Damage Detection Based on Transmissibility of a Vehicle and Bridge Coupled System - Review and Report 筑波大学大学院 システム情報工学研究科 構造エネルギー工学専攻 高橋 悠太 Yuta TAKAHASHI X. Kong, C. S. Cai; and B. Kong, " Damage Detection Based on Transmissibility of a Vehicle and Bridge Coupled System ", J. Eng. Mech., 2015, 141(1): 04014102 YMMTLAB seminar 2018/06/07

Transmissibility between V & B Introduction センサーの設置コストが高い 走りながら計測できれば（山口大：宮本先生とか2011**, 2013*** 車両橋梁相互作用における振動の伝達率に着目 高ければよくゆれる＝壊れていると考えられる？ 固有振動数が同じところで卓越＝壊れていると考えられる？ 伝達率損傷指標（TDI）を提案し，数値計算でさまざまな数値検討を行う Transmissibility between V & B （車両橋梁間の振動伝達率） ** Miyamoto, A., and Yabe, A. (2011). “Bridge condition assessment based on vibration responses of passenger vehicle.” J. Phys. Conf. Ser., 305(1),012103. *** Miyamoto, A., and Yabe, A. (2013). “Development of a bridge health monitoring system for short- and medium-span bridges based on bus vibration.” Proc., 3rd Int. Conf. on Sustainable Construction Materials and Technologies (SCMT 2013), Coventry Univ., Coventry, U.K., and Univ. of Wisconsin–Milwaukee Center for By-Products Utilization, Milwaukee, 1–12.

Theory Equation of Motion

Fourier transformation and coupling Theory Fourier transformation and coupling Modal shapes satisfy as + Fourier transformation and several manipulation …. 𝑑 𝑏 : displacement of bridge 𝑑 𝑏 𝑥,𝑡 = 𝑗=1 ∞ 𝛷 𝑗 𝑥 𝑦 𝑗 𝑡 𝑑 𝑣 : displacement of vehicle 𝛷 𝑗 𝑥 = √2𝑠𝑖𝑛⁡(𝑗𝜋𝑥/𝐿) 0 𝐿 𝛷 𝑗 𝑥 𝛷 𝑘 𝑥 𝑑𝑥= 0 𝐿 𝛷 𝑗 2 𝑥 𝑑𝑥= 𝛺 𝑗 , 𝑗=𝑘 CAOUTION : 𝑑=𝑉𝑡　𝑉:𝑣𝑒ℎ𝑖𝑐𝑙𝑒 𝑠𝑝𝑒𝑒𝑑 𝐻 𝑏𝑣 : transfer function between B & V 𝐷 𝑏 𝑥,𝜔 = 𝐻 𝑏𝑣 𝐷 𝑣 (𝜔) 𝐷 𝑏 , 𝐷 𝑣 : Fourier transformation of 𝑑 𝑏 , 𝑑 𝑣 T R 𝑚𝑛 = 𝑗=1 ∞ 𝛷 𝑗 𝑥 𝑚 𝛷 𝑗 𝑑 𝐻 𝑗 (𝜔) 𝑗=1 ∞ 𝛷 𝑗 𝑥 𝑛 𝛷 𝑗 𝑑 𝐻 𝑗 (𝜔) 𝑥 𝑚 & 𝑥 𝑛 : node location on the bridge

Numerical Study – Theoretical Verification Analytical solution of 𝐻 𝑏𝑣 on SDOF and single beam model Analytical solution of 𝑇 𝑅 𝑚𝑛 𝐻 𝑏𝑣 = 𝜔 2 𝑀 𝑣 𝑀 𝑏 𝐿 𝑗=1 ∞ 2 sin 𝑗𝜋𝑥 𝐿 sin⁡(𝑗𝜋𝑑/𝐿) 𝜔 𝑗 2 − 𝜔 2 T R 𝑚𝑛 = 𝑗=1 ∞ sin 𝑗𝜋 𝑥 𝑚 𝐿 sin 𝑗𝜋𝑑 𝐿 ( 𝜔 𝑗 2 − 𝜔 2 ) sin 𝑗𝜋 𝑥 𝑛 𝐿 sin 𝑗𝜋𝑑 𝐿 ( 𝜔 𝑗 2 − 𝜔 2 ) Peaks of Natural frequency appear at almost same frequency

Numerical study – Transmissibility in a Bridge - Only System Transmissibility Damage Index (TDI) TDI= 1 𝑁 𝜔 𝜔= 𝜔 1 𝜔 2 𝑗=1 𝑀 𝑛=1 𝑁 𝑚=1 𝑁 𝑑 𝑇 𝑅 𝑚𝑛 𝑗 𝜔 ∙𝑇 𝑅 𝑚𝑛 𝑗 𝜔 2 𝑗=1 𝑀 𝑛=1 𝑁 𝑚=1 𝑁 𝑑 𝑇 𝑅 𝑚𝑛 𝑗 𝜔 ∙ 𝑑 𝑇 𝑅 𝑚𝑛 𝑗 𝜔 ∙ 𝑗=1 𝑀 𝑛=1 𝑁 𝑚=1 𝑁 𝑇 𝑅 𝑚𝑛 𝑗 𝜔 ∙𝑇 𝑅 𝑚𝑛 𝑗 𝜔

Numerical study – Transmissibility in a VBC System 11 sensing vehicle were deployed at an interval of 2.5m They are not exciter vehicle

Numerical study - Effect of Road Surface Roughness and V

Numerical Method – I. One Reference Vehicle and One Moving Vehicle The response of reference vehicle is used for calculation of mode shape

Numerical Method – II. Two Vehicles at a Constant Distance

Numerical study - Two Vehicles at a Constant Distance

Method I is affected by the position of reference vehicle. Remark and Conclusion The transmissibility extracted from a bridge-only system embodies very stable and effective results. Several parametric studies show they affect to TDI in small damage cases. Method I is affected by the position of reference vehicle. Method II doesn't need a reference, but it is little worse than in Method I. Ideally, both vehicles should be able to take measurements while they are moving along the bridge, which will be the subject of further research in relation to this study.

参考にしたい点 気になる点 Comment 高次モード（3次）についても見ている 数値計算と数値検討の手順が丁寧 グラフがわかりやすい 参照車両を置く，複数車両を同時に走らせる条件は試して見たい 気になる点 Mode shape自体の推定精度はやはり悪い． 計測ノイズについての言及はなかった．実用性はわからない 橋梁の中心より終端側に参照車両がいるとき，Mode shapeの推定精度が大 きく落ちているのが気になる．

Author : X. Kong, C. S. Cai; and B. Kong 引用論文 Author : X. Kong, C. S. Cai; and B. Kong Title : " Damage Detection Based on Transmissibility of a Vehicle and Bridge Coupled System " Journal : J. Eng. Mech., 2015, 141(1): 04014102