EMBEDDED DIGITAL IMAGE CORRELATION IN A FULL-FIELD DISPLACEMENT SENSOR. A Thesis. Presented to. The Graduate Faculty of The University of Akron

Transcription

1 EMBEDDED DIGITAL IMAGE CORRELATIO I A FULL-FIELD DIPLACEMET EOR A Thesis Presented to The Graduate Faculty o The University o Akron In Partial Fulillment o the Requirements or the Degree Master o cience hilpa Kunchum December, 2012

2 EMBEDDED DIGITAL IMAGE CORRELATIO I A FULL-FIELD DIPLACEMET EOR hilpa Kunchum Thesis Approved: Accepted: Advisor Dr. Joan Carletta Dean o the College Dr. George H. Haritos Committee Member Dr. Robert Veillette Dean o the Graduate chool Dr. George R. ewkome Committee Member Dr. Tom T. Hartley Date Committee Member Dr. GunJin Yun Department Chair Dr. Alex De Abreu Garcia ii

3 ABTRACT This thesis presents an embedded implementation o the digital image correlation algorithm, which is used or measuring the ull-ield displacement o the surace o a structure under load. The main goal o this thesis is to develop technology needed or a portable sensing unit or calculating the ull-ield displacement. The portable sensing unit consists o an embedded microprocessor module, a low-cost webcam and a communication module. The digital image correlation algorithm is implemented on an embedded microprocessor module so that it is easily deployable in the ield. The algorithm is written in the C language using ixed-point and loating-point mathematics. The system transmits the measured displacement o 36 surace points wirelessly to the base station via a Bluetooth communication link, which has a transmission range o up to 20 meters. The dierence in the maximum correlation values measured using the DIC algorithm implemented in ixed-point mathematics and the DIC algorithm implemented in loating-point mathematics lies in the range o The execution time taken to calculate displacement o approximately 36 selected coordinates to the nearest integer pixel is around 0.8 seconds on an embedded microprocessor module. This data is based on experiments conducted on a rectangular specimen with and without notches. iii

4 ACKOWLEDGEMET I express my heartelt gratitude to Dr. Joan Carletta, a wonderul advisor and a teacher who has been the guiding orce behind this research work. I also wish to thank Dr. GunJin Yun or all his help during the entire time o the research work. I express my sincere gratitude to Dr. Robert Veillette and Dr. Tom.T.Hartley or their insightul corrections and suggestions. I wish to thank Dr. Alex or granting me with teaching assistantship and Proessor Kult or giving me an opportunity to learn and assist students in the lab which helped me a lot during my study. This research would not have been possible without the help and support rom David McVaney, hen hang, Tom Gambone and hilpa Chakinala. I wish to thank all o them or helping me in various aspects o the research. I wish to dedicate this work to the most important people in my lie, my parents, my brother and Kaushik without whose support and encouragement I would not have made it this ar. Last but not the least I want to thank my riends who have always been there or me. iv

5 TABLE OF COTET... Page LIT OF TABLE... viii LIT OF FIGURE... ix CHAPTER I. ITRODUCTIO Overview Motivation Goals o thesis Organization o thesis...3 II. LITERATURE REVIEW Description o commonly used correlation measures Description o common search strategies Optimization o computation o correlation measures Digital image correlation using FPGA III. EXPERIMETAL ET-UP AD PROCEDURE Experimental set-up The specimen v

6 3.1.2 The ITRO machine The LOGITECH webcam The extensometer The laptop computer The embedded microprocessor module Wireless set-up Experimental procedure IV. IMPLEMETATIO AD VERIFICATIO OF DIGITAL IMAGE CORRELATIO ALGORITHM Details o implementation o the digital image correlation algorithm Fixed-point computation o the correlation measure Rearrangement o terms in correlation measure Fixed-point implementation o the term D Implementation o Implementation o division o by Implementation o the product 35 by Implementation o Veriication o the DIC algorithm implementation V. REULT AD DICUIO vi

7 5.1 Experimental results using the rectangular specimen without notch Experimental results using the rectangular specimen with notches VI. COCLUIO AD FUTURE WORK ummary Future Work BIBLIOGRAPHY vii

8 LIT OF TABLE Table Page 4.1 Correlation values under dierent implementations or a set o ten surace points Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage1) or dierent set o points using laptop computer Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage2) or dierent set o points using laptop computer Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage3) or dierent set o points using laptop computer Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage4) or dierent set o points using laptop computer Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage5) or dierent set o points using laptop computer Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage4) or dierent set o points using embedded microprocessor module Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage5) or dierent set o points using embedded microprocessor module..62 viii

9 LIT OF FIGURE Figure Page 3.1 Block diagram o the experimental set-up with laptop computer Block diagram o the experimental set-up with embedded microprocessor module Dimensions o the specimens in inches:(a) Rectangular specimen without notch (b) Rectangular specimen with notches pecimens considered or evaluating ull-ield dispalcement calculated using DIC algorithm: (a) Rectangular specimen without notch (b) Rectangular specimen with notches Experimental set-up o the rectangular specimen without notch with checker board and extensometer attached Correlation maps using acets o various sizes Diagram representing how to calculate the term Diagram representing how to calculate the term Undeormed and deormed images o the specimen with the selected ten surace points Load pattern o the extensometer Images taken during the experiment with a rectangular specimen without notch using laptop computer...45 ix

10 5.3 Plot showing the ull-ield displacement calculated using DIC at stage1 o the experiment using laptop computer, with respect to the initial stage Plot showing the ull-ield displacement calculated using DIC at stage2 o the experiment using laptop computer, with respect to the initial stage Plot showing the ull-ield displacement calculated using DIC at stage3 o the experiment using laptop computer, with respect to the initial stage Plot showing the ull-ield displacement calculated using DIC at stage4 o the experiment using laptop computer, with respect to the initial stage Plot showing the ull-ield displacement calculated using DIC at stage5 o the experiment using laptop computer, with respect to the initial stage Images taken during the experiment with rectangular specimen without notch using embedded microprocessor module Plot showing the ull-ield displacement calculated using DIC at stage4 o the experiment using embedded microprocessor module, with respect to the initial stage Plot showing the ull-ield displacement calculated using DIC at stage5 o the experiment using embedded microprocessor module, with respect to the initial stage Images taken during the experiment with rectangular specimen with notches using laptop computer Pixel movement or our example surace points on the undeormed image using experimental set-up with laptop computer Images taken during the experiment with rectangular specimen with notches using embedded microprocessor module Pixel movement or our example surace points on the undeormed image using experimental set-up with embedded microprocessor module...69 x

11 CHAPTER I ITRODUCTIO 1.1 Overview Digital image correlation is an optical method that is widely used in many areas o science and engineering to measure deormation on an object surace [9]. Digital image correlation techniques are becoming popular due to the relative ease o their implementation in micro and nano-scale mechanical testing applications [3]. Digital image correlation is used to measure the ull-ield displacement o structures under various load conditions in order to perorm deormation analysis. It involves tracking o points on the surace o a specimen based on the gray scale values o the images taken o the specimen under test. The tracking is done by identiying an area o an image around the surace point o interest, and then inding the area in a second image, taken under dierent loading conditions, that most closely correlates with the irst. Thus, the method can calculate displacement at any point on the surace o a specimen [9]. 1.2 Motivation Digital image correlation is one o the common methods used to ind the accurate ull-ield displacement o various specimens. train can be calculated by dierentiating the displacement ield. Digital image correlation [1] helps in the characterization o 1

12 behavior o materials and the response o the structures to various external load conditions. Full-ield displacement helps in determining the location o maximum strain, which is important or various material testing operations [1]. Digital image correlation is also used in racture mechanics investigation to analyze phenomena such as crack growth [1]. Digital image correlation can also be used or determining material parameters such as the Young s Modulus and Poisson ratio [1]. Although the potential o digital image correlation technique is immense in damage and mechanical identiications, the expensive cost o current DIC systems makes them diicult to use or health monitoring o structures in the ield. A low-cost sensor that is capable o calculating the ull-ield displacement and that is deployable in any ield application is needed or DIC to reach its ull potential. It is challenging to implement the digital image correlation algorithm or accurate ull-ield displacement calculations on a low-cost sensor in real time because o the high computational eort involved. 1.3 Goals o thesis In this thesis, the implementation o the digital image correlation on an embedded microprocessor module is discussed. The digital image correlation algorithm takes input images which are captured with a low-cost webcam. In order to be able to transmit data wirelessly to the base station, we have implemented a wireless technology standard known as Bluetooth or exchanging data over short distances; using this wireless link, the embedded microprocessor module communicates the calculated displacements to a base station. 2

