A micro-accelerometer MDO benchmark problem

Many optimization and coordination methods for multidisciplinary design optimization (MDO) have been proposed in the last three decades. Suitable MDO benchmark problems for testing and comparing these methods are few however. This article presents a new MDO benchmark problem based on the design optimization of an ADXL150 type lateral capacitive micro-accelerometer. The behavioral models describe structural and dynamic effects, as well as electrostatic and amplification circuit contributions. Models for important performance indicators such as sensitivity, range, noise, and footprint area are presented. Geometric and functional constraints are included in these models to enforce proper functioning of the device. The developed models are analytical, and therefore highly suitable for benchmark and educational purposes. Four different problem decompositions are suggested for four design cases, each of which can be used for testing MDO coordination algorithms. As a reference, results for an all-in-one implementation, and a number of augmented Lagrangian coordination algorithms are given.

[1]  J. Sobieszczanski-Sobieski,et al.  Structural optimization by multilevel decomposition , 1983 .

[2]  Walter Murray,et al.  A local convergence analysis of bilevel decomposition algorithms , 2006 .

[3]  J. Rooda,et al.  An augmented Lagrangian decomposition method for quasi-separable problems in MDO , 2007 .

[4]  R. Howe,et al.  Viscous damping model for laterally oscillating microstructures , 1994 .

[5]  B. Boser,et al.  Surface micromachined accelerometers , 1995, Proceedings of the IEEE 1995 Custom Integrated Circuits Conference.

[6]  Robert D. Braun,et al.  Collaborative optimization: an architecture for large-scale distributed design , 1996 .

[7]  L Padula Sharon,et al.  MDO Test Suite at NASA Langley Research Center , 1996 .

[8]  Ashwin A. Seshia,et al.  On the optimization of compliant force amplifier mechanisms for surface micromachined resonant accelerometers , 2004 .

[9]  Kamran Behdinan,et al.  Evaluation of Multidisciplinary Optimization Approaches for Aircraft Conceptual D esign , 2004 .

[10]  Timo Veijola,et al.  Extending the validity of squeezed-film damper models with elongations of surface dimensions , 2005 .

[11]  J. Sobieszczanski-Sobieski,et al.  Bilevel Integrated System Synthesis for Concurrent and Distributed Processing , 2002 .

[12]  Ilan Kroo,et al.  Use of the Collaborative Optimization Architecture for Launch Vehicle Design , 1996 .

[13]  J. E. Rooda,et al.  An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers , 2006 .

[14]  Tamal Mukherjee,et al.  Optimization-based synthesis of microresonators , 1998 .

[15]  Raphael T. Haftka,et al.  Piezoresistive Microphone Design Pareto Optimization: Tradeoff Between Sensitivity and Noise Floor , 2006 .

[16]  Honglong Chang,et al.  Application of an optimization methodology for multidisciplinary system design of microgyroscopes , 2006 .

[17]  C. Leondes.  MEMS/NEMS : handbook techniques and applications , 2006 .

[18]  S. Senturia.  Microsystem Design , 2000 .

[19]  Richard J. Balling,et al.  Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems , 1997 .

[20]  Panos Y. Papalambros,et al.  A SYSTEM PARTITIONING AND OPTIMIZATION APPROACH TO TARGET CASCADING , 1999 .

[21]  Jaroslaw Sobieszczanski-Sobieski,et al.  OPTIMIZATION OF COUPLED SYSTEMS: A CRITICAL OVERVIEW OF APPROACHES , 1994 .

[22]  J. E. Rooda,et al.  Block-separable linking constraints in augmented Lagrangian coordination , 2009 .

[23]  Jaroslaw Sobieszczanski-Sobieski,et al.  Supersonic Business Jet Design Through Bi-Level Integrated System Synthesis , 1999 .

[24]  G.K. Fedder,et al.  Automated optimal synthesis of microaccelerometers , 1999, Technical Digest. IEEE International MEMS 99 Conference. Twelfth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.99CH36291).

[25]  Gyung-Jin Park,et al.  Comparison of MDO methods with mathematical examples , 2008 .

[26]  Jeremy J. Michalek,et al.  BB-ATC: Analytical Target Cascading Using Branch and Bound for Mixed-Integer Nonlinear Programming , 2006, DAC 2006.

[27]  T. Mukheljee,et al.  Mems design and verification , 2003, International Test Conference, 2003. Proceedings. ITC 2003..

[28]  J. Rooda,et al.  Augmented Lagrangian coordination for distributed optimal design in MDO , 2008 .

[29]  Jacobus E. Rooda,et al.  A classification of methods for distributed system optimization based on formulation structure , 2009 .

[30]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[31]  Layne T. Watson,et al.  Multidisciplinary Design Optimization with Quasiseparable Subsystems , 2005 .

[32]  Natalia Alexandrov,et al.  Comparative properties of collaborative optimization and other approaches to MDO , 1999 .