The information and work presented here is part of the M.S. thesis of graduate student Lemuel González Hernández under the guidance of Dr. Cortés-Delgado, titled Development of UPRM hybrid simulation facilities for dynamic analysis, to be published on the Fall of 2018.


Hybrid simulation test (HST), also known as pseudo-dynamic test, hardware-in-the-loop simulation, or virtual prototyping, is a computer controlled technique that combines physical testing and analytical models to analyze the behavior of structures subjected to dynamic loads, usually seismic loads [1]. This method is similar to a conventional quasi-static test but differs in the loading protocol. The loading protocol, which can be displacements or forces, are not predetermined but calculated by a numerical analysis that runs simultaneously with the experimental test.


The hybrid simulation test can be quasi-static or real-time depending on the loading rate. Quasi-static simulation applies the loading protocol in a step-to-step manner, at a much lower rate than a real event. The real-time hybrid simulation uses a one-to-one time scale loading protocol to evaluate components that contributes in damping and inertia. In general, real-time hybrid simulation is more adequate for earthquake engineering while quasi-static tests are carried out to study structural performance of structures and structural members such as resistance, propagation of cracks, collapse mechanism and levels of damage when they are subjected to cyclic loads [2].


The hybrid simulation method is based in the pseudo-dynamic testing method developed by Takanashi (1975) about 40 years ago. Nakashima and Takaoka (1992) introduced improvements to pseudo-dynamic testing giving way to the hybrid simulation test or hybrid technique [3]. In terms of control theory terminology, it can be described as a closed-loop feedback system [1]. The process, illustrated in Figure 1, starts with the prediction of the displacements by the numerical analysis. The displacements are sent to the control system and imposed to the structure by means of hydraulic actuators. The forces produced in the structure are measured and fed back to the numerical model to compute the displacements for the next step.

Figure 1 Hybrid simulation process. [4]

The hybrid simulation test assumes that the structure to be tested can be represented as a discrete system. The discrete degrees of freedom (DOFs) with lumped masses are controlled by actuators in a quasi-static manner while the inertia and damping effects are analytically modeled. The numerical equation that considers both analytical and experimental substructures can be expressed as:


                                                                                                                        (M ∙ ü)^A + (C ∙ u)^A + (R^A + R^E) = F                                                          1

in which ? is the mass matrix, ?̈ is the nodal acceleration vector, ? is the damping matrix, ?̇ is the nodal velocity vector, ? is the restoring force vector and ? is the external excitation. For a linearly elastic system, ? = ? ∙ ?, where ? is the stiffness matrix and ? is the vector of nodal displacements. For a non-linear system, ? will change during loading. The superscripts A and E correspond to the analytical and experimental substructures, respectively. The term ?^? is the stiffness component measured from the experimental specimen during the test. If the structure is subjected to a ground motion excitation, ? = −?^? ∙ ? ∙ ??, where ?^? is the total mass matrix, ? is the influence vector and ?? is the ground acceleration. The relation between the equation of motion and the numerical and experimental substructures is illustrated in Figure 2.

Figure 2 Hybrid simulation with numerical and experimental substructures. [4]

Table 1 compares some characteristic of the hybrid simulation with other experimental methods.

Table 1 Summary of experimental methods. [5]

Hybrid simulation has many advantages comparing to other test methods. Unlike the conventional quasi-static test, the hybrid simulation method applies a loading protocol calculated from the numerical dynamic analysis, resulting in a more earthquake-like motion. Hence, it provides a better response of the performance of a structure during an earthquake, which is important in performance-based design [5].

The HST allows to test only the parts of interest of the structure (experimental substructure) and model the rest numerically (numerical substructure). This reduces the load and power capacities, resulting in lower costs compared to a shaking table test [6]. Because the majority of the structure inertial and rate-dependent effects are considered in the numerical model, there is no need to perform the test at real time scale [6]. This is useful to test non-rate-dependent elements, but the system can be improved to real-time capacity to capture accurately the rate-dependent effects from the physical model.

The capacity of HST of substructuring and load at a lower rate allows to study larger specimen avoiding errors due to specimen scaling [5]. A more realistic scaling allows for a better understanding of local behavior of structure. Moreover, quasi-static hybrid simulation permits for monitoring the specimen during the test and stop the test at any moment. In this way, effects like cracking, yielding, and collapse mechanism can be carefully observed [7].


[1]      A. S. Elnashai, A. Y. El-Ghazouli, and P. J. Dowling, “Verification of Pseudo-Dynamic Testing of Steel Members,” J. Constr. Steel Res., vol. 16, no. 2, pp. 153–161, 1990.
[2]      H. Jamal, “About Civil Engineering,” Quasi Static Test – What, Why, How, 2017. [Online]. Available:
[3]      C. Dion, N. Bouaanani, R. Tremblay, and C.-P. Lamarche, “Real-Time Dynamic Substructuring Testing of a Bridge Equipped with Friction-Based Seismic Isolators,” J.                                   Bridg. Eng., vol. 17, no. 1, pp. 4–14, 2012.
[4]      L. González, “DEVELOPMENT OF UPRM HYBRID SIMULATION FACILITIES FOR DYNAMIC ANALYSIS,” University of Puerto Rico, Mayagüez Campus, 2018, to be published.
[5]      M. Nakashima, J. McCormick, and T. Wang, “Hybrid simulation: A historical perspective,” in Hybrid Simulation: Theory, Implementation and Applications, V. Souma and M.                        Sivaselvan, Eds. London, UK: Taylor & Francis/Balkema, 2008, pp. 3–13.
[6]      J. Donea, P. M. Jones, G. Magonette, and G. Verzeletti, “The Pseudo-Dynamic Test Method for Earthquake Engineering: An Overview,” 1990.
[7]      R. T. Leon and G. G. Deierlein, “Considerations for the Use of Quasi‐Static Testing,” Earthq. Spectra, vol. 12, no. 1, pp. 87–109, 1996.
[8]      MTS, “Series 252 Servovalves Product Information,” 2013.
[9]      M. Del Carpio, “HYBRID SIMULATION OF THE SEISMIC RESPONSE OF A STEEL MOMENT FRAME BUILDING STUCTURE THROUGH COLLAPSE,” State University of New                                 York at Buffalo, 2013.
[10]    D. G. Lignos and H. Krawinkler, “Deterioration Modeling of Steel Components in Support of Collapse Prediction of Steel Moment Frames under Earthquake Loading,” J.                           Struct. Eng., vol. 137, no. 11, pp. 1291–1302, 2011.