基于生成对抗网络的化工过程低成本mGAN-NN建模

doi:10.16085/j.issn.1000-6613.2024-0540

摘要/Abstract

摘要：

使用深度学习建立化工过程模型往往面临数据获取成本高、数据短缺等问题。对此，本文提出了一种基于生成对抗网络（GANs）的低成本数据增强建模方法mGAN-NN。该方法在GANs生成器的损失函数中引入最大均值差异（MMD）判据，提高了生成数据与真实数据分布特征的相似度；然后利用生成的数据建立神经网络模型，进而使用真实实验数据对所建模型进行调整。这种方法明显的优势在于，即使在数据量有限的情况下，也能构建出鲁棒性强的模型。采用此方法建立了微反应器中制备脂肪酸甲酯磺酸盐（MES）活性物质量分数的预测模型，其拟合系数（R²）可达0.91，相较神经网络（ANN）提高了236%，相较支持向量机回归（SVR）提高了32%。同时，平均绝对误差（MAE）降至3.38，相较ANN减小了58%，相较SVR减小了45%，展示出了较高的泛化性以及预测精度。

关键词: 生成对抗网络, 数据增强, 微反应器, 建模, 算法

Abstract:

Establishing chemical process models using deep learning often faces challenges such as high costs of data acquisition and scarcity of data. In response to this, this paper proposed a low-cost data augmentation modeling method called mGAN-NN, which was based on generative adversarial networks (GANs). The method introduced the maximum mean discrepancy (MMD) into the loss function of the generator of GANs, thereby improving the similarity of the distribution features between the generated data and the real data. Then, the generated data were used to establish a neural network model, which was subsequently fine-tuned using real experimental data. The significant advantage of this method was its ability to construct robust models with limited data. The proposed method was applied to establish a prediction model for the active content of fatty acid methyl ester sulfonate (MES) in a microreactor. The model achieved a coefficient of determination (R²) of 0.91, representing a 236% improvement over the traditional neural network (ANN) and a 32% improvement over the support vector regression (SVR). Moreover, the mean absolute error (MAE) was reduced to 3.38, which was 58% lower than that of ANN and 45% lower than that of SVR, demonstrating excellent generalization and prediction accuracy.

Key words: generative adversarial networks, data augmentation, microreactor, modeling, algorithm

中图分类号:

TP183

李梓良, 张玮, 胡恒, 王盈锦, 徐娜. 基于生成对抗网络的化工过程低成本mGAN-NN建模[J]. 化工进展, 2025, 44(4): 1978-1986.

LI Ziliang, ZHANG Wei, HU Heng, WANG Yingjin, XU Na. mGAN-NN method for low-cost chemical process modeling based on generative adversarial networks[J]. Chemical Industry and Engineering Progress, 2025, 44(4): 1978-1986.

图/表 16

图1 生成对抗网络结构示意图

图2 mGAN-NN建模示意图

图3 反应装置结构示意图

表1 气液微磺化系统制备MES的工艺条件变化范围

工艺条件	最小值	最大值
磺化温度/℃	60	90
SO₃-MS摩尔比	0.8	1.6
老化时间/min	20	60
老化温度/℃	50	100

表2 气液微磺化系统制备MES部分实验数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	60	1.2	40	80	66.50
2	60	1.2	20	80	61.56
3	60	1.2	60	80	68.83
4	60	1.2	20	60	41.64
5	60	1.2	40	60	46.16
6	60	1.2	60	60	48.32
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
59	80	1.6	20	80	79.50
60	80	1.6	40	80	81.30
61	80	1.6	60	80	83.11
62	80	1.6	20	60	73.42
63	80	1.6	40	60	74.87
64	90	1.6	60	60	77.74
65	90	1.6	30	70	80.92
66	90	1.6	50	70	81.75

表2 气液微磺化系统制备MES部分实验数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	60	1.2	40	80	66.50
2	60	1.2	20	80	61.56
3	60	1.2	60	80	68.83
4	60	1.2	20	60	41.64
5	60	1.2	40	60	46.16
6	60	1.2	60	60	48.32
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
59	80	1.6	20	80	79.50
60	80	1.6	40	80	81.30
61	80	1.6	60	80	83.11
62	80	1.6	20	60	73.42
63	80	1.6	40	60	74.87
64	90	1.6	60	60	77.74
65	90	1.6	30	70	80.92
66	90	1.6	50	70	81.75

