基于多阶段LHS-EPRCC方法的青霉素发酵过程建模

doi:10.16182/j.issn1004731x.joss.25-0948E

摘要/Abstract

摘要：

聚焦于生产环境变化条件下的微生物发酵过程建模问题，并提出了一种全新的思路。考虑到微生物不同成长阶段的动态特征不同，引入了多阶段灵敏度分析的概念，对各生长阶段分别展开研究。利用模糊C均值(fuzzy c-means, FCM)算法，在标称条件下对过程数据进行聚类分析，划分青霉素发酵过程各生长阶段。采用带有偏秩相关系数的拉丁超立方抽样(latin hypercube sampling with partial rank correlation coefficient, LHS-EPRCC)方法，对各阶段分别进行灵敏度分析，识别出符合阶段性生长特征的重要性参数集(importance parameter set, IPS)。通过对IPS的重新估计与修正来提高模型预测的准确性。在一个偏离标称条件的青霉素发酵过程中，应用该方法对模型进行修正。仿真结果表明：修正后的模型能够与实际过程保持一致，验证了所提出的多阶段灵敏度分析方法在应对复杂发酵过程和环境不确定性方面的有效性。

关键词: 青霉素发酵过程, FCM算法, LHS-EPRCC方法, 重要性参数集, 模型修正

Abstract:

This paper focused on the modeling of microbial fermentation processes under varying production environments and proposed a novel approach. Considering that the dynamic characteristics of microorganisms differ across growth stages, we introduced the concept of multi-stage sensitivity analysis, in which each stage was investigated separately. The fuzzy C-means (FCM) algorithm was employed to cluster process data under nominal conditions, thereby dividing the penicillin fermentation process into distinct growth stages. Based on this division, the Latin hypercube sampling with partial rank correlation coefficient (LHS-EPRCC) method was applied to conduct sensitivity analysis for each stage, identifying an importance parameter set (IPS) that corresponds to the stage-specific growth characteristics. Re-estimation and correction of the IPS were then performed to enhance the predictive accuracy of the model. In a penicillin fermentation process deviating from nominal conditions, the proposed method was applied for model correction. Simulation results demonstrate that the corrected model aligns well with the actual process, thereby verifying the effectiveness of the proposed multi-stage sensitivity analysis approach in addressing complex fermentation processes and environmental uncertainties.

Key words: penicillin fermentation process, FCM algorithm, LHS-EPRCC method, importance parameter set, model correction

中图分类号:

TP391.9

李权,苏鹏,万海英等 . 基于多阶段LHS-EPRCC方法的青霉素发酵过程建模[J]. 系统仿真学报, 2026, 38(5): 1255-1276.

Li Quan,Su Peng,Wan Haiying,et al . Modeling of Penicillin Fermentation Process Based on a Multi-stage LHS-EPRCC Method[J]. Journal of System Simulation, 2026, 38(5): 1255-1276.

图/表 16

Variable	Value
Biomass concentration $X 0$ /(g/L)	0.1
Penicillin concentration $P 0$ /(g/L)	0
Glucose concentration $S 0$ /(g/L)	15
Initial culture volume $V 0$ /L	100
Feed flow rate $F$ /(L/h)	0.04

Parameter	Value	Parameter	Value
$u X$	0.092	$K H$	0.04
$K X$	0.15	$Y X / S$	0.45
$u P$	0.005	$Y P / S$	0.9
$K P$	0.000 2	$m X$	0.14
$K I$	0.1	$S f$	600

