高可靠小条件数压缩感知叶尖定时信号辨识

High reliability identification method of blade tip timing signals based on compressed sensing under small condition number

为增强基于任意角度压缩感知(CS)叶尖定时信号(BTT)重构的稳定性,采用小生境微种群遗传算法提出了基于小条件数的高稳定性传感器安装布置方法。研究发现:任意角度CS的恢复矩阵条件数越小,不同信噪比下同步和非同步振动信号重构误差越趋于稳定在较低范围,优化后发现条件数为1的排布方案下,相邻传感器角度间隔趋向于均布2m取K的形式。利用条件数为1的矩阵冗余特性,设计了高可靠性的传感器排布方案,数值试验和有限元仿真验证表明叶尖定时系统在失效一个传感器的情况下仍可稳定得到准确的重构结果。在信噪比为5 dB时,冗余排布相比参考排布的主倍频幅值重构误差降低4.4%以上,验证了采用最小条件数排布的任意角度CS信号辨识方法在噪声及传感器失效情况下仍可保证BTT测量结果的有效性和可靠性。

In order to enhance the stability of blade tip timing(BTT) signals reconstruction based on arbitrary angle compressed sensing(CS), the niching micro genetic algorithm was used to propose a high stability sensor placement method based on small condition number. It was found that in the case of smaller condition number of restoration matrix of arbitrary angle CS, the reconstruction error of synchronous and asynchronous vibration signals tended to stabilize in a lower range under different signal-to-noise ratios. After optimization, it was found that the adjacent sensors angle spacing tended to be uniformly distributed in the form of 2m to take K under the arrangement scheme with condition number of 1. Using the redundancy property of matrix with condition number equal to 1, a high reliability sensor placement scheme was designed. The numerical experiments and finite element simulation results showed that the blade tip timing system could obtain accurate reconstruction results stably even if one sensor failed. When the signal-to-noise ratio was 5 dB, the reconstruction error of the main engine order amplitude of the redundant arrangement was reduced by more than 4.4% compared with the reference arrangement. The identification method of arbitrary angle CS with minimum condition number arrangement can still ensure the validity and reliability of BTT measurement results in the case of noise and sensor failure.