化工生产过程中的设备处于长周期连续运行的状态，金属疲劳、腐蚀、污渍等现象使设备的健康状态逐渐恶化，降低设备运行效率，甚至引发安全事故。换热器是一种广泛用于流程工业的重要设备，换热物流中的杂质、离子等会与管壁发生复杂的物理化学作用形成污垢，导致换热效率下降，甚至堵塞设备，必须定期对换热器进行清垢和维护。因此，准确预测换热器结垢状态，制定科学的换热器预测性维护方案，是保障换热器高效运行和延长其使用寿命的关键措施。本文提出一种基于卷积神经网络（CNN）和长短期记忆网络（LSTM）的换热器污垢因子预测方法，实现了换热器污垢因子的准确预测。将上述方法应用于原料预热系统，预测换热器的服役状态，采用遗传算法（GA）得到换热器预测性清垢的最优方案，保证换热器健康服役并减小维护操作对原料预热系统正常运行的影响。本文的主要结论如下：

（1）   提出了一种基于CNN-LSTM的换热器污垢因子预测模型。该模型综合考虑了影响换热器结垢的七个因素：流体类型、流体温度、流体速度、表面温度、操作时间、等效直径和流体氧含量。通过相关性分析，确认污垢因子的二次根与上述七个因素具有最强相关性，建立CNN和LSTM组合的神经网络模型，充分发挥CNN的强特征提取能力和LSTM的时间序列建模能力，实现对污垢因子的准确预测。

（2）   通过引入Dropout机制进一步提高所提出模型的泛化能力和预测精度。通过灵敏度分析优化Dropout比率、卷积步长和隐藏层神经元个数。经过优化的模型在所展示的数据集上可达到决定系数（R²）=0.9866，平均绝对误差（MAE）=1.196×10^-3，均方误差（MSE）=1.430×10^-4，优于多层感知器神经网络（MLPNN）模型（R²=0.9778）和传统的单一CNN（R²=0.8247）或LSTM（R²=0.7898）模型。

（3）   基于上述已训练的CNN-LSTM模型预测污垢因子并计算换热器污垢热阻，优化某原料预热过程的预测性清垢方案。目标函数为最小化换热器操作和维护的总费用，包括公用工程费、泵功费和维护费，公用工程费和泵功费基于上述CNN-LSTM模型预测的污垢因子得到。清垢方案的优化则采用遗传算法（GA）求解，在优化模型中充分考虑了工业应用场景需求，设定了合理的流速区间、禁止连续清垢等约束条件，确保了设备运行的安全性和优化方案的实用性。结果表明，优化后的预测性清垢方案比实际清垢方案降低了约28.68%费用。

本文提出的基于CNN-LSTM的换热器污垢因子预测方法对换热器污垢因子具有较高的预测准确性。基于对污垢因子的准确预测，进一步对原料预热系统的换热器清垢方案进行了优化，案例分析说明了所提出方法的准确性和可行性。为换热器的高效运行和工业设备预测性维护提供了新思路。

In chemical production processes, equipment typically operates under long-term, continuous conditions. However, phenomena such as metal fatigue, corrosion, and fouling gradually deteriorate the health condition of the equipment, reducing operational efficiency and potentially leading to safety incidents. Heat exchangers are critical devices widely employed in process industries. Impurities and ions present in the heat transfer fluids can interact with the tube walls through complex physicochemical mechanisms, resulting in fouling. This degrades heat transfer efficiency and may even cause blockage, necessitating periodic cleaning and maintenance. Therefore, accurately predicting the fouling condition of heat exchangers and formulating a scientifically sound predictive maintenance strategy are essential for ensuring efficient operation and prolonging service life. This study proposes a predictive method for heat exchanger fouling factors based on a Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) network, which enables accurate prediction of fouling behavior. The proposed method is applied to the raw material preheating system to forecast the service condition of heat exchangers, a Genetic Algorithm (GA) is then used to determine the optimal predictive cleaning schedule, ensuring the reliable operation of the heat exchangers while minimizing the impact of maintenance on the normal functioning of the preheating system. The main conclusions of this article are as follows:

