… 86
4.4.3.1 原取樣信號 ……………………………………… 86
4.4.3.2 視窗法 …………………………………………… 88
4.4.3.3 零補位法 ………………………………………… 90
4.4.3.4 整數週期擴充法 ………………………………… 92
4.4.3.5 最佳化法 ………………………………………… 93
4.4.4 應用 ……………………………………..……………… 95
4.4.4.1 簡單的情況 ………………………….……… 95
4.4.4.2 特徵分析 ………………………..…………… 95
4.4.4.3 頻帶分析 ……………………………..……… 98

第五章 電機狀況監視 ……………………………..…………………… 99
5.1 前言 …………………………………………….……………… 99
5.2 聲音信號的處理 ………………..………………………… 101
5.2.1 頻帶的漂移 ………………………….………………… 104
5.2.1.1 波峰頻率的計算 ………………………………… 104
5.2.1.2 頻率軸等比校正 ………………………………… 106
5.2.2 振幅的變化 ……………………………………….…… 107
5.2.2.1 負載分段 ………………………………………… 107
5.2.2.2 特徵萃取 ………………………………………… 107
5.2.3 評估 ………………………………………….….……… 110
5.2.3.1 頻率軸等比校正的結果 ………………………… 110
5.2.3.2 負載分段的結果 ………………………………… 110
5.2.3.3 特徵萃取的結果 ………………………………… 110
5.3 類神經網路與辨識系統 ……………………..………… 115
5.3.1 類神經網路 ………………………………….………… 115
5.3.2 辨識系統 ……………………………………….……… 118
5.3.3 訓練與辨識 ………………………………….………… 119
5.3.3.1 訓練過程 ……………………….……………… 119
5.3.3.2 辨識過程 ………………………………………… 121
5.4 設備架構 ………………………………………..…………… 122
5.5 運轉狀況監視 …………………………….………………… 123
5.5.1 資料庫建立 …………………………….……………… 123
5.5.2 波峰頻率所對應的轉速 ………….………………… 124
5.5.3 結果與討論 ………………………………………….… 125
5.5.3.1 轉速的偵測 ……………………………………… 125
5.5.3.2 輸入功率的偵測 ………………….…………… 126
5.6 故障狀況辨識 ……………………….……………………… 127
5.6.1 處理程序 …………………………………….………… 127
5.6.2 參數設定 ………………………………….…………… 129
5.6.2.1 狀況模擬 ………………………………………… 129
5.6.2.2信號處理的參數設定 ……………………….… 129
5.6.2.3 訓練樣本與辨識樣本 …………………………… 129
5.6.2.4 類神經網路的參數設定 ………………………… 131
5.6.3 結果與討論 …………………………….……………… 132
5.6.3.1 辨識率 …………………………………………… 132
5.6.3.2 不同方法的比較 ………………………………… 134
5.6.3.3 不同對象的適應 ………………………………… 136

第六章 結論與研究展望 …………………………….………………… 138
6.1 結論 ……………………………………………….…………… 138
6.1.1 信號參數評估 ………………………….……………… 138
6.1.2 頻譜分析的最佳化 …………………………………… 139
6.1.3 電機狀況監視 ……………………………………….… 140
6.2 未來研究展望 …………………………………….………… 142
6.2.1 時域的參數評估 ……………………………………… 142
6.2.2 系統模型參數的建立 …………..…………………… 142
6.2.3 電磁信號分析在監測系統上的應用 ……..……… 142

參考文獻 …………………………………………………………..…………… 144
附錄一 週期信號參數計算式的推導 ……..…………………… 149
附錄二 複數指數參數計算式的推導 ………..………………… 155
附錄三 最小洩漏量的推導 …………………………………..……… 163
發表著作……………..…………….………………………………..…………… 167
作者簡歷……………………………………………………………..…………… 168

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