基于改进的Chahine迭代算法的粒径分布反演

反演算法的速度、精度及稳定性一直是颗粒测量领域中的研究重点。针对传统的Chahine迭代算法在反演过程中出现毛刺、伪峰及震荡等不稳定现象,将正则化理论与Chahine迭代算法相结合的改进算法用于颗粒粒径分布的重建。通过引入正则化理论建立新的线性方程,采用L曲线法确定正则化参数,再利用Chahine迭代算法求解该线性方程。仿真及实验结果表明:改进的算法解决了Chahine迭代算法的缺点,提高了反演结果的稳定性和平滑性。利用改进的算法实现国家标准颗粒的测量,其迭代15 000次所得中值粒径D50的相对误差在2%以内,用于描述分布曲线展宽的D10、D90的相对误差均在5%以内,且反演时间小于1 min,可满足颗粒粒径在线测量的需求。

Inversion of particle size distribution based on improved Chahine algorithm

The speed, precision and stability of inversion algorithm are research emphasis in the field of particle measurement. To counter the problems such as burrs, false peaks and concussion etc. in the process of inversion with traditional Chahine algorithm, an improved algorithm that combines regularization theory with Chahine algorithm was used to reconstruct particle size distribution. A new linear equation was constructed by introducing the regularization theory, the regularization parameter was determined by using L-curve, and Chahine algorithm was used to solve the linear equations. Simulation and experiment results show that the improved algorithm overcomes the disadvantages of traditional Chahine algorithm and improves the stability and gliding property of inversion results. Measured results of standardized polystyrene microsphere is measured by using the improved algorithm, which shows that the relative errors for median diameter D50 is within 2%, and D10, D90(characterize broadening of distribution curve) are both within 5% when the number of inversion is 15 000. In addition, the inversion time is less than 1 minute, which meets online particle size measurement.