Journal of the Earthquake Engineering Society of Korea (한국지진공학회논문집)

Earthquake Engineering Society of Korea (한국지진공학회)
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Determination of Optimal Accelerometer Locations using Mode-Shape Sensitivity

진동형상 민감도에 의한 가속도계 최적위치 결정

  • Published : 2006.12.31
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Abstract

This paper proposes a new algorithm of MS-EIDV (modal sensitivity-effective independence distribution vector) for determining optimal accelerometer locations (OAL) by using the Fisher Information Matrix (FIM) derived from mode-shape sensitivities. Also, the paper provides a reasonable guideline for selecting OAL which can reflect dynamic responses of a structure effectively. Since OAL should be determined with known values of structural parameters but since the parameters can be estimated by applying an inverse method such as SI (system identification) using measured response, the paper proposes a statistical method to overcome the paradox by considering the error bound of the structural parameters. To examine the proposed methods, a frequency-domain SI method has been applied. By using the identified results, the minimum necessary number of accelerometers could be selected depending on the number of target measurable modes. Through simulation studies, the results by applying EIDV method directly using the information of mode shapes were compared with those by applying the proposed MS-EIDV.

이 논문에서는 진동형상의 민감도로 유도한 피셔정보행렬(Fisher Information Matrix)를 이용하는 가속도계의 최적위치 결정 기법 MS-EIDV(modal sensitivity-effective independence distribution vector)을 제안하고, 이를 사용하여 구조물의 동적 거동을 잘 반영하여 가속도계의 최적위치를 결정할 수 있는 합리적인 기준을 제시한다. 실험을 위한 가속도계의 최적위치는 구조물의 변수가 기지값이어야 결정되지만 구조물의 변수값은 실험결과를 사용한 SI(system identification)기법과 같은 역해석을 통해 구해지기 때문에, 본 논문에서는 구조변수의 오차를 감안하여 미지의 구조물의 현 상태를 통계적으로 반영하는 방법을 제시하였다. 제안된 방법들의 검증을 위해 주파수영역 SI기법을 적용하였으며, 구조변수 추정 결과를 통해 현장에서 계측하고자하는 진동형상의 수에 따른 최소 필요 가속도계의 개수를 제시하였다. 수치예제에서는 진동형상만을 이용한 최적위치 결정법인 EIDV기법과 제안된 MS-EIDV기법에 의해 추정된 구조 변수 결과를 비교하였다.

Keywords

References

  1. Hjelrnstad, K.D. and Shin, S., 'Crack identification in a cantilever beam from modal response,' J. of Sound and Vibration, Vol. 198, No.5, 1996, pp. 527-545 https://doi.org/10.1006/jsvi.1996.0587
  2. Jang, J,H,, Yeo, I.H., Shin, S. and Chang, S.P., 'Experimental Investigation of System- Identification-Based Damage Assessment on Structures,' J. of Struc. Eng., ASCE, Vol. 12,8 No.5, 2002, pp. 673-682
  3. Vestouni, F. and Capecchi, D., 'Damage detection in beam structures based on frequency measurements,' J. of Engineering Mechanics, ASCE, Vol. 126, No.7, 2000, pp. 761-768 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(761)
  4. Ge, L. and Soong, T.T., 'Damage identification through Regularization Method 1: Theory,' J. of Engineering Mechanics, ASCE, Vol. 124, Issue I, 1998, pp. 103-108 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:1(103)
  5. Hjelmstad, K.D. and Banan, M.R., 'Time-Domain Parameter Estimation Algorithm for Structures I: Computational Aspects,' J. of Engineering Mechanics, ASCE, Vol. 121, Issues 3, 1995, pp. 424-434 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:3(424)
  6. Huang, C.-H., 'A non-linear inverse vibration problem of estimating the time-dependent stiffuess coefficients by conjugate gradient method,' Int. J. for Numerical Methods in Engineering, Vol. 50, 2001, pp. 1545-1558 https://doi.org/10.1002/nme.83
  7. Kang, J.S., Park, S.-K., Shin, S. and Lee, H.S., 'Structural system identification in time domain using measured acceleration,' J. of Sound and Vibration, Vol. 288, Issues 1, 2005, pp. 215-234 https://doi.org/10.1016/j.jsv.2005.01.041
  8. 정대성, 김철영, 김남식, 윤자걸, '상시진동실험을 이용한 남해대교의 동특성 평가',, 대한토목학회논문집, 제 22권, 제 6-A 호, 2002, pp. 1501- 1514
  9. Penny, J.E.T, Friswell, M.l. and Garvey, S.D., 'Automatic choice of measurement locations for dynamic testing,' AlAA J., Vol. 32, No.2, 1994, pp. 407-414
  10. Udwadia, F.E., 'Methodology for optimum sensor locations for parameter identification in dynamic systems,' J. of Eng. Mech., ASCE, Vol. 120, No.2, 1994, pp. 368-390 https://doi.org/10.1061/(ASCE)0733-9399(1994)120:2(368)
  11. Fadale, T.D., Nenarokomov, A.V. and Emery, A.F., 'Two Approaches to Optimal Sensor Locations,' J. of Heat Transfer, Vol. 117, 1995, pp. 373-379 https://doi.org/10.1115/1.2822532
  12. Kammer, D.C., 'Optimal Sensor Placement for Modal Identification Using System- Realization Methods,' J. of Guidance, AlAA, Vol. 19, No.3, 1996, pp. 729-731 https://doi.org/10.2514/3.21688
  13. Cherng A.P. 'Optimal sensor placement for modal parameter identification using signal subspace correlation techniques,' Mechanical Systems and Signal Processing, Vol. 17, Issue 2, 2003, pp. 361-378 https://doi.org/10.1006/mssp.2001.1400
  14. Li, Y.Y. and Yam, L.H., 'Sensitivity analyses of sensor location for vibration control and damage detection of thin-plate systems,' J. of Sound and Vibration, Vol. 240, Issues 4, 2001, pp. 623-636 https://doi.org/10.1006/jsvi.2000.3265
  15. Liu, C. and Tasker, F., 'Sensor Placement for Time-Domain Modal Parameter Estimation,' J. of Guidance, control, and Dynamics, AIAA, Vol. 19, No.6, 1996, pp. 1349-1356 https://doi.org/10.2514/3.21793
  16. O'Connor J.J. and Robertson E.F, 'MacTutor History of Mathematics,' http://www-history.mcs.st-andrews.ac.uk/ Mathematicians/Fisher.html, 2003
  17. Goodwin, G.C. and Payne, R.L., Dynamic System identification Experiment Design and Data Analysis, Academic Press, New York, 1977
  18. 권순정, '주파수영역과 시간영역에서의 가속도계 최적위치 결정 및 SI기법에 의한 검증', 박사학위논문, 인하대학교,2006
  19. Lee, I.-W. and Jung, G.-H., 'An efficient algebraic method for the computation of natural frequency and mode shape sensitivities-part I. distinct natural frequencies,' Computers & Structures, Vol. 62, No.3, 1997, pp. 429-435 https://doi.org/10.1016/S0045-7949(96)00206-4