Structural damage detection based onl₁regularization using natural frequencies and mode shapes

Abstract

Summary Conventional vibration‐based damage detection methods employ the Tikhonov regularization in model updating to deal with the problems of underdeterminacy and measurement noise. However, the Tikhonov regularization technique tends to provide over smooth solutions that the identified damage is distributed to many structural elements. This result does not match the sparsity property of the actual damage scenario, in which structural damage typically occurs at a small number of locations only in comparison with the total elements of the entire structure. In this study, an l1 regularization‐based model updating technique is developed by utilizing the sparsity of the structural damage. Both natural frequencies and mode shapes are employed during the model updating. A strategy of selecting the regularization parameter for the l1 regularization problem is also developed. A numerical and an experimental examples are utilized to demonstrate the effectiveness of the proposed damage detection method. The results showed that the proposed l1 regularization‐based method is able to locate and quantify the sparse damage correctly over a large number of elements. The effects of the mode number on the damage detection results are also investigated. The advantage of the present l1 regularization over the traditional l2 regularization method in damage detection is also demonstrated.

Sparse Bayesian learning for structural damage detection using expectation–maximization technique

“…If all damage parameters θ are assumed to have a uniform Gaussian prior distribution, the hyperparameter α becomes a single value. The resulting objective function (Equation ) is equivalent to the l 2 regularization, which may cause the identified damage distributed to many structural elements and fail to obtain the sparse solution . If a Laplace prior is applied to the damage parameter, then the corresponding objective function is equivalent to the l 1 regularization .…”

“…Another difficulty in structural damage detection is that the problem is essentially an inverse problem and is typically ill‐posed. As the number of available vibration measurements is limited, such detection is usually an underdetermined problem in mathematics . In practice, structural damage commonly appears in a few sections or members only, especially at the early stage.…”

“…As the number of available vibration measurements is limited, such detection is usually an underdetermined problem in mathematics. 18 In practice, structural damage commonly appears in a few sections or members only, especially at the early stage. Therefore, it possesses sparsity compared with the numerous elements of the entire structure.…”

Recent progress and future trends on damage identification methods for bridge structures

“…The objective of this review paper is to survey latest research in the area of damage identification methods for bridges, with the intent to identify state‐of‐the‐art examples that could be leveraged to stimulate research on condition assessment. Several state‐of‐the‐art review papers in this field prior to 2011 have been published, although some new researches have been conducted after 2017, this paper only reviews efforts between 2011 and 2017 due to the page limit. Two main classification approaches to review damage identification methods of bridges may be employed.…”

Improved Kalman filter damage detection approach based on l p regularization

“…Thus, the damage parameter vector is a sparse vector because most of the damage parameters have a zero value. Consequently, the l 1 regularization has begun to be applied in structural damage identification to improve the identification accuracy by considering the damage sparsity . For example, Hou et al proposed a damage detection method based on a model updating and l 1 regularization technique, two experimental examples demonstrated the effectiveness and superiority of the method.…”