Large-Scale Experimental Studies of Structural Control Algorithms for Structures with Magnetorheological Dampers Using Real-Time Hybrid Simulation

Magneto-rheological (MR) fluid dampers can be used to reduce the traffic induced vibration in highway bridges and protect critical structural components from fatigue. Experimental verification is needed to verify the applicability of the MR dampers for this purpose. Real-time hybrid simulation (RTHS), where the MR dampers are physically tested and dynamically linked to a numerical model of the highway bridge and truck traffic, provides an efficient and effective means to experimentally examine the efficacy of MR dampers for fatigue protection of highway bridges. In this paper a complex highway bridge model with 263 178 degrees-of-freedom under truck loading is tested using the proposed convolution integral (CI) method of RTHS for a semiactive structural control strategy employing two large-scale 200 kN MR dampers. The formation of RTHS using the CI method is first presented, followed by details of the various components in the RTHS and a description of the implementation of the CI method for this particular test. The experimental results confirm the practicability of the CI method for conducting RTHS of complex systems.

This paper presents an experimental program using real-time hybrid simulation to verify the performance-based seismic design of a two story, four-bay steel moment resisting frame (MRF) building with compressed elastomer dampers. The laboratory specimens, referred to as experimental substructures, are two individual compressed elastomer dampers, while the remaining part of the building is modeled as an analytical substructure. The proposed experimental technique enables an ensemble of ground motions to be applied to the building, resulting in various levels of damage, without the need to repair the experimental substructures since the damage is within the analytical substructure. Statistical experimental response results incorporating the ground motion variability show that an MRF with compressed elastomer dampers can be designed to perform better than a conventional steel special moment resisting frame (SMRF), even when the MRF with dampers is significantly lighter in weight than the conventional SMRF.

This paper presents an experimental program based on the use of real-time hybrid simulation to verify the performance-based seismic design of a two story, four-bay steel moment resisting frame equipped with compressed elastomer dampers. The laboratory specimens, referred to as experimental substructures, are two individual compressed elastomer dampers, while the remaining part of the building is modelled as an analytical substructure. The proposed experimental technique enables an ensemble of ground motions to be applied to the building, resulting in various levels of damage, without the need to repair the experimental substructures since the damage will be within the analytical substructure. Statistical experimental response results incorporating the ground motion variability show that a steel moment resisting frame (MRF) with compressed elastomer dampers can be designed to perform better than a conventional steel special moment resisting frame (SMRF), even when the MRF with dampers is significantly lighter in weight than the conventional SMRF.

Real-time hybrid simulation combines experimental testing and numerical simulation by dividing a structural system into experimental and analytical substructures. Servohydraulic actuators are typically used in a real-time hybrid simulation to apply command displacements to the experimental substructure(s). Servohydraulic actuators may develop a time delay due to inherent actuator dynamics that results in a desynchronization between the measured restoring force(s) and the integration algorithm in a real-time hybrid simulation. Inaccuracy or even instability will occur in a hybrid simulation if actuator delay is not compensated properly. This paper presents an adaptive compensation method for actuator delay. An adaptive control law is developed using an error tracking indicator to adapt a compensation parameter used in the proposed compensation method. Laboratory tests involving large-scale real-time hybrid simulations of a single degree of freedom moment resisting frame with an elastomeric damper are conducted to experimentally demonstrate the effectiveness of the proposed adaptive compensation method. The actuator tracking capability is shown to be greatly improved and exceptional experimental results are still achieved when a good estimate of actuator delay is not available.

Model-based feedforward–feedback tracking control has been shown as one of the most effective methods for real-time hybrid simulation (RTHS). This approach assumes that the servo-hydraulic system is a linear time-invariant model. However, the servo-control closed-loop is intrinsically nonlinear and time-variant, particularly when one considers the nonlinear nature of typical experimental components (e.g., magnetorheological dampers). In this paper, an adaptive control scheme applying on a model-based feedforward–feedback controller is proposed to accommodate specimen nonlinearity and improve the tracking performance of the actuator, and thus, the accuracy of RTHS. This adaptive strategy is used to estimate the system parameters for the feedforward controller online during a test. The robust stability of this adaptive controller is provided by introducing Routh’s stability criteria and applying a parameter projection algorithm. The tracking performance of the proposed control scheme is analytically evaluated and experimentally investigated using a broadband displacement command, and the results indicates better tracking performance for the servo-hydraulic system can be attained. Subsequently, RTHS of a nine-story shear building controlled by a full-scale magnetorheological damper is conducted to verify the efficacy of the proposed control method. Experimental results are presented for the semi-actively controlled building subjected to two historical earthquakes. RTHS using the adaptive feedforward–feedback control scheme is demonstrated to be effective for structural performance assessment.

