近年來，如何提取有效的資料以及移除冗餘的雜訊逐漸成為研究焦點。對於各種的工程分析而言，資料壓縮是不可或缺的，有效率的壓縮方式將對各種工程研究有助益。數位影像相依性(Digital Image Correlation)演算法系統是一種基於雙數位相機的立體視覺量測系統，該系統已經被廣泛的應用在力學的應變分析上，因為其可以直接量測選取區域之位移場的簡便性。目前，這項量測系統已經逐漸被應用於動態的工程量測上，但正是由於測量儀器是數位像相機而又產生了新的問題。其中最主要的問題就是資料量變成非常龐大，通常會有幾千個資料點的時序資料肇因於高取樣頻率、高空間解析度以及長取樣時間的要求。在本研究中，主要探討如何有效的壓縮立體視覺數位影像相依性系統所量取的位移場圖序列。作為一種非接觸的光學全域量測技術，立體視覺數位影像相依性系統的應用越來越廣泛。本論文中提出應用稀疏表示來處理由立體視覺數位影像相依性系統量測所產生的龐大資料。目標是發展能夠保留位移場圖中的細部資訊以及維持形狀描述子(Shape Descriptor)表示的簡潔性。此研究中提出了兩個有效的資料壓縮方法基於知名的K-SVD演算法以及壓縮感知(Compressed Sensing)技術來算出具有代表性又簡潔的資料表示。
首先，本研究提出一種新的演算法來有效的處理全域的資料，藉由資料本身的特性以及結合形狀描述子與格拉姆-施密特單範正交化(Gram-Schmidt Orthonormalisation)，使表示資料的基底函數數量減少，但仍可建立更簡潔的分解。在模擬與實際量測的案例中，資料大小與訊號數量的壓縮比都有明顯提升，顯示了本演算法的有效性。新基底函數的資料表示所重建的位移場圖，符合了指定的相依性係數的閥值條件。
另外，通常在工作結構的監測中，會量測很多組的資料，可能會造成資料傳輸以及儲存的問題，這個問題尤其明顯當量測儀器是數位相機時，也就是立體視覺數位影像相依性系統。一張位移圖有數千個量測點，一組有意義的量測通常包含數千張位移場圖，而通常為了降低雜訊的影響，振動量測又會測量數組的數據，如此大量的資料必須要以有效率的方式處理，以方便之後的遠端重建與分析，尤其是操作模態分析(Operational Modal Analysis)。本研究正是因為此需求而提出結合形狀描述子與壓縮感知的資料壓縮方法，因為只使用壓縮感知技術並不能更有效的壓縮資料。本整合的方法被示範應用於部分可觀測的工業電路板之分析上，用操作模態分析藉由l_1最佳化壓縮與重建位移場圖。壓縮與重建的流程可於該例子中瞭解，而其壓縮效果更勝單獨使用形狀描述子方法，且從操作模態分析結果中，可以驗證壓縮感知重建的資料保留了原始資料的核心資訊。
總結，基底函數更新演算法是一個有效降低用於表示之基底函數數量的工具，並且其產生的基底函數更適合應用於壓縮立體視覺數位影像相依性系統量測的資料上，該演算法能夠由初始基底函數更新，進而找到一組有代表性的形狀基底函數去代表位移場圖。另一方面，整合壓縮感知與形狀描述子的方法提供了一種新的方式去提取量測資料中的核心資訊，這種後處理的技術不只提升了壓縮比，也提供了結構健康監測(Structural Health Monitoring)新的可行性。

