( iISL ) Intelligent Infrastructure Systems Laboratory Intelligent Infrastructure Systems Laboratory ( iISL ) Purdue University, West Lafayette, IN Phone: (765) Fax: (765) An Innovative Simulation Tool for Real-time Hybrid Testing of Mechanical Systems Preliminary Progress Report PhD Candidate: Nestor Castaneda Faculty: Shirley J. Dyke and Rudolf Eigenmann

( iISL ) Intelligent Infrastructure Systems Laboratory  Motivation  Objective  Simulation tool – Current state Development  Research component: Development Validation  Research component: Validation  Preliminary results  Summary Outline

( iISL ) Intelligent Infrastructure Systems Laboratory Motivation  Performance validation is critical for the acceptance of new structural systems.  Hybrid testing techniques can reduce the cost involved with fabrication and full-scale testing of large-scale structures.  Within a hybrid test implementation, critical components of the structural system under evaluation can be physically tested to be better understood while the more predictable ones can be represented with computational models.  However, their ability for testing rate-dependent devices is limited due to their expanded time scale execution. Consequently, continuous or real-time strategies are desired to reproduce more realistic motions.  Real-time hybrid testing of mechanical systems, in which computational models and physical components must be integrated with high fidelity at real-time, represents a grand challenge in the emerging area of cyber-physical systems.

( iISL ) Intelligent Infrastructure Systems Laboratory Motivation A schematic of a real- time hybrid test implementation to evaluate the performance of a damper device for mitigating large vibrations of a building structure is shown in the next figure

( iISL ) Intelligent Infrastructure Systems Laboratory Objective  The objective of the present research focuses on the: The focus of this research is to develop, implement and validate a computational simulation tool adequate for real‐time hybrid testing of mechanical systems.  The simulation tool is co-designed to achieve two main goals : Perform nonlinear dynamic analysis of structures (with an initial emphasis in building structures). Perform nonlinear dynamic analysis of structures (with an initial emphasis in building structures). Achieve robust real-time execution to ensure stability and compatibility between the simulated and experimental components during testing. Achieve robust real-time execution to ensure stability and compatibility between the simulated and experimental components during testing.

( iISL ) Intelligent Infrastructure Systems Laboratory Simulation tool – Current state  A preliminary prototype simulation tool for the analysis of nonlinear building structures and originally proposed by Ohtori and Spencer for a benchmark control problem has already been developed and implemented as an Embedded MATLAB subset function adequate for real-time execution in xPC target/MATLAB environment.  The current state of the tool includes the next main components: Nonlinear beam-element for building structures. Nonlinear beam-element for building structures. Bilinear hysteresis rule for plastic hinge modeling. Bilinear hysteresis rule for plastic hinge modeling. Numerical integration scheme. Numerical integration scheme.  Ohtori, Y. and Spencer, B.F., Jr. (1999). “A MATLAB-Based Tool for Nonlinear Structural Analysis”, In the Proceedings of the 13th ASCE Engineering Mechanics Division Specialty Conference, Johns Hopkins University, Baltimore, June 13-16, 6 pages, (CD-ROM)

( iISL ) Intelligent Infrastructure Systems Laboratory Bilinear hysteresis rule A bilinear hysteresis model is used to model the formation and evolution of plastic hinges on structural members. A kinematic hardening rule is assumed in the proposed hysteresis rule. No isotropic hardening is assumed. The bilinear bending properties are predefined for each structural member and are assumed to occur at the moment resisting column beam and column-column connections A nonlinear beam-element is utilized to account for material nonlinearity effect in the building dynamics. The element allows for plastic hinge formation at the beam- column beam-beam connections. Plastic hinges at elements ends can be modeled either by two models, the spread plasticity model (SPM) or the concentrated plasticity model (CPM). Nonlinear beam-element

( iISL ) Intelligent Infrastructure Systems Laboratory Numerical integration scheme An unconditionally stable - implicit integration scheme Newmark method with coefficients is utilized as integration scheme for evaluating the dynamic response. An unbalanced force approach is used to compensate the difference between the restoring force evaluated using the hysteresis model and the restoring force assuming constant linear stiffness at time during the time interval ( t ~ t+∆t) as shown in the figure. This unbalanced force is handled at the next time step as external pseudo-force.

