special attention as **semi**-**active** devices for mitigation of struc- tural vibrations. Because of the inherent nonlinearity of these devices, it is difcult to obtain a reasonable mathematical **inverse** **model**. This paper is concerned with two related concepts. On one hand, it presents a **new** **inverse** **model** of **MR** **dampers** based on the normalized Bouc-Wen **model**. On the other hand, it considers a hybrid seismic **control** system for building **structures**, which combines a class of passive nonlinear **base** isolator with a **semi**-**active** **control** system. In this application, the **MR** damper is used as a **semi**-**active** device in which the voltage is updated by a feedback **control** loop.The management of **MR** **dampers** is performed in a hierarchical way according to the desired **control** force, the actual force of the **dampers** and its capacity to react. The **control** is applied to a numerical three-dimensional benchmark problem which is used by the structural **control** community as a state-of-the-art **model** for numerical experiments of seismic **control** attenuation. The performance indices show that the proposed **semi**-**active** controller behaves satisfactorily.

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Magnetorheological (**MR**) **dampers** have received special attention as **semi**-**active** devices for mitigation of structural vibrations. Because of the inherent nonlinearity of these devices, it is difﬁcult to obtain a rea- sonable mathematical **inverse** **model**. This paper is concerned with two related concepts. On one hand, it presents a **new** **inverse** **model** of **MR** **dampers** based on the normalized Bouc–Wen **model**. On the other hand, it considers a hybrid seismic **control** system for building **structures**, which combines a class of pas- sive nonlinear **base** isolator with a **semi**-**active** **control** system. In this application, the **MR** damper is used as a **semi**-**active** device in which the voltage is updated by a feedback **control** loop. The management of **MR** **dampers** is performed in a hierarchical way according to the desired **control** force, the actual force of the **dampers** and its capacity to react. The **control** is applied to a numerical three-dimensional benchmark problem which is used by the structural **control** community as a state-of-the-art **model** for numerical experiments of seismic **control** attenuation. The performance indices show that the proposed **semi**-**active** controller behaves satisfactorily.

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The training is carried out upon the generated data **using** the Levenberg-Marquardt algorithm [12], which is encoded in Neural Networks Toolbox in MAT- LAB [13] under the `trainlm' routine. Finally, testing and validation of the trained network is investigated **using** a few sets of **new** data for a 30 s period. Figure 5 shows the training testing and validation velocity, forces and voltage records used in constructing the NIMR **model**. Additionally, Figure 5 compares the forces computed by the **MR** damper **model** based on the generated random voltage to the forces computed by the **MR** damper **model** based on the predicted voltages by NIMR. Moreover, the predicted voltage record from the NIMR is compared to the randomly generated targets and presented in Figure 5. It is clear that, in general, the predicted voltages are reasonably close to the target voltages. The near perfect match in the training region indicates that the NIMR **model** is well trained. Henceforth, the NIMR **model** will be used to compute the required voltage for a specic force and velocity. This will alleviate problems resulting when **using** a **control** algorithm that computes only the optimal **control** forces.

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To **control** **structures** against wind and earthquake excitations, Adaptive Neuro Fuzzy Inference Systems and Neural Networks are combined in this study. The **control** scheme consists of an ANFIS **inverse** **model** of the structure to assess the **control** force. Considering existing ANFIS controllers, which require a second controller to generate training data, the authors’ approach does not need another controller. To generate **control** force, **active** and **semi**-**active** devices could be used. Since the **active** ANFIS **inverse** controller may not guarantee a satisfactory response due to different uncertainties associated with operating conditions and noisy training data, this paper uses **MR** **dampers** as **semi**-**active** devices to provide **control** forces. To overcome the difficulty of tuning command voltage of **MR** **dampers**, a neural network **inverse** **model** is developed. The effectiveness of the proposed strategy is verified and illustrated **using** simulated response of the 3-story full-scale nonlinear benchmark building excited by several earthquake records through computer simulation. Moreover, the recommended **control** algorithm is validated **using** the wind-excited 76-story benchmark building equipped with **MR** and TMD **dampers**. Comparing results with other controllers demonstrates that the proposed method can reduce displacement, drift and acceleration, significantly.

