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  本文選題：小波變換　切入點：提取相位　出處：《煙臺大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在高速流場測量等領(lǐng)域,常用干涉法得到條紋圖,通過提取干涉條紋的相位進而得到所需待測信息,因此研究干涉條紋圖相位的提取具有非常重要的意義。本文主要研究了高速流場中干涉條紋圖相位的提取,主要內(nèi)容包括以下幾個方面:(1)介紹了幾種目前常用的提取干涉條紋圖相位的方法,主要有相移法、傅里葉變換法和時頻分析法,其中,時頻分析法中介紹了加窗傅里葉變換法和小波變換法。介紹了每一種算法的優(yōu)點,同時總結(jié)出相移法、傅里葉變換法及加窗傅里葉變換法提取干涉條紋相位的局限性,最后提出本文所用的二維連續(xù)小波變換法。(2)二維連續(xù)小波變換具有靈活的時頻分析窗,可以實現(xiàn)對信號的多尺度細化分析。為了解決傳統(tǒng)二維連續(xù)小波變換耗時時間長的問題,將傳統(tǒng)二維連續(xù)小波變換算法進行改進,提出將傳統(tǒng)二維連續(xù)小波變換中連續(xù)的尺度因子和旋轉(zhuǎn)角用少量的離散尺度因子和旋轉(zhuǎn)角代替,這樣就大大降低了處理的時間。在計算小波系數(shù)的過程中,由于存在卷積計算而使得計算仍然很耗時,引入了快速傅里葉變換,從而進一步降低處理的時間。在計算得到小波系數(shù)后,通過脊檢測算法找出小波脊,進而得到干涉條紋相位。(3)利用傳統(tǒng)二維連續(xù)小波變換法和本文改進的二維連續(xù)小波變換法首先對計算機仿真干涉條紋圖及實驗得到的干涉條紋圖進行相位提取與分析,然后再利用這兩種算法對高速流場中幾組不同的干涉條紋圖進行相位提取,在提取相位之前,對干涉條紋圖進行中值濾波、同態(tài)濾波及二值化的預(yù)處理過程,然后利用傳統(tǒng)二維連續(xù)小波變換法和本文改進的二維連續(xù)小波變換法分別對干涉條紋圖進行相位提取,通過比較干涉條紋圖在這兩種算法下處理前后的峰值信噪比PSNR和均方根誤差RMSE可以得到在準確性基本保持不變的情況下,本文改進的二維連續(xù)小波變換法是可以準確提取出干涉條紋圖相位的。同時,根據(jù)本文提出的覆蓋圖的方法,大大減少了傳統(tǒng)二維連續(xù)小波變換法計算過程中參數(shù)對的數(shù)量,加快了處理時間。分析結(jié)果表明,本文改進的二維連續(xù)小波變換算法可以快速準確的提取出干涉條紋圖的相位,對于提取高速流場中干涉條紋圖的相位具有一定的可行性。
[Abstract]:In the field of high speed flow field measurement, the fringes are obtained by interferometry, and the information to be measured is obtained by extracting the phase of interference fringes. Therefore, it is very important to study the phase extraction of interference fringes. In this paper, the phase extraction of interference fringes in high velocity flow is studied. The main contents include the following aspects: 1) this paper introduces several commonly used methods for extracting the phase of interference fringes, such as phase-shift method, Fourier transform method and time-frequency analysis method. In time-frequency analysis, the windowed Fourier transform method and wavelet transform method are introduced. The advantages of each algorithm are introduced. At the same time, the limitation of phase shift method, Fourier transform method and windowed Fourier transform method for extracting interference fringe phase is summarized. Finally, the two-dimensional continuous wavelet transform is presented in this paper. The two-dimensional continuous wavelet transform has a flexible time-frequency analysis window, which can realize the multi-scale thinning analysis of the signal. In order to solve the problem of the traditional two-dimensional continuous wavelet transform, it takes a long time. The traditional two-dimensional continuous wavelet transform algorithm is improved, and the continuous scale factor and rotation angle in the traditional two-dimensional continuous wavelet transform are replaced by a small amount of discrete scale factor and rotation angle. In this way, the processing time is greatly reduced. In the process of calculating wavelet coefficients, the computation is still time-consuming due to the existence of convolution calculation, and the fast Fourier transform is introduced. In order to further reduce the processing time. After the wavelet coefficients are calculated, the wavelet ridges are found by ridge detection algorithm. Then the phase of interference fringes is obtained. The traditional two-dimensional continuous wavelet transform method and the improved two-dimensional continuous wavelet transform method are used to extract and analyze the phase of the computer simulation interference fringe image and the experimental interference fringe image. Then the two algorithms are used to extract the phase of several different interference fringes in the high-speed flow field. Before the phase extraction, the median filtering, homomorphic filtering and binary preprocessing of the interference fringes are carried out. Then the traditional two-dimensional continuous wavelet transform method and the improved two-dimensional continuous wavelet transform method are used to extract the phase of interference fringes. By comparing the peak signal-to-noise ratio (PSNR) and root mean square error (RMSE) of interferometric fringe images before and after processing under these two algorithms, we can get that the accuracy is basically unchanged. The improved two-dimensional continuous wavelet transform method can accurately extract the phase of interference fringes. At the same time, the number of parameter pairs in the calculation process of traditional two-dimensional continuous wavelet transform method is greatly reduced according to the method of covering image proposed in this paper. The analysis results show that the improved two-dimensional continuous wavelet transform algorithm can extract the phase of interference fringes quickly and accurately, and it is feasible to extract the phase of interference fringes in high-speed flow field.
【學(xué)位授予單位】：煙臺大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O436.1

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