9th International Congress on Advances in Civil Engineering, 27-30 September 2010 Karadeniz Technical University, Trabzon, Turkey
Application of Digital Image Processing Technique on the Study of Dynamic Response of Structural Models on an Educational Shake Table H. T. Türker1, C.Mertayak2, S.Kocaman3 1
Department of Civil Engineering, Mustafa Kemal University, Hatay, Turkey,
[email protected] Department of Civil Engineering, Mustafa Kemal University, Hatay, Turkey,
[email protected] 3 Department of Civil Engineering, Mustafa Kemal University, Hatay, Turkey,
[email protected] 2
Abstract The paper presents an experimental study to investigate the Digital Image Processing (DIP) technique to be alternative to the existing displacement and acceleration measurement methods. The experimental tests were performed using an educational sake table developed in this work. A portable, unidirectional, shake table was manufactured. Different scaled structural models were constructed. These models were tested on the instructional shake table. Digital Image Processing technique was used to record the data from the experiment. A regular web camera was used to record the data. Although this study is based on a simple structure, the benefits of Image Processing technique include speed and ease is shown. Keywords: Digital Image Processing, Shake table, Dynamic, Vibration
1 Introduction One of the most important challenges facing civil engineers of today is the mitigation of the human and economic consequences of earthquakes. Civil engineers must have an understanding of the dynamic response of structures to ground motion caused by earthquakes. It is necessary to integrate this important topic into the undergraduate civil engineering curriculum. Experiments are very effective way of introducing basic concepts in structural dynamics and earthquake engineering. Even at the undergraduate level, concepts in dynamics such as natural frequencies and mode shapes can clearly be portrayed during such experiments. Earthquake simulator tables, or shake tables, are traditionally used for experimental research in earthquake engineering. There are several works (Dyke et all., 2003, 2006, Kinay, G. Ve Turan. G., 2006, Kutanis, M. 2007) which have been done on making educational shake table to introduce basic concepts in structural dynamics and earthquake engineering for undergraduate and graduate students. In all these works, data measurements are done by accelerometers attached at certain points of models. Displacements are not directly measured in time interval with these devices. The most common method of measuring the components of a motion like displacement, velocity and acceleration is applied by using conventional devices like transducers, strain gages and accelerometers. These devices are mounted in a model to record the data at a definite point and in a definite direction. During a simple test there should be more than one device mounted for each part or degree of freedom of the model. In this work, a portable, unidirectional educational shake table is manufactured by using very common materials in low cost (Mertayak C., 2009). The shake table consists of a tri-phase electrical motor with a redactor, frequency control driver and mechanical steel parts. Data which are necessary to calculate dynamic response of
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the structure (displacement, velocity, acceleration) are recorded at selected points with Digital Image Processing (DIP) technique. The purpose of this study is to investigate the Digital Image Processing technique (DIP) to be alternative to the existing measurement methods. DIP technique has been applied to different fields of engineering (Kocaman, S. 2007, McGinnis, M., Pessiki, S., Turker, H 2004, 2005). Low cost and non contact technique in measuring the displacement field of a structural member are the main reason to use the DIP for this study. Digital Image Processing is an optical method for full-field displacement by comparing images of deformed and undeformed shapes. Digital Image Processing method has great potential to become a new reliable technique in the measuring of structural component deformation in the future to replace the conventional method. During the vibration of the shake table, displacements of points at the shake plate and at storey levels are recorded during a definite time interval at the frequency adjusted by frequency driver. To examine DIP technique, various scaled structural models having different storey, masses and stiffness were constructed. The models were tested for free vibration and forced vibration in various frequencies. Based on the use of a known input excitation, the small-scale structure models were tested on the shake-table. Displacement, velocity and acceleration of selected points on structure models were recorded in time interval by DIP technique. Experimental results obtained from the shake table experiments were compared with theory. The consistency of the theoretical and the experimental results proved that DIP technique is good alternative for measuring displacements and accelerations.
2 Shake Table The shake table shown in Figure 1 is composed of an electrical motor mounted on a steel frame, a gear box to reduce the motors velocity, a variable frequency tri-phase electrical driver and a steel mechanism. The moving table has a dimension of 40 cm x 40 cm. The mechanism transferring the rotational movement of the redactor attracted by the motor into the unidirectional movement of a plate connected to the table. It can produce a vibration motion at 0-200 rpm range.