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The **new** designed encoding scheme for learning the T-S fuzzy **model** of **MR** damper from data is based on non-dominated sorting genetic algorithm (NSGAII). The proposed encoding scheme consists of two parts. First part is related to input selection and the second one is related to antecedent structure of T- S fuzzy **model** (selection of rules, number of rules and parameters of MFs). The main aim of the proposed scheme is to reduce both model’s complexity and error. The subtractive clustering method with least square estimator has been used for determining the initial structure of fuzzy **model**. So the centre’s range of influence (r a ) for each of the data dimensions is considered as an adjustable parameter in order to

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Abstract: Structure are mainly subjected to various types of loading conditions such as earthquake, wind loads etc. For earthquake zone areas, the **structures** are designed considering seismic forces. The **structures** which are present in higher earthquake zone area are liable to get damaged or collapse, hence to increase the safety of these structure few retrofitting techniques or additional of materials to stabilize the **structures** against the earthquake forces are done. And if the retrofitting techniques are adopted then cost plays an important role and possibly few spaces will be compromised depend upon the type of methods adopted. Later the structure may be strengthened by adding materials externally to transfer the lateral loads i.e. some protective devices have been developed. In modern seismic design, the damping devices are used to reduce the seismic energy and enable the **control** of the structural response of the structure to that1earthquake excitation. For the present study, an 10-story structure which is symmetrical in plan is modelled and analyzed **using** the ETABs 2015 software. The earthquake loads are defined as perIS1893-2002 (Part 1). To analyze the structure, the static and dynamic analysis method is adopted. The response spectrum function is defined to carry out dynamic analysis. To **control** the seismic response and to increase the stiffness of the structure, Friction **dampers** are provided to the structure. The results obtained and compared in the form of displacement, story drift and story shear are compared.

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To implement the **semi**-**active** **control** law, the **semi**-**active** damper must be adjustable in real time. Currently, **semi**- **active** **dampers** can be adjusted hydraulically or electromagnetically. The first category uses mechanical valves driven by a solenoid or stepper motor to **control** damper force in a hydraulic damper. In the latter category, the rheological effect of controllable fluids, such as magneto rheological or electro rheological fluid, is used to provide adjustable damping forces. Although mechanical **control** **dampers** have been researched and developed extensively, the rheological controllable **dampers** have only received much more attention in the past few years, mainly due to great advances in magneto rheological fluids.

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Vibration suppression can be considered as one of the most important parameter affecting the performance of Mechanical **structures** and related safety and comfort. To reduce the system vibration of such systems, an **active** vibration **control** mechanism is required. Generally, vibration **control** techniques can been categorized into passive and **active**. Most of the existing systems falls under the passive category. **Active** damping is another very useful approach, which can adjust to different loading conditions, which uses sensed structural responses to determine the **control** forces generated on the structure. The **active** vibration reduction system can reduce different vibrations modes efficiently. However, these systems require considerable amounts of external power for their working. Another type of vibration reduction system, called as **semi**-**active** **control** approach has been examined by several researchers. This method is observed to be having better performance than passive **control** and required less power than **active** **control**. Magneto-Rheological (**MR**) **dampers** and Electro-Rheological (ER) **dampers** are two main examples of this type. However due to various advantages of **MR** **dampers** over ER **dampers**, **MR** **dampers** used for more no. of applications

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where Wi is a portion of the total weight W located at level i. This equation describes the vertical distribution of lateral force based on an assumed uniform distribution of seismic acceleration over the height of the superstructure. A similar assumption had been proposed by Skinner and McVerryl3.4) as discussed in Section 3.2.1. The only difference lies on the specific limitation set for the two approaches. Skinner and McVerry applied the assumption for **isolated** **structures** with a fundamental period (on fixed-**base**) not greater than 0.5 sees, whereas SEAONC required that the fixed- **base** fundamental period should not be greater than 20% of the "effective period". It shoul be noted, however, that the same effective fundamental period can be obtained for short period **structures** mounted on a BI system with either thin or fat hysteresis loops. As will be shown later in Chapter 4, **structures** on a BI system with thin history analized loops have a uniform shear force distribution as predicted by Eq. 3.28. However if the structure has a fat loop BI system, this equation may lead to severely underestimated storey shears, especially in the upper storeys.

