Dual K-Type Ridge Estimation of Inverse Problem with Morbid Equality Constraints

2013 ◽  
Vol 416-417 ◽  
pp. 1289-1295
Author(s):  
Chao Zhong Ma ◽  
Ji Fu ◽  
Yuan Lu Du ◽  
Qing Ming Gui ◽  
Yong Wei Gu
Keyword(s):  
Inverse Problem ◽  
Adverse Effects ◽  
Coefficient Matrix ◽  
Equality Constraints ◽  
Inversion Problem ◽  
Constraint Matrix ◽  
Ridge Estimation ◽  
Master Model

Based on non-precision observation, it researches the inversion problem with morbid equality constraints. And according to the pathological problems exist for the coefficient matrix and the constraint matrix, and it suggests the ridge estimation of the double-k type derived Ridge to determine these parameters. The results show that a variety of programs and double k ridge estimate not only removes the constraint matrix morbid adverse effects, but also can better overcome the master model morbidity and constraint matrix caused by the presence of instability, which is a good estimate.

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>

A New Algorithm for Calculating the Degrees of Freedom of Complex Mechanisms

2011 ◽  
Vol 346 ◽  
pp. 324-331
Author(s):  
Wei Jiang ◽  
Xin Luo ◽  
Wen Chuan Jia ◽  
Yuan Tai Hu ◽  
Hong Ping Hu
Keyword(s):  
Degrees Of Freedom ◽  
Linear Equations ◽  
Linear Constraint ◽  
Coefficient Matrix ◽  
Constraint Matrix ◽  
Constraint Equations ◽  
Complex Mechanisms ◽  
Traditional Approaches ◽  
Homogeneous Linear

A new algorithm is presented to calculate the degrees of freedom (DOFs) of spatial complex mechanisms by using the coefficient matrix of the linear constraint equations. A joint constraint matrix is firstly put forward for each kind of joint to formulate linear constraint equations in terms of spatial fine displacements of joint acting point with respect to joint frame. Two kinds of transformation are then proposed to rewrite all the constraint equations in terms of a set of fine displacements of all bodies and it leads to a set of homogeneous linear equations. The rank of the resulting coefficient matrix stands for the number of effective constraints and therefore the DOFs of the mechanism can be easily figured out. The proposed method can be widely used to solve the problem of DOFs for many spatial complex mechanisms, which may not be correctly solved with traditional approaches. Besides, the proposed method is very easy for implementation.

scholarly journals TIMING OPTIMIZATION OF HEAD AND NECK CT ANGIOGRAPHY VIA THE INVERSE PROBLEM ALGORITHM: IN VIVO SURVEY FOR 1001 PATIENTS IN 2020–2021

2021 ◽  
Author(s):  
CHUN-CHIEH LIANG ◽  
LUNG-FA PAN ◽  
MING-HSIANG CHEN ◽  
JIE DENG ◽  
DENG-HO YANG ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Correlation Coefficient ◽  
Ct Angiography ◽  
Empirical Formula ◽  
Coefficient Matrix ◽  
Biological Data ◽  
Survey Results ◽  
Matrix Formula ◽  
Semi Empirical

This study processed the recent in vivo survey results for over a thousand patients and optimized their neck and head CT angiography triggered timing (CTA-TT) via the inverse problem algorithm, which ensured the maximal ratio of both left and right arterial to upper sinuses (LRA/US). These results are instrumental in examining the ischemic stroke syndromes along the neck and head. These 1001 patients were randomly categorized into test surveyed (802 patients) and verification group (199 patients), then a six factors semi-empirical formula was constructed by the STATISTICA program. The six factors were assigned a patient’s biological data and preset of the CTA facility; namely Age, mean arterial pressure (MAP), heart rate (HR), contrast media dose (CMD), Pre (injected pressure of CMD), and body surface area (BSA). Each factor was normalized into dimensionless values and incorporated into the dataset matrix [Formula: see text] to analyze the coefficient matrix [Formula: see text]. The derived semi-empirical formula closely correlated with experimental data, according to the loss function [Formula: see text], correlation coefficient [Formula: see text], and variance of 0.8965. The formula verification for 199 more patients (verification group) yielded a correlation coefficient [Formula: see text]. Thus, it can be used for the CTA-TT estimation of patients without their preliminary tests, avoiding unnecessary irradiation. The estimated LRA/US was [Formula: see text] for the verification group in this study. A simplified three-factor formula, featuring only age, MAP, and BSA, was also proposed.

