数据变换技术与gm11模型研究

南京航空航天大学 硕士学位论文 数据变换技术与GM（1,1）模型研究 姓名：钱吴永 申请学位级别：硕士 专业：数量经济 指导教师：党耀国 20081201 南京航空航天大学硕士学位论文 I 摘摘 要要 本文旨在对数据变换技术与 GM(1,1)模型进行深入研究，在其理论基础、技术方法和实际 应用等方面获得一些新的研究成果，为提高灰色预测模型精度提供新思路、新方法，从而丰富 灰色预测理论，拓宽灰色预测方法的应用范围。文章采用理论研究与应用研究相结合的方法对 数据变换技术和 GM(1,1)模型进行研究，并得到了一些新方法和新结论。具体研究内容和研究 成果如下： 1. 许多学者对数据变换进行了研究。 但是， 数据变换满足什么样的条件才能提高灰色预测模型 的预测精度以及如何构造新型数据变换等问题尚未得到很好的解决。本文从差异信息的角度对 数据变换进行研究，提出了数据变换需满足：提高光滑性，为一级比压缩变换，保持凸凹性， 不增大还原误差才能提高模型精度，并首次提出了数据变换构造准则，在数据变换构造准则的 基础上构造了若干实用的数据变换，其中反余切变换与反余弦变换是本文首次提出，这一部分 研究扩展了数据变换技术的应用，在实际应用中具有一定的指导意义与参考价值。 2. 从 GM(1,1)模型的建模机理入手，研究了 GM(1,1)模型的性质，得到一些新的结论，在性质 研究的基础上首次提出了加权累加生成的概念并用加权累加生成的方法对 GM(1,1)模型进行改 进，提高了模型的精度，同时还从影响模型精度的因素入手，提出了基于优化初值和最优背景 值的 GM(1,1)新模型，以改进传统的 GM(1,1)模型，提高模拟和预测精度。 3. 针对 GM(1,1)模型在应用于振荡序列建模时，其模拟和预测精度不理想的情况，首次提出了 加速平移变换，并将该变换与加权均值生成相结合对振荡序列进行处理，并建立 GM(1,1)模型， 研究表明该法能够提高模型的模拟和预测精度，从而扩大了 GM(1,1)模型的应用范围。 4. 运用改进的 GM(1,1)模型对江苏省 2007-2010 年间的三次产业的产值进行预测， 根据三次产 业产值的预测结果对产业结构的变动进行预测,对预测结果进行分析,给出了对江苏省产业结构 进一步调整和优化的对策和建议。 关键词：关键词：灰色系统，数据变换，GM(1,1)模型，加权累加生成，振荡序列，改进，产业结构 数据变换技术与 GM（1，1）模型研究 II Abstract This thesis aims at the research on the technology of date transformation and GM (1, 1) model. Several innovations such as theoretical basis, technological methods and practical applications are obtained, which are benefit to provide new thoughts and methods for improving precision of GM (1, 1) model. These outcomes have great significance in developing the theory of grey model and widening the range of grey system theory. The thesis studies on grey transformation and GM (1, 1) model and get some new methods and new conclusions with both theory research and applied research.The contents as follows: 1. Many scholars have studied the technology of transformation. However, many issues have not been resolved, such as what conditions should the transformation meet can we improve the forecast accuracy of grey model and how to structure the new data transformation. The paper gives comprehensive research on the date transformation from a new viewpoint of the difference information, and other issues from the difference between information. The paper also explores some main influence factors of the date transformation on the precision of model, such as the smooth ratio, the class ratio, the convex and cave of original sequence. Then the paper proposes guidelines for the construction of the transformation and constructs a series of new type of transformation, which extends the application of technology of transformation, and has some instructional meaning and referenced value in practice. 2. The paper studies the GM (1, 1) model from the mechanism of modeling, gives research on the nature of the model, and gets some new conclusions. The concept of weighting accumulated generating operation is proposed for the first time, and then the model base on that is established. Application shows that this approach can improve the accuracy of the forecast model. A new model based on optimization of the initial value and optimize the value of the background is established. This research can improve the forecast accuracy of models and expand the application of the model. 3. The GM (1, 1) model has high prediction accuracy for the non-negative smooth monotone sequence, but it is not suitable for oscillation sequences. This paper puts forward the method to solve this problem. Firstly, oscillation sequences are turned into the monotone sequences by the accelerated translation transforms, and then weighting mean value generating is applied to the sequences .Lastly, the processing sequences is used to establish GM (1, 1) model. The example verifies that the method can raise forecast accuracy of GM (1, 1) model, and this method expands the application scope of GM 南京航空航天大学硕士学位论文 III (1, 1) model. 4. We predict the output values of tertiary industries of Jiangsu Province during 2007 to 2010 by the improved model. According to the result, we predict the changes of industrial structure and give the strategies and recommendations of adjustment and optimization for the industrial structure of Jiangsu. Key Words: Grey system，Date transformation，GM (1, 1)Model，Weighting accumulate degenerating operation， Oscillation sequence， Improvement， Industrial structure 数据变换技术与 GM(1,1)模型研究 VI 图、表清单 图 1.1 文章研究技术路线 .6 图 5.1 2001-2010 年江苏省三次产业的比重变动趋势 .50 表 3.1 模型预测结果比较 .25 表 4.1 断裂韧度数据 .34 表 4.2 模型计算结果比较 .34 表 4.3 新模型与原模型的模拟与预测误差 .39 表 4.4 1978-1983 我国人均粮食产量原始数据 .