Hybrid Simulation:Integration MethodsBozidar Stojadinovic, Associate ProfessorUniversity of California, Berkeley2Solution StrategyTime-stepping integration: Acquire the state Assemble computed and measured state data Extrapolate to the new state: Explicit (knowing only the current state) Implicit (iterate, assuming something about the futurestate and/or the way of getting there) Move to the new state Actuate the physical specimens Iterate the computer specimensCommunication (data transfer) is included inall states, too3LimitationsThe physical model is alive: Relaxes while under constant displacementor force Sticks when starting to move Develops a hysteresis when it unloads Accumulates damageThere is no way to erase an achievedstate if it is found to be wrong, and goback to a previously converged stateThe computer model is fine4Stepping Out to a New StatePhysical modelmoves forward intimeDisplacement orforce control No snap-back (displ) No softening (force)Computer modelmay iterate!ttRDR5Choice of Integration AlgorithmExplicit methods: Target displacement is computed using onlycurrent (or previous) state data No iteration required Conditionally stable: short time-stepImplicit methods: Unconditionally stable: longer time-step Less sensitive to higher-mode excitation Require an assumption about the target state anditeration on that assumption Physical substructures cannot be iterated Require an accurate tangent stiffness matrix6Explicit MethodsCentralDifferenceNewmark’smethod family: Constantaccelerationmethod Linearaccelerationmethod1/ 4; 1/ 2! "= =1/ 6; 1/ 2! "= =7Explicit MethodsModified Newton method:Select parameters to control numericaldamping of higher modes0; 0! "< #8Implicit MethodsNewmark alpha-method (HHT)Must adjust during time-step9Variations ofNewmark’s Alpha-MethodAnalog/digital hybrid scheme: Use available force measurements duringthe time-stepIterative corrector scheme: Use a Newton-Raphson method and atangent stiffness estimate to advancethrough the time-stepOperator splitting methods: Explicit and implicit operators applied todifferent substructures10Data FlowIntegrator assembles state andextrapolates a new stateSub-structures implement the new stateand report it backIntegratorSub-structureOld stateNew stateSub-structureOld stateNew state11ImplementationData bus links sub-structures to theintegrator: Local bus: localimplementation Use the internet as thebus: geographicallydistributedimplementation sub-structures andintegrator are resources ona network, such as NEESIntegratorSub-structureSub-structureSub-structure12Timing ConstraintsProcesses run atdifferent rate: Actuation 1000Hz Integration 100Hz Observation 10Hz(video?)To maintain continuoussignal feed to theactuator we generatecommand signals duringthe integration timestepintegration Δtactuation δt t13Real-Time SimulationIntegration timestep governs theduration of all otheractivities: Acquisition of state(communication,assembly) Extrapolation of thenew state (solving) Motion to the newstate(communication,actuation, iteration)integration Δtactuation δt tacquisitionextrapolationmotion14Sources of DelaysCommunication while assembling stateSolution while extrapolating a stepCommunication while sending a newstateDelay while applying a new state: Physical model: actuator time delay Computer model: iterationThese are random! we know the distributions, but not theduration of a particular delay15Event-Driven SimulationDefine states of the hybrid simulationTransition on available information16Finite State MachineIf there are no delays, then statetransitions are not an overload, and thesimulation is real-timeIf delays prevail, the simulations slowsdown and/or halts: Error is incurred due to: Low velocity Discontinuity (stop and go)Simulation may fail if data does notarrive!17ImplementationSeparate integrator andsub-structureprocesses: Start issuing actuatorcommands using a local(fast) estimator(predictor) of the new(target) state Correct the trajectorywhen the true targetstate arrives from theintegratorError is incurred in theprocess!integratoractuation δt Δtacquisitionextrapolationmotionpredictioncorrectionsub-structure18Three-loop ArchitectureLocal estimators(predictor andcorrector) at sub-structure level act asbuffers between theasynchronousintegrator andactuation systemsIntegratorSub-structuresp/cactuationp/cactuationp/cactuation19ExtensionsUse local estimatorson both sides ofdata links: They are system IDunits that model ofthe interactionbetween the rest ofthe structure and thesub-structure in asimplified way They are fast andlocal (no delay)Sub-structuresest.actuationest.actuationest.actuationest.est.est.integrationThank you!Development and operation of the nees@berkeley equipment site issponsored by NSF.http://nees.berkeley.eduContributions to this presentation from Prof. Gilberto Mosqueda aregratefully