This paper investigates a new robust optimization framework based on density-convex reliability model and applies it to the dimensional optimization of magnetic resonance (MR) compatible surgical robot. As a justified tool for assessing reliability, the density-convex model is proposed on account of the reality that available data information is always insufficient. Based on the density-convex model, reliability functions of structure are constructed and taken as constraint conditions. The Euclidean norm of the sensitivity Jacobian matrix is selected as robust index and stated as the ultimate objective function. By using finite element method and artificial neural network (FEM–ANN) method, the explicit functions of mechanical response are achieved effectively. The optimization is solved by a gradient-based optimization algorithm in the framework. As an application of the above optimization framework, a prototype robot is designed and manufactured. Finally, a test experiment verifies the high reliability of the robot and further proves the validity and effectiveness of this proposed method.
Issue Section:
Research Papers
References
1.
Gomes
, P.
, 2011
, “Surgical Robotics: Reviewing the Past, Analysing the Present, Imagining the Future
,” Rob. Comput.-Integr. Manuf.
, 27
(2
), pp. 261
–266
.10.1016/j.rcim.2010.06.0092.
Vaida
, C.
, Plitea
, N.
, Pisla
, D.
, and Gherman
, B.
, 2013
, “Orientation Module for Surgical Instrumentsła Systematical Approach
,” Meccanica
, 48
(1
), pp. 145
–158
.10.1007/s11012-012-9590-x3.
Thompson
, J.
, and Supple
, W.
, 1973
, “Erosion of Optimum Designs by Compound Branching Phenomena
,” J. Mech. Phys. Solids
, 21
(3
), pp. 135
–144
.10.1016/0022-5096(73)90015-X4.
Lin
, P. T.
, Gea
, H. C.
, and Jaluria
, Y.
, 2011
, “A Modified Reliability Index Approach for Reliability-Based Design Optimization
,” ASME J. Mech. Des.
, 133
(8), p. 044501
.10.1115/1.40044425.
Mashayekhi
, M.
, Salajegheh
, E.
, Salajegheh
, J.
, and Fadaee
, M. J.
, 2012
, “Reliability-Based Topology Optimization of Double Layer Grids Using a Two-Stage Optimization Method
,” Struct. Multidisc. Optim.
, 45
(6
), pp. 815
–833
.10.1007/s00158-011-0744-66.
Saha
, A.
, and Ray
, T.
, 2011
, “Practical Robust Design Optimization Using Evolutionary Algorithms
,” ASME J. Mech. Des.
, 133
(10), p. 101012
.10.1115/1.40048077.
Diez
, M.
, and Peri
, D.
, 2010
, “Robust Optimization for Ship Conceptual Design
,” Ocean Eng.
, 37
(11
), pp. 966
–977
.10.1016/j.oceaneng.2010.03.0108.
Doltsinis
, I.
, and Kang
, Z.
, 2004
, “Robust Design of Structures Using Optimization Methods
,” Comput. Methods Appl. Mech. Eng.
, 193
(23
), pp. 2221
–2237
.10.1016/j.cma.2003.12.0559.
Elishakoff
, I.
, 1995
, “Essay on Uncertainties in Elastic and Viscoelastic Structures: From AM Freudenthal's Criticisms to Modern Convex Modeling
,” Comput. Struct.
, 56
(6
), pp. 871
–895
.10.1016/0045-7949(94)00499-S10.
Moens
, D.
, and Vandepitte
, D.
, 2006
, “Recent Advances in Non-Probabilistic Approaches for Non-Deterministic Dynamic Finite Element Analysis
,” Archiv. Comput. Methods Eng.
, 13
(3
), pp. 389
–464
.10.1007/BF0273639811.
Venter
, G.
, and Haftka
, R.
, 1999
, “Using Response Surface Approximations in Fuzzy Set Based Design Optimization
,” Struct. Optim.
, 18
(4
), pp. 218
–227
.10.1007/BF0122330312.
Carreras
, C.
, and Walker
, I. D.
, 2000
, “Interval Methods for Improved Robot Reliability Estimation
,” Proceedings of Reliability and Maintainability Symposium, Annual, IEEE
, pp. 22
–27
.13.
Zhang
, A. R.
, and Liu
, X.
, 2012
, “Research on the Non-Probabilistic Reliability Based on Interval Model
,” Appl. Mech. Mater.
, 166
, pp. 1908
–1912
.10.4028/www.scientific.net/AMM.166-169.190814.
Ben-Haim
, Y.
, 1995
, “A Non-Probabilistic Measure of Reliability of Linear Systems Based on Expansion of Convex Models
,” Struct. Saf.
, 17
(2
), pp. 91
–109
.10.1016/0167-4730(95)00004-N15.
Qiu
, Z.
, Ma
, L.
, and Wang
, X.
, 2006
, “Ellipsoidal-Bound Convex Model for the Non-Linear Buckling of a Column With Uncertain Initial Imperfection
,” Int. J. Nonlinear Mech.
, 41
(8
), pp. 919
–925
.10.1016/j.ijnonlinmec.2006.07.00116.
Ben-Haim
, Y.
, 1994
, “A Non-Probabilistic Concept of Reliability
,” Struct. Saf.
, 14
(4
), pp. 227
–245
.10.1016/0167-4730(94)90013-217.
Ben-Haim
, Y.
, and Elishakoff
, I.
, 1995
, “Discussion on: A Non-Probabilistic Concept of Reliability
,” Struct. Saf.
, 17
(3
), pp. 195
–199
.10.1016/0167-4730(95)00010-218.
Lombardi
, M.
, and Haftka
, R. T.
, 1998
, “Anti-Optimization Technique for Structural Design Under Load Uncertainties
,” Comput. Methods Appl. Mech. Eng.
, 157
(1–2
), pp. 19
–31
.10.1016/S0045-7825(97)00148-519.
Qiu
, Z.
, and Elishakoff
, I.
, 2001
, “Anti-Optimization Technique—A Generalization of Interval Analysis for Nonprobabilistic Treatment of Uncertainty
,” Chaos, Solitons Fractals
, 12
(9
), pp. 1747
–1759
.10.1016/S0960-0779(00)00102-820.
Kang
, Z.
, Luo
, Y.
, and Li
, A.
, 2011
, “On Non-Probabilistic Reliability-Based Design Optimization of Structures With Uncertain-but-Bounded Parameters
,” Struct. Saf.
, 33
(3
), pp. 196
–205
.10.1016/j.strusafe.2011.03.00221.
Kang
, Z.
, and Luo
, Y.
, 2009
, “Non-Probabilistic Reliability-Based Topology Optimization of Geometrically Nonlinear Structures Using Convex Models
,” Comput. Methods Appl. Mech. Eng.
, 198
(41
), pp. 3228
–3238
.10.1016/j.cma.2009.06.00122.
Au
, F.
, Cheng
, Y.
, Tham
, L.
, and Zeng
, G.
, 2003
, “Robust Design of Structures Using Convex Models
,” Comput. Struct.
, 81
(28
), pp. 2611
–2619
.10.1016/S0045-7949(03)00322-523.
Jiang
, C.
, Han
, X.
, and Liu
, G.
, 2007
, “Optimization of Structures With Uncertain Constraints Based on Convex Model and Satisfaction Degree of Interval
,” Comput. Methods Appl. Mech. Eng.
, 196
(49
), pp. 4791
–4800
.10.1016/j.cma.2007.03.02424.
Jiang
, C.
, Han
, X.
, Lu
, G.
, Liu
, J.
, Zhang
, Z.
, and Bai
, Y.
, 2011
, “Correlation Analysis of Non-Probabilistic Convex Model and Corresponding Structural Reliability Technique
,” Comput. Methods Appl. Mech. Eng.
, 200
(33
), pp. 2528
–2546
.10.1016/j.cma.2011.04.00725.
Pantelides
, C. P.
, and Ganzerli
, S.
, 1998
, “Design of Trusses Under Uncertain Loads Using Convex Models
,” J. Struct. Eng.
, 124
(3
), pp. 318
–329
.10.1061/(ASCE)0733-9445(1998)124:3(318)26.
Jiang
, C.
, Bi
, R.
, Lu
, G.
, and Han
, X.
, 2013
, “Structural Reliability Analysis Using Non-Probabilistic Convex Model
,” Comput. Methods Appl. Mech. Eng.
, 254
, pp. 83
–98
.10.1016/j.cma.2012.10.02027.
Yanfang
, Z.
, Yanlin
, Z.
, and Yimin
, Z.
, 2011
, “Reliability Sensitivity Based on First-Order Reliability Method
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 225
(9
), pp. 2189
–2197
.10.1177/095440621140593828.
Caro
, S.
, Bennis
, F.
, and Wenger
, P.
, 2005
, “Tolerance Synthesis of Mechanisms: A Robust Design Approach
,” ASME J. Mech. Des.
, 127
(1), p. 86
–94
.10.1115/1.182504729.
Lauzier
, N.
, and Gosselin
, C.
, 2012
, “Performance Indices for Collaborative Serial Robots With Optimally Adjusted Series Clutch Actuators
,” ASME J. Mech. Rob.
, 4
(2
), p. 021002
.10.1115/1.400572330.
Jiang
, S.
, Liu
, S.
, and Feng
, W.
, 2011
, “PVA Hydrogel Properties for Biomedical Application
,” J. Mech. Behav. Biomed. Mater.
, 4
(7
), pp. 1228
–1233
.10.1016/j.jmbbm.2011.04.005Copyright © 2013 by ASME
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