13 To be able to implement the algorithm in real time the digital image correlation algorithm has to be implemented using ixed-point mathematics. The digital image correlation algorithm returns the displacement calculated to the nearest integer pixel; the displacement can then be used o-line or deormation analysis. The major contribution in this thesis is the development o a low-cost sensing unit deployable in any ield application or health monitoring o various structures. The lowcost sensing unit consists o a high-perormance embedded microprocessor module, a low-cost webcam and a communication module, and is able to measure displacement to the nearest integer pixel. 1.4 Organization o thesis The remainder o this document is organized as ollows. Chapter 2 describes the related work. Chapter 3 explains about the experimental set-up and the various steps taken to measure displacement o points on the surace o the specimens. Chapter 4 explains the details about the implementation o the digital image correlation algorithm. The simulation results are discussed in Chapter 5. Finally Chapter 6 draws conclusions and makes suggestions or uture work. 3

14 CHAPTER II LITERATURE REVIEW Digital image correlation (DIC) is a non-contacting method or inding the displacement o a single surace point. The DIC algorithm may be applied repeatedly or ull-ield displacement measurement, by independently measuring displacement o points in a grid on the surace o a specimen. DIC is widely used to measure the ull-ield displacement o structures under various load conditions in order to perorm deormation analysis. The input to the DIC algorithm is two images, one o the undeormed object and the other o the deormed object, which we reer to as the undeormed image and deormed image, respectively. The main purpose is to ind pixel coordinates, say (x, y ), in the deormed image that correspond to a set o pixel coordinates, say (x, y), in the undeormed image. Then the displacement o the single point located at (x, y) on the surace o the undeormed object is (x - x) pixels in the x-direction and (y - y) pixels in the y-direction. The x-direction and y-direction displacements in inches are then given as,, 4

15 where and denote the displacements in the x and y directions, respectively, denotes the length o the specimen along the x-direction in inches, denotes width o the specimen along the y-direction in inches, and and denote the total number o pixels along the length and width o the specimen, respectively. The pixel coordinates (x, y ) in the deormed image that correspond to a particular point in the undeormed image are ound by making a comparison between the region or acet surrounding the points in the undeormed image and regions or windows in the deormed image. The digital image correlation algorithm searches or the window in the deormed image that best matches the acet in the undeormed image. Digital image correlation methods can be classiied into various categories depending on the way the correlation between the acet and the window is calculated, the type o searching employed, and whether the method calculates displacement o each point on the surace o the object to the nearest integer number o pixels or with a subpixel resolution. The complexity o an algorithm and the cost o the hardware required to implement it are important considerations when the method is implemented in an embedded microprocessor module. In order to evaluate the degree o similarity between the undeormed and the deormed images, a correlation measure should be deined. The search strategy should be selected in such a way that the DIC algorithm calculates displacement o a single surace point to the nearest integer pixel eiciently. Thereore, the successul implementation o the DIC algorithm requires proper selection o the correlation measure and an appropriate search strategy. The various correlation measures and search strategies employed to ind the digital image correlation are discussed below. 5

16 The details about the implementation o digital image correlation are also discussed in this chapter. 2.1 Description o commonly used correlation measures The key to any DIC algorithm is the correlation measure used to ind the degree o match between a acet in the undeormed image and a window g in the deormed image, each o size pixels pixels, reindexed as they are cut out o their original images so that the pixels in a acet or window are indexed rom (1, 1) to (, ). The luminance values o pixel ( i, j) rom the acet and window are denoted by ( i, j) and g ( i, j), respectively. A description o some o the commonly used correlation measures ollows. The work in [2] uses a measure o match that the authors call the imple ormalized Correlation Coeicient that gives the measure o match between the acet and window g as C i1 j1 ( i, j) g( i, i1 j1 ( i, j) j) 2. (2.1) C is a basic type o digital image correlation measure that requires relatively ew computations to be implemented. The point o best match is ound when the correlation coeicient is minimum. The work in [3] uses a correlation measure called the ormalized Cross Correlation Coeicient that gives the correlation between the acet and window g as 6

17 C C i1 j1 i1 j1 2 ( i, j) g( i, j) ( i, j) i1 j1 g 2 ( i, j). (2.2) The advantage o using this correlation measure over the previous one is that it is insensitive to linear scaling o the luminances in the undeormed and deormed images due to varying light conditions [21]. The disadvantage is that the correlation measure is sensitive to the oset in the luminances between the undeormed and deormed images [21]. The point o best match is ound when the correlation coeicient is maximum. The work in [4] uses a correlation measure called the Zero Mean ormalized Cross Correlation that gives the correlation between the acet and window g as C ZM ( i, j) g( i, j) g 2 ( i, j) g( i, j) g i1 j1 i1 j1 i1 j1 2, (2.3) where and g denote the mean o the luminance values o the pixels in the acet and window, respectively. The advantage o subtracting the mean is that it makes the correlation measure invariant to changes in both the linear scaling and oset o the luminances between the two images [21]. The point o best match is ound when the correlation coeicient is maximum. This correlation measure is preerred as it oers the most robust perormance in the presence o noise in the images [21]. In this research we have used the Zero Mean ormalized Cross Correlation measure to compute the correlation during the experiment. 7

18 2.2 Description o common search strategies The simplest strategy or inding the window in a deormed image that best matches a acet in the undeormed image is to slide the acet around the entire deormed image, calculating its correlation with respect to every possible window in the deormed image. The point o maximum correlation is the point o best match. We reer to such a method as an exhaustive search. Making use o an exhaustive search requires a great deal o processing time. Moreover, i the acet is large it is diicult to use the exhaustive search as it would take lot o computation time to execute the DIC algorithm. Thereore, various search strategies that reduce the processing time are discussed below. The work described in [2] makes use o the imple ormalized Correlation measure described in equation (2.1) and inds the point where the correlation between the acet and the window are maximized. As described in [2] the point o best match is ound by employing a maximum-value-oriented searching method. In this method, the best match or a given pixel coordinate selected on the undeormed image is ound by beginning at the corresponding location with the same absolute pixel coordinates in the deormed image. A series o iterative moves is then made, each in the direction o maximum increase in correlation. Each move is made by considering the correlations or windows centered at the current pixel and at the eight neighboring pixels. I, o the nine pixels considered, the one corresponding to the highest correlation is one o the eight neighbors, it becomes the new current pixel, and the iterations continue. I the current pixel corresponds to the largest correlation o the nine, the search is complete, and the center pixel corresponds to the point o maximum correlation. The execution time when 8

19 using this kind o search strategy is said to be twenty times shorter than the execution time taken to calculate the displacement using an exhaustive search strategy [2]. The work described in [5] uses two steps to ind the displacement o a single pixel coordinate located at (x, y), in a way that allows much o the work to be done using a smaller acet size and thereore less computation. First the correlation measure is computed or every possible window using a small acet size. Then, the correlation measure is recomputed or a larger acet size, but only or those windows corresponding to correlations rom the irst step that are above a threshold. The experimental results conirm that the total processing time can be approximately reduced to a twentieth o that o the exhaustive search strategy. The maximum-value-oriented search strategy is used in this research ind the point o best match (x, y ) in a deormed image corresponding to a point (x, y) in the undeormed image. Given the point o best match, the displacement o the point in units o pixels is x -x in the x-direction and y -y in the y-direction. The details about the computation time taken to compute the displacements on a grid o points are provided in Chapter Optimization o computation o correlation measures Calculating ull-ield displacement is a computationally intensive process. Implementation o the DIC algorithm in real time requires careul consideration o the complexity o the algorithm being used and the cost o the hardware required to implement the algorithm. Because the bulk o the execution time is spent repeatedly evaluating the correlation measure, it is critical to consider methods or eicient computation o correlation. A brie explanation o how the computation o digital image 9

