Finite element Model Updating by using Maximum Likelihood Estimation

Abstract

In recent years, the problem of vibration-based model updating of structures has been increasingly attracting the attention of researchers. In general sense, the corresponding studies available in the literature can be classified as deterministic and probabilistic methods. In this context, various implementations are available for the deterministic and probabilistic approaches. This study, however, presents an alternative approach based on the maximum likelihood estimation. In the proposed methodology, the modelling errors are considered by using a non-dimensional Rayleigh ratio, in addition to the measurement errors. System model parameters are updated via a probability density function obtained by the assumption that the measurement and modelling errors follow normal distribution. The reliability of the proposed method has been verified by one numerical and one experimental application. According to the results, it is observed that the proposed method gives rather reasonable solution.

Keywords

• Model updating
• maximum likelihood estimation
• modal identification
• multiple measurement sets

Sonlu Eleman Modellerinin Maksimum Olasılık Tahmini ile Güncellenmesi

Abstract

Matematiksel yapı modellerinin titreşim verileri kullanılarak güncellenmesi konusu, son yıllarda giderek artan bir şekilde araştırmacıların ilgisini çekmektedir. Bu hususta literatüre sunulan yöntemler genel olarak deterministik ve olasılıksal olarak sınıflandırılmaktadır. Bu bağlamda hem deterministik hem de olasılıksal model güncelleme yöntemlerinin birçok varyasyonu yer almaktadır. Bu çalışmada ise maksimum olasılık tahminine dayalı alternatif bir yaklaşım sunulmaktadır. Önerilen yöntemde, modal tanılama sırasında öngörülen ölçüm hatalarının yanı sıra model hatası da boyutsuz bir Rayleigh oranı üzerinden dikkate alınmaktadır. Sisteme ait model parametreler, ölçüm ve modelleme hatalarının normal dağılım göstereceği kabulüyle oluşturulan bir olasılık yoğunluk fonksiyonu üzerinden hesaplanmaktadır. Sunulan yöntemin güvenirliği bir sayısal ve bir deneysel uygulama üzerinden değerlendirilmiştir. Elde edilen verilere göre önerilen yöntemin oldukça makul sonuçlar verdiği gözlemlenmektedir.

Keywords

• Model güncelleme
• Maksimum olasılık kestirimi
• modal tanılama
• çoklu ölçüm setleri

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