Author(s)

Nan Yang^1,2*, Dawei Zhang¹, Yanling Tian¹

¹School of Mechanical Engineering, Tianjin University, Tianjin, China.
²Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, China.

The data topology structure of uniform experiment design (UD) is too complex to be reasonable regressed. In this paper, the principle and method of distinguish the training data and testing data were described to make a reasonable regression when uniform experiment design combined with support vector regression (SVR). Two equivalent ways which were the smallest enclosing hypersphere perceptron (SEH) and the enclosing simplex perceptron (ES) were provided to discover the topology relationship of the process parameter datum. To give an application, a series of experiments about laser cladding layer quality were conducted by UD to get the relationship of load, velocity and wearing capacity. Results showed that only the testing datum recommended by the two perceptrons got a good forecasting by SVR. Therefore, the two perceptrons could guide experiments with process parameter data of complex topology structure. Further, the application could be extended over a much wider field of experiments.

the enclosing simplex, support vector machine, uniform experiment design, the smallest enclosing hyper sphere

Yang, N. , Zhang, D. and Tian, Y. (2015) The Validity Analysis of Regression: Combining Uniform Experiment Design with Nonlinear Regression. Applied Mathematics, 6, 996-1008. doi: 10.4236/am.2015.66092.