Application of Reconstruction Algorithm of Improved Approximate Function in Fault Signal of Rolling Bearing
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摘要: 为改进优化压缩感知理论中以凸优化方式的重构算法在滚动轴承故障信号的应用中存在重构误差较大、重构迭代次数多及重构误差信噪比低等问题。本文提出采用反正弦函数取代双曲函数近似逼近l0范数，使得函数曲线与l0范数的逼近程度更高且更为光滑，同时加入衰减因子，加快迭代速度。实验结果表明该算法加入衰减因子后在一定程度上减少了迭代次数，却损失了部分重构精度，但整体重构效果相对已有算法具有重构精度高、迭代次数少及重构信噪比高的优势。Abstract: According to compressed sensing theory, the reconstruction algorithm with convex optimization method has some problems such as larger reconstruction error, more reconstruction iterations and lower reconstruction error signal-to-noise ratio in the application of rolling bearing fault signals. In order to improve these shortcomings, this paper proposes a new algorithm that uses the arc sine function instead of the hyperbolic function to approximate the l0 norm, which makes the approximation degree of the function curve and the l0 norm higher and smoother. At the same time, the attenuation factor is added to accelerate the iteration speed. The experimental results show that the proposed algorithm reduces the number of iterations to some extent, but loses some reconstruction accuracy. However, compared with the existing algorithms, the overall reconstruction effect has the advantages of higher reconstruction accuracy, fewer iterations and higher reconstruction SNR.
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表 4 各算法重构用时及误差对比
算法 SNR 时间/s 误差/(m·s−2) SL0 62.9446 0.1708 0.0159 NSL0 31.1427 0.1565 0.0510 ONSL0（含衰减） 64.5242 0.1738 0.0125 ONSL0（无衰减） 261.1287 0.3681 1.854 5×10−12 
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