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Real-time hybrid simulation (RTHS) is increasingly being recognized as a powerful cyber-physical technique that offers the opportunity for system evaluation of civil structures subject to extreme dynamic loading. Advances in this field are enabling researchers to evaluate new structural components/systems in cost-effective and efficient ways, under more realistic conditions. For RTHS, performance metric clearly needs to be developed to predict and evaluate the accuracy of various partitioning choices while incorporating the dynamics of the transfer system, and computational/communication delays. In addition, because of the dynamics of the transfer system, communication delays, and computation delays, the RTHS equilibrium force at the interface between numerical and physical substructures is subject to phase discrepancy. Thus, the transfer system dynamics must be accommodated by appropriate actuator controllers. In this paper, a new performance indicator, predictive performance indicator (PPI), is proposed to assess the sensitivity of an RTHS configuration to any phase discrepancy resulting from transfer system dynamics and computational/communication delays. The predictive performance indicator provides a structural engineer with two sets of information as follows: (i) in the absence of a reference response, what is the level of fidelity of the RTHS response? and (ii) if needed, what partitioning adjustments can be made to effectively enhance the fidelity of the response? Moreover, along with the RTHS stability switch criterion, this performance metric may be used as an acceptance criteria for conducting single-degree-of-freedom RTHS.

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In a real-time hybrid simulation, a transfer system is used to enforce the interface interaction between computational and physical substructures. A model-based, multilayer nonlinear control system is developed to accommodate extensive performance variations and uncertainties in a physical substructure. The aim of this work is to extend the application of real-time hybrid simulation to investigating failure, nonlinearity, and nonstationary behavior. This Self-tuning Robust Control System (SRCSys) consists of two layers: robustness and adaptation. The robustness layer synthesizes a nonlinear control law such that the closed-loop dynamics perform as intended under a broad range of parametric and nonparametric uncertainties. Sliding mode control is employed as the control scheme in this layer. Then, the adaptation layer reduces uncertainties at run time through slow and controlled learning of the control plant. The tracking performance of the SRCSys is evaluated in two experiments that have highly uncertain physical specimens.

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Real-time hybrid simulation (RTHS) is a promising cyber-physical technique used in the experimental evaluation of civil infrastructure systems subject to dynamic loading. In RTHS, the response of a structural system is simulated by partitioning it into physical and numerical substructures, and coupling at the interface is achieved by enforcing equilibrium and compatibility in real-time. The choice of partitioning parameters will influence the overall success of the experiment. In addition, due to the dynamics of the transfer system, communication and computation delays, the feedback force signals are dependent on the system state subject to delay. Thus, the transfer system dynamics must be accommodated by appropriate actuator controllers. In light of this, guidelines should be established to facilitate successful RTHS and clearly specify: (i) the minimum requirements of the transfer system control, (ii) the minimum required sampling frequency, and (iii) the most effective ways to stabilize an unstable simulation due to the limitations of the available transfer system. The objective of this paper is to establish a stability switch criterion due to systematic experimental errors. The RTHS stability switch criterion will provide a basis for the partitioning and design of successful RTHS.

Summary Real‐time hybrid simulation (RTHS) is an effective and versatile tool for the examination of complex structural systems with rate dependent behaviors. To meet the objectives of such a test, appropriate consideration must be given to the partitioning of the system into physical and computational portions (i.e., the configuration of the RTHS). Predictive stability and performance indicators (PSI and PPI) were initially established for use with only single degree‐of‐freedom systems. These indicators allow researchers to plan a RTHS, to quantitatively examine the impact of partitioning choices on stability and performance, and to assess the sensitivity of an RTHS configuration to de‐synchronization at the interface. In this study, PSI is extended to any linear multi‐degree‐of‐freedom (MDOF) system. The PSI is obtained analytically and it is independent of the transfer system and controller dynamics, providing a relatively easy and extremely useful method to examine many partitioning choices. A novel matrix method is adopted to convert a delay differential equation to a generalized eigenvalue problem using a set of vectorization mappings, and then to analytically solve the delay differential equations in a computationally efficient way. Through two illustrative examples, the PSI is demonstrated and validated. Validation of the MDOF PSI also includes comparisons to a MDOF dynamic model that includes realistic models of the hydraulic actuators and the control‐structure interaction effects. Results demonstrate that the proposed PSI can be used as an effective design tool for conducting successful RTHS. Copyright © 2016 John Wiley & Sons, Ltd

Real-time hybrid simulation (RTHS) is a powerful cyber-physical technique that is a relatively cost-effective method to perform global/local system evaluation of structural systems. A major factor that determines the ability of an RTHS to represent true system-level behavior is the fidelity of the numerical substructure. While the use of higher-order models increases fidelity of the simulation, it also increases the demand for computational resources. Because RTHS is executed at real-time, in a conventional RTHS configuration, this increase in computational resources may limit the achievable sampling frequencies and/or introduce delays that can degrade its stability and performance. In this study, the Adaptive Multi-rate Interface rate-transitioning and compensation technique is developed to enable the use of more complex numerical models. Such a multirate RTHS is strictly executed at real-time, although it employs different time steps in the numerical and the physical substructures while including rate-transitioning to link the components appropriately. Typically, a higher-order numerical substructure model is solved at larger time intervals, and is coupled with a physical substructure that is driven at smaller time intervals for actuator control purposes. Through a series of simulations, the performance of the AMRI and several existing approaches for multi-rate RTHS is compared. It is noted that compared with existing methods, AMRI leads to a smaller error, especially at higher ratios of sampling frequency between the numerical and physical substructures and for input signals with highfrequency content. Further, it does not induce signal chattering at the coupling frequency. The effectiveness of AMRI is also verified experimentally. Figure 7. Simulation results of transfer system tracking.Figure 8. Determining acceptable/unacceptable ranges for a specific multi-rate implementation error.Case study II: Two significant strengths of the AMRI are its effective performance for input signals with high-frequency content and large sampling frequency ratios. To evaluate the performance of the proposed interface, a series of simulated case studies are implemented in which the input is a sinusoidal signal with various frequencies between 1-49 Hz and sampling frequency ratios of 2, 4, 5, 8, and 10. The corresponding normalized tracking errors using Equation (17) are shown in Figure 8. The simulation results shown in Figure 8 allow the researcher to have a better understanding of the error stemming from the multi-rate implementation of a realtime hybrid simulation using the AMRI. In this analysis, the frequency spectrum of the command signal is assumed to be known. For instance, the shaded region in Figure 8 results in less than 5% transfer system tracking error using the AMRI ratetransitioning scheme. Moreover, Figure 8 shows that in the majority of cases, the normalized error is less than 1%. Case study III: Finally, to systematically compare the performance of the three existing methods (method I-III) and the AMRI, a set...