Digital Image Correlation for Structural Health Monitoring

Gereon Welschof, summer semester 2018

Digital Image Correlation (DIC) can be used for periodic or long term monitoring of buildings and constructions in the fields of civil or mechanical engineering. Images of the object are taken at different times. These two states are optically compared by software and local deformation can be computed. Continuous monitoring can be achieved by collecting images from different dates.^[1] By using camera technique the method is suitable for holistic observation in large scale.

Motivation

The target of Structural Health Monitoring (SHM) can be summarized to the documentation of the condition of a building or construction. Analysing the condition the prevention of damage is possible and therefore the reduction of repair and maintenance as well as the assurance of safety. Constructions and buildings in the context of civil engineering are mostly designed to last over decades. Therefore the usual aging process of the material is a problem and has to be observed. Especially constructions in the context of infrastructure (e.g. bridges) are nowadays increasingly stressed by heavier and more frequent loads then it was designed for. Usually non-destructive measuring techniques are required to keep the functionality of the construction. In case of historic preservation or difficult access the applied method sometimes has to be even non-contact.^[2]

A conventional method in this field is the Terristic Laser Scan (TLS). To measure large scale objects nearly one million laser points per second scan the surface of the object. The laser beam is reflected from the objects suface and the geometrical deflection as well as the time delay can be computed to an image. Therefore this method is laserpoint based and needs time collect the data needed. To have a holistic image of the object within a short slot of time camera technique is required.^[3]

Digital Image Correlation

Principle

Developed from the so called least-squares matching the DIC is a non-destructive, non-contact material testing method on an optical measurement base. The principle is a comparison of grey values of single pixel and their distribution in measurement fields within images taken in two different states.^[4][5]

In the image taken the object is marked with the measurement field, as shown in figure 1, which has the size of NxN pixels. The measurement field is separated into many correlation fields of nxn pixels with equal spacing. These squares represent the area around observation points of the objects surface which have to be compared. The measurement field also reduces the calculation time by decreasing the evaluated area. The size of the correlation fields can be adjusted according to resolution of the picture and grain size of the texture of the objects surface in order to have optimal detection by the software.^[6]

According to Lehmann a possible approach is to use a cross correlation algorithm which compares the correlation fields of a second image with the reference correlation fields from the first image. Therefore a correlation coefficient $//<![CDATA[ \begin{array}{l}C_{corr}\end{array} //]]>$ is needed:^[8]

$//<![CDATA[ \begin{array}{l}C_{corr}=\frac{\sum_{i=1}^{n^2}(g_{i,1}-g_{a,1})(g_{i,2}-g_{a,2})}{\sqrt{\sum_{i=1}^{n^2}(g_{i,1}-g_{a,1})^2\sum_{i=1}^{n^2}(g_{i,2}-g_{a,2})^2}}\end{array} //]]>$

In this equation $//<![CDATA[ \begin{array}{l}g_{i,1}\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}g_{i,2}\end{array} //]]>$ are the grey values of the pixel within the reference field. Additionally $//<![CDATA[ \begin{array}{l}g_{a,1}\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}g_{a,1}\end{array} //]]>$ are average grey values to have the calculation independent from the deviation of the intensity of the overall grey value. Ideal correlation occurs if $//<![CDATA[ \begin{array}{l}C_{corr}=1\end{array} //]]>$, no correlation leads to $//<![CDATA[ \begin{array}{l}C_{corr}=0\end{array} //]]>$. This coefficient is calculated on each possible position of the objects surface.

The information of the first and second position is calculated into a shifting vector $//<![CDATA[ \begin{array}{l}u(x,y)\end{array} //]]>$ with a value on the $//<![CDATA[ \begin{array}{l}x\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}y\end{array} //]]>$ axis. Measuring accuracy is improved by a regression analysis by Gauss method of least squares. For the Calculation of the deformation the Green’s strain tensor is used. The resulting functions are the base of the strain evaluation.

$//<![CDATA[ \begin{array}{l}E_{jk}=\frac{1}{2}(u_{j,k}+u_{k,j}+u_{i,j}u_{i,k})\end{array} //]]>$

In direction of the x axis the tensor calculates to:

$//<![CDATA[ \begin{array}{l}E_{xx}=u_{x,x}+\frac{1}{2}{(u_{x,x}}^2+{u_{y,x}}^2)\end{array} //]]>$

Respecting the elongation ratio $//<![CDATA[ \begin{array}{l}\lambda\end{array} //]]>$ in $//<![CDATA[ \begin{array}{l}x\end{array} //]]>$ direction

$//<![CDATA[ \begin{array}{l}\lambda=\sqrt{1+2E_{xx}}\end{array} //]]>$

The logarithmical strain $//<![CDATA[ \begin{array}{l}\varphi\end{array} //]]>$ can be calculated:

$//<![CDATA[ \begin{array}{l}\varphi=ln(\lambda)\end{array} //]]>$

Experimental setup

The object measured has to have a clear texture for the algorithm to read off. For material science and micro scale applications the texture can be improved by painting on a black and white speckle pattern mostly by hand or using templates. As visible in figure 1 some big black dots are to coarse for the software used to be recognized. If two or more cameras are installed 3D models can be created. Depending on the geometry a Digital Volume Correlation (DVC) can even be required to avoid optical distortion by single angle perspective.^[9] The calibration of the cameras is done by using a calibration plate with a black and white pattern. All cameras are focussed on this plate for the software to have a consistent coordinate system to combine the different angles.^[10] Originally the DIC was developed for material and component testing and therefore working on a micro scale. The process for big scale DIC measurement like buildings is transferable and differs only in the grain size of the pattern detected by the software.

Field studies

To investigate the accuracy of DIC in large scale SHM application a sustainability experiment was implemented on a train bridge made out of stone. In the experiment the bridge was loaded asymmetrical in 1 MN steps up to 6 MN maximum load.

This load corresponds to six times the weight of an average locomotive. In figure 2 the four hydraulic pull anchors are visible on the right half of the arch of the bridge. In this case a two dimensional imaging with one camera would have been sufficient but in order to achieve higher resolution three cameras with a resolution of 6 megapixels were installed. The correlation fields were implemented with a grid width of 5 pixels as shown in figure 2. The texture of the brick stone wall offers enough texture to be detected whereas uniform surfaces may have to be modified. If only certain points of the buildings have to be measured it is possible to glue metal sheets with speckle pattern onto single spots of the construction.^[12]

In figure 2 the level of local deformation is shown by the coloured layer placed on the arch while the bridge is loaded with 4 MN. The bigger the strain the further the colours reach into the blue end of the scale also shown next to the graph in figure 3. The graph itself demonstrates the deflection of the bridge in y direction on a designated line over the whole length of the bridge. The maximum deflection of the structure is 6,3mm and due to the asymmetrical load located on the right side of the highest point of the arch.

Parallel the load test was documented with Terristic Laser Scans which showed a discrepancy to the DIC measuring on a scale of few tenth millimetres. DIC can also be used to measure vibration characteristics and will be relevant in future applications and a major process of the structural health monitoring (SHM).^[14] Another project focussed on the monitoring of 3 and 4-point bend tests of reinforced concrete. Due to the fine texture of the concrete a spackle pattern was painted onto the surface. It was shown that the DIC is able to detect non-visible cracks based on strain amplification. The same project also involved observation of spalling on reinforced concrete due to corrosion of the metal reinforcement. The Problem here is that a spackle pattern would spall of with the chips of concrete. Therefore a pattern was projected onto the surface with a high power projector to work in direct sunlight. Obviously no strain can be measured with this technique and its only applicable for surface measurement. The sensitivity for detected structures could be defined to less than 1mm on a measured field of 3x5metres.^[15]

Literature

1. Nonis, C. et al. Implementation of Digital Image Correlation for Structural Health Monitoring of Bridges. Plymouth : s.n., 2013. p.679
2. Große, C. U. Einführung in die Zerstörungsfreie Prüfung im Ingenieurwesen. Grundlagen und Anwendungsbeispiele. Technische Universität München, 2015. p.213
3. Tzuyang Yu et al. Structural Health Monitoring of Bridges using Digital Image Correlation. Proceedings of SPIE - The International Society for Optical Engineering. p.1
4. Burger, M.;Neitzel, F.;Lichtenberger, R. Einsatzpotential der digitalen Bildkorrelation zur Bauwerksüberwachung. 2017. p.2
5. Tzuyang Yu et al. Structural Health Monitoring of Bridges using Digital Image Correlation. Lowell : Proceedings of SPIE - The International Society for Optical Engineering, 2018. p.1-2
6. Lehmann, T. Experimentell numerische Analyse mechanischer Eigenschaften von Al-Mg-Werkstoffverbunden. Chemnitz : Dissertation, Technische Universität Chemnitz, 2011. p.83
7. Welschof, G. Mechanische Charakterisierung von Verbundgusskörpern mittels Biegeprüfung. München: Semesterarbeit, Technische Universität München, 2017. p.35
8. Lehmann, T. Experimentell numerische Analyse mechanischer Eigenschaften von Al-Mg-Werkstoffverbunden. Chemnitz : Dissertation, Technische Universität Chemnitz, 2011. p.83-85
9. Tzuyang Yu et al. Structural Health Monitoring of Bridges using Digital Image Correlation. Lowell : Proceedings of SPIE - The International Society for Optical Engineering, 2018. p.2
10. GOM mbH. ARAMIS Benutzerhandbuch - Software. Braunschweig, 2009. p.3-7
11. Burger, M.;Neitzel, F.;Lichtenberger, R. Einsatzpotential der digitalen Bildkorrelation zur Bauwerksüberwachung. 2017. p.10
12. Bell, Erin Santini. Digital Image Correlation Application to Structural Health Monitoring. University of New Hampshire. p.30-33
13. Burger, M.;Neitzel, F.;Lichtenberger, R. Einsatzpotential der digitalen Bildkorrelation zur Bauwerksüberwachung. 2017. p.4
14. Burger, M.;Neitzel, F.;Lichtenberger, R. Einsatzpotential der digitalen Bildkorrelation zur Bauwerksüberwachung. 2017. p.7-14
15. Tzuyang Yu et al. Structural Health Monitoring of Bridges using Digital Image Correlation. Lowell : Proceedings of SPIE - The International Society for Optical Engineering, 2018 p.2-6