Reliability-Based Design Optimization of Structures using Modified Weighted Simulation Method
Authors
Abstract
Weighted Simulation-based Design Method (WSDM) is recently developed as an efficient method for Reliability-
Based Design Optimization (RBDO). Despite simplicity, this method degrades effectiveness to obtain accurate optimum design for
high dimension RBDO. Besides, its application range is restricted to RBDOs including only random design variables. In the
present study, local search strategy is employed to enhance the accuracy of conventional WSDOM, and to reduce the computational cost. Besides, a shifting strategy is proposed to increase the application range of WSDM for handling general RBDO problems. The efficiency of the proposed methods is investigated by solving some structural reliability problems.
Comparisonof the obtained results with exact solutions confirms accuracy and superiority of the proposed method for
solving various engineering problems.
Based Design Optimization (RBDO). Despite simplicity, this method degrades effectiveness to obtain accurate optimum design for
high dimension RBDO. Besides, its application range is restricted to RBDOs including only random design variables. In the
present study, local search strategy is employed to enhance the accuracy of conventional WSDOM, and to reduce the computational cost. Besides, a shifting strategy is proposed to increase the application range of WSDM for handling general RBDO problems. The efficiency of the proposed methods is investigated by solving some structural reliability problems.
Comparisonof the obtained results with exact solutions confirms accuracy and superiority of the proposed method for
solving various engineering problems.
Keywords
1. Cornell, C. A., “A Probability Based Structural
Code”, Journal of the American Concrete Institute,
Vol. 12, pp. 974-985, 1969.
2. Hasofer, A. M., and Lind, N. C., “Exact and
Invariant Second-Moment Code Format”, Journal of
the Engineering Mechanics Division ASCE, Vol.
100, pp. 111-121, 1974.
3. Rackwitz, R., and Fiessler, B., “Structural Reliability
under Combined Random Load Sequences”,
Computers and Structures, Vol. 9, pp. 489-494,
1978.
4. Qin, Q., Lin, D., Mei, G., and Chen, H., “Effects of
Variable Transformations on Errors in FORM
Results”, Reliability Engineering and Systems Safety,
Vol. 91, pp. 112-118, 2006.
5. Fiessler, B., Neumann, H. J., and Rackwitz, R.,
“Quadratic Limit States in Structural Reliability”,
Journal of Engineering Mechanics, Vol. 105, pp.
661-676, 1979.
6. Choi, S. K., and Grandhi, R. A., Reliability-Based
Structural Design, Springer, London, 2007.
7. Metropolis, N., and Ulam, S., “The Monte Carlo
Method”, Journal of the American Statistical
Association, Vol. 44, pp. 335-341, 1949.
8. Melchers, R. E., Structural Reliability Analysis and
Prediction, John Wiley & Sons, Chichester, 1999.
9. Olsson, A., Sandberg, G., and Dahlblom, O., “On
Latin Hypercube Sampling for Structural Reliability
Analysis”, Structural Safety, Vol. 25, pp. 47-68,
2003.
10. Ibrahim, Y., “Observations on Applications of
Importance Sampling in Structural Reliability
Analysis”, Structural Safety, Vol. 9, pp. 269-281,
1991.
11. Pradlwarter, H. J., and Schuëller, G. I., “Local
Domain Monte Carlo simulation”, Structural Safety,
Vol. 32, pp. 275-280, 2010.
12.Au, S. K., Ching, J., and Beck, J. L., “Application of
Subset Simulation Methods to Reliability Benchmark
Problems”, Structural Safety, Vol. 29, pp. 183-193,
2007.
13. Miao, F., and Ghosn, M., “Modified Subset
Simulation Method for Reliability Analysis of
Structural Systems”, Structural Safety, Vol. 33, pp.
251-260, 2011.
14. Pradlwarter, H. J., Schueller, G. I., Koutsourelakis, P.
S., and Charmpis, D. C., “Application of Line
Sampling Simulation Method to Reliability
Benchmark Problems”, Structural Safety, Vol. 29,
pp. 208-221, 2007.
15.Allaix, D. L., and Carbone, V. I., “An Improvement
of the Response Surface Method”, Structural Safety,
Vol. 33, pp. 165-172, 2011.
16. Faulim, J., Juan, A. A., Jose, S. M., and Marquez, E.
R., Simulation Methods for Reliability and
Availability of Complex Systems, Springer, London,
2010.
17. Torrie, G. M., and Valleau, P. J., “Nonphysical
Sampling Distribution in Monte Carlo Free-Energy
Estimation: Umbrella Sampling”, Journal of
Computational Physics, Vol. 23, pp. 187-199, 1977.
