时栅传感器动态测量误差补偿

Compensation for dynamic measurement errors of time grating sensor

针对动态测量误差特点,提出了对系统误差和随机误差分别进行建模和组合补偿的思想来提高时栅传感器的动态测量精度。对具有周期性变化特征的系统误差采用傅里叶级数逼近的方法进行建模,运用最小二乘求解超定方程组的方法计算出系统误差的补偿参数。对于系统误差补偿后残留的随机误差采用灰色预测GM(1,1)模型进行预测,通过模型残差检验和修正提高预测的准确度。实验结果表明,利用傅里叶级数逼近模型有效地补偿了系统误差,误差由±35″降至±7.8″,通过最小二乘参数寻优得到的补偿参数与传感器实际的误差成分相吻合;灰色预测模型则很好地预测补偿了残留的随机误差,误差由±7.8″降至±3″。得到的结果表明,利用这种对误差分别建模和补偿的方法大幅度地降低了动态测量误差,有效地提高了传感器的测量精度。

According to the error characteristics in dynamic measurement,a targeted respective modeling and a combined compensation idea for systematic errors and random errors were proposed to improve the dynamic measuring accuracy of a time grating sensor.The Fourier series approach was presented to establish the model for the systematic errors with periodical changes,in which the compensation parameters for the systemic errors were calculated by using least square to solve overdetermined equation.Moreover,the grey model GM（1,1）was used for modeling random errorsafter compensation systemic errors and the forecast accuracy was improved by a residual error test and modification.The actual experiments show that systematic errors have been effectively compensated by Fourier series approach model,the original errors are reduced from ±35″to ±7.8″,and the compensation parameters are consistent with that of actual sensor.The random errors have been forecasted and compensated by GM（1,1）model,and the random errors are reduced from ±7.8″to±3″.These results demonstrate that proposed method compensates the dynamic errors greatly and the dynamic measurement accuracy of the embedded time grating sensor is effectively improved by using this modeling and compensation method.