Abstract
Reliability-based design optimization (RBDO) is an effective method for structural optimization due to its ability to take into consideration uncertainties in design variables. Performance measure approach (PMA) based methods are commonly utilized to evaluate the probabilistic constraints of RBDO problems. The advanced mean value (AMV) method is a very commonly used due to its simpleness and effectiveness. However, the AMV method sometimes produces unstable and inefficient results for concave and highly nonlinear limit-state functions. In order to improve robustness and efficiency, many methods have been developed, for example, chaos control based and conjugate gradient-based methods. These methods lead to more stable results as compared with the AMV approach but they are inefficient for use in complex and convex limit-state functions. The RBDO of structural components is often a difficult issue due to complicated constraints. In this paper, a novel hybrid approach, referred to as “hybrid gradient analysis (HGA)” is introduced for the evaluation of both convex and concave constraint functions in RBDO. The HGA method combines AMV and conjugate gradient analysis (CGA). The robustness, simpleness and effectiveness of the proposed HGA method are compared with various PMA methods aimed at reliability such as AMV, chaos control (CC), conjugate mean value (CMV), modified chaos control (MCC), hybrid mean value (HMV) and CGA methods by means of several nonlinear convex/concave limit-state functions and structural RBDO problems. Reliability analysis and RBDO results point out that the HGA approach introduced here is more effective and robust than the well-known approaches.
References
1 B. S.Yildiz, A. R.Yildiz: Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod, Materials Testing60 (2018) No. 3, pp. 311–31510.3139/120.111153Search in Google Scholar
2 N.Pholdee, S.Bureerat, A. R.Yildiz: Hybrid real-code population-based incremental learning and differential evolution for many-objective optimization of an automotive floor-frame, International Journal of Vehicle Design70 (2017), No. 1–3, pp. 20–5310.1504/IJVD.2017.082578Search in Google Scholar
3 T.Guler, E.Demirci, A. R.Yildiz, U.Yavuz: Lightweight design of an automobile hinge component using glass fiber polyamide composites, Materials Testing60 (2018), No. 3, pp. 306–31010.3139/120.111152Search in Google Scholar
4 A. R.Yildiz, A.Alankuş, N.Kaya, F.Öztürk: Optimal design of vehicle components using topology design and optimisation, International Journal of Vehicle Design34 (2004), No. 4, pp. 387–39810.1504/IJVD.2004.004064Search in Google Scholar
5 A. R.Yildiz, E.Kurtulus, E.Demirci, B. S.Yildiz, S.Karagöz: Optimization of thin-wall structures using hybrid gravitational search and Nelder-Mead algorithm, Materials Testing58 (2016), No. 1, pp. 75–7810.3139/120.110823Search in Google Scholar
6 B. S.Yildiz, H.Lekesiz, A. R.Yildiz: Structural design of vehicle components using gravitational search and charged system search algorithms, Materials Testing58 (2016), No. 1, pp. 79–8110.3139/120.110819Search in Google Scholar
7 A. R.Yildiz, K. N.Solanki: Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach, International Journal of Advanced Manufacturing Technology59 (2012), No. 1, pp. 367–376, 10.1007/s00170-011-3496-ySearch in Google Scholar
8 A. R.Yildiz: Optimal structural design of vehicle components using topology design and optimization, Materials Testing50 (2008), No. 4, pp. 224–22810.3139/120.100880Search in Google Scholar
9 A. R.Yildiz: A new hybrid particle swarm optimization approach for structural design optimization in the automotive industry, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 226 (2012), No. 10, pp. 1340–135110.1177/0954407012443636Search in Google Scholar