20 correlation measures can be structured to be more amenable to real time computation is given below Digital image correlation using FPGA According to [4], an FPGA can be used to implement the DIC algorithm in real time. In [4], the Zero Mean ormalized Cross Correlation, already given by equation (2.3), is used, but in a modiied orm that can be computed more quickly on an FPGA. The key is to rewrite equation (2.3) as C ZM w w ww w w, (2.4) 2 where ( i, j), ww i1 j1 2 g( i, j), w i1 j1 i1 j1 i1 j1 g( i, j), ( i, j), and the cross-correlation term w i1 j1 ( i, j) g( i, j). The term is precalculated, as this term is based on only the acet, which is ixed when computing the displacement o a single point on the surace o the specimen. The numerator and the term w w ww must be calculated or each point searched. Two types o architectures, namely spatial and spectral, are described in [4] or the implementation o the correlation metric. The spatial architecture results rom the 10

21 direct implementation o the cross-correlation term and other terms as shown in equation (2.4). The speed o computation o the terms on a spatial architecture depends on the number o multiply-accumulation (MAC) hardware units the FPGA has. The other kind o architecture mentioned in [4] is the spectral architecture. For this architecture the computations are done in the requency domain. Only the details about the implementation o the cross-correlation term are discussed, as the same methods can also be applied to the rest o terms in the correlation measure. The crosscorrelation term in the spectral domain is given by w 1 F ( F( )* F( g)), (2.5) where * denotes the convolution, F is the two-dimensional Fast Fourier transorm o an image, F denotes the complex conjugate o F and 1 F is the two-dimensional inverse Fast Fourier transorm. Equation (2.5) requires computation o two direct twodimensional Fast Fourier transorms and one two-dimensional inverse Fast Fourier transorm. The computation o w can be reduced to one direct two-dimensional FFT, one two-dimensional inverse FFT and a complex multiplication, based on the assumption that the FFT o the acet can be precomputed and stored. Experimental results [4] show that the spatial FPGA implementation or a acet on an image o size pixels perorms 244 times aster than the spectral implementation implemented on a modern personal computer while providing the same accuracy. This research uses a spatial approach to digital image correlation, doing correlation computations in the spatial domain. The correlation computation is not done in the spectral domain as the spectral approach can be applied only to an image size that is a power o two and may be more aected by rounding errors than a spatial approach 11

22 [4]. It is also disadvantageous to use the spectral approach i ull-ield rather than single surace point displacements are required, since a large amount o memory would be required to store the precomputed FFTs corresponding to each point on the surace. The main contribution o this thesis is the development o methods or computing the displacement on an embedded microprocessor module to the nearest integer pixel correctly. This is an important step or the development o an embedded sensor or displacement measurement that could be easily used in applications in the ield. The results show that a relatively inexpensive embedded microprocessor module and webcam can be successully used to calculate displacements accurately and quickly, using ixedpoint mathematics. The system is able to calculate displacements to the nearest integer pixel or a 36-point grid in 0.8 seconds. The rest o the thesis is organized as ollows. Chapter 3 gives details about the experimental set-up needed to take an accurate ull-ield displacement measurement. It also explains the details involved in coniguring the embedded microprocessor module to calculate ull-ield displacement o specimens under test. Chapter 4 provides a detailed description o how the digital image correlation algorithm is implemented on an embedded microprocessor module. Chapter 5 discusses the results obtained by implementing the digital image correlation on various specimens under test. Chapter 6 draws conclusions and discusses uture work that can be done in developing an embedded microprocessor module that can compute ull-ield displacement. 12

23 CHAPTER III EXPERIMETAL ET-UP AD PROCEDURE The main goal o this research is to work towards development o a low-cost sensor that can be used in ield applications to ind ull-ield displacement. The low-cost sensor consists o a high-perormance embedded microprocessor module, a low-cost webcam and a communication module. To be able to calculate ull-ield displacement accurately, an experimental set-up is required in which the various components o the low-cost sensor are conigured and used correctly. This chapter describes the various steps involved in the experimental set-up used to develop the low-cost sensor or ullield displacement measurement. Two variations on the experimental set-up are used. The irst perorms the DIC calculations on a laptop computer. The second perorms the DIC calculations on an embedded microprocessor module. The experimental set-up with laptop computer is used initially to veriy whether the DIC algorithm calculates accurate displacements. Once the DIC algorithm has been veriied, the same experimental set-up is used, but with the laptop computer replaced by the embedded microprocessor module. This is done to show that the displacement calculations can be implemented in the embedded microprocessor module. 13

24 The rest o chapter is organized as ollows. An overview o the experimental setups is provided. Description o the various components in the experimental set-up and how they are conigured to be able to calculate ull-ield displacement are also provided. 3.1 Experimental set-up This section gives an overview o the two variations on the experimental set-up used. Figure 3.1 shows a block diagram o the experimental set-up with the laptop computer. The experimental set-up consists o the ollowing components. A specimen is mounted in an ITRO machine [6] that is employed to apply tension to the specimen. The parameters required or setting up the ITRO machine are controlled by BLUEHILL [6] sotware that is installed on a computer. An extensometer is used to measure the change in the length o region o interest in inches. A Logitech webcam [7] is used to capture images o the specimen. The webcam is connected to the laptop computer that uses the DIC algorithm to calculate ull-ield displacement. The calculated ull-ield displacement can be transmitted rom the laptop computer via Bluetooth to the base station. Figure 3.1: Block diagram o the experimental set-up with laptop computer. 14

25 Figure 3.2 shows a block diagram o the experimental set-up with the embedded microprocessor module. Most o the set-up is identical to the experimental set-up with laptop computer. The only dierence is that the webcam is connected to an embedded microprocessor module, which is a single-board computer that uses the DIC algorithm to calculate ull-ield displacement. The calculated ull-ield displacement can then be transmitted rom the embedded microprocessor module via Bluetooth to the base station. Figure 3.2: Block diagram o the experimental set-up with embedded microprocessor module. 15

26 3.1.1 The specimen Two kinds o specimens, both made o steel, are used in our experiments. The irst kind is rectangular, and is reerred to here as a rectangular specimen without notch. The second kind has two semi-circular notches, and is reerred to as a rectangular specimen with notches. The dimensions o the rectangular specimen with and without notches are shown in Figure 3.3. The position o the grips when a specimen is mounted in the ITRO machine is shown in Figure 3.3 near the top and the bottom edges o the specimen. The region o interest is a two-inch high region in the middle o the specimen. The specimens must be prepared by applying a speckle pattern. For the DIC algorithm to be able to distinguish between dierent locations using the correlation measure, it is essential that there be adequate speckle pattern consisting o black speckles o various shapes and sizes. In order to have a ine pattern o random speckles, the surace o the specimen is irst sprayed with a layer o white paint and then sprinkled with black paint. The region o interest on both the specimens is indicated with red marks drawn on with marker. A region o interest that is 2 inches in length and 1 inch in width is selected on the rectangular specimen without notch and a region o interest that is 2 inches in length and 2 inches in width is selected on the rectangular specimen with notches. Figure 3.4 shows the rectangular specimen without notch and rectangular specimen with notches ater preparation and identiication o the region o interest. 16

27 (a) (b) Figure 3.3: Dimensions o the specimens in inches: (a) Rectangular specimen without notch (b) Rectangular specimen with notches. (a) (b) Figure 3.4: pecimens considered or evaluating ull-ield displacement using DIC algorithm: (a) Rectangular specimen without notch (b) Rectangular specimen with notches. 17

28 3.1.2 The ITRO machine The ITRO machine [6] being used in the experiment belongs to the category o HDX tatic Hydraulic Universal Testing systems. The ITRO machine consists o a load rame structure unit and I-series control unit. The I-series control unit is a communication unit that receives messages rom the computer being operated by the user and sends messages to the testing system to execute the required operation. The I-series control unit communicates with the computer through an Ethernet Frame Interace. The computer being operated by the user has BLUEHILL sotware designed to run the ITRO machine. The BLUEHILL sotware associated with the ITRO machine is conigured such that it does a uniaxial test. The parameters that need to be speciied in the BLUEHILL sotware or a uniaxial test are the interval or data capture, amount o displacement applied on the grip and criteria or end o the test The LOGITECH webcam A Logitech webcam [7] with resolution o pixels and variable ocus is used to capture the images o the test specimen. This particular webcam is selected because it has Linux driver support, which makes it easy to interace with the embedded microprocessor module selected or this research. Among the webcams compatible with the embedded microprocessor module, the Logitech webcam is selected because it has the highest resolution. The webcam set-up must be careully calibrated to ensure that the images taken are appropriate as input to the DIC algorithm. The Logitech webcam is mounted on a magnetic base that is placed at a particular distance rom the specimen. The distance at which the webcam is placed is chosen based on how clearly it can capture an image o the region o interest. The webcam must be 18

