Sediment-laden flow measurement with Particle Tracking Velocimetry （PTV） introduces a series of finite-sized sampling bins along the vertical of the flow. Instantaneous velocities are collected at each bin and a sig...Sediment-laden flow measurement with Particle Tracking Velocimetry （PTV） introduces a series of finite-sized sampling bins along the vertical of the flow. Instantaneous velocities are collected at each bin and a significantly large sample is established to evaluate mean and root mean square （rms） velocities of the flow. Due to the presence of concentration gradient, the established sample for the solid phase involves more data from the lower part of the sampling bin than from the upper part. The concentration effect causes bias errors in the measured mean and rms velocities when velocity varies across the bin. These bias errors are analyti- cally quantified in this study based on simplified linear velocity and concentration distributions. Typical bulk flow characteristics from sediment-laden flow measurements are used to demonstrate rough estimation of the error magnitude. Results indicate that the mean velocity is underestimated while the rms velocity is overestimated in the ensemble-averaged measurement. The extent of devia- tion is commensurate with the bin size and the rate of concentration gradient. Procedures are proposed to assist determining an appro- priate sampling bin size in certain error limits.展开更多
There are many possible bias errors in the measurement of structural intensity and some of them have been theoretically examined. Attempting to analyse all the bias errors at the same time results in a very complicate...There are many possible bias errors in the measurement of structural intensity and some of them have been theoretically examined. Attempting to analyse all the bias errors at the same time results in a very complicated analysis and makes it difficult to draw clear conclusions.The bias errors are usually analysed individually. In this paper a theoretical study of three bias errors in the measurement of structural intensity is presented by using the twor-accelerometer array technique. It is assumed that the physical and material properties of the test structure are known. The analysis will be restricted to one-dimensional beams, but it can be extended to two-dimensional plates.展开更多
The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed e...The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Esti...In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.50779023)
文摘Sediment-laden flow measurement with Particle Tracking Velocimetry （PTV） introduces a series of finite-sized sampling bins along the vertical of the flow. Instantaneous velocities are collected at each bin and a significantly large sample is established to evaluate mean and root mean square （rms） velocities of the flow. Due to the presence of concentration gradient, the established sample for the solid phase involves more data from the lower part of the sampling bin than from the upper part. The concentration effect causes bias errors in the measured mean and rms velocities when velocity varies across the bin. These bias errors are analyti- cally quantified in this study based on simplified linear velocity and concentration distributions. Typical bulk flow characteristics from sediment-laden flow measurements are used to demonstrate rough estimation of the error magnitude. Results indicate that the mean velocity is underestimated while the rms velocity is overestimated in the ensemble-averaged measurement. The extent of devia- tion is commensurate with the bin size and the rate of concentration gradient. Procedures are proposed to assist determining an appro- priate sampling bin size in certain error limits.
文摘There are many possible bias errors in the measurement of structural intensity and some of them have been theoretically examined. Attempting to analyse all the bias errors at the same time results in a very complicated analysis and makes it difficult to draw clear conclusions.The bias errors are usually analysed individually. In this paper a theoretical study of three bias errors in the measurement of structural intensity is presented by using the twor-accelerometer array technique. It is assumed that the physical and material properties of the test structure are known. The analysis will be restricted to one-dimensional beams, but it can be extended to two-dimensional plates.
文摘The paper introduces a new biased estimator namely Generalized Optimal Estimator (GOE) in a multiple linear regression when there exists multicollinearity among predictor variables. Stochastic properties of proposed estimator were derived, and the proposed estimator was compared with other existing biased estimators based on sample information in the the Scalar Mean Square Error (SMSE) criterion by using a Monte Carlo simulation study and two numerical illustrations.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
文摘In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.