10 B. S.Yildiz: A comparative investigation of eight recent population-based optimization algorithms for mechanical and structural design problems, International Journal of Vehicle Design73 (2017), No. 1–3, pp. 208–21810.1504/IJVD.2017.10003412Search in Google Scholar
11 B. S.Yildiz: Natural frequency optimization of vehicle components using the interior search algorithm, Materials Testing59 (2017), No. 5, pp. 456–45810.3139/120.111018Search in Google Scholar
12 M.Kiani, A. R.Yildiz: A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization, Archives of Computational Methods in Engineering23 (2016), No. 4, pp. 723–73410.1007/s11831-015-9155-ySearch in Google Scholar
13 E.Nikolaidis, R.Burdisso: Reliability-based optimization: a safety index approach, Computers and Structures28 (1988), No. 6, pp. 781–78810.1016/0045-7949(88)90418-XSearch in Google Scholar
14 J.Tu, K. K.Choi, Y. H.Park: A new study on reliability-based design optimization, ASME Journal of Mechanical Design121 (1999), No. 4, pp. 557–56410.1115/1.2829499Search in Google Scholar
15 M. V.Reddy, R. V.Grandhi, D. A.Hopkins: Reliability based structural optimization: a simplified safety index approach, Computers and Structures53 (1994), No. 6, pp. 1407–141810.1016/0045-7949(94)90406-5Search in Google Scholar
16 S-K.Choi, R. V.Grandhi, R. A.Canfield: Reliability-based Structural Design, Springer-Verlag, London, UK (2007)Search in Google Scholar
17 Y.Aoues, A.Chateauneuf: Benchmark study of numerical methods for reliability-based design optimization, Structural and Multidisciplinary Optimization41 (2010), No. 2, pp. 277–29410.1007/s00158-009-0412-2Search in Google Scholar
18 I.Enevoldsen, J. D.Sørensen: Reliability-based optimization in structural engineering, Structural Safety15 (1994), No. 3, pp. 169–19610.1016/0167-4730(94)90039-6Search in Google Scholar
19 J. O.Lee, Y. S.Yang, W. S.Ruy: A comparative study on reliability-index and target-performance-based probabilistic structural design optimization, Computers and Structures80 (2002), No. 3–4, pp. 257–26910.1016/S0045-7949(02)00006-8Search in Google Scholar
20 B. D.Youn, K. K.Choi: An investigation of nonlinearity of reliability based design optimization approaches, ASME Journal of Mechanical Design126 (2004), No. 3, pp. 403–41110.1115/1.1701880Search in Google Scholar
21 B. D.Youn, K. K.Choi, Y. H.Park: Hybrid analysis method for reliability-based design optimization, ASME Journal of Mechanical Design125 (2003), No. 2, pp. 221–23210.1115/1.1561042Search in Google Scholar
22 B. D.Youn, K. K.Choi, L.Du: Adaptive probability analysis using an enhanced hybrid mean value method, Structural and Multidisciplinary Optimization29 (2005), No. 2, pp. 134–14810.1007/s00158-004-0452-6Search in Google Scholar
23 D.Yang, P.Yi: Chaos control of performance measure approach for evaluation of probabilistic constraints, Structural and Multidisciplinary Optimization38 (2009), No. 1, pp. 83–9210.1007/s00158-008-0270-3Search in Google Scholar
24 Y. T.Wu, H. R.Millwater, T. A.Cruse: Advanced probabilistic structural analysis method for implicit performance functions, AIAA Journal28 (1990), No. 9, pp. 1663–166910.2514/3.25266Search in Google Scholar
25 Z.Meng, GLi, B. P.Wang, P.Hao: A hybrid chaos control approach of the performance measure functions for reliability-based design optimization, Computers and Structures146 (2015), pp. 32–4310.1016/j.compstruc.2014.08.011Search in Google Scholar
26 G.Ezzati, M.Mammadov, S.Kulkarni: A new reliability analysis method based on the conjugate gradient direction, Structural and Multidisciplinary Optimization51 (2015), No. 1, pp. 89–9810.1007/s00158-014-1113-zSearch in Google Scholar
27 P.Hao, B.Wang, G.Li, Z.Meng, L.Wang: Hybrid framework for reliability-based design optimization of imperfect stiffened shells, AIAA Journal53 (2015), No. 10, pp. 2878–287910.2514/1.J053816Search in Google Scholar