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could provide either the road comfort if high damping coefficient **dampers** are used or the road holding condition if low damping coefficient **dampers** are used. So, to overcome this conflicting problem, Hrovart [2] in 1997, published a survey on electronically controlled suspension system, which could vary damping coefficient on the basis of road obstacles and thus can fulfill the objective of both ride comfort and road holding. The effect on performance of these electronically controlled suspension system was explained theoretically. Electronically controlled suspension system is further classified as **active** suspension system and **semi**-**active** suspension system based on their use of energy to actuate the damper. **Semi**-**active** suspension system uses relatively small amount of energy as compared to **active** suspension system to actuate the damper to change its damping coefficient. Later, in 2009, Wang et al.[3] compared the **semi**-**active** suspension system with passive suspension system, although he has used different system which is railway vehicle, rather than a car **model**, but vertical acceleration was observed to be low in case of **semi**-**active** suspension system, thus **semi**-**active** suspension system is better irrespective of system. Speltaa et al.[4] did a **new** analytical study by changing both spring stiffness and damping coefficient of the **semi**-**active** suspension system with a variable damping and stiffness and checked the performance of system in terms of comfort and again found it to be better than passive system. Eltantawie [5] in 2012, used decentralized neuro-fuzzy controller to analyse the ride comfort and stability of the vehicle. simulink was used to estimate ride comfort in terms of acceleration and again the results were compared with the passive suspension system. Again in 2015, Hrovart et al. [6] provided a insight to the **active** and **semi**-**active** suspension system by discussing various results on basis of hardware implementation of this suspension system. Deshpande et al.[7] in 2016, provided the additional performance parameters to observe the nature of suspension system other than body acceleration, that is, relative suspension deflection and relative tyre force, however simulation was carried out on **active** suspension system, but not on **semi**-**active** suspension system.

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Application of the **base**-isolation systems, as a means to limit the seismic-induced response of **structures**, has attracted the attention of many engineers and researchers. Due to their importance, the Uniform Building Code (UBC) has incorporated a special section for the seismic analysis and design of **base**-**isolated** **structures** since its 1991 edition. The present work investigates the vertical distribution of the lateral seismic force for **base**-**isolated** **structures** provided by the 1997 edition of UBC (UBC97). Dierent 6 and 8-story, 3-D **base**-**isolated** structural models with LRB isolators are considered, having a variety of eective periods and eective damping ratios. The UBC97 analysis procedure for the **base**-**isolated** **structures** is used to determine the minimum lateral seismic force and its vertical distribution for dierent oors. Since the number of stories above the isolation interface is more than four for the considered **isolated** structural models, the response spectrum analysis is used, considering the equivalent linear properties for isolation systems. Also, the UBC97 recommended that the 5%-damped design spectra be properly modied to account for the actual modal damping ratios of an **isolated** structure. Extensive nonlinear dynamic analyses were performed for 8 types of LRB isolators, **using** appropriately normalized earthquake accelerograms recorded on S

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One of the most difficult but important tasks in **control** system design for seismically excited building **structures** is the development of an accurate explicit mathematical **model** of the building system to be controlled because precise mathematical information related to the building structure is used for calculation of **control** forces. However, development of a mathematical **model** for a nonlinear building system as a dynamic system is still a challenging problem. One example of a nonlinear building structure occurs when magnetorheological (**MR**) **dampers**, which are highly nonlinear hysteretic devices, are applied to the building systems for efficient energy dissipation. In this case, the integrated building-**MR** damper system behaves nonlinearly although the building structure itself is usually assumed to remain linear (Ramallo et al. 2004). The development of an appropriate nonlinear **model** of the integrated system that includes the interaction between the structural system and the nonlinear **MR** damper plays a key role in **control** system design because the building structure equipped with a nonlinear **MR** damper is intrinsically nonlinear. A solution can be found in nonlinear system identification based on TS fuzzy **model**.

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To analyze the optimal explicit MPC approach, the quarter car **semi**-**active** suspension **model** was chosen. We have shown that the explicit MPC is a promis- ing method to increase the practical applicability of the MPC to such real systems where the time con- suming online optimization is not allowed because fast **control** action is required. After a detailed theoreti- cal summary of the explicit/hybrid MPC the practical questions of the **control** method have been analyzed. Through the explicit MPC we have shown that the op- timal MPC **control** does have a linear state feedback form. Two main disadvantages of the explicit MPC are the exponential blow-up of the number of regions with increasing the prediction horizon and the require- ments of the full state measurement. In explicit MPC we pointed out that regions may exist where no opti- mal solution exists which is not allowed in a real sys- tem. We can reach such regions in many cases such as: independently designed observer from the controller, disturbance input or modeling uncertainty. In order to treat this problem soft constraints and combined clipped LQ/MPC have been suggested.