Rank	Glucose				Biomass					Penicillin
Rank	$k i$	$γ ¯ k 1, y 1 1$	$k i$	$G ¯ k 1, y 1 1$	$k i$	$γ ¯ k 1, y 2 1$	$k i$	$γ ¯ k 1, y 2 1$	$k i$	$γ ¯ k 1, y 3 1$	$k i$	$γ ¯ k 1, y 3 1$
1	$u X *$	-0.980 5	$u X * *$	0.446 2	$u X *$	0.999 9	$u X * *$	0.999 3	$K I *$	0.960 4	$K I * *$	0.4232
2	$S f *$	0.973 5	$S f * *$	0.510 4	$K X *$	-0.657 1	$Y X / S$	0.000 1	$u X *$	0.910 0	$u X * *$	0.416 6
3	$Y X / S *$	0.909 0	$Y X / S * *$	0.045 1	$S f *$	0.295 6	$K X$	6.34×10^-5	$u P *$	0.908 4	$u P * *$	0.152 0
4	$m X$	-0.169 5	$m X$	0.000 2	$Y X / S *$	0.202 1	$S f$	3.99×10^-5	$K H *$	-0.486 3	$K H * *$	0.006 4
5	$K X$	0.049 4	$K X$	5.24×10^-5	$K I$	-0.028 2	$m X$	4.53×10^-7	$S f *$	-0.451 1	$S f * *$	0.006 2
6	$u P$	0.038 9	$K I$	1.07×10^-8	$Y P / S$	0.023 2	$K I$	5.75×10^-9	$Y X / S$	-0.224 2	$Y X / S * *$	0.004 9
7	$k d u m m y$	-0.028 0	$u P$	1.93×10^-9	$u P$	-0.017 9	$u P$	1.39×10^-9	$Y P / S$	0.038 4	$K X$	0.000 2
8	$Y P / S$	-0.023 1	$Y P / S$	1.21×10^-9	$m X$	-0.012 9	$K H$	2.25×10^-10	$k d u m m y$	-0.029 6	$m X$	2.23×10^-5
9	$K H$	-0.017 7	$K H$	1.86×10^-10	$k d u m m y$	-0.011 9	$Y P / S$	1.88×10^-11	$m X$	0.024 8	$Y P / S$	1.02×10^-8
10	$K I$	-0.012 4	$K P$	2.33×10^-18	$K H$	-0.010 6	$K P$	5.09×10^-20	$K X$	-0.024 9	$K P$	6.20×10^-13
11	$K P$	-0.006 9			$K P$	-0.006 3			$K P$	-0.023 0

Rank	Glucose				Biomass				Penicillin
Rank	$k i$	$γ ¯ k 3, y 1 1$	$k i$	$G ¯ k 3, y 1 1$	$k i$	$γ ¯ k 3, y 2 1$	$k i$	$γ ¯ k 3, y 2 1$	$k i$	$γ ¯ k 3, y 3 1$	$k i$	$γ ¯ k 3, y 3 1$
1	$Y X / S *$	-0.973 2	$Y X / S * *$	0.510 4	$S f *$	0.967 8	$S f * *$	0.627 0	$S f *$	0.919 1	$S f * *$	0.350 2
2	$m X *$	-0.947 8	$m X * *$	0.243 7	$m X *$	-0.921 7	$m X * *$	0.260 8	$K H *$	-0.886 4	$m X * *$	0.261 0
3	$S f *$	0.907 8	$S f * *$	0.133 5	$Y X / S *$	0.725 0	$Y X / S * *$	0.077 0	$m X *$	-0.879 9	$K H * *$	0.230 2
4	$u X *$	0.755 4	$u X * *$	0.042 0	$u P *$	-0.638 3	$Y P / S * *$	0.033 1	$u P *$	0.774 9	$u P * *$	0.102 2
5	$u P *$	-0.738 8	$Y P / S * *$	0.037 3	$Y P / S *$	0.624 2	$u P * *$	0.031 0	$Y P / S *$	0.579 5	$Y X / S * *$	0.074 4
6	$Y P / S *$	0.732 2	$u P * *$	0.035 9	$u X *$	-0.360 3	$S f *$	0.014 5	$Y X / S *$	-0.449 2	$Y P / S * *$	0.032 6
7	$K P$	0.257 8	$K I * *$	0.003 4	$K I$	-0.116 4	$K I$	0.000 6	$u X *$	0.177 6	$u X * *$	0.018 22
8	$K X$	0.239 7	$K X * *$	0.002 2	$k d u m m y$	0.014 2	$K P$	8.82×10^-5	$K I$	0.144 3	$K I * *$	0.001
9	$K I$	0.234 7	$K P * *$	0.002 1	$K P$	0.013 7	$K X$	3.42×10^-5	$K P$	-0.078 1	$K P$	0.000 5
10	$K H$	-0.033 9	$K H$	5.13×10^-6	$K H$	0.013 7	$K H$	1.04×10^-7	$K X$	0.055 4	$K X$	0.000 1
11	$k d u m m y$	0.027 5			$K X$	-0.008 1			$k d u m m y$	0.017 5

