A review of robust optimal design and its application in dynamics

The objective of robust design is to optimise the mean and minimize the variability that results from uncertainty represented by noise factors. The various objective functions and analysis techniques used for the Taguchi based approaches and optimisation methods are reviewed. Most applications of robust design have been concerned with static performance in mechanical engineering and process systems, and applications in structural dynamics are rare. The robust design of a vibration absorber with mass and stiffness uncertainty in the main system is used to demonstrate the robust design approach in dynamics. The results show a significant improvement in performance compared with the conventional solution.

[1]  James M. Lucas,et al.  How to Achieve a Robust Process Using Response Surface Methodology , 1994 .

[2]  Wei Chen,et al.  Quality utility : a Compromise Programming approach to robust design , 1999 .

[3]  Subrata Chakraborty,et al.  A stochastic finite element dynamic analysis of structures with uncertain parameters , 1998 .

[4]  Gyung-Jin Park,et al.  Robust optimization of an automobile rearview mirror for vibration reduction , 2001 .

[5]  Carl D. Sorensen,et al.  A general approach for robust optimal design , 1993 .

[6]  G. I. Schuëller,et al.  Computational stochastic mechanics – recent advances , 2001 .

[7]  Alan R. Parkinson,et al.  Robust optimal design using a second-order tolerance model , 1994 .

[8]  Genichi Taguchi,et al.  Quality Engineering through Design Optimization , 1989 .

[9]  Peter S. Pande,et al.  The Six Sigma Way: How GE, Motorola, and Other Top Companies are Honing Their Performance , 2000 .

[10]  Wei Chen,et al.  Exploration of the effectiveness of physical programming in robust design , 2000 .

[11]  George E. P. Box,et al.  Studies in Quality Improvement: Minimizing Transmitted Variation by Parameter Design , 1986 .

[12]  P. Hajela Nongradient Methods in Multidisciplinary Design Optimization-Status and Potential , 1999 .

[13]  G. Geoffrey Vining,et al.  Taguchi's parameter design: a panel discussion , 1992 .

[14]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[15]  Kwon-Hee Lee,et al.  Robust design for unconstrained optimization problems using the Taguchi method , 1996 .

[16]  Zissimos P. Mourelatos,et al.  Robust Design Using Preference Aggregation Methods , 2003, DAC 2003.

[17]  Shih-Pin Chen,et al.  Robust design with dynamic characteristics using stochastic sequential quadratic programming , 2003 .

[18]  Warren R. DeVries,et al.  Computer-Aided Tolerancing, Second Edition , 1991 .

[19]  P. A. Newman,et al.  Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives , 2001 .

[20]  R. Bishop Mechanical Vibration , 1958, Nature.

[21]  Farrokh Mistree,et al.  A procedure for robust design: Minimizing variations caused by noise factors and control factors , 1996 .

[22]  Peter R. Nelson,et al.  Design and Analysis of Experiments, 3rd Ed. , 1991 .

[23]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[24]  Achille Messac,et al.  Control-Structure Integrated Design , 1992 .

[25]  Singiresu S Rao,et al.  Robust optimization approach using Taguchi's loss function for solving nonlinear optimization problems , 1991, DAC 1991.

[26]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[27]  Indraneel Das,et al.  ROBUSTNESS OPTIMIZATION FOR CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS , 2000 .

[28]  Alan R. Parkinson,et al.  Robust Mechanical Design Using Engineering Models , 1995 .

[29]  D. B. Parkinson,et al.  Robust design employing a genetic algorithm , 2000 .

[30]  Kwok-Leung Tsui,et al.  AN OVERVIEW OF TAGUCHI METHOD AND NEWLY DEVELOPED STATISTICAL METHODS FOR ROBUST DESIGN , 1992 .

[31]  Donald R. Houser,et al.  A ROBUST OPTIMIZATION PROCEDURE WITH VARIATIONS ON DESIGN VARIABLES AND CONSTRAINTS , 1995 .

[32]  Liping Wang,et al.  AN EFFICIENT METHOD FOR PROBABILISTIC AND ROBUST DESIGN WITH NON -NORMAL DISTRIBUTIONS , 2002 .

[33]  Wei Chen,et al.  Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design , 2000 .

