Incorporating Uncertainty in the Physical Substructure During Hybrid Substructuring

This paper demonstrates a real-time hybrid substructuring (RTHS) shake table test to evaluate the seismic performance of a base isolated building. Since RTHS involves a feedback loop in the test implementation, the frequency dependent magnitude and inherent time delay of the actuator dynamics can introduce inaccuracy and instability. The paper presents a robust stability and performance analysis method for the RTHS test. The robust stability method involves casting the actuator dynamics as a multiplicative uncertainty and applying the small gain theorem to derive the sufficient conditions for robust stability and performance. The attractive feature of this robust stability and performance analysis method is that it accommodates linearized modeled or measured frequency response functions for both the physical substructure and actuator dynamics. Significant experimental research has been conducted on base isolators and dampers toward developing high fidelity numerical models. Shake table testing, where the building superstructure is tested while the isolation layer is numerically modeled, can allow for a range of isolation strategies to be examined for a single shake table experiment. Further, recent concerns in base isolation for long period, long duration earthquakes necessitate adding damping at the isolation layer, which can allow higher frequency energy to be transmitted into the superstructure and can result in damage to structural and nonstructural components that can be difficult to numerically model and accurately predict. As such, physical testing of the superstructure while numerically modeling the isolation layer may be desired. The RTHS approach has been previously proposed for base isolated buildings, however, to date it has not been conducted on a base isolated structure isolated at the ground level and where the isolation layer itself is numerically simulated. This configuration provides multiple challenges in the RTHS stability associated with higher physical substructure frequencies and a low numerical to physical mass ratio. This paper demonstrates a base isolated RTHS test and the robust stability and performance analysis necessary to ensure the stability and accuracy. The tests consist of a scaled idealized 4-story superstructure building model placed directly onto a shake table and the isolation layer simulated in MATLAB/Simulink using a dSpace real-time controller.

Real-time hybrid substructuring (RTHS) is a relatively new method of vibration testing that enables system-level characterization of highly complex, rate-dependent, or nonlinear physical components. Its predecessors are pseudo-dynamic testing in civil earthquake engineering and hardware-in-the-loop testing in mechanical and aerospace engineering. RTHS allows a coupled dynamic system to be partitioned into separate physical and numerical components or substructures. Feedback control using servo-hydraulic actuation is then used to interface the physical and numerical substructures together in real-time as a closed-loop hybrid test. This paper describes the mathematical framework for RTHS of marine structural systems, including the details of the control architecture for coupling physical and numerical substructures together and techniques for modeling the effects of fluid loading in real-time. This paper also presents a modification to a model-based feedforward–feedback actuator tracking controller using a minimum-phase inverse of the modeled actuator dynamics for the feedforward compensator. RTHS is applied to a notional marine structural system comprised of a one-dimensional (1D) fluid-loaded mass–spring system. Initial experimental results from uniaxial RTHS testing at the University of Connecticut Structures Research Laboratory are also presented.

Due to the inherent nonlinear nature of magnetorheological (MR) fluid dampers, one of thechallenging aspects for utilizing these devices to achieve high system performance is thedevelopment of accurate models and control algorithms that can take advantage of theirunique characteristics. In this paper, the direct identification and inverse dynamic modelingfor MR fluid dampers using feedforward and recurrent neural networks are studied. Thetrained direct identification neural network model can be used to predict the damping forceof the MR fluid damper on line, on the basis of the dynamic responses across the MRfluid damper and the command voltage, and the inverse dynamic neural networkmodel can be used to generate the command voltage according to the desireddamping force through supervised learning. The architectures and the learningmethods of the dynamic neural network models and inverse neural network modelsfor MR fluid dampers are presented, and some simulation results are discussed.Finally, the trained neural network models are applied to predict and controlthe damping force of the MR fluid damper. Moreover, validation methods forthe neural network models developed are proposed and used to evaluate theirperformance. Validation results with different data sets indicate that the proposed directidentification dynamic model using the recurrent neural network can be used topredict the damping force accurately and the inverse identification dynamic modelusing the recurrent neural network can act as a damper controller to generatethe command voltage when the MR fluid damper is used in a semi-active mode.

