基于降方差采样策略的随机重构法

doi:10.11949/0438-1157.20231182

摘要/Abstract

摘要：

在随机重构法的采样过程中，每一个结构特征需要的采样数量是不相等且变化的。为了将拉丁超立方采样用于降低随机重构模型的方差，基于随机重构法采样过程的特征和拉丁超立方采样的原理，提出了适用于随机重构法的新型拉丁超立方采样方法，探究了在多种分子数量设定情况下应用该方法对随机重构模型的方差和精度的影响。结果表明，应用该方法能够显著降低随机重构模型的方差，提高模型的精度，在分子数量为1000-50000范围内，新模型的标准差相较传统模型降低了71.36%-74.53%，目标函数值降低了1.69%-13.82%。综合模型精度和模拟过程的运算开销，选择4000-6000作为新模型最优的分子数量设定。

关键词: 随机重构法, 降方差采样策略, 方差, 模型, 模拟, 蒙特卡罗模拟

Abstract:

In the sampling procedure of the stochastic reconstruction(SR) method, the number of samples for each structural attribute is unequal and varying. To reduce the variance of the SR method by Latin hypercube sampling, a novel Latin hypercube sampling was proposed based on the characteristics of the sampling procedure in the SR method and the principle of Latin hypercube sampling. In the novel Latin hypercube sampling, the sampling number for each structural attribute is determined by the values of preorder structural attributes. A novel Latin hypercube sampling-based SR(DLHS-SR) model for a vacuum gas oil sample was developed. The determination of the sampling number for each structural attribute in the model was introduced in detail with the building diagram. Multiple cases with different predefined molecular numbers were designed to investigate the effects of the novel Latin hypercube sampling on the variance and accuracy of the DLHS-SR model. The results showed that the novel Latin hypercube sampling can significantly reduce the variance and objective function value of the model. As the molecular number ranging from 1,000 to 50,000, the standard deviations of the new model are 71.36%-74.53% lower than the traditional model, and the objective function values are 1.69%-13.82% lower than the traditional model. Based on the model accuracy and the computational cost of the simulation process, 4000-6000 was selected as the optimal molecule numbers for the new model. By comparing the values of objective function, bulk properties and mass fraction distributions in saturates and aromatics, it was found that the performance of the DLHS-SR model when the molecular number is 2000 is consistent with the performance of the traditional SR when the molecular number is 10000, and the computing time of the DLHS-SR model is only 22.54% of that of the traditional SR.

Key words: stochastic reconstruction method, novel Latin hypercube sampling, variance, model, simulation, Monte Carlo simulation

中图分类号:

TQ 028.8

赵光耀, 杨明磊, 钱锋. 基于降方差采样策略的随机重构法[J]. 化工学报, DOI: 10.11949/0438-1157.20231182.

Guangyao ZHAO, Minglei YANG, Feng QIAN. Variance reduction sampling strategy-based stochastic reconstruction method[J]. CIESC Journal, DOI: 10.11949/0438-1157.20231182.

图/表 14

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性质	实验值	性质	实验值	性质	实验值
密度/g·cm^-3	0.9127	硫元素组成/wppm of S		模拟蒸馏/K
碳元素/wt%	85.68	四氢苯并噻吩	566	初馏点	482
氢元素/wt%	12.38	苯并噻吩	7681	5%	605
硫元素/wt%	2.24	四氢二苯并噻吩	853	10%	637
氮元素/wppm	456	二苯并噻吩	7141	20%	670
氢碳比/mol·mol^-1	1.72	四氢苯并萘噻吩	1269	30%	693
SARA组成/wt%		苯并萘噻吩	3393	40%	710
饱和烃	64.2	二苯并萘噻吩	1507	50%	725
芳烃	35.8	¹³C核磁/wt%		60%	739
同系物组成/wt%		脂肪烃 CH₃	14.5	70%	753
烷烃	22.1	脂肪烃 CH₂	52.5	80%	768
环烷烃	42.0	脂肪烃 CH	16.2	90%	785
单环芳烃	6.1	芳烃 CH	9.7	95%	797
双环芳烃	12.5	芳烃取代位 C	6.3	终馏点	827
三环芳烃	10.4	芳烃桥位 C	0.8
四环芳烃	6.2
五环芳烃	0.7