29 placed so that the region o interest is always within the ield o view throughout the test, even when the specimen is stretched. The ocus on the webcam is also adjusted such that the speckles are in sharp ocus. In order to make sure the specimen is perpendicular to the line o sight o the webcam, a checkerboard is aixed to the specimen within the ield o view o the webcam, near the region o interest. The specimen is perpendicular to the line o sight i the squares in the checkerboard are squares in the image. During set-up o the experiment, the position o the webcam is adjusted until the specimen is perpendicular to the line o sight The extensometer An extensometer is optionally used or measuring changes in the linear dimensions o the specimen. The extensometer used in this research belongs to the 2630 series strain gauge extensometers rom ITRO. In our experiments, we have attached the extensometer along the length side o the region o interest o the specimen using spring clips. The extensometer measures the changes in the length o region o interest. The values generated by the extensometer are compared with those o the DIC algorithm. This is an optional extra step done to provide additional evidence that the DIC algorithm calculates displacements correctly by checking that the extensometer and the DIC results both show the same amount o change in the length o the region o interest. An image o the rectangular specimen with the checkerboard and the extensometer captured with the webcam is provided in Figure

30 Figure 3.5: Experimental set-up o the rectangular specimen without notch with checker board and extensometer attached The laptop computer A laptop computer is used to perorm DIC calculations. This is done to check whether the experimental set-up works well and veriy the correct operation o the DIC algorithm. The laptop computer uses a Windows 7 operating system. The C code or the DIC algorithm is compiled on the laptop computer using the gcc compiler The embedded microprocessor module Ater the initial set-up is successully done using the laptop computer, an embedded microprocessor module called the FOX G20 [7] is used to perorm the DIC calculations. The embedded microprocessor module uses an Atmel AT91AM9G20 microcontroller. The embedded microprocessor module runs the Linux operating system. The gcc compiler installed on the embedded microprocessor module is used to compile the C code or the DIC algorithm. 20

31 The embedded microprocessor module has to be conigured beore it can be used in the experimental set-up. The embedded microprocessor module has been assigned with an IP address so that the iles o the embedded microprocessor module can be accessed over the internet. The webcam is connected to the embedded microprocessor module to take images o the specimen when desired. To be able to take images o the specimen at various intervals, sotware called the uvc capture [8] is installed on the embedded microprocessor module Wireless set-up The experimental set-up can be made wireless by making use o Bluetooth. The wireless experimental hardware used in the experiment is the UB Mini Bluetooth adapter [7], which has a transmission range o up to 20 meters in open space. The images and the displacement data are sent to the base station, which is either a laptop computer or a desktop computer. 3.2 Experimental procedure Ater the BLUEHILL parameters are set, the desired specimen is secured using the grips o the ITRO machine. Using the BLUEHILL sotware, the displacement applied to the specimen at the grips is speciied. Once the specimen has reached a steadystate position, the webcam, controlled by either the laptop computer or the embedded microprocessor module, is used to take ive images. When the laptop computer is used, the webcam is controlled with the help o the Logitech Webcam sotware; when the embedded microprocessor module is used, the webcam is controlled with the help o a shell script that is written using uvc capture sotware. 21

32 The images taken by the webcam are preprocessed beore applying the DIC algorithm. A coordinate system or the images is set, such that the origin is placed at one corner o the region o interest. The direction o the x-axis is along the horizontal direction and the y-axis is orthogonal to the x-axis. The underlying assumption here is that the image is already squarely lined up so that the vertical axis o the specimen is captured as a vertical line in the image. The red mark that is on the bottom let corner is used or setting up the origin o the coordinate system. A particular pixel point is selected on the bottom-letmost red mark on the undeormed image, and the DIC algorithm explained in Chapter 4 is used to ind its corresponding pixel point on the deormed image. That corresponding pixel point on the deormed image is set as the origin o the coordinate system. The red mark on the upper-rightmost corner is used or deining the bounds o the region o interest on the undeormed and deormed images. It is an important step to have the correct coordinate system or both the undeormed and deormed images as the maximum-value-oriented search strategy will give wrong displacement results i the coordinate system is not set properly. As the main goal is to calculate correct displacements, the DIC algorithm explained in Chapter 4 is applied to the prepared images, running either on the laptop computer or the embedded microprocessor module. The DIC algorithm takes any two images stored in a speciied location in the directory structure as the input, inds the correlation at the speciied pixel point and returns a single displacement value. In order to ind the ull-ield displacement, a set o speciied pixel points saved in a text document is provided as input. The DIC algorithm is then applied to each o the speciied pixel points. The displacement data provided by the DIC algorithm is saved in a text document. The 22

33 displacement data is then sent wirelessly to the base station using the Bluetooth communication link. All the steps needed to set-up the experiment in order to calculate the displacement o the selected pixel points on various specimens are provided in this chapter. The next chapter discusses about the details involved in implementation o digital image correlation on an embedded microprocessor module. 23

34 CHAPTER IV IMPLEMETATIO AD VERIFICATIO OF DIGITAL IMAGE CORRELATIO ALGORITHM The main purpose o this research is to develop a low-cost sensing unit that is deployable in the ield and can be used or measuring ull-ield displacement o a specimen under test. To be able to successully measure ull-ield displacement on a lowcost sensing unit, approximations have to be made to the DIC algorithm based on the hardware constraints. The approximations made should be such that the algorithm yields accurate results. This chapter describes the implementation o the digital image correlation algorithm and how it is implemented using ixed-point mathematics on an embedded microprocessor module. It also presents a veriication o the embedded implementation o the DIC algorithm, done by comparing its output to the output generated using a laptop computer. 4.1 Details o implementation o the digital image correlation algorithm The DIC algorithm calculates the displacement o the single point on the surace o a test specimen under load. It does this by irst cutting a acet out around the point in the undeormed image, and then searching the deormed image or the window that best matches the acet using an appropriate search strategy, using a correlation measure between acet and window to assess the degree o match. 24

35 The correlation measure used in the algorithm is the Zero Mean ormalized Cross Correlation Coeicient, irst given in Chapter 2, is C ZM ( i, j) g( i, j) g 2 ( i, j) g( i, j) g i1 j1 i1 j1 i1 j1 2, (4.1) where ( i, j) and g ( i, j) denote the luminance values o pixel (i, j) rom the acet and the window, respectively, and and g denote the mean o the luminance o all the pixels in the acet and the window, respectively. Displacement is measured rom the middle o the acet to the middle o the window by making use o the maximum-valueoriented search strategy. o, i the pixel coordinate is (x, y), in the undeormed image and its corresponding pixel coordinate on the deormed image is (x, y ), the displacement in the x-direction is (x - x) pixels and the displacement in the y-direction is (y - y) pixels. The search strategy employed to ind the best matching window in the deormed image is the maximum-value-oriented searching strategy. The detailed description o the search strategy is given in Chapter 2. It is important to select a proper acet size in order to compute the DIC calculations correctly. The acet is the region that surrounds the surace point in the undeormed image or which displacement is to be calculated. The acet size should be selected in such a way that there are at least 3 3 speckles in an average acet in order to ensure accuracy in the subset matching process [9]. This means that the acet size depends on the preparation o the specimen and the selection and the set-up o the camera. 25

36 An appropriate acet size was ound by conducting experiments with various acet sizes. ample results are shown in Figure 4.1. Images o a test specimen beore and ater deormation captured using the webcam are considered. Facets o various sizes or an example point in the undeormed image were chosen. Each acet is slid over the entire deormed image, calculating correlation values or windows centered at every pixel position. It is in this correlation space that the DIC algorithm searches or the point o maximum correlation. Color maps o the correlation spaces or acets o three dierent sizes are shown in Figure 4.1, where reds and blacks correspond to the largest correlations. ( a) undeormed image with acet (b) deormed image with window (c) correlation map using acet (d) correlation map using acet (e) correlation map using acet () correlation scale (g) Magniied view o undeormed image with acet (h) Magniied view o deormed image with window (i) Magniied view o correlation map with acet (j) Magniied view o correlation map with acet (k) Magniied view o correlation map using acet Figure 4.1: Correlation maps using acets o various sizes. 26