scholarly journals An optimal approach to the inverse problem

1988 ◽  
Vol 123 ◽  
pp. 129-132
Author(s):  
W. Jeffrey ◽  
R. Rosner
Keyword(s):  
Remote Sensing ◽  
Inverse Problem ◽  
Optimization Problem ◽  
Solution Process ◽  
Optimization Theory ◽  
Global Optimization Problem ◽  
Inversion Problem ◽  
Global Extremum ◽  
Local Extrema ◽  
Optimal Approach

We describe how remote sensing problems can be reformulated within the framework of optimization theory. This reformulation allows any prior knowledge about the solution to be naturally incorporated into the solution process. The inversion problem then reduces to a search for the global extremum in the possible presence of local extrema. Two algorithms are presented that can be used to solve this global optimization problem, and their application to the helioseismology inverse problem is detailed.

scholarly journals A Simultaneous Inversion Problem for the Variable-Order Time Fractional Differential Equation with Variable Coefficient

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shengnan Wang ◽  
Zhendong Wang ◽  
Gongsheng Li ◽  
Yingmei Wang
Keyword(s):  
Inverse Problem ◽  
Noisy Data ◽  
Fractional Diffusion ◽  
Basis Functions ◽  
Variable Order ◽  
Inversion Problem ◽  
Inversion Algorithm ◽  
Regularization Algorithm ◽  
Simultaneous Inversion ◽  
Fractional Differential

This paper deals with an inverse problem of simultaneously determining the space-dependent diffusion coefficient and the fractional order in the variable-order time fractional diffusion equation by the measurements at one interior point. Numerical solution to the forward problem is given by the finite difference scheme, and the homotopy regularization algorithm is applied to solve the inverse problem utilizing Legendre polynomials as the basis functions of the approximate space. The inversion solutions with noisy data which give good approximations to the exact solution demonstrate effectiveness of the inversion algorithm for the simultaneous inversion problem.

A New Class of Biased Estimate

2013 ◽  
Vol 416-417 ◽  
pp. 1296-1304
Author(s):  
Chao Zhong Ma ◽  
Yuan Lu Du ◽  
Qing Ming Gui ◽  
Yong Wei Gu ◽  
Ji Fu
Keyword(s):  
Adverse Effects ◽  
Principal Component ◽  
Unbiased Estimation ◽  
Design Matrix ◽  
Leverage Points ◽  
Ridge Estimation ◽  
New Class ◽  
Component Estimation ◽  
M Estimation ◽  
Better Than

In this paper, the GM estimation is integrated with ridge estimation, principal component estimation and LIU estimation, resulting in a new class of robust unbiased estimation, and given the appropriate method of calculating. The example shows that such a new biased estimate is not only resistant to the interference of design matrix multicollinearity, but also withstands the adverse effects of outliers and high leverage points. They are really better than the LS estimation, unbiased estimation, robust M estimation and robust M-type biased estimation.

Linear aspects of tomographic velocity analysis

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 483-495 ◽  
Author(s):  
C. Stork ◽  
R. W. Clayton
Keyword(s):  
Inverse Problem ◽  
Velocity Field ◽  
A Priori ◽  
Complex Structure ◽  
Velocity Analysis ◽  
Inversion Problem ◽  
Reflection Seismology ◽  
Conceptual Tool ◽  
Wide Range ◽  
Ray Trace

Prestack velocity analysis in areas of complex structure is a coupled migration and transmission inversion problem that can be analyzed from a tomographic perspective. By making as few a priori assumptions about the solution as possible in parameterizing the inverse problem, generalized tomographic velocity analysis is applicable to a wide range of geologic cases. Constraints modify the method to the unique characteristics of each application. The ray trace/traveltime formulation for tomography, as proposed by Bishop et al. (1985), provides a conceptual tool for presenting features that are important to automated prestack velocity analysis in complex structure, such as (1) the coupling of the velocity field to the reflector positions, (2) the nonuniform coverage of the model by the data, (3) the ability to perform a controlled inversion of large matrices over a wide eigenvalue range, and (4) the implementation of constraints in the inversion. These features may impact other automated prestack velocity analysis methods for reflection seismology.

The Influence of Specimen Thickness in Quantitative Electron Energy Loss Spectroscopy

1980 ◽  
Vol 38 ◽  
pp. 112-113
Author(s):  
Nestor J. Zaluzec
Keyword(s):  
Quantitative Analysis ◽  
Adverse Effects ◽  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Light Element ◽  
Specimen Thickness ◽  
Element Analysis ◽  
Electron Energy Loss

The application of electron energy loss spectroscopy (EELS) to light element analysis is rapidly becoming an important aspect of the microcharacterization of solids in materials science, however relatively stringent requirements exist on the specimen thickness under which one can obtain EELS data due to the adverse effects of multiple inelastic scattering.1,2 This study was initiated to determine the limitations on quantitative analysis of EELS data due to specimen thickness.

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