McGinnis, MJ, Barbachyn, S., Kurama, YC. Application of multiple digital image correlation sensors in earthquake engineering. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering
Research Institute, Anchorage, AK, 2014.
APPLICATION OF MULTIPLE DIGITAL
IMAGE CORRELATION SENSORS IN
EARTHQUAKE ENGINEERING
M. J. McGinnis
1, S. Barbachyn
2, and Y. C. Kurama
3ABSTRACT
As structural testing has become more expensive, researchers are pushing to capture more and better data with each structural test conducted. Digital image correlation (DIC) is a tool that is gaining popularity as one way to capture more detailed information in testing programs. In three-dimensional DIC (3D-DIC), the measured object is photographed with a pair of digital cameras before and after a load event and a stochastic pattern marked on the object is tracked through the images such that a near full field of displacements is derived. Setup of the system involves mounting the two cameras securely to a rigid bar, and capturing photographs of a NIST certified calibration object. These calibration images are used to determine the orientation of the cameras with respect to one another, and then during testing, 3D locations of pattern sub-regions (called facets) are determined via photogrammetric triangulation principles. Historically, the cost of the system, knowledge of how to correctly specify appropriate testing protocol, and how to correctly interpret the results have limited the application of this promising technology to structural testing. The current paper focuses on three main aspects of DIC technology. First, a treatment of the basic theory behind the method is provided. Included are recommendations and guidelines for accuracy and other lessons learned during deployment over a broad range of projects. The final portion of the paper is a case study of the deployment of DIC on the large scale lateral load testing of a novel reinforced concrete coupled wall system. The bottom three stories of an eight story building were constructed in the laboratory – the top five stories were simulated using hydraulic actuators at the top of the test specimen. Fourteen DIC sensors were deployed simultaneously during the test, believed to be the largest number of simultaneous deployment for structural testing.
________________________
1Associate Professor, Dept. of Civil Engineering, University of Texas at Tyler, Tyler, TX 75799
2Ph.D. Candidate, Dept. of Civil & Env. Eng. & Earth Sci., Univ. of Notre Dame, Notre Dame, IN 46556 3Professor, Dept. of Civil & Env. Eng. & Earth Sci., Univ. of Notre Dame, Notre Dame, IN 46556
McGinnis, MJ, Barbachyn, S., Kurama, YC. Application of multiple digital image correlation sensors in earthquake engineering. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering
Research Institute, Anchorage, AK, 2014.
Application of Multiple Digital Image Correlation Sensors in
Earthquake Engineering
M. J. McGinnis1, S. Barbachyn2, and Y. C. Kurama3
ABSTRACT
As structural testing has become more expensive, researchers are pushing to capture more and better data with each structural test conducted. Digital image correlation (DIC) is a tool that is gaining popularity as one way to capture more detailed information in testing programs. In three-dimensional DIC (3D-DIC), the measured object is photographed with a pair of digital cameras before and after a load event and a stochastic pattern marked on the object is tracked through the images such that a near full field of displacements is derived. Setup of the system involves mounting the two cameras securely to a rigid bar, and capturing photographs of a NIST certified calibration object. These calibration images are used to determine the orientation of the cameras with respect to one another, and then during testing, 3D locations of pattern sub-regions (called facets) are determined via photogrammetric triangulation principles. Historically, the cost of the system, knowledge of how to correctly specify appropriate testing protocol, and how to correctly interpret the results have limited the application of this promising technology to structural testing. The current paper focuses on three main aspects of DIC technology. First, a treatment of the basic theory behind the method is provided. Included are recommendations and guidelines for accuracy and other lessons learned during deployment over a broad range of projects. The final portion of the paper is a case study of the deployment of DIC on the large scale lateral load testing of a novel reinforced concrete coupled wall system. The bottom three stories of an eight story building were constructed in the laboratory – the top five stories were simulated using hydraulic actuators at the top of the test specimen. Fourteen DIC sensors were deployed simultaneously during the test, believed to be the largest number of simultaneous deployment for structural testing.
Introduction
Digital image correlation (DIC) is a promising technology that is beginning to be used in the structural testing field. In three-dimensional DIC (3D-DIC), the measured object is photographed with a pair of digital cameras (see Figure 1) before, during and after a load event
________________________
1Associate Professor, Dept. of Civil Engineering, University of Texas at Tyler, Tyler, TX 75799
2Ph.D. Candidate, Dept. of Civil & Env. Eng. & Earth Sciences, University of Notre Dame, Notre Dame, IN 46556 3Professor, Dept. of Civil & Env. Eng. & Earth Sciences, University of Notre Dame, Notre Dame, IN 46556
and a random pattern marked on the surface of the object is tracked from one set of images to the next such that a full field of displacements is derived in 3D. Historically, along with the cost of the system, factors such as how to correctly specify an appropriate testing protocol and how to correctly interpret the results have limited the application of this promising technology to structural testing. The current paper focuses on three main aspects of DIC technology. First, a treatment of the basic theorybehind the method is provided, highlighting the strengths and limitations of use for structural testing. Included are recommendations and guidelines for accuracy and other lessons learned during deployment over a broad range of projects. The final portion of the paper is a case study of the deployment of DIC on the large scale lateral load testing of a novel reinforced concrete coupled wall system.
The paper is written for users of the technology and to provide practical information – there are many available references (e.g. [1] and [2]) available for software developers or others interested in advanced theoretical explorations of the topic. Furthermore, while it is possible for researchers to develop their own software formulations for the technology, the data and discussion presented herein revolve around a commonly available commercial system.
Basic Background on DIC
3D-DIC ([3], [4]) combines techniques of image correlation with photogrammetric location principles and is practical only with the advent of high-speed computers. In photogrammetry, multiple photographs (from different orientations) of a series of targets are captured in order to determine the 3D coordinates of the targets. Three major analytical functions that must be performed to analyze photogrammetric data are: (1) triangulation; (2) resection (the process of determining the camera’s position and orientation); and (3) self-calibration of the camera to eliminate errors such as those due to lens and camera imperfections, temperature and humidity effects, etc. Accuracy and precision in industrial photogrammetry are related to the size of the measured object and numerous other factors, including the resolution of the captured images, camera calibration, angles between captured photos, redundancy in the appearance of targets appearing in multiple images, and the placement of the targets.
In 3D-DIC, sample preparation consists of applying a regular or random pattern with good contrast to the surface of the measured specimen. The pattern will then deform with the specimen under load. The specimen is captured in a stereo pair of high quality cameras while it is loaded. Typically, these two cameras are mounted at either end of a base bar such that their relative position and orientation with respect to one another is fixed and known.
Before using a 3D-DIC system as described above, the system must be calibrated using a NIST-traceable calibration object for each field of view (FOV). A sequence of pictures of the object at different distances and orientations is captured and a bundle adjustment is used to establish the precise relationship between the two cameras and to compensate for any distortions in the individual camera lenses. Each dot on the calibration panel occupies more than 100 pixels Figure 1. 3D-DIC equipment
on each camera sensor (depending on the FOV), and dot centers can be interpolated to an accuracy of at least 1/30 of a pixel. The fixed position of the two cameras with respect to one another simplifies the photogrammetric calculations discussed previously, but if the camera positions with respect to one another are altered (even accidentally) during testing, a new calibration sequence is required.
Once calibrated, thousands of unique correlation areas known as facets (typically 15-75 pixels square for the system used herein, with the variability driven by the pixel density of the cameras used) are defined across the entire imaging area of the measured object. The center of each facet is a measurement point that is tracked in each successive pair of images by employing a similarity measure such as the normalized cross correlation. An image correlation algorithm, as for example, the iterative spatial domain cross correlation algorithm, tracks facets by maximizing this similarity measure. Three-dimensional locations of these facets are calculated before and after each load step, yielding displacements. Tracking the dense cloud of points within the applied pattern provides displacement information that is ‘near’ full field.
3D-DIC is often more practical than other full-field methods that require interferometric stability between the sensor and the test part in order to acquire data. Significant rigid body motions can first be quantified and then removed. Since strains are calculated from the derivative of displacement, rigid body motion is intrinsically eliminated from strain data. As long as non-blurred pictures can be captured, 3D coordinates, displacements and strains can be measured. Using high speed cameras allows the technology to be tailored to situations involving measurement in the dynamic environment.
The optimum angle between the cameras is 25 degrees. Lower angles reduce accuracy in triangulation, and thus reduce accuracy in the out-of-plane (z-axis) coordinates and displacements. Wider angles increase accuracy of the z coordinates, but the increased perspective reduces the useful FOV. Many researchers use 2D-DIC (which involves using only one camera and does not require triangulation) when the out-of-plane deformations of the monitored specimen are deemed unimportant. Some of the complexities involved in choosing between 2D and 3D formulations are discussed later in the paper.
The 1/30 figure discussed previously includes precision in the image correlation algorithm and in the triangulation function, which are both critical for the determination of out-of-plane displacements. For displacements in the plane of a set of photographs, the displacement accuracy will be better because in this case the precision is governed primarily by the image correlation algorithm and the discrepancies introduced during the triangulation function are minimized. Furthermore, the resolution of the technique follows many of the same prescripts for industrial photogrammetry, as well as being influenced by the accuracy of the image correlation algorithm. Many different cameras were used in the case study described later in this paper. As an example, for a camera capturing images of 1600 x 1200 pixels (a 2 megapixel camera), the overall accuracy of the system used herein can be conservatively stated as 1/30,000 the FOV for out-of-plane displacements and better for in-plane displacements. For a 10 mm FOV, for example, that equates to a displacement sensitivity of 0.21 microns. The displacement sensitivity scales linearly with the FOV, decreasing to 2 microns for a FOV of 100 mm and 21 microns for a FOV of 1 m, assuming 1600 pixels across the FOV. When the system is implemented with higher resolution
cameras, a higher degree of accuracy is possible. For example, cameras with 10 mega-pixel resolution are currently available as part of commercial 3D-DIC systems.
Application Lessons Learned
The following presents lessons learned by the authors over many projects. It is not an all-inclusive list, but should give the reader a sense of the primary issues to be considered when implementing DIC in a structural investigation.
(1) Patterns are important. The pattern must be such that the facets (often 15 pixels across) contain a mix of light and dark sections that allow them to be uniquely identified. This means patterns for different size fields of view must be different size, and it is important to verify that the pattern is acceptable for use before testing (see Lesson 4). The authors have often used permanent markers or spray paint to apply patterns – neither requires expensive or technologically advanced products. Users often prefer that the appearance of their specimen is not permanently altered in this way – sometimes these wishes can be accommodated by using a product that can be removed. However, if the pattern does not deform along with the surface to which it is attached, error in measured quantities will result. The figures that follow provide many examples of successful patterns.
(2) Portability and flexibility are major strengths. The authors have used the technology in numerous laboratories across the U.S., in field testing, to measure deformations in vessels floating in lakes, etc. The system accepts images from many available cameras, increasing the flexibility. Materials tested include steel, concrete, timber, glass, gypsum, rammed earth, and more. The authors have used the technique in static applications, dynamic applications with frame rates of 500 fps (and others have captured data in excess of 5000 fps), room temperature applications and those where the temperatures involved reached over 500 C. Properly packed, the system can be transported via commercial airline, and thus a single system can be used anywhere in the world over the course of a few days.
(3) If you can see it you can (probably) measure it. The non-contact nature of DIC is an advantage, but the cameras must be able to focus on the specimen in order to gather data. The cameras need to be installed the proper distance from the specimen and from each other. These distances must be larger when the desired FOV is larger (assuming the lenses and cameras used are the same for each application), which often results in complications when large FOV are desired. Different lenses can be used in order to modify the offset distance and camera base distance. For perspective, a rough guideline based on the authors’ experience is that the base distance between cameras needs to be approximately twice the FOV, and the offset distance from the test object approximately three times the FOV (for 17 mm lenses and 2 megapixel cameras). A related issue is that the lighting must be such that the object surface is appropriately illuminated in the images captured. There is some flexibility in this regard – camera aperture and exposure settings can be modified, but a simple synopsis might simply be that ‘good lighting yields good data’. This is particularly important for dynamic testing with fast shutter speeds. Preplanning of these aspects of testing is essential.