37 In Figure 4.1(a) to (e), the scale o the images is so large that it is diicult to see the acets and the eatures in the correlation spaces. For this reason, magniied versions are shown in Figure 4.1(g) to (k). The location o the acet in the undeormed image, and o the best matching window in the deormed image, are identiied in Figure 4.1(g) and (h) with turquoise boxes. From Figure 4.1, it is clear that too small a acet size makes it diicult to identiy a unique point on the deormed image; many spots are nearly equally good matches, because the acet is not big enough to contain unique eatures. Too large a acet is also a problem; the underlying assumption in using the correlation measure is that deormation does not change the shape in a local neighborhood around the point being matched, and large acet may contain signiicant changes as the specimen deorms. Too large a acet may also lead to diiculties in implementation; the larger the acet size, the more computations are required or each correlation computation. From Figure 4.1, the correlation map corresponding to the acet looks similar to the correlation map corresponding to acet, and both uniquely identiy the right point on the surace, with one clear point o maximum correlation. The disadvantage o using a acet over acet is that it requires more computations. Hence, a acet o size pixels is chosen as appropriate or our experimental set-up. 4.2 Fixed-point computation o the correlation measure The digital image correlation code was implemented in Matlab using loatingpoint mathematics, in C using loating-point mathematics and in C using ixed-point mathematics. The code was written in Matlab using loating-point mathematics initially to test the correctness o the algorithm. In order to be able to implement the digital image correlation code on an embedded microprocessor module the code has to be written using 27

38 a general-purpose computer programming language such as C or C++. At the irst step towards the embedded implementation, the code was written in the C language using loating-point mathematics in order to make sure it generates the same results as those o Matlab using loating-point mathematics. In order to be able to run the algorithm aster, the code then had to be converted into ixed-point. The embedded system used in the research is the FOX G20 embedded microprocessor module. It uses an Atmel processor. The goal o the ixed-point implementation o the correlation measure is to make sure to use the 32 bits available or each o the terms in the correlation measure in the most eicient way. This involves using the minimum number o integer bits that will give a result that never overlows and using the rest or raction. While selecting the number o integer bits, one bit is reserved or the sign bit. It is important that the calculated correlations be accurate, so as to ensure that the point o maximum correlation is distinctive; otherwise, the DIC algorithm would not be able to ind the correct correlation match to determine displacement correctly to the nearest integer pixel Rearrangement o terms in correlation measure The terms required or the computation measure given in (4.1) are rearranged in order to reduce the number o multiplications and additions required. First, the measure is expressed as: C ZM T, D 1 D 2 28

39 where T = ( i, j) g( i, j) g i1 j1, D = i, j) 1 i1 j1 2 (, and 2 D = g i, j) g i1 j1 2 (. The implementation o each expression is considered separately. We note that in this original orm, beore rearrangement, the numerator T requires 2 2 subtractions, 2 multiplications, and 2 1 additions. There are two actors in the denominator o the correlation measure. Each actor in the denominator requires 2 subtractions, 2 multiplications, 2 1 additions and one square root. Combining the expressions requires one multiplication and one division. Thereore, the total number o operations required beore rearrangement is 2 4 subtractions, multiplications, 3( 2 1) additions and one division and two square roots. D The rearrangement o one o the expressions o the correlation measure, 1 ) i1 j1 i, j 2 (, is described in detail as an example. As denotes the average luminance o the acet, can be written as i1 j1 ( i, j). (4.2) 2 The D 1 term is rewritten as 29

40 30 i j i j i j j i j i D ), ( 2 1 ), ( (4.3) = ) ( 2 ) ( ), ( j i i j ) ( ), ( j i i j. j i j i j i D i j i j i j ), ( ), ( ), (. (4.4) When the other terms in the zero mean normalized cross correlation measure are reorganized using the same approach as described or 1 D, the result is the simpliied orm C w w ww w w ZM. (4.5) where i j j i ), (, i j j i 1 1 ), (, i j ww j i g ), (, i j w j i g 1 1 ), (, i j w j i g j i 1 1 ), ( ), (. This is the orm used or sotware implementation o the correlation measure. The main advantage o this orm is a reduction in the number o operations needed to complete the

41 computation. The rearrangement o the correlation measure results in reducing the number o subtractions rom 2 2 to one subtraction in the numerator term and rom to one subtraction in each o the denominator terms. Thereore, the total number o 2 operations required is three subtractions, multiplications, 3( 2 1) additions and one division and two square roots. The computational load to implement the correlation measure ater rearrangement is lower as the number o subtractions is reduced. The summation terms, w,, ww and w involve only sums o integer pixel values, and can be completed with integer arithmetic; raction bits are needed when using the summation terms to compute T, D 1 and D 2. To implement the correlation measure using ixed-point mathematics, each o the terms in the correlation measure T, D 1 and D 2 has to be implemented in ixed-point mathematics. A notation o the orm n, is used to represent the ixed-point ormat, where n denotes the total number o bits altogether, o which are raction bits and n o which are integer bits; thus, the least signiicant bit is weighted by 2. I is negative, it means that the total number o integer bits is n ( ), i.e. n, where the least signiicant bit is weighted by 2 ; the bottom integer bits, which are not stored, are presumed to have zero value. The implementation o the term D 1 in ixed-point mathematics is explained in the next section as an example; implementation o the other terms is similar Fixed-point implementation o the term D1 As the acet size selected is 35, we have =35. Implementation o the term D 1 involves calculating the product irst and then subtracting it rom. Let us 31

42 irst consider computing the term in ixed-point mathematics. Computing this term involves two steps. The irst step is to compute 35. The next step is to compute the product o 35 with itsel Implementation o The term is the sum o all the pixels in the acet. Its computation requires a double nested or loop whose indices range rom 1 to 35. At each loop iteration, one new pixel is added to the term. ince the acet size is pixels and each pixel is in the range [0, 255], the range o required to represent the term is [0, ]. The maximum number o integer bits is log 2 (312375) ; thereore, should be implemented as an integer o at least 19 bits to ensure that no overlow will ever occur Implementation o division o by 35 The next step is to produce, which is done by multiplying by the 35 reciprocal o 35. Given the range o, the term 35 has a range o [0, 8925], which requires a maximum o log 2 (8925) 14 integer bits. A inal ormat o (32, 12) was chosen or ; this ormat has 20 integer bits, including the sign bit, which is suicient to prevent overlow, and 12 raction bits. However, intermediate computations producing are done with additional raction bits. This is needed because the low order bits o these computations may sum to make signiicant contribution to the upper bits; generally, 32

43 our or ive additional raction bits must be used internally to ensure good accuracy in the least signiicant bit o the result. In our case, the intermediate computations are done with 24 raction bits; thus the approximation chosen or the reciprocal o 35 is As the embedded microprocessor module being used or the DIC algorithm calculations is limited to 32-bit numbers, the intermediate computations needed or 35 cannot be done in one piece; a ull computation requires 14 integer bits and 24 raction bits, or a total o 38 bits. Thereore the term 35 is split as ollows: ( As multiplication by a power o two can be accomplished with a shit, ). 35 (( 5) ( 4) ( 3) ( 1)) (( 12) ( 6) ( 5) ( 4) ( 2) ( 0)) 12 1 is thereore represented as the sum o two terms such that when the ollowing 35 computation is done on 32-bit integer hardware, the result has the correct value or 35 interpreted in a (32, 12) ormat: 1 35 ( x 1) ( y 12). where x ( 5) ( 4) ( 3) ( 1) and 33

44 y ( 12) ( 6) ( 5) ( 4) ( 2) ( 0). Figure 4.2 is a diagram showing the operations used to calculate the term 35 using ixed-point implementation. Figure 4.2: Diagram representing how to calculate the term

