A distributed remote collaborative hybrid test method for complex substructures based on OpenFresco

A distributed remote collaborative hybrid test (RCHT) method for complex substructures based on OpenFresco is presented in this paper. Challenges in the RCHT include the modeling of the numerical substructure, boundary degree-of-freedom (DOF) loading, and equivalent communication of the multi-story space frame as a test substructure in OpenFresco. The effectiveness and accuracy of the proposed RCHT method are verified by a series of remote distributed tests that reproduce the seismic response of a three-story five-span space Y-shaped eccentric brace steel frame model consisting of two test substructures and a numerical substructure. The main contributions of this study are the realization of the multi DOF loading RCHT of the space global frame and reasonable simplification of the substructure boundaries, which further promotes the use of the RCHT method to realize the seismic performance simulation of complex substructures.


Introduction
impact of remote host distance on the feasibility, precision, and performance of hybrid tests and implemented the RCHT of five sites of a three-span R/C highway overpass between the European Union, the USA, and Canada. Wang et al. (2012) and Zhang et al. (2017) used the domain overlapping technique between the numerical and test substructures to simplify the boundary loading conditions of the test device for a four-story plane steel frame structure. A standard interface was used to encapsulate each substructure (Pan et al. 2006) which improved the compatibility between laboratories by using different hardware equipment and numerical substructures.
In summary, it can be seen that, although the concept of RCHT was first proposed 20 years ago, the research objects have mostly been single degree of freedom (DOF) bridge structures. The frame model has many DOFs and a global space effect. It is more difficult to realize extensive application of the RCHT method in high-rise frame structures than in bridge structures. Based on the Open-source Framework for Experimental Setup and Control (OpenFresco) test platform (Stojadinovic et al. 2006;Schellenberg et al. 2008;Li et al. 2019;Cai et al. 2022) and the existing substructure boundary simplification idea, this study attempted to explore the effectiveness of multi-substructure boundary loading with multi-DOF for frame structures. The goal was to further expand the application of the RCHT method and OpenFresco test platform to full-scale or large-scale multi-story global space frame structure models. This study consisted of three parts. First, the construction process of the RCHT system based on OpenFresco was introduced. Second, a three-story five-span space Y-shaped eccentric brace steel frame (Y-EBF) model was selected as the RCHT global model. The three-story Y-EBF of the second span and bottom-story Y-EBF of the fourth span in the global model were taken as the test substructures, whereas the remaining structural part was taken as the numerical substructure. The challenges in the RCHT include the modeling method of the numerical substructure, the boundary DOF loading, and the equivalent communication of a multi-story space frame as a test substructure in OpenFresco. Third, a new hybrid test system containing only one test substructure and one test site was established. The factors influencing the boundary simplification of the bottom-story frame as the test substructure were further analyzed, and the effects of the translation, rotational DOF, and vertical load of the control node position on the accuracy of the hybrid test results were discussed.

Distributed RCHT system based on OpenFresco
The primary goal of RCHT development is to establish a software protocol framework that can connect the test equipment and computing resources of multiple structured laboratories distributed in different regions. To this end, the University of California, Berkeley, developed the RCHT platform OpenFresco, which provides a standard interface with the control system of the test setup equipment (such as the MTS control system). The calculation engine of OpenFresco adopts the finite element analysis software OpenSees and provides an interface with ABAQUS, MATLAB, and other calculation software. The experimental element, experimental site, experimental setup, and experimental control in the OpenFresco test system were incorporated into standard modules, and they were connected with OpenSees as a part of the OpenSees domain to form a global system. Presently, OpenFresco provides several simple test loading modules for substructure boundary condition simulations. Because it adopts an object-oriented software development method, it provides development space for researchers to further expand the research and application of RCHT (Schellenberg et al. 2009). The distributed RCHT system based on OpenFresco established in this study is shown in Fig. 1, including a local physical test site and remote physical test site. OpenSees was used to establish the numerical substructure model and the dynamic response analysis of the global model. OpenFresco was used for the equivalent communication between the experimental element and loading of each test substructure. The loading control system of the two test sites adopted an MTS electro-hydraulic servo loading control system, which is most widely used in civil engineering structural tests. In this test system, OpenSees was installed on the same computer as the MTS control system software in the local test-loading system. Therefore, it is necessary to establish a local experimental site in OpenFresco to realize data communication between the two. For the remote test part, because OpenSees and MTS control system software are installed in computers in different regions, the data communication between them needs to be realized by means of a client/server. The specific approach is to establish a remote experimental site in OpenFresco of the local test computer (client-side), an actor experimental site in the remote test computer (server-side), and realize communication between the two sites via the TCP/IP protocol of the Internet.

