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反演算法是光散射颗粒测试技术中的关键问题之一,以Tikhonov正则化方法为代表的单参数正则化算法被广泛应用于激光粒度仪颗粒粒径分布函数(PSD)的反演计算中。该算法的缺点之一是所得到的反演解呈现出振荡特征,并伴随负值。为改善这一状况,提出了一种多参数正则化算法。通过构建一个由多个参数控制的带通滤波函数,分别控制正则化解的振荡程度和解的高度,并对正则化解进行非负约束。模拟计算和实验研究结果表明,对多参数进行优化后能够降低正则化算法带来的振荡和负值。此外,所提出的算法具有较好的多峰识别能力,可实现颗粒粒径分布的有效重建。
The inversion algorithm is one of the key problems in the light scattering particle testing technology. The one-parameter regularization algorithm represented by the Tikhonov regularization method is widely used in the inversion of the particle size distribution function (PSD) of the laser particle sizer. One of the drawbacks of this algorithm is that the resulting inversion solution exhibits oscillatory characteristics with negative values. To improve this situation, a multi-parameter regularization algorithm is proposed. By constructing a band-pass filter function controlled by multiple parameters, the oscillation degree and the solution height of the regularization solution are respectively controlled, and the nonnegative constraint on the regularization solution is obtained. Simulation results and experimental results show that the optimization of multiple parameters can reduce the oscillation and negative values brought by the regularization algorithm. In addition, the proposed algorithm has better multi-peak recognition ability and can effectively reconstruct particle size distribution.