Adaptive model reference control method for real-time hybrid simulation

Real-time hybrid simulation (RTHS) is a promising cyber-physical technique for the experimental evaluation of civil infrastructure systems subject to extreme dynamic loading. It allows for simulation of highly complicated civil infrastructure systems in a cost effective manner by partitioning them into numerical and physical substructures. And the coupling at the interface is achieved by enforcing equilibrium and compatibility at real-time. In RTHS, development of some systematic and random errors in the physical substructure are inevitable and can have substantial impacts on the quality of the simulation results. It has been shown that the reliability of RTHS results is highly dependent upon how successfully these sources of error in the physical substructure are mitigated. Some significant sources of error in RTHS are transfer system dynamics, e.g. dynamics of hydraulic actuator, and time delay, e.g. communication and computation delays. In this paper, we will show how a multi-degree of freedom (MDOF) RTHS system can be modeled with delay differential equations (DDE). Afterwards, a 4-story RTHS will be used as an illustrative numerical example to delineate how this DDE model can capture some important features of RTHS. Finally, the effects of transfer system dynamics on the quality of RTHS results will be shown for a 2-story structure and then the DDE model will be verified.

Due to the depletion of fossil fuels, offshore wind turbines have become significant contributors to energy production. The offshore wind turbines are subjected to severe environmental loads like wind, wave, and current. The combined effect of these loads induces significant vibrations in the structure, which may cause economic loss and reduce the power production capacity. Thus, the structure is designed to have a small response under environmental load, but it also increases the cost. Another alternative to reduce the structure’s response is implementing structural control devices. MR dampers are semi-active devices widely used in controlling onshore structures because of their adaptability to various loads. Since the environmental loads on the wind turbine have a wide range of spectral content, semi-active control is best suited due to their adaptability. The force generated by the MR damper is enormous for small input energy, and thus it is an attractive option for adaptive structural control in civil structures. Several semi-active control algorithms are available in the literature for nonlinear MR dampers. The semi-active algorithm obtains the optimal control force of the linearized system and smartly switches off the MR damper according to the system requirement. The offshore structure is nonlinear, so a nonlinear control algorithm is expected to have advantage over other techniques. One of the commonly used nonlinear control algorithms is the backstepping method. This method involves a systematic development of the Lyapunov function for a given nonlinear system. The nonlinearity in the MR damper arises due to the hysteretic property of the MR fluid. Many phenomenological models are studied in the literature to capture MR dampers' nonlinearities effectively. Bouc wen model is one such model that is widely used for modeling MR dampers.The backstepping controller requires full state feedback to produce the control signal but measuring many variables is difficult in real-time. Some controllers do not require an accurate structure model, and the control action is based on the measured response. This paper uses the feed-forward neural network controller (NNC) to control nonlinear dynamic systems. The controller is trained using the displacement time histories of the structure to predict the MR damper voltage. The NNC is trained with the output from the backstepping controller for various environmental conditions. In this study, a fixed offshore wind turbine in a water depth of 64.5m is controlled using NNC and backstepping controllers. Further, the control efficiency of the NNC is compared for different load cases.

This paper aims to investigate the performances of a semi-active tuned mass damper (STMD) used to reduce the vibrations of buildings under different seismic excitation by the real-time hybrid simulation (RTHS) method. In the STMD, the MR damper is used as a control element with a variable damping feature. The RTHS method is an alternative to experimentally studying the STMD system. MR damper is critically significant for the system and is experimentally installed. At the same time, the other parts are designed in numerical simulation and tested simultaneously. MR damper is a control element whose damping value can change according to the amount of voltage transmitted. Therefore, the groundhook control method determines the MR damper voltage variations. The results show that the control method applied to MR damper-controlled STMD effectively suppresses structural vibrations.

