Presentation on theme: "An Introduction to Hybrid Simulation – Displacement-Controlled Methods"— Presentation transcript:
1 An Introduction to Hybrid Simulation – Displacement-Controlled Methods CIE Fall 2010Experimental Methods in Structural Engineering Prof. Andrei M ReinhornAn Introduction to Hybrid Simulation – Displacement-Controlled MethodsMehdi Ahmadizadeh, PhDAndrei M Reinhorn, PE, PhDInitially Prepared: Spring 2007
2 Presentation OutlineStructural Test Methods and Hybrid SimulationDisplacement-Controlled Hybrid SimulationDevelopment ChallengesHybrid Simulation System at SEESLA Typical Hybrid SimulationSimulation Models
3 Structural Seismic Test Methods Shake Table TestsThe most realistic experimentation of structural systems for seismic events.
4 Structural Seismic Test Methods Shake Table TestsLimitations:Limited capacity of shaking tablesScaling requirements and resulting unrealistic gravitational loads It is generally accepted that shake table tests provide an understanding of overall performance of structures subjected to seismic events.
5 Structural Seismic Test Methods Quasi-Static TestsGenerally used for evaluation of lateral resistance of structural elements.
6 Structural Seismic Test Methods Quasi-Static TestsLimitations:Unable to capture rate-dependent properties of structural componentsSlow application of loads may result in stress relaxation and creep, even in rate-independent specimens The results of quasi-static tests generally have limited dynamic interpretation.
7 Structural Seismic Test Methods Hybrid Simulation – Pseudo-DynamicA parallel numerical and experimental simulation.
10 Displacement Controlled Hybrid Simulation Equation of Motion (SDF):Numerical Solution:A time-stepping method, such as Newmark’s Beta:For solution in implicit form, tangential stiffness matrix is needed, or iterations should be used.
11 Displacement Controlled Hybrid Simulation Equation of Motion (for Hybrid Simulation)Numerical Solution:Newmark’s Beta Method:Tangential stiffness matrix or iterations?
14 Structural Seismic Test Methods Hybrid SimulationAdvantages:Lower cost than shake table tests (construction, moving mass)Less scaling and size requirementsAble to capture rate-dependent properties of experimental substructureProvides better understanding of component behaviorLimitationsInertia and rate-dependent terms are artificialThe number and quality of boundary conditionsUnrealistic gravitational loads
15 Development Challenges Error SourcesAnalytical:Discretization of structural system in time and space, and simplifications such as lumped-mass modelsErrors of the utilized integration methodsExperimentalMeasurement contaminationsFor example, noise in measurements may lead to excitation of high-frequency modes; if not, it will certainly affect the accuracyActuator tracking errorsThe most important error source in hybrid simulation – the achieved displacement almost never equals the desired displacement
16 Development Challenges Delay in servo-hydraulic actuatorsCommandAchievedDisplacementDelayTime
17 Development Challenges Delay in servo-hydraulic actuatorsHow delay affects the simulation:ForceLinear SpecimenWithout DelayDisplacement
18 Development Challenges Delay in servo-hydraulic actuatorsHow delay affects the simulation:ForceLinear SpecimenWith DelayDisplacement
19 Development Challenges Delay in servo-hydraulic actuatorsHow to compensate delay:First, measure the delay amount (in order of a few milliseconds)Extrapolate displacements: send a command ahead of desired displacement to the actuatorOr modify forces: extrapolate force measurements, or seek the desired displacements in the force and displacement measurements
20 Development Challenges In hybrid simulations experimental substructures are involvedIterations should be avoided, as they may damage the experimental substructures,A complete tangent stiffness matrix of the experimental substructure may be difficult to establish due to contaminated or insufficient measurements.As a result, most integration procedures are either explicit, or use initial stiffness matrix approximations, whose applications are limited.
21 Development Challenges Use explicit Newmark’s Beta method ,Apply displacement, measure restoring force, update acceleration and velocity vectors. Explicit methods are conditionally stable, and have stringent time step requirements for stiff systems and systems containing high-frequency modes.
22 Development Challenges Or use initial linear stiffness matrix instead of its tangent stiffness,Apply explicit displacement:Measure the restoring force and find velocity and acceleration, while updating displacement and measured force vectors: This is only an approximation. The accuracy may not be sufficient for highly nonlinear systems.
23 Development Challenges Or use an iterative scheme only in numerical substructure,Or find a way for global iterations without damage to the experimental setup,Or use “non-physical” iterations on the measurements,Or develop a fast method for finding tangential stiffness matrix during the simulation.
26 UB Real-Time Hybrid Simulation Available test setup
27 UB Real-Time Hybrid Simulation Test Setup Properties:Degrees of Freedom: up to 2Actuators: ± 3.0 inches, ± 5.0 kipsExperimental stiffness matrix can be altered by using different number of coupons. With two pairs in the first story and one pair in the second story:Experimental mass is very small:The rate-dependency of specimens is negligible
28 UB Real-Time Hybrid Simulation Fundamental periods of 0.4 s and above have been tested to work fine with the available equipment; a fundamental period of 0.6 s and above is recommended to minimize the noise in the measurements.If time scaling is acceptable, virtually any natural period can be tested.Available procedures allow for linear numerical system and linear transformations only.
30 A Typical Hybrid Simulation Required information:Total number of degrees of freedom: 4Experimental degrees of freedom: 2Numerical stiffness and total mass matrices:
31 A Typical Hybrid Simulation Required information:Inherent damping ratio: 5%Numerical damping matrix (in addition to the inherent damping):Influence vector:
32 A Typical Hybrid Simulation Required information:Transformation matrix for displacement (from global to actuator local coordinate system):Displacement factor in actuator coordinate system: 1Measured force factor: 1Ground motion: 1940 El Centro, 200%
33 A Typical Hybrid Simulation Additional requirements for model-based integration:Total number of essential stiffness parameters: 2Transformation matrix to parameter coordinate system:
34 Detailed Description of Simulation Models Simulation and control models are prepared in MATLAB Simulink environment on Host PC.The models are then ‘downloaded’ to real time computers running MATLAB xPC kernel.After simulation, the results are ‘uploaded’ to Host PC for observation and analysis.