稀疏信号分解-分段拟合逼近及其无转速计阶比应用

Sparse signal decomposition-segmental fitting and integral approximation and its application in no-tachometer order analysis

针对传统无转速阶比存在低阶拟合阶次模糊和高阶拟合频率积分方程难求解的问题,提出了一种基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法。根据啮合频率的稀疏信号分解动态时间支撑区对瞬时转频分段,并进行低阶多项式拟合,采用积分逼近方法代替求解方程,确定等角度重采样时刻,准确实现无转速计下的阶比分析。仿真和实测信号试验结果表明:基于啮合频率动态时间支撑区对瞬时转频分段,既能保证各段内频率变化简单,又能使分段最少;在各分段内采用2阶多项式就能准确拟合,解决了单个多项式整体拟合精度不高、缺乏自适应性的问题;积分逼近求解等角度重采样时刻,不需要求解方程,有效解决了方程无解、无实数解影响阶比结果的问题;基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法,为无转速计条件下旋转机械变转速过程信号阶比分析提供了一种新的有效途径。

Aim at the problem of order-blur caused by low order fitting and the difficulty to solve the fitting frequency integral equation caused by the high order fitting,a method of no-tachometer order based on sparse signal decomposition combined with segmental fitting and integral approximation（NTO-SSDFIA）is presented.The instantaneous frequency is segmented according to the dynamic time support area（DTSA）and fitted by low order polynomial.The angle resample time ticks is ascertained by integral approximation instead of solving the equation,so the no-tachometer order is carried out precisely.The experimental results of simulating signal and practical signal show that the rotating frequency changing simply in the segments whose number is least segmented by DTSA;the problem of low precision and bad adaptability of whole fitting by single polynomial is solved by the exact fitting in segments by low order polynomial;the influence of solution of equation on the result of order analysis is resolved effectively by integral approximation,which is able to ascertain the angle resample time ticks without solving the equation;The NTO-SSDFIA is an new effective method of the order analysis of rotating machinery under the condition of no-tachometer.