scholarly journals Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

2020 ◽  
Vol 27 (6) ◽  
Author(s):  
Daniel T. Bartilson ◽  
Jinwoo Jang ◽  
Andrew W. Smyth
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Finite Element Model ◽  
Model Updating ◽  
Element Model ◽  
Singular Value ◽  
Finite Element Model Updating ◽  
Value Decomposition

Structural deformation reconstruction by the Penrose–Moore pseudo-inverse and singular value decomposition–estimated equivalent force

2020 ◽  
pp. 147592172095233
Author(s):  
Yixian Li ◽  
Limin Sun
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Finite Element Model ◽  
Singular Values ◽  
Element Model ◽  
Singular Value ◽  
Structural Deformation ◽  
Nodal Force ◽  
Influence Line ◽  
Value Decomposition

For structural health monitoring, estimating the external load is a typical ill-posed problem but significant. Because with the external force and the structural finite element model, any required response can be calculated, which is advantageous for further structural health monitoring works. This article first defines an underdetermined equation using a limited number of in-field measurements and the finite element model–calculated influence line matrix, and it proposes a load estimation method using the Penrose–Moore pseudo-inverse (generalized inverse). The objective of the proposed method is to obtain the equivalent nodal force vector with minimum length among all possible force vectors satisfying the deformation constraints. The estimated force is an equivalent nodal force, since it only satisfies limited deformation constraints. With the estimated nodal force, full structure static response can be easily calculated by multiplying the influence line matrix and the equivalent force vector. Besides, the truncated singular value decomposition is used to process the finite element model–calculated influence line matrix to avoid the over-fitting effect due to the measurement noise. The singular values of singular value decomposition represent the significance of the structural deformation modes, and the decreasing rate of the singular values is a good complexity indicator for a structure. The proposed frame can involve any types of static measurements, and it can realize real-time computation because it merely involves the matrix multiplying calculation. Finally, the sensitivity analysis is conducted by numerical simulation, and a large-scale model-based experiment has demonstrated that the algorithm is appropriate for in-field applications.

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

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881492 ◽  
Author(s):  
QW Yang ◽  
BX Sun ◽  
C Lu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Perturbation Method ◽  
Spectral Decomposition ◽  
Model Updating ◽  
Element Model ◽  
Singular Value ◽  
Finite Element Model Updating ◽  
Noisy Environment ◽  
Initial Method

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.

A new method for finite element model updating in structural dynamics

2010 ◽  
Vol 24 (7) ◽  
pp. 2137-2159 ◽  
Author(s):  
J.L. Zapico-Valle ◽  
R. Alonso-Camblor ◽  
M.P. González-Martínez ◽  
M. García-Diéguez
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Structural Dynamics ◽  
Model Updating ◽  
Element Model ◽  
New Method ◽  
Finite Element Model Updating

Estimation of Distributed Unbalance of Rotors

2001 ◽  
Author(s):  
Tachung Yang ◽  
Chunyi Lin
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Element Model ◽  
Singular Value ◽  
Lumped Mass ◽  
Piecewise Polynomials ◽  
Mass Unbalance ◽  
Thick Disks ◽  
Value Decomposition ◽  
Thin Disks

Mass unbalance commonly causes vibration of rotor-bearing systems. Lumped mass modeling of unbalance was adapted in most previous research. The lumped unbalance assumption is adequate for thin disks or impellers, but not for thick disks or shafts. Lee et al. (1993) proposed that the unbalance of shafts should be continuously distributed. Balancing methods based on discrete unbalance models may not be very appropriate for rotors with distributed unbalance. A better alternative is to identify the distributed unbalance of shafts before balancing. In this study, the eccentricity distribution of the shaft is assumed in piecewise polynomials. A finite element model for the distributed unbalance is provided. Singular value decomposition is used to identify the eccentricity curves of the rotor. Numerical validation of this method is presented and examples are given to show the effectiveness of the identification method.

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