Estimation for the multi-way error components model with ill-conditioned panel data

Lee, Jaejun; Cheon, Sooyoung

doi:10.1016/j.jkss.2016.05.008

Cited by 2 publications

(1 citation statement)

References 20 publications

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“…Many methods, such as L-curve method and ridge trace method, have been proposed for choosing the ridge parameters in the last decades. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] But so far, these processes for choosing the ridge parameters all require very complex calculations, and the ridge parameters obtained are often not the optimal solutions. It is very necessary to develop a new BE method for solving the ill-posed problems more effectively.…”

Section: Introductionmentioning

confidence: 99%

A new biased estimation method based on Neumann series for solving ill-posed problems

Yang

2019

International Journal of Advanced Robotic Systems

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The ill-posed least squares problems often arise in many engineering applications such as machine learning, intelligent navigation algorithms, surveying and mapping adjustment model, and linear regression model. A new biased estimation (BE) method based on Neumann series is proposed in this article to solve the ill-posed problems more effectively. Using Neumann series expansion, the unbiased estimate can be expressed as the sum of infinite items. When all the high-order items are omitted, the proposed method degenerates into the ridge estimation or generalized ridge estimation method, whereas a series of new biased estimates can be acquired by including some high-order items. Using the comparative analysis, the optimal biased estimate can be found out with less computation. The developed theory establishes the essential relationship between BE and unbiased estimation and can unify the existing unbiased and biased estimate formulas. Moreover, the proposed algorithm suits for not only ill-conditioned equations but also rank-defect equations. Numerical results show that the proposed BE method has improved accuracy over the existing robust estimation methods to a certain extent.

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Section: Introductionmentioning

confidence: 99%

A new biased estimation method based on Neumann series for solving ill-posed problems

Yang

2019

International Journal of Advanced Robotic Systems

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Optimal Sensor Placement Algorithm for Structural Damage Identification

C.H.

Q.W.

2020

ENG

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Background: Structural damage identification is a very important subject in the field of civil, mechanical and aerospace engineering according to recent patents. Optimal sensor placement is one of the key problems to be solved in structural damage identification. Methods: This paper presents a simple and convenient algorithm for optimizing sensor locations for structural damage identification. Unlike other algorithms found in the published papers, the optimization procedure of sensor placement is divided into two stages. The first stage is to determine the key parts in the whole structure by their contribution to the global flexibility perturbation. The second stage is to place sensors on the nodes associated with those key parts for monitoring possible damage more efficiently. With the sensor locations determined by the proposed optimization process, structural damage can be readily identified by using the incomplete modes yielded from these optimized sensor measurements. In addition, an Improved Ridge Estimate (IRE) technique is proposed in this study to effectively resist the data errors due to modal truncation and measurement noise. Two truss structures and a frame structure are used as examples to demonstrate the feasibility and efficiency of the presented algorithm. Results: From the numerical results, structural damages can be successfully detected by the proposed method using the partial modes yielded by the optimal measurement with 5% noise level. Conclusion: It has been shown that the proposed method is simple to implement and effective for structural damage identification.

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Estimation for the multi-way error components model with ill-conditioned panel data

Cited by 2 publications

References 20 publications

A new biased estimation method based on Neumann series for solving ill-posed problems

A new biased estimation method based on Neumann series for solving ill-posed problems

Optimal Sensor Placement Algorithm for Structural Damage Identification

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