18. Rashki, M., Miri, M., and Azhdary Moghaddam, M.
A., “A New Efficient Simulation Method to
Approximate the Probability of Failure and Most
Probable Point”, Structural Safety, Vol. 39, pp. 22-
29, 2012.
19.Nikolaidis, E., and Burdisso, R., “Reliability Based
Optimization: A Safety Index Approach”, Computers
& Structures, Vol. 28, pp. 781-788, 1988.
20. Tu, J., Choi, K. K., and Park, Y. H., “A New Study
on Reliability-Based Design Optimization”, Journal
of Mechanical Design, Vol. 121, pp. 557-564, 1999.
21.Ohk, J. L., Yang, Y. S., and Ruy, W. S., “A
Comparative Study on Reliability-Index and Target-
Performance-Based Probabilistic Structural Design
Optimization”, Computers & Structures, Vol. 80, pp.
257-269, 2002.
22. Mohsine, A., and El Hami, A., “A Robust Study of
Reliability-Based Optimization Methods under
Eigen-Frequency”, Computer Methods in Applied
Mechanics and Engineering, Vol. 199, pp. 1006-
1018, 2010.
23.Dubourg, V., Sudret, B., and Bourinet, J. M.,
“Reliability-Based Design Optimization using
Kriging Surrogates and Subset Simulation”,
Structural Multidisciplinary Optimum, Vol. 44, pp.
673-690, 2011.
24. Royset, J. O., Der Kiureghian, A., and Polak, E.,
“Reliability-Based Optimal Structural Design by the
Decoupling Approach”, Reliable Engineering &
System Safety, Vol. 73, pp. 213-221, 2001.
25.Du, X., and Chen, W., “Sequential Optimization and
Reliability Assessment Method for Efficient
Probabilistic Design”, Journal of Mechanical
Design, Vol. 126, pp. 225-233, 2004.
26. Chen, Z., Qiu, H., Gao, L., and Li, P., “An Adaptive
Decoupling Approach for Reliability-Based Design
Optimization”, Computers & Structures, Vol. 117,
pp. 58-66, 2013.
27.Yang, T., and Hsieh, Y. H., “Reliability-Based
Design Optimization with Discrete Design Variables
and Non-Smooth Performance Functions: AB-PSO
Algorithm”, Automation in Construction, Vol. 20,
610-619, 2011.
28. Schuëller, G. I., and Jensen, H. A., “Computational
Methods in Optimization Considering Uncertainties-
An Overview”, Computer Methods in Applied
Mechanics and Engineering, Vol. 198, pp. 2-13,
2008.
29.Aoues, Y., and Chateauneuf, A., “Benchmark Study
of Numerical Methods for Reliability-Based Design
Optimization”, Structural Multidisciplinary
Optimum, Vol. 41, pp. 277-294, 2010.
30. Chen, X., Hasselman, T. K., and Neill, D. J.,
“Reliability Based Structural Design Optimization
for Practical Applications”, AIAA Journal, Vol. 97,
pp. 1403-1415, 1997.
31. Shan, S., and Wang, G. G., “Reliable Design Space
and Complete Single-Loop Reliability-Based Design
Optimization”, Reliable Engineering and System
Safety, Vol. 93, pp. 1218-30, 2008.
32. Rashki, M., Miri, M., and Azhdary Moghaddam, M.,
“A Simulation-Based Method for Reliability Based
Design Optimization Problems with Highly
Nonlinear Constraints”, Automation in Construction,
Vol. 47, pp. 24-26, 2014.
33. Madsen, H. O., “Omission Sensitivity Factors”,
Structural Safety, Vol. 5, pp. 35-45, 1988.
34.Hamed, M. M., and Bedient, P. B., “On the Effect of
Probability Distributions of Input Variables in Public
Health Risk Assessment”, Risk Analysis, Vol. 17(1),
pp. 97-105, 1997.
35. Zhang, Y. M., and Yang. Z., “Reliability-Based
Sensitivity Analysis of Vehicle Components with
Non-Normal Distribution Parameters”, International
Journal of Automotive Technology, Vol. 10, pp. 181-
194, 2009.
36. Hsu, K. S., and Chan, K. Y., “A Filter-Based Sample
Average SQP for Optimization Problems with
Highly Nonlinear Probabilistic Constraints”, Journal
of Mechanical Design, Vol. 132, pp. 111002-111009,
2010. DOI: 10.1115/DETC2009-86183.
37.Wu, Y. T., Shin, Y., Sues, R., and Cesare, M.,
“Safety-Factor Based Approach for Probability-
Based Design Optimization”, 19th AIAA Applied
Aerodynamics Conference, Fluid Dynamics and Colocated
Conferences, Anaheim, CA, U.S.A, pp. 1522,
2001.
