[论文解读] Robust Bayesian compressive sensing with data loss recovery for structural health monitoring signals

Yong Huang, James L. Beck+2 more|arXiv (Cornell University)|Mar 28, 2015

Sparse and Compressive Sensing Techniques参考文献 7被引用 3

一句话总结

本文提出了一种用于结构健康监测信号的鲁棒贝叶斯压缩感知方法，可处理近似稀疏数据及传输过程中的数据丢失。通过将预测误差精度作为干扰参数进行积分，该方法在重建精度和不确定性量化方面优于现有的贝叶斯与非贝叶斯压缩感知技术，尤其在数据丢失条件下表现更优。

ABSTRACT

The application of compressive sensing (CS) to structural health monitoring is an emerging research topic. The basic idea in CS is to use a specially-designed wireless sensor to sample signals that are sparse in some basis (e.g. wavelet basis) directly in a compressed form, and then to reconstruct (decompress) these signals accurately using some inversion algorithm after transmission to a central processing unit. However, most signals in structural health monitoring are only approximately sparse, i.e. only a relatively small number of the signal coefficients in some basis are significant, but the other coefficients are usually not exactly zero. In this case, perfect reconstruction from compressed measurements is not expected. A new Bayesian CS algorithm is proposed in which robust treatment of the uncertain parameters is explored, including integration over the prediction-error precision parameter to remove it as a "nuisance" parameter. The performance of the new CS algorithm is investigated using compressed data from accelerometers installed on a space-frame structure and on a cable-stayed bridge. Compared with other state-of-the-art CS methods including our previously-published Bayesian method which uses MAP (maximum a posteriori) estimation of the prediction-error precision parameter, the new algorithm shows superior performance in reconstruction robustness and posterior uncertainty quantification. Furthermore, our method can be utilized for recovery of lost data during wireless transmission, regardless of the level of sparseness in the signal.

研究动机与目标

• 解决从压缩测量中重建近似稀疏的结构健康监测信号的挑战。
• 在预测误差精度不确定或估计不佳时，提升信号重建的鲁棒性。
• 实现在结构监测系统中无线传输过程中丢失数据的有效恢复。
• 提升压缩感知在实际应用中后验不确定性量化的性能。

提出的方法

• 该方法采用层次化贝叶斯模型，通过积分对预测误差精度进行边际化处理，从而将其从干扰参数中去除。
• 在信号系数上使用拉普拉斯先验以在变换基（如小波基）中促进稀疏性。
• 使用马尔可夫链蒙特卡洛（MCMC）采样进行后验推断，以估计信号并量化不确定性。
• 通过将缺失数据视为隐变量，该框架支持从不完整或丢失的测量中进行重建。
• 使用来自空间框架结构和斜拉桥的真实加速度计数据对算法进行验证。
• 通过避免依赖精度参数的点估计值实现鲁棒性，与以往基于MAP的贝叶斯方法不同。

实验结果

研究问题

• RQ1 如何使贝叶斯压缩感知对预测误差精度参数的不确定性更具鲁棒性？
• RQ2 所提出的方法是否能在重建近似稀疏的结构健康监测信号方面优于现有最先进的压缩感知技术？
• RQ3 该方法在结构监测应用中无线传输过程中对丢失数据的恢复能力在多大程度上有效？
• RQ4 对精度参数的积分处理如何影响信号重建中的后验不确定性量化？

主要发现

• 与标准压缩感知及以往采用精度参数MAP估计的贝叶斯方法相比，所提方法在重建精度方面表现更优。
• 即使信号仅为近似稀疏而非完全稀疏，该方法仍表现出优异的鲁棒性能。
• 无论信号的稀疏度如何，该方法都能有效恢复传输过程中丢失的数据。
• 由于精度参数的边际化处理，后验不确定性量化显著改善。
• 该算法在空间框架结构和斜拉桥的真实世界数据上均保持了高重建保真度。