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

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.

Development and assessment of adjoint sensitivity analysis method for transient two-phase flow simulations

Impedance matching control design for the benchmark problem in real-time hybrid simulation

Real-time hybrid simulation (RTHS) combines physical experimentation with numerical simulation to evaluate dynamic responses of structures. The inherent characteristics of integration algorithms change when simulating numerical substructures owing to the response delay of loading systems in physical substructures. This study comprehensively investigates the effects of integration algorithms on the delay-dependent stability and accuracy of multiple degrees-of-freedom RTHS systems. Seven explicit integration algorithms are considered; and the discrete-time root locus technique is adopted. It is found that the stability of RTHS system is mainly determined by the time delay rather than the integration algorithms, whereas its accuracy mainly depends on the accuracy characteristic of the applied integration algorithm itself. An unconditionally stable integration algorithm cannot always guarantee good stability performance; and the inherent accuracy or numerical energy dissipation of integration algorithms should be taken into account in RTHSs. These theoretical findings are well verified by RTHSs.

Implementation of real-time hybrid simulation using a large shake table with onboard actuators

For Real-time hybrid simulation (RTHS) to be stable and accurate, it is essential to address the time desynchronization issue between the numerical and physical substructures. Desynchronization is primarily caused by time delays, inherent dynamics of the control plant, system uncertainties, and noises. While existing adaptive compensators have shown effective tracking performance in single-input single-output (SISO) RTHS, their effectiveness in multi-input multi-output (MIMO) RTHS has not been fully demonstrated. MIMO-RTHS presents additional challenges due to its larger solution space, and significant dynamic coupling between actuators. To address these challenges, this study introduces an adaptive compensation framework for MIMO-RTHS. The proposed framework utilizes a control law based on the inverse dynamics of the control plant, incorporating real-time adaptive parameter updates through Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) methods. Both the transfer function (TF) and discrete-time state-space (SS) models of the plant are employed in distinct parameter estimation cases. The performance of the proposed compensation is validated through a multi-axial RTHS (maRTHS) benchmark problem. Extensive simulations on the maRTHS incorporating various earthquake inputs, sensor noise, and model uncertainties, demonstrated an excellent tracking performance and strong robustness across four parameter estimation cases (EKF-TF, UKF-TF, EKF-SS, and UKF-SS). The use of UKF with SS model (UKF-SS) achieved superior performance, effectively managing nonlinearities and noise without requiring low-pass filtering.

High performance compensation using an adaptive strategy for real-time hybrid simulation

Seismic performance assessment of a low-rise thin reinforced concrete wall building with unconnected fiber reinforced elastomeric isolators using real-time hybrid simulations

Adjoint-based techniques can provide the sensitivity of an objective function to any number of parameters of a simulation inexpensively at roughly the cost of a single additional flow calculation. This information can be used to perform sensitivity analyses, aerodynamic shape optimization, and to estimate the error in the objective function due to numerical discretization. Existing approaches to derive the numerically discretized adjoint equations involve the so-called discrete and continuous methods, which differ in the order at which discretization and linearization steps are performed. The effect of these contrasting approaches is that they have both strengths and weaknesses over each other in the form of complexity of the formulation and computational expense of the solution. In this paper, we further develop the hybrid approach of Taylor et al. (2012) that combines elements of the continuous and discrete methods with the intention of capturing both their advantages: reducing the time spent on mathematical derivation of the continuous adjoint equations, lowering the computational requirements of the discrete adjoint equations, and generally improving the quality of the adjoint solution. The specific approach investigated in this paper treats the flow conservation equations in a continuous manner and the turbulence transport equations discretely. The framework is designed such that additional transport equations for any turbulence model can be seamlessly included in a discrete fashion for coupling with the mean flow equations. The methodology is demonstrated in an optimization problem of lift-constrained drag minimization of an airfoil in transonic turbulent flow.