EACS 2016 Paper No. 105This paper investigates the impact of inerter nonlinearities on the performance of tunedinerter- dampers (TID). The inerter completes the force-current analogy between mechanical and electrical networks, and it represents the mechanical element equivalent to a capacitor. The TID is a vibration suppression system designed to limit unwanted vibrations of civil engineering structures and has a layout similar to that of a tuned-mass-damper (TMD), where the mass element was replaced by an inerter, making it a two-terminal device. The TID offers significant advantages over TMDs, in terms of performance over a wider frequency band, installation and dimensions. Nevertheless, the study carried out to date has been mainly numerical, considering a linear, purely inertial model of the inerter, where the generated force was proportional to the relative acceleration between the devices terminals. In practice, the dynamics of an inerter include nonlinearities, especially at the low frequencies associated with civil engineering applications. Here, the identification of these nonlinearities is done experimentally, based on an off-the-shelf inerter. The structural system, a single-degree-of-freedom host structure with an attached TID, is tested using Real Time Dynamic Substructuring (RTDS). The inerter represents the physical substructure, while the remaining elements of the TID and the host structure form the numerical substructure. This split allows the optimisation of the TID parameters, since the values of the spring and the damper can be changed without altering the experimental setup. In addition, this configuration takes into account the inerters potentially complex dynamics by testing it experimentally together with the characteristics of the host structure. The experimental and numerical results show that with appropriate retuning of the stiffness and damping components of the nonlinear TID system, the performance of the linear TID can be regained.

Proposed in this paper is an online hybrid test framework using a static and dynamic separated model scheme, where the equations of motion are solved by the operator-splitting (OS) algorithm, while the restoring force is obtained from a static analysis or quasi-static test of substructures. One of the keys of a successful substructure online hybrid test is the boundary coordination between the numerical and physical substructures. This is easily determined for the dynamic boundary whose displacement target is determined by the displacement predictor of the OS algorithm. However, the coordination is not straightforward for boundaries associated with static forces. This paper proposes an approximate method to determine the compatibility of the boundaries of static degrees of freedom, where the numerical substructure is analyzed first with the static boundary at the displacement of the previous step. The reaction force is then acquired from the analysis results as the target force of the corresponding degree of freedom of the physical substructure. The measured displacement is used as the target for the numerical substructure in the next step. In this procedure, the numerical substructure and the physical substructure alternatively move forward. Therefore, it is call staggered coordination. This is not a rigorous method to analyze boundary compatibility and equilibrium. However, it does make the substructure online hybrid test much easier and more feasible. Here, the staggered coordination scheme is examined by a six-story RC frame equipped with BRBs through both numerical simulation and physical testing. An energy-based index shows that the error introduced by this method can be ignored and that the proposed framework of online hybrid test works precisely without any malfunction.

This paper examines the ASCE first generation benchmark problem for a seismically excited cable-stayed bridge, and proposes a new semiactive control strategy focusing on inclusion of effects of control-structure interaction. The subject of the ASCE benchmark problem is a cable-stayed bridge in Cape Girardeau, Missouri, for which construction is expected to be completed in 2003. The goal of the benchmark study is to provide a \Itestbed\N structure on which researchers can systematically compare and evaluate the relative merits of proposed structural protection for cable stayed-bridges. In this paper, magnetorheological (MR) fluid dampers, which belong to the class of controllable fluid dampers, are proposed for use in a control strategy for protecting the bridge. A clipped-optimal control algorithm, shown to perform well in previous studies involving MR fluid dampers, is employed. A comprehensive study of the adequacy of various types of dynamic models for MR fluid dampers, such as a Bingham model, a Bouc-Wen model, and a modified Bouc-Wen model, is provided. In contrast to previous studies, models considered in this study are based on experimental data for a full-scale MR fluid damper. Because the MR fluid damper is a controllable energy-dissipation device that cannot add mechanical energy to the structural system, the proposed control strategy is fail-safe in that bounded-input, bounded-output stability of the controlled structure is guaranteed. Numerical simulation results considering several historical earthquakes scaled to various magnitudes show that the proposed semiactive control strategy using MR fluid dampers is the promising one of the applicable control methods to reduce seismic responses of cable-stayed bridges.

Gain-margin based discrete-continuous method for the stability analysis of real-time hybrid simulation systems

Vibration isolation methods that vary damping and stiffness have demonstrated excellent authority over system vibration, thus, potentially making them attractive for many applications. However, conventional devices for controlling variable stiffness are typically complicated and difficult to implement in most applications. To address this issue, a new method is proposed that requires two magnetorheological (MR) fluid dampers placed in series. With this configuration, variable damping and stiffness vibration control is simultaneously achieved by varying a small current to the MR dampers. This paper presents a theoretical and experimental analysis of a two degree-of-freedom system that is controlled by the MR dampers. Five different control schemes involving the variable damping and stiffness are explored. The time and frequency responses of the two degree-of-freedom system to a random input show that combined variable damping and stiffness control provides the best vibration isolation over a frequency range spanning the system’s two structural vibration modes. The experimental results agree well with the theoretical analysis.

