---

In the area of semi-active control of civil structures, Magneto-Rheological (MR) damper has been an efficient mechanism for reducing the seismic response of structures. In this paper, an effective method based on defining an optimization problem for designing MR dampers has been proposed. In the proposed method, the parameters of semi-active control system are determined so that the maximum response of structure is minimized. To solve the optimization problem, the Genetic algorithm (GA) has been utilized. The modified Bouc-Wen model has been used to represent the dynamic behavior of MR damper while to determine the input voltage at any time step, the clipped optimal control algorithm with LQR controller has been applied. To evaluate the performance of the proposed method, a ten-storey shear frame subjected to the El-Centro excitation and for two different kinds of objective functions, optimal MR dampers have been designed. Then the performance of optimal MR damper has been tested under different excitations. The results of the numerical simulations have shown the effectiveness of the proposed method in designing optimal MR dampers that have the capability of reducing the response of the structures up to a significant level. In addition, the effect of selecting a proper objective function to achieve the best performance of MR dampers in decreasing different responses of structure has been shown.

---

This study investigates the efficacy of optimal semi-active dampers for achieving the best results in seismic response mitigation of adjacent buildings connected to each other by magnetorheological (MR) dampers under earthquakes. One of the challenges in the application of this study is to develop an effective optimal control strategy that can fully utilize the capabilities of the MR dampers. Hence, a SIMULINK block in MATLAB program was developed to compute the desired control forces at each floor level and to the obtain number of dampers. Linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers are used for obtaining the desired control forces, while the desired voltage is calculated based on clipped voltage law (CVL). The control objective is to minimize both the maximum displacement and acceleration responses of the structure. As a result, MR dampers can provide significant displacement response control that is possible with less voltage for the shorter building.

---

An optimal semi-active Cuckoo- Fuzzy algorithm is developed to drive the hydraulic semi-active damper for effective control of the dynamic deformation of building structures under earthquake loadings, in this paper. Hydraulic semi-active dampers (MR dampers) are semi active control devices that are managed by sending external voltage supply. A new adaptive fuzzy logic controller (FLC) is introduced to manage MR damper intelligently. Furthermore, a novel evolutionary algorithm of cuckoo search (CS) was employed to optimize the placement and the number of MR dampers and sensors in the sense of minimum resultant vibration magnitude. Numerical efforts were accomplished to validate the efficiency of proposed FLC. In designer’s point of view, the proposed CS-FLC controller can find the optimal solutions during a reasonable number of iterations. Finally, The simulation results show that the developed semi‐active damper can significantly enhance the seismic performance of the buildings in terms of controlled story drift and roof displacement and acceleration. CS-FLC controller uses less input energy and could find the appropriate control force and attenuates the excessive responses in several buildings. The findings in this study will help engineers to design control systems for seismic risk mitigation and effectively facilitate the performance‐based seismic design.

---

This article presents numerical studies on semi-active seismic response control of structures equipped with Magneto-Rheological (MR) dampers. A multi-layer artificial neural network (ANN) was employed to mitigate the influence of time delay, This ANN was trained using data from the El-Centro earthquake. The inputs of ANN are the seismic responses of the structure in the current step, and the outputs are the MR damper voltages in the current step. The required training data for the neural controller is generated using genetic algorithm (GA). Using the El-Centro earthquake data, GA calculates the optimal damper force at each time step. The optimal voltage is obtained using the inverse model of the Bouc-Wen based on the predicted force and the corresponding velocity of the MR damper. This data is stored and used to train a multi-layer perceptron neural network. The ANN is then employed as a controller in the structure. To evaluate the efficiency of the proposed method, three- story, seven- story and twenty-story structures with a different number of MR dampers were subjected to the Kobe, Northridge, and Hachinohe earthquakes. The maximum reduction in structural drifts in the three-story structure are 13.05%, 39.90%, 15.89%, and 8.21%, for the El-Centro, Hachinohe, Kobe, and Northridge earthquakes, respectively. As the control structure is using a pre-trained neural network, the computation load in the event of an earthquake is extremely low. Additionally, as the ANN is trained on seismic pre-step data to predict the damper's current voltage, the influence of time lag is also minimized.

---

In this study, the response of semi-actively controlled structures is investigated, with a focus on the effects of magneto-rheological (MR) damper distribution on the seismic response of structures such as drift and acceleration. The proposed model is closed loop, and the structure's response is used to determine the optimal MR damper voltage. A Fuzzy logic controller (FLC) is employed to calculate the optimum voltage of MR dampers. Drifts and velocities of the structure’s stories are used as FLC inputs. The FLC parameters and the distribution of MR dampers across stories are determined using the NSGA-II, when the structure is subjected to the El-Centro earthquake, so as to minimize the peak inter-story drift ratio and peak acceleration simultaneously. The efficiency of the proposed approach is illustrated through a twenty-story nonlinear benchmark structure. Non-dominated solutions are obtained to minimize the inter-story drift and acceleration of structures and Pareto front produced. Then, the non-dominated solutions are used to control the seismic response of the benchmark structure, which was subjected to the Northridge, Kobe, and Hachinohe earthquake records. In the numerical example the maximum drift and acceleration decrease by about 36.3% and 15%, respectively, in the El-Centro earthquake. The results also demonstrate that the proposed controller is more efficient in reducing drift than reducing acceleration.
 

---

The semi-active bracing system locks or unlocks the stand-by braces in an on-off mode utilizing a variable stiffness device (VSD). In this paper, the optimal design of a semi-active bracing mechanism and evaluating its performance in mitigating structural vibration under seismic loading have been studied. The optimal stiffness values of the semi-active braces have been determined by solving two optimization problems including minimizing the maximum acceleration and also minimizing the maximum inter-story drift by imposing a constraint on the maximum acceleration. The genetic algorithm (GA) has been applied to solve the optimization problems. To illustrate the design procedure, an eight-story linear shear frame under earthquake record has been considered and the optimal semi-active braces have been designed. In addition, to assess the performance of optimal bracing system under other records which are different from design record in terms of intensity and frequency content, the structure equipped with optimally designed semi-active braces has been tested under several ground motion records. The results show that the optimal semi-active bracing system has simultaneously reduced different responses of the structure although the acceleration reduction has mainly been less compared to the drift reduction.
 

---

In recent years, semi-active control has been introduced as a promising method for the seismic control of structures, potentially combining the benefits of both passive and active control systems. Magneto-rheological damper (MR) is one of the semi-active devices and its dynamic model is expressed by the Bouc-Wen model. The sliding sector control (SSC) strategy as a robust control approach is a class of variable structure (VS) systems for linear and nonlinear continuous-time systems with a special type of sliding sector using a new equivalent sector control. The purpose of this study is to evaluate the effectiveness of the SSC strategy in determining the optimal voltage of MR at each step of time. For a numerical example, a three-story benchmark shear structure is considered subjected to normal (100%), high (150%), and low (50%) excitation levels of the El Centro earthquake. The results of the numerical simulations show that the semi-active control system consisting of the SSC strategy and an MR damper can be beneficial in reducing the seismic responses of structures. Furthermore, the efficiency of the SSC strategy is also compared against that of the fuzzy and clipped-optimal controllers. Comparative results of the numerical simulation confirm the robustness and ability of the SSC strategy.