[34]  Farrokh Mistree,et al.  CONFIGURING TURBINE PROPULSION SYSTEMS USING ROBUST CONCEPT EXPLORATION , 1996 .

[35]  J. N. Siddall,et al.  A New Approach to Probability in Engineering Design and Optimization , 1984 .

[36]  John R. D'Errico,et al.  Statistical tolerancing using a modification of Taguchi's method , 1988 .

[37]  Kevin Otto,et al.  Extensions to the Taguchi method of product design , 1993 .

[38]  J. I The Design of Experiments , 1936, Nature.

[39]  Achille Messac,et al.  Physical programming - Effective optimization for computational design , 1996 .

[40]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[41]  Pierre Apkarian,et al.  Robust control via sequential semidefinite programming , 2001, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[42]  Alan R. Parkinson,et al.  Robust Optimal Design for Worst-Case Tolerances , 1994 .

[43]  Achille Messac Control-Structure Integrated Design with Closed-Form Design Metrics Using Physical Programming , 1998 .

[44]  Øyvind Bjørke,et al.  Computer Aided Tolerancing , 1989 .

[45]  R. H. Myers,et al.  Response Surface Alternatives to the Taguchi Robust Parameter Design Approach , 1992 .

[46]  Christopher A. Mattson,et al.  Handling Equality Constraints in Robust Design Optimization , 2003 .

[47]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[48]  Richard J. Balling,et al.  Consideration of Worst-Case Manufacturing Tolerances in Design Optimization , 1986 .

[49]  Timothy M. Cameron,et al.  Robust design optimization of structures through consideration of variation , 2002 .

[50]  I. Doltsinis,et al.  ROBUST DESIGN OF STRUCTURES USING OPTIMIZATION METHODS , 2004 .

[51]  Eyre,et al.  TWO CASE STUDIES IN THE USE OF TUNED VIBRATION ABSORBERS ON FOOT BRIDGES , 1981 .

[52]  Marcos Esterman,et al.  ROBUST DESIGN FOR DYNAMIC PERFORMANCE: OPTICAL PICK-UP EXAMPLE , 1997 .

[53]  Kwon-Hee Lee,et al.  Robust optimization considering tolerances of design variables , 2001 .

[54]  Singiresu S Rao,et al.  Efficient strategy for the robust optimization of large scale nonlinear design problems , 1994 .

[55]  Madhan Shridhar Phadke,et al.  Quality Engineering Using Robust Design , 1989 .

[56]  Mikel J. Harry,et al.  The Nature of Six Sigma Quality , 1988 .

[57]  R. Wets,et al.  Stochastic programming , 1989 .

[58]  Dimitri N. Mavris,et al.  A Probabilistic Approach to Multivariate Constrained Robust Design Simulation , 1997 .

[59]  T. Simpson,et al.  Conceptual design of a family of products through the use of the robust concept exploration method , 1996 .

[60]  R. W. Mayne,et al.  Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions , 1993 .

[61]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[62]  Arthur C. Taylor,et al.  Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives , 2001 .

[63]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[64]  Jianmin Li,et al.  Robust design optimization with mathematical programming neural networks , 2000 .

[65]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[66]  Achille Messac,et al.  From Dubious Construction of Objective Functions to the Application of Physical Programming , 2000 .

[67]  A. Ismail-Yahaya,et al.  Multiobjective robust design using physical programming , 2002 .

[68]  E. Beale ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[69]  K. Ishii,et al.  Design optimization for robustness using performance simulation programs , 1992 .

[70]  J. W. Smith,et al.  Vibration of Structures: Applications in civil engineering design , 1988 .

[71]  Jian Su,et al.  Automatic Differentiation in Robust Optimization , 1997 .

[72]  M. Shinozuka,et al.  Improved finite element method for stochastic problems , 1995 .

[73]  Wei Chen,et al.  A CONCEPT EXPLORATION METHOD FOR DETERMINING ROBUST TOP-LEVEL SPECIFICATIONS , 1996 .

[74]  William Y. Fowlkes,et al.  Engineering Methods for Robust Product Design: Using Taguchi Methods in Technology and Product Development , 1995 .

[75]  D. Draper,et al.  Stochastic Optimization: a Review , 2002 .

[76]  A. Belegundu,et al.  Robustness of Design Through Minimum Sensitivity , 1992 .