Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method

Zuo, Wenjie; Bai, Jiantao; Yu, J. Chulsoo

doi:10.1007/s00158-015-1368-z

Cited by 37 publications

(9 citation statements)

References 21 publications

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“…For the purpose of fully utilized mode information, Kaouk and Zimmerman [14][15][16] defined the residual mode equation for damage detection based on mode information of structure, which can accomplish the dual tasks of determining the damage location and solving the damage situation effectively. is kind of damage detection method has received the widespread attention over the last decade [17][18][19][20][21]. ere exists a common obstacle in the aforementioned detection methods, which is to obtain higher order of structural modal shapes.…”

Section: Introductionmentioning

confidence: 99%

Residual Mode Vector‐Based Structural Damage Identification with First‐Order Modal Information

Luo

Zhuang

Wang

et al. 2021

Advances in Materials Science and Engineering

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Damage identification based on the change of dynamic properties is an issue worthy of attention in structure safety assessment, nevertheless, only a small number of discontinuous members in existing structure are damaged under service condition, and the most remaining members are in good condition. According to this feather, we developed an effective damage location and situation assessment algorithm based on residual mode vector with the first mode information of targeted structure, which utilized the quantitative relationship between first natural modes of global structure with the change of the element stiffness. Firstly, the element damage location is determined with exploitation of the sparseness of element stiffness matrices based on the discontinuity of damaged members. Then, according to the distribution characteristics of the corresponding residual mode vector, the nodal equilibrium equation about the damage parameter is established based on the residual mode vector, and the damage coefficients of structural elements are evaluated with the proposed equations. Two numerical examples are given to verify the proposed algorithm. The results showed that the proposed damage identification method is consistent with the preset damage. It can even accurately identify large-degree damages. The proposed algorithm only required the first-order modal information of the target structures and held few requirements of analysis resource; hence when compared with existing methods, it has obvious advantages for structural damage identification.

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Section: Introductionmentioning

confidence: 99%

Residual Mode Vector‐Based Structural Damage Identification with First‐Order Modal Information

Luo

Zhuang

Wang

et al. 2021

Advances in Materials Science and Engineering

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“…Sipple et al [24] proposed a new FE model updating method that uses numerical sensitivity instead of analytical sensitivity to solve inverse problems, which does not need model reduction and data extension, and has good robustness, stability and fault tolerance; Weng et al [25] proposed a new iterative substructuring method to accurately obtain the characteristic solution and characteristic sensitivity of the structure, which is suitable for model updating of large and complex structures; Jiang et al [26] expressed the thermal dependent elastic constants and thermal expansion coefficients as intermediate function by temperature independent variables, and used the perturbation method to calculate the sensitivity for parameter identification; On the basis of the basic concept of unconstrained optimization problem and three regularization solutions, Mohammad et al [27] proposed a novel sensitivity based FE model updating method, and simultaneously updated the element mass matrix and stiffness matrix of the FE model; Esfandiari et al [28] proposed a FE model updating method using incomplete strain data in frequency domain to detect variations in stiffness and mass parameters. The common sensitivity analysis methods using FRFs are the finite difference method [29] or the combined approximations (CAs) method [30]. These methods are based on obtaining the stiffness matrix, damping matrix, and mass matrix of the structures.…”

Section: Introductionmentioning

confidence: 99%

Model Updating Using Frequency Response Functions Based on Sherman–Morrison Formula

Zhu

Cao

et al. 2020

Applied Sciences

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Model updating plays an important role in dynamics modeling with high accuracy, which is widely used in mechanical engineering. In this paper, a model updating method using frequency response function (FRF) is proposed based on Sherman–Morrison formula, in which only the initial FRFs and parameter perturbations are employed to calculate the sensitivity avoiding repeated finite element (FE) analyses and improving the computational efficiency. Firstly, the sensitivity of FRFs to the design parameters is calculated by Sherman–Morrison formula based on the QR decomposition of the system dynamic stiffness matrix variation after parameter perturbations, then the influence of damping on the amplitude of FRFs is considered to select an appropriate frequency range, and finally conduct the model updating according to the sensitivity of the FRFs. By employing simulation examples of a truss and a solar wing and the experiment of an aluminum frame, the updating error is still within ±1.00% in the condition of 5% random white noise, which shows the proposed method has high accuracy and a certain anti-noise capability. When only a few numbers of frequency points are selected near the resonance peak of the FRFs, the result shows that selecting the appropriate frequency range and points can reduce the computational cost. The results of the experiment study show that the proposed method can effectively identify the structural parameters. The above results verify the feasibility and effectiveness of proposed model updating method using FRFs.

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“…One important group of FEM updating techniques is the perturbation methods (also known as the sensitivity methods). In last few decades, the perturbation methods have been widely used in model updating, [1][2][3][4][5] damage detection, [6][7][8][9][10][11][12][13] structural reanalysis, [14][15][16][17][18][19][20] vibration control, [21][22][23][24][25] nonlinear mechanics, [26][27][28][29][30] and so on. The traditional perturbation techniques are all the linear approximation methods based on the series expansion (Taylor series or Neumann series).…”

Section: Introductionmentioning

confidence: 99%

An improved spectral decomposition flexibility perturbation method for finite element model updating

Yang

Sun

2018

Advances in Mechanical Engineering

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Finite element analysis is the most powerful tool to predict the behavior of a structure in engineering practice. Generally, the initial finite element model must be corrected with experimental data due to its complexity. Thus, it is very necessary to study a finite element model updating method with high precision and high efficiency. To this end, this article presented an improved spectral decomposition flexibility perturbation method for structural finite element model updating. The improvements of the proposed method lie in two aspects. First, using the uniform correction model, the proposed method is more economical in computation than the initial method because the spectral decomposition and reorganization of elemental stiffness matrices can be avoided. Second, using the twice singular-value-truncation method, the proposed method has better performance than the initial method in combating data noise. A beam structure is employed to demonstrate the proposed method for model updating in a noisy environment. It was found that the result obtained by least squares estimate is seriously distorted and the result obtained by the first singular value truncation is also not entirely satisfactory. Only the result obtained by the second singular value truncation is the most stable and accurate. Overall, the improved spectral decomposition flexibility perturbation method is robust and effective in small modification case, large modification case, adjacent modification case, and multiple modifications case. The proposed method may be very useful for structural finite element model updating in the noisy environment.

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Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method

Cited by 37 publications

References 21 publications

Residual Mode Vector‐Based Structural Damage Identification with First‐Order Modal Information

Residual Mode Vector‐Based Structural Damage Identification with First‐Order Modal Information

Model Updating Using Frequency Response Functions Based on Sherman–Morrison Formula

An improved spectral decomposition flexibility perturbation method for finite element model updating

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