38. Li, F., Wu, T., Hu, M., and Dong, J., “An Accurate
Penalty-Based Approach for Reliability-Based
Design Optimization”, Research in Engineering
Design, Vol. 21, pp. 87-98, 2010.
39. Lee, J. O., Yang, Y. S., and Ruy, W. S., “A
Comparative Study on Reliability-Index and Target
Performance-Based Probabilistic Structural Design
Optimization”, Computers & Structures, Vol. 80, pp.
257-269, 2002.
40. Shayanfar, M., Abbasnia, R., and Khodam, A.,
“Development of a GA-Based Method for
Reliability-Based Optimization of Structures with
Discrete and Continuous Design Variables Using
OpenSees and Tcl”, Finite Element Analysis and
Design, Vol. 90, pp. 61-73, 2014.
Code”, Journal of the American Concrete Institute,
Vol. 12, pp. 974-985, 1969.
2. Hasofer, A. M., and Lind, N. C., “Exact and
Invariant Second-Moment Code Format”, Journal of
the Engineering Mechanics Division ASCE, Vol.
100, pp. 111-121, 1974.
3. Rackwitz, R., and Fiessler, B., “Structural Reliability
under Combined Random Load Sequences”,
Computers and Structures, Vol. 9, pp. 489-494,
1978.
4. Qin, Q., Lin, D., Mei, G., and Chen, H., “Effects of
Variable Transformations on Errors in FORM
Results”, Reliability Engineering and Systems Safety,
Vol. 91, pp. 112-118, 2006.
5. Fiessler, B., Neumann, H. J., and Rackwitz, R.,
“Quadratic Limit States in Structural Reliability”,
Journal of Engineering Mechanics, Vol. 105, pp.
661-676, 1979.
6. Choi, S. K., and Grandhi, R. A., Reliability-Based
Structural Design, Springer, London, 2007.
7. Metropolis, N., and Ulam, S., “The Monte Carlo
Method”, Journal of the American Statistical
Association, Vol. 44, pp. 335-341, 1949.
8. Melchers, R. E., Structural Reliability Analysis and
Prediction, John Wiley & Sons, Chichester, 1999.
9. Olsson, A., Sandberg, G., and Dahlblom, O., “On
Latin Hypercube Sampling for Structural Reliability
Analysis”, Structural Safety, Vol. 25, pp. 47-68,
2003.
10. Ibrahim, Y., “Observations on Applications of
Importance Sampling in Structural Reliability
Analysis”, Structural Safety, Vol. 9, pp. 269-281,
1991.
11. Pradlwarter, H. J., and Schuëller, G. I., “Local
Domain Monte Carlo simulation”, Structural Safety,
Vol. 32, pp. 275-280, 2010.
12.Au, S. K., Ching, J., and Beck, J. L., “Application of
Subset Simulation Methods to Reliability Benchmark
Problems”, Structural Safety, Vol. 29, pp. 183-193,
2007.
13. Miao, F., and Ghosn, M., “Modified Subset
Simulation Method for Reliability Analysis of
Structural Systems”, Structural Safety, Vol. 33, pp.
251-260, 2011.
14. Pradlwarter, H. J., Schueller, G. I., Koutsourelakis, P.
S., and Charmpis, D. C., “Application of Line
Sampling Simulation Method to Reliability
Benchmark Problems”, Structural Safety, Vol. 29,
pp. 208-221, 2007.
15.Allaix, D. L., and Carbone, V. I., “An Improvement
of the Response Surface Method”, Structural Safety,
Vol. 33, pp. 165-172, 2011.
16. Faulim, J., Juan, A. A., Jose, S. M., and Marquez, E.
R., Simulation Methods for Reliability and
Availability of Complex Systems, Springer, London,
2010.
17. Torrie, G. M., and Valleau, P. J., “Nonphysical
Sampling Distribution in Monte Carlo Free-Energy
Estimation: Umbrella Sampling”, Journal of
Computational Physics, Vol. 23, pp. 187-199, 1977.
18. Rashki, M., Miri, M., and Azhdary Moghaddam, M.
A., “A New Efficient Simulation Method to
Approximate the Probability of Failure and Most
Probable Point”, Structural Safety, Vol. 39, pp. 22-
29, 2012.
19.Nikolaidis, E., and Burdisso, R., “Reliability Based
Optimization: A Safety Index Approach”, Computers
& Structures, Vol. 28, pp. 781-788, 1988.
20. Tu, J., Choi, K. K., and Park, Y. H., “A New Study
on Reliability-Based Design Optimization”, Journal
of Mechanical Design, Vol. 121, pp. 557-564, 1999.
21.Ohk, J. L., Yang, Y. S., and Ruy, W. S., “A
Comparative Study on Reliability-Index and Target-
Performance-Based Probabilistic Structural Design
Optimization”, Computers & Structures, Vol. 80, pp.