Configuration of the RCHT for complex substructures
The purpose of this test was to verify the effectiveness of using full-scale or large-scale multi-story global space frame models as substructures to conduct an RCHT. A threestory and five-span global-space Y-EBF structure model was used as the research object. The settings of the distributed RCHT scheme were introduced. The modeling of the numerical substructure, OpenFresco parameter settings, and actual loading setups of the test substructures are discussed in this section.

RCHT scheme
The RCHT scheme and substructure settings are shown in Fig. 2. The test model was a three-story five-span Y-EBF with a story height of 1.800 m and a span of 2.825 m. The length of the link in the YEB was 0.35 m. The specific dimensions of all members are listed in Table 1. All members of the model were welded in such a way that one end of the link was connected to the lower flange of the frame beam and the other end was connected to the intersection of the brace. The entire structure was partitioned into three substructures, as shown in Fig. 2. The three-story Y-EBF of the second span in the global model was taken as the local test substructure to be physically loaded in the structural laboratory at the Caotang Campus of the Xi'an University of Architecture and Technology (XAUAT). The bottom-story Y-EBF of the fourth span in the global model was considered the remote test substructure to be physically loaded in the structural laboratory at the Yanta Campus (1). During the test, the numerical model was calculated using OpenSees to obtain the target displacement matrix X i corresponding to the test substructures, and the command X i was sent to the MTS controller through OpenFresco and the MTS Computer Simulation Interface Software (MTSCSI) in turn. The actuators execute the loading command, measure the feedback force matrix F i , and then send F i back to OpenSees in time to calculate the next target displacement X i+1 . It is worth noting that the client/server method, commonly used for network communication, is used in the loading process of the remote test substructure. In this setting, the client side carries the main numerical substructure model and coordinates testing. The server side completes the loading of the test substructure and responds to requests from the client side. The effectiveness of the RCHT results will be affected by the numerical model calculation, response force of the test substructure boundary feedback, communication time between substructure systems, and fast and accurate loading of actuators, which will be discussed in the following sections.
where Ẍ i , Ẋ i , and X i are the acceleration, velocity, and displacement matrices, respectively, of the global structure. M n , M tl , and M tr are the mass matrices of the numerical, local test, and remote test substructures, respectively. C n , C tl , and C tr are the damping matrices of the numerical, local test, and remote test substructures, respectively. K n , K tl , and K tr are the stiffness matrices of the numerical, local test, and remote test substructures, respectively. Ẍ g i is the input acceleration of the external ground motion.

Local test substructure establishment
The establishment of the local test substructure mainly includes the simplified simulation method of boundary DOFs, installation of the test loading setup, and parameter setting of the OpenFresco test platform.

Boundary DOF simulation of the local test substructure
As shown in Fig. 3, the local test substructure was a three-story space Y-EBF. Under the action of a horizontal earthquake, there are six DOFs at each node connected to adjacent frame beams in the test substructure (see Fig. 3a). Therefore, if the compatibility and balance at the boundary of the local test substructure are to be met, a total of 72 DOFs of 12 nodes must be controlled, which is evidently impossible to achieve. To realize reasonable boundary loading of the test substructure, it is necessary to consider the rationality of the existing resources of the laboratory and the boundary simplification of the substructure. According to the deformation characteristics of the frame structure, under the action of a unidirectional horizontal earthquake and gravity load, the local test substructure mainly produces a horizontal displacement in the plane. Therefore, DOF 1 of each (1) node can be set as the main DOF, whereas the DOFs in other directions of the node can be ignored owing to the small deformation (see Fig. 3b). Moreover, the rigid floor of the frame structure assumes that the horizontal displacement of all nodes remains consistent within the floor plane of the same floor; therefore, the local test substructure can be equivalent to a multi-DOF model with mass concentrated at the floor height (see Fig. 3c). Through the above processing method, only three horizontal loading DOFs must be controlled in the actual RCHT. The actual loading setup for the local test substructure is shown in Fig. 4. During the test, the frame column and the ground beam were connected through anchor bolts to realize the boundary condition of the fixed-end constraint of the column base, and the friction between the ground beam and the foundation was used to prevent relative sliding between the ground beam and the foundation. Three MTS hydraulic servo actuators (250 t for the first and second stories and 100 t for the third story) were used to perform the three-particle hybrid test loading on the test specimen. One end of the actuator was fixed to the reaction wall, and the other end was connected to the middle of the distribution beam at the height of the floor.  The entire loading process of the test specimen was controlled by the displacement of the actuator. The vertical load was applied using a counterweight.

