非线性模型的非线性强度及其在变形分析中的应用
来源期刊：中南大学学报(自然科学版)2001年第4期
论文作者：李志伟 朱建军 王仁谦 李陶
文章页码：339 - 343
关键词：非线性强度;固有曲率;参数效应曲率;偏差;模拟
Key words：nonlinear strength; intrinsic curvature; parameter-effects curvature; bias; simulating
摘 要：介绍了Bates和Watts的非线性强度度量指标———最大固有曲率和最大参数效应曲率,提出了当模型固有非线性不显著而参数效应非线性显著时,利用M.J.Box提出的偏差计算和模拟研究重新参数化的方法.结合某实测边坡的变形监测资料,选用非线性模型lt=α-βexp(-γtδ)+εt描述边坡变形规律.对该边坡上73个点的监测资料分别进行非线性回归计算,发现其中大部分点不能收敛于LS估计,该模型有较强的非线性特性;研究该模型的非线性性态时,发现其最大固有非线性曲率不显著,而模型的最大参数效应曲率非常显著.模拟结果表明,估计量类似对数正态分布,因此,用新参数φ=-lgγ对模型重新参数化.用重新参数化后的模型对该边坡的实测资料进行回归计算时,只有4个点未能收敛于LS估计,而模型的最大固有非线性曲率和最大参数效应曲率则基本符合要求.
Abstract: This paper introduces Bates and Watts′index of nonlinear strength, the maximal intrinsic curvature and the maximal parameter-effects curvature. It presents a re-parameterizing method which utilizes M.J.Boxbias computation and simulating studies when the nonlinear model has significant parameter-effects curvature and insignificant intrinsic curvature. Combined with an example of slope deformation analysis, several points of the method are discussed. According to the mechanism of the slope deformation, the nonlinear model lt=α-βexp(-γtδ)+εt was recommended to describe the deformation. But when implementing the regression calculation for the seventy three points respectively, most of them could not converge to LS estimation. It can be inferred that the model has strong nonlinear nature. Study on the model shows that their intrinsic curvatures are acceptable, but the maximal parameter-effects curvature are not. It is shown that most of the parameter-effects curvature come from parameterγ. Simulating research reveals that estimations ^γ is approximately in a logarithm normal distribution, thus a new parameterφ=-lgγis used to re-parametrize the model. The regression calculation for the seventy three points respectively based on the revised model shows that only four of them can not converge to LS estimation, and both the maximal intrinsic curvature and the maximal parameter-effects curvature are acceptable.
