全域應變場估計與嚴謹誤差評估法

結構物之健康監測對人民生命財產的保護相當重要，一般結構監測常以變形為主要觀測量，藉由各種測量方法可得到待測物在不同時間的空間資訊，用以判定待測物的變形行為。近年來隨著各種觀測技術的發展，利用觀測所得之空間資訊可用以推估待測物之位移與應變，並進一步依材料之應變破壞準則判斷結構物之健康狀況。一般由待測物位移場求取對應的應變時，常採用有限差分法或有限元素法分析；惟結構變形時若含有剛體運動，則無法全然正確偵測與排除。為克服此點，本研究首先建立以線性轉換作為應變分析的解算方法，該法具有簡單且明確的幾何意涵，適用於各類均質空間資料的轉換。運用線性轉換法於結構應變分析時，除能正確獲得應變參數外，同時具有解算求解單元剛體運動分量之優點。此外，應變場估計後之參數品質為後續相關應用工作時所需之資料，本研究根據誤差傳播理論建立出參數向量估計值方差協方差矩陣之解析表示式。而透過數值模擬以及各種不同尺度下影像量測的實驗成果顯示，本法皆能夠成功辨識剛體與應變場域之實際行為，並合理評估應變參數之不確定性，對於結構物之破壞評估與相關規劃任務將可提供更為明確的指標依據。

關鍵字

應變場估計；剛體運動；自然變形；非迭代線性轉換；誤差傳播；品質評估

並列摘要

Structural health monitoring is an ongoing issue. Knowing the state of strain can help to evaluate a structure’s health status by employing strain failure criteria. In this study, a full strain field determination based on the non-iterative solution for linear transformations (NISLT) technique is developed with a main emphasis of identifying rigid-body motion and natural deformation coupled in the displacement fields. Furthermore, an analytical expression of the covariance matrix of the linear transformation parameters determined from the NISLT approach is rigorously derived. By attaining the quality of the displacement field, one can assess the quality of the determined strain parameters. The derivation was verified in numerical simulations and in various types and scales of laboratory experiments which demonstrated that the estimated strain fields differ from the originally assumed principal strain (real strain) or the strain gauge reading within the range of 1.96 times the standard deviation. The derived quality assessment of the NISLT approach provides a fair estimation of how accurate the strain would be under certain observation noise while the corresponding rigid body motion could be explicitly identified. Thereby, the quality of a structural health monitoring system under strain failure criteria could be properly regulated, which is important for the planning of structural monitoring tasks.

並列關鍵字

strain analysis ； error propagation ； quality assessment ； non-iterative solution for linear transformations (NISLT) ； rigid-body motion ； natural deformation

參考文獻

Ansari F. Practical implementation of optical fiber sensors in civil structural health monitoring. Journal of Intelligent Material Systems and Structures 2007, 18(8): 879-889.

Besnard G, Hild F and Roux S. “Finite-element” displacement fields analysis from digital images: application to Portevin-Le Châtelier bands. Experimental Mechanics 2006, 46(6): 789-803.

Billington EW and Tate A. The Physics of Deformation and Flow. McGraw-Hill Inc., New York, 1981, pp. 51-54 and pp. 269-283.

Cardini AJ and DeWolf JT. Long-term structural health monitoring of a multi-girder steel composite bridge using strain data. Structural Health Monitoring 2009, 8(1): 47-58.

Chang PC, Flatau A and Liu SC. Review paper: health monitoring of civil infrastructure. Structural Health Monitoring 2003, 2(3): 257-267.

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全域應變場估計與嚴謹誤差評估法

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