The extraction of useful information and removal of redundant noise from data has become a major research topic in recent years. Data compression is necessary for all kinds of analysis, and the demand for efficient compression techniques has gained much attention. Digital image correlation (DIC) is a camera-based, optical measuring system, which has been widely applied in strain analysis because of the convenience of measuring displacement fields by simply selecting a region of interest. Currently, there is interest in applying such methods to engineering structures in dynamics. However, one of the major issues related to the integration of camera-based systems with dynamic measurement is the generation of huge amounts of data, typically extending to many thousands of data points, because of the requirements of high sampling rate, spatial resolution, and long duration of recording. In this study, the problem of data compression of displacement maps from 3D-DIC measurement is addressed. As a non-contact optical full-field measurement technique, 3D-DIC displacement measurement is becoming more widely applied to various kinds of dynamic issues. The research presented in this thesis attempts to apply the algorithms of sparse representation to deal with the huge amount of data acquired from 3D-DIC measurement. It aims to develop methods that have the capability of preserving nuances of displacement measurement and retaining the compactness of shape descriptor (SD) decomposition. Accordingly, two useful compression methods based upon the well-known K-SVD algorithm and compressed sensing (CS) method are developed for the purpose of a succinct and representative decomposition of displacement maps from 3D-DIC measurement.
Firstly, a new algorithm is presented that addresses the need for efficiency in full-field data processing. By making use of the data itself and combining the concept of SD representation with Gram-Schmidt orthonormalisation (GSO), the number of basis functions used to represent the data can be reduced and a concise decomposition established. In both simulated and experimental cases, the compression ratios for data size and number of signals used in operational modal analysis are substantially diminished, thereby demonstrating the effectiveness of the proposed algorithm. A reduced number of new basis functions is determined for the representation of data under the condition that the reconstructed displacement map reproduces the raw measured data to within a chosen threshold of correlation coefficient.
Secondly, the monitoring of an operating structure usually dealing with multiple set of data, which could pose an issue for transmission or storage and is particularly important when data acquisition is implemented with cameras, such as 3D-DIC system. Single images regularly extend to tens or even hundreds of thousands of data points and many thousands of images may be required for a single set of vibration tests. Such data must be handled efficiently for later remote reconstruction and analysis, typically OMA. It is this requirement that is addressed and solved by the integrated SD-CS method because CS alone is found to be prohibitively expensive for the processing of many thousands of camera images. Data reduction by a combination of SD decomposition and CS is applied to an industrial printed circuit board and reconstructed for OMA by l_1 optimisation. This procedure is demonstrated on industrial DIC data from a partially observed printed circuit board and further significant compression, which is beyond the reduction effect provided by SD method alone, is achieved and OMA is carried out successfully on CS-recovered data.
In summary, the basis-updating algorithm is a powerful tool for the adaptation of kernel functions to the data set collected by 3D-DIC displacement measurement system. The algorithm is capable of finding a representative set of shape descriptors for displacement maps from an initial basis. On the other hand, the integration of CS theory and SD method offers a new way to extract the core information from the measured data. This post-processing technique not only improves the compression ratio but also provides the possibility of structural health monitoring.

Abstract I
摘要 IV
Acknowledgement VI
Contents VII
Nomenclature XI
Acronyms XV
List of Figures XVII
List of Tables XXI
1 Introduction 1
1.1 Problem overview 1
1.2 Objective of the study 1
1.3 DIC method 2
1.4 Operational modal analysis (OMA) 3
1.5 Full-field shape-descriptor method 4
1.6 Compressed sensing 5
1.7 Outline of the thesis 5
1.8 Contribution by the author 7
2 Literature Review 10
2.1 Digital image correlation (DIC) 11
2.2 Operational modal analysis (OMA) 14
2.2.1 Time-domain methods 14
2.2.2 Frequency-domain methods 15
2.3 Shape descriptors (SD) 17
2.4 Compressed sensing (CS) 18
2.5 Closure 20
3 Digital Image Correlation 22
3.1 2D and 3D DIC system 22
3.2 The geometric optics behind 3D DIC system 24
3.3 Local and global DIC algorithms 27
3.4 The local correlation algorithm 28
3.5 Closure 30
4 Operational Modal Analysis 32
4.1 Linear equation of motion (EoM) 32
4.2 Continuous-time deterministic state-space model 32
4.3 Discrete-time stochastic state-space model 33
4.4 OMA methods 34
4.4.1 Time-domain method 35
4.4.2 Frequency-domain method 39
4.4.2.A Frequency-domain decomposition (FDD) method 39
4.4.2.B Poly-reference least square complex frequency-domain (P-LSCF) method 41
4.4.2.C Bayesian method 44
4.5 Closure 47
5 Decomposition of Images by using Shape Descriptors 49
5.1 Image decomposition and reconstruction 50
5.2 Geometric moment descriptor 51
5.3 Tchebichef moment descriptor 54
5.3.1 Theory 54
5.3.2 Example 57
5.4 Zernike moment descriptor 61
5.4.1 Theory 61
5.4.2 Example 62
5.5 Adaptive geometric moment descriptor (AGMD) 67
5.5.1 Theory 67
5.5.2 Example 71
5.6 Closure 76
6 Basis-Updating Algorithm 78
6.1 Basis learning & sparse representation 79
6.2 K-means & K-SVD 81
6.2.1 K-means algorithm 81
6.2.2 K-SVD algorithm 83
6.3 Basis-updating algorithm 85
6.4 Analysis procedure 87
6.5 Case Studies 88
6.5.1 Simulated data 88
6.5.2 Experimental PCB circuit board 90
6.6 Result and discussion 91
6.6.1 Simulated data 91
6.6.2 Printed circuit board (PCB) 96
6.7 Closure 103
7 Compressed Sensing 105
7.1 Compressed sensing theory 105
7.2 Experimental case study 110
7.3 CS procedure 111
7.4 CS of a single image 114
7.5 CS for OMA 118
7.6 Closure 122
8 Conclusion and Future Studies 124
8.1 Conclusions 124
8.2 Future studies 126
Appendices 129
A. Basic Mathematical Definitions 129
A.1 Gram-Schmidt orthonormalisation (GSO) 129
A.2 The Norm of a Vector (or Matrix) 130
A.2.1 l_p vector norm 130
A.2.2 l_0 vector norm 131
A.2.3 Frobenius matrix norm 131
B. Verification of OMA methods 133
C. Conference Paper C1 143
D. Journal Paper J1 145
E. Journal Paper J2 147
Reference 149

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