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The Validity Analysis of Regression: Combining Uniform Experiment Design with Nonlinear Regression

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DOI: 10.4236/am.2015.66092    2,762 Downloads   3,012 Views  


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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.


[1] Li, Y.W., Su, L., Zhang, X.Y., Huang, X.Y. and Zhai, H.L. (2011) Prediction of Association Constants of Cesium Chelates Based on Uniform Design Optimized Support Vector Machine. Chemometrics and Intelligent Laboratory Systems, 105, 106-113.
[2] Li, W.H., Liu, L.J. and Gong, W.G. (2011) Multi-Objective Uniform Design as a SVM Model Selection Tool for Face Recognition. Expert Systems with Applications, 38, 6689-6695.
[3] Yu, X.L., Zheng, H.B., Yan, Q.S. and Li, W. (2011) A Least Square Support Vector Machine Approach Based on Uniform Design Method for Structural Reliability Analysis. Advanced Materials Research, 163-167, 3348-3353.
[4] Zhang, G.Y. and Ge, H.H. (2012) Prediction of Xylanase Optimal Temperature by Support Vector Regression. Electronic Journal of Biotechnology, 15.
[5] Ni, L.J., Zhang, L.G., Tang, M.Y., Xue, Z.B., Zhang, X., Gu, X. and Huang, S.X. (2012) Discrimination of Adulteration Cow Milk by Improved v-Support Vector Machines and near Infrared Spectroscopy. 2012 8th International Conference on Natural Computation, Chongqing, 29-31 May 2012, 69-73.
[6] Yu, X.L. and Yan, Q.S. (2011) Reliability Analysis of Self-Anchored Suspension Bridge by Improved Response Surface Method. Applied Mechanics and Materials, 90-93, 869-873.
[7] Xiang, C.S., Yuan, Z.M. and Zhou, Z.Y. (2011) Parameters Joint Optimization of Chaotic Time Series Prediction Model. Information and Control, 40, 673-679.
[8] Wang, Z.M., Tan, X.S., Yuan, Z.M. and Wu, Z.H. (2010) Parameters Optimization of SVM Based on Self-Calling SVR. Journal of System Simulation, 22, 376-378.
[9] Chuang, S.C. and Hung, Y.C. (2010) Uniform Design over General Input Domains with Applications to Target Region Estimation in Computer Experiments. Computational Statistics & Data Analysis, 54, 219-232.
[10] Pan, J.-S., Hong, M.-Z., Zhou, Q.-F., Cai, J.-Y., Wang, H.-Z., Luo, L.-K., Yang, D.-Q., Dong, J., Shi, H.-X. and Ren, J.-L. (2009) Integrated Application of Uniform Design and Least-Squares Support Vector Machines to Transfection Optimization. BMC Biotechnology, 9, 52.
[11] Wang, X., Zhang, C., Li, P., Wang, K., Hu, Y., Zhang, P. and Liu, H.X. (2012) Modeling and Optimization of Joint Quality for Laser Transmission Joint of Thermoplastic Using an Artificial Neural Network and a Genetic Algorithm. Optics and Lasers in Engineering, 50, 1522-1532.
[12] Sun, Y.W. and Hao, M.Z. (2012) Statistical Analysis and Optimization of Process Parameters in Ti6Al4V Laser Cladding Using Nd:YAG Laser. Optics and Lasers in Engineering, 50, 985-995.
[13] Yang, D.X., Li, X.Y., He, D.Y., Nie, Z.R. and Huang, H. (2012) Optimization of Weld Bead Geometry in Laser Welding with Filler Wire Process Using Taguchi’s Approach. Optics & Laser Technology, 44, 2020-2025.
[14] Beygi, H., Vafaeenezhad, H. and Sajjadi, S.A. (2012) Modeling the Electroless Nickel Deposition on Aluminum Nanoparticles. Applied Surface Science, 258, 7744-7750.
[15] Wang, Z.F. and Wang, H. (2012) Inflatable Wing Design Parameter Optimization Using Orthogonal Testing and Support Vector Machines. Chinese Journal of Aeronautics, 25, 887-895.
[16] Wang, Y. and Fang, K.T. (1981) About Uniform Distribution and Experimental Design: Number Theory Method. Chinese Science Bulletin, 2, 65-70.

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