(1) A CNN-LSTM-based prediction model for heat exchanger fouling factors is proposed. The model comprehensively considers seven key factors influencing fouling: fluid type, fluid temperature, fluid velocity, surface temperature, operating time, equivalent diameter, and fluid oxygen content. Correlation analysis confirms that the square root of the fouling factor has the strongest correlation with these seven variables. By combining the powerful feature extraction capability of Convolutional Neural Networks (CNN) with the temporal modeling strength of Long Short-Term Memory (LSTM) networks, the proposed model achieves accurate prediction of the fouling factor

(2) To further enhance the generalization and prediction accuracy of the proposed model, a Dropout mechanism is introduced. Sensitivity analysis is conducted to optimize the Dropout rate, convolution stride, and the number of neurons in the hidden layers. The optimized model achieves a coefficient of determination (R²) of 0.9866, a mean absolute error (MAE) of 1.196×10^-3, and a mean squared error (MSE) of 1.430×10^-4 on the given dataset, these results outperform those of models, including the multilayer perceptron neural network (MLPNN, R²=0.9778), as well as conventional single CNN (R²=0.8247) and LSTM (R²=0.7898) models.

(3) Based on the trained CNN-LSTM model, the fouling factor is predicted and used to calculate the thermal resistance due to fouling in heat exchangers, enabling the optimization of a predictive cleaning schedule for the raw material preheating system. The objective function is to minimize the total cost of operation and maintenance, including utility costs, pump power consumption, and maintenance expenses. The utility and pump power costs are derived from the fouling factor predicted by the CNN-LSTM model. The optimization of the cleaning schedule is performed using a Genetic Algorithm (GA), the optimization model incorporates practical industrial constraints, such as allowable flow rate ranges and restrictions on consecutive cleanings, to ensure operational safety and the feasibility of the cleaning strategy. The results show that the optimized predictive scaling scheme reduces the cost by approximately 28.68% compared with the actual scaling scheme.

The CNN-LSTM-based method proposed in this study demonstrates high accuracy in predicting heat exchanger fouling factors. Building on these accurate predictions, an optimized cleaning strategy for heat exchangers in the raw material preheating system was developed. A case study validates the accuracy and feasibility of the proposed approach, offering a new perspective for the efficient operation of heat exchangers and predictive maintenance of industrial equipment.

[1] 李赫, 徐蒙. 石油化工装置设计中的能源优化与节能减排研究[J]. 石化技术, 2024, 31(07): 57-59.

[2] Mohapatra S, Das D K, Singh A K. Mechanical design of plate-fin heat exchangers for industry using social learning chaotic based kho-kho optimization[J]. Annals of Nuclear Energy, 2023, 181: 109517.

[3] 杨斌, 任爽, 张华. 混油处理装置分馏塔、换热器结垢原因分析及应对措施[J]. 石化技术, 2024, 31(12): 15-17.

[4] Tang S Z, Wang F L, Ren Q, et al. Fouling characteristics analysis and morphology prediction of heat exchangers with a particulate fouling model considering deposition and removal mechanisms[J]. Fuel, 2017, 203: 725-738.

[5] Sadeghianjahromi A, Wang C C. Heat transfer enhancement in fin-and-tube heat exchangers-A review on different mechanisms[J]. Renewable and Sustainable Energy Reviews, 2021, 137: 110470.

[6] 刘琪. 化工设备换热器的常见腐蚀问题与防腐措施探讨[J]. 中国设备工程, 2025, (04): 185-187.

[7] Rao R V, Saroj A. Economic optimization of shell-and-tube heat exchanger using jaya algorithm with maintenance consideration[J]. Applied Thermal Engineering, 2017, 116: 473-487.

[8] Mohanty D K, Singru P M. Fouling analysis of a shell and tube heat exchanger using local linear wavelet neural network[J]. International Journal of Heat and Mass Transfer, 2014, 77: 946-955.

[9] Steinhagen R, Müller-Steinhagen H, Maani K. Problems and costs due to heat exchanger fouling in New Zealand industries[J]. Heat Transfer Engineering, 1993, 14(1): 19-30.