表3 GANs与mGANs所用结构参数

超参数类型	生成器	鉴别器
网络结构	6-10-10-5	5-10-10-1
激活函数	Leaky ReLU	Leaky ReLU、Sigmoid
优化器	SGD（0.04）	SGD（0.08）

表4 基于GANs的部分生成数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	83.27961	1.161183	47.10971	81.89867	74.68918
2	86.30283	1.542565	33.57725	79.20454	86.05156
3	82.25621	1.208560	53.55812	74.62836	71.41930
4	72.73076	1.220473	56.39626	75.22123	68.25865
5	76.97067	1.519895	41.43793	93.79734	82.20417
6	79.32157	1.191388	50.84287	72.67689	68.36164
7	84.47624	1.593823	44.77314	87.52930	90.21171
8	88.42137	1.576962	48.98761	76.60762	88.80512
9	87.34681	1.532673	36.57060	81.57395	85.15310
10	72.72450	1.243067	52.85953	76.38229	59.94243
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
321	72.43844	1.418137	33.72336	86.06310	71.13159
322	87.74216	1.430092	25.99235	76.36067	69.06212
323	68.57316	1.467843	34.66464	93.57615	78.95146
324	67.15241	1.368005	48.84736	82.07817	45.17392
325	78.86573	1.366410	35.56188	68.77293	74.44617
326	89.28074	1.590475	22.41597	89.54008	87.87235
327	72.53215	1.027140	54.35593	61.22787	51.96266
328	65.12947	1.431815	24.65830	86.62648	51.53531
329	88.03262	1.594808	15.37602	89.72716	88.92242
330	71.01549	1.508555	27.28651	80.10245	75.49440

表4 基于GANs的部分生成数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	83.27961	1.161183	47.10971	81.89867	74.68918
2	86.30283	1.542565	33.57725	79.20454	86.05156
3	82.25621	1.208560	53.55812	74.62836	71.41930
4	72.73076	1.220473	56.39626	75.22123	68.25865
5	76.97067	1.519895	41.43793	93.79734	82.20417
6	79.32157	1.191388	50.84287	72.67689	68.36164
7	84.47624	1.593823	44.77314	87.52930	90.21171
8	88.42137	1.576962	48.98761	76.60762	88.80512
9	87.34681	1.532673	36.57060	81.57395	85.15310
10	72.72450	1.243067	52.85953	76.38229	59.94243
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
321	72.43844	1.418137	33.72336	86.06310	71.13159
322	87.74216	1.430092	25.99235	76.36067	69.06212
323	68.57316	1.467843	34.66464	93.57615	78.95146
324	67.15241	1.368005	48.84736	82.07817	45.17392
325	78.86573	1.366410	35.56188	68.77293	74.44617
326	89.28074	1.590475	22.41597	89.54008	87.87235
327	72.53215	1.027140	54.35593	61.22787	51.96266
328	65.12947	1.431815	24.65830	86.62648	51.53531
329	88.03262	1.594808	15.37602	89.72716	88.92242
330	71.01549	1.508555	27.28651	80.10245	75.49440

图4 基于GANs生成的数据分布

图5 基于mGANs生成的数据分布

表5 基于mGANs的部分生成数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	81.94295	1.589290	31.05080	53.97002	71.62635
2	85.71674	1.421059	54.15529	56.86942	79.99052
3	82.14872	1.557661	57.56562	82.33545	86.41391
4	65.56925	1.539463	38.97818	89.36489	84.61324
5	65.05901	1.102045	25.34751	69.97029	50.40371
6	83.24004	1.025123	45.12223	93.86857	79.09521
7	84.33916	1.494957	50.29488	61.54058	81.87912
8	85.11316	1.566982	18.85036	69.96391	82.20627
9	87.60520	1.297932	53.58565	68.32281	80.14999
10	55.89097	1.438010	31.89855	63.09228	53.58462
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
321	80.31209	1.484724	18.93740	91.06848	85.47252
322	89.57048	1.075123	45.77487	86.36514	74.65433
323	78.25847	0.994669	57.22416	66.59568	47.54068
324	70.41580	1.226993	58.36410	88.38225	81.18542
325	88.71901	1.592107	59.51335	81.95000	87.65301
326	85.77462	0.895628	39.64196	88.54185	65.74517
327	71.96869	1.531543	32.88764	75.05962	77.64820
328	53.58275	1.583197	52.03275	78.53060	80.30246
329	81.92057	1.586589	56.66399	58.78035	81.71073
330	63.53111	1.173218	58.87420	87.53125	73.50951

