The kinetic parameters of stochastic primary nucleation were estimated for the batch-cooling crystallization of L-arginine. It is difficult for process analytical tools to detect the first nucleus. In this study, the latent period for the total number of crystals to be increased to a predetermined threshold was repeatedly measured with focused-beam reflectance measurements. Consequently, the latent periods were different in each measurement due to the stochastic behavior of both primary and secondary nucleation. Therefore, at first, the distribution of the latent periods was estimated by a Monte Carlo simulation for some combinations of the kinetic parameters of primary nucleation. In the simulation, stochastic integrals of the population and mass balance equations were solved. Then, the parameters of the distribution of latent periods were estimated and correlated with the kinetic parameters of primary nucleation. The resulting correlation was represented by a mapping. Finally, the parameters of the actual distribution were input into the inverse mapping, and the kinetic parameters were estimated as the outputs. The estimated kinetic parameters were validated using statistical techniques, which implied that the observed distribution function of the latent periods for the thresholds used in the estimation coincided reasonably with the simulated one based on the estimated parameters.

中文翻译：

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使用聚焦光束反射率测量通过随机积分对随机初级成核动力学进行参数估计

估计L-精氨酸的间歇冷却结晶的随机一次成核的动力学参数。过程分析工具很难检测到第一个核。在这项研究中，用聚焦光束反射率测量重复测量了将晶体总数增加到预定阈值的潜伏期。因此，由于一次和二次成核的随机行为，每次测量的潜伏期都不同。因此，首先，对于一次成核动力学参数的一些组合，通过蒙特卡洛模拟来估计潜伏期的分布。在仿真中，求解了种群和质量平衡方程的随机积分。然后，估计潜伏期的分布参数，并将其与一次成核的动力学参数相关联。所产生的相关性由映射表示。最后，将实际分布的参数输入到逆映射中，并将动力学参数估计为输出。使用统计技术对估计的动力学参数进行了验证，这意味着用于估计的阈值的潜伏期的观测分布函数与基于估计参数的模拟合理地吻合。并将动力学参数估计为输出。使用统计技术对估计的动力学参数进行了验证，这意味着用于估计的阈值的潜伏期的观测分布函数与基于估计参数的模拟合理地吻合。并将动力学参数估计为输出。使用统计技术对估计的动力学参数进行了验证，这意味着用于估计的阈值的潜伏期的观测分布函数与基于估计参数的模拟合理地吻合。