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>

Parameter Estimation of an Electrohydraulic Servo System Using a Markov Chain Monte Carlo Method

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Junhong Liu ◽  
Huapeng Wu ◽  
Heikki Handroos ◽  
Heikki Haario
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Measurement Data ◽  
Estimation Method ◽  
Operating Conditions ◽  
Point Estimate ◽  
Best Fitting ◽  
The One

A parameter estimation method is presented by an example of an electrohydraulic position servo. The method is based on the Markov chain Monte Carlo approach. The method allows utilization of noisy measurement data in identification process, making use of original physical data possible without the requirement of a filter. The method seeks for the best fitting point estimate of the unknown model parameter vector, but the solution to the parameter estimation problem is given as a statistical distribution that contains “all” the possible parameter combinations. The robustness of the model developed with the proposed method is further demonstrated by verification in operating conditions that are independent of each other and the one used in the identification step. Results show that the system model with the hybrid leakage formula for the studied valve describes the system dynamics more precisely and matches the real responses better.

Application of the Weighted Least Squares Parameter Estimation Method to the Robot Calibration

1994 ◽  
Vol 116 (3) ◽  
pp. 890-893 ◽  
Author(s):  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
I. Saban
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Kinematic Model ◽  
Measurement Data ◽  
Estimation Method ◽  
Kinematic Parameter ◽  
Measuring System ◽  
Parameter Estimates ◽  
Robot Calibration

Significant attention has been paid recently to the topic of robot calibration. To improve the robot’s accuracy, various approaches to the measurement of the robot’s position and orientation (pose) and correction of its kinematic model have been proposed. Little attention, however, has been given to the method of estimation of the kinematic parameters from the measurement data. Typically, a least-squares solution method is used to estimate the corrections to the parameters of the model. In this paper, a method of kinematic parameter estimation is proposed where a standard least-squares estimation procedure is replaced by weighted least-squares. The weighting factors are calculated based on all the a priori available statistical information about the robot and the pose-measuring system. By giving greater weight to the measurements made where the standard deviation of the noise in the data is expected to be lower, a significant reduction in the error of the kinematic parameter estimates is made possible. The improvement in the calibration results was verified using a calibration simulation algorithm.

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

scholarly journals A Parameter-Estimation Method Using the Ensemble Kalman Filter for Flow and Thermal Simulation in an Engine Compartment

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Kazuya Kusano ◽  
Hironobu Yamakawa ◽  
Kenich Hano
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Measurement Data ◽  
Estimation Method ◽  
Observation Error ◽  
Model Errors ◽  
Engine Compartment ◽  
Actual Measurement ◽  
Parameter Estimation Method

The feasibility of the parameter estimation on the basis of the ensemble Kalman filter (EnKF) for a practical simulation involving model errors was investigated. The three-dimensional flow and thermal simulations for the engine compartment of a test excavator were simulated, and several unknown temperatures used for boundary conditions were estimated with the method. The estimation method was validated in two steps. First, the estimation method was tested with the influence of the model errors removed by virtually creating true values with a simulation. These results showed that the proposed parameter-estimation method can successfully estimate surface temperatures. They also suggested that the appropriate ensemble size can be evaluated from the number of unknown parameters. Second, the estimation method was tested under a practical condition including model errors by using actual measurement data. Model errors were statistically estimated using prior obtained error data concerning other design configurations, and they were added to the observation error in the EnKF. These results showed that taking model errors into account in the EnKF provides more-accurate parameter-estimation results. Moreover, the uncertainty of an estimated parameter can be evaluated with the standard deviation of its distribution.

scholarly journals Solution of the Ill-Posed Semiparametric Regression Model Based on Singular Value Modification Restriction

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yan Zhou ◽  
Fengxiang Jin ◽  
Depeng Ma
Keyword(s):  
Parameter Estimation ◽  
Regression Model ◽  
Semiparametric Regression ◽  
Singular Values ◽  
Coefficient Matrix ◽  
Singular Value ◽  
Normal Matrix ◽  
Semiparametric Regression Model ◽  
Model Based ◽  
Ill Posed