28 G.Li, Z.Meng, H.Hu: An adaptive hybrid approach for reliability-based design optimization, Structural and Multidisciplinary Optimization51 (2015), No. 5, pp. 1051–106510.1007/s00158-014-1195-7Search in Google Scholar
29 P.Wolfe: Convergence conditions for ascent methods, SIAM Review. 11 (1969), No. 2, pp. 226–23510.1137/1011036Search in Google Scholar
30 P.Wolfe: Convergence conditions for ascent methods. II: some corrections, SIAM Review13 (1971), No. 2, pp. 185–18810.1137/1013035Search in Google Scholar
31 X.Du, W.Chen: Sequential optimization and reliability assessment method for efficient probabilistic design, ASME Journal of Mechanical Design126 (2004), No. 2, pp. 225–23310.1115/1.1649968Search in Google Scholar
32 G.Cheng, L.Xu, L.Jiang: A sequential approximate programming strategy for reliability-based structural optimization, Computers and Structures84 (2006), No. 21, pp. 1353–136710.1016/j.compstruc.2006.03.006Search in Google Scholar
33 D.Pingel, P.Schmelcher, F. K.Diakonos: Stability transformation: a tool to solve nonlinear problems, Physics Reports400 (2004), No. 2, pp. 67–14810.1016/j.physrep.2004.07.003Search in Google Scholar
34 R.Fletcher, C. M.Reeves: Function minimization by conjugate gradients, The Computer Journal7 (1964), No. 2, pp. 149–15410.1093/comjnl/7.2.149Search in Google Scholar
35 R.Pytlak: Conjugate Gradient Algorithms in Nonconvex Optimization, Springer-Verlag, Berlin (2009)Search in Google Scholar
36 J.Nocedal, S. J.Wright: Numerical Optimization, Springer-Verlag, New York, USA (2006)Search in Google Scholar
37 L. P.Wang, R. V.Grandhi: Safety index calculation using intervening variables for structural reliability analysis, Computers and Structures59 (1996), No. 6, pp. 11139–114810.1016/0045-7949(96)00291-XSearch in Google Scholar
38 L. P.Wang, R. V.Grandhi: Efficient safety index calculation for structural reliability analysis, Computers and Structures52 (1994), No. 1, pp. 103–11110.1016/0045-7949(94)90260-7Search in Google Scholar
39 P.Wang, Z.Lu, Z.Tang: An application of the Kriging method in global sensitivity analysis with parameter uncertainty, Applied Mathematical Modelling372013), No. 9, pp. 6543–655510.1016/j.apm.2013.01.019Search in Google Scholar
40 B.Keshtegar, M.Bagheri: Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map, Nonlinear Dynamics91 (2018), No. 3, pp. 1443–145910.1007/s11071-017-3957-4Search in Google Scholar
41 B.Keshtegar, S.Chakraborty: Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints, Reliability Engineering and System Safety178 (2018), pp. 69–8310.1016/j.ress.2018.05.015Search in Google Scholar
42 B. D.Youn, K. K.Choi: An investigation of nonlinearity of reliability based design optimization approaches, ASME Journal of Mechanical Design126 (2018), No. 3, pp. 403–41110.1115/1.1701880Search in Google Scholar
43 L.Gu, R. J.Yang, C. H.Tho, M.Makowskit, O.Faruquet, Y.Li: Optimization and robustness for crashworthiness of side impact, International Journal of Vehicle Design26 (2001), No. 4, pp. 348–36010.1504/IJVD.2001.005210Search in Google Scholar
44 S.Karagöz, A. R.Yıldız: A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects, International Journal of Vehicle Design, 73 (2017), No. 1–3, pp. 179–18810.1504/IJVD.2017.10003410Search in Google Scholar
45 A. R.Yildiz, F.Ozturk: Hybrid taguchi-harmony search approach for shape optimization, Z.Geem (Ed.): Recent Advances in Harmony Search Algorithm, Springer, Berlin, Germany (2010), pp. 89–98Search in Google Scholar
46 A. R.Yildiz: A new hybrid particle swarm optimization approach for structural design optimization in the automotive industry, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering226 (2012), No. 10, pp. 1340–135110.1177/0954407012443636Search in Google Scholar