OpenFresco parameter setting for the local test substructure
To realize equivalent communication between the local test control system and OpenSees, the definitions of the experimental element, experimental site, experimental setup, and experimental control need to be set in the OpenFresco platform. With the help of the object-oriented design method, the experimental element was added to OpenSees. This experimental element is different from the ordinary element in finite element analysis software. Its restoring force model is not selected and defined in advance but is measured in the field physical test. Therefore, a reasonable selection and definition of the experimental element is the first step in the OpenFresco parameter setting. The generic Experimental Element (Schellenberg et al. 2009) is an open experimental element provided by OpenFresco. It can customize multiple nodes and DOFs on nodes for users. To be equivalent to the three-actuator horizontal loading of the local test substructure, a three-node generic experimental element was established (see Fig. 3d). The height of the element node corresponds to the floor height of the model. The floor mass was concentrated at the floor height and defined at the corresponding node position of the test element. Each node retains only DOF 1 in the horizontal direction, and the DOFs in the remaining directions are constrained. The mass matrix and initial stiffness matrix that must be defined for the generic Experimental Element are shown in Eqs.
The local test substructure and the numerical simulation computer are located in the same laboratory; therefore, only one local site needs to be defined in OpenFresco.
The experimental setup uses the actuator to apply boundary conditions to the experimental element to realize DOF conversion between the experimental element and actuator according to the geometry and kinematic relationship of the loading system. When a different experimental setup is selected for the same experimental element, the method for transforming the DOF of the experimental element into the signal command of the control system is different (Takahashi and Fenves 2013). The local test substructure loading includes three horizontally placed actuators, which correspond to the three nodes of the generic Experimental Element. Therefore, the NoTransformation Experimental Setup provided by OpenFresco is adopted, in which the transfer between the response amount of the Experimental Element and that of the test control system does not require a geometric coordinate transformation. In other words, DOF 1 of the first node of the experimental element corresponds to control direction 1 of the experimental setup (i.e., the first-story actuator), DOF 1 of the second node of the experimental element corresponds to control direction 2 of the experimental setup (i.e., the second-story actuator), and DOF 1 of the third node of the experimental element corresponds to control direction 3 of the experimental setup (i.e., the third-story actuator). During the test, the displacement matrix signal received by the experimental element was directly sent to the experimental setup module, and the feedback force matrix signal received by the experimental setup module was also directly sent back to the experimental element. There was no need for geometric conversion between the two signals.
After determining the experimental element, site, and setup, it is also necessary to define the experimental control module. Experimental control was used to realize the interface connection between the OpenFresco platform and MTS test control system. As shown in Fig. 5, the test interface software used in this test was MTSCSI, developed by MTS Systems. First, the displacement command signals corresponding to the three control points of the experimental setup, as well as the displacement and force feedback signals of the control points, were established in the experimental control module. Second, the control channels and feedback signals corresponding to the three actuators were established in MTSCSI. Finally, the file address corresponding to the established MTSCSI program was defined in the experimental control module so that the signal transmission between the experimental setup module and MTS control system could be realized. The loading step time of the local test loading was defined as 0.5 s.
The detailed command flow for setting the OpenFresco parameters in the local test computer is presented in "Appendix".

Remote test substructure establishment
The establishment of the remote test substructure mainly includes the simplified simulation method of the boundary DOFs, installation of the test loading setup, and parameter setting of the OpenFresco test platform.

