Comparative Study of Response Surface Designs with Errors-in-Variables Model

This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares(ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

消除复共线性影响的一种新的解决办法

基于响应变量和解释变量的数据中都含有观测误差这一新的认识，将设计矩阵中有复共线性的多元线性回归模型修正为一种多元线性Ｅｒｒｏｒｓ－ｉｎ－ｖａｒｉａｂｌｅｓ模型，从而尽量消除复共线性的影响，得到较好的回归系数估计。文中给出了两个模拟例子，表明了用此修正模型所得的估计结果非常接近参数真值。从而说明提出的方法是一种很有效的消除复共线性影响的方法。

Robust estimation algorithm for multiple-structural data

This paper proposes a robust method of parameter estimation and data classification for multiple-structural data based on the linear error in variable（EIV） model.The traditional EIV model fitting problem is analyzed and a robust growing algorithm is developed to extract the underlying linear structure of the observed data.Under the structural density assumption,the C-step technique borrowed from the Rousseeuw＇s robust MCD estimator is used to keep the algorithm robust and the mean-shift algorithm is adopted to ensure a good initialization.To eliminate the model ambiguities of the multiple-structural data,statistical hypotheses tests are used to refine the data classification and improve the accuracy of the model parameter estimation.Experiments show that the efficiency and robustness of the proposed algorithm.

Multi-class Classification Methods of Enhanced LS-TWSVM for Strip Steel Surface Defects

Considering strip steel surface defect samples, a multi-class classification method was proposed based on enhanced least squares twin support vector machines （ELS-TWSVMs） and binary tree. Firstly, pruning region samples center method with adjustable pruning scale was used to prune data samples. This method could reduce classifierr s training time and testing time. Secondly, ELS-TWSVM was proposed to classify the data samples. By introducing error variable contribution parameter and weight parameter, ELS-TWSVM could restrain the impact of noise sam- ples and have better classification accuracy. Finally, multi-class classification algorithms of ELS-TWSVM were pro- posed by combining ELS-TWSVM and complete binary tree. Some experiments were made on two-dimensional data- sets and strip steel surface defect datasets. The experiments showed that the multi-class classification methods of ELS-TWSVM had higher classification speed and accuracy for the datasets with large-scale, unbalanced and noise samples.