1. Modal parameter estimation of low-rise building using sine sweep vibration tests Le Thai Hoa Wind Engineering Research Center Tokyo Polytechnic University

2. Contents 1. Sine Sweep Force (Measured & Simulated) 2. Frequency Response Functions (FRF) 3. Smoothing Techniques for FRF 4. Modal Parameter Estimation [DX1 only]

3. Objectives o Estimating modal parameters (natural frequencies and damping ratios) using sine sweep vibration data o Sine sweep input force has been measured and simulated theoretically o Identifying Frequency Response Functions (FRFs) from measured/theoretical input and measured response

4. Exciter o Linear sine sweep force o Constant sweep force (Constant amplitude) o Variable frequency range o Starting frequency fo= 2Hz o Ending frequency fe  6Hz o Sweep rate  =0.01 Hz/s Reference (Exciter) S-ACC TABLE-ACC: Input acceleration TABLE-DISP: Input displacement

5. Sensors Exciter 1F 2F PU4-X (CH4) PU4-Y (CH5) X Y PU6-X (CH7) PU6-Y (CH8) PU5-X (CH6) PU1-X (CH1) X Y PU3-X (CH3) PU2-X (CH2) Sampling rate: 100Hz Accelerometer

6. Sine sweep excitation Measured sweep force Simulated sweep force

7. Measurement of sine sweep force DX1-Small Amplitude Input displacement Input acceleration PSD

8. Input / Output (PSD) Input Output 0-360s360-720s Input Response DX1-Small Amplitude Spectral leakage due to periodic excitation

9. Input / Output (Wavelet) Input Response 100÷300s300÷500s500÷700s DX1-Small Amplitude

10. Input / Output (Wavelet) Input Response

11. o Sine sweep excitation: Simulation of sine sweep force o Linear sweep: : Argument (rad) : Amplitude (m) : Instantaneous frequency : Starting frequency (Hz) : Ending frequency (Hz) : Sweep rate (Hz/s) o Linear argument: o Input sweep: Amplitude SweepInitial frequency& phase

12. Simulation of sine sweep force o Setting initial parameters To=0.5s0.18s Simulated sine sweep input Initial condition (phase)

13. Comparison bt. simulation & measure Simulated and measured input Simulated input Phase difference happens

14. Frequency Response Function (FRF) Measured FRF Theoretical FRF Smoothing techniques for FRF

15. FRF o FRFs: Relationship between input forces x(t) and output responses y(t) in the frequency domain x(t) Inputs Exciter Second order FRFs: Phase: Coherence: Type1: Cross spectrum Type2: Auto spectrum

16. Measured FRF DX1-Small Amplitude Floor 1 Floor 2 3.67Hz

17. Measured FRF DX1-Small Amplitude FRF Phase Coherence PU4X and Measured Input 3.67Hz

18. Theoretical FRF DX1-Small Amplitude Floor 2 3.67Hz Floor 1

19. Theoretical FRF DX1-Small Amplitude FRF Phase Coherence PU4X and Measured Input 3.67Hz

20. Smoothing techniques for FRF o Single Block Technique (SBT): One block o Block Overlapping Technique (BOT): Many blocks o Frequency Averaging Technique (FAT): Many blocks BOT FAT SBT 2N data blocks 1 data blocks Block=4096 samples Total 10 blocks Frequency resolution Block 1Block 2 nfftnfft samples No overlapping nfftnfft samples 50% overlapping

21. Smoothing FRF DX1-Small AmplitudeDX1-Medium Amplitude Effects of smoothing techniques on frequencies and damping (DX1 - Small amplitude) Smoothing techniques Natural frequency [Hz] Damping ratio [%] Single block3.670.27 Block overlapping (No overlapping) 3.670.28 Block overlapping (50%overlapping) 3.670.57

22. Natural frequencies & Damping ratio estimation Half-power bandwidth method (HPB) Least-squares complex frequency domain method (LSCF)

23. Half power bandwidth (SDOF system) DX1-Small Amplitude DX1-Medium amplitude Amplitudef [Hz]  [%] Small3.670.27 Medium3.670.26 Large no data

24. Lease squares complex frequency domain (MDOF system) o Relationship bt. input force and output response : Complex value FRF matrix m: Number of measured points n: Number of excited points f: Frequency variable o Least squares solution o FRF matrix identified by measured inputs/ outputs Min

25. Further work Natural frequencies can be estimated using identified FRFs. Smoothing should be applied to reduce noise Both theoretical or measured inputs can be used to identified FRFs Damping estimation of the first mode can be obtained by the half power method, however, comprehensive approach via LSCF should be used Next work will be based on the LSCF method for estimating damping ratios

26. Thank you for your attention