Figure 1. Shake table.
3 Structural Models The structural models are composed of elastic steel saws and aluminum frames. Various structural models with different stiffness, masses and stories were constructed and tested. Steel saws are used as columns in the structural models. Aluminum rectangular frames are used as floor system. The materials used in the models allow to preparation of structure models with different storey easily. Figure 2 shows three storey building model on the educational shake table.
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Figure 2. Structural Model.
To track the movement of the aluminum frame at the pictures of the video record, markers shown in Figure 3 are used to capture easier in pixels of the flowing frames of the video. The markers are attached to the frames as shown in Figure 3.
Figure 3. Markers attached to the model.
Steel saws used as columns make the structural system very flexible. Flexible structure allows seeing clearly the first tree modes of structure models by bare eyes and response of the structures under forced vibration.
4 Digital Image Processing (DIP) Technique Vibrations of structural models on the shake table were recorded by a web camera. The recorded video images were digitized as 320x480 pixels at 60 fps frame rates. To convert the pixels into meters, namely, to perform metric calibration one needs a predetermined reference length on the image like a map scale. For this purpose, a black line in lengths of 10 cm was drawn on floor frame (Fig.4). The pixel coordinates are converted to real measurements by calibration which is a proportional calculation of pixels versus real measurement value. From the video images, corresponding value of the reference length in the pixel was determined. Hence, ratio of pixel to length (cm) was computed. The software of “ImageJ” was used in obtaining the displacement of structural models in time interval from digitized images by converting pixels to meters. ImageJ can read many image formats and calculate pixel value statistics of userdefined selections. It can also measure distances and supports standard image processing functions such as contrast manipulations, sharpening, smoothing edge detection, and median filtering (Rasband 2005).
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Figure 4. Calibration of the Motion
At the first frame of the video, the marker is selected manually as reference point to track data in time interval. Then the rest of the frames are automatically tracked and each change in the position of the marker inside the rectangle is recorded as a coordinate in terms of pixel at each picture frame.
Figure 5. Image Processing Software.
By equalizing the corresponding number of pixels into 10 cm length, program calculates the change in the position of markers in terms of cm. So by the time intervals between frames, time dependent deflection values are obtained. They can be also converted to a graph or worksheet format (Figure 6).
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Deplasman (cm)
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38 37 36 35 34 33 32 0.00
1.01
2.01
3.02
4.03
5.03
6.04
7.05
8.05
9.06
10.07
Zaman (sn)
Figure 6. Motion Record of a free vibration.
When the tracking operation is repeated for another marker movement, all of the digital data can be added into the same worksheet or graph. By combining all motion of markers on the same graph as shown in Figure 7, the relative deflections can be calculated.
Figure 7. Forced vibration data (base and the frame response) Once getting the displacement in small time interval as shown in Figure 7, the dynamic response of a multi degree of freedom structure on the shake table can be analyzed during a free or forced vibration at a desired frequency and amplitude.
5 Comparison of Theory and Experiment
The experimental results obtained using DIP technique were compared to the results of theory.
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In this study, fundamental concepts of structural dynamics have been tested with the educational shake table. Periods, eigenvector, damping and response of structure model for 1 and 3 storey structure model have been found by both experiment using DIP technique and theory. Measurements of data from testing of structural model have been done by DIP technique. Comparison of theory with experimental data for 1 and 3 storey structural models are shown in Table 1 and Table 2. Table 1 shows the natural period of 1 storey structural model. Natural period of one storey structural model for different masses were calculated by theory (Chopra, Anıl K., 1995). Natural periods of the structural models were also found from shake table experiment by free vibration.
Table.1 Natural period of 1 storey structure model.
Experiment using DIP technique
Masses
Theory
% err
Mass-1
0.3892
0.3953
1.5
Mass-2
0.4661
0.4726
1.4
Mass-3
0.552
0.5576
1.0
In order to make experiment for 3 stories structural models, first, natural frequencies of the models were calculated by theory. Then by changing frequencies of the motors in small increments, first three frequencies of structure model were found by shake table experiment under harmonic motion. Figure 8 shows the second mode of the 3 storey structural model. Table 2 shows frequencies of the structure models for first 3 modes.
