Abstract
The multivariate statistical method such as principal component analysis based on linear dimension reduction and kernel principal component analysis based on nonlinear dimension reduction as the modified principal component analysis method are commonly used. Because of the diversity and correlation of robotic global performance indexes, the two multivariate statistical methods principal component analysis and kernel principal component analysis methods can be used, respectively, to comprehensively evaluate the global performance of PUMA560 robot with different dimensions. When using the kernel principal component analysis method, the kernel function and parameters directly have an effect on the result of comprehensive performance evaluation. Because kernel principal component analysis with polynomial kernel function is time-consuming and inefficient, a new kernel function based on similarity degree is proposed for the big sample data. The new kernel function is proved according to Mercer’s theorem. By comparing different dimension reduction effects of principal component analysis method, the kernel principal component analysis method with polynomial kernel function, and the kernel principal component analysis method with the new kernel function, the kernel principal component analysis method with the new kernel function could deal more effectively with the nonlinear relationship among indexes, and its calculation result is more reasonable for containing more comprehensive information. The simulation shows that the kernel principal component analysis method with the new kernel function has the advantage of low time consuming, good real-time performance, and good ability of generalization.
Highlights
With the development of robot to high-speed and highprecision direction, evaluation of robotic performance properly becomes an important topic in the field of robotic research
When using the kernel principal component analysis (KPCA) method, the kernel function and parameters directly have an effect on the result of comprehensive performance evaluation
As the KPCA method calculation with polynomial kernel function is time-consuming and less efficient, a new kernel function based on similarity degree is proposed for the big sample data in the article
Summary
With the development of robot to high-speed and highprecision direction, evaluation of robotic performance properly becomes an important topic in the field of robotic research. The global performance of PUMA560 robot with different dimensions has been comprehensive evaluated by using the KPCA method, and polynomial kernel function has been used in KPCA calculation after comparison.[10] As the KPCA method calculation with polynomial kernel function is time-consuming and less efficient, a new kernel function based on similarity degree is proposed for the big sample data in the article. The comparison between the dimension reductions of the three methods mentioned above indicates that indexes’ nonlinear relationship can be solved effectively by KPCA with the new kernel function, which can provide more information according to the first principal component so that the solution is reasonable. The main steps[9] of PCA are as follows: 1. Standardize the primitive data to eliminate the adverse effects caused by different dimensions
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