A Framework for Multi-Site Distributed Simulation and Application to Complex Structural Systems

The paper addresses the challenge of realistically assessing complex structural–geotechnical systems subjected to seismic loading when full-scale dynamic testing is impractical due to limitations of shaking table size, capacity, and applicability to extended structures. Pseudo-dynamic (PSD) testing, especially when combined with sub-structuring, offers an alternative but is constrained by experimental facility capabilities and analysis software limitations. The research question is how to create a flexible, efficient framework that enables multi-site, distributed hybrid simulations combining experimental and analytical substructures and leveraging multiple analysis platforms. The purpose is to develop a coordinator that decouples time integration from stiffness formulation, enabling static tests/analyses to participate in dynamic simulations. The importance lies in enabling realistic, scalable assessment of complex systems by linking geographically distributed facilities and diverse software tools through a common protocol and architecture.

The authors review the evolution of PSD testing since the 1970s (Takanashi et al., 1975), including verification and advancements at Imperial College, UC Berkeley, and Japan’s Building Research Institute. A recent full-scale 3D irregular RC frame PSD test in Ispra is noted. They contrast capabilities and limitations of common analysis platforms: Zeus-NL excels at inelastic frame collapse but lacks plate/shell/solid elements; ABAQUS has rich element libraries but limitations in reinforced concrete modeling; OpenSees includes advanced geotechnical constitutive models. Prior PSD integration schemes include iterative implicit methods, operator splitting (OS), and the predictor–corrector (PC) algorithm by Ghaboussi et al. (2004), with stability/accuracy characteristics of the α-modified Newmark OS method summarized from Combescure and Pegon (1997). This background motivates a framework that can integrate diverse tools and facilities.

The proposed framework, UI-SIMCOR, separates the time-step integration from stiffness evaluation to enable modular, distributed hybrid simulations. - Time integration: The integration scheme is independent of the modules; the current implementation uses the α-operator splitting (α-OS) method with modified Newmark parameters. The algorithm predicts displacements/velocities, imposes deformations on substructures, measures restoring forces and displacements, corrects for initial stiffness, computes effective restoring forces, solves for accelerations using an equivalent mass matrix, and updates states. Initial stiffness K' is required (estimated via pre-tests/analyses) to form the equivalent mass and correct measured forces. - Communication: UI-SIMCOR acts as the simulation coordinator, sending displacement commands and receiving force/displacement responses from each substructure module. Earlier versions used TCP/IP with Winsock; the current system supports the NEESgrid Teleoperation Control Protocol (NTCP) for secure, multi-site operation. The architecture allows arbitrary numbers and types of modules, including analytical platforms (e.g., OpenSees, Zeus-NL, FEDEAS Lab) and experimental equipment (via LabView/Matlab plugins), connected through NTCP servers. - Sub-structuring and static condensation: The complex system is partitioned into modules. Degrees of freedom (DOF) not directly controlled or of immediate interest are condensed using static condensation. Only DOF with mass contribute to inertia; Rayleigh damping (if used) is treated via mass/stiffness combinations but is omitted in the derivation for clarity. When full element stiffness matrices are not accessible from software, condensed stiffness matrices are obtained via pre-tests: apply unit deformations at control DOF, measure reactions, and assemble condensed stiffness. The overall condensed mass and stiffness are formed by summing module contributions. During simulation, only the mass matrix is specified initially; condensed stiffness is supplied from the pre-tests/analyses. UI-SIMCOR conducts the dynamic integration while each module performs quasi-static steps (applying imposed displacements and returning forces). - Implementation flow: 1) Define system partition, control DOF, and mass matrix; 2) Perform pre-tests to estimate initial and condensed stiffness matrices per module; 3) Configure NTCP connections to all modules; 4) Execute α-OS integration in UI-SIMCOR, iteratively commanding module deformations and collecting restoring forces; 5) Aggregate module responses, compute global states, and proceed through the excitation time history. The framework readily accommodates replacement or addition of modules and different integration schemes (e.g., forthcoming predictor–corrector).

- Architectural contribution: Clear separation of time-step integration from stiffness formulation enables inclusion of static analyses and physical tests as modules in a dynamic simulation, and facilitates multi-platform coupling (e.g., OpenSees for soil with Zeus-NL for frame components). - Stability/accuracy context: The chosen α-OS scheme is unconditionally stable when initial stiffness is not less than tangent stiffness, accurate for relevant frequency bands with appropriate time step, and remains reliable for dominant low-frequency modes even under significant stiffness degradation (per literature). UI-SIMCOR is agnostic to integration scheme, allowing future algorithms (e.g., predictor–corrector) to be incorporated. - Verification 1 (MISST hybrid PSD): A bridge substructure was partitioned into three modules; the left pier was physically tested while other parts were simulated. The hybrid substructure PSD simulation produced lateral deck displacement at the left abutment identical to that of a single, monolithic analytical model, demonstrating correctness of the coordinator and coupling. - Verification 2 (multi-platform soil–foundation–structure): Soil modeled in OpenSees (plane strain) and the superstructure in Zeus-NL were coupled via UI-SIMCOR. The top displacement time history of the column matched that from a full OpenSees single-model analysis, validating cross-platform consistency. - Practicality: The framework successfully integrated multiple software and experimental modules over NTCP, showing feasibility for multi-site distributed hybrid simulations.

The findings demonstrate that decoupling integration from stiffness calculation effectively addresses the main barriers to distributed hybrid simulation: differing software capabilities, limited access to full stiffness matrices, and the need to combine experimental and analytical substructures. By relying on pre-tests for condensed stiffness and letting modules operate quasi-statically under imposed deformations, the coordinator can incorporate diverse components without modifying their source codes. The verification cases confirm that multi-site, multi-platform simulations can reproduce the responses of conventional single-model analyses, indicating that the approach preserves accuracy while expanding flexibility. This enables realistic assessment of complex structural–geotechnical systems by leveraging the strengths of specialized facilities and software, and supports the NEES vision of geographically distributed experimentation.

The paper introduces UI-SIMCOR, a framework for multi-site substructure testing and simulation whose key innovation is separating time-step integration from stiffness assembly. This simplification yields a versatile, easily extensible simulation coordinator capable of integrating static analysis software and static laboratory tests into dynamic simulations that include inertia effects. The framework also enables coupling multiple analysis platforms to employ the most suitable models across domains (e.g., soil and structural components). Two verification examples—hybrid experimental–analytical bridge substructure testing (MISST) and a soil–foundation–structure system using OpenSees and Zeus-NL—show that distributed hybrid and multi-platform simulations can match single-model analysis results. Future work should investigate the accuracy and stability of hybrid PSD algorithms within this framework and extend applications to more complex, distributed-mass systems.

- Even in distributed hybrid simulations, large portions of structures often must be modeled analytically; results may depend on the fidelity of these numerical models. - Systems with truly distributed mass (e.g., earth dams) still require dynamic testing and cannot always be discretized effectively for hybrid PSD. - The paper does not present a thorough investigation of the accuracy and stability of the hybrid PSD algorithms within the proposed framework; this remains for future studies. - Access to initial and condensed stiffness requires pre-tests or auxiliary static analyses, which may introduce additional preparation effort and potential estimation errors.