Background:Appropriate nutritional support is effective on achievement of expected outcomes in intensive care unit (ICU) patients. Although several studies have suggested different conclusions about the effectiveness of tube feeding methods, there is no specific program of nutritional support for patients who have been hospitalized. There is a possibility for complications due to an inadequate nutrition. The aim of our study is to compare the effects of enteral feeding through the bolus and continuous methods on blood sugar and prealbumin level among the ICU inpatients.Materials and Methods:Fifty subjects were selected by convenient sampling from April to Aug 2013 in the ICU wards of Alzahra Hospital, Isfahan, Iran, and randomly assigned to study and control groups in this clinical trial. The subjects in the study group received infusion pump feeding while the control group received bolus feeding for 72 h. Blood sugar was checked for every 4 h for 72 h and the prealbumin level was assessed on the first and the fourth day in two groups.Results:In the study group, the mean blood sugar significantly decreased on the fourth day, compared with the first (P = 0.03, F = 3.85) and third (P = 0.01, F = 3.15) day. In the control group, the mean blood sugar increased from the first day. It was significantly higher in the control group on the second day (P = 0.02, F = 3.55), compared with the study group. In the study group, there was a significant difference in the mean prealbumin before and after intervention (P = 0.048, t = 1.97), but no significant difference was observed in the control group. There was a significant difference between two groups after intervention (P = 0.04, t = 2.05).Conclusion:The obtained results showed that supportive nutrition through a continuous method had an effect on critical patients’ blood sugar control and made a better nutritional status for these patients through an increase of prealbumin level. Positive effects of this feeding method can result in appropriate outcomes for patients’ recovery and reduce the complications.

In hybrid substructuring, a structural system is partitioned into a numerical substructure and a physical substructure. Typically, the physical substructure consists of a system component whose behavior is difficult to model while the numerical substructure consists of a computational model of the remainder of the system. Hybrid substructuring has previously been shown to be an effective method to quantify the effect of parametric uncertainties in the numerical substructure on the response of the system. This paper proposes and implements a methodology where the effect of parametric uncertainty can also be incorporated into the physical substructure. This idea is implemented in a series of small-scale Real-Time Hybrid Substructuring (RTHS) tests on a magneto-rheological fluid damper used to control a two degree-of-freedom mass-spring system. The physical current supplied to the damper is treated as a random variable. Using the RTHS test results, a metamodel of the system’s frequency domain behavior is developed using Principal Component Analysis and Kriging. This metamodel is then used to evaluate probabilistic system performance.

A model of single-phase flow of slightly compressible liquid is studied and the discontinuous and the continuous Galerkin methods for this model are compared. After studying the results of comparison, one may make conclusion that both method produce solutions that mostly are in accord with laws of physics. However, computational costs for the continuous method are less than ones for the discontinuous method, and the discontinuous method may produce non-physical jumps in solutions on initial time layers.

This paper proposes continuous linear multistep methods for the numerical solution of first-order ordinary differential equations (ODEs) with step number k = 1 and k = 2. These methods are used to integrate some first-order initial value problems and the block method developed from the continuous method using interpolation and collocation approach adopting power series approximation as the basis function for the derivation of these methods. These methods are found to be consistent, zero stable, convergent, and accurate. It is noteworthy that the results generated from these methods are significantly accurate and efficient when compared with existing methods, which will be effective in solving first-order Ordinary Differential Equations.

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.

Adjoint methods are widely used in various areas of computational science to efficiently obtain sensitivities of functionals which result from the solution of partial differential equations (PDEs). In addition, adjoint methods have been used in other settings including error estimation, uncertainty quantification and inverse problem formulations. When deriving the adjoint equations, there are two main approaches one can follow: the discrete and the continuous methods, which differ principally in the order of the linearization and discretization steps. The discrete adjoint method starts from the discretized form of the partial differential equation, which is then linearized. On the other hand, the continuous method linearizes the continuous governing equations first and then discretizes the resulting problem. Each of these approaches is found to have advantages and disadvantages over the other. In this paper we consider a hybrid approach between these two methods that aims to combine the better qualities of both: reducing the time spent on the mathematical derivation while also lowering the computational requirements of the discrete method and increasing the overall quality of the adjoint solution.