本研究發展一套數值方法配合便宜的電容式麥克風數據搜集系統以量測與分析聲音訊號，及用來偵測振動和流場訊息。硬體部份由個人電腦或筆記型電腦、類比數位轉換音效卡、以及小型電容式麥克風等所組成。所需的軟體為電腦中植入的軟體及公用Goldwave軟體。後處理工具包括使用一組快速擴散型濾波器作為數據串所隱含的趨勢線之移除器、傅氏正弦頻譜產生器、修正型Gabor轉換式、以及Hilbert轉換式。其中快速擴散型濾波器和修正型Gabor轉換式是本研究以解析方式所推演的新方法。
本研究中的濾波器是一種疊代式擴散型濾波器，不會引入非物理的相角偏移。假設數據串之趨勢線可用一個有限階的多項式表示之，則可用不同階之濾波器經有限次數之疊代後，完全移除之。濾波器之階次、濾波過渡區寬度、允許誤差、疊代次數、及平滑參數等由兩個方程式組合的聯立方程式所限制而形成一族的解。因為可以在頻譜空間解之，一旦這些參數給定之後，所需的計算時間比使用兩次快速傅氏轉換多一些，所以是快速濾波法。本研究的濾波器經使用一個測試函數作數值實驗，可以找出一組產生最小誤差的非疊代式濾波器。
使用一組設定的函數測試之數值實驗證明，該組濾波器之準確度比現有的數個趨勢線移除法準確度都高。數個著名的實例應用也顯示本組濾波器所拆出的趨勢線和使用這些方法之結果差異不大。使用本濾波器的過程簡易，而其它方法則需經過冗長的試誤過程才能得到合理的結果。
本研究所提出的時頻轉換式使用和加上高斯窗之原始Gabor轉換式略為不同的公式。經過離散傅氏級數展開後，修正型Gabor轉換式近似於將傅氏頻譜加上對應的高斯窗，其誤差小於 。此一近似轉換沒有積分的截尾誤差，只有再加上有效位數的捨去誤差。使用含有許多傅氏波組且頻率極為相近之實例測試，發現新轉換式可以捕捉到這些波的組合波組之振幅呈現振盪的group velocity現象，但原Gabor轉換式未能捕捉到此一現象，可見新轉換式避開了原Gabor轉換式的過度壓縮功能。
在驗證的過程中，本研究使用加速規量測一個振動器的訊號，驗證了麥克風聲音數據搜集系統可以正確地捕捉到振動器的主要頻率，也可以得到許多較細小的訊號。本研究亦設計一套實驗驗證方法，將光碟片鑽一小孔，一端貼上小型揚聲器，另一端貼上小型麥克風。實驗結果證明可以清楚地捕捉到0.5至10Hz的低頻聲音訊息。若將此麥克風的塑膠外套移除，直接將麥克風之收音孔的那一面貼到被測物之表面，也可以捕捉到兩個實例的極低頻訊號。
本研究應用此一麥克風聲音數據搜集系統量測三個無人飛機的訊息，以進行其內涵資訊之分析。從小型電動直升機的訊號，捕捉到很多振動訊息。因為能夠捕捉到次頻訊號，而可以證實該直升機處於良好狀態。無人飛機的例子也拆解出許多引擎操作時的訊息，可清楚的表達出起飛時的加速滑行和離地訊息。從無人遙控直升機的訊號量測與分析過程中，除了可獲知許多引擎振動訊號，更可捕捉到陣風將層流旋翼流場轉變為紊流的狀態時的資訊。
總結測試驗證，由本研究開發的數學方法中用解析法推導新的濾波器和時頻轉換，可以測試證明適用於0.5至20KHz的聲音訊號做可靠的分析。因為這是一種可攜式的非接觸性數據搜集系統，其機動性極高，相信它未來能夠廣泛的推廣到許多有關訊號分析的工程應用之中。

A numerical algorithm equipped to a cheap data acquisition system which using a small electret condenser microphone has been developed. The hardware includes a personal or notebook computer, it’s built-in Analogy to Digital (A/D) converting board, and a small microphone. The software used for data acquisition are Goldwave software and built-in software of the computer. The software of post processing involves: a class of fast and diffusive filter to service as the trend removal, the Fourier sine spectrum, the modified Gabor transform and the Hilbert transform. Among these tools, the diffusive filter and modified Gabor transform are both analytically developed in this dissertation.
The responses of the filters expressed in analytic forms are proven to be diffusive in this dissertation. If it is a polynomial of finite degree, the embedded trend can be decoupled by the filters with specific order and iteration steps. The filters’ order, transition zone, error tolerance, iteration number and smoothing factor are subject to two algebraic equations to form a specific class. The operation counts of all filters are slightly larger than twice that applying a fast Fourier Transform (FFT). It has been numerically shown for a given transition zone and tolerance, there is a filter generating the shortest error penetration distance among all the filters.
The accuracy of these filters has been proved successfully by numerical testing cases. For a specified signal, the accuracy of the results offered by the proposed fast filter is better than those by using existing trend removals. On several applications show that all the trends extracted by the proposed tool do not deviate much from the results offered by the existing tools. Moreover, the proposed filter is much simpler than all the other tools which require lengthy try and error procedure to attain reasonable results.
The proposed time-frequency transform is slightly different from the original Gabor transform with the Gaussian window. In terms of the discrete Fourier series expansion, the results from the modified transform are proven to be almost equal to the results by imposing an associated Gaussian window to the Fourier spectrum. The proposed transform has a relative error less than and is free from the integration error. The test data of a vibration exciter shows that this algorithm the group velocity property is properly captured. The original transform miss this capability so that it introduces excessive compression to these Fourier modes.
In order to examine the effective frequency response in the extremely low frequency region, a specific experimental setup was designed. It is a tiny air cell constructed by drilling a small hole in a digital versatile disk (DVD) plate and a small speaker as well as an electret condenser microphone is attached to the opposite sides of the plate on the hole. The results show that it can resolves the signal in the range of 0.5 to 20 Hz. Moreover, by removing the plastic cover of the microphone and attaching the microphone head to the vibration surface, the lower frequency signal can be effectively resolved too.
The proposed system was used to examine the operation of three unmanned aircrafts. The resulting spectrum and spectrogram of the measured acoustic data capture a great deal of information concerning the dominate modes and corresponding harmonics which clearly show that the operating conditions. On the examination of datum from a small electrical helicopter and an Unmanned Aerial Vehicle (UAV) confirms that both are in good operational states. The test results of an unmanned helicopter can even resolving the characteristics of a flow field. All the results indicate that the proposed algorithm can monitor the operation and health conditions of a system.

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