A Comparative Study of Uncertainty Propagation Methods in Structural Problems
 Manuele Corradi,
 Marco Gherlone,
 Massimiliano Mattone,
 Marco Di Sciuva
 … show all 4 hide
Abstract
Several uncertainty propagation algorithms are available in literature: (i) MonteCarlo simulations based on response surfaces, (ii) approximate uncertainty propagation algorithms, and (iii) non probabilistic algorithms. All of these approaches are based on some a priori assumptions about the nature of design variables uncertainty and on the models and systems behavior. Some of these assumptions could misrepresent the original problem and, consequently, could yield to erroneous design solutions, in particular where the prior information is poor or inexistent (complete ignorance). Therefore, when selecting a method to solve an uncertainty based design problem, several aspects should be considered: prior assumptions, nonlinearity of the performance function, number of input random variables and required accuracy. It could be useful to develop some guidelines to choose an appropriate method for a specific situation.
In the present work some classical structural problems will be studied in order to investigate which probabilistic approach, in terms of accuracy and computational cost, better propagates the uncertainty from input to output data. The methods under analysis will be: Univariate Dimension Reduction methods, Polynomial Chaos Expansion, FirstOrder Second Moment method, and algorithms based on the Evidence Theory for epistemic uncertainty. The performances of these methods will be compared in terms of moment estimations and probability density function construction corresponding to several scenarios of reliability based design and robust design. The structural problems presented will be: (1) the static, dynamic and buckling behavior of a composite plate, (2) the reconstruction of the deformed shape of a structure from measured surface strains.
 Lee, S.H., Chen, W. (2009) A Comparative study of uncertainty propagation methods for blackboxtype problems. Struct. Multidiscip. Optim. 37: pp. 239253 CrossRef
 Cerracchio, P., Gherlone, M., Mattone, M., Sciuva, M., Tessler, A. (2010) Shape sensing of threedimensional frame structures using the inverse finite element method. Proc. Fifth European Workshop on Structural Health Monitoring. pp. 615620
 Cerracchio, P., Gherlone, M., Mattone, M., Di Sciuva, M., Tessler, A.: Inverse finite element method for threedimensional frame structures. DIASP Report Politecnico di Torino 285 (2010)
 Xu, H., Rahman, S. (2003) A momentbased stochastic method for response moment and reliability analysis. Proc. Second MIT Conference on Computational Fluid and Solid Mechanics.
 Rahman, S., Xu, H. (2004) A univariate dimensionreduction method for multidimensional integration in stochastic mechanics. Probab. Eng. Mech. 19: pp. 393408 CrossRef
 Xu, H., Rahman, S. (2004) A generalized dimensionreduction method for multidimensional integration in stochastic mechanics. Int. J. Numer. Methods Eng. 65: pp. 19922019 CrossRef
 Wiener, N. (1938) The homogeneous chaos. Am. J. Math. 60: pp. 897936 CrossRef
 Cameron, R.H., Martin, W.T. (1947) The orthogonal development of nonlinear functionals in series of Fourier–Hermite functionals. Ann. Math. 48: pp. 385392 CrossRef
 Xiu, D., Karniadakis, G.M. (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24: pp. 619644 CrossRef
 Ticky, M. (1993) Applied Methods of Structural Reliability. Springer, Berlin CrossRef
 Helton, J.C., Johnson, J.D., Oberkampf, W.L., Storli, C.B.: A samplingbased computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Sandia report SAND20065557, Sandia National Laboratories (2006). http://prod.sandia.gov/techlib/accesscontrol.cgi/2006/065557.pdf
 Sentz, K., Ferson, S.: Combination of evidence in Dempster–Shafer theory. Sandia report SAND2002083, Sandia National Laboratories (2002). http://www.sandia.gov/epistemic/Reports/SAND20020835.pdf
 Saltelli, A., Chan, K., Scott, E.M. (2008) Sensitivity Analysis. Wiley, New York
 Crestaux, T., Maitre, O., Martinez, J.M. (2009) Polynomial chaos expansion for sensitivity analysis. Reliab. Eng. Syst. Saf. 94: pp. 11611172 CrossRef
 Tessler, A., Di Sciuva, M., Gherlone, M.: Refined zigzag theory for laminated composite and sandwich plates. NASA/TP2009215561, Langley Research Center (2009)
 Tessler, A., Sciuva, M., Gherlone, M. (2010) A consistent refinement of firstorder sheardeformation theory for laminated composite and sandwich plates using improved zigzag kinematics. J. Mech. Mater. Struct. 5: pp. 341367 CrossRef
 Tessler, A., Sciuva, M., Gherlone, M. (2008) A sheardeformation theory for composite and sandwich plates using improved zigzag kinematics. IX International Conference on Computational Structural Technology.
 Tessler, A., Sciuva, M., Gherlone, M. (2011) Refined zigzag theory for homogeneous, laminate composite, and sandwich plates: a homogeneous limit methodology for zigzag function selection. Numer. Methods Partial Differ. Equ. 27: pp. 208229 CrossRef
 Tessler, A., Spangler, J.L. (2005) A leastsquares variational method for fullfield reconstruction of elastic deformations in sheardeformable plates and shells. Comput. Methods Appl. Mech. Eng. 94: pp. 327339 CrossRef
 Corradi, M.: Uncertainty management techniques for aerospace structural design. Ph.D. thesis, Politecnico di Torino (2011)
 Title
 A Comparative Study of Uncertainty Propagation Methods in Structural Problems
 Book Title
 Computational Methods in Stochastic Dynamics
 Book Subtitle
 Volume 2
 Pages
 pp 87111
 Copyright
 2013
 DOI
 10.1007/9789400751347_6
 Print ISBN
 9789400751330
 Online ISBN
 9789400751347
 Series Title
 Computational Methods in Applied Sciences
 Series Volume
 26
 Series ISSN
 18713033
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media Dordrecht
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Manolis Papadrakakis ^{(ID1)}
 George Stefanou ^{(ID2)}
 Vissarion Papadopoulos ^{(ID3)}
 Editor Affiliations

 ID1. Inst. Structural Analysis & Seismic Res., National Technical University of Athens
 ID2. Inst. Structural Analysis & Seismic Res., National Technical University of Athens
 ID3. Inst. Structural Analysis & Seismic Res., National Technical University of Athens
 Authors

 Manuele Corradi ^{(1)}
 Marco Gherlone ^{(1)}
 Massimiliano Mattone ^{(1)}
 Marco Di Sciuva ^{(1)}
 Author Affiliations

 1. Department of Aeronautics and Space Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
Continue reading...
To view the rest of this content please follow the download PDF link above.