We propose a solution of the ill-posed semi-parametric regression model based on singular value modification restriction, aimed at the ill-posed problem of the normal matrix which may occur in the process of solving the semiparametric regression model. First, the coefficient matrix is decomposed into singular values, and the smaller singular values are selected according to the criterion ∑i=1r1/σi/∑i=1n1/σi≤5% (in the singular value matrix, σ1>σ1>⋯>σr>⋯σn). Second, the relatively smaller singular values are modified by the biased parameter to suppress the magnification of the estimated variance so as to effectively reduce the variance of parameter estimation, reduce the introduction of deviation and obtain more reliable parameter estimation. The results of the numerical experiments show that the improved singular value modification restriction method can not only overcome the effect of the ill-posed normal matrix on the parameter estimation solution but also correctly separate the systematic errors and improve the accuracy of semiparametric regression model calculation results.

scholarly journals A Bayesian estimation method for variational phase-field fracture problems

2020 ◽  
Vol 66 (4) ◽  
pp. 827-849 ◽  
Author(s):  
Amirreza Khodadadian ◽  
Nima Noii ◽  
Maryam Parvizi ◽  
Mostafa Abbaszadeh ◽  
Thomas Wick ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Phase Field ◽  
Measurement Data ◽  
Estimation Method ◽  
Reference Value ◽  
Solid Material ◽  
Critical Energy ◽  
Field Method ◽  
Phase Field Method ◽  
Critical Energy Release Rate

Abstract In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.

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.

scholarly journals Validity and Reliability of Hydraulic-Analogy Bioenergetic Models in Sprint Roller Skiing

2021 ◽  
Vol 12 ◽  
Author(s):  
Julius Lidar ◽  
Erik P. Andersson ◽  
David Sundström
Keyword(s):  
Parameter Estimation ◽  
Metabolic Rate ◽  
Measurement Data ◽  
Time Trial ◽  
Model Parameters ◽  
Validity And Reliability ◽  
Bioenergetic Model ◽  
Mean Differences ◽  
Hydraulic Analogy ◽  
Aerobic And Anaerobic

Purpose: To develop a method for individual parameter estimation of four hydraulic-analogy bioenergetic models and to assess the validity and reliability of these models’ prediction of aerobic and anaerobic metabolic utilization during sprint roller-skiing.Methods: Eleven elite cross-country skiers performed two treadmill roller-skiing time trials on a course consisting of three flat sections interspersed by two uphill sections. Aerobic and anaerobic metabolic rate contributions, external power output, and gross efficiency were determined. Two versions each (fixed or free maximal aerobic metabolic rate) of a two-tank hydraulic-analogy bioenergetic model (2TM-fixed and 2TM-free) and a more complex three-tank model (3TM-fixed and 3TM-free) were programmed into MATLAB. The aerobic metabolic rate (MRae) and the accumulated anaerobic energy expenditure (Ean,acc) from the first time trial (STT1) together with a gray-box model in MATLAB, were used to estimate the bioenergetic model parameters. Validity was assessed by simulation of each bioenergetic model using the estimated parameters from STT1 and the total metabolic rate (MRtot) in the second time trial (STT2).Results: The validity and reliability of the parameter estimation method based on STT1 revealed valid and reliable overall results for all the four models vs. measurement data with the 2TM-free model being the most valid. Mean differences in model-vs.-measured MRae ranged between -0.005 and 0.016 kW with typical errors between 0.002 and 0.009 kW. Mean differences in Ean,acc at STT termination ranged between −4.3 and 0.5 kJ and typical errors were between 0.6 and 2.1 kJ. The root mean square error (RMSE) for 2TM-free on the instantaneous STT1 data was 0.05 kW for MRae and 0.61 kJ for Ean,acc, which was lower than the other three models (all P < 0.05). Compared to the results in STT1, the validity and reliability of each individually adapted bioenergetic model was worse during STT2 with models underpredicting MRae and overpredicting Ean,acc vs. measurement data (all P < 0.05). Moreover, the 2TM-free had the lowest RMSEs during STT2.Conclusion: The 2TM-free provided the highest validity and reliability in MRae and Ean,acc for both the parameter estimation in STT1 and the model validity and reliability evaluation in the succeeding STT2.

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