Boundary DOFs simulation of the remote test substructure
In contrast to the local test substructure, the bottom-story Y-EBF of the fourth span in the global model is selected as the remote test substructure. As shown in Fig. 6a, the boundary DOFs are more complex, including not only the forces in six directions from the adjacent frame beam, but also the forces in six directions from the bottom of the second-story frame column. To simplify the DOFs at the boundary loading, researchers often approximate the midspan reverse bending point of the frame beam and column as the boundary for joint specimens or plane frame specimens; this is done so that the bending moment at the boundary can be ignored for practical test loading. As shown in Fig. 6b, the midspans of the adjacent beams and columns of the bottom frame were taken as reverse bending points. Because the bottom frame contains braces, even if the rotational DOFs of all the boundary positions are ignored, many DOFs are still required, which is difficult to achieve for a space global frame.
As shown in Fig. 7, it is necessary to reasonably simplify the boundary DOFs of the remote test substructure. Unlike the local test substructure, the remote test substructure not only considers the displacement in the horizontal direction but also simulates the boundary rotation constraints generated by the superstructure. This idea is considered in the TwoActuator Experimental Setup mode provided in OpenFresco. As shown in Fig. 7d, the two actuators were placed horizontally at both ends of the black part of the specimen. The black part represents a rigid column whose stiffness is much greater than that of the bottom substructure. The purpose was to ensure that the rigid column did not deform during the loading process so that the translational and rotational DOFs of the bottom substructure could be controlled by controlling the loading displacement of the two actuators. Preliminary simulation analysis of the global model showed that the vertical displacement and rotation angle at the beam-column joints were only approximately 1/100 and 1/10000 of the horizontal displacement, respectively. Therefore, it is proposed to simplify the DOFs of the boundary nodes of the substructure and assume that the rotation angle is zero. As shown in Fig. 7a, corresponding to the TwoActuators Experimental Setup mode in OpenFresco, a loading frame with a stiffness much greater than its own stiffness needs to be set on the upper part of the remote test substructure. In this study, a 0.9 m high centrally braced steel frame was designed as the loading frame. Through numerical simulation and actual loading, it can be observed that the stiffness of the loading frame was approximately six times that of the lower test substructure. Therefore, it can be assumed that the lower test substructure produces only in-plane horizontal displacement deformation under earthquake action. The actual test substructure loading setup is shown in Fig. 8. Horizontal displacement was applied through two 100 t MTS electrohydraulic servo actuators in the horizontal direction, and the column base was connected to the ground trough through anchor bolts to realize the fixed constraint of the column base. A jack was used to apply a vertical load to the remote test substructure.

OpenFresco parameter setting for the remote test substructure
After simplification of the boundary DOFs, if the remote test substructure is regarded as a whole, its stress state is similar to that of a cantilever column with a rigid connection at the bottom and synchronous loading of double actuators at the top. Therefore, the beamColumn Experimental Element (Schellenberg et al. 2009) provided by OpenFresco can be used to realize the equivalent communication of the test substructure (see Fig. 7c). This element is a type of test element defined by two nodes, and all the floor masses of the test substructure are concentrated at the top node. The element mass matrix is shown in Eq. (4). Only the translational DOFs at the boundary were considered; thus, the stiffness matrix of the test element retained only the in-plane horizontal stiffness. The initial stiffness matrix of the remote test substructure obtained by preloading is given by Eq. (5), where k 22 represents the stiffness of the test substructure in the in-plane loading horizontal direction.
For the remote test loading part, because OpenSeees was installed on the local test computer, and the MTS loading control system was installed on the remote computer, it was necessary to use the OpenFresco test platform to establish a Remote Experimental Site on the local test computer and an Actor Experimental Site on the remote test computer.
The geometric conversion of signals is required between the beamColumn Experimental Element used in the remote test substructure and the TwoActuator Experimental Setup mode. As shown in Fig. 7c, d, it was assumed that the horizontal displacement of the top of the test element was X 1 , the rotation angle was θ 1 , and the height of the rigid loading frame was h. For the loading equipment of the two horizontal actuators, the horizontal displacement of actuator 1 was X 1 , and the horizontal displacement of actuator 2 was X 1θ = X 1 + hθ 1 . In other words, the relationship between the displacement signal matrix X ′ 1r received by the actuator equipment and displacement signal matrix X 1r of the test element is Because only the horizontal displacement at the top of the element was considered when establishing the test element, θ 1 was taken to be 0 during the actual test loading, that is, the rotational DOFs of the test element were constrained. Therefore, Eq. (6) can be rewritten as Suppose that after the actuator devices were loaded with the displacement signal X ′ 1r , the feedback force signal measured by actuator 1 was F 1r and the feedback force signal measured by actuator 2 was F 1θ . For the test element, the received signals were the horizontal shear force F 1r + F 1θ and the bending moment hF 1θ measured at the top of the element. The relationship between the feedback force signal matrix F ′ 1r received by the test element and the feedback force signal matrix F 1r loaded by the actuators can be obtained as follows: The experimental control mode of the remote test system still adopted the MTSCSI. It is necessary to define the command and feedback signals of the two actuators, in which the command signals include two horizontal displacements corresponding to the TwoActuators Experimental Setup, and the feedback signals include the feedback displacements and feedback forces of the two actuators. The loading step of the remote test part was defined as 0.5 s.
The detailed command flow for setting the OpenFresco parameters in the remote test computer is presented in "Appendix".