45 Implementation o the product 35 by 35 The next thing that must be computed is the product o 35 with itsel. The range o the product term is [0, ] which requires a maximum log 2 ( ) 27 integer bits. Thereore, a inal ormat o (32, 4) is chosen or the product term As beore, intermediate computations are done with additional raction bits. The product is ormed in pieces that are then summed; this is accomplished by splitting the second 35 term into sections, where each section comes rom a set o consecutive bits o the original number. Thus, the term is written as ( r a r b r c r d r e ). The bit ranges or the terms r, a r b, r c, r d and r e are chosen in such a way that the product o the individual terms with 35 can be computed using the 32-bit hardware. In what ollows, an explanation o how the chosen ormats make the best use o the available 32 bits is given. The main idea while choosing the ormats is to make sure that the number o integer bits chosen is suicient to accommodate the range o the individual terms. The equations and ormats chosen or the individual terms r a, r b, r c, r d and r e are also shown. 35

46 Figure 4.3: Diagram representing how to calculate the term Figure 4.3 is a diagram showing the operations used to calculate the term rom 35 using ixed-point implementation. The term sa is the product o 35 and r a, where r a is computed by and thereore comes rom the irst 36

47 twelve integer bits o the term 35. Hence, the ormat chosen or r a is (32, 8). Given the ormat o r a, the product term s a has a ormat o (32, 4), which means it uses 28 integer bits and 4 raction bits. The maximum value o s a is or Thus, the ormat chosen or s a has a suicient number o integer bits to accommodate the range o s as log 2 ( ) 27 integer bits is the maximum needed. a The term s b is the product o 35 and r b, where r b is computed by & 0x000FC and thereore comes rom the next six integer bits o the term 35. Hence, the ormat chosen or r b is (32, 2). Given the ormat o r b, the product term s b has a ormat o (32, 10), which means it uses 22 integer bits and 10 raction bits. The maximum value o s b is or Thus, the ormat chosen or sb has a suicient number o integer bits to accommodate the range o log 2 (562275) 20 integer bits is the maximum needed. sb as The term s c is the product o 35 and r c, where r c is computed by & 0x00003E and thereore comes rom the next two integer bits and irst three raction bits o the term 35. Hence, the ormat chosen or r c is (32, 3). Given the ormat o r c, the product term s c has a ormat o (32, 15), which means it uses 17 37

48 integer bits and 15 raction bits. The maximum value o sc is or Thus, the ormat chosen or sc has a suicient number o integer bits to accommodate the range o s c as log 2 ( ) 16 integer bits is the maximum needed. The term sd is the product o 35 and r d, where r d is computed by & 0x000001F and thereore comes rom the next ive raction bits o the term 35. Hence, the ormat chosen or r d is (32, 8). Given the ormat o r d, the product term s d has a ormat o (32, 20), which means it uses 12 integer bits and 20 raction bits. The maximum value o s d is or Thus, the ormat chosen or sd has a suicient number o integer bits to accommodate the range o s as log 2 ( ) 11 integer bits is the maximum needed. d The term s e is the product o 35 and r e, where r e is computed by 35 & 0x F and thereore comes rom the last our raction bits o the term 35. Hence, the ormat chosen or r e is (32, 12). Given the ormat o r e, the product term s e has a ormat o (32, 24), which means it uses 8 integer bits and 24 raction bits. The maximum value o s e is or Thus, the ormat chosen or 38

49 s e has a suicient number o integer bits to accommodate the range o s e as log 2 ( ) 6 integer bits is the maximum needed. The inal product is the sum o s a, s b, s c, s d and s e. Given its range, it requires 27 integer bits, and a inal ormat o (32, 4). For the summation, all o the terms are irst shited into a (32, 4) ormat. There are many ways to have all the terms shited into a (32, 4) ormat; the one chosen was suicient or our needs. Thus, the product s 35 s s s s a b c d e is implemented on the hardware as s a ( s b 6) ( s c 11) ( s d 16) ( s e 20) Implementation o The inal term needed to compute D1 is. It is the summation o integer values, and so is also an integer. The maximum value o is = , and so log 2 ( ) 27 integer bits are suicient to avoid overlow. Because must be added to a quantity that is in a (32, 4) ormat, it must also be put into this ormat; this requires that the original integer summation value be shited our bit positions. Thereore, D 1 can now be calculated by subtracting rom using the ollowing computation on the hardware: D 1 = ( 4), where the term D 1 is interpreted as being in a (32, 4) ormat. 39

50 All together, the computational steps documented here compute D1 in a way that uses only 32-bit integer hardware, and that avoids all possibility o overlow, while giving a result that is suiciently accurate or the application. The two additional terms in the correlation measure, T and D 2, are computed in ixed-point in a similar way. These terms are implemented using ixed-point mathematics because the resulting computations can be done much more quickly than the corresponding loating-point computations. However, the inal remaining steps needed to compute the correlation, which include square root, multiplication, and division, are inconvenient when done in ixed-point. Thereore, they are done using sotware emulation o loating-point mathematics on the integer hardware; support or this is provided by the compiler. Converting just the computations o T, D 1 and D 2 to ixed-point made the code run three times aster than the original loating-point version run in sotware emulation on the same hardware. 4.3 Veriication o the DIC algorithm implementation An experiment was done to veriy that the ixed-point implementation o the correlation computation gives results with adequate accuracy. An undeormed and a deormed image o the one o the specimens mentioned in Chapter 3 are considered. The correlation is calculated using the DIC algorithm at ten surace points using our dierent implementations: loating-point implementation in Matlab, loating-point implementation in C on the laptop computer, ixed-point implementation in C on the laptop computer, and ixed-point implementation in C on the embedded microprocessor module. Figure 4.4 shows the undeormed and deormed images with the selected ten surace points. 40

51 (a) undeormed image (b) deormed image Figure 4.4: Undeormed and deormed images o the specimen with the selected ten surace points. Table 4.1 shows the pixel coordinates in the undeormed image o each o the ten surace points. For each point, a search or the point o maximum correlation in the deormed image was conducted, using correlation measures computed with the our dierent implementations. In each case, the our dierent implementations all identiied the same pixel location in the deormed image as being the point o best match. The table shows the value o the correlation at the point o best match, or the our dierent implementations. The correlation values are shown using eight decimal digits o raction so that dierences can be seen. It is clear rom Table 4.1 that the error between the correlation values implemented using loating-point mathematics and ixed-point 6 mathematics is less than10 6. An error less than approximately 10 is observed between the correlation values calculated using loating-point mathematics and ixed-point mathematics. 41

52 Table 4.1: Correlation values under dierent implementations or a set o ten surace points. Coordinate on the undeormed image or which the correlation is ound Maximum correlation value using loatingpoint mathematics in Matlab on laptop computer Maximum correlation value using loatingpoint mathematics in C on laptop computer Maximum correlation value using ixed-point mathematics in C on laptop computer Maximum correlation value using ixed-point mathematics in C on embedded microprocessor module (786, 30) (747, 599) (668, 333) (434, 303) (461, 527) (300, 270) (570, 569) (107, 122) (43, 736) (49, 26) From the veriication experiment, it is seen that the embedded implementation o the sotware computes the correlation measure with suicient accuracy, and correctly implements the DIC algorithm, providing correct displacements to the nearest integer pixel. The time it takes to run the DIC algorithm or 36 coordinate points on the embedded microprocessor module using loating-point mathematics is approximately 2.5 seconds, whereas the time it takes to run the DIC algorithm to ind the displacement o one coordinate point on the embedded microprocessor module using ixed-point mathematics is 0.02 seconds; or the 36 coordinates used in the veriication experiment, the total time or the 36 points on the embedded microprocessor module, including time to retrieve and decode the image iles, is approximately 0.8 seconds. This is ast enough or the embedded DIC algorithm to be useul to measure static stresses in a ield application. 42