While numerical simulations can be used to predict the dynamic performance of structural systems, there are some instances where the dynamical behaviour and uncertainties of specific system components may be difficult to accurately model. In these instances, structural reliability assessments may be conducted by employing the cyber-physical real-time hybrid sub-structuring (RTHS) test method. In this approach, a numerical model of a larger structural system, incorporating uncertainty in specific parameters, is coupled with a physical test specimen of a system component to fully capture system-level dynamic interactions and facilitate uncertainty propagation. This paper specifically details a study performed to experimentally validate the previously proposed adaptive Kriging-Hybrid simulation (AK-HS) structural reliability method. The AK-HS method combines Kriging metamodeling, an adaptive learning algorithm, Monte Carlo simulation, and RTHS testing to iteratively estimate a structural system's probability of failure given random parameters in the numerical model. The method is validated with a series of bench-scale RTHS tests on a viscous damper connecting two adjacent 6-degree-of-freedom rigid body structures. The AK-HS method is shown to accurately predict probabilities of failure for systems with up to 24 random variables using a reasonable number of RTHS tests.

Nonlinear substructuring control for parameter changes in multi-degree-of-freedom systems

Dynamically substructured system testing method divides an original system into several substructures. In the numerical substructure, linear components are simulated via real-time computation. In the physical substructure, a transfer system, which includes actuators and sensors, is installed to interface the numerical and physical parts. During the test, the unwanted disturbances and noise from the actuator inevitably cause synchronization errors between the outputs of numerical and physical substructures at the interface, and consequently result in unsuccessful tests. Therefore, this study proposes advanced control using the feedforward state-space linear substructuring controller plus the mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> feedback controller to ensure optimal and robust synchronization. The synchronization problem is transformed to tracking design according to a numerical-substructure-based framework and is solved based on Riccati-like equations and linear matrix inequality. A multivariable mass-spring-damper substructured system is developed to verify the proposed control strategy via numerical studies.

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.

The hybrid simulation (HS) testing method combines physical test and numerical simulation, and provides a viable alternative to evaluate the structural seismic performance. Most studies focused on the accuracy, stability and reliability of the HS method in the small-scale tests. It is a challenge to evaluate the seismic performance of a twelve-story pre-cast reinforced concrete shear-wall structure using this HS method which takes the full-scale bottom three-story structural model as the physical substructure and the elastic non-linear model as the numerical substructure. This paper employs an equivalent force control (EFC) method with implicit integration algorithm to deal with the numerical integration of the equation of motion (EOM) and the control of the loading device. Because of the arrangement of the test model, an elastic non-linear numerical model is used to simulate the numerical substructure. And non-subdivision strategy for the displacement inflection point of numerical substructure is used to easily realize the simulation of the numerical substructure and thus reduce the measured error. The parameters of the EFC method are calculated basing on analytical and numerical studies and used to the actual full-scale HS test. Finally, the accuracy and feasibility of the EFC-based HS method is verified experimentally through the substructure HS tests of the pre-cast reinforced concrete shear-wall structure model. And the testing results of the descending stage can be conveniently obtained from the EFC-based HS method.

In recent years, both pseudo-dynamic and real time heterogeneous testing with dynamic substructuring — hybrid testing — have gained significant popularity for their applicability to testing several types of nonlinear structures/systems. In a hybrid test, a heterogeneous model of the emulated system is created by combining a Physical Substructure (PS) with a Numerical Substructure (NS) that describes the remainder of the system. Nevertheless, an efficient implementation of this technique requires overcoming certain problems, e. g., proper dynamic substructuring, reduction of external forces and actuator delay compensation. This paper presents a pseudo-dynamic test campaign undertaken by the University of Trento, Italy, on a typical full-scale industrial piping system subjected to earthquake loading in order to investigate its seismic performance. Some challenges faced during the implementation are shown and strategies adopted to overcome these problems are illustrated. Experimental activities will be described and performances of different components of the piping system, i.e., elbows, tee-joints, bolted flange joints and straight pipes under earthquake loading with the presence of an internal pressure of 3.2 MPa will be presented and commented.

The catastrophic damages of past earthquakes show that irregular structures are more vulnerable to seismic excitation. On the other hand, dynamic responses depend on the severity of irregularity which is hard to be determined precisely. In this study, performance and reliability of magnetorheological (MR) fluid dampers in controlling torsional-lateral responses of irregular structures are evaluated. In this regard, plan-asymmetry is studied by considering mass eccentricity; whereas vertical-irregularity is investigated by creating mass difference in adjacent stories of the structure. The performance of MR dampers in seismic control of the structure is then evaluated for passive and semi-active control scenarios. The reliability of the structure-MR damper system is then studied by considering uncertainties in severity of irregularities using the Monte Carlo simulation method. Six types of limit state function are defined and the reliability of the system for controlling the desired responses are derived. The results show satisfactory performance of MR dampers in controlling coupled torsional-lateral responses of the structure in which semi-active control system outperforms the passive control system. The results also confirm that the performance of the control system highly depends on the structure irregularity which should be taken into account for design of a safe and reliable structure.