A Study On Robust Optimization And Diagnostic Analysis Of Multidimensional System Based On MTS

Mahalanobis-Taguchi System (MTS) method effectively integrates feature subset selection with diagnostic analysis for multidimensional system. MTS method shares many advantages of other multivariate methods, but it still needs to be studied in order to be more effectively applied to robust optimization and diagnostic analysis for multidimensional system.For the diagnosis or prediction analysis of multidimensional system, traditional Mahalanobis distance function ignores the relative importance of every variable, which leads the accuracy to decrease significantly. Thus, it needs to be combined with subjective weight assignment method to measure the degree of abnormality of multidimensional observations. In the stage of construction and optimization of the measurement scale, traditional Mahalanobis distance function with the same weights for every variable is adopted. For the optimized measurement scale, different weights should be assigned to the variables according to their relative importance, i.e. weighted Mahalanobis distance function should be used to measure the degree of abnormality in order to improve the accuracy of diagnosis or prediction of multidimensional system.For abnormal observations diagnosed by the optimized measurement scale, it is important to analyze their potential causes and identify their directions of abnormality. Based on the difference between weighted Mahalanobis distance function and traditional Mahalanobis distance function, Mason-Young-Tracy (MYT) orthogonal decomposition method of weighted Mahalanobis distance is put forward, and applied to potential causes analysis of multidimensional abnormal points. Meanwhile, based on the MYT orthogonal decomposition, a new method identifying the direction of abnormality of multidimensional abnormal observations is brought forward. This method is robust and appropriate to inverse matrix method, adjoint matrix method and Gram-Schmidt method of MTS.For both Gram-Schmidt method and adjoint matrix method of MTS, multicollinearity is solved by improving Mahalanobis distance function. M-P generalized inverse matrix method of MTS which effectively solves multicollinearity in the stage of optimization analysis of multidimensional system is put forward based on the strong competence of generalized inverse matrix for dealing with strong correlation problem and M-P generalized inverse matrix's only existence. At the same time, function of degree of disagreement (FDOD) measurement is used to measure the degree of abnormality of multidimensional observations, and combines with Taguchi method to optimize the multidimensional system, which minimizes the effect of multicollinearity on multivariate optimization.Finally, a hospital viscosity of plasma diagnostic system is optimized by adjoint matrix method and M-P generalized inverse matrix method of MTS. The results show that adjoint matrix method can't select effective variables and M-P generalized inverse matrix method is robust. In the optimized viscosity of plasma diagnostic system, multidimensional observations are diagnosed and controlled effectively by weighted Mahalanobis distance. The potential causes of multidimensional abnormal points are analyzed and the direction of abnormality is correctly determined using MYT orthogonal decomposition method of weighted Mahalanobis distance.