Rank	Glucose				Biomass				Penicillin
Rank	$k i$	$γ ¯ k 2, y 1 1$	$k i$	$G ¯ k 2, y 1 1$	$k i$	$γ ¯ k 2, y 2 1$	$k i$	$γ ¯ k 2, y 2 1$	$k i$	$γ ¯ k 2, y 3 1$	$k i$	$γ ¯ k 2, y 3 1$
1	$m X *$	-0.899 5	$Y X / S * *$	0.464 77	$u X *$	-0.743 0	$u X * *$	0.085 5	$u P *$	0.726 2	$Y X / S * *$	0.266 4
2	$S f *$	0.898 5	$m X * *$	0.209 0	$S f *$	0.731 2	$S f * *$	0.469 8	$K H *$	-0.615	$u P * *$	0.193 3
3	$Y X / S *$	-0.855 6	$S f * *$	0.149 44	$Y X / S *$	0.677 3	$Y X / S * *$	0.325 9	$Y X / S *$	0.413	$u X * *$	0.192 2
4	$u P *$	-0.696 1	$u X * *$	0.114 55	$m X *$	-0.562 5	$m X * *$	0.130 2	$S f *$	0.364 3	$S f * *$	0.185 2
5	$Y P / S *$	0.690 2	$Y P / S * *$	3.80×10^-2	$u P *$	-0.318 1	$Y P / S * *$	0.014 1	$K I *$	0.292 7	$m X * *$	0.161 5
6	$u X *$	0.648 4	$u P * *$	3.55×10^-2	$Y P / S *$	0.314 1	$u P * *$	0.013 2	$u X *$	0.183	$K H * *$	0.150 0
7	$K X$	0.198 7	$K X * *$	4.86×10^-3	$K X *$	-0.228 7	$K I$	0.000 9	$m X *$	-0.155 3	$Y P / S * *$	0.022 7
8	$K P$	0.063 2	$K I$	8.99×10^-4	$K I$	-0.112 3	$K X$	0.000 3	$K X *$	-0.119 3	$K I * *$	0.014 0
9	$K H$	-0.027 2	$K P$	1.19×10^-4	$K P$	-0.019 4	$K P$	1.26×10^-5	$Y P / S$	0.074 3	$K X$	0.000 3
10	$K I$	-0.027 1	$K H$	5.72×10^-7	$k d u m m y$	0.017 4	$K H$	6.03×10^-9	$K P$	-0.042 7	$K P$	0.000 2
11	$k d u m m y$	0.021 2			$K H$	-0.009 5			$k d u m m y$	-0.010 9

Parameter	Value	Parameter	Value
$u X$	0.094 8	$K H$	0.036 7
$K X$	0.137 4	$Y X / S$	0.409 3
$u P$	0.005 5	$Y P / S$	0.881 3
$K P$	1.988 0×10^-4	$m X$	0.014 0
$K I$	0.098 1	$S f$	647.081 1

Metabolite	Nominal model		Modified model
	Nominal model		IPS $(K 1, K 2, K 3)$		IPS $(K)$ ^[24]		Total parameter
	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Biomass	0.158 6	0.681 7	2.455 3×10^-6	0.000 9	1.859 7×10^-5	0.411 0	7.170 5×10^-7	0.000 3
Penicillin	0.072 5	0.240 9	1.164 8×10^-8	0.000 8	8.193 8×10^-6	0.022 1	2.978 2×10^-8	0.000 2
Glucose	0.243 1	0.226 0	1.238 8×10^-6	0.000 3	5.420 0×10^-5	0.113 9	8.161 7×10^-7	0.000 3

Modified model	P-value	Signed rank
IPS $(K 1, K 2, K 3)$	1.800 8×10^-216	1.220 9×10⁶
IPS $(K)$	1.852 8×10^-194	905 46
Total parameter	2.261 7×10^-216	1.220 7×10⁶

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