System Identification and Model Updating of the Four Seasons Building

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1 System Identification and Model Updating of the Four Seasons Building Eunjong Yu, Ying Lei, Derek Skolnik, John W. Wallace OVERVIEW Building Description Testing & Data Acquisition System Identification Determine modal properties based on the measured response of system known/unknown excitation Finite Element Modeling Model Updating Update parameters of FE model for better correlation between identified and analytical properties Conclusions D. Skolnik, et al. 1

BUILDING DESCRIPTION Four Seasons Office Building (Sherman Oaks, CA) 4story RC

punching and joint cracks UCLA NEES pilot project 4/04 to 8/04 TESTING & DATA

Identification and updating performed with data from the linear shaker white noise

2 BUILDING DESCRIPTION Four Seasons Office Building (Sherman Oaks, CA) 4story RC structure with perimeter SMF, PTslabs Damaged in the 1994 Northridge earthquake: slab punching and joint cracks UCLA NEES pilot project 4/04 to 8/04 TESTING & DATA ACQUISITION v1 v4 u1 y u4 vc A B rc uc x C N v2 u2 v3 u3 D Identification and updating performed with data from the linear shaker white noise excitation Data recorded with four triaxial accelerometers used derive three story responses D. Skolnik, et al. 2

SYSTEM IDENTIFICATION N4SID (Numerical Algorithm for Subspace State Space System Identification) Discrete time domain method uses measured data directly Makes projections of certain subspaces

3 SYSTEM IDENTIFICATION N4SID (Numerical Algorithm for Subspace State Space System Identification) Discrete time domain method uses measured data directly Makes projections of certain subspaces generated from the input/output observations to estimate state sequence using linear algebra tools such as QRD and SVD. Identifies system matrices from estimated states based on a linear least squares solution Can be applied to systems subjected to known or unknown excitation Well implemented in MATLAB s System Identification Toolbox u: input force applied with linear shaker y: output measured floor responses X = + AX + Bu y = CX + Du k 1 k k k k k f = λ i i 2π ( ) ζ = Re λ 2π f i i i ( C ) φi = Cψi sign Re ψi State Space Model Order =? SYSTEM IDENTIFICATION Stability Plot Model Order > 2NDOF Stability Tolerances f 1.5% ζ 5% MAC 98% EW NS Tor D. Skolnik, et al. 3

SYSTEM IDENTIFICATION Frequencies and Damping Ratios Mode Forced f (Hz) ζ (%) Ambient f (Hz) ζ (%) Ambient / Forced 1 EW 0.88 5.6 1.09 3.4 1.24 0.61 2 NS 0.94 6.9 1.25 3.1 1.33 0.45 3 Tor 1.26 6.0 1.

4 SYSTEM IDENTIFICATION Frequencies and Damping Ratios Mode Forced f (Hz) ζ (%) Ambient f (Hz) ζ (%) Ambient / Forced 1 EW NS Tor EW NS Tor Mix For Amb EW NS Tor Modeling Assumptions Lumped Mass Rigid Diaphragms Classical Damping FINITE ELEMENT MODELING From Core Tests ρ n =140pcf, ρ l = 115pcf E cn = 4028ksi, E cl = 2517ksi Effective Stiffness (FEMA 356) Columns: 0.5E cn N Beams: 0.42E cn Slabs: 0.4E cl D. Skolnik, et al. 4

FINITE ELEMENT MODELING Natural Frequencies

05 2 NS 1.12 0.94 1.19 3 Tor 1.35 1.26 1.

