非线性系统中结构突变的稳健检测与统计模型的稀疏重构

项目名称： 非线性系统中结构突变的稳健检测与统计模型的稀疏重构

项目编号： No.11201372

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 夏志明

作者单位： 西北大学

项目金额： 22万元

中文摘要： 非线性系统中的结构突变问题受到应用与理论的驱动，成为现代统计学的一个热点问题，但已有研究常会在突变检测方面过多依赖于预设条件且在突变结构建模方面简单归结为变点估计。本项目拟采用具有"稳健性"的突变检测手段和具有"稀疏性"的模型重构方法，具体研究内容为：①基于"未突变结构"下的估计方程或残差，结合先验知识构造稳健的加权残差以避免"模型误设"风险,在此基础上选择稳健泛函如"比型"泛函以避免方差估计误差，获得最终检测统计量；②选定合适的"阈值"作为显著突变与偶然跳跃之间的分界，从而能适应数据特点自动选择变点参数值，对非变点参数加合适的"罚"以稀疏选定突变响应因素，最终建立稀疏突变模型。非线性系统突变结构的稳健检测与稀疏重构在气候水文、过程控制、图像信息处理等领域有重要应用，丰富了统计诊断方法和非连续、非光滑条件下的统计建模理论，对于揭示系统结构、勾勒外在冲击在系统内的突变响应机制提供有力支撑。

中文关键词： 质量控制；突变；稀疏性；稳健性；

英文摘要： The problems about structural abrupt changes in nonlinear system are driven by applications and theories, and becomes one of important issues, however, existing researches focus on dectection which relies much on preassumptions and model reconstruction which is simply due to change-point estimation. The project plans to introduce robust dectection method in abrupt changes and sparse ideas in model reconstruction. The specific route includes two aspects. Firstly,based estimating equations and classical residuals under constant structure assumption, together with existing experience we construct weighted residuals to avoid error of "model misspecification", and furtherly we construct robust functionals especially including ratio-type ones to avoid estimation errors, and get the final test statistics. Secondly, to adapt data features, we choose appropriate threshold as the the boudary between sigificant abrupt changes and jump by chance, and to select response factors sparsely, we add an appropriate penalty on the other parameters different from change points. Research in structural abrupt changes has important applications in climate，process control and image processing etc., and richens statistical diagnosis methods and statistical modelling theory under the condition of discontiuity and nonsmoothing, and provi

英文关键词： quality control；abrupt change；sparsity；robustness；