Adaptive Enhanced Beluga Whale Optimization for Structural Reliability Analysis of Engineering Structures
-
摘要: 结构可靠性分析是衡量工程结构不确定性的重要手段，其中一阶可靠度方法(FORM)因简单高效而被广泛使用，但依赖于梯度信息，且对高维非线性问题可能陷入不收敛. 该文引入自适应改进白鲸优化算法(hybrid Alibaba-beluga whale optimization, HABWO)进行工程结构可靠性分析，其中白鲸优化算法(beluga whale optimization, BWO)更新策略控制算法开发阶段，结合阿里巴巴与四十大盗优化算法(Alibaba and the forty thieves algorithm, AFT)的智慧等级与更新机制控制算法探索阶段，并发展了自适应策略来平衡算法的探索和开发能力. HABWO结合一阶可靠度方法寻优可靠指标，具有较好的全局寻优和收敛能力. 最后，通过三个工程结构可靠度分析案例进行验证，比较了6种不同的群智能优化算法. 分析结果表明，所提方法比其他智能优化算法具有更高的计算精度和稳定性.
-
关键词:
- 智能优化算法 /
- 白鲸优化算法 /
- 结构可靠性分析 /
- 一阶可靠度法 /
- 阿里巴巴与四十大盗优化算法
Abstract: Structural reliability analysis is an important technique in the uncertainty quantification of engineering structures, while the 1st-order reliability method (FORM) is popular due to its simplicity and efficiency. However, the FORM depends on the gradient information and may fall into local convergence for high-dimensional and highly nonlinear problems. The adaptive enhanced beluga whale optimization (BWO) was proposed for structural reliability analysis. The BWO with its updating rules was utilized to control the exploitation capacity, and the intelligence level of Alibaba and the forty thieves algorithm was combined with the updating mechanism to control the exploration capacity. Moreover, the adaptive strategy was developed to balance the exploration and exploitation, and the adaptive enhanced BWO was combined with the FORM to find the global reliability index in structural reliability analysis. Finally, 3 structural reliability problems in engineering were used to validate the HABWO-FORM, compared with 6 different metaheuristic algorithms. The results indicate that, the proposed method outperforms the comparative algorithms in terms of accuracy and robustness. -
图 4 屋架结构可靠度分析迭代曲线
Figure 4. Iterative curves of reliability analysis of a roof structure
图 6 框架结构可靠度分析迭代曲线
Figure 6. Iterative curves of reliability analysis of the frame structure
图 8 布洛溪大桥可靠度分析迭代曲线
Figure 8. Iterative curves of reliability analysis of the large span bridge structure
表 1 智能优化算法参数
Table 1. Algorithmic parameters for metaheuristics
algorithm parameter value all algorithms population size, maximum iterations, replication times 100, 600, 20 PSO cognitive and social constant，inertia weight linearly decreased at interval c1=2, c2=2，[0.9，0.1] EO α1, α2, GP 2, 1, 0.5 GEO Pα: propensity to attack
Pc: propensity to cruise[0.5，-2]
[1，-0.5]SSA leader position update probability 0.5 HHO probability thresholds of escaping, escaping energy 0.5, 0.5 BWO probability of whale fall decreased at interval Wf [0.1，0.05] HABWO control parameter 0.5, 0.5 
下载: 导出CSV
表 2 屋架结构随机变量分布
Table 2. A roof structure random variable distribution
variable description distribution pattern mean value μ variable coefficient q/(kN/m) mean vertical load normal distribution 20 0.07 l/m roof truss span normal distribution 12 0.01 As/m2 cross-sectional area normal distribution 9.82×10-4 0.06 Ac/m2 cross-sectional area normal distribution 4×10-2 0.12 Es/(kN/m2) modulus of elasticity normal distribution 1.0×1011 0.06 Ec/(kN/m2) modulus of elasticity normal distribution 2.0×1010 0.06
下载: 导出CSV
表 3 屋架结构可靠指标计算结果
Table 3. Calculation results of reliability indexes for a roof structure
method min mean max std CPU time/s PSO-FORM 2.434 1 2.491 0 2.787 0 0.102 0 0.44 EO-FORM 2.428 7 2.428 7 2.428 7 3.799 3×10-6 1.21 GEO-FORM 3.441 6 4.932 0 5.125 4 0.523 6 7.39 SSA-FORM 2.430 8 2.437 3 2.513 6 0.018 6 2.33 HHO-FORM 2.520 8 2.789 2 4.118 1 0.409 6 2.25 BWO-FORM 3.065 3 4.360 4 5.585 7 0.658 9 2.13 HABWO-FORM 2.428 7 2.428 7 2.428 7 2.267 4×10-7 1.06
