Damage quantification of beam structures using deflection influence line changes and sparse regularization

Chen, Z.W.; Zhao, Long; Zhang, Jian; Cai, Qinlin; Li, Jun; Zhu, Songye

doi:10.1177/1369433221992482

Cited by 15 publications

(8 citation statements)

References 50 publications

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“…where x 0 , x 1 , ÁÁÁ, x n is the given node coordinate, Φ i x ð Þ represents the curve of the i-th segment, and n is the number of segments. The interpolation function curves Φ f x ð Þ can be rewritten as a matrix multiplied by quadratic interpolation function coefficients 9 :…”

Section: Bil Identification Deterministic Modelmentioning

confidence: 99%

“…Since, it is assumed that the BIL is a series of interpolation function curve segments given by

boldX goodbreak= Φ_{f} ((), x) goodbreak= ({, \begin{matrix} center \\ {normalΦ}_{1} (x) \\ {normalΦ}_{2} (x) \\ \begin{array}{c} ⋮ \\ Φ_{i} ((), x) \\ ⋮ \end{array} \\ {normalΦ}_{n} (x) \end{matrix} \begin{matrix} center \\ x_{o} \leq x < x_{1} \\ \begin{array}{c} x_{1} \leq x < x_{2} \\ ⋮ \\ x_{i - 1} \leq x < x_{1} \end{array} \\ ⋮ \\ x_{n - 1} \leq x \leq x_{n} \end{matrix})

where

x_{0}, x_{1}, \dots, x_{n}

is the given node coordinate,

Φ_{i} ((), x)

represents the curve of the i‐th segment, and n is the number of segments. The interpolation function curves

Φ_{f} ((), x)

can be rewritten as a matrix multiplied by quadratic interpolation function coefficients 9 :

boldX = Φ_{f} ((), x) = normalΩ boldc

where

normalΩ

is the fitting matrix and

boldc

is the coefficient vector of the interpolation function.…”

Section: Bil Identification Deterministic Modelmentioning

confidence: 99%

“…They allow bridge designers to calculate the maximum unfavorable responses such as the reaction, displacement, and stress by properly arranging the live loads. Furthermore, as a very promising tool, the BIL has been successfully applied to bridge weight-in-motion (WIM), [2][3][4] model updating, 5,6 damage detection, [7][8][9][10] and condition evaluation. [11][12][13] Therefore, the accurate and reliable identification of BILs is a prerequisite for their follow-up engineering applications.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A statistical influence line identification method using Bayesian regularization and a polynomial interpolating function

Chen

Zhao

Yan

et al. 2022

Structural Contr & Hlth

Self Cite

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As inherent characteristics of bridge structures, influence lines have been successfully applied in the fields of model updating, damage detection, and condition evaluation. The fast and accurate identification of a bridge influence line (BIL) is the premise and foundation of the above applications. BIL identification can be regarded as a typically ill-posed problem for which it is usually necessary to establish a regularization model to identify the model parameters and reconstruct the BIL. In this study, a BIL identification method that can automatically determine the regularization coefficient and quantify the uncertainties of BIL identification results is proposed. To accommodate the uncertainties involved in the measurements as well as the modeling error, an interpolation function-aided influence line model is embedded into the Bayesian framework with Gaussian prior distribution. The most probable values (MPVs) and variance of the interpolation function coefficients are derived analytically and then further used to infer the posterior probability density function of the influence line. Numerical example of a concrete continuous beam and field test for a box girder bridge show the accuracy, efficiency and qualitative evaluation of the proposed method. The results indicate that Bayesian regularization can be used to select the optimal regularization coefficient more accurately and effectively than traditional methods. More importantly, the uncertainty quantification for the influence line can qualitatively reflect the accuracy of the results as well as the effects of the parameters of the BIL identification model.