表5 基于mGANs的部分生成数据

编号	磺化温度/℃	SO₃-MS 摩尔比	老化时间/min	老化温度/℃	活性物质量分数/%
1	81.94295	1.589290	31.05080	53.97002	71.62635
2	85.71674	1.421059	54.15529	56.86942	79.99052
3	82.14872	1.557661	57.56562	82.33545	86.41391
4	65.56925	1.539463	38.97818	89.36489	84.61324
5	65.05901	1.102045	25.34751	69.97029	50.40371
6	83.24004	1.025123	45.12223	93.86857	79.09521
7	84.33916	1.494957	50.29488	61.54058	81.87912
8	85.11316	1.566982	18.85036	69.96391	82.20627
9	87.60520	1.297932	53.58565	68.32281	80.14999
10	55.89097	1.438010	31.89855	63.09228	53.58462
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
321	80.31209	1.484724	18.93740	91.06848	85.47252
322	89.57048	1.075123	45.77487	86.36514	74.65433
323	78.25847	0.994669	57.22416	66.59568	47.54068
324	70.41580	1.226993	58.36410	88.38225	81.18542
325	88.71901	1.592107	59.51335	81.95000	87.65301
326	85.77462	0.895628	39.64196	88.54185	65.74517
327	71.96869	1.531543	32.88764	75.05962	77.64820
328	53.58275	1.583197	52.03275	78.53060	80.30246
329	81.92057	1.586589	56.66399	58.78035	81.71073
330	63.53111	1.173218	58.87420	87.53125	73.50951

表6 基于GANs与mGANs生成的数据与真实数据的分布距离

评价指标	GANs	mGANs
W距离	113.40	74.45
MMD	0.4129	0.0056

表7 预测模型使用的神经网络结构参数

神经网络结构	激活函数	优化器	权重衰减
4-8-12-8-1	Leaky ReLU（0.02）	SGD（0.01）	0.001

表8 8次随机划分数据集基于mGAN-NN建模的性能

评价指标	（a）	（b）	（c）	（d）	（e）	（f）	（g）	（h）	平均值
训练集R²	0.82	0.82	0.87	0.90	0.87	0.88	0.85	0.88	0.86
测试集R²	0.83	0.96	0.92	0.83	0.91	0.90	0.93	0.96	0.91
训练集MAE	3.93	3.32	3.37	3.11	3.31	3.40	3.04	3.10	3.32
测试集MAE	3.42	2.86	3.18	4.63	3.10	3.84	2.98	3.05	3.38

表9 8次随机划分66组实验数据集基于ANN的模型性能

评价指标	（a）	（b）	（c）	（d）	（e）	（f）	（g）	（h）	平均值
训练集R²	0.097	0.850	0.007	0.860	0.001	0.037	0.440	0.060	0.294
测试集R²	0.006	0.800	0.030	0.820	0.004	0.067	0.430	0.010	0.271
训练集MAE	9.140	3.800	9.650	3.470	9.670	10.280	7.010	8.960	7.748
测试集MAE	10.930	4.200	7.830	5.600	9.460	8.710	6.830	11.50	8.133

表10 8次随机划分66组实验数据集基于SVR的模型性能

评价指标	（a）	（b）	（c）	（d）	（e）	（f）	（g）	（h）	平均值
训练集R²	0.85	0.83	0.84	0.83	0.87	0.83	0.83	0.83	0.84
测试集R²	0.61	0.75	0.67	0.79	0.45	0.76	0.75	0.76	0.69
训练集MAE	4.97	4.94	4.62	4.97	4.40	4.72	4.70	5.01	4.79
测试集MAE	4.90	5.98	6.71	5.57	7.85	5.98	6.25	5.91	6.14

表11 最优条件下3次独立重复实验结果

次数	活性物质量分数/%
1	88.15
2	89.14
3	90.67
平均值	89.32

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