47 A. R.Yildiz, K.Saitou: Topology synthesis of multi-component structural assemblies in continuum domains, Transactions of ASME, Journal of Mechanical Design133 (2011), No. 1, pp. 1–910.1115/1.4003038Search in Google Scholar
48 A. R.Yildiz: A novel particle swarm optimization approach for product design and manufacturing. International Journal of Advance Manufacturing Technology40 (2009), pp. 617–62810.1007/s00170-008-1453-1Search in Google Scholar
49 A. R.Yıldız: A new hybrid artificial bee colony algorithm for robust optimal design and manufacturing, Applied Soft Computing13 (2013), pp. 2906–291210.1016/j.asoc.2012.04.013Search in Google Scholar
50 A. R.Yıldız: A comparative study of population-based optimization algorithms for turning operations, Information Sciences210 (2012), pp. 81–8810.1016/j.ins.2012.03.005Search in Google Scholar
51 A. R.Yildiz: Hybrid immune-simulated annealing algorithm for optimal design and manufacturing, International Journal of Materials and Product Technology34 (2009), No. 3, pp. 217–22610.1504/IJMPT.2009.024655Search in Google Scholar
52 I.Durgun, A. R.Yildiz: Structural Design Optimization of Vehicle Components Using Cuckoo Search Algorithm, Materials Testing, 54 (2017), No. 3, pp. 185–18810.3139/120.110317Search in Google Scholar
53 A. R.Yildiz: A novel hybrid immune algorithm for global optimization in design and manufacturing, Robotics and Computer-Integrated Manufacturing25 (2009), No. 2, pp. 261–27010.1016/j.rcim.2007.08.002Search in Google Scholar
54 A. R.Yildiz: An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry, Journal of Materials Processing Technology50 (2009), No. 4, pp. 224–22810.1016/j.jmatprotec.2008.06.028Search in Google Scholar
55 N.Öztürk, A. R.Yildiz, N.Kaya, F.Öztürk: Neuro-genetic design optimization framework to support the integrated robust design optimization process in CE, Journal of Intelligent Systems14 (2006), No. 1, pp. 5–1610.1177/1063293X06063314Search in Google Scholar
56 B. S.Yildiz, H.Lekesiz: Fatigue-based structural optimisation of vehicle components, International Journal of Vehicle Design73 (2017), pp. 54–6210.1504/IJVD.2017.10003398Search in Google Scholar
57 A. R.Yildiz, N.Kaya, N.Öztürk, F.Öztürk: Hybrid approach for genetic algorithm and Taguchi's method based design optimization in the automotive industry, International Journal of Production Research44 (2006), No. 22, pp. 4897–491410.1080/00207540600619932Search in Google Scholar
58 H.Gökdağ, A. R.Yildiz: Structural damage detection using modal parameters and particle swarm optimization Materials Testing54 (2012), No. 6, pp. 416–42010.3139/120.110346Search in Google Scholar
59 A. R.Yildiz, N.Öztürk, N.Kaya, F.Öztürk: Integrated optimal topology design and shape optimization using neural networks, Structural and Multidisciplinary Optimization25 (2003), No. 4, pp. 251–26010.1007/s00158-003-0300-013Search in Google Scholar
60 A. R.Yildiz, N.Öztürk, N.Kaya, F.Öztürk: Hybrid multi-objective shape design optimization using Taguchi's method and genetic algorithm, Structural and Multidisciplinary Optimization34 (2007), No. 4, pp. 317–33210.1007/s00158-006-0079-xSearch in Google Scholar
61 F.Hamza, H.Abderazek, S.Lakhdar, D.Ferhat, A. R.Yildiz: Optimum design of cam-roller follower mechanism using a new evolutionary algorithm, International Journal of Advance Manufacturing Technology99 (2018), No. 5–8, pp. 1267–128210.1007/s00170-018-2543-3Search in Google Scholar
62 A. R.Yildiz: Designing of optimum vehicle components using new generation optimization methods, Journal of Polytechnic20 (2017), No. 2, pp. 319–32310.2339/2017.20.2325-332Search in Google Scholar
63 B. S.Yildiz, A. R.Yildiz: Moth-flame optimization algorithm to determine optimal machining parameters in manufacturing processes, Materials Testing59 (2017), No. 5, pp. 425–42910.3139/120.111024Search in Google Scholar
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