基于持续同调的边坡破坏过程的拓扑特征研究

Topological feature study of slope failure process based on persistent homology machine learning

首先利用软件UDEC对边坡处于地震荷载作用下的失稳破坏过程进行模拟,研究了边坡失稳破坏时的动态响应,得到了边坡的变形特征和位移云图,然后运用持续同调理论对边坡失稳状态进行分析,生成条码图,从条码图中提取边坡的拓扑特征,找到边坡失稳临界状态对应的拓扑特征,建立拓扑特征与失稳演化的关系。最终为边坡失稳破坏预测提供一种拓扑化研究工具。研究表明,最长贝蒂1条码的变化反映了边坡的演变过程及失稳破坏规律,贝蒂1条码的突变意味着边坡发生了失稳破坏。运用离散元法和持续同调理论对边坡处于外荷载作用下的破坏特征进行研究,可以更好地了解边坡的破坏机理,为工程防护提供理论依据,同时也为边坡安全设计与灾害预报研究提供了一种全新的数学方法。

Firstly,this paper uses software UDEC to simulate the instability failure process of a slope under seismic load,studies the dynamic response of slope failure,obtains the deformation characteristics and displacement cloud map of the slope,then analyzes the instability state of the slope by using the theory of persistent homology,generates bar code map,and extracts the topological characteristics of the slope from its bar code map.The topological characteristics corresponding to the critical state of slope instability are found,and the relationship between the topological characteristics and the instability evolution is established.Finally,it provides a topological research tool for slope failure prediction.The results show that the change of the longest Betty 1 bar code reflects the evolution process of the slope and the law of instability failure.Using discrete element method and persistent homology theory to study the failure characteristics of the slope under external load can better understand the failure mechanism of the slope,provide theoretical basis for engineering protection,and also provide a new mathematical method for slope safety design and disaster prediction research.