Uncertainty quantification of damage detection results for a plane frame model

Year 2024, Volume: 13 Issue: 1, 188 - 195, 15.01.2024

Umut Yücel Erkan Durmazgezer

https://doi.org/10.28948/ngumuh.1361253

Abstract

In this study, uncertainty quantification was carried out on the damage detection results obtained through the sensitivity-based finite element model updating method for a two-story, single-span plane frame model, where damage was simulated as a regional stiffness reduction at the ends of columns and beams. The damage detection method employed is based on iteratively reducing the differences in modal parameters between damaged and undamaged conditions. The presence of noise in dynamic measurements introduces uncertainties in damage detection results by affecting the estimation of modal parameters. The reliability of the obtained results is possible by quantifying the amount of uncertainty they encompass. In the presented study, uncertainty quantification of damage detection results was carried out by adding noise data associated with different coefficient of variations to modal parameters related to the damaged condition. The model updating process was performed by using modal parameters with added noise data for the damaged condition and modal parameters for the undamaged condition, as well as by updating the element stiffness values of the finite element model representing the undamaged condition. Stiffness reductions of elements were calculated using the determined stiffness values before and after updating, thus enabling the detection of the location and extent of damage. Uncertainty quantification of the damage results obtained under different noise conditions was conducted using analysis of variance, meta-modeling, and sensitivity analysis methods. In this way, factors that introduce substantial uncertainty in damage detection results have been identified.

Keywords

Damage detection, uncertainty quantification, analysis of variance, meta-modeling, sensitivity analysis

Düzlem çerçeve modelinin hasar tespit sonuçlarının belirsizlik ölçümü

Abstract

Bu çalışmada, hasarın kolon ve kiriş uçlarında bölgesel rijitlik azalması olarak simüle edildiği, iki katlı, tek açıklıklı düzlem çerçeve modelinin duyarlık tabanlı sonlu elemanlar modeli güncellemesi yöntemiyle elde edilen hasar tespit sonuçlarının belirsizlik ölçümüne yer verilmiştir. Kullanılan hasar tespit yöntemi, hasarlı ve hasarsız durumlara ait modal parametreler arasındaki farkların iteratif bir şekilde küçültülmesi esasına dayanmaktadır. Dinamik ölçümlerdeki gürültü varlığı, modal parametrelerin tahminini etkileyerek hasar tespit sonuçlarında belirsizliklere neden olmaktadır. Elde edilen sonuçların güvenirliği, içerdikleri belirsizlik miktarının saptanması ile mümkündür. Sunulan çalışma kapsamında hasar tespit sonuçlarının belirsizlik ölçümü, hasarlı duruma ait modal parametreler üzerine farklı varyasyon katsayıları ile ilişkili gürültü verisi eklenmesi ile gerçekleştirilmiştir. Model güncelleme işlemi, hasarlı duruma ait gürültü verisi eklenmiş modal parametreler ile hasarsız durumun modal parametrelerinin kullanılması ve hasarsız durumu temsil eden sonlu elemanlar modelinin eleman rijitlik değerlerinin güncellenmesi ile yapılmıştır. Güncelleme öncesi ve sonrası belirlenen rijitlik değerleri kullanılarak elemanlara ait rijitlik azalmaları hesaplanmış, böylece hasarların yerleri ve miktarları tespit edilmiştir. Farklı gürültü koşullarına ait verilerin kullanılması ile elde edilen hasar sonuçlarının belirsizlik ölçümü varyans analizi, meta-modelleme ve hassasiyet analizi yöntemleri ile gerçekleştirilmiştir. Bu şekilde, hasar tespit sonuçlarında önemli mertebede belirsizlik oluşturan etkenler belirlenmiştir.

Keywords

Hasar tespiti, belirsizlik ölçümü, varyans analizi, meta-modelleme, hassasiyet analizi

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