Multi-fidelity analysis and uncertainty quantification of beam vibration using correction response surfaces

Abstract A multi-fidelity model for beam vibration is developed by coupling a low-fidelity Euler-Bernoulli beam finite element model with a high-fidelity Timoshenko beam finite element model. Natural frequencies are used as the response measure of the physical system. A second order response surface is created for the low-fidelity Euler-Bernoulli model using the face centered design. Correction response surfaces for multi-fidelity analysis are created by utilizing the high-fidelity finite element predictions and the low-fidelity finite element predictions. It is shown that the multi-fidelity model gives accurate results with high computational efficiency when compared to the high-fidelity finite element model.

[1]  A. C. Aitken.  IV.—On Least Squares and Linear Combination of Observations , 1936 .

[2]  W. Thomson.  Theory of vibration with applications , 1965 .

[3]  H. H. Mabie,et al.  Transverse Vibrations of Double‐Tapered Cantilever Beams , 1972 .

[4]  R. S. Gupta,et al.  Finite element eigenvalue analysis of tapered and twisted Timoshenko beams , 1978 .

[5]  Sheldon M. Ross,et al.  Introduction to Probability and Statistics for Engineers and Scientists , 1987 .

[6]  Yu. G. Reshetnyak.  Space mappings with bounded distortion , 1967 .

[7]  J. Reddy.  An introduction to the finite element method , 1989 .

[8]  Raphael T. Haftka,et al.  Analysis and design of composite curved channel frames , 1994 .

[9]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[10]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[11]  Bernard Grossman,et al.  Variable-complexity response surface aerodynamic design of an HSCT wing , 1995 .

[12]  J. Mark.  Introduction to radial basis function networks , 1996 .

[13]  Bernard Grossman,et al.  MULTIFIDELITY RESPONSE SURFACE MODEL FOR HSCT WING BENDING MATERIAL WEIGHT , 1998 .

[14]  Timothy M. Mauery,et al.  COMPARISON OF RESPONSE SURFACE AND KRIGING MODELS FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION , 1998 .

[15]  Raphael T. Haftka,et al.  CORRECTION RESPONSE SURFACE APPROXIMATIONS FOR STRESS INTENSITY FACTORS OF A COMPOSITE STIFFENED PLATE , 1998 .

[16]  David Levin,et al.  The approximation power of moving least-squares , 1998, Math. Comput..

[17]  Jiawei Han,et al.  Data Mining: Concepts and Techniques , 2000 .

[18]  I A Basheer,et al.  Artificial neural networks: fundamentals, computing, design, and application. , 2000, Journal of microbiological methods.

[19]  Mikael A. Langthjem,et al.  Multifidelity Response Surface Approximations for the Optimum Design of Diffuser Flows , 2001 .

[20]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[21]  T. Simpson,et al.  A Study on the Use of Kriging Models to Approximate Deterministic Computer Models , 2003, DAC 2003.

[22]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[23]  Jeremy E. Oakley,et al.  Probability is perfect, but we can't elicit it perfectly , 2004, Reliab. Eng. Syst. Saf..

[24]  V. Toropov,et al.  Use of Moving Least Squares Method in Collaborative Optimization , 2005 .

[25]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[26]  J. Arbocz,et al.  Multi-fidelity optimization of laminated conical shells for buckling , 2005 .

[27]  Lipo Wang.  Support vector machines : theory and applications , 2005 .

[28]  Ramana V. Grandhi,et al.  Reliability-based Structural Design , 2006 .

[29]  A. Forrester,et al.  Design and analysis of 'noisy' computer experiments , 2006 .

[30]  Alexander I. J. Forrester,et al.  Multi-fidelity optimization via surrogate modelling , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Mathias Wintzer,et al.  Multifidelity design optimization of low-boom supersonic jets , 2008 .

[32]  M. Chandrashekhar,et al.  Uncertainty handling in structural damage detection using fuzzy logic and probabilistic simulation , 2009 .

[33]  Ranjan Ganguli,et al.  Effect of matrix cracking and material uncertainty on composite plates , 2010, Reliab. Eng. Syst. Saf..

[34]  Maurice Petyt,et al.  Introduction to Finite Element Vibration Analysis: Frontmatter , 2010 .

[35]  Qing Li,et al.  A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials , 2010 .

[36]  Chen Ying-guo.  Optimized Latin Hypercube Sampling Method and Its Application , 2011 .

[37]  Ranjan Ganguli.  Engineering Optimization: A Modern Approach , 2012 .

[38]  Z. Gao,et al.  Variable-fidelity optimization with design space reduction , 2013 .

[39]  Zhenghong Gao,et al.  Research on multi-fidelity aerodynamic optimization methods , 2013 .

[40]  Massimiliano Vasile,et al.  Robust Design of a Reentry Unmanned Space Vehicle by Multifidelity Evolution Control , 2013 .

[41]  Jlm Jan Hensen,et al.  Development of surrogate models using artificial neural network for building shell energy labelling , 2014 .

[42]  Michael S. Eldred,et al.  Multi-Fidelity Uncertainty Quantification: Application to a Vertical Axis Wind Turbine Under an Extreme Gust , 2014 .

[43]  Richard P. Dwight,et al.  Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging , 2015 .

[44]  R. Haftka,et al.  Review of multi-fidelity models , 2016, Advances in Computational Science and Engineering.

[45]  Shigeru Obayashi,et al.  Kriging surrogate model with coordinate transformation based on likelihood and gradient , 2017, J. Glob. Optim..

[46]  Benjamin Peherstorfer,et al.  Survey of multifidelity methods in uncertainty propagation, inference, and optimization , 2018, SIAM Rev..