5 FINITE ELEMENT MODELING Natural Frequencies (Hz) Mode FE SID FE / SID 1 EW NS Tor EW NS Tor EW NS Tor FINITE ELEMENT MODELING FRF NS direction D. Skolnik, et al. 5

6 SensitivityBased Model Updating Procedure Unitless Ratios Mass (10) ratios of initial translational and rotational story masses Stiffness (52) ratios of initial effective stiffness values of structural members Damping (9) Damping ratios of last nine modes Realistic upper & lower bounds Parameter Vector p = [,,, ] T p1 p2 p k Parameter(s) associated with Mass of 2F Mass of 3F & 4F Mass of RF Mass of PH Radius of gyration of 2F & 3F Radius of gyration of 4F Radius of gyration of RF Radius of gyration of PH Column Stiffness at 2F RF Column Stiffness at PH Slab Stiffness at 2F RF Slab Stiffness at PH Beam Stiffness at 2F RF Damping ratios Bounds 85 % 115 % 50 % 150 % 75 % 135 % 35 % 150 % 2.5 % 20 % Initial Values 65.0 (kips sec 2 /ft) 64.7 (kips sec 2 /ft) 62.1 (kips sec 2 /ft) 7.6 (kips sec 2 /ft) 64.2 (ft) 64.0 (ft) 57.5 (ft) 26.7 (ft) 0.5E cn 0.75E cn, (NS) 2.5E cn (EW) 0.4E cl, 0.6E cl (NS) 2.0E cl (EW) 0.42E cn 5 % D. Skolnik, et al. 6

7 Define Error Residuals Frequency Response Function (FRF) Modal Frequencies (First 6) M x( t) + Cx( t) + Kx( t) = L f( t) 2 KΦ =Ω MΦ M+ C+ K = 2 ω iω x( ω) L f( ω) 2 B( ω) = ω M+ iωc+ K H( ω) = x( ω)/ f ( ω) B( ω)h( ω ) = L Nonlinear functions of p ε = L B(p, ω)h( ω) F ε = Ω Ω(p) M Linearize with a first order Taylor series expansion B(p, ω) ε F = H( ω) p (p, ω)h( ω) p p= p 0 Ω(p) ε M = p Ω p p= p 0 { Ω (p 0) } ε F CF df = p ε M CM dm { L B 0 } D. Skolnik, et al. 7

8 Objective Function Min WC p Wd p 2 such that p p + p p lb 0 ub and p p < 1 cor(c,c ), if cor(c,c ) > c i j i j i j lim C is often illconditioned Weighting Matrix Correlation Constraint Ratios of Initial Mass 2F 3F 4F RF PH Translational Mass 94% 97% 104% 105% 97% Radius of gyration 102% 104% 97% 102% 104% Stiffness Factors 2F 3F 4F RF PH NS Interior, North & South Frame Columns NS of East Frame Columns NS of West Frame Columns EW of Interior, East & West Frame Columns EW of North Frame Columns EW of South Frame Columns East Frame Girders West Frame Girders South Frame Girders North Frame Girders Slab NS Slab EW Damping 7th 8th 9th 10th 11th 12th 13th 14th 15th Ratios 9.6% 15.9% 7.3% 15.5% 2.5% 8.8% 8.8% 5.4% 13.5% D. Skolnik, et al. 8

26 4 EW 2.6 2.72 2.73 5 NS 2.94 2.93 2.94 6 Tor 3.53 3.

9 Natural Frequencies (Hz) Mode Initial Updated SID 1 EW NS Tor EW NS Tor EW NS Tor FRF NS direction D. Skolnik, et al. 9

Predicted and Measured NS response to 0.

10 Predicted and Measured NS response to Hz linear shaker sine sweep Penthouse Roof 4 th Floor 3 rd Floor 2 nd Floor CONCLUSIONS Identified modal properties of the first 7 modes using N4SID Frequencies identified from ambient vibrations represent a stiffer structure than that identified from white noise excitation FE model is updated using a sensitivitybased method Modal Properties and FRF of the updated model compare well with those identified Predicted acceleration response of the updated model compares quite well with the measured data Thank You D. Skolnik, et al. 10

System Identification and Health Monitoring Studies on Two Buildings in Los Angeles

System Identification and Health Monitoring Studies on Two Buildings in Los Angeles Derek Skolnik, Graduate Student Researcher, UCLA Eunjong Yu, Assistant Professor, Hanyang University, Korea Ertugrul