REAL-TIME DYNAMIC HYBRID TESTING OF STRUCTURAL SYSTEMS Andrei REINHORN Clifford C. Furnas Professor Mettupalayam V. SIVASELVAN and Zach LIANG Project Engineers, G. E. Brown Network for Earthq. Eng. Simulation (NEES) Xiaoyun SHAO Ph.D. Candidate Department of Civil, Structural and Environmental Engineering University at Buffalo
Outline Definition of hybrid testing Computation Issues Objective of Testing Feasibility issues Implementations Possible Applications Remarks INTERFACE FORCES ACTIVE FEEDBACK FROM SIMULATED STRUCTURE APPLIED BY ACTUATORS AGAINST REACTION WALL REACTION WALL SHAKING TABLES (100 ton) SIMULATED STRUCTURE FULL OR NEAR FULL SCALE TESTED SUBSTRUCTURE Fig.1. Real-Time Hybrid Seismic Testing System (Substructure Dynamic Testing)
New trends in analytical simulations New approach to nonlinear time history analysis using energy principles Mixed Lagrangian Formulation - Simple Systems Lagrangian and Dissipation functions Generalized Momentum Reciprocal Structures Mixed Lagrangian Formulation - Frame Structure Effect of Finite Deformation on Lagrangian Numerical Method starting from Weak Statement leading to constraint optimization type solution.
Series and Parallel Systems Parallel (Kelvin) System Series (Maxwell) System Equilibrium expressed in Compatibility expressed in terms of displacement terms of momentum mu + cu + ku = P 1 J + 1 J + 1 J = vin v k c m 0 k L c 1 1 2 2 2 2 ( uu, ) = mu ku 1 ϕ = 2 2 ( u ) cu ( u ) T T T ϕ δi = δ L ( u, u ) dt + δudt Pδudt u 0 0 0 m P Lagrangian Formulation J J 11 11 2 J 2 m J L(, ) = k Lagrangian Function 11 2 ϕ ( J ) = J 2 c Dissipation Function Action Integral v in k 2 2 T T ϕ ( J T ) L (, ) 0 0 0 () 0 δi = δ J J dt + δjdt + vin t + v δjdt J c m
Combined Kelvin-Maxwell System - Mixed Formulation Mixed Lagrangian Function L 1 1 J u J = mu + J T AJ + J T B T u 2 2 ( ) 2,, k 1 F 1 u J = T { J1 J2}, Impulse vector k 2 c 1 c 2 m P A 1 0 k 0 1 k 2 1 = B = [ 1 1], Flexibility matrix, Equilibrium matrix F 2 Mixed Dissipation Function Action Integral 1 1 1 ϕ uj = cu + J (, ) 2 2 2 1 2 2 2 c2 Note: BT = Compatibility matrix T T T T ϕ ( u ) ϕ ( J 2 ) L ( J,, ) 2 δi = δ u u dt + δudt + δj dt Pδudt u J 0 0 0 2 0
1D Plasticity Dissipation Form F y ε p ε k F Add dashpot in parallel (Regularization) η F dashpot 0 if F F = F Fslider if F > F y y = F F F y sgn ( ) 1 = η p F damper = F Fy sgn ( F) ε 1 η 1 Define ϕ ( F ) = 2η F F y Dissipation Function 2 ε p ϕ F = F ( )
Elastic-Plastic System - Dissipation Viscous ϕ(f) k 1 F 1 u c 1 m P Visco-plastic ϕ(f) F k 2 c 2 F 2 F -F y F y Ideal-plastic/Friction ϕ(f) Formulation does not change -F y F y F
Numerical Example - Time history analysis of Portal Frame W12 40 W8 31 W8 31 3600 7200
Case 1: No Vertical Loads Horizontal Displacement Vertical Displacement 150.0 0.6 0.5 Horizontal Displacement (mm) 100.0 50.0 0.0-50.0-100.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Time (s) Lagrangian Method DRAIN-2DX Vertical Displacement (mm) 0.4 0.3 0.2 0.1 0.0-0.1-0.2-0.3-0.4 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 Time (s) Lagrangian Method DRAIN-2DX 100.0 Case 2: Vertical Load = 50% of Axial Yield Horizontal Displacement Horizontal Reaction vs. Displacement 80.0 0.0 60.0 Horizontal Displacement (mm) -100.0-200.0-300.0-400.0-500.0 Horizontal Reaction (kn) 40.0 20.0 0.0-20.0 Collapse -600.0 Lagrangian Method DRAIN-2DX -40.0 Lagrangian Method DRAIN-2DX -700.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Time (s) -60.0-250.0-200.0-150.0-100.0-50.0 0.0 50.0 Horizontal Displacement (mm)
Remarks Analytical Approaches Numerical developed for the time integration starting from Hamilton ton s s principle Preserves the energy and momentum characteristics of the continuous ous time structure At each time step the problem becomes one of constrained minimization in forces Principle of Incremental Complementary Potential Energy Linearly constrained Augmented Lagrangian Method Numerical examples demonstrate the feasibility of the method NEEDS VALIDATION - EXPERIMENTATION ONLY ALTERNATIVE
Objectives of Hybrid Testing Ultimately allow production of computational tools validated by experiments Allow testing of full size structures or substructures Allow to test strain rate effects Allow to develop inertial effects in distributed mass systems Test integrally the computational tools as well as the physical specimens
Real-time dynamic hybrid testing Well understood ` Structural Actuator Foundation Focus of interest Laminar Soil Box Shake Table
Real-time dynamic hybrid testing Response Feedback ` Distributed mass Acceleration input: Table introduces inertia forces Foundation Laminar Soil Box Shake Table Structural Actuator Has to operate in Force Control
Real-time dynamic hybrid testing Combined use of earthquake simulators, actuators and computational engines for simulation Response Feedback ` Computational Substructure Physical Substructure Physical Substructure Structural Actuator Computational Substructure Shake Table Ground/Shake Table
Substructure Testing Unified Approach Response Feedback ` Computational Substructure Physical Substructure Physical Substructure Structural Actuator Computational Substructure Shake Table Ground/Shake Table Shake table acceleration, ( ) A ctuator Force, F a = 1 α s m k u t = α 1 s u 1 3 s x 3 x 2 m 2 3 ( ) α ( ) ( ) First story contribution to shake table acceleration Third story contribution to shake table acceleration u + 1 α ( s) k ( x x ) 1 2 1 3 3 3 2 First story contribution Third story contribution to actuator force to actuator force
α ( s) α ( s) = 0 and = 0 1 3 Unified approach to substructure testing If α ( s) 0 and α ( s) 0, then the control requires a 1 3 shake table and an actuator to implement the substructure testing. If α ( s) = 0 and α ( s) = 0, then the controller require just 1 3 an actuator to implement the substructure testing as pseudo-dynamic dynamic testing: Note: in pseudo-dynamic dynamic testing, inertia effects are computed. In dynamic hybrid testing ( α1( s) 0 or α3( s) 0 ), the actuator should operate in force control.