( iISL ) Intelligent Infrastructure Systems Laboratory Research component: Development  As realized from previous slides, the current simulation tool requires additional capabilities to account for:  Additional sources of non-linear behavior for building structures  Adequate real-time processing performance  Therefore, a set of new features are being developed progressively so both requirements can be achieved in parallel includes: Analytical mass and second order effects Analytical mass and second order effects Structural joint modeling Structural joint modeling Phenomenological modeling of hysteretic behavior Phenomenological modeling of hysteretic behavior Integration scheme Integration scheme Parallel computing scheme Parallel computing scheme Integration with a real-time hybrid test platform Integration with a real-time hybrid test platform

( iISL ) Intelligent Infrastructure Systems Laboratory Analytical mass and second order effects The insertion of mass into the experimental scheme for RTHT implementations is complicated because “real” mass is not present during experimentation. Therefore, mass and second order effects are computationally considered using a lean‐on column approach. Lean‐on columns are gravity load‐type columns usually utilized as a tool for practical stability analysis of steel frames.

( iISL ) Intelligent Infrastructure Systems Laboratory Structural joint modeling (Panel zone)  Structural joints can be conceived as a combination of two components, the panel zone and the connection area. In the current implementation a panel zone model is missing  The next factors are being considered for selection and addition of a panel zone model: The influence of the panel zone configuration (geometric nonlinearity / material nonlinearity) on the overall frame response such as strength, stiffness, inelastic deformation or softening. The influence of the panel zone configuration (geometric nonlinearity / material nonlinearity) on the overall frame response such as strength, stiffness, inelastic deformation or softening. Its feasibility to be implemented accordingly with the current connectivity schemes. Its feasibility to be implemented accordingly with the current connectivity schemes. Its computational efficient when evaluated within a real-time processing context. Its computational efficient when evaluated within a real-time processing context.

( iISL ) Intelligent Infrastructure Systems Laboratory Phenomenological modeling of hysteretic behavior  Despite the existence of well defined hysteretic models, their ability to accurately replicate what is expected during testing relies on the appropriate selection of parameters.  A phenomenological scheme for calibration of hysteretic model parameters is proposed. A MATLAB interface constructed with a constrained non-linear curve- fitting function is used to perform the calibration of a selected hysteretic model based on experimental data.  The proposed interface is designed as a user-defined interface so explicit mathematical expressions for different hysteretic schemes can be directly uploaded and calibrated.  The resulting model can then be evaluated by the hysteresis function that is used to track the hysteresis development during analysis in the simulation tool.

( iISL ) Intelligent Infrastructure Systems Laboratory Integration scheme Explicit:  Displacement at t(i+1) is known and therefore iteration is no needed to achieve convergence in the non-linear response  Stiffness matrix inversion is not needed through computation (Computationally efficient)  Usually conditional stable Implicit:  Displacement at t(i+1) is unknown and therefore iteration is needed to achieve convergence in the non-linear response  Stiffness matrix inversion is required through computation (Computationally inefficient)  Usually unconditional stable An unconditionally stable, explicit integration scheme is desired for the proposed RTHT implementation

( iISL ) Intelligent Infrastructure Systems Laboratory  Most of the exhaustive computational tasks of a non‐linear dynamic analysis are associated with the updating process of the time varying structural parameters. These updating routines require large computation demands in both calculation speed and information management because computational tasks are subsequently performed for each structural element. This effort may be significantly reduce by the implementation of a parallel processing scheme. We intend to parallelize the simulation through simultaneous use of more than one processor to accelerate computational tasks and execution time. Parallel computing scheme

( iISL ) Intelligent Infrastructure Systems Laboratory  The simulation tool is implemented as a Embedded MATLAB subset function format. The Embedded function (Embedded MATLAB toolbox) supports efficient code generation to accelerate fixed-point algorithm execution for embedded systems.  SIMULINK is used to integrate the simulation tool with the remaining RTHT components so a unique platform can be generated for real-time execution.  The MATLAB/xPC Target is used to generate and compile a C-source code from the SIMULINK model (host PC) that can be downloaded into a target real-time kernel (target PC) for execution.  xPC Target is a high performance host-target system that allows SIMULINK models to be integrated with physical systems for real-time execution purposes. Integration with a real-time hybrid test platform

( iISL ) Intelligent Infrastructure Systems Laboratory Research component: Validation  The experimental portion of the proposed research plan involves the implementation and completion of three experiments to validate the real-time processing and modeling capabilities of the proposed simulation tool.