Coupled aero-hydro-geotech real-time hybrid simulation of offshore wind turbine monopile structures

Seismic control performance of the magnetorheological (MR) damper, which has strong nonlinearity, varies with the dynamic characteristics of the structure and ground motion such as natural period, peak ground acceleration. The MR damper has a property of the friction damper so that the relative magnitude of the friction force over excitation intensity affects the control performance. In this study, through numerical analyses of single-degree-of-freedom (SDOF) structures, design spectra for the passive MR damper and optimal non-dimensional friction forces are suggested. Additionally, simple semi-active control algorithms modulating the friction force of the MR damper in accordance with structural responses are proposed and compared with each other and the passive MR damper. Finally, the condition that the semi-active control is more appropriate than the passive one is identified for reasonable selection of the control strategy.

To explore the addressed issue of closed-loop vibration control using semi-active magneto-rheological (MR) fluid damper, an innovative control algorithm based on feedback of acceleration response at several points along stay cable for active/semi-active control of stay cables is firstly proposed in the present paper. Theoretical analysis, laboratory investigation, and in-situ tests are conducted in this study to verify the proposed control algorithm. Moreover, this paper presents the negative stiffness characteristic of the combined stay cable/semi-active MR damper system. These investigations indicate that the semi-active MR damper can achieve much better mitigation efficacy than the other passive MR dampers and the proposed control algorithm is proved to be practical. The effect of the negative stiffness on response reduction is demonstrated by the improved energy dissipation ability of the damper due to the enhanced displacement of the stay cable at the location attached with the damper. Introduction In the past few decades, many control methods have been proposed and some have been implemented to mitigate the unaccepted stay cable vibration (Johnson, 2003). At present, semi-active dampers have been proven to be effective in many applications and can potentially achieve performance levels that are almost the same as comparable active devices. For stay cables vibration control incorporated with semi-active dampers, most of the existing control strategies are based on full-state feedback of generalized coordinates. However, the generalized displacements and velocities of the stay cable cannot be measured directly. Since accelerometers can readily provide reliable and inexpensive measurements of the stay cable accelerations at strategic points on a stay cable, development of control method based on acceleration feedback at limited locations along stay cable is an ideal solution to solve the addressed practical problem. Moreover, even though the characteristic of negative stiffness of active control of stay cable vibration has been observed by some researchers(Johnson, 2003), the effects of negative stiffness on the stay cable vibration control using active/semi-active dampers 2 has not been fully researched in the present literatures. In this paper, a control algorithm based on feedback of acceleration response at several points for active and semi-active control of mass-distributed dynamic systems, e.g. stay cables is firstly proposed. Using the proposed control algorithm, the vibration control for the stay cable model attached with one MR damper and a series of field tests are carried out to investigate the control efficacy achieved by different control strategies. These investigations address that the semi-active MR damper can achieve much better mitigation efficacy than other passive MR dampers and the proposed control algorithm is proved to be practicable and available. Moreover, the effect of the negative stiffness provided by semi-active MR dampers on response reduction of cables is theoretically and numerically demonstrated by the improved energy dissipation ability of the damper due to the enhanced displacement of the cable at the location attached with the damper. Control Algorithm Based on Acceleration Feedback at Several Locations Governing equation of the combined stay cable/MR damper system shown in Figure 1 is given as (Irvine, 1981) ) ( ) ( ) , ( ) , ( ) , ( ) , ( d s x x t u t x f t x v c t x v T t x v m − + = + ′ ′ − δ & & & (1) with the boundary conditions v(0,t)=v(l,t)=0 for all t .where v(x,t) is the transverse deflection of the cable, l is the length of the cable, T is the cable tension, m and c are the cable mass and viscous damping per unit length, respectively, xd is the distance of the installed MR damper position from the left end, us(t) is the transverse control force provided by the MR damper at location x= xd, f(x,t) is the distributed load along the cable. δ(.) is the Dirac delta function. Figure1. Combined stay cable/MR damper system The transverse deflection could be approximated using a finite series ) ( ) ( ) , ( ∑ = = r j j j x t q t x v 1 φ (2) where the φj(x) is a set of shape modal functions and continuous with piecewise continuous slope to satisfy the geometric boundary conditionsφj(0)= φj(l)=0. Utilizing the approximate series solution and a standard Galerkin approach, the motion equation of the cable-MR damper system in matrix form is written as ) ( ) ( f Kq q C q M q t u x s d φ + = + + & & & (3)

