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Error Assessment in Stereo-based Deformation Measurements

Part II: Experimental Validation of Uncertainty and Bias Estimates

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Abstract

Increasing interest in the use of digital image correlation (DIC) for full-field surface shape and deformation measurements has led to an on-going need for both the development of theoretical formulae capable of providing quantitative confidence margins and controlled experiments for validation of the theoretical predictions. In the enclosed work, a series of stereo vision experiments are performed in a manner that provides sufficient information for direct comparison with theoretical predictions using formulae developed in Part I. Specifically, experiments are performed to obtain appropriate optimal estimates and the uncertainty margins for the image locations/displacements, 3-D locations/displacements and strains when using the method of subset-based digital image correlation for image matching. The uncertainty of locating the 3-D space points using subset-based pattern matching is estimated by using theoretical formulae developed in Part I and the experimentally defined confidence margins for image locations. Finally, the uncertainty in strains is predicted using formulae that involves both the variance and covariance of intermediate variables during the strain calculation process. Results from both theoretical predictions and the experimental work show the feasibility and accuracy of the predictive formulae for estimating the uncertainty in the stereo-based deformation measurements.

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Notes

  1. The number of views of the 12 × 9 calibration grid was in the range 30 ≤ Nviews ≤ 100 when performing the calibration processes for other camera systems and setups. Results indicate Nviews > 30 has a minor effect on the optimal parameter values.

  2. The combination of scale factor and focal length shown in equation (13) in Part I are used in this work in the same way as described previously. Since the scale factors, λx and λy are set equal to 156 pixels/mm in this study, the value provided by the camera manufacturer, only the optimally estimated focal length is shown in Table 2. Direct multiplication of scale factor by focal length corresponds to the term used in Part I.

  3. All image correlation measurements in this work were performed using the commercial code, VIC-3D, developed by Correlated Solutions, Incorporated www.correlatedsolutions.com

  4. Since the specimen is nominally planar, if all coordinates for deformed and undeformed positions are converted to the (x,y,z) system shown in Fig. 1, then there is no need for further transformations to define a planar surface patch.

  5. The strain values in this work are quite small, so that the linear approximation for strain is entirely adequate (e.g., εxx ≈ ∂u/∂x).

  6. Theoretical results based on analyses outlined in Part I for variance in 3D positions were found to be in excellent agreement with predictions provided by Correlated Solutions, Incorporated.

References

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Acknowledgements

The financial support of Sandia National Laboratory through Sandia Contract PO#551836, the support of Dr. Bruce Lamattina through ARO# W911NF-06-1-0216 and the support provided by Dr. Stephen Smith through NASA NNX07AB46A are gratefully acknowledged. In addition, the research support provided by the Department of Mechanical Engineering at the University of South Carolina is also gratefully acknowledged.

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Authors and Affiliations

  1. Correlated Solutions Inc, 120 Kaminer Way Parkway Suite A, Columbia, SC, 29210, USA

    X.-D. Ke (SEM member) & H. W. Schreier (SEM member)

  2. Department of Mechanical Engineering, University of South Carolina, 300 South Main Street, Columbia, SC, 29208, USA

    M. A. Sutton (SEM fellow) & Y. Q. Wang

Authors
  1. X.-D. Ke
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  2. H. W. Schreier
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  3. M. A. Sutton
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  4. Y. Q. Wang
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Correspondence to M. A. Sutton.

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Ke, XD., Schreier, H.W., Sutton, M.A. et al. Error Assessment in Stereo-based Deformation Measurements. Exp Mech 51, 423–441 (2011). https://doi.org/10.1007/s11340-010-9450-3

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  • DOI: https://doi.org/10.1007/s11340-010-9450-3

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