变形分析与预测模型中病态问题分析

本文对变形分析与预测模型中的线性回归分析法、时间序列分析模型、灰色系统分析模型中的病态问题进行了理论分析和数值模拟。通过对变形观测资料施加干扰噪声,采用最小二乘原理,得出了三种模型中每一个参数与干扰噪声的数值关系表达式。指出在变形解释和变形预测中,用这三种模型进行建模分析时必须先检查信息矩阵A=XTX的病态程度,采取有效方法减轻A=XTX的病态程度后方可使用这三种模型。

The analysis of ill-posed problems in deformation analysis and predictions models

Firstly,theoretical analysis and numerical simulation of ill-posed problem have been done for linear regression analysis,time series analysis model and gray system model in deformation analysis and forecasting model.Then,by imposing interference noise on deformation observational data,the numerical expression relation between every three model parameters and the noise interference is derived based on least square principle.Finally,The paper points out that if one use any of the three models for modeling analysis to explain the deformation and deformation forecast,it is required to inspect the information matrix A=XTX no matter it is ill-posed or not,and to reduce ill-condition of A=XTX with effective method before using these three models.