In this study, a structural optimisation problem, addressed through a stochastic multi-objective approach, is formulated and solved. The problem deals with the optimal design of exoskeleton structures, conceived as vibration control systems under seismic loading. The exoskeleton structure is assumed to be coupled to an existing primary inner structure for seismic retrofit: the aim is to limit the dynamic response of the primary structure to prevent structural damage. A non-stationary filtered Gaussian white noise stochastic process is taken as the seismic input. Design variables pertain to the mechanical properties (stiffness, damping) of the exoskeleton structure. Two concurrent and competing objective functions are introduced, in order to take into account not only safety performance but also economic cost considerations. The resulting trade-off is solved searching the Pareto front by way of a controlled elitist genetic algorithm, derived from the Non-dominated Sorting Genetic Algorithm-II. Sensitivities of Pareto fronts and Pareto optimal sets to different system parameters are finally investigated by way of a numerical application.

中文翻译：

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外骨骼结构的随机多目标优化

在这项研究中，制定并解决了通过随机多目标方法解决的结构优化问题。该问题涉及外骨骼结构的优化设计，被认为是地震载荷下的振动控制系统。假设外骨骼结构与现有的主要内部结构耦合以进行抗震改造：目的是限制主要结构的动态响应以防止结构损坏。将非平稳滤波高斯白噪声随机过程作为地震输入。设计变量与外骨骼结构的机械特性（刚度、阻尼）有关。引入了两个并发和竞争的目标函数，不仅要考虑安全性能，还要考虑经济成本。由此产生的权衡通过从非支配排序遗传算法 II 派生的受控精英遗传算法搜索帕累托前沿来解决。最后通过数值应用研究了帕累托前沿和帕累托最优集对不同系统参数的敏感性。