改进博弈论四重组合赋权法下的开口甲板多目标拓扑优化设计

Multi-objective Topology Optimization Design of Opening Decks Using Improved Fourfold Combination Weighting Model of Game Theory

结构刚度、振动及开口处强度影响开口甲板服役寿命。针对开口甲板型式,以多项式惩罚模型(Polynomial penalization model,PPM)为理论依据并辅以三段式延拓(Three-stage continuation,TSC)法,提出一种基于折衷规划法(Compromise programming method,CPM)和改进博弈论四重组合赋权法(Improved fourfold combination weighting model of game theory,IFCWGT)的强度-刚度-振动多目标拓扑优化(Topology optimization,TO)综合策略。为缓解传统变密度法收敛至局部最优解及局部模态问题,将应用TSC技术的PPM引入至开口甲板多目标概念设计领域。建立结合CPM和PPM-TSC的最大单元应力最小化、静态多应变能最小化、动态多频率最大化的多目标TO模型并应用β法以获取Pareto妥协解。提出利用博弈论思想无偏好耦合层次分析(Analytic hierarchy process,AHP)法、熵权法(Entropy weight method,EWM)、基于层间相关性(Criteria importance through intercriteria correlation,CRITIC)法及变异系数法(Coefficient of variation method,CVM)的IFCWGT策略,以得到兼具设计决策者主观价值和数据客观性的子目标综合权重因子。研究表明,所提出的融合四种主客观赋权法的IFCWGT技术在子目标权重分配及开口甲板拓扑性能、拓扑布局方面更具先进性。

Structural stiffness,vibration,and strength at openings impact the service life of the opening deck.Using the polynomial penalization model(PPM)as the theoretical basis and the three-stage continuation(TSC)method,a multi-objective topology optimization(TO)integrated strategy of strength-stiffness-vibration based on the compromise programming method(CPM)and the improved fourfold combination weighting model of game theory(IFCWGT)is suggested for the opening deck.To alleviate the issue of convergence of the conventional variable density method to the local optimal solution and local modalities,PPM applying the TSC technique is introduced into the field of multi-objective concept design for the opening deck.A multi-objective TO model combining CPM and PPM-TSC for maximum unit stress minimization,static multi-strain energy minimization,and dynamic multi-frequency maximization is developed and theβmethod is applied to obtain the Pareto compromise solution.The IFCWGT strategy utilizing the game theory idea preference-free coupled the analytic hierarchy process(AHP),entropy weight method(EWM),criteria importance through intercriteria correlation(CRITIC)method,and coefficient of variation method(CVM)is presented to obtain sub-objective combination weight factors that combine the subjective value of design decision-makers and the objectivity of data.The results show that the proposed IFCWGT technique integrating four subjective and objective weighting methods is more advanced in terms of the sub-objective weight assignment as well as the topology performance and topology layout regarding the opening deck.