基于可靠灰色粒子群算法的盾构机行星减速器轮系的多目标优化设计

Multi-objective Optimization Design on Gear Train of Planetary Reducer in Shield Tunneling Machine Based on Reliably Grey Particle Swarm Optimization

将方差的概念引入灰色关联度,创造性地提出可靠灰色关联度,以此作为变异策略来驾驭基本粒子群算法,可以很好地避免算法过早陷入局部最优。对要求为整数的各变量,将其初始位置与每次飞行速度均取为整数,即可确保所求得的解为整数解。同时,为易于理解和便于操作,对算法机理与算法流程进行阐述,从而,为复杂非线性约束条件下求解多目标混合整数规划问题提供一套切实可行的便捷方法。在4个假设条件的基础上,建立盾构机行星减速器的轮系在满足配齿、变位系数、干涉、强度、等强度、等寿命等约束条件下其体积最小、效率最高、接触强度与抗弯强度可靠性最高的四目标函数的数学模型,再运用上述可靠灰色粒子群算法编写Matlab程序对所建数学模型进行求解。研究结果表明,该算法的泛化能力不但解决该减速器原第三级强度偏弱的问题,而且在保证高可靠性条件下,使体积减少11.55%,效率提高0.56%,传动比提高3.67%,各级强度与寿命基本相等。

The sigma is introduced into grey relational degree,the notion of reliably grey relational degree is creatively put forward to be used as mutation strategy to control the basic particle swarm optimization（PSO）,which may avoid the problem that the algorithm prematurely falls into local optimum.For those variables called for integers,their initial position and speed of each flight are taken as integers,to ensure that the obtained solutions are integral.Meanwhile,to understand easily and operate conveniently,the mechanism and processes of the algorithm are illustrated,thus,a practical and convenient method is provided for multi-objective mixed integer programming problems subject to complex non-linear conditions.The mathematical models are constructed for planetary gear reducer in shield tunneling machine（STM） with 4 objective functions,that is to make its volume smallest,its efficiency highest and the reliability of its contacting and bending strength highest,which are subject to the conditions such as teeth,modification coefficient,interference,strength,equal strength and equal life on the basis of the 4 assumptions,which are solved by means of Matlab programming language compiled by using the reliably grey PSO.The research results show that generalization ability not only resolves the strength problem which is a little weak in the original 3rd grade of the planetary gear reducer,but also decreases the volume by 11.55% and increases the efficiency by 0.56% and the transmission ratio by 3.67%,and the strength and life in every grade are basically equal under the condition of ensuring high reliability.