scholarly journals Applications of the RST Algorithm to Nonlinear Systems in Real-Time Hybrid Simulation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yu Tang ◽  
Hui Qin
Keyword(s):  
Nonlinear Systems ◽  
Real Time ◽  
Damping Ratio ◽  
Hybrid Simulation ◽  
Stability Limit ◽  
Numerical Dispersion ◽  
Dynamic Problems ◽  
Dispersion Energy ◽  
Instantaneous Degree Of Nonlinearity ◽  
Stiffness Softening

Real-time substructure testing (RST) algorithm is a newly developed integration method for real-time hybrid simulation (RTHS) which has structure-dependent and explicit formulations for both displacement and velocity. The most favourable characteristics of the RST algorithm is unconditionally stable for linear and no iterations are needed. In order to fully evaluate the performance of the RST method in solving dynamic problems for nonlinear systems, stability, numerical dispersion, energy dissipation, and overshooting properties are discussed. Stability analysis shows that the RST method is only conditionally stable when applied to nonlinear systems. The upper stability limit increases for stiffness-softening systems with an increasing value of the instantaneous degree of nonlinearity while decreases for stiffness-hardening systems when the instantaneous degree of nonlinearity becomes larger. Meanwhile, the initial damping ratio of the system has a negative impact on the upper stability limit especially for instantaneous stiffness softening systems, and a larger value of the damping ratio will significantly decrease the upper stability limit of the RST method. It is shown in the accuracy analysis that the RST method has relatively smaller period errors and numerical damping ratios for nonlinear systems when compared with other two well-developed algorithms. Three simplified engineering cases are presented to investigate the dynamic performance of the RST method, and the numerical results indicate that this method has a more desirable accuracy than other methods in solving dynamic problems for both linear and nonliner systems.

Analysis of Newmark Explicit Integration Method for Nonlinear Systems

2006 ◽  
Vol 22 (4) ◽  
pp. 321-329 ◽  
Author(s):  
S.-Y. Chang ◽  
Y.-C. Huang ◽  
C.-H. Wang
Keyword(s):  
Nonlinear Systems ◽  
Integration Method ◽  
Stability Limit ◽  
Explicit Method ◽  
Initial Stiffness ◽  
Explicit Integration ◽  
Time Step ◽  
Linear Elastic ◽  
Stiffness Softening ◽  
Theoretical Results

AbstractNumerical properties of the Newmark explicit method in the solution of nonlinear systems are explored. It is found that the upper stability limit is no longer equal to 2 for the Newmark explicit method for nonlinear systems. In fact, it is enlarged for stiffness softening and is reduced for stiffness hardening. Furthermore, its relative period error increases with the increase of the step degree of nonlinearity for a given value of the product of the natural frequency and the time step. It is also verified that the viscous damping determined from an initial stiffness is effective to reduce displacement response in the solution of a nonlinear system as that for solving a linear elastic system. All the theoretical results are confirmed with numerical examples.

Accurate Integration of Nonlinear Systems Using Newmark Explicit Method

2009 ◽  
Vol 25 (3) ◽  
pp. 289-297 ◽  
Author(s):  
S.-Y. Chang
Keyword(s):  
Nonlinear System ◽  
Elastic System ◽  
Stability Limit ◽  
Explicit Method ◽  
Analytical Evaluation ◽  
Time Step ◽  
Linear Elastic ◽  
Instantaneous Degree Of Nonlinearity ◽  
Stiffness Softening ◽  
Relative Period

AbstractIn the step-by-step solution of a linear elastic system, an appropriate time step can be selected based on analytical evaluation resultsHowever, there is no way to select an appropriate time step for accurate integration of a nonlinear system. In this study, numerical properties of the Newmark explicit method are analytically evaluated after introducing the instantaneous degree of nonlinearity. It is found that the upper stability limit is equal to 2 only for a linear elastic system. In general, it reduces for instantaneous stiffness hardening and it is enlarged for instantaneous stiffness softening. Furthermore, the absolute relative period error increases with the increase of instantaneous degree of nonlinearity for a given product of the natural frequency and the time step. The rough guidelines for accurate integration of a nonlinear system are also proposed in this paper based on the analytical evaluation results. Analytical evaluation results and the feasibility of the rough guidelines proposed for accurate integration of a nonlinear system are confirmed with numerical examples.

A Generalized Structure-Dependent Semi-Explicit Method for Structural Dynamics

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Jinze Li ◽  
Kaiping Yu ◽  
Xiangyang Li
Keyword(s):  
Second Order ◽  
Numerical Dispersion ◽  
The Novel ◽  
Explicit Method ◽  
Dispersion Energy ◽  
Time Step ◽  
Linear Elastic ◽  
Special Cases ◽  
Stability And Accuracy ◽  
Stiffness Softening

In this paper, a novel generalized structure-dependent semi-explicit method is presented for solving dynamical problems. Some existing algorithms with the same displacement and velocity update formulas are included as the special cases, such as three Chang algorithms. In general, the proposed method is shown to be second-order accurate and unconditionally stable for linear elastic and stiffness softening systems. The comprehensive stability and accuracy analysis, including numerical dispersion, energy dissipation, and the overshoot behavior, are carried out in order to gain insight into the numerical characteristics of the proposed method. Some numerical examples are presented to show the suitable capability and efficiency of the proposed method by comparing with other existing algorithms, including three Chang algorithms and Newmark explicit method (NEM). The unconditional stability and second-order accuracy make the novel methods take a larger time-step, and the explicitness of displacement at each time-step succeeds in avoiding nonlinear iterations for solving nonlinear stiffness systems.

Implementation and application of the unconditionally stable explicit parametrically dissipative KR-αmethod for real-time hybrid simulation

2014 ◽  
Vol 44 (5) ◽  
pp. 735-755 ◽  
Author(s):  
Chinmoy Kolay ◽  
James M. Ricles ◽  
Thomas M. Marullo ◽  
Akbar Mahvashmohammadi ◽  
Richard Sause
Keyword(s):  
Real Time ◽  
Hybrid Simulation ◽  
Unconditionally Stable

Multi-rate Real Time Hybrid Simulation operated on a flexible LabVIEW real-time platform

2021 ◽  
Vol 239 ◽  
pp. 112308
Author(s):  
Jacob P. Waldbjoern ◽  
Amin Maghareh ◽  
Ge Ou ◽  
Shirley J. Dyke ◽  
Henrik Stang
Keyword(s):  
Real Time ◽  
Hybrid Simulation

Real-Time Modular Deep Neural Network-Based Adaptive Control of Nonlinear Systems

2021 ◽  
pp. 1-1
Author(s):  
Duc M. Le ◽  
Max L. Greene ◽  
Wanjiku A. Makumi ◽  
Warren E. Dixon
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Real Time ◽  
Deep Neural Network

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

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