The increased prevalence of semi-active control systems is largely due to the emergence of cost effective commercially available controllable damper technology such as Magneto-Rheological (MR) devices. Unfortunately, MR dampers are highly nonlinear, which presents an often over-looked complexity to the control system designer. The well-known Skyhook Damping control algorithm has enjoyed great success for both fully active and semi-active control problems. The Skyhook design strategy is to create a control force that emulates what a passive linear damper would create when connected to an inertial reference frame. Skyhook control is device independent since it generates a desired control force command output that must be produced by the control system. For simplicity, MR dampers are often assumed to have a linear relationship between the current input and the force output at a given relative velocity. Often this assumption is made implicitly and without knowledge of the underlying nonlinearity. In this paper, we show that the overall performance of a semi-active Skyhook control system can be improved by explicitly inverting the nonlinear relationship between input current and output force. The proposed modification will work with any semi-active control algorithm, such as Skyhook, to insure that the controller performance is at least as good as the performance without the proposed modification. This technique is demonstrated through simulation on a quarter-vehicle system.

The semi-active control system is widely used to reduce the seismic response of building structures. Its control performance mainly depends on the applied control algorithms. Various semi-active control algorithms have been developed to date. Recently, machine learning has been applied to various engineering fields and provided successful results. Because reinforcement learning (RL) has shown good performance for real-time decision-making problems, structural control engineers have become interested in RL. In this study, RL was applied to the development of a semi-active control algorithm. Among various RL methods, a Deep Q-network (DQN) was selected because of its successful application to many control problems. A sample building structure was constructed by using a semi-active mid-story isolation system (SMIS) with a magnetorheological damper. Artificial ground motions were generated for numerical simulation. In this study, the sample building structure and seismic excitation were used to make the RL environment. The reward of RL was designed to reduce the peak story drift and the isolation story drift. Skyhook and groundhook control algorithms were applied for comparative study. Based on numerical results, this paper shows that the proposed control algorithm can effectively reduce the seismic responses of building structures with a SMIS.

The jacket structure is one of the most important structures in the offshore industry. It is mainly installed in relatively shallow water conditions. The jacket structures are subjected to continuous wave forces, which severely affect the life of the offshore platform. Generally, the jacket structures are designed such that their response is small under its environmental loads, but it also increases the cost. So, controlling its response is a good alternative to increase its life span. In this study, a 2D jacket structure in a water depth of 120m is studied for its response control using Magneto-Rheological damper (MR damper). MR dampers have been successfully implemented in semi-active control of civil structures. They have been well proven in controlling the structural responses subjected to multiple frequency excitations. The MR damper's semi-active control algorithm requires the calculation of optimal force by assuming the structure to be linear. This optimal force can be obtained using various methods, and one such widely used method is the Linear Quadratic Regulator (LQR) strategy. The ocean waves are random, and hence the stochastic LQR Linear Quadratic Gaussian (LQG) has to be used to compute the optimal control force on the structure. This optimal force calculated can further be used by the MR damper's semi-active control algorithm to obtain the controlled response. From the theory of the LQG method, the input excitation has to be a white noise process, but the ocean waves that excite the offshore platforms are a narrow band process. So, the spectral content of the input excitation is captured using the shaping filters. The shaping filters are designed to obtain the required narrow banded spectrum of the water particle kinematics at different points of the structure. The filters are designed such that the cross-correlation of the excitation at various offshore platform points is maintained. The Cholesky factorization of the spectral matrix at various grid points degenerates the problem into a single input multiple output problem. Thus, individual fitting of the factorized spectral matrix components is sufficient to obtain the correct cross-correlation along with the depth. The 2D jacket requires the water particle kinematics to be calculated at different horizontal locations also. This horizontal propagation problem requires developing an ‘All-Pass’ filter, which allows one to design the phase shift at different frequency components while maintaining the unit magnitude transfer function. The developed filter equations are then augmented to the original jacket structure, and LQR gains are computed for the stochastic regulator problem. A Kalman filter is designed, and the state estimate is obtained for each time step, which is further used in the calculation of the optimal force. It is shown that stochastic structural control works for an offshore structure like the jacket, and control efficiencies and limitations under various conditions are discussed.