基於第一模態振形之損傷診斷方法於懸臂梁之應用

First Mode Shape Based Damage Detection Methods for Cantilever Beams

江和峰(Ho-Feng Chiang)

指導教授 ： 張家銘

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202000889

摘要

大部分的結構存在內部損壞，其損傷位置和損傷程度很難由外觀判斷，所以需要損傷診斷方法。但是材料和高度等因素互不相同，診斷方法不一定適用全部類型的結構。本研究採用以模態振形為主的損傷診斷方法和不同類型的懸臂梁結構進行比較。
藉由建立和修改一維的懸臂梁數值模型，可提供分析者觀察和研究。利用兩種結構梁：Euler-Bernoulli梁和Timoshenko梁，以建立不同類型的懸臂梁數值模型，並得到不同的結構動力參數。各項損傷診斷方法可分為三組(1)基於曲率的損傷診斷方法，如模態振形曲率診斷法、基於曲率的模態應變能診斷指標、基於曲率的連續小波轉換診斷指標(2)基於斜率的損傷診斷方法，如模態振形斜率診斷方法、基於斜率的模態應變能診斷指標、基於斜率的連續小波轉換診斷指標(3)適用剪切結構的損傷診斷方法，如第一模態振形斜率變化方法和勁度最小平方法。
以模態振形為主的損傷診斷方法主要適用撓曲型結構和剪切型結構，未有適用撓曲-剪切型結構的損傷診斷方法，為了比較不同類型的懸臂梁結構的損傷診斷能力，將不同類型的第一模態振形可分離成撓曲部分和剪切部分，分別帶入適用撓曲型結構和剪切型結構的損傷診斷方法，得到損傷區域診斷結果和損傷診斷指標靈敏度分析，並且比較損傷診斷方法。
本研究也建立另一個分離方法，並討論分離方法的可行性和分離結果的誤差，以及討論代入各項損傷診斷方法的誤差對損傷區域診斷結果和損傷診斷指標靈敏度分析的影響。最後，利用上述各項損傷診斷方法建立適用於不同類型懸臂梁的組合診斷指標，並利用不同類型懸臂梁和不同損傷案例的損傷診斷結果驗證。
本研究透過數值分析和案例比較，得出模態振形曲率或斜率損傷診斷方法、基於曲率或斜率的連續小波轉換診斷指標，和第一模態振形斜率變化方法的損傷診斷能力較好。而且利用有限元素模型的模態振形代入另一個分離方法，以確認方法的可行性，以及得知在不同類型懸臂梁撓曲部分和剪切部分，自由度太少會出現較大的誤差，以及誤差會影響到各項損傷診斷方法的診斷結果。最後，由不同類型懸臂梁和不同損傷案例，得以驗證組合診斷指標能應用於不同類型懸臂梁。

關鍵字

懸臂梁結構 ； 第一模態振形 ； 模態振形斜率 ； 模態振形曲率 ； 結構損傷位置診斷 ； 模態振形擬合方法 ； 靈敏度分析

並列摘要

Most of the structures have internal damage, and the location and degree of damage are difficult to judge by appearance, so damage diagnosis methods are needed. However, factors such as material and height are different from each other, and the diagnosis method may not be applicable to all types of structures. In this study, mode shape-based damage diagnosis methods and different types of cantilever beam structures were used for comparison.
Establishing and modifying a one-dimensional cantilever beam model can provide analyst observation and research. Different types of cantilever beam models are established using two structural beams: Euler-Bernoulli beam and Timoshenko beam, and different structural dynamic parameters are derived from the cantilever beam model. The various damage diagnosis methods can be divided into three categories. (1) curvature-based damage diagnosis methods, such as mode shape curvature method, curvature-based modal strain energy damage index, and curvature-based continuous wavelet transform damage index. (2) slope-based damage diagnosis methods, such as mode slope diagnosis method, slope-based modal strain energy damage index, and slope-based continuous wavelet transform damage index. (3) The damage diagnosis method applicable to shear structures, such as change in the first mode shape slope and least square stiffness method.
The mode shape based damage diagnosis method is mainly applicable to bending-type structures and shear-type structures. There is no damage diagnosis method suitable for bending-shear-type structures. Different types of first mode shape can be separated into bending and shear parts, and brought into damage diagnosis methods applicable to flexure structure and shear structure, respectively, to obtain the damage location diagnosis results and sensitivity analysis of damage index, and compare damage diagnosis methods.
In addition, another method for separating the bending part and the shear part is established, called approximate method. The capability of approximate method and the error of the separation result are discussed. The influence of errors on the damage location diagnosis results and on sensitivity analysis of damage index are discussed by the diagnostic results based on the separation result. Finally, various damage diagnosis methods are used to establish combined damage index, which are applicable to different types of cantilever beams. This study will use different types of cantilever beams and different cases of damage diagnosis results to verify their suitability for different types of cantilever beams.
The comparison results of this study shows that mode shape curvature method, mode shape slope method, curvature-based continuous wavelet transform damage index, slope-based continuous wavelet transform damage index, and change in the first mode shape slope, these five methods are better than other methods. Moreover, the mode shape of finite element model is substituted into another separation method to confirm the capability of this method. It shows that the bending part and shear part of cantilever beams with less degrees of freedom have larger errors. The errors of new separation method affect the diagnosis results of various damage diagnosis methods. Finally, different types of cantilever beams and different damage cases verify that the combined damage index can be applied to different types of cantilever beams.

並列關鍵字

cantilever beam structure ； first mode shape ； mode shape slope ； mode shape curvature ； structural damage localization ； mode shape fitting method ； sensitivity analysis

參考文獻

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