( iISL ) Intelligent Infrastructure Systems Laboratory Research component: Validation  Comparison of the first two experiments is intended to evaluate the feasibility of the simulation tool to be implemented in real-time. Comparison between the second and third scenario is intended to evaluate the ability of the simulation tool to accurately replicate the dynamic response of the structure specimen.  A list of tasks required for completion for the implementation of the proposed experimental plans is listed below: Structure specimen design Structure specimen design Model updating Model updating Hysteretic model calibration Hysteretic model calibration Damper device calibration Damper device calibration

( iISL ) Intelligent Infrastructure Systems Laboratory Structure specimen design  A scaled 2D 2-story-one bay steel frame building specimen is introduced as the structure component of the proposed experimental plan.  Non-linear response extent is limited to connections during experimentation to guarantee the structure integrity for later applications.  Geometry with an appropriate aspect ratio, member sections and mass distribution will be designed in accordance to the force operational range of the damper device

( iISL ) Intelligent Infrastructure Systems Laboratory Model updating  A simple methodology, proposed by Giraldo, will be implemented to update the analytical model of the structural specimen and perform linear response simulations for control algorithm design (This is also required for the servo- hydraulic actuator controller design).  The Eigensystem Realization Algorithm (ERA) (Juang and Pappa, 1985), a time- domain modal identification technique, is applied to estimate the corresponding modal parameters.  Giraldo, D., Yoshida, O., Dyke, S.J. and Giacosa, L. (2004). “Control-oriented system identification using ERA”. Structural Control and Health Monitoring.  Juang, J.N. and Pappa, R.S. (1985),”An eigensystem realization algorithm for modal parameter identification and model reduction”, J. of Guidance Control and Dyn., 8:

( iISL ) Intelligent Infrastructure Systems Laboratory Hysteretic model calibration  Connectivity elements for the structure specimen are designed as fuse elements with moderate reduced bending capacity to ensure localized plasticity and keep the structure specimen re-usable.  An experimental study for evaluating the bending properties of the fuse elements is performed based on moment- curvature interaction.  Many fuse element specimens are planned to be tested so a representative moment-curvature data set can be reached.

( iISL ) Intelligent Infrastructure Systems Laboratory Damper device calibration  A magneto-rheological (MR) damper specimen, currently available at the Intelligent Infrastructure Systems Laboratory at Purdue University, is utilized as the damper device component in the proposed experimental plan.  Parameters of MR model based on a phenomenological Bouc-Wen model are calibrated to experimental data using a constrained non-linear optimization.

( iISL ) Intelligent Infrastructure Systems Laboratory  Non-linear dynamic analysis of a 3-story-one bay (Model 1), a 4-story-two bay (Model 2), a 3-story-four bay (Model 3), a 9-story-five bay (Model 4) and a 20-story- five bay (Model 5) building models was performed using a real time processor.  Every structural scenario is subjected to the N-S component recorded at the Kobe Japanese Meteorological Agency (JMA) station during the Kobe earthquake of January 17, The MATLAB Real-Time Workshop and xPC (Real time processor) Target System was used to evaluate every scenario Preliminary results

( iISL ) Intelligent Infrastructure Systems Laboratory Summary  Development and validation of a MATLAB-based simulation tool, adequate for performing real-time hybrid testing of mechanical system, is proposed in the current research plan.  Development and experimental components are adopted for completion of the proposed tool. The development step is aimed to include relevant sources of non-linear behavior in structural analysis. The experimental stage is aimed to validate the tool in terms of both real-time processing capacity and non-linear analysis accuracy.  The ability of the tool to run in real-time can be dramatically reduced when structural models with large number of DOF are evaluated. Careful selection of non-linear modeling techniques in conjunction with parallel processing strategies are expected to improve the overall real-time processing performance without scarifying the accuracy of the tool.