Numerical substructure establishment
After the RCHT system is built and the parameter setting of the OpenFresco platform is completed, OpenSees can be used to model the numerical substructure and define analysis cases. The Force-Based Beam-Column Element was selected to simulate the frame beam and frame column, the Truss Element hinged at both ends was used to simulate the brace member, and the Zero-Length Element was used to simulate the shear deformation of the link in the YEB. As shown in Fig. 9, to ensure the modeling accuracy of the numerical substructure in the RCHT model, the quasi-static test results of the Y-EBF specimen completed by Wang et al. (2016) were verified before the RCHT was officially started. It can be seen that the simulated hysteretic loop and skeleton curve are consistent with the test results, and the simulation error of the ultimate load of the two frames does not exceed 10%. This shows that the accuracy of the numerical simulation meets the modeling requirements and can be used to model the numerical substructure in the RCHT. To ensure deformation coordination between each substructure, all boundary nodes connected to the test substructure in the numerical substructure were defined with constraints to curtail all DOFs on the nodes, except for the in-plane translational DOF.
RCHT dynamic time history analyses were conducted with three seismic wave records (El Centro, Taft, and Lanzhou waves), considering the magnitudes, soil conditions, and design seismic groups. A total of 1500 steps for the El Centro and Taft Waves and 1000 steps for the Lanzhou Wave were executed, while the time integration step was set equal to 0.01 s. Rayleigh damping, which is widely used in structural dynamic analysis, was adopted as the damping option in OpenSees. The integral algorithm adopts the combined numerical integration algorithm α-OS method (Nakashima et al. 1993), which is unconditionally stable and can effectively control cumulative error growth.

RCHT steps
According to the discussion on RCHT modeling in Sects. 3.1 to 3.4, the RCHT steps can be summarized in the flow chart shown in Fig. 10. The RCHT can be roughly divided into two steps: test preparation and formal test loading. The work to be completed in the test preparation stage includes the following: (1) MTS loading setups of the local and remote test substructures are installed in different laboratories, and the initial stiffness of the substructures is measured; (2) the OpenFresco parameters of the two test substructures are set, including the experimental element, site, setup, and control; (3) the modeling of the numerical substructure and the setting of the analysis cases are carried out in OpenSees; (4) OpenSees is run, and then the local MTS control system is successfully connected with OpenSees and waits for remote test site access; and (5) the remote test site is ready to load and waits for a response from the local test site. The main steps in the formal RCHT loading stage include the following: (1) OpenSees confirms that the remote test site is successfully connected and starts the numerical simulation analysis; (2) the target displacement is calculated, and the displacement  (3) the local test substructure completes the target displacement loading and obtains the feedback displacement and force from the internal sensors of the actuators; (4) the remote test substructure completes the target displacement loading and obtains the feedback displacement and feedback force from the internal sensors of the actuators; (5) in case of any remaining analysis step, the flow returns to step (2) and repeats steps (2)-(4). If there is no new analysis step, the test loading is completed, and the RCHT ends.