257-269, 2002.
22. Mohsine, A., and El Hami, A., “A Robust Study of
Reliability-Based Optimization Methods under
Eigen-Frequency”, Computer Methods in Applied
Mechanics and Engineering, Vol. 199, pp. 1006-
1018, 2010.
23.Dubourg, V., Sudret, B., and Bourinet, J. M.,
“Reliability-Based Design Optimization using
Kriging Surrogates and Subset Simulation”,
Structural Multidisciplinary Optimum, Vol. 44, pp.
673-690, 2011.
24. Royset, J. O., Der Kiureghian, A., and Polak, E.,
“Reliability-Based Optimal Structural Design by the
Decoupling Approach”, Reliable Engineering &
System Safety, Vol. 73, pp. 213-221, 2001.
25.Du, X., and Chen, W., “Sequential Optimization and
Reliability Assessment Method for Efficient
Probabilistic Design”, Journal of Mechanical
Design, Vol. 126, pp. 225-233, 2004.
26. Chen, Z., Qiu, H., Gao, L., and Li, P., “An Adaptive
Decoupling Approach for Reliability-Based Design
Optimization”, Computers & Structures, Vol. 117,
pp. 58-66, 2013.
27.Yang, T., and Hsieh, Y. H., “Reliability-Based
Design Optimization with Discrete Design Variables
and Non-Smooth Performance Functions: AB-PSO
Algorithm”, Automation in Construction, Vol. 20,
610-619, 2011.
28. Schuëller, G. I., and Jensen, H. A., “Computational
Methods in Optimization Considering Uncertainties-
An Overview”, Computer Methods in Applied
Mechanics and Engineering, Vol. 198, pp. 2-13,
2008.
29.Aoues, Y., and Chateauneuf, A., “Benchmark Study
of Numerical Methods for Reliability-Based Design
Optimization”, Structural Multidisciplinary
Optimum, Vol. 41, pp. 277-294, 2010.
30. Chen, X., Hasselman, T. K., and Neill, D. J.,
“Reliability Based Structural Design Optimization
for Practical Applications”, AIAA Journal, Vol. 97,
pp. 1403-1415, 1997.
31. Shan, S., and Wang, G. G., “Reliable Design Space
and Complete Single-Loop Reliability-Based Design
Optimization”, Reliable Engineering and System
Safety, Vol. 93, pp. 1218-30, 2008.
32. Rashki, M., Miri, M., and Azhdary Moghaddam, M.,
“A Simulation-Based Method for Reliability Based
Design Optimization Problems with Highly
Nonlinear Constraints”, Automation in Construction,
Vol. 47, pp. 24-26, 2014.
33. Madsen, H. O., “Omission Sensitivity Factors”,
Structural Safety, Vol. 5, pp. 35-45, 1988.
34.Hamed, M. M., and Bedient, P. B., “On the Effect of
Probability Distributions of Input Variables in Public
Health Risk Assessment”, Risk Analysis, Vol. 17(1),
pp. 97-105, 1997.
35. Zhang, Y. M., and Yang. Z., “Reliability-Based
Sensitivity Analysis of Vehicle Components with
Non-Normal Distribution Parameters”, International
Journal of Automotive Technology, Vol. 10, pp. 181-
194, 2009.
36. Hsu, K. S., and Chan, K. Y., “A Filter-Based Sample
Average SQP for Optimization Problems with
Highly Nonlinear Probabilistic Constraints”, Journal
of Mechanical Design, Vol. 132, pp. 111002-111009,
2010. DOI: 10.1115/DETC2009-86183.
37.Wu, Y. T., Shin, Y., Sues, R., and Cesare, M.,
“Safety-Factor Based Approach for Probability-
Based Design Optimization”, 19th AIAA Applied
Aerodynamics Conference, Fluid Dynamics and Colocated
Conferences, Anaheim, CA, U.S.A, pp. 1522,
2001.
38. Li, F., Wu, T., Hu, M., and Dong, J., “An Accurate
Penalty-Based Approach for Reliability-Based
Design Optimization”, Research in Engineering
Design, Vol. 21, pp. 87-98, 2010.
39. Lee, J. O., Yang, Y. S., and Ruy, W. S., “A
Comparative Study on Reliability-Index and Target
Performance-Based Probabilistic Structural Design
Optimization”, Computers & Structures, Vol. 80, pp.
257-269, 2002.
40. Shayanfar, M., Abbasnia, R., and Khodam, A.,
“Development of a GA-Based Method for
Reliability-Based Optimization of Structures with
Discrete and Continuous Design Variables Using
OpenSees and Tcl”, Finite Element Analysis and
Design, Vol. 90, pp. 61-73, 2014.
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