A new ridge estimation method on rank-deficient adjustment model

2021 ◽  
Author(s):  
Yingchun Song ◽  
Wenna Li ◽  
Caihua Deng ◽  
Xianqiang Cui
Keyword(s):  
Estimation Method ◽  
Ridge Estimation ◽  
Adjustment Model

Ridge estimation iterative algorithm to ill-posed uncertainty adjustment model

2020 ◽  
Author(s):  
tieding lu
Keyword(s):  
Parameter Estimation ◽  
Iterative Algorithm ◽  
Measurement Data ◽  
Estimation Method ◽  
Coefficient Matrix ◽  
Observation Equation ◽  
Validity And Reliability ◽  
Ridge Estimation ◽  
Adjustment Model ◽  
Ill Posed

<p> Uncertainties usually exist in the process of acquisition of measurement data, which affect the results of the parameter estimation. The solution of the uncertainty adjustment model can effectively improve the validity and reliability of parameter estimation. When the coefficient matrix of the observation equation has a singular value close to zero, i.e., the coefficient matrix is ill-posed, the ridge estimation can effectively suppress the influence of the ill-posed problem of the observation equation on the parameter estimation. When the uncertainty adjustment model is ill-posed, it is more seriously affected by the error of the coefficient matrix and observation vector. In this paper, the ridge estimation method is applied to ill-posed uncertainty adjustment model, deriving an iterative algorithm to improve the stability and reliability of the results. The derived algorithm is verified by two examples, and the results show that the new method is effective and feasible.</p>

scholarly journals Improvement in Ridge Coefficient Optimization Criterion for Ridge Estimation-Based Dynamic System Response Curve Method in Flood Forecasting

Water ◽  
2021 ◽  
Vol 13 (24) ◽  
pp. 3483
Author(s):  
Kexin Liu ◽  
Weimin Bao ◽  
Yufeng Hu ◽  
Yiqun Sun ◽  
Dongjing Li ◽  
...  
Keyword(s):  
Dynamic System ◽  
Response Curve ◽  
Estimation Method ◽  
Real Data ◽  
Optimization Criterion ◽  
Sum Of Squares ◽  
System Response ◽  
Ridge Estimation ◽  
Coefficient Optimization ◽  
Curve Method

The ridge estimation-based dynamic system response curve (DSRC-R) method, which is an improvement of the dynamic system response curve (DSRC) method via the ridge estimation method, has illustrated its good robustness. However, the optimization criterion for the ridge coefficient in the DSRC-R method still needs further study. In view of this, a new optimization criterion called the balance and random degree criterion considering the sum of squares of flow errors (BSR) is proposed in this paper according to the properties of model-simulated residuals. In this criterion, two indexes, namely, the random degree of simulated residuals and the balance degree of simulated residuals, are introduced to describe the independence and the zero mean property of simulated residuals, respectively. Therefore, the BSR criterion is constructed by combining the sum of squares of flow errors with the two indexes. The BSR criterion, L-curve criterion and the minimum sum of squares of flow errors (MSSFE) criterion are tested on both synthetic cases and real-data cases. The results show that the BSR criterion is better than the L-curve criterion in minimizing the sum of squares of flow residuals and increasing the ridge coefficient optimization speed. Moreover, the BSR criterion has an advantage over the MSSFE criterion in making the estimated rainfall error more stable.

Structural Damage Detection Based on Ridge Estimation Method

2014 ◽  
Vol 578-579 ◽  
pp. 1028-1031
Author(s):  
Hui Yong Guo ◽  
Mao Sheng ◽  
Zheng Liang Li
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Strain Energy ◽  
Good Accuracy ◽  
Detection Method ◽  
Estimation Method ◽  
Structural Damage Detection ◽  
Modal Strain Energy ◽  
Ridge Estimation ◽  
Damage Equation

In order to identify structural damage locations and extent, a method based on ridge estimation and modal strain energy is presented in this paper. First, structural modal strain energy is given and a modal strain energy sensitivity damage equation is obtained. Then, considering the TikhonovTT regularization theoryTT, a ridge estimation method is proposed to solve the damage equation and ridge parameter of the method is optimized. Simulation results demonstrate that the proposed damage detection method based on ridge estimation and modal strain energy can identify structural damage locations and extent with good accuracy.

scholarly journals Analyze and improve the influence of geomagnetic gradient on aeromagnetic compensation in a towed bird

2021 ◽  
Author(s):  
Zhijian Zhou ◽  
Zhilong Liu ◽  
Wenduo Li ◽  
Yihang Wang ◽  
Chao Wang
Keyword(s):  
Estimation Method ◽  
Vertical Gradient ◽  
Compensation Method ◽  
Interference Model ◽  
Horizontal Gradient ◽  
Flight Tests ◽  
Ridge Estimation ◽  
Motion Modes ◽  
Low Altitude

Abstract. Aeromagnetic exploration is an important method of geophysical exploration. We study the compensation method of towed bird system and establish the towed bird interference model. Due to the low altitude of the helicopter, the geomagnetic gradient changes greatly, so the geomagnetic gradient is considered in the towed bird interference model. In this paper, we model the gradient of the geomagnetic field as vertical gradient and horizontal gradient components, analyze the influence of the towed bird system on the compensation results under different motion modes, and apply the ridge estimation method to solve the problem. We verify the feasibility of this compensation method through actual flight tests, and further improve the data quality of the towed bird interference.

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

2019 ◽  
Vol 16 (4) ◽  
pp. 172988141987205 ◽  
Author(s):  
QW Yang
Keyword(s):  
Estimation Method ◽  
Neumann Series ◽  
High Order ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Biased Estimation ◽  
Ridge Estimation ◽  
Rank Defect ◽  
Ill Posed ◽  
Neumann Series Expansion

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.

Coaches estimation method for the athletes (CEM)

1995 ◽  
Author(s):  
Nagykaldi Csaba ◽  
Manohar Singh Badhan
Keyword(s):  
Estimation Method
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