VIBRATION CONTROL OF STRUCTURE USING CMAC

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HYBRID SYSTEM CONTROLLED BY A  -SYNTHESIS METHOD International Symposium on Earthquake Engineering Commemorating 10 th Anniversary of the 1995 Kobe Earthquake.

Aristotelis Charalampakis and Vlasis Koumousis

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Modal Control for Seismically Excited Structures using MR Damper

LOCATION AND IDENTIFICATION OF DAMPING PARAMETERS

A BRIDGE WITH VEHICLE LOADS

KAIST-Kyoto Univ. Joint Seminar

반능동 MR 유체 감쇠기를 이용한 지진하중을 받는 구조물의 신경망제어 이헌재, 한국과학기술원 건설환경공학과 석사과정

Implementation of Modal Control for

Modified Sturm Sequence Property for Damped Systems

ISEC-02 Second International Conference on Structural Engineering and Construction Algebraic Method for Sensitivity Analysis of Eigensystems with Repeated.

A Survey on State Feedback AMD Control

한국지진공학회 추계학술발표회 IMPROVED SENSITIVITY METHOD FOR NATURAL FREQUENCY AND MODE SHAPE OF DAMPED SYSTEM Hong-Ki Jo1), *Man-Gi Ko2) and In-Won Lee3) 1) Graduate.

Modified Modal Methods in Asymmetric Systems

a Bang-Bang Type Controller

Motion Notes Ms. Rudisill.

Control of a Hybrid System using a -Synthesis Method

Presentation transcript:

VIBRATION CONTROL OF STRUCTURE USING CMAC ICSSD 2000 VIBRATION CONTROL OF STRUCTURE USING CMAC * Dong-Hyawn Kim: Postdoctoral Researcher, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST In-Won Lee: Professor, KAIST Jong-Heon Lee: Professor, Kyungil University

CONTENTS 1 INTRODUCTION 2 CMAC* FOR VIBRATION CONTROL 3 NUMERICAL EXAMPLES 4 CONCLUSIONS *Cerebellar Model Articulation Controller Structural Dynamics & Vibration Control Lab., KAIST, Korea

1 INTRODUCTION Background Features of neural network control mathematical model is not required in designing controller Application areas - control of structures with uncertainty or nonlinearity Structural Dynamics & Vibration Control Lab., KAIST, Korea

Structural control using neural network external load neural network structure response sensor Structural Dynamics & Vibration Control Lab., KAIST, Korea

Multilayer Neural Network (MLNN) Wij control force state of structure (displacement) (velocity) Wij : weights Structural Dynamics & Vibration Control Lab., KAIST, Korea

Previous studies 1) H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng. 2) J. Ghaboussi et al. (1995). ASCE J. Eng. Mech. 3) K. Nikzad et al. (1996). ASCE J. Eng. Mech. 4) K. Bani-Hani et al. (1998). ASCE J. Eng. Mech. 5) J. T. Kim et al. (2000). ASCE J. Eng. Mech. - All methods are based on multilayer neural network, whose learning speed is too slow Structural Dynamics & Vibration Control Lab., KAIST, Korea

Objective and Scope To reduce learning time, we apply CMAC* neural network for structural control *Cerebellar Model Articulation Controller Structural Dynamics & Vibration Control Lab., KAIST, Korea

2 CMAC FOR VIBRATION CONTROL CMAC - proposed by J. S. Albus(1975) - a neural network with fast learning speed - mainly used for manipulator control Structural Dynamics & Vibration Control Lab., KAIST, Korea

Procedure of CMAC memory space input space output space x   u W1 W2   u displacement velocity Wn-1 control signal Wn weights Structural Dynamics & Vibration Control Lab., KAIST, Korea

Output calculation (1) x1 input x layer 1 layer 2 layer 3 layer 4 W11 W12 W13 W14 W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44 output W12+W22+W32+W42 Structural Dynamics & Vibration Control Lab., KAIST, Korea

Output calculation (2) x1 x2 input x layer 1 layer 2 layer 3 layer 4 W11 W12 W13 W14 W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44 output W13+W23+W32+W42 Structural Dynamics & Vibration Control Lab., KAIST, Korea

CMAC vs. MLNN items CMAC MLNN memory size Large Small computing mode Local Global learning speed Fast Slow real-time application Feasible Impossible Structural Dynamics & Vibration Control Lab., KAIST, Korea

Vibration Control using CMAC learning rule external load structure response CMAC sensor Structural Dynamics & Vibration Control Lab., KAIST, Korea

Control criterion: cost function (1) : state vector : control vector : relative weighting matrix : time step : final time step Structural Dynamics & Vibration Control Lab., KAIST, Korea

Learning rule proposed method (2) (3) (4) : learning rate (5) Structural Dynamics & Vibration Control Lab., KAIST, Korea

3. NUMERICAL EXAMPLES Model structure Structural Dynamics & Vibration Control Lab., KAIST, Korea

Equation of motion (6) : displacement vector : ground acceleration : control force : Mass matrix : Damping matrix : Restoring force : Location vector Structural Dynamics & Vibration Control Lab., KAIST, Korea

Nonlinear restoring force (Bouc-Wen, 1981) (7) (8) : linear stiffness : contribution of k0 : constants Structural Dynamics & Vibration Control Lab., KAIST, Korea

