Based on the model structure of the influence coefficient method analyzed in depth by matrix theory ,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS in...Based on the model structure of the influence coefficient method analyzed in depth by matrix theory ,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing. It also presencd the new ridge regression method for solving correction masses according to the Tikhonov regularization theory, and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.展开更多
This work is geared towards detecting and solving the problem of multicolinearity in regression analysis. As such, Variance Inflation Factor (VIF) and the Condition Index (CI) were used as measures of such detection. ...This work is geared towards detecting and solving the problem of multicolinearity in regression analysis. As such, Variance Inflation Factor (VIF) and the Condition Index (CI) were used as measures of such detection. Ridge Regression (RR) and the Principal Component Regression (PCR) were the two other approaches used in modeling apart from the conventional simple linear regression. For the purpose of comparing the two methods, simulated data were used. Our task is to ascertain the effectiveness of each of the methods based on their respective mean square errors. From the result, we found that Ridge Regression (RR) method is better than principal component regression when multicollinearity exists among the predictors.展开更多
Longitudinal trends of observations can be estimated using the generalized multivariate analysis of variance (GMANOVA) model proposed by [10]. In the present paper, we consider estimating the trends nonparametrically ...Longitudinal trends of observations can be estimated using the generalized multivariate analysis of variance (GMANOVA) model proposed by [10]. In the present paper, we consider estimating the trends nonparametrically using known basis functions. Then, as in nonparametric regression, an overfitting problem occurs. [13] showed that the GMANOVA model is equivalent to the varying coefficient model with non-longitudinal covariates. Hence, as in the case of the ordinary linear regression model, when the number of covariates becomes large, the estimator of the varying coefficient becomes unstable. In the present paper, we avoid the overfitting problem and the instability problem by applying the concept behind penalized smoothing spline regression and multivariate generalized ridge regression. In addition, we propose two criteria to optimize hyper parameters, namely, a smoothing parameter and ridge parameters. Finally, we compare the ordinary least square estimator and the new estimator.展开更多
文摘Based on the model structure of the influence coefficient method analyzed in depth by matrix theory ,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing. It also presencd the new ridge regression method for solving correction masses according to the Tikhonov regularization theory, and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.
文摘This work is geared towards detecting and solving the problem of multicolinearity in regression analysis. As such, Variance Inflation Factor (VIF) and the Condition Index (CI) were used as measures of such detection. Ridge Regression (RR) and the Principal Component Regression (PCR) were the two other approaches used in modeling apart from the conventional simple linear regression. For the purpose of comparing the two methods, simulated data were used. Our task is to ascertain the effectiveness of each of the methods based on their respective mean square errors. From the result, we found that Ridge Regression (RR) method is better than principal component regression when multicollinearity exists among the predictors.
文摘Longitudinal trends of observations can be estimated using the generalized multivariate analysis of variance (GMANOVA) model proposed by [10]. In the present paper, we consider estimating the trends nonparametrically using known basis functions. Then, as in nonparametric regression, an overfitting problem occurs. [13] showed that the GMANOVA model is equivalent to the varying coefficient model with non-longitudinal covariates. Hence, as in the case of the ordinary linear regression model, when the number of covariates becomes large, the estimator of the varying coefficient becomes unstable. In the present paper, we avoid the overfitting problem and the instability problem by applying the concept behind penalized smoothing spline regression and multivariate generalized ridge regression. In addition, we propose two criteria to optimize hyper parameters, namely, a smoothing parameter and ridge parameters. Finally, we compare the ordinary least square estimator and the new estimator.
基金Supported by Natural Science Foundation of China(404740040074006) and NationalScience Fund of China for Distinguished Young Scholars of China(40125013).
