基于小波变换的灰色马尔可夫链模型及其工程应用研究

发布时间：2018-06-09 04:04

本文选题：变形监测 + 小波变换阈值去噪　；参考：《长安大学》2014年硕士论文

【摘要】：近些年来，得益于城镇化和现代化步伐不断提速，基础设施建设得到了大幅度的发展,在我们的生活之中越来越多的大型建筑物和构筑物如雨后春笋般拔地而起，毋庸置疑这些大型建筑物给我们的生活带来很多便利，但是同时也隐藏着许多安全问题。在建筑物施工建设和运营管理过程中，为了避免可能出现的突发状况,需要定期的监测建筑物的沉降,以获得沉降变形数据。采取一些方法对所获得的数据进行处理和分析,尽量准确地预测出建筑物变形的大致趋势,这样我们才能有针对性地采取一些防范措施，避免突发状况或灾难的发生。根据观测和分析可以知道,建筑物沉降观测数据是一系列短序列的离散数据,它具有包含噪声并且波动性较大的特点。本文在进行研究工作时分析了目前常用的一些变形监测数据处理以及变形预测的理论和方法,并且在前人研究的基础上,结合自己对变形监测研究的一些思考,提出了基于小波变换阈值去噪的灰色马尔可夫链预测模型,并采用监测实例对其加以应用和验证。论文以西安宏信国际花园4号楼沉降变形监测数据为作为例子,根据该项目沉降监测点位布设情况，，应用提出的方法对其中若干个代表性较强的监测点进行了分析研究。在数据处理方面,首先,用MATLAB编写小波去噪程序用以小波分解及小波重构,得到去噪后的有用数据；其次,利用去经过小波噪后的拟合数据建立自适应加权灰色预测模型并预测其沉降值,以预测值与观测值的相对误差为划分标准对预测值划分状态区间,再利用马尔可夫链预测方法判断出未来某一时刻沉降量的状态可能处于的区间,得出状态概率矩阵，从而利用马氏链理论求得建筑物的更优化的沉降预测值；最后,将小波变换灰色马尔科夫链、单纯的灰色模型以及小波灰色模型三种预测方法所得到的预测结果进行对比分析，得出有益结论。根据对比结果可知,小波变换灰色马尔可夫预测结果要优于单纯的灰色模型预测和小波变换灰色预测结果,也就是说它可以进一步提高预测精度。在处理波动性较大的数据时,利用基于小波变换的灰色马尔可夫链模型能得出更优化的预测结果,因此，这个模型也为随机波动性较大的数据序列提供了一种新的数据处理与预测方法。
[Abstract]:In recent years, thanks to the increasing pace of urbanization and modernization, infrastructure construction has been greatly developed, and more large buildings and structures have sprung up in our lives. There is no doubt that these large buildings bring a lot of convenience to our life, but there are also many safety problems. In the process of building construction and operation management, in order to avoid the unexpected situation, it is necessary to monitor the settlement of buildings regularly in order to obtain settlement deformation data. We should take some methods to process and analyze the obtained data, and try our best to predict the approximate trend of the deformation of the building, so that we can take some preventive measures in a targeted way. According to the observation and analysis, we can know that the observation data of building settlement is a series of discrete data of short series, which has the characteristics of noise and volatility. In this paper, some commonly used theories and methods of deformation monitoring data processing and deformation prediction are analyzed, and based on previous studies, some thoughts on deformation monitoring research are combined. A grey Markov chain prediction model based on wavelet transform threshold denoising is proposed, and it is applied and verified by a monitoring example. Based on the monitoring data of settlement deformation in the 4th Building of Hongxin International Garden in Xi'an as an example, according to the settlement monitoring site layout of the project, several representative monitoring points are analyzed and studied by using the proposed method. In the aspect of data processing, firstly, the wavelet de-noising program is written with MATLAB to decompose and reconstruct the wavelet to get the useful data after denoising. The adaptive weighted grey prediction model is established and its settlement value is predicted by using the fitting data after wavelet denoising. The state interval of the predicted value is divided according to the relative error between the predicted value and the observed value. Then the Markov chain prediction method is used to determine the possible interval of the state of settlement at a certain time in the future, and the state probability matrix is obtained, thus the more optimal settlement prediction value of the building can be obtained by using Markov chain theory. Finally, The prediction results obtained by wavelet transform grey Markov chain, simple grey model and wavelet grey model are compared and analyzed, and some useful conclusions are drawn. According to the comparative results, the grey Markov prediction results of wavelet transform are superior to those of pure grey model prediction and wavelet transform grey prediction results, that is to say, it can further improve the prediction accuracy. When dealing with volatile data, the grey Markov chain model based on wavelet transform can be used to obtain more optimized prediction results. This model also provides a new method of data processing and prediction for random data series with high volatility.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU196

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