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, 新型拉丁超立方采样, 方差, 模拟, Monte Carlo模拟

Abstract:

In the sampling procedure of the stochastic reconstruction method, the number of samples for each structural attribute is unequal and varying. To use Latin hypercube sampling to reduce the variance of the random reconstruction model, based on the characteristics of the sampling process of the stochastic reconstruction method and the principle of Latin hypercube sampling, a new Latin hypercube sampling method suitable for the stochastic reconstruction method was proposed. In the novel Latin hypercube sampling, the sampling number for each structural attribute is determined by the values of the preorder structural attribute. A Latin hypercube sampling-based stochastic reconstruction model for a vacuum gas oil sample was developed. The determination of the sampling number for each structural attribute 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 stochastic reconstruction model. The results showed that the novel Latin hypercube sampling method can significantly reduce the variance and objective function value of the model. As the molecular number ranging from 1000 to 50000, 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 new model when the molecular number is 2000 is consistent with the performance of the traditional model when the molecular number is 10000, and the computing time of the new model is only 22.54% of that of the traditional model.

Key words: stochastic reconstruction method, novel Latin hypercube sampling, variance, 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, 2024, 75(5): 1939-1950.

Guangyao ZHAO, Minglei YANG, Feng QIAN. Variance reduction sampling strategy-based stochastic reconstruction method[J]. CIESC Journal, 2024, 75(5): 1939-1950.

图/表 14

图1 简单随机采样(a)和拉丁超立方采样(b)

Fig.1 Simple random sampling (a) and Latin hypercube sampling (b)

图2 结合新型拉丁超立方采样生成虚拟混合物中结构特征数值的流程示意图

Fig.2 Diagram for generation process of values of structural attributes in pseduo mixtures with novel Latin hypercube sampling

图3 基于新型拉丁超立方采样的随机重构法流程示意图

Fig.3 Diagram of novel Latin hypercube sampling-based stochastic reconstruction method

表1 蜡油样本的宏观性质

Table 1 Properties of VGO sample

性　质	实验值	性　质	实验值	性　质	实验值
密度/(g/cm³)	0.9127	硫元素组成/10^-6		模拟蒸馏/K
碳元素/%(质量分数)	85.68	四氢苯并噻吩	566	初馏点	482
氢元素/%(质量分数)	12.38	苯并噻吩	7681	5%	605
硫元素/%(质量分数)	2.24	四氢二苯并噻吩	853	10%	637
氮元素/10^-6	456	二苯并噻吩	7141	20%	670
氢碳比(摩尔比)	1.72	四氢苯并萘噻吩	1269	30%	693
SARA组成/%(质量分数)		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/%(质量分数)		60%	739
同系物组成/%(质量分数)		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

表2 结构特征的设定

Table 2 Setting of structural attributes

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

表3 模型参数的边界和直方图分布中参数的约束

Table 3 Boundaries for parameters and constraints for parameters in histogram distributions

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

图4 分子构造步骤示意图

Fig.4 Building diagram of molecular construction

表4 链烷烃分子中结构特征值的匹配过程

Table 4 Alignment of structural attribute values in paraffins

分子序数	SA₁	SA₂	SA₃	SA₄
1	s_1,1	—	—	—
2	s_2,1	s_1,2	s_1,3	s_1,4
3	s_3,1	s_2,2	—	s_2,4
4	s_4,1	—	—	—
5	s_5,1	s_3,2	s_2,3	s_3,4
6	s_6,1	s_4,2	—	s_4,4
︙	︙	︙	︙	︙
k₂	$s_{k_{2}, 1}$	︙	$s_{n_{3}, 3}$	︙
︙	︙	︙	—	︙
k₁	$s_{k_{1}, 1}$	$s_{n_{2}, 1}$	—	$s_{n_{4}, 4}$
︙	︙	—	—	—
n	$s_{n_{1}, 1}$	—	—	—

表4 链烷烃分子中结构特征值的匹配过程

Table 4 Alignment of structural attribute values in paraffins

分子序数	SA₁	SA₂	SA₃	SA₄
1	s_1,1	—	—	—
2	s_2,1	s_1,2	s_1,3	s_1,4
3	s_3,1	s_2,2	—	s_2,4
4	s_4,1	—	—	—
5	s_5,1	s_3,2	s_2,3	s_3,4
6	s_6,1	s_4,2	—	s_4,4
︙	︙	︙	︙	︙
k₂	$s_{k_{2}, 1}$	︙	$s_{n_{3}, 3}$	︙
︙	︙	︙	—	︙
k₁	$s_{k_{1}, 1}$	$s_{n_{2}, 1}$	—	$s_{n_{4}, 4}$
︙	︙	—	—	—
n	$s_{n_{1}, 1}$	—	—	—

表5 在不同工况中采用的分子数量

Table 5 Number of molecules in different cases

工况	分子数量	工况	分子数量	工况	分子数量
1	1000	6	6000	11	20000
2	2000	7	7000	12	30000
3	3000	8	8000	13	40000
4	4000	9	9000	14	50000
5	5000	10	10000

图5 两个模型的目标函数值对比

Fig. 5 Comparison of objective function values in two models

图 6 两种模型中参数评价过程的标准差对比

Fig.6 Comparison of standard deviations for parameter evaluation process in two models

表6 宏观性质计算值和实验值的对比

Table 6 Comparison of bulk properties between estimation and experiment

性　质	实验值	文献^[48]	传统模型	本模型
密度/(g/cm³)	0.9127	0.9170	0.9269	0.9292
碳元素/%(质量分数)	85.68	85.40	85.54	85.51
氢元素/%(质量分数)	12.38	12.30	12.30	12.18
硫元素/%(质量分数)	2.24	2.24	2.12	2.26
氮元素/10^-6	456	608	458	448
氢碳比(摩尔比)	1.72	1.72	1.72	1.71
SARA组成/%(质量分数)
饱和烃	64.2	64.1	63.6	63.8
芳烃	35.8	35.9	36.4	36.2
同系物组成/%(质量分数)
烷烃	22.1	21.3	23.2	21.9
环烷烃	42.0	42.8	39.9	41.9
单环芳烃	6.1	6.2	6.2	5.4
双环芳烃	12.5	13.2	11.5	11.9
三环芳烃	10.4	9.8	10.2	10.3
四环芳烃	6.2	5.0	5.9	5.7
五环芳烃	0.7	1.8	3.0	3.0
硫元素组成/10^-6
四氢苯并噻吩	566	577	555	491
苯并噻吩	7681	7772	8194	8469
四氢二苯并噻吩	853	904	853	981
二苯并噻吩	7141	7061	5916	6628
四氢苯并萘噻吩	1269	1126	845	1023
苯并萘噻吩	3393	3391	3300	3478
二苯并萘噻吩	1507	1592	1538	1514
¹³C核磁/%(质量分数)
脂肪烃 CH₃	14.5	13.0	14.6	14.2
脂肪烃 CH₂	52.5	54.3	56.0	55.9
脂肪烃 CH	16.2	15.9	15.7	16.0
芳烃 CH	9.7	8.0	5.4	5.2
芳烃取代位 C	6.3	4.3	4.0	4.3
芳烃桥位 C	0.8	4.4	4.3	4.4

图7 蒸馏数据计算值和实验值的对比

Fig.7 Comparison of distillation curve data between estimation and experiment

图8 传统模型和本模型的预测分子组成

Fig.8 Predicted molecular composition in the traditional model and the new model

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