[10] Kapustenko P, Klemeš J J, Arsenyeva O. Plate heat exchangers fouling mitigation effects in heating of water solutions: A review[J]. Renewable and Sustainable Energy Reviews, 2023, 179: 113283.

[11] Shaikh K, Newaz K M S, Zubir M N M, et al. A review of recent advancements in the crystallization fouling of heat exchangers[J]. Journal of Thermal Analysis and Calorimetry, 2023, 148(22): 12369-12392.

[12] Hou G, Zhang D, Yan Q, et al. Application of machine learning algorithms in real-time fouling monitoring of plate heat exchangers[J]. International Communications in Heat and Mass Transfer, 2025, 164: 108809.

[13] 刘若楠. 原油预热系统中考虑结垢问题的换热网络性能优化[D]. 中国石油大学, 2018.

[14] Hosseini S, Khandakar A, Chowdhury M E H, et al. Novel and robust machine learning approach for estimating the fouling factor in heat exchangers[J]. Energy Reports, 2022, 8: 8767-8776.

[15] 张盼盼, 常家超, 邹诚, 等. 基于改进遗传算法的低轨通信卫星跳波束调度策略[J]. 中国科学院大学学报, 2025, 42(03): 382-391.

[16] Diaz-Bejarano E, Coletti F, Macchietto S. A model-based method for visualization, monitoring, and diagnosis of fouling in heat exchangers[J]. Industrial & Engineering Chemistry Research, 2020, 59(10): 4602-4619.

[17] 赵国新, 吴数龙, 陈化淳, 等. 换热器导热管结垢诊断仿真研究[J]. 计算机仿真, 2019, 36(07): 427-431+458.

[18] 殷小明, 陈艺, 宋友立, 等. 换热器内结垢特性研究进展[J]. 化工装备技术, 2021, 42(06): 1-6.

[19] Zaman M A, Wang S. Experimental investigation of surface roughness/wettability pattern effect on crystallization fouling over falling-film flow[J]. Desalination, 2024, 575: 117324.

[20] 马恒瑞, 袁傲添, 王波, 等. 基于深度学习的负荷预测研究综述与展望[J]. 高电压技术, 2025, 51(03): 1233-1250.

[21] Anitha Kumari S, Vimala Starbino A, Priya Esther B, et al. Statistical model identification and variable selection for prediction of heat exchanger fouling[J]. Mathematical Problems in Engineering, 2023, 2023(1): 3040310.

[22] Liang Y, Zhu L, Wang Y, et al. Fouling Prediction of a Heat Exchanger Based on wavelet neural network optimized by improved particle swarm optimization algorithm[J]. Processes, 2024, 12(11): 2412.

[23] 朱文琦, 王彧斐, 冯霄. 不同操作周期下考虑结垢问题的换热网络优化[J]. 大连理工大学学报, 2019, 59(03): 264-270.

[24] 常润秀, 孙琳, 罗雄麟. 换热器结垢与换热网络裕量设计方法研究进展[J]. 化工进展, 2016, 35(02): 358-363.

[25] 刘新, 伍俊楠, 潘殿琦, 等. 基于改进FMEA的污水厂设备故障风险评估模型[J]. 中国安全科学学报, 2024, 34(08): 101-107.

[26] 周怡, 彭国文, 黄召, 等. 基于SBAS-InSAR和BPNN的铀尾矿坝形变智能监测与预测[J]. 中国安全科学学报, 2024, 34(04): 145-152.

[27] 徐源, 陶苗苗, 孙灵芳. 基于灰色神经网络的换热器污垢预测研究[J]. 吉林农业科技学院学报, 2014, 23(01): 45-48.

[28] 余文敏, 余刃, 毛伟, 等. 基于SWLSTM的换热器在线性能预测[J]. 舰船科学技术, 2023, 45(21): 153-157.

[29] Lalot S, Pálsson H. Detection of fouling in a cross-flow heat exchanger using a neural network based technique[J]. International Journal of Thermal Sciences, 2010, 49(4): 675-679.