(4) A pre-test is vital. In consideration of the first three points noted here, it is critical to conduct a pre-test before collecting data for the actual application. A pre-test can be nothing more that snapping two sets of images of the completed pattern in the lighting that will be used during actual testing. These images should be taken as closely as possible in time from one another, such that no physical movement is expected to take place between them. The two sets of
images are then processed, and the results examined. This examination will reveal if the system has been calibrated correctly, if the lighting is appropriate, if there are portions of the pattern that are not able to be divided into trackable facets, and other issues. Since it is expected that the strains and displacements between the two sets of images will be zero, any measured values represent problems with the set-up, or simply noise in the system. Without conducting a pre-test, it is possible to complete an entire structural investigation, only to realize afterward (and too late) that useful data was not being collected.
(5) Strain data collected may not match conventional sensors. Calculation of strain involves selecting the appropriate gauge length. In a full-field application, it is difficult to specify what length is to be used to calculate the strain values. The length of the computational strain ‘gauges’ is dependent on the pixel density of the camera images, the size of the FOV, and other factors. For the images shown herein, the length over which strain is computed is on the order of 50 mm, and varies depending on the camera used. Although smaller lengths can be chosen, there is a balance between capture of local effects and noise values. If traditional strain gauges with a length of ~10 mm are installed in a highly varying strain field, then the difference between the DIC computational strain gauge length and the traditional strain gauge length will impact comparisons. Furthermore, gauges embedded within objects (for example on rebar embedded within concrete) will not always match values obtained at the object surface, since out-of-plane bending and other factors can mean that the strains at the two locations are different. Spalling, cracking, and burning of surfaces also mean that data may be lost or more difficult to interpret.
Case Study – Multiple DIC Deployment on a Large Scale Coupled Shear Wall Test Tested Structure
The structure tested was a novel coupled concrete shear wall system. The system uses posttensioned coupling beams (with single centrally located posttensioning tendons) that allow concentrated crack opening at the beam ends during lateral motion of the system. This design greatly simplifies construction compared to traditionally reinforced coupling beams, which require substantial diagonal steel reinforcement. The system also has the potential to improve earthquake performance, concentrating beam deformations and damage within the end regions. Furthermore, the posttensioning force provides a restoring force that causes some self centering of the system during and after an earthquake.
To test this concept, the researchers constructed the bottom three stories of an eight story prototype building designed for a site in Los Angeles CA, see Fig.
2. The upper five stories were simulated with hydraulic actuators that provided the shear, axial force, and overturning moment required by equilibrium (and determined with a companion analytical model) at the top of the constructed portion of the building. The specimen was tested to failure in a pseudo-static testing procedure similar to ACI ITG 5.1 [5], with three fully reversed
cycles of lateral loading at ever increasing drift levels until failure. Reference [6] describes the test structure in more detail. The following examples provide illumination of many of the DIC principles discussed in the previous sections.
Sensor Layout
The arrangement of the 14 DIC sensors on the specimen is shown in Fig. 3, and details of each sensor are given in Table 1. Fig. 3(b) shows the numerous computers necessary to control all of the sensors – control involved operating six separate computing platforms.
Figure 3. DIC locations and computers necessary for sensor control: (a) locations; (b) computers Fig. 4 shows examples of the 2D and 3D sensor setups, and the patterns used in their FOV. Each sensor was fixed to a stationary base mount. Although movement of the sensor mount does not impact measured strains, it does impact measured displacements, and displacements are often a measured quantity of interest.
Figure 4. Examples of DIC setups
* 2D5, 2D7 and 2D11 locations on the north side not shown – they mirror 2D1, 2D3 and 2D9 from the south side of the structure
West
Table 1. Sensor details
2D Versus 3D Concerns
2D sensors were primarily used on the faces of the wall piers (sensors 2D1-2D8), where out of plane displacements are expected to be small. In 2D, if the measured object moves toward the DIC sensor, this will appear as a superimposed, fictitious tension field, with similar but compressive impacts for opposite movements. A simple ray tracing diagram can be used to show that the impact of unanticipated out of plane movements on the accuracy of measured in plane displacements and strains (for 2D) scales directly with the offset distance of the camera and the magnitude of the out of plane movement. For sensors 2D1-2D8, the offset distances were relatively large. Furthermore, for these eight sensors, there were 3D sensors nearby (3D1 and 3D2 for 2D1-2D4, and 3D3 for 2D5-2D8) that captured out of plane motions and verified that these displacements were small.
Three 2D sensors (2D9-2D11) were used to measure deformations of the tops of floor slabs, at locations where 3D sensors (3D1-3D3) were used to measure the deformations at the bottom of the slabs. For these three 2D sensors, the offset distances were significantly smaller due to space considerations around the structure. It may be necessary to adjust the measurements of these 2D sensors as post processing of their results continues. Since 3D sensors were used on the slab bottoms at these locations, and thus the full field of out of plane motions for each image has been independently captured (assuming no through thickness strain in the slabs), this should be possible.
Examples of Measured Results
In support of the purpose of this paper (to describe the utility, strengths, challenges and mechanics of using multiple DIC sensors simultaneously) some example results are provided here. Fig. 5 shows the vertical displacements in the wall pier bases captured by sensors 2D1 and 2D2 when the structure was subjected to an initial lateral load of 45 kips (the ultimate load carried by the structure exceeded 420 kips). By plotting the displacements along horizontal axes coinciding with the pier bases and determining the slopes of these lines, the effect of base rotation on the initial lateral stiffness of the wall piers was determined, as shown in the figure.
Sensor Location 2D/3D Image Pixel
Density
Approx. FOV Width (in)
Approx. Offset Distance (in)
3D1 1st Story South Beam, Slab, Piers 3D 2 MP 70 120
3D2 1st Story North Beam, Slab, Piers 3D 1.3 MP 65 96
3D3 3rd Story South Beam, Slab, Piers 3D 2 MP 60 90
2D1 1st Story Southwest Pier 2D 1.3 MP 80 84
2D2 1st Story Southeast Pier 2D 1.3 MP 80 84
2D3 2nd Story Southwest Pier 2D 12 MP 160 60
2D4 2nd Story Southeast Pier 2D 12 MP 160 60
2D5 1st Story Northwest Pier 2D 12 MP 200 84
2D6 1st Story Northeast Pier 2D 10 MP 70 84
2D7 2nd Story Northwest Pier 2D 12 MP 200 72
2D8 2nd Story Northeast Pier 2D 12 MP 140 60
2D9 1st Story South Slab Top 2D 12 MP 60 36
2D10 3rd Story South Slab Top 2D 12 MP 60 36
Figure 5. Vertical displacements of wall pier bases
Fig. 6 shows the vertical displacements of the beam, slab, and upper portions of the wall piers of the 1st floor south location captured by sensor 3D1. The figure shows the east-most portion of the west pier and the west-most portion of the east pier. The images show that, as expected, the east portion of the west pier experiences compression and the west portion of the east pier experiences tension (uplift) when the structural system experiences drift towards the east, while this trend reverses under drift towards the west. The bending of the slab is evident as well, with positive (upward) displacement on the east side and negative on the west side for drift toward the east, with the trend again reversing for drift to the west. Holes in the captured data represent where traditional sensors (e.g. LVDTs) were installed. Lesson 3 earlier addresses this – since the camera view was obscured, no data was collected.
Figure 6. Vertical displacements of sensor 3D1: (a) lateral load 355 kips east; (b) 355 kips west Fig. 7 shows the horizontal strains for the same drifts as Fig. 6. The cracking of the bottom of the slab is visible in the red shaded regions (note that the width of the red shaded regions is not indicative of the actual crack widths), especially on the west side of the FOV when the structure
y = -0.00002487x + 0.02268011 y = -0.00002660x + 0.03502414 -0.040 -0.020 0.000 0.020 0.040 0.060 0.080 0 200 400 600 800 1000 1200 1400 Dis p lac ement (mm)
Width Across Pier (mm)
Southwest Pier (data from 2D1) Southeast Pier (data from 2D2) East East East East
experiences drift to the east, and as an approximately 45-degree crack originating from the east beam end when the structure experiences drift to the west. In some cases, cracks that show large positive (i.e., tensile) strains in earlier images do not in later images, as the drift behavior of the structure forces them closed. During the test, cracking was heard prior to the indication of slab cracking in the DIC sensors. Based on visual observations during the test, the slab in this location cracked initially outside the FOV of sensor 3D1, reinforcing Lesson 3 presented earlier. Additionally, concentrated crack opening at the lower boundary of the beam ends is indicated by the large tensile strains at the west beam end (for lateral drift to the east) and the east beam end (for lateral drift to the west). These key parameters will be used to validate the analytical models created to predict the performance of this novel system. More information about the research can be found at the project website at http://ptcoupledwalls.nd.edu.