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In particular, structures whose lateral strength is provided by shear walls which carry a comparatively small proportion of the total gravity load (Fig. 12) may rock despite their ap[r]

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for the input variables is [–1, 1] and for the output variables is [0, 1]. When the velocity and the displacement of the damper are in the same directions, the rule-bases use a major current to generate a large **control** force. If they are in different directions, no significant **control** force needed. Gaussian curve membership function was used. The sensors signal convert into linguistic fuzzy values through the fuzzification process. The Mamdani-type fuzzy logic was considered which is well suited for **control** systems. The scale factor and quantification factor is very important to determine the **control** force. The selection of the fuzzy functions, fuzzification and de-fuzzification were chosen by trial and error to achieve the best responses. The membership functions for both input and output variables were shown in Fig.2. The details of inference rules were shown in Table 1. Resulted mechanical **model** of **MR** damper was shown in Fig.3. Each of the input and output fuzzy variables are defined in the fuzzy space, in the form of nine linguistic values namely ND (Negative Displacement), ZD (Zero Displacement), PD (Positive Displacement), NV (Negative Velocity), ZV (Zero Velocity), PV (Positive Velocity), Z (Zero), S (Small) and L (Large).

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The double panel **model** problem has been chosen in order to reflect the vibroacoustic properties of double panels in transportation vehicles. The primary aim of this section is twofold. First, is to investigate how the vibroacoustic response varies when parameters of the components of the **model** are changed. This type of study facilitates the interpretation of the physical phenomena for the airborne and structure-borne sound transmission through the panel. Second, is to validate the **model** by comparing the simulations with other results obtained from well established analytical models [2]. It is known that for double partitions, important parameters can be the material properties of the panels, their dimensions, the distance between them, and the stiffness of elastic mounts which structurally connect the two panels. In order to perform a realistic study, the variation of these properties is selected with reference to materials and dimensions representative of a transportation vehicle skin. Normally the material properties and construction geometry of the bodywork of transportation vehicles are chosen by designers to meet functionality and safety requirements. In contrast, trim panels are designed for noise reduction and other constraints such as functionality, style, thermal insulation etc. Therefore, for the purpose of the parametric study the thickness and material of the radiating panel have been varied, whereas the source panel properties have been held fixed.

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Consider a simple quarter vehicle **model** (see Fig. 1) made up of sprung ( m s ) and unsprung masses ( m us ). A spring with stiffness coefficient k s and an **MR** damper connect both masses. The wheel tire is represented by a spring with the stiffness coefficient k t . In this **model**, z s (respectively z us ) is the vertical position of m s (respectively m us ) and z r is the road profile. It is assumed that the wheel-road contact is ensured.

To date, most of the research has been focused on concepts of structural **control** in line with the definition of Yao [1]. Structural **control** and its notion as an alternative approach for addressing the serviceability and safety problem in structural engineering systems led to the development of a range of passive, **active** and hybrid techniques for structural vibration mitigation. Amongst the most reliable and effective **control** techniques is the use of tuned mass **dampers** (TMDs) as energy absorbing devices. The TMD was firstly introduced in the engineering community by Frahm in 1911[2] and since then a large number of studies have been published validating the applicability and enhanced performance for a combination of different TMD devices and configurations of structural systems [3-6]. While TMDs have been proven to be successful at alleviating structural response under generic dynamic loading, such devices being tuned to a single mode of the structure ’s vibration are limited to a narrow band of operating frequencies [7]. This limitation of the TMD is quite significant particularly when dealing with high-rise **structures** excited in more than the first few modes. An additional and important limitation of the use of TMD is its sensitivity to parametric variation of the structural system. When parametric variation occurs either as a result of material degradation or structural damage (or e.g. due to environmental conditions; see aerodynamic stiffness), a purely passive TMD will unavoidably become de-tuned resulting in reduced vibration attenuation capacity and even in some cases increase of the vibration levels of the system, due to its neighboring side lobes strength [8-10].

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Abstract —The focus of this paper is on determination of the dynamic parameters of structural systems with viscoelastic (VE) **dampers** described by Maxwell rheological models. Such parameters could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frames with VE **dampers**. The solution to the nonlinear eigenvalue problem is obtained by equating to zero the determinant of the considered system of equations. Apart from complex conjugate eigenvalues, the real ones occurred when **dampers** that are described by the classic Maxwell **model**, are also determined.

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In civil engineering design, especially in designing complex **structures**, optimization has a special impor- tance and value. Basically, the optimization process nds a set of quantities for design parameters that yield optimal values of objective functions. Most optimiza- tion methods used in the design of structural vibration **control** systems are traditional, gradient-based search techniques. However, for these techniques, there are diculties, both in selecting a suitable continuously dierentiable cost function as well as incorporating the nonlinearities involved in the problem. Compared to these gradient-based methods, Genetic Algorithms (GAs) are very simple and powerful optimal search techniques, because GAs do not need a continuous and dierentiable function to solve the problem, and are able to take into account the nonlinearities (if any) of the problem [29].

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