【作者】 陈文义；

【导师】 孔繁亮；

【作者基本信息】 哈尔滨理工大学 ， 应用数学， 2003， 硕士

【摘要】 本文将动力分析与统计分析有机结合起来，在充分研究气温演变过程的物理机制基础上，用新的数学的前沿理论建立气温演变过程预测的现代分析理论与方法，综合与发展随机过程的统计理论，对我国东北北部地区短期气温演变过程进行研究，分析与预报。结合时空系统机制和历史资料的分析，建立非线性时空序列预测理论与方法。本文主要进行了以下几方面的工作：1探讨了一种动态系统的时变参数的估计方法，克服了以往把一个时变参数的动态过程当作了非时变参数的静态过程，而用非时变参数模型预报时变参数系统的状态时带来的较大误差问题。2应用逐段线性化的方法推导出了多维AR（r）自适应模型时变系数矩阵的递推公式，克服了单变量AR（r）自适应模型没有考虑其他变元对因变元的作用的缺陷。3讨论了非线性模型统计性质的评估。可以概括为先对模型检验，然后再对残差进行检验。实际上是对非线性统计模型进行逐步优化的过程，最终使模型达到拟合最优，残差为iidN。4综合随机过程的统计理论与气候动力学原理，研究短期气温演变过程的机理，将物理成因分析与随机过程的统计分析结合起来，选择预报因子，建立符合气温演变特征的非线性时空序列的数学模型框架。5对黑龙江省某地气温进行了调研，把气温的变化规律看成一个随时间变化而变化的动态系统，用上述方法对黑龙江某地气温进行预测。总结出一套有效的区域性短期气温的非线性预测理论与方法。从文中对比预报，我们可以看到本文提出的这种动态系统预报方法优于传统的预报方法。本文中所研究的气温演变过程的非线性预测方法是正确的、经回顾性验证是可行的，而且是行之有效的。我们相信它在非线性预测方面将会有广阔的应用前景。更多还原

【Abstract】 The short-term evolving process of air temperature at the north of east-north in our country is researched, analyses and forecasted by combining dynamical analysis with mathematical statistics analysis, researching physical mechanism of the evolving process of air temperature and establishing the modern analysis theory and method of the evolving process of air temperature with later mathematical theories. Simultaneously, the forecast theory and method of nonlinear time series is established, which combines mechanism of the time space system with analyzing historical data.The paper consists of several parts as following:Firstly, we probe an estimating method with the time-change parameters to overcome the problem with greater errors that us think a dynamical process with the time-change parameters as a static process with the no time-change parameters and forecast the time-change parameters system by the model with the no time-change parameters.Secondly, overcoming drawback of single variable fitting AR models lacking of other variables acting on factor variable, a set of the trace formulas are given about the time-change coefficient matrixes of multivariable fitting AR models.Thirdly, evaluating to statistics quality of the nonlinear model is discussed. That is, firstly to test models and secondly to test residual errors. In fact, it is that nonlinear statistics models have the optimization process step by step. Ultimately, models are up to fitting optima and residual errors are iidN.Fourthly, in this paper, we integrate theories of time series analysis and principles of climate dynamics, research mechanism of the evolving process of air temperature, combine physical analysis with statistical analysis of stochastic process, select forecast factors and construct the mathematical model framework of nonlinear time series according with the evolving feature of air temperature.Fifthly, thinking the evolving regulation of air temperature as a dynamical system in pace with time changing, we investigate the air temperature at certain region in province Heilongjiang and forecast the air temperature at the region by the above method. We also summarize a set of effective nonlinear forecast theories and methods about the short-term regional air temperature.From the contradistinctive forecast in this paper we can see that the method of the dynamic forecast is better than the general method .The method is right, feasible and effective by the proof. We believe that it has the broad prospects in the aspect of<WP=9>the nonlinear forecast theory.更多还原