基于改进压缩感知的缺损光纤Bragg光栅传感信号修复方法

光纤光栅传感在实际的应用中，存在采样信号数据丢失问题，该文提出一种改进重构算法的压缩感知信号修复方法。根据缺损信号特征，选取与之匹配的观测矩阵与稀疏字典。基于压缩感知重构算法，提出匹配光纤布拉格光栅(FBG)信号特征的自适应阈值函数，同时增设阈值判决条件。分析了信号修复与传感测量精度的关系，采用重建信号的寻峰误差来验证信号的修复效果。仿真结果显示，在FBG光谱数据缺失30%的情况下，恢复信号的平均相对误差为10-6；均方根误差为0.0707，比对比算法低0.0232~0.1159；且系统平均运行时间远低于对比算法，表明采用该文算法修复缺损的FBG传感信号具有较高的重构精度与较好的实用性。

A Repaired Algorithm Based on Improved Compressed Sensing to Repair Damaged Fiber Bragg Grating Sensing Signal

To solve the problem of data loss in the field of Fiber Bragg Grating (FBG) sensing, a signal repaired method based on compressed sensing with improved reconstruction algorithm is proposed. According to the characteristics of signal, the suitable observation matrix and sparse dictionary are selected to repair the damaged spectral signal. An adaptive threshold function, which is used to match the characteristics of signal, is proposed in the reconstruction algorithm, and the criterion of threshold rationality is added. The relationship between the recovery precision of signal and sensing accuracy of fiber Bragg grating is analyzed, and the repairing effects are validated by peak-detected error of reconstructed signal. Simulation results show that the average relative error is10-6 when 30% of the data is lost. The root mean square error is 0.0707, which is 0.0232~0.1159 lower than the contrast algorithms. The peak-detected error is lower than the others. Besides, the average running time of the system is much lower than the compared algorithms. All the results show that the proposed algorithm can well achieve the recovery of missing data, so as to improve the measurement precision of fiber Bragg grating sensor.