基于压缩感知的地铁安全监测数据重构与施工安全风险评估

Safety management is playing an increasingly important role in Metro construction. But the current safety monitoring is mainly done by manual way in Metro construction, which makes the resulted data being incomplete. This proposal is going to use compressive sensing to solve this problem. The incomplete monitoring data of one monitoring point can be regarded as a compressive sampling of original signal, which can be reconstructed and filtered by 1-dimension compressive sensing. As for the monitoring field which contains many monitoring points, the monitoring data in this field with a 2-dimension time-varying property can be reconstructed based tow different assumptions: data sparsity and signal sources sparsity. So a unified data recovering framework of safety monitoring is established, which makes the common monitoring data analysis methods to be used freely on recovered data. Since compressive sensing can recover the original signal with much less data than that required by Shannon sampling theory, the research result of monitoring data recovery can be used to define a theoretical lower bound of sampling frequency of safety monitoring from the point of view of data recovery. So a more concrete safety monitoring regulation can be partly supported by this point. To assess the risk of Metro construction, a MIC (Maximization Information Coefficiency)-based method of correlation analysis is utilized to explore the associations between related factors of safety with generality and equality. The result can be used to support the structure modeling of Bayesian network. Combining with the probability distribution getting from statistical analysis, a Bayesian network assessment model of Metro construction safety is set up, which can change the traditional manual risk decision into a computational process. By this model, safety monitoring data can be integrated seamlessly with safety risk assessment which makes the evaluation result of safety risk more close to actual.

目前地铁施工安全监测主要以人工监测为主，其结果受到施工环境、天气条件、监测精度以及人为因素等的影响，存在缺失和失真现象。本研究针对单监测点的数据缺失问题，将现有监测数据视作对原始信号的压缩采样，采用一维信号压缩感知方法，对其进行滤波与恢复。包含多个监测点的安全监控区域的监测数据是一个具有时空分布特性的二维时变信号，采用信号本身稀疏和信号源稀疏两种思路对其进行重构，从而以统一的框架解决数据缺失和失真问题。由于压缩感知对具备稀疏特性的信号，只需远少于香农采样定理所要求的采样数目就能以很高的概率重建原始信号，可为安全监测采样频率的确定提供一个理论下限。通过采用基于最大信息系数的关联性分析方法，探索地铁施工安全影响因素之间的关系，解决贝叶斯网络的结构建模，结合统计分析得到的概率分布，建立施工安全状态的贝叶斯网络模型，将传统的人工判断转化为一个可计算的过程，实现施工安全监测数据与风险评估的有机结合。

目前地铁施工安全监测主要以人工监测为主，其结果受到施工环境、天气条件、监测精度以及人为因素等的影响，存在缺失和失真现象，导致监测数据难以有效利用。本研究针对该问题采用压缩感知的方法解决数据缺失问题。在比较分析不同稀疏基在监测数据重构中的效果的基础上，从冗余字典中找出一个能够使得曲线重构最优的小波基。然后针对监测点的数据缺失问题设计了适用于地铁施工安全监测数据重构的观测矩阵，并通过实际案例检验其等距特性。仿真实验证明：对于类似地铁施工监测这样的数据有缺失且含有较大噪声的情况，压缩感知重构完整数据的效果要优于传统插值方法。对于监测区域，考虑到监测区域内多个监测点之间的数据存在时间和空间相关性，采用分布式压缩感知方法能在数据有较大缺失的情况下重构监测数据，且基于分布式压缩感知的地表沉降数据重构结果要比基于回归分析法、RPCA、SPAMS方法的恢复精度高。基于上述两种方法，本项目建立了一个统一的地铁监控数据重构框架，使得大量的常规分析方法可以有效使用。利用压缩感知技术的采样频率低于Nyquist采样频率的特点，本项目提出一种基于压缩感知理论来确定信号采样频率下限的方法，为安全监测标准的进一步优化和细化提供了理论支持。采用最大信息系数MIC，分析地表沉降之间以及地表沉降与建筑物沉降之间的关联性，证明地表沉降和建筑物沉降间的关联性与距离的自然对数近似成线性关系，给出了临近建筑受施工影响的范围估计。利用基于联合稀疏模型的方法对地表沉降区域监测数据进行在线预测，尽早识别出数据中的拐点，为安全监测的预警提供基础数据支持。