Figure 8. Vibration of a 3 DOF model in 2nd modal shape. Use of Digital Image Processing (DIP) technique gives also an opportunity to determine the damping characteristics (Fig 6), relationship between base motion and internal forces at any stage of motion at a definite frequency and amplitude adjusted by the shake table.
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Table.2 Natural frequencies of 3-stories structural model.
Masses
Theory
Experiment using DIP technique
Mod 1
10.88
10.8
-0.74
Mod 2
41.72
41.8
0.19
Mod 3
70.63
70.6
-0.04
% err
6 Discussion of Results An instructional shake table was developed with material available in market in low price. There is no attached instrument to record data on the system. Data (displacement, velocity, acceleration) in time interval were measured effectively by digital image processing techniques. Vibrations of the structural models from shake table experiment were recorded by a simple web camera in 60 frame/sec rate by 320x480 pixel pictures. Displacements were directly measured in time interval. The experimental results obtained using DIP technique were compared to both the results of theory and those obtained by numerical simulation models generated using SAP2000 software. As seen from Figure 7 first three modes of structural models are seen clearly by bare eyes. Although the capacity and the quality of the equipment is not so high, results obtained by DIP is satisfactory. Overall, the results of this study are encouraging in regards to the feasibility of using DIP technique for civil engineering problem.
References Baran, T. 2008. Yapıların Dinamik Davranışının Deneysel ve Teorik İncelenmesi, Doktora Tezi Çukurova Üniversitesi, Adana-Türkiye. Chopra, Anıl K., 1995. Dynamics of Structures. Theory and Applications to Earthquake Engineering Prentice Hall, 19-149 s, NJ-USA. Dyke. S.J.. Caiceclo. J.M. and Soto-Founiier. M. (2003).“University Consortium of Instructional Shake Tables: Enhancing Education in Earthquake Engineering.. Proceedings of the International Congress on Civil Engineering Education. Cuidad Real. Spain. Sept. 18-20. 2003. Dyke. S.J.. Johnson. SM.. Ranf R.T.. Caicedo. J.M. and Soto-Fournier. M. (2002).‘Advancing Earthquake Engineering Education through a Cooperative Effort Based on Instructional Shake Tables”. Proceedings of the Seventh US. National Conference on Earthquake Engineering. Boston. Massachusetts. Dyke. S.J.. Vaziri. P. and Roblee. C.(2006). Execution of the Vision for NEES Education. Outreach and Training. Proceedings of the International Conference on Engineering Education. Puerto Rico. McGinnis, M., Pessiki, S., Turker, H., "Digital Image Correlation Applied to Nondestructive Evaluation of Insitu Stresses in Concrete," Experimental Mechanics, Aug 2005; 45: 359 - 367. McGinnis, M., Pessiki, S., Turker, H., "Application of 3D Image Correlation Photogrammetry and Classical Photogrammetry to the Core-Drilling Method for Measuring In-Situ Stresses in Concrete Structures," ATLSS Report No. 04-16, Center for Advances Technology for Large Structural Systems, July 2004, 45 pp. Kinay, G. Ve Turan. G., (2006). Bir Masaüstü Deprem simülatörünün İmalatı ye Kontrolü, Yapısal Onarım ye Güçlendirme Sempozyumu (YOGS), Pamukkale, Denizli. (2006). pp 80-85. Kocaman, S. 2007. Baraj Yıkılması Probleminin Deneysel ve Teorik Olarak İncelenmesi, Doktora Tezi Çukurova Üniversitesi, Hatay-Türkiye. Kutanis, M. (2007) Eğitim Amaçlı Bir Deprem Similatörünün Tasarımı. Altıncı Ulusal Deprem Mühendisliği Konferaransı. İstanbul. Mertayak C., 2009 Yapı Modellerinin dinamik Davranışlarının Deneysel ve Teorik İncelenmesi, Yüksek Lisans Tezi Mustafa Kemal Üniversitesi, Hatay –Türkiye. Rasband, W.S., ImageJ, (1997-2005). U. S. Natdional Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/
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