53 CHAPTER V REULT AD DICUIO To be able to veriy the ull-ield displacement calculations using the digital image correlation algorithm we have conducted experiments on two dierent steel specimens, the dimensions o which were given in Chapter 2. Experimental results are provided in this chapter. The experimental results are divided into two parts. The irst part shows results obtained by making use o the irst specimen, the rectangular specimen without notch. The second part shows results obtained by making use o the second specimen, the rectangular specimen with notches. Each set o experiments is conducted both using the set-up with laptop computer and the set-up with the embedded microprocessor module as previously described in Chapter 3. An extensometer is connected in the set o experiments that are done using the rectangular specimen without notch, and is used to measure the changes in the length o the region o interest, parallel to the applied orce. 5.1 Experimental results using the rectangular specimen without notch The irst set o experiments is conducted by making use o the rectangular specimen without notch. The BLUEHILL sotware controlling the ITRO machine is conigured to go through a sequence o stages, with each stage consisting o a loading phase and a holding phase. The sequence starts with the specimen in the grips with no 43

54 orce applied. The loading phase in each stage applies orce to stretch the specimen such that the region o interest is stretched by an additional 0.02 inches beyond the previous stage, at a rate o inches per second, or a total phase o 40 seconds. A holding phase then completes the stage by holding the specimen in place or 40 seconds so that the images may be taken. During the holding phase, ive images are taken, using manual control. In this way, the test is quasi-static. The control sequence is common to all o the experiments. In our experiment, the load pattern resembles a staircase waveorm. Figure 5.1 shows the load pattern o the extensometer with the relative displacement o the extensometer shown as a unction o time. The experiment is initially conducted by using a laptop computer to which the webcam is connected. The laptop computer is conigured to take ive static images during the holding phase. Beore the experiment, is started an image o the specimen is taken which is considered as stage0. In our experiment, we have taken images at ive stages, namely stage1, stage2, stage3, stage4 and stage5. Figure 5.2 shows the images taken at stage0, stage1, stage2, stage3, stage4 and stage5. These images are rotated. Each o the stages diers rom one another by the amount o stretch being applied. Relative Displacement (inches) Load pattern o the extensometer stage5 stage4 stage3 stage2 stage Time (sec) Figure 5.1: Load pattern o the extensometer. 44

55 stage0 stage1 stage2 stage3 stage4 stage5 Figure 5.2: Images taken during the experiment with a rectangular specimen without notch using laptop computer. Ater the images are taken using the webcam connected to the laptop computer, the DIC algorithm implemented using ixed-point mathematics measures the ull-ield displacement at every quasi-static stage o the experiment, with respect to the initial stage. The ull-ield displacement is deined in terms o 36 surace points, equally spaced throughout the region o interest, which is two inches in length and one inch in width. These points are arranged in our sets o nine points each, at 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, respectively, along the length o the region o interest. Thus, each set contains points that are arranged in a line parallel to the applied orce. The our sets 45

56 are spaced evenly along the width o the region o interest at 0, 0.33, 0.67 and 1 inch, respectively. Because the specimen is uniorm, we would expect the corresponding points rom dierent sets to experience the same displacement. At each stage o the experiment, the y-component o the ull-ield displacement is calculated relative to stage0. This is done by providing the 36 surace points as input to the DIC algorithm already explained in Chapter 4. The results are plotted in the Figures 5.3 to 5.7. In the igures, the relative displacement in inches is plotted against the vertical distance o the surace point above the origin o the region o interest in undeormed image. The data is plotted with a separate line or each o the our sets; because we expect two corresponding points rom dierent sets to move the same amount, we expect the lines to coincide. The x-component o the displacement was also calculated or each o the 36 surace points; in theory, there should be no movement in this direction or the rectangular specimens without notches because the test applies uniaxial orce along the y- axis. The results showed movements o no more than two pixels along the x-axis; these small measured movements are most likely because o imperections in the test set-up and in the construction o the specimen. The x-component o displacement is not presented urther or this specimen. The physical size o a pixel is calculated by inding the physical length o the region o interest, which is two inches, by its length in pixels, and the physical width o the region o interest, which is one inch, by its width in pixels. In the experimental set-up with the laptop computer connected, there were 921 pixels along the length o region o 46

57 interest and 460 pixels along the width o the region o interest. Thereore, each pixel is approximately inches by inches. The DIC algorithm calculates displacements to the nearest integer pixel. The extensometer connected in the experiment measures changes in the length o the region o interest. As per the load pattern o the ITRO machine, we would expect that two corresponding points rom dierent sets move by the same amount relative to that o the extensometer reading. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage1 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line o slope passing through the origin, recalling that any relative overall translation o the images has been eliminated in a preprocessing step that identiied a common origin or the two images. Thus, at 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we would ideally expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.1, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is greater than 0.5 pixels, i.e., the error is greater than inches or most o the surace points. The DIC algorithm was not able to measure displacements correctly to the nearest integer pixel at stage1. One possible explanation is that during the initial small movement o the grips, the grips may not have applied orce evenly along the grip lines, and so the displacements may also not have been uniorm across the width o the specimen; the extensometer measured the displacement only along one side. 47

58 Table 5.1: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage1) or dierent sets o points using laptop computer. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

59 Relative displacement o point in deormed image(inches) stage Vertical distance o point above origin o region o interest in undeormed image (inches) irst set o points second set o points third set o points ourth set o points Extensometer reading Figure 5.3: Plot showing the ull-ield displacement calculated using DIC at stage1o the experiment using laptop computer, with respect to the initial stage. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage2 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.2, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is never more than 0.5 pixels, i.e., the error is always less than inches or all the surace points. This shows that the relative displacement o the 36 surace points is calculated correctly to the nearest integer pixel. 49

60 Table 5.2: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage2) or dierent sets o points using laptop computer. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

61 Relative displacement o point in deormed image(inches stage Vertical distance o point above origin o region o interest in undeormed image (inches) irst set o points second set o points third set o points ourth set o points extensometer reading Figure 5.4: Plot showing the ull-ield displacement calculated using DIC at stage2 o the experiment using laptop computer, with respect to the initial stage. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage3 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.3, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is never more than 0.5 pixels, i.e., the error is always less than inches or all the surace points. This shows that the relative displacement o the 36 surace points is calculated correctly to the nearest integer pixel. 51

62 Table 5.3: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage3) or dierent sets o points using laptop computer. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

63 Relative displacement o point in deormed image(inches) stage irst set o points second set o points third set o points ourth set o points Extensometer reading Vertical distance o point above origin o region o interest in undeormed image (inches) Figure 5.5: Plot showing the ull-ield displacement calculated using DIC at stage3 o the experiment using laptop computer, with respect to the initial stage. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage4 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.4, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is never more than 0.5 pixels, i.e., the error is always less than inches or all the surace points. This shows that the relative displacement o the 36 surace points is calculated correctly to the nearest integer pixel. 53

64 Table 5.4: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage4) or dierent sets o points using laptop computer. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

65 Relative displacement o point in deormed image(inches) stage Vertical distance o point above origin o region o interest in undeormed image (inches) irst set o points second set o points third set o points ourth set o points Extensometer reading Figure 5.6: Plot showing the ull-ield displacement calculated using DIC at stage4 o the experiment using laptop computer, with respect to the initial stage. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage5 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.5, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is never more than 0.5 pixels, i.e., the error is always less than inches or all the surace points. This shows that the relative displacement o the 36 surace points is calculated correctly to the nearest integer pixel. 55

66 Table 5.5: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage5) or dierent sets o points using laptop computer. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

67 Relative displacement o point in deormed image(inches stage Vertical distance o point above origin o region o interest in undeormed image (inches) irst set o points second set o points third set o points ourth set o points extensometer reading Figure 5.7: Plot showing the ull-ield displacement calculated using DIC at stage5 o the experiment using laptop computer, with respect to the initial stage. As the error between the calculated relative displacements o the surace points and the expected relative displacements lies within a pixel or stage2, stage3, stage4 and stage5, it is concluded that the DIC algorithm calculates displacements to the nearest integer pixel that correctly correspond to expected values based on the extensometer reading, except at stage1. The main purpose o this research is to be able to develop an embedded sensor that is capable o calculating ull-ield displacement to the nearest integer pixel. In the experiment just described, images were captured using the laptop computer connected to the webcam; such an approach is not possible in a ully embedded implementation. Thereore, the experiment was repeated, this time using the embedded microprocessor module to interace with the webcam. The only signiicant dierence between this experiment and the previous one is the resolution o the images. The UB bus o the embedded microprocessor module restricts the resolution o the webcam to

