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Aiming at the difficulty of analyzing the meshing contact characteristics of gear transmission system under the big data formed by multiple working conditions and uncertain parameters, a meshing contact characteristics analysis method of gear transmission system based on data mining technology is proposed. Based on the principle of multi-dimensional Gaussian distribution and the finite element model of gear transmission system, the meshing contact characteristic data set of the system is constructed. The correlation between system parameters and meshing contact characteristics is analyzed using the maximum information coefficient, which provides a candidate feature subset for the prediction model. Then, the prediction model of meshing contact characteristics of the system is established using support vector machine and random forest algorithm, which realizes the efficient prediction of meshing contact characteristics of the system. The results show that the prediction error of the prediction model based on support vector machine is the smallest, and the average absolute percentage error is 3.87%, which is far less than the theoretical calculation error. Under the optimal feature subset, the prediction error index of contact characteristics of the prediction model based on support vector machine decreases significantly, and its average absolute percentage error reaches 3.03%, which is 21.71% lower than the prediction error of contact characteristics before optimization. These have verified the accuracy and effectiveness of the proposed method.

Compositional data are known as a sort of complex multidimensional data with the feature that reflect the relative information rather than absolute information. There are a variety of models for regression analysis with compositional variables. Similar to the traditional regression analysis, the heteroskedasticity still exists in these models. However, the existing heteroskedastic regression analysis methods cannot apply in these models with compositional error term. In this paper, we mainly study the heteroskedastic linear regression model with compositional response and covariates. The parameter estimator is obtained through weighted least squares method. For the hypothesis test of parameter, the test statistic is based on the original least squares estimator and corresponding heteroskedasticity-consistent covariance matrix estimator. When the proposed method is applied to both simulation and real example, we use the original least squares method as a comparison during the whole process. The results implicate the model's practicality and effectiveness in regression analysis with heteroskedasticity. [ABSTRACT FROM AUTHOR]

The standard regression model designed for real space is not suitable for compositional variables; it should be considered, whether the response and/or covariates are of compositional nature. There are usually three types of multiple regression model with compositional variables: Type 1 refers to the case where all the covariates are compositional data and the response is real; Type 2 is the opposite of Type 1; Type 3 relates to the model with compositional response and covariates. There have been some models for the three types. In this paper, we focus on Type 3 and propose multiple linear regression models including model in the simplex and model in isometric log-ratio (ilr) coordinates. The model in the simplex is based on matrix product, which can project a-part composition to another-part composition, and can deal with different number of parts of compositional variables. Some theorems are given to point out the relationship of parameters between the proposed models. Moreover, the inference for parameters in proposed models is also given. Real example is studied to verify the validity and usefulness of proposed models. [ABSTRACT FROM AUTHOR]

We study the exact controllability of q uncoupled damped string equations by means of the same control function. This property is called simultaneous controllability. An observability inequality is proved, which implies the simultaneous controllability of the system. Our results generalize the previous results on the linear wave without the dampings. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]