[30] Delmotte F, Dambrine M, Delrot S, et al. Fouling detection in a heat exchanger: A polynomial fuzzy observer approach[J]. Control Engineering Practice, 2013, 21(10): 1386-1395.

[31] Delrot S, Guerra T M, Dambrine M, et al. Fouling detection in a heat exchanger by observer of Takagi-Sugeno type for systems with unknown polynomial inputs[J]. Engineering Applications of Artificial Intelligence, 2012, 25(8): 1558-1566.

[32] Sundar S, Rajagopal M C, Zhao H, et al. Fouling modeling and prediction approach for heat exchangers using deep learning[J]. International Journal of Heat and Mass Transfer, 2020, 159: 120112.

[33] Tang S Z, Li M J, Wang F L, et al. Fouling potential prediction and multi-objective optimization of a flue gas heat exchanger using neural networks and genetic algorithms[J]. International Journal of Heat and Mass Transfer, 2020, 152: 119488.

[34] Wang S, Fan S. Prediction of fouling in condenser based on k-means algorithms and improved Chebyshev neural network[C].//2012 International Conference on Automatic Control and Artificial Intelligence, 2012: 1596-1600.

[35] Madhu PK R, Subbaiah J, Krithivasan K. RF-LSTM-based method for prediction and diagnosis of fouling in heat exchanger[J]. Asia-Pacific Journal of Chemical Engineering, 2021, 16(5): e2684.

[36] Sun L, Zhang Y, Zheng X, et al. Research on the fouling prediction of heat exchanger based on support vector machine[C].//2008 International Conference on Intelligent Computation Technology and Automation. IEEE, 2008, 1: 240-244.

[37] Jonsson G R, Lalot S, Palsson O P, et al. Use of extended Kalman filtering in detecting fouling in heat exchangers[J]. International Journal of Heat and Mass Transfer, 2007, 50(13-14): 2643-2655.

[38] Shaosheng F, Ju W. Application of diagonal recurrent neural network for measuring fouling in condenser[C].//2007 2nd IEEE Conference on Industrial Electronics and Applications. 2007: 169-171.

[39] Alshingiti Z, Alaqel R, Al-Muhtadi J, et al. A deep learning-based phishing detection system using CNN, LSTM, and LSTM-CNN[J]. Electronics, 2023, 12(1): 232.

[40] 王建荣, 邓黎明, 程伟, 等. 基于CNN-LSTM-SE的心电图分类算法研究[J]. 测试技术学报, 2024, 38(03): 264-273.

[41] 高欣. 基于Attention机制的CNN-LSTM概率预测模型的股指预测[J]. 现代信息科技, 2024, 8(12): 155-159+163.

[42] 汤泽慧, 赵丹, 王晟由. 基于CNN-LSTM-AM的短时交通流量预测[J]. 科学技术与工程, 2024, 24(31): 13562-13567.

[43] 任永良, 代岳成, 高生亮, 等. 基于贝叶斯优化的CNN-LSTM的油田注水管网压力预测[J]. 数学的实践与认识, 2024, 54(12): 160-174.

[44] Kim T Y, Cho S B. Predicting residential energy consumption using CNN-LSTM neural networks[J]. Energy, 2019, 182: 72-81.

[45] Zha W, Liu Y, Wan Y, et al. Forecasting monthly gas field production based on the CNN-LSTM model[J]. Energy, 2022: 124889.

[46] Alhussein M, Aurangzeb K, Haider S I. Hybrid CNN-LSTM model for short-term individual household load forecasting[J]. Access, 2020, 8: 180544-180557.

[47] Barzegar R, Aalami M T, Adamowski J. Short-term water quality variable prediction using a hybrid CNN-LSTM deep learning model[J]. Stochastic Environmental Research and Risk Assessment, 2020, 34(2): 415-433.

[48] Luo S, Wang B, Gao Q, et al. Stacking integration algorithm based on CNN-BiLSTM-Attention with XGBoost for short-term electricity load forecasting[J]. Energy Reports, 2024, 12: 2676-2689.

[49] Garcia C I, Grasso F, Luchetta A, et al. A comparison of power quality disturbance detection and classification methods using CNN, LSTM and CNