为了有效地将激光粒度仪所获得的光能分布反演为颗粒粒度分布,提出了一种无模式综合反演算法,即二阶段迭代算法。该算法综合采用了改进的共轭梯度法和松弛迭代法的优点,使用共轭梯度法做第一步预迭代,利用其快速收敛性和解的平滑性得到第二步迭代的初始解;然后,使用正则化方法对原问题进行修正处理以得到具有较好稳定性的正则化方程;最后,采用改进的松弛迭代法把第一步预迭代的解作为初始解对改进后的正则化方程进行行迭代求解。对算法进行了分块操作,并对所有模块如共轭迭代法、正则化法、松弛迭代法进行分析,指出各模块的可行性与必要性,同时进行各模块参数的独立和综合的最优化选择。相比于单独地使用以上某一种方法,该综合方法能同时改进解的稳定性和准确性,对单峰和多峰分布的国家标准样品及具备噪声的模拟信息测试也取得了较好的分辨精度。

A hybrid algorithm combining the characteristics of a conjugate gradient iteration method,a regularization equation and a Successive Over Relaxation (SOR) technique,namely,two-segment iterative method,is proposed to reverse efficiently the light intensity distribution into the particle size distribution in a laser particle sizer. The process of convergence can be speeded up and the smoothness of the solution can be enhanced by taking the conjugate gradient iteration as the pre-iteration of next SOR iteration. The solution obtained from the first step treatment is used as the initial solution for the second step. Then,a regularization method is used to correct to the original problem to obtain a stable regularized equation. Finally,the improved SOR method is taken to resolve the regularized equation.Experimental results show the two-segment method can achieve an accurate and stable final solution to this problem. This method is examined with the national standard particulate samples and the theoretical noisy signal,and the results indicate the method is able to distinguish multi-peak particle size distribution (PSD) and can smooth noisy signals.