Effect of parameters Structural Dynamics & Vibration Control Lab., KAIST, Korea

Active Mass Driver (AMD) pump mass piston Structural Dynamics & Vibration Control Lab., KAIST, Korea

Parameters Structure AMD mass : 200 kg (story) stiffness : 2.25105 N/m (inter-story) damping ratios : 0.6, 0.7, 0.3% (modal) AMD mass : 18 kg (3% of building total mass) stiffness : 3.71103 N/m damping ratio : 8.65% Structural Dynamics & Vibration Control Lab., KAIST, Korea

CMAC structure input: 2 (disp., vel. of 3rd floor) output: 1 (control signal) no. of divisions: 3 per variable no. of layers: 200 no. of weights: 1800 Structural Dynamics & Vibration Control Lab., KAIST, Korea

Simulation integration time: 0.25 ms sampling time: 5.0 ms delay time: 0.5 ms Structural Dynamics & Vibration Control Lab., KAIST, Korea

Case studies model linear nonlinear earthquake simulation El Centro train El Centro control Northridge control Kern County control El Centro train El Centro control Northridge control Kern County control Structural Dynamics & Vibration Control Lab., KAIST, Korea

Linear cases (=1.0) training under El Centro earthquake CMAC MLNN ※1 Epoch = 0.005 s × 2000 steps Structural Dynamics & Vibration Control Lab., KAIST, Korea

Training results Jmin epoch neural network MLNN 1.77  10-2 412 CMAC 1.77  10-2 412 (1.00) (1.00) 1.94  10-2 65 (1.09) (0.15) Structural Dynamics & Vibration Control Lab., KAIST, Korea

El Centro earthquake (3rd floor) w/o control w/ control Displacement (m) Velocity(m/sec) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

El Centro earthquake (3rd floor) - continued w/o control w/ control Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Northridge earthquake (3rd floor) w/o control w/ control Displacement (m) Velocity(m/sec) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Northridge earthquake (3rd floor) - continued w/o control w/ control Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Kern County earthquake (3rd floor) w/o control w/ control Displacement (m) Velocity(m/sec) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Kern County earthquake (3rd floor) - continued w/o control w/ control Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Nonlinear cases (=0.5) Learning under El Centro earthquake CMAC MLNN Structural Dynamics & Vibration Control Lab., KAIST, Korea

Training results Jmin epoch neural network MLNN 1.91  10-2 427 CMAC 1.91  10-2 427 (1.00) (1.00) 2.02  10-2 34 (1.06) (0.08) Structural Dynamics & Vibration Control Lab., KAIST, Korea

El Centro earthquake (1st floor) w/o control w/ control Structural Dynamics & Vibration Control Lab., KAIST, Korea

Northridge earthquake (1st floor) w/o control w/ control Structural Dynamics & Vibration Control Lab., KAIST, Korea

Kern County earthquake (1st floor) w/o control w/ control Structural Dynamics & Vibration Control Lab., KAIST, Korea

Comparison of control results (linear, 3rd floor) El Centro MLNN CMAC Northridge Displacement (m) Kern County Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Comparison of control results (nonlinear, 3rd floor) El Centro MLNN CMAC Northridge Displacement (m) Kern County Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Maximum responses of 3rd floor (cm) w/ control CMAC MLNN Earthquake w/o control El Centro Northridge Kern County El Centro Northridge Kern County 5.01 2.06 1.65 (3.04) (1.24) (1.00) 6.15 2.14 1.38 (4.46) (1.55) (1.00) 3.42 0.97 0.72 (4.75) (1.35) (1.00) 3.48 2.54 2.34 (1.49) (1.09) (1.00) 3.94 2.20 1.63 (2.42) (1.35) (1.00) 2.68 0.97 0.80 (3.35) (1.21) (1.00) linear nonlinear Structural Dynamics & Vibration Control Lab., KAIST, Korea

4. CONCLUSIONS Learning speed of CMAC is much faster than that of MLNN. Response controlled by CMAC is slightly larger than that by MLNN. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Future work Further reduction of response controlled by CMAC with fast learning speed. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Thank you for your attention. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Pump dynamics (9) : oil flow rate : control signal : time constant : valve gains Structural Dynamics & Vibration Control Lab., KAIST, Korea

Piston dynamics (10) : displacement of ram : area of ram : compression coefficient : volume of cylinder : leakage coefficient Structural Dynamics & Vibration Control Lab., KAIST, Korea

Sensitivity Evaluation State equation (s-1) : state vector : control force vector : system matrix : control matrix Structural Dynamics & Vibration Control Lab., KAIST, Korea

Discretized equation using ZOH : sampling time Sensitivity matrix (s-5) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Computation of H (s-6) initial condition: (s-7) loading condition: measurement: Structural Dynamics & Vibration Control Lab., KAIST, Korea

Emulator minutes ~ hours Evaluation time Method Time Emulator minutes ~ hours Proposed m sampling time Structural Dynamics & Vibration Control Lab., KAIST, Korea

Convergence of learning rule Structural Dynamics & Vibration Control Lab., KAIST, Korea

Inserting (3), (4) into (2) (c-6) (c-7) (c-8) (c-9) Structural Dynamics & Vibration Control Lab., KAIST, Korea