基于集对分析和模糊马尔可夫链的滑坡变形预测新方法研究

滑坡体的变形表现出复杂的非线性演化特征，为克服传统分析方法在处理系统不确定性方面的不足，引入集对分析（SPA）理论，并结合模糊马尔可夫（fuzzy-Markov）理论来对滑坡SPA模型中的不确定系数进行二次预测，提出了滑坡变形SPA-fuzzy-Markov预测新模型。针对fuzzy-Markov子系统，分别提出了基于相关系数和特征值方差的多维空间模糊马尔可夫链拟合效果检验的两个新方法，并据此定量考察fuzzy-Markov子系统对参数响应的敏感性，用以确定最佳的模型参数组合。运用上述理论模型对刘家沱滑坡变形监测成果进行分析，综合定量考察了模型对模糊区间重合等级和马尔可夫状态转移步数这两个参数的敏感程度。结果表明：该算例条件下状态转移步数为敏感因子；与单纯SPA模型相比，复合模型能够进一步提高整体预测精度，在岩土监测分析领域中具有良好的实用价值；同时fuzzy-Markov理论的引入也为深化SPA基础理论研究提供了一条途径，不仅在岩土监测领域，在其他相关领域也具有理论和实用价值。

A new model for landslide displacement prediction based on set pair analysis and fuzzy-Markov chain

As a explicit behaviors of the complicated nonlinear dynamic system, the displacement of landslide is characterized with many uncertain factors. In order to reduce the limitation of traditional method, the set pair analysis (SPA) theory combined with fuzzy-Markov theory is introduced to describe the landslide dynamic system, and then the SPA-fuzzy-Markov prediction model for landslide displacement is set up. In this new model, the fuzzy-Markov theory is applied to analyze and predict the state transition of the uncertain factor in SPA model. By this way, the precision can obtained a significant improvement. Based on the correlation coefficient and mean square deviation of eigenvalue, two verify methods for fuzzy-Markov fitting in multidimensional space are suggested. Furthermore, based on these two verification methods; the sensitivity analysis for fuzzy-Markov model in two factors, such as fuzzy interval overlap and state transfer steps, can be done. By this way, the optimal parameter combination can be recommended. As a test, the SPA-fuzzy-Markov composite model is used to analyze the displacement of Liujiatuo landslide. The results indicate that the state transfer step is more sensitive than fuzzy interval overlap in this case. It is proved this new model can conspicuously improve the short-term prediction precision than just single SPA model; and this new model is worth popularizing in geotechnical monitoring. Moreover, the introducing of fuzzy-Markov guides a new way to develop basic research of SPA theory. This new method has theoretical and practical values not only in geotechnical monitoring, but also in other related fields.