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Section: Bil Identification Deterministic Modelmentioning

confidence: 99%

“…Since, it is assumed that the BIL is a series of interpolation function curve segments given by

boldX goodbreak= Φ_{f} ((), x) goodbreak= ({, \begin{matrix} center \\ {normalΦ}_{1} (x) \\ {normalΦ}_{2} (x) \\ \begin{array}{c} ⋮ \\ Φ_{i} ((), x) \\ ⋮ \end{array} \\ {normalΦ}_{n} (x) \end{matrix} \begin{matrix} center \\ x_{o} \leq x < x_{1} \\ \begin{array}{c} x_{1} \leq x < x_{2} \\ ⋮ \\ x_{i - 1} \leq x < x_{1} \end{array} \\ ⋮ \\ x_{n - 1} \leq x \leq x_{n} \end{matrix})

where

x_{0}, x_{1}, \dots, x_{n}

is the given node coordinate,

Φ_{i} ((), x)

represents the curve of the i‐th segment, and n is the number of segments. The interpolation function curves

Φ_{f} ((), x)

can be rewritten as a matrix multiplied by quadratic interpolation function coefficients 9 :

boldX = Φ_{f} ((), x) = normalΩ boldc

where

normalΩ

is the fitting matrix and

boldc

is the coefficient vector of the interpolation function.…”

Section: Bil Identification Deterministic Modelmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

A statistical influence line identification method using Bayesian regularization and a polynomial interpolating function

Chen

Zhao

Yan

et al. 2022

Structural Contr & Hlth

Self Cite

View full text Add to dashboard Cite

show abstract

“…The identification of influence lines is dependent on moving vehicles load on bridges. Influence lines contain the stiffness information for the entire bridge and require only a few sensors and short-time bridge tests (Chen et al, 2021). Therefore, influence lines-based model updating has several advantages, including high accuracy, a large amount of data, and a low cost.…”

Section: Introductionmentioning

confidence: 99%

Influence lines-based model updating of suspension bridges considering boundary conditions

Lin

et al. 2022

Advances in Structural Engineering

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The boundary conditions of the main girder are complicated for suspension bridges. And they have a significant impact on the static and dynamic response of the structure. This study proposes a model updating method based on influence lines considering boundary conditions. First, rotational and translational spring elements are used to simulate the boundary conditions of the main girder. Then, rotational spring stiffness is estimated by constructing a sensitive objective function based on the influence lines. Translational spring stiffness is estimated by constructing a sensitive objective function based on the temperature-induced displacements at both ends of the girder. To improve calculation efficiency, a Gaussian process model is used instead of the finite element model (FEM). The estimation of boundary conditions is expressed as an optimization whose main goal is to iteratively estimate the boundary conditions to minimize the objective functions. After the boundary conditions are determined, the influence lines-based model updating is carried out by using the adaptive metamodel global optimization method. To validate the proposed method, a long-span suspension bridge is taken as a case study. The results show that the boundary conditions of the main girder have been successfully estimated. The accuracy of the model updating is improved after the boundary conditions are considered. The updated FEM with accurate boundary conditions can be a benchmark model for bridge damage identification or condition assessment.

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“…The bridge's influence line (IL) is a static characteristic that represents the internal force and reaction variations at a given place of the structure, generated by a unit moving load [14][15][16][17]. The measured IL of the bridge might represent the structure's current operational state.…”

Section: Introductionmentioning

confidence: 99%

Serious Damage Localization of Continuous Girder Bridge by Support Reaction Influence Lines

et al. 2022

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A novel damage detection approach is proposed in this study for a continuous girder bridge in which support reaction influence lines (ILs) are adopted. First, the relationship between the local damage of a continuous girder bridge and a damage index, based on support reaction ILs, is established through analytical derivation. Subsequently, the sensitivity of a support reaction IL-based damage index is analyzed using Dempster-Shafer(D-S) evidence theory, and it shows that the support reaction IL-based damage index is more noise-resistant if more support reaction ILs from a variety of locations are used. Three case studies (a simple numerical study of a two-span continuous beam, a laboratory experimental study of a two-span aluminum beam, and a complicated numerical study of a continuous girder bridge in Xiamen) have been conducted to validate the effectiveness of the proposed method in different damage scenarios, including single damage and multiple damages. Satisfactory damage identification results can be obtained even in high-level measurement noise conditions, showing that the proposed approach offers a promising field detection technique for identifying local structural damages in continuous girder bridges.

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Damage quantification of beam structures using deflection influence line changes and sparse regularization

Cited by 15 publications

References 50 publications

A statistical influence line identification method using Bayesian regularization and a polynomial interpolating function

A statistical influence line identification method using Bayesian regularization and a polynomial interpolating function

Influence lines-based model updating of suspension bridges considering boundary conditions

Serious Damage Localization of Continuous Girder Bridge by Support Reaction Influence Lines

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