An Exact Method for Calculating the Eigenvector Sensitivities

Yang, Qiuwei; Peng, Xi

doi:10.3390/app10072577

Cited by 8 publications

(18 citation statements)

References 33 publications

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“…where A ′ is the remaining matrix of A after removing some column vectors related to those undamaged elements and x ′ is the remaining vector of x after removing the corresponding coefficients. From equation (36), the second AIE solution can be obtained again using the SVT as…”

Section: The Proposed Aie Methodsmentioning

confidence: 99%

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A Robust Estimate Method for Damage Detection of Concrete Structures Using Contaminated Data

Peng

Qin

Yang

et al. 2021

Advances in Civil Engineering

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Damage detection of concrete structures based on finite element model and measured response parameters has been an important research topic in recent years. It is well known that test data of mechanical behavior of concrete show great scatterness. As a result, the measured response parameters of concrete structures sometimes have gross errors. The gross error is a physical quantity that is much larger than data noise, which may lead to serious distortion of calculation results. To this end, a new robust estimate method termed as the augmented inverse estimate is proposed in this work for damage detection of concrete structures to resist gross errors in data. It has the advantages of very simple programming, convenient utilization, high computational accuracy, and broad prospect of application. Central to the augmented inverse estimate are the augmentation of coefficient matrix and the multiple computations based on feedback evaluation. A reinforced concrete beam structure is used as an example to verify the proposed method. It was found that the proposed method can successfully identify the location and extent of structural damage even if the used data have gross errors.

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Section: The Proposed Aie Methodsmentioning

confidence: 99%

“…Note that the computation of the eigenvector sensitivity using equation ( 3) is very computationally expensive, since it requires the availability of all the mode shapes of the intact structure. In view of this, the formula presented by Yang and Peng [36] is used in this paper to compute the mode shape sensitivity as…”

Section: Damage Detection Equationsmentioning

confidence: 99%

A Robust Estimate Method for Damage Detection of Concrete Structures Using Contaminated Data

Peng

Qin

Yang

et al. 2021

Advances in Civil Engineering

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“…where ∆φ j is the jth mode shape change, {α} is the damage parameter vector for the possible damaged elements, S is the corresponding sensitivity matrix of the jth mode shape. The mode shape sensitivity can be calculated by the following formula [43] as…”

Section: Shear Structures ξ Imentioning

confidence: 99%

Damage Identification for Shear-Type Structures Using the Change of Generalized Shear Energy

2022

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Structural damage identification has become an important topic in the field of civil engineering in recent years. The shear-type structure, such as shear frame structure, is a common type used in civil engineering. In this paper, a damage identification method based on the change of generalized shear energy is proposed for shear-type structures. The main steps of the proposed method are as follows. Firstly, the element stiffness matrix in the structural finite element model is decomposed to obtain the elementary shear force vector. Secondly, the elementary generalized shear energy is calculated by the dot product of the vibration mode shape vector and the elementary shear force vector. Thirdly, structural damage locations can be determined by the changes of elementary generalized shear energy. Finally, more accurate damage localization and quantification are achieved by solving the mode shape sensitivity equation. A 20-storey numerical example and a three-storey experimental model are used to demonstrate the proposed damage identification algorithm. From the numerical and experimental results, it was found that the proposed approach can accurately identify the location and extent of the damage in the shear structures even if the data contain noise. It has been shown that the presented algorithm may be useful in the damage identification of shear-type structures.

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“…Then, the general solution and the special solution are solved, respectively. Based on Nelson’s method, Yang and Peng [ 31 ] present a direct calculation formula for eigenvector sensitivity as:

…”

Section: Review Of Sensitivity Calculation Formulasmentioning

confidence: 99%

“…Lin and Ng [ 30 ] used Nelson’s method to analyze the eigenpair sensitivities of fractional vibration systems. Recently, Yang and Peng [ 31 ] proposed an exact method for calculating the eigenvector sensitivities, which can be seen as an improvement of Nelson’s method due to its simple operation.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis Using a Reduced Finite Element Model for Structural Damage Identification

Yang

Peng

2021

Materials

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Sensitivity analysis is widely used in engineering fields, such as structural damage identification, model correction, and vibration control. In general, the existing sensitivity calculation formulas are derived from th,,,e complete finite element model, which requires a large amount of calculation for large-scale structures. In view of this, a fast sensitivity analysis algorithm based on the reduced finite element model is proposed in this paper. The basic idea of the proposed sensitivity analysis algorithm is to use a model reduction technique to avoid the complex calculation required in solving eigenvalues and eigenvectors by the complete model. Compared with the existing sensitivity calculation formulas, the proposed approach may increase efficiency, with a small loss of accuracy of sensitivity analysis. Using the fast sensitivity analysis, the linear equations for structural damage identification can be established to solve the desired elemental damage parameters. Moreover, a feedback-generalized inverse algorithm is proposed in this work in order to improve the calculation accuracy of damage identification. The core principle of this feedback operation is to reduce the number of unknowns, step by step, according to the generalized inverse solution. Numerical and experimental examples show that the fast sensitivity analysis based on the reduced model can obtain almost the same results as those obtained by the complete model for low eigenvalues and eigenvectors. The feedback-generalized inverse algorithm can effectively overcome the ill-posed problem of the linear equations and obtain accurate results of damage identification under data noise interference. The proposed method may be a very promising tool for sensitivity analysis and damage identification based on the reduced finite element model.

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An Exact Method for Calculating the Eigenvector Sensitivities

Cited by 8 publications

References 33 publications

A Robust Estimate Method for Damage Detection of Concrete Structures Using Contaminated Data

A Robust Estimate Method for Damage Detection of Concrete Structures Using Contaminated Data

Damage Identification for Shear-Type Structures Using the Change of Generalized Shear Energy

Sensitivity Analysis Using a Reduced Finite Element Model for Structural Damage Identification

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