Figure 7. Horizontal strains from sensor 3D1: (a) lateral load of 355 kips east; (b) 355 kips west
Summary and Conclusions
This paper has presented a synopsis of DIC measurement of deformations associated with structural testing. Key lessons learned presented included the importance of sizing patterns for the measured field of view, the inability to measure areas of the specimen that are visible obscured from the DIC sensors, and the vital nature of performing a pretest to ensure quality data is being captured before a test commences. A case study of DIC use on a large scale reinforced concrete coupled wall lateral load test was presented. On this project, a total of 14 DIC sensors were used simultaneously, believed to be the largest number ever deployed for a structural test. The mix of 2D and 3D sensors was used to capture cracking, gap opening, bending strains, in-plane and out-of-plane displacements, structural rotations, and other items of interest that can be used to validate structural behavior and improve analytical models that are used to predict future structural performance.
Acknowledgements
This project is a collaborative effort that includes the University of Notre Dame, the University of Texas at Tyler, and Lehigh University. The research is funded by the National Science Foundation (NSF) under Grant No. CMMI 1041598 as a part of the “George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Research (NEESR).” This award is a part of the National Earthquake Hazards Reduction Program (NEHRP). Support of the NSF Program Director
Dr. J. Pauschke is gratefully acknowledged. At the University of Texas at Tyler, students M. Lisk and M. Holloman worked on the development of the multiple DIC sensor protocol. At the Lehigh University NEES equipment site, laboratory staff (C. Bowman, P. Bryan, D. Fritchman, T. Maurullo, G. Novak, and E. Tomlinson), faculty members (R. Sause and J. Ricles), graduate students (K. Petersen, M. Tillotson, and K. Kazemibidokhti), and undergraduate students (A. Breden, M. Davis, F. Tao, E. Salazar, C. Fallon, and K. Brinkhoff) worked on the construction, instrumentation, and testing of the coupled wall specimen. The design of the test specimen was conducted in collaboration with practicing engineers from Magnusson Klemencic Associates (D. Fields, A. Haaland, and J. Mouras). The contributions of K. Bondy, Consulting Structural Engineer, to the project are also acknowledged. The concrete used to construct the test specimen was donated by Essroc Italcementi Group, the PT anchors were donated by Hayes Industries, Ltd., the PT strand was donated by Sumiden Wire Products Corporation (SWPC), and the formwork was donated by A.H. Harris & Sons, Inc. Additional material donations were made by Dayton Superior and Casilio Concrete. The findings, conclusions and/or recommendations expressed in this paper are those of the authors and do not necessarily represent the views of the individuals or organizations noted above.
References
1. Bing, P., Hui-min, X., Bo-qin, X., Fu-long, D. (2006). “Performance of Sub-pixel Registration Algorithms in Digital Image Correlation,” Measurement Science and Technology, 17, (6), 1615-1621.
2. Orteu, J. (2009). “3-D Computer Vision in Experimental Mechanics,” Optics and Lasers in Engineering, 47, (3-4), 282-291.
3. Tyson, J. Schmidt, T., Galanulis, K. (2002). “Advanced Photogrammetry for Robust Deformation and Strain Measurement,” SEM 2002 Annual Conference, Milwaukee, WI.
4. McGinnis, M. J., Smith, B., Holloman, M., Lisk, M., O’Donnell, A., Kurama, Y. (2012). “3-D Digital Image Correlation – An Underused Asset for Structural Testing,” ASCE Structures Congress, American Society of Civil Engineers, Chicago, Illinois.
5. ACI Innovation Task Group 5. 2007. Acceptance Criteria for Special Unbonded Post-Tensioned Precast Structural Walls Based on Validation Testing and Commentary (ACI ITG-5.1). Farmington Hills, MI: ACI. 6. Barbachyn S., Kurama Y., McGinnis M., Sause R., Peterson K. (2014). “Lateral Load Behavior of a
Post-Tensioned Coupled Core Wall,” 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK.
