---

Semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. In this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (MR) damper has been studied for controlling superstructure acceleration and base drift separately and simultaneously. A multi-objective optimization problem has been defined for optimal design of semi-active base isolation system which considers a linear combination of maximum acceleration and base drift as objective function where Genetic algorithm (GA) has been used to solve the optimization problem. H₂/Linear Quadratic Gaussian (LQG) and clipped-optimal control algorithms have been used to determine the desired control force and the voltage of MR damper in each time step. For numerical simulation, a four-story base isolated shear frame has been considered and for different values of weighting parameter in objective function, optimal semi-active base isolation system has been designed under various design earthquakes. The results show that by using base isolation system and supplemental MR damper, the superstructure acceleration and base drift can be suppressed significantly. Also, it has been concluded that by selecting proper values for maximum acceleration and base drift related weighting parameters in objective function, it is possible to mitigate the maximum acceleration and base drift simultaneously. Furthermore, semi-active control system has worked successfully under testing earthquakes regarding design criteria.

---

Hybrid control system composed of a base isolation system and a magneto-rheological damper so-called smart base isolation is one of effective semi-active control system in controlling the seismic response of structures. In this paper, a design method is proposed for designing the smart base isolation system in order to achieve an effective performance under multiple earthquakes. The base mass, the base stiffness and the weighting parameter of H₂/linear quadratic Gaussian control algorithm, which is used to determine the desired control force, have been considered as the design variables and different earthquake records have been considered as design earthquakes. First, the optimum values of these variables under each of the considered earthquakes have been determined by using the genetic algorithm and then, an optimum control system has been designed with multiple earthquakes-based design approach. The defined design objective is minimizing the peak base drift while the peak inter-story drift has been constrained. For numerical simulation, smart base isolation system is designed for controlling a four-story shear frame. The results show that when the control system designed for a specific earthquake is subjected to another earthquake, difference between the performance of this control system and the optimal case under that earthquake is considerable. Hence, the specific earthquake-based design approach is an inappropriate design procedure for smart base isolation. Also, it has been found that control system designed based on multiple earthquakes-based design approach shows effective performance in controlling the response of structure under a wide range of earthquakes.

---

In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based on minimization of maximum inter-story drift of nonlinear structure which genetic algorithm(GA) has been used to solve the optimization problem. For numerical analysis, a nonlinear eight-story shear building with bilinear hysteresis material behavior has been used. Fragility curves for the structure equipped with optimal variable damping and stiffness SATMDs have been developed for different performance levels and compared with that of uncontrolled structure as well as structure controlled using passive TMD. Numerical analysis has shown that for most range of intensity measure optimal SATMDs have been effective in enhancement of the seismic fragility of the nonlinear structures which the improvement has been more than passive TMDs. Also, it has been found that, although variable stiffness SATMD shows to be more reliable in lower mass ratios, however in higher mass ratios variable stiffness and damping SATMDs performs similarly to improve reliability of the structure.

---

In this paper, a design method is proposed for base isolation system under blast loading that this method is based on transforming design problem into an optimization problem. Genetic algorithm has been employed to solve the optimization problem whereas base isolation system properties have been considered as design variables and a linear combination of base drift and inter-story drift has been defined as objective function. A sensitivity analysis has been also conducted to investigate the effect of base isolation system properties on the blast performance of isolated structure. For numerical simulation, base isolation system is designed using the proposed method for controlling the response of an eight-story nonlinear shear-type building frame under blast loading. It has been found from the results that base isolation system is an effective control system under blast loading that its performance is dependent on the base isolation system characteristics especially the base mass. The optimization results also show that base isolation system designed using the proposed method is a well-designed control system for mitigating the blast response of structure and the proposed design method can be considered as an effective design approach under blast loading.

---

This paper introduces a reliability-based multi-objective design method for spatial truss structures. A multi-objective optimization problem has been defined considering three conflicting objective functions including truss weight, nodal deflection, and failure probability of the entire truss structure with design variables of cross sectional area of the truss members. The failure probability of the entire truss system has been determined considering the truss structure as a series system. To this end, the uncertainties of the applied load and the resistance of the truss members have been accounted by generating a set of 50 random numbers. The limitations of members' allowable have been defined as constraints. To explain the methodology, a 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the game theory concept and genetic algorithm (GA). The results show effectiveness and simplicity of the proposed method which can provide Pareto optimal solution. These optimal solutions can provide both safety and reliability for the truss structure.