Test results and validation of the RCHT
A large series of RCHTs was conducted to examine the effectiveness of using the full-scale or large-scale global space frame structure model as a substructure. The primary targets for verification included (1) the communication performance of the RCHT system, (2) applicability of the RCHT system, and (3) efficiency of the RCHT results.

Communication performance of the RCHT system
The RCHT can realize collaborative work between laboratories in different regions and even countries. If the network communication speed is slow or the network communication is interrupted, the test loading will remain for a long time at a certain step, which is not in line with the goal of real-time data exchange and will cause additional damage to the test specimen.

Response comparison of local and remote test substructures
The first stories of the test substructures 1 and 2 have the same stress state under ideal boundary conditions; therefore, the two test substructures should have the same displacement and base shear response under the same command displacement. Figure 11 shows the displacement and base shear time history curves of the two test substructures under the action of the El Centro, Taft, and Lanzhou waves with a peak ground acceleration (PGA) of 0.240 g. It can be seen that the coincidence degree of the displacement time history curves of the two test substructures is relatively higher than that of the base shear time history curves of the two test substructures. The relative error of the two feedback displacements was maintained within 5%, mainly because the rigid floor assumption ensured that the two test substructures could receive the same displacement command. The relative errors of the base shear of the two test substructures were relatively large, but they were maintained within 15%. by the data measurement fluctuations. Generally, the error is within the acceptable range; therefore, the RCHT results are considered reliable. Figure 12b, pure numerical simulation results are consistent with the RCHT results, and the change trends of the two are basically the same. The maximum relative error of the two was 12.5%.

Factors influencing the boundary simplification of the test substructure
Under the action of a horizontal earthquake, each node on the boundary of the remote test substructure introduced in Sect. 3.3 produces translation and rotation. However, because of the loading limits in the test, it is difficult to use the actuators to simulate all the translation and rotation at the nodes of the frame structure, so the DOFs of the boundary nodes must be simplified accordingly.

Hybrid test system and global structure model
As shown in Fig. 13, a new hybrid test system containing only one test substructure and one test site was established to study the boundary simplification factors of the remote test substructure introduced in Sect. 3.3. As shown in Fig. 14, two-, three-, and fourstory three-span space Y-EBF models were established. The geometric dimensions, member section, and material constitutive of the model were the same as those of the RCHT model. For the three global structural models, the bottom-story space Y-EBF was used as the test substructure, and the rest of the model was simulated using OpenSees as the numerical substructure.

Substructure boundary loading conditions
During the hybrid test, the El Centro wave was selected as the original input seismic wave, and the PGA amplitude was modulated to 0.084 and 0.168 g. The loading was divided into three different cases, as shown in Table 2, according to whether the horizontal load was applied with a single actuator or a double actuator, and whether the upper part of the test substructure was subjected to a gravity load. Case 1 refers to the

Fig. 15
Loading displacement comparison of the two actuators: a displacement response and b zoomed view synchronous horizontal loading through two actuators, and the application of an upper gravity load through the vertical jack. Case 2 refers to synchronous horizontal loading through two actuators without application of a gravity load. Case 3 refers to horizontal loading through an actuator and the application of an upper gravity load through a vertical jack. Figure 15 shows the displacement loading records of the actuators corresponding to the three-story structural model (Fig. 14b) under the action of the El Centro wave with a PGA of 0.168 g. It can be seen that the loading displacement of the actuator at the floor height of the test substructure is almost the same as that of the actuator at the floor height of the loading frame, and the maximum peak displacement error of the two is 1.46%, which shows that the translational loading at the boundary of the remote test substructure proposed in Sect. 3.3.2 can be realized by the TwoActuator Experimental Setup mode. Figure 16 shows a comparison of the actuator feedback forces corresponding to the three-story structural model under the action of an El Centro wave with a PGA of 0.168 g. It can be seen that the actuator at the floor height of the test substructure bears most of the total base shear, while the actuator at the floor height of the loading frame bears about 30% of the total base shear. If only a single actuator is used for the horizontal loading in the hybrid test, the feedback force of the test substructure may be lower than the actual value.