Explanation of force control scheme Target Force = F Displacement command = F / k spring Displacement command = F / k spring + Structure Displacement Structure Displacement Feedback
Innovative scheme for force control Target Force 1 / K LC Measured Force Command Signal Actuator in Displacement Control Series Spring, K LC Structure Compensator Structure Displacement
Smith predictor compensator Smith Predictive Compensator 1/K LC + + Σ + Corrective Displcement + Σ Predictive Displcement T = e -sτ Actuator + - Σ K LC Series Spring Σ - + ˆT Delay Model 1 ms cs kˆ Kˆ 2 ˆ + ˆ + + LC Model of Structure- Spring System 1 + + 2 ms cs k Structure
Hybrid Controller Implementation (UB-NEES) Flexible architecture using parallel processing (see right side of diagram below) Delays of less than 5 milliseconds. Optional Optional Computationa l Substructure Physical Substructur Computationa l Substructure Physical Substructur Shake Table Structural Actuator MTS Actuator Controller (STS) MTS Hydraulic Power Controller (HPC) SCRAMNET I Compensation Controller xpc Target Network Simulator Real-time Simulator General Purpose Data Acquisition System Data Acquisition Ground/Shake Table MTS Shake Table Controller (469D) SCRAMNET II Hybrid Testing CONTROL OF LOADING SYSTEM HYBRID CONTROLLER UB-NEES NODE Design done jointly between MTS and UB
Implementation of RTDHT Actuator Structure Shake Table
Substructure response Actuator Structure 0.014 0.012 0.010 Calculated Second floor Measured -Calculated Shake Table 0.008 0.006 0.004 0.002 0.000 0.0 2.0 4.0 6.0 8.0 10.0 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Calculated Measured First floor 0.00 0.0 2.0 4.0 6.0 8.0 10.0 Hybrid test Analytical
Possible applications
Hybrid Testing of Electrical Systems Bushing Bushing Bushing Interface Reduced-Model Representation Bushing Interface Shake table Dynamically condensed model to simulate the transformer with bushing interface Transformer Ground Motion
Possible Application - Distributed Testing University at Buffalo
Fast-MOST FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID 6-span bridge model FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID - test in progress Span and one column are numerical models Other 4 columns are experimental models Achieved speeds of 100 milliseconds (based on UB-NEES developments) Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast MOST Structural Model 6-span bridge model test in progress Span and one column are numerical models Other 4 columns are experimental models Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast-MOST FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID 6-span bridge model FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID - test in progress Span and one column are numerical models Other 4 columns are experimental model Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast MOST Structural Model 6-span bridge model test in progress Span and one column are numerical models Other 4 columns are experimental models Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast-MOST FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID 6-span bridge model FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID - test in progress Span and one column are numerical models Other 4 columns are experimental model Slide courtesy of Gilberto Mosqueda Computational Sites: UIUC/NCSA Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast MOST Structural Model 6-span bridge model test in progress Span and one column are numerical models Other 4 columns are experimental models Achieved speeds of 100 milliseconds (based on UB-NEES developments) Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast-MOST FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID 6-span bridge model FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID - test in progress Span and one column are numerical models Other 4 columns are experimental model Slide courtesy of Gilberto Mosqueda Computational Sites: UIUC/NCSA Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast MOST Structural Model 6-span bridge model test in progress Span and one column are numerical models Other 4 columns are experimental models Computational Sites: UIUC/NCSA Slide courtesy of Gilberto Mosqueda Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Fast-MOST FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID 6-span bridge model FAST-PSEUDO PSEUDO-DYNAMIC-HYBRID - test in progress Span and one column are numerical models Other 4 columns are experimental model Slide courtesy of Gilberto Mosqueda Computational Sites: UIUC/NCSA Experimental Sites: Berkeley Boulder UIUC Buffalo Lehigh
Remarks Experimental Approaches Full scale (or large scale) testing of assemblies can be implemented only as substructure testing in the NEES Collaboratory Advanced analytical techniques require validation Hybrid testing may provide the framework for both of the above The current new technology allows for distributed hybrid dynamic testing although many issues need further solutions New experimentation and computing infrastructure in US and networking of such infrastructure can allow the advances necessary for such testing
Thank you! Questions?