Yapısal hasar teşhisinde dalgacık dönüşümüne dayalı bir yöntem geliştirilmesi
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Date
2010-09-17
Authors
Gökdağ, Hakan
Journal Title
Journal ISSN
Volume Title
Publisher
Uludağ Üniversitesi
Abstract
Doğal frekanslar, sönüm oranları ve doğal titreşim modları hasar sebebiyle yapının fiziksel özelliklerinde meydana gelen değişimlere duyarlı temel titreşim verileridirler. Titreşim modları, diğerlerinden farklı olarak, hasar yerine ait bilgiyi de içerir. Hasarlı bölgede mod verisinde hasar derecesi ile orantılı lokal süreksizlikler ortaya çıkar. Veride ölçümden kaynaklanan bir miktar parazit de mevcuttur. Dalgacık dönüşümü (DD) ölçüme karışan belli derecede parazite rağmen hasar kaynaklı süreksizliklerin yerini ve derecesini belirleyebilen bir matematiksel araçtır. DD'nin bu özelliğinden yararlanılarak, titreşim modları gibi konum verilerinin DD katsayıları ile hasar teşhisi yapılmaktadır. Bu konuda genellikle iki yaklaşım uygulanmaktadır. Birincisinde sadece hasarlı yapı verisine ait DD katsayıları kullanılır. İkincisinde sağlıklı haldeki verinin de DD katsayıları hesaplanır ve birincisinden çıkarılır. Birinci yaklaşımın üstün tarafı sağlıklı yapıya ait veriye ihtiyaç duymamasıdır. Çünkü bu tür bir referans veriyi elde etmek çoğu durumda zordur. Fakat hasar derecesi küçüldüğünde ve yüksek indisli titreşim modları kullanıldığında ikinci yaklaşım daha avantajlı olur. Bu çalışmada, sadece hasarlı haldeki veriyi kullanan, fakat performansı ikinci yaklaşımdakine yakın bir hasar teşhis yöntemi geliştirilmiştir. Yöntemin esası; uygun bir dalgacık fonksiyonu kullanarak ayrık DD (ADD) ile orijinal veriden bir yaklaşım fonksiyonu elde etmek ve bunu referans olarak kullanmaktır. Bunun için, öncelikle veri sınırlarda bozulma en az olacak şekilde genişletilir. Bu amaçla, performansı sıkça kullanılagelen yöntemlerden daha iyi olan, polinom uydurma esaslı basit ve etkili bir yöntem geliştirilmiştir. İkinci adımda, genişletilen veriden, sağlıklı haldeki mod şekli yerine kullanılmak üzere uygun bir yaklaşım fonksiyonu elde edilir. Bunun için ADD'nin çok-çözünürlüklü analiz özelliğinden ve sıfıra eşit momentlerinin sayısı yüksek dalgacıkların veri sıkıştırma kabiliyetinden yararlanılmıştır. ADD'de kullanılacak dalgacığın moment sayısı ve uygun ADD ayrışım düzeyinin nasıl belirleneceği izah edilmiş, yöntemin performansı kiriş, düzlem levha ve karmaşık şekilli sac parça gibi yapıların sayısal ve deneysel titreşim modları ile test edilmiştir.
Natural frequencies, damping ratios and vibration modes are the fundamental vibration parameters sensitive to changes in physical properties of structure due to damage. Apart from the others, vibration modes contain damage location info, as well. Mode shapes have local discontinuties which are proportional to damage extents. Moreover, measurement noise exists in vibration modes. The wavelet transform (WT) is a mathematical tool capable of identifying defect locations in modal shapes in spite of certain noise interference. In wavelet-based damage detection of spatial data such as mode shapes, there have been two major approaches. In the first, only the WT coefficients of damaged structural response are analyzed for defect identification. In the second, however, the WT coefficients of a reference data such as healthy structural mode shape are computed and subtracted from the former. The first method is advantegous in comparison to the second in that it does not require a reference data. Because, it is difficult to obtain such data in most cases, especially for the old structures. But, in the cases of small-extent damage and employement of higher order vibration modes, the second method becomes preferable. In this thesis, a new method using only the mode shapes of damaged structure but having more sensitivity to singularity then the first approach is proposed. This new method is based on extracting a suitable approximation function from the mode shape of damaged structure through the discrete WT (DWT), and employing this as reference like in the second method above. To this end, vibration mode of damaged structure is, first, extended at the ends to reduce border distortions as much as possible. In this regard, a new, simple and efficient extention method based on polynomial curve fitting is introduced. It is shown that this extention method is both capable of reducing distortion considerably and superior to the frequently used other approaches. In the second step, a suitable approximation function to use as reference is extracted from this extended mode shape by the DWT. For this purpose, the multiresolution property of the DWT and the data compression capability of wavelets having higher vanishing moments are utilised. The issues of selecting suitable number of vanishing moments and deciding on the correct DWT decomposition level are explained in detail. The performance of this new damage detection method is compared to the others? by applying to numerical and experimental vibration modes of beam, plate-like structure as well as a sheet metal part having complex geometry.
Natural frequencies, damping ratios and vibration modes are the fundamental vibration parameters sensitive to changes in physical properties of structure due to damage. Apart from the others, vibration modes contain damage location info, as well. Mode shapes have local discontinuties which are proportional to damage extents. Moreover, measurement noise exists in vibration modes. The wavelet transform (WT) is a mathematical tool capable of identifying defect locations in modal shapes in spite of certain noise interference. In wavelet-based damage detection of spatial data such as mode shapes, there have been two major approaches. In the first, only the WT coefficients of damaged structural response are analyzed for defect identification. In the second, however, the WT coefficients of a reference data such as healthy structural mode shape are computed and subtracted from the former. The first method is advantegous in comparison to the second in that it does not require a reference data. Because, it is difficult to obtain such data in most cases, especially for the old structures. But, in the cases of small-extent damage and employement of higher order vibration modes, the second method becomes preferable. In this thesis, a new method using only the mode shapes of damaged structure but having more sensitivity to singularity then the first approach is proposed. This new method is based on extracting a suitable approximation function from the mode shape of damaged structure through the discrete WT (DWT), and employing this as reference like in the second method above. To this end, vibration mode of damaged structure is, first, extended at the ends to reduce border distortions as much as possible. In this regard, a new, simple and efficient extention method based on polynomial curve fitting is introduced. It is shown that this extention method is both capable of reducing distortion considerably and superior to the frequently used other approaches. In the second step, a suitable approximation function to use as reference is extracted from this extended mode shape by the DWT. For this purpose, the multiresolution property of the DWT and the data compression capability of wavelets having higher vanishing moments are utilised. The issues of selecting suitable number of vanishing moments and deciding on the correct DWT decomposition level are explained in detail. The performance of this new damage detection method is compared to the others? by applying to numerical and experimental vibration modes of beam, plate-like structure as well as a sheet metal part having complex geometry.
Description
Keywords
Yapısal hasar teşhisi, Titreşim modları, Dalgacık dönüşümü, Structural damage detection, Vibration modes, Wavelet transform
Citation
Gökdağ, H. (2010). Yapısal hasar teşhisinde dalgacık dönüşümüne dayalı bir yöntem geliştirilmesi. Yayınlanmamış doktora tezi. Uludağ Üniversitesi Fen Bilimleri Enstitüsü.