Study on the Curvature Reducing Method of Non-linear Regression Model

Jin-Mei Wu,Ya-Wei Hou,Yi Wang,Yu-Xin Zhang,Xiao-Dong Ling,J.C.M Kao,W.-P Sung

doi:10.1051/matecconf/20166305033

Abstract

The method to reduce the non-linear strength (curvature)of non-linear regression model was studied in this paper. Firstly, the reference point of the non-linear strength was analyzed. Based on the definition of curvature cubic matrix, a computing method of curvature cubic matrix was proposed based on the Cholesky disassembling. Then the common ways to reduce the non-linear strength was also discussed. Pointed at some common non-linear models in real engineering applications, such as non-linear models used for multiple-measurement and mutual-calibration of different instruments, or non-linear models prior information, a new least square method with weight was given, which can evidently reduce the curvature of these multi-structure non-linear regression models, therefore evidently reduce the non-linear strength. Finally, the Numerical simulation results were given to validate the effectiveness and feasibility of this weighted least square method. The method to reduce the non-linear strength (curvature) of non-linear regression model was studied in this paper. Firstly, the reference point of the non-linear strength was analyzed. Based on the definition of curvature cubic matrix, a computing method of curvature cubic matrix was proposed based on the Cholesky disassembling. Then the common ways to reduce the non-linear strength was also discussed. Pointed at some common non-linear models in real engineering applications, such as non-linear models used for multiple-measurement and mutual-calibration of different instruments, or non-linear models with prior informations, a new least square method with weight was given, which can evidently reduce the curvature of these multi-structure non-linear regression models, therefore evidently reduce the non-linear strength. Finally, the Numerical simulation results ware given to validated the effectiveness and feasibility of this weighted least square method.

Highlights

Because of the complexity of non-linear function, currently the parameter estimate of non-linear regression mainly solved by linear approximating
Disassembling of V .Curvature cubic matrix is the standard of non-linear strength
Document [3] pointed out that inherent curvature is the inherent characteristic of the model

Summary

Introduction

Because of the complexity of non-linear function, currently the parameter estimate of non-linear regression mainly solved by linear approximating. We are investigating how to reduce curvature of non-linear model. The definition is as follows: The inherent curvature and parameter effect curvature cubic matrixes of non-linear model Y f X , E H are. That is QR disassembling of V .Curvature cubic matrix is the standard of non-linear strength. An important direction is reducing the non-linear strength of the model or reducing the curvature. Document [3] pointed out that inherent curvature is the inherent characteristic of the model It will remain unchanged if parameter varies. Document [4] put forward the method of increasing sampling and proofed that if provided enough sampling data, the non-linear model can approach the linear model adequately. Be aimed at non-linear multi-structure, least square estimation with weight can reduce curvature and raise precision.

Set up

Conclusion