Comparison with the simulation results of a pure numerical model
The pure numerical model of the global structure established by OpenSees, corresponding to the complete boundary conditions, was used as a reference to verify the reliability of the simplified loading mode of the substructure boundary, as shown in Fig. 7. Figure 17 shows the comparisons between the displacement and base shear time history curves of the test substructure and pure numerical simulation results. It can be observed that the displacement and base shear responses of the test substructure under Case 1 are consistent with the simulation results of the pure numerical model.

Factors influencing the substructure boundary loading
In Sect. 5.3, the effectiveness of the boundary simplification method in Case 1 with synchronous horizontal loading was verified through two actuators. In the following section, Case 1 is used as a reference to discuss the application of horizontal loading

Horizontal loading through an actuator
As an example, the results of the hybrid test for the three-story, three-span structural model were used. The displacement time history curves, base shear time history curves, and hysteresis loops of the test substructure when the El Centro wave with a PGA of 0.168 g acts under the loading modes of Cases 1 and 3 are compared in Fig. 18. The displacement time history curves of the test substructure under the two cases have essentially the same tendency, with the peak displacement of Case 3 being somewhat larger than that of Case 1. The trend of the base shear time history curves was generally the same for the two cases, and the peak shear of Case 1 was slightly larger than that of Case 3. The stiffness of the test substructure in Case 3 is slightly lower than that of the test substructure in Case 1, as shown in Fig. 18c. This is because loading Case 3 adopts horizontal single-actuator loading, which ignores the constraint effect of the superstructure on the test substructure part and considers the substructure boundary nodes in the free rotation state, resulting in the small stiffness of the test substructure part in Case 3. Table 3 lists the relative errors of the peak displacement and peak base shear for the test substructure parts corresponding to Cases 1 and 3 with different PGA. Table 4 lists the relative errors of the peak roof displacement and peak base shear of the global structural model corresponding to Cases 1 and 3 with different PGA. The relative errors of the peak displacement and peak base shear of the test substructure increased as the PGA increased, as did the relative errors of the peak displacement and peak base shear of the global structural model. It can be seen that with an increase in PGA, the influence of the horizontal load applied by a single actuator, ignoring the rotation restraint of the superstructure on the stiffness of the test substructure, increases. As the test substructure is an important part of the global structural model, the stiffness of the global structural model will change because of the change in the stiffness of the test substructure. Therefore, the relative error of the response of the global structural model under the two cases also increases, but the effect of boundary simplification in Case 3 on the global structural model is relatively smaller than that on the test substructure part.