性质	实验值	性质	实验值	性质	实验值
密度/g·cm^-3	0.9127	硫元素组成/wppm of S		模拟蒸馏/K
碳元素/wt%	85.68	四氢苯并噻吩	566	初馏点	482
氢元素/wt%	12.38	苯并噻吩	7681	5%	605
硫元素/wt%	2.24	四氢二苯并噻吩	853	10%	637
氮元素/wppm	456	二苯并噻吩	7141	20%	670
氢碳比/mol·mol^-1	1.72	四氢苯并萘噻吩	1269	30%	693
SARA组成/wt%		苯并萘噻吩	3393	40%	710
饱和烃	64.2	二苯并萘噻吩	1507	50%	725
芳烃	35.8	¹³C核磁/wt%		60%	739
同系物组成/wt%		脂肪烃 CH₃	14.5	70%	753
烷烃	22.1	脂肪烃 CH₂	52.5	80%	768
环烷烃	42.0	脂肪烃 CH	16.2	90%	785
单环芳烃	6.1	芳烃 CH	9.7	95%	797
双环芳烃	12.5	芳烃取代位 C	6.3	终馏点	827
三环芳烃	10.4	芳烃桥位 C	0.8
四环芳烃	6.2
五环芳烃	0.7

序数	结构特征	缩写	分布类型	数值范围	参数	采样数量
1	分子类型	SA₁	直方图分布	1,2或3	x₁, x₂	n₁
2	链烷烃上是否存在侧链	SA₂	直方图分布	0或1	x₃	n₂
3	链烷烃上侧链的数量	SA₃	直方图分布	1,2或3	x₄, x₅	n₃
4	链烷烃的长度	SA₄	伽马分布	10-40	x₆, x₇	n₄
5	脂肪环数量	SA₅	伽马分布	1-6	x₈, x₉	n₅
6	苯环数量	SA₆	伽马分布	1-5	x₁₀, x₁₁	n₆
7	芳烃中脂肪环数量	SA₇	直方图分布	0,1或2	x₁₂, x₁₃	n₇
8	噻吩环数量	SA₈	直方图分布	0或1	x₁₄	n₈
9	吡咯环数量	SA₉	直方图分布	0或1	x₁₅	n₉
10	吡啶环数量	SA₁₀	直方图分布	0或1	x₁₆	n₁₀
11	环状结构上侧链的数量	SA₁₁	直方图分布	1,2,3或4	x₁₇, x₁₈, x₁₉	n₁₁
12	环状结构上侧链的长度	SA₁₂	伽马分布	1-29	x₂₀, x₂₁	n₁₂

序数	结构特征	缩写	分布类型	数值范围	参数	采样数量
1	分子类型	SA₁	直方图分布	1,2或3	x₁, x₂	n₁
2	链烷烃上是否存在侧链	SA₂	直方图分布	0或1	x₃	n₂
3	链烷烃上侧链的数量	SA₃	直方图分布	1,2或3	x₄, x₅	n₃
4	链烷烃的长度	SA₄	伽马分布	10-40	x₆, x₇	n₄
5	脂肪环数量	SA₅	伽马分布	1-6	x₈, x₉	n₅
6	苯环数量	SA₆	伽马分布	1-5	x₁₀, x₁₁	n₆
7	芳烃中脂肪环数量	SA₇	直方图分布	0,1或2	x₁₂, x₁₃	n₇
8	噻吩环数量	SA₈	直方图分布	0或1	x₁₄	n₈
9	吡咯环数量	SA₉	直方图分布	0或1	x₁₅	n₉
10	吡啶环数量	SA₁₀	直方图分布	0或1	x₁₆	n₁₀
11	环状结构上侧链的数量	SA₁₁	直方图分布	1,2,3或4	x₁₇, x₁₈, x₁₉	n₁₁
12	环状结构上侧链的长度	SA₁₂	伽马分布	1-29	x₂₀, x₂₁	n₁₂

参数	上限	递增约束	参数	下限	上限	参数	下限	上限
x₁, x₂	1	x₁< x₂	x₆	1	20	x₇	9	41
x₄, x₅	1	x₄< x₅	x₈	0	20	x₉	0	7
x₁₂, x₁₃	1	x₁₂< x₁₃	x₁₀	0	20	x₁₁	0	6
x₁₇, x₁₈, x₁₉	1	x₁₇< x₁₈< x₁₉	x₂₀	1	20	x₂₁	0	30
x₃, x₁₄, x₁₅, x₁₆	1