Multi-objective optimisation for improving the seismic protection performance of a multi-storey adaptive negative stiffness system based on modified NSGA-II with DCD

Installing adaptive negative stiffness devices (ANSD) on multiple storeys of a building structure to develop a smart seismic protection system, namely multi-storey adaptive negative stiffness system (MANSS), is an effective approach to mitigate the structural responses under earthquake events. However, like other base isolators, the MANSS cannot reach its full potential to address the contradiction between effective vibration isolation and suppression, due to improper setting of structural parameters. In this paper, a comprehensive multi-objective nonlinear optimisation for obtaining the optimal structural parameters of the ANSD is conducted to effectively improve the performance of MANSS on seismic protection. After the characteristic analysis of the ANSD, six optimisation variables and one constraint are determined. Four objective functions are defined by considering the two adverse requirements simultaneously, i.e. enhancing vibration isolation and improving vibration suppression. The highly nonlinear optimisation problem can be adequately resolved by the modified non-dominated sorting genetic algorithm type II (NSGA-II) with dynamic crowding distance (DCD) algorithm, which generates a series of Pareto front, hence obtaining the optimal parameter combination. Furthermore, to verify and evaluate the feasibility and capacity of the proposed optimisation method, a numerical case study is conducted based on a five-storey benchmark building model subjected to six different earthquakes. Four systems, including bare building, bare building with ANSD on the first floor, bare building with dampers on each floor and preliminarily designed MANSS are also investigated to conduct comparative analysis. The results demonstrate that the optimised MANSS can largely reduce both peak and root mean square (RMS) values of inter-storey drift, acceleration, and displacement responses of the benchmark building under all six earthquakes, which proves the effectiveness and superiority of the proposed optimisation method and the optimised MANSS.