68 pixels, whereas the resolution o the webcam or the previous experiment was When an embedded microprocessor module is used, there are 395 pixels along the length o the region o interest and 200 pixels along the width, and so each pixel is approximately inches by inches. The DIC algorithm did not give correct results in the irst three stages, and so those stages are not shown. Figure 5.8 shows the images taken using the embedded microprocessor module at stage4 and stage5. Using the images taken with the webcam connected to the embedded microprocessor module, the DIC algorithm calculates the displacements o the same 36 surace points, equally spaced throughout the region o interest, used in the previous experiment. stage0 stage4 stage5 Figure 5.8: Images taken during the experiment with rectangular specimen without notch using embedded microprocessor module. 58

69 At each stage o the experiment, the ull-ield displacement is calculated relative to stage0. This is done by providing the 36 surace points as input to the DIC algorithm already explained in Chapter 4. The results are plotted in Figures 5.9 to In the igures, the displacement in inches o a surace point is plotted against the vertical distance o the surace point above the origin o the region o interest in undeormed image. The data is plotted with a separate line or each o the our sets, because we expect two corresponding points rom dierent sets to move the same amount. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage4 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. However, rom Table 5.6, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is greater than 0.5 pixels, i.e., the error is greater than inches or most o the surace points. At stage4, the DIC algorithm was not able to measure displacements correctly to the nearest integer pixel. One possible explanation involves the set-up o the webcam in the experiment with the embedded microprocessor module. Because in this coniguration the webcam must be used in a lower resolution mode, its ocus must be adjusted, so that a ewer number o pixels covers the region o interest. Because o this change, it is possible that noise aects the results dierently than or the previous set o experiments; noise in the pixels aects the correlation values. 59

70 Table 5.6: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage4) or dierent sets o points using embedded microprocessor module. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

71 Relative displacement o point in deormed image(inches) stage Vertical distance o point above origin o region o interest in undeormed image (inches) irst set o points second set o points third set o points ourth set o points extensometer reading Figure 5.9: Plot showing the ull-ield displacement calculated using DIC at stage4 o the experiment using embedded microprocessor module, with respect to the initial stage. The extensometer reading or a vertical distance o two inches above the origin o the region o interest in stage5 is inches. Ideally, we would expect that the data corresponding to the dierent sets o points would all lie within 0.5 pixels o the line passing through the origin and having a slope o At 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2 inches, we expect the relative displacement to be within inches o 0, , , , , , , and inches, respectively. From Table 5.7, we see that the error between the computed displacement and the expected displacement based on the extensometer reading, is never more than 0.5 pixels, i.e., the error is always less than inches or all the surace points. This shows that the relative displacement o the 36 surace points is calculated correctly to the nearest integer pixel. 61

72 Table 5.7: Comparison o relative displacement o points measured along the major axis o deormation in the deormed image (stage5) or dierent sets o points using embedded microprocessor module. Dierent sets o points Vertical distance o point above origin o region o interest in undeormed image (inches) Expected relative displacement o points in the deormed image (inches) Computed relative displacement o points in the deormed image (inches) Magnitude o error between computed and actual relative displacements (inches) First set econd set Third set Fourth set

73 Relative displacement o point in deormed image(inches) stage irst set o points second set o points third set o points ourth set o points extensometer reading Vertical distance o point above origin o region o interest in undeormed image (inches) Figure 5.10: Plot showing the ull-ield displacement calculated using DIC at stage5 o the experiment using embedded microprocessor module, with respect to the initial stage. As the error between the calculated relative displacements o the surace points and the expected relative displacements lies within a pixel, it is concluded that the DIC algorithm calculates displacements correctly to the nearest integer pixel based on the extensometer provided that the movement is suicient to avoid the problems associated with the resolution o the webcam. For the rectangular specimen, which is uniorm in thickness and width, results have been veriied by comparing them with the readings obtained using the extensometer. A second set o experiments is done with a dierent specimen, the rectangular specimen with notches previously described in Chapter 3. For this specimen, which is less regular in shape, it is more diicult to know analytically what the correct displacement ield should be. Thereore, the results are veriied visually, by looking at the movement o points in overlaid versions o the undeormed and deormed images. 63

74 5.2 Experimental results using the rectangular specimen with notches The region o interest o the rectangular specimen with notches is two inches in length and two inches in width. The same experimental procedure is used as in the previous experiments. The images are initially taken using the webcam connected to the laptop computer; these images are shown in Figure When the experiment was conducted, no image was taken at stage5, inadvertently. Thereore, an image o stage5 is not shown in Figure Given the webcam set-up the size o the pixel is approximately inches by inches. stage0 stage1 stage2 stage3 stage4 Figure 5.11: Images taken during the experiment with rectangular specimen with notches using laptop computer. 64

75 An extensometer was not connected during this experiment as we did not have the required clips to connect the extensometer to a specimen o irregular shape. Thereore, a dierent procedure is adopted to veriy whether the ull-ield displacement calculated at each stage is correct to the nearest integer pixel. For individual surace points in the undeormed image, the coordinates o the matching point in the deormed image are ound by manual visual inspection, and compared to the coordinates reported by the DIC algorithm. The undeormed and deormed images are overlapped such that the red marks at the bottom let and right corners in both the images coincide. Then the pixels in the undeormed image are made white and the pixels in the deormed image are made black so that the pixels corresponding to both the undeormed and deormed images are easily distinguishable. The results are then veriied by visually calculating the pixel movement between the white pixels corresponding to the selected set o coordinates and the black pixels on the overlapped image. This process is repeated or a set o points. Figure 5.12 shows the results obtained by using this procedure or our coordinate points using the stage0 image as the undeormed image and the stage2 image as the deormed image. On the let o each part o Figure 5.12, one particular surace point is identiied in green, and the corresponding point in the deormed image as ound by the DIC algorithm is identiied in red. The magniied version on the right shows the individual pixels clearly, with the same points identiied. The correctness o the DIC result is veriied by visual inspection; it can be seen that the red pixel is in the same location relative to a black eature (rom the deormed image) as the green pixel relative to a white eature (in the undeormed image).this shows that DIC algorithm works even when a dierent specimen having an irregular shape is used. 65

76 (a) Pixel movement or a coordinate value o (161, 137) on the undeormed image. (b) Pixel movement or a coordinate value o (440, 10) on the undeormed image. Figure 5.12: Pixel movement or our example surace points on the undeormed image using experimental set-up with laptop computer. 66

77 (c) Pixel movement or a coordinate value o (122, 454) on the undeormed image. (d) Pixel movement or a coordinate value o (34, 18) on the undeormed image. Figure 5.12, continued: Pixel movement or our example surace points on the undeormed image using experimental set-up with laptop computer. 67

78 stage0 stages2 stage3 stage4 Figure 5.13: Images taken during the experiment with rectangular specimen with notches using embedded microprocessor module. The same experimental procedure is repeated or the experiment where the images o the rectangular specimen with notches are taken by the webcam connected to the embedded microprocessor module. When the experiment was conducted, no images were taken at stage1 and stage5. Thereore, images o stage1 and stage5 are not shown in Figure Figure 5.13 shows the images o the rectangular specimen with notches taken using the webcam connected to the embedded microprocessor module. For this webcam set-up, a pixel is approximately inches by inches. In order to veriy the results given by the DIC algorithm, the visual inspection procedure is used to veriy correct operation at a number o surace points, this time using stage0 as the undeormed image and stage4 as the deormed image. Figure 5.14 shows the results obtained by using this procedure or our coordinate points. Figure 5.14 shows the undeormed image coordinates selected and the corresponding deormed image coordinates given by the DIC algorithm. The movement o the surace points that is calculated rom the DIC algorithm is again veriied by using the visual inspection procedure. This shows that DIC algorithm works even when a dierent specimen having an irregular shape is used. 68

79 (a) Pixel movement or a coordinate value o (176, 129) on the undeormed image. (b) Pixel movement or a coordinate value o (196, 294) on the undeormed image. Figure 5.14: Pixel movement or our example surace points on the undeormed image using experimental set-up with embedded microprocessor module. 69

80 (c) Pixel movement or a coordinate value o (394, 116) on the undeormed image. (d) Pixel movement or a coordinate value o (22, 64) on the undeormed image. Figure 5.14, continued: Pixel movement or our example surace points on the undeormed image using experimental set-up with embedded microprocessor module. 70