Enhanced Morris for the extraction of significant parameters in high-dimensional design optimization

The traditional Morris method cannot ensure the consistent extraction of significant parameters because its random sampling strategy often leads to an improper coverage of the input space, especially when the number of sample points is small. To overcome the drawbacks, we developed an improved sampling strategy to enhance the performance of Morris method based on Latin hypercube sampling (LHS) with the idea of Central composite design (CCD) and a fluctuant step to generate a more uniform points set. A comparison on the results of a numerical example obtained by the enhanced Morris, the traditional methods and CCS-Morris demonstrated that the former had a much better performance. The application of the enhanced Morris method in the high-dimensional optimization of a compressor shell with 15 design parameters aimed at increasing its natural frequencies and keeping its mass relatively light demonstrates that the method is effective and applicable in engineering design.

[1]  G. Gary Wang,et al.  Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions , 2010 .

[2]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[3]  Richard Baumgartner,et al.  Mapping high-dimensional data onto a relative distance plane - an exact method for visualizing and characterizing high-dimensional patterns , 2004, J. Biomed. Informatics.

[4]  Kamran Behdinan,et al.  Multidisciplinary wing design optimization considering global sensitivity and uncertainty of approximation models , 2014 .

[5]  M. Gevrey,et al.  Review and comparison of methods to study the contribution of variables in artificial neural network models , 2003 .

[6]  Alexander J. Smola,et al.  Support Vector Method for Function Approximation, Regression Estimation and Signal Processing , 1996, NIPS.

[7]  Antonio J. Conejo,et al.  A closed formula for local sensitivity analysis in mathematical programming , 2006 .

[8]  Wei-Xin Ren,et al.  Parameter Selection in Finite-Element-Model Updating by Global Sensitivity Analysis Using Gaussian Process Metamodel , 2015 .

[9]  Paola Annoni,et al.  Sixth International Conference on Sensitivity Analysis of Model Output How to avoid a perfunctory sensitivity analysis , 2010 .

[10]  T. Simpson,et al.  Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization , 2004 .

[11]  C. Rauch.  On uncertainty and local sensitivity analysis for transient conjugate heat transfer problems , 2012 .

[12]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[13]  Benjamin Lamoureux,et al.  A combined sensitivity analysis and kriging surrogate modeling for early validation of health indicators , 2014, Reliab. Eng. Syst. Saf..

[14]  H. Yang,et al.  Global sensitivity analysis and coupling effects of forming parameters on wall thinning and cross-sectional distortion of rotary draw bending of thin-walled rectangular tube with small bending radius , 2014 .

[15]  H. Rabitz,et al.  High Dimensional Model Representations Generated from Low Dimensional Data Samples. I. mp-Cut-HDMR , 2001 .

[16]  T. Y. Li,et al.  Space harmonic analysis of sound radiation from a submerged periodic ring-stiffened cylindrical shell , 2006 .

[17]  M. Gevrey,et al.  Two-way interaction of input variables in the sensitivity analysis of neural network models , 2006 .

[18]  Jonathan A. Wright,et al.  Variable convergence in evolutionary optimization and its relationship to sensitivity analysis , 2012 .

[19]  C. Shoemaker,et al.  Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization , 2013 .

[20]  Abdelkhalak El-Hami,et al.  Global sensitivity analysis and multi-objective optimisation of loading path in tube hydroforming process based on metamodelling techniques , 2014 .

[21]  Jay Kim,et al.  SOUND TRANSMISSION THROUGH PERIODICALLY STIFFENED CYLINDRICAL SHELLS , 2002 .

[22]  Peter Winker,et al.  Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs , 2002, Math. Comput..

[23]  Dong-Hoon Choi,et al.  Adaptive parallel decomposition for multidisciplinary design , 2004 .

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

[25]  Kang Tai,et al.  Mathematical modelling of burr height of the drilling process using a statistical-based multi-gene genetic programming approach , 2014 .

[26]  Mark J. Embrechts,et al.  SVM sensitivity analysis: an application to currency crises aftermaths , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[27]  Kai Zhao,et al.  Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search , 2011, Appl. Soft Comput..

[28]  José Ferrer,et al.  An improved sampling strategy based on trajectory design for application of the Morris method to systems with many input factors , 2012, Environ. Model. Softw..

[29]  Mohammad Rasouli,et al.  Uncertainties in energy and economic performance of HVAC systems and energy recovery ventilators due to uncertainties in building and HVAC parameters , 2013 .

[30]  Svend Svendsen,et al.  Method and simulation program informed decisions in the early stages of building design , 2010 .

[31]  Dae-Sung Bae,et al.  Sensitivity analysis of suspension characteristics for Korean high speed train , 2009 .

[32]  Vincent Lemort,et al.  Global Sensitivity Analysis applied to Total Energy Use in Buildings , 2012 .

[33]  Jue Yang,et al.  Stability region of floating intermediate support in a shaft system with multiple universal joints , 2014 .

[34]  Jun Xia,et al.  An efficient integrated approach for global sensitivity analysis of hydrological model parameters , 2013, Environ. Model. Softw..

[35]  Andrea Saltelli,et al.  An effective screening design for sensitivity analysis of large models , 2007, Environ. Model. Softw..