Effect of the gravity load
Owing to upper structures, gravity loads are employed in engineering structural analysis to determine the additional internal forces induced by axial pressure in structural members with deflection or inter-story lateral displacement, which are also known as gravity second-order effects. When a horizontal displacement is induced under a horizontal earthquake, the structure is subjected to second-order effects caused by gravity loads in a typical substructure hybrid test. The deformation of a typical frame structure generated by the horizontal seismic force F e is depicted by the dotted line in Fig. 19a, corresponding to a horizontal displacement of d e and a column-end bending moment of M e,max1 . When the action of the gravity load N g is considered, additional deformation is produced in the structure, resulting in a horizontal displacement of d g and a column-end bending moment of M g,max1 . The final deformation of the structure is indicated by a solid line in Fig. 19a. The horizontal displacement is d e + d g , column . 19 Deformation of a typical frame structure generated by the horizontal seismic force F e : a with gravity load and b without gravity load bottom shear is F 1 , and column end bending moment M max1 = M e,max1 + M g,max1 . In the actual substructure hybrid test loading, the deformation of the structure in the horizontal direction is realized by controlling the loading displacement of the actuator,  and the gravity load is often realized by jacking. In other words, the actuator loading displacement is d e + d g , and the actuator applies a vertical load N g to achieve the same response as the structure under seismic loading. As shown in Fig. 19b, if the action of the gravity load on the substructure is not considered, only displacement d e + d g is applied using the horizontal actuator, where the column end bending moment M e,max2 caused by the action of d e is equal to M e,max1 , while the column end bending moment M g,max2 caused by d g only considers the secondary bending moment caused by the horizontal deformation of the structure due to the gravity load and fails to consider the additional bending moment caused by the gravity load carried by the column. As a result, the column end bending moment M max2 and column end horizontal shear force F 2 are smaller than the corresponding structural internal force in Fig. 19a. As a result, the structural stiffness measured by the actuator was small.
As shown in Fig. 20, the response of the three-story structural model under the action of the El Centro wave with a PGA of 0.168 g is considered as an example. The displacement responses in Cases 1 and 2 are approximately the same, as can be seen from the displacement time history curves, and in most cases, the peak displacement corresponding to loading Case 2 is higher than that of Case 1. The base shear response of the substructure in the two cases is virtually the same, as can be seen from the shear time history curves. In most cases, the peak shear corresponding to loading Case 1 is higher than that of Case 2. Consequently, when the gravity load loading was not considered, the stiffness of the test substructure measured by the actuator was small, resulting in a large displacement response in the first story of the model, which is consistent with the results of a previous analysis. Table 5 lists the relative errors of the peak displacement and peak base shear for the test substructure parts of the two-, three-, and four-story hybrid test models for Cases 1 and 2. The displacement response error and base shear error of both loading cases tended to increase as the PGA increased, and the number of model stories increased, as shown by the comparison of displacement and shear error. This is mainly due to the increase in the horizontal displacement and gravity load of the test substructure, which leads to a more obvious second-order effect of the frame column, and the impact of ignoring the gravity load on the test results becomes increasingly substantial at this point. The maximum relative error in the displacement of the two loading cases was 7.98%, and the maximum base shear error was 8.51%. Considering the low height of the model established in this study and the small horizontal lateral displacement, the test substructure was still dominated by first-order deformation. For super-tall or complex structures considering initial geometric defects, the second-order effects caused by gravity loads need to be further studied.
The above analysis and discussion show that when the bottom frame of the structure is selected as the test substructure for the hybrid test, the TwoActuator experimental setup mode should be used, and the upper gravity load should be considered.

Conclusions
This study confirms that the RCHT based on the OpenFresco test platform is an effective test method for experimentally evaluating the seismic performance of full-scale or largescale global space frame models. Two key issues were investigated: (1) the boundary DOF loading of a multi-story space frame as a test substructure and the equivalent communication problem with OpenFresco, and (2) the factors influencing the boundary DOF loading of the bottom space frame as a test substructure. A distributed RCHT system was built to simulate the seismic response of a three-story five-span spatial Y-EBF model. The modeling method of the numerical substructures and the implementation of the substructure boundaries are discussed. The experimental results of the RCHT were compared with the simulation results of the pure numerical model. The experimental findings are summarized as follows: (1) A framework for the distributed RCHT of multiple substructures based on the OpenFresco platform is presented in this paper. Based on the existing substructure boundary simplification idea, the framework realizes the application of multisubstructure boundary loading with multi-DOF a space global frame model. The proposed RCHT framework was experimentally validated using a three-story Y-EBF structural model consisting of two test substructures and one numerical substructure.
(2) The average communication time per step during the RCHT was 0.0397 s, accounting for approximately 7.94% of the total test simulation step. The maximum relative error of the feedback displacement of the two test substructures was maintained within 5%, and the maximum relative error of the base shear was maintained at 15%. The above data indicate that this RCHT system for studying the seismic performance of multistory Y-EBFs has good loading accuracy, communication performance, and remote collaborative performance. (3) The relative errors of the displacement response and base shear response between the RCHT and the pure numerical model simulation were kept within 15%. The causes of the error include the systematic errors caused by the boundary simplification and numerical modeling as well as random errors caused by data measurement fluctuations. However, the overall errors were within the acceptable range, proving the applicability of the RCHT method in studying the seismic performance of multi-story Y-EBFs, as well as the effectiveness of the RCHT system and the accuracy of the RCHT model. (4) The TwoActuators experimental setup mode in OpenFresco was used to achieve translational loading of the space global frame model, which can effectively consider the boundary constraints of the upper numerical substructure on the test substructure.
Disregarding the upper gravity load of the test substructure also caused the stiffness of the test substructure to be small and caused more errors in the simulation results of the hybrid test. When the bottom frame of the structure is selected as the test substructure for the hybrid test, the TwoActuator experimental setup mode should be used and the upper gravity load should be considered.