下载: 导出CSV
表 4 框架结构可靠度分析的随机变量
Table 4. Frame structure random variable distributions
variable distribution pattern mean value standard deviation P1~P7/kN lognormal distribution 80 8 E/GPa normal distribution 200 20 (AB1~AB21)/m2 normal distribution 1.3×10-2 1.3×10-3 (IB1~IB21)/m4 normal distribution 7.0×10-4 7.0×10-5 (AC1~AC28)/m2 normal distribution 1.3×10-2 1.3×10-3 (IC1~IC28)/m4 normal distribution 3.0×10-4 3.0×10-5
下载: 导出CSV
表 5 框架结构可靠指标计算结果
Table 5. Calculation results of reliability indexes for the frame structure
method min mean max std CPU time/s PSO-FORM 4.828 9 6.823 4 9.807 5 1.237 0 569.38 EO-FORM 3.993 3 4.028 2 4.058 0 0.019 7 575.99 GEO-FORM 9.295 1 9.713 7 10.797 0 0.403 9 540.60 SSA-FORM 4.167 0 4.256 6 4.566 5 0.091 3 524.90 HHO-FORM 4.030 1 4.038 7 4.067 8 0.008 3 1 324.09 BWO-FORM 6.535 4 13.120 7 18.394 7 3.263 3 600.21 HABWO-FORM 3.965 1 3.973 3 4.002 7 0.009 0 538.16
下载: 导出CSV
表 6 布洛溪大桥可靠度分析的随机变量
Table 6. Large span bridge structure random variable distributions
variable distribution pattern mean value variable coefficient (A1~A34)/m2 normal distribution 0.076 18 0.1 (A35~A68)/m2 normal distribution 0.037 16 0.1 (A69-A103)/m2 normal distribution 0.039 02 0.1 (A104~A137)/m2 normal distribution 0.018 58 0.1 (E1~E137)/GPa normal distribution 201.097 0.08 P1/kN extreme typeⅠ distribution 2 035.266 0.18 P2/kN extreme typeⅠ distribution 1 017.633 0.17 P3/kN extreme typeⅠ distribution 1 017.633 0.16 P4/kN extreme typeⅠ distribution 1 017.633 0.15 P5/kN extreme typeⅠ distribution 1 017.633 0.14 P6/kN extreme typeⅠ distribution 1 017.633 0.13 P7/kN extreme typeⅠ distribution 1 017.633 0.12 P8/kN extreme typeⅠ distribution 1 017.633 0.11 P9/kN extreme typeⅠ distribution 1 017.633 0.10
下载: 导出CSV
表 7 布洛溪大桥可靠指标计算结果
Table 7. Calculation results of reliability indexes for the large span bridge structure
method min mean max std CPU time/s PSO-FORM 22.782 9 27.427 7 28.746 6 1.307 6 556.75 EO-FORM 4.929 7 6.278 9 8.429 4 0.830 6 547.15 GEO-FORM 3.826 2 4.130 5 4.879 7 0.246 2 551.98 SSA-FORM 4.058 6 4.376 3 4.732 8 0.186 3 533.18 HHO-FORM 3.241 3 4.438 3 5.496 2 0.719 0 1 346.84 BWO-FORM 21.430 7 23.567 8 26.948 2 1.656 7 595.23 HABWO-FORM 2.873 8 2.962 7 3.102 6 0.062 1 550.28
下载: 导出CSV
-
[1] ZHOU T, PENG Y, LI J. An efficient reliability method combining adaptive global metamodel and probability density evolution method[J]. Mechanical Systems and Signal Processing, 2019, 131: 592-616. doi: 10.1016/j.ymssp.2019.06.009 [2] 李彬, 郝鹏, 孟增, 等. 基于改进自适应混沌控制的逆可靠度分析方法[J]. 应用数学和力学, 2017, 38(9): 979-987. doi: 10.21656/1000-0887.380001LI Bin, HAO Peng, MENG Zeng, et al. An improved adaptive chaos control method for inverse reliability analysis[J]. Applied Mathematics and Mechanics, 2017, 38(9): 979-987. (in Chinese) doi: 10.21656/1000-0887.380001 [3] ZHANG R, DAI H. Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 403: 115689. doi: 10.1016/j.cma.2022.115689 [4] OU Y, CAI Y, ZENG L, et al. A teaching-learning-based optimization algorithm for reliability analysis with an adaptive penalty coefficient[J]. Structures, 2024, 65: 106695. doi: 10.1016/j.istruc.2024.106695 [5] GONG J X, YI P. A robust iterative algorithm for structural reliability analysis[J]. Structural and Multidisciplinary Optimization, 2011, 43(4): 519-527. doi: 10.1007/s00158-010-0582-y [6] HEIDARI A A, MIRJALILI S, FARIS H, et al. Harris Hawks optimization: algorithm and applications[J]. Future Generation Computer Systems, 2019, 97: 849-872. doi: 10.1016/j.future.2019.02.028 [7] RAO R V, SAVSANI V J, VAKHARIA D P. Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems[J]. Computer-Aided Design, 2011, 43(3): 303-315. doi: 10.1016/j.cad.2010.12.015 [8] 钟昌廷. 基于智能优化算法的工程结构可靠度研究[D]. 长沙: 湖南大学, 2020.ZHONG Changting. Study on reliability analysis of engineering structure based on intelligent optimization algorithms[D]. Changsha: Hunan University, 2020. (in Chinese) [9] 钟昌廷, 李刚. 基于生物地理-海鸥群优化的高维结构可靠性分析[J]. 计算力学学报, 2022, 39(1): 1-6.ZHONG Changting, LI Gang. Biogeography-based seagull optimization for high-dimensional structural reliability analysis[J]. Chinese Journal of Computational Mechanics, 2022, 39(1): 1-6. (in Chinese) [10] 杨小猛, 李亮, 胡雄飞, 等. 基于改进正余弦算法的抱杆结构优化[J]. 应用数学和力学, 2024, 45(5): 529-538. doi: 10.21656/1000-0887.440354YANG Xiaomeng, LI Liang, HU Xiongfei, et al. Structure optimization of holding poles based on the improved sine cosine algorithm[J]. Applied Mathematics and Mechanics, 2024, 45(5): 529-538. (in Chinese) doi: 10.21656/1000-0887.440354 [11] CHEN H, CHEN G, YANG D, et al. Neural network-based DPIM for uncertainty quantification of imperfect cylindrical stiffened shells with multiple random parameters[J]. Engineering Analysis With Boundary Elements, 2024, 166: 105795. doi: 10.1016/j.enganabound.2024.105795 [12] ZHONG C, LI G, MENG Z. Beluga whale optimization: a novel nature-inspired metaheuristic algorithm[J]. Knowledge-Based Systems, 2022, 251: 109215. doi: 10.1016/j.knosys.2022.109215 [13] JIA H, WEN Q, WU D, et al. Modified beluga whale optimization with multi-strategies for solving engineering problems[J]. Journal of Computational Design and Engineering, 2023, 10(6): 2065-2093. doi: 10.1093/jcde/qwad089 [14] LIU Y, WU G, GUO Y, et al. A new noncontact detection method for assessing the aging state of composite insulators[J]. IEEE Transactions on Industrial Informatics, 2024, 20(4): 6802-6813. doi: 10.1109/TII.2024.3352089 [15] WANG X, MEI X, WANG X, et al. Motion position prediction and machining accuracy compensation of galvanometer scanner based on BWO-GRU model[J]. Mechanical Systems and Signal Processing, 2024, 210: 111081. doi: 10.1016/j.ymssp.2023.111081 [16] BRAIK M, RYALAT M H, AL-ZOUBI H. A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves[J]. Neural Computing and Applications, 2022, 34(1): 409-455. doi: 10.1007/s00521-021-06392-x [17] HASOFER A M, LIND N C. Exact and invariant second-moment code format[J]. Journal of the Engineering Mechanics Division, 1974, 100(1): 111-121. doi: 10.1061/JMCEA3.0001848 [18] RACKWITZ R, FLESSLER B. Structural reliability under combined random load sequences[J]. Computers & Structures, 1978, 9(5): 489-494. [19] MEZURA-MONTES E, COELLO C A. Constraint-handling in nature-inspired numerical optimization: past, present and future[J]. Swarm and Evolutionary Computation, 2011, 1(4): 173-194. doi: 10.1016/j.swevo.2011.10.001 [20] EBERHART R, KENNEDY J. A new optimizer using particle swarm theory[C]//MHS' 95 Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya, Japan. IEEE, 1995: 39-43. [21] FARAMARZI A, HEIDARINEJAD M, STEPHENS B, et al. Equilibrium optimizer: a novel optimization algorithm[J]. Knowledge-Based Systems, 2020, 191: 105190. doi: 10.1016/j.knosys.2019.105190 [22] MOHAMMADI-BALANI A, DEHGHAN NAYERI M, AZAR A, et al. Golden eagle optimizer: a nature-inspired metaheuristic algorithm[J]. Computers & Industrial Engineering, 2021, 152: 107050. [23] MIRJALILI S, GANDOMI A H, MIRJALILI S Z, et al. Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems[J]. Advances in Engineering Software, 2017, 114: 163-191. doi: 10.1016/j.advengsoft.2017.07.002 -
图(8) / 表(7)
计量
- 文章访问数: 86
- HTML全文浏览量: 26
- PDF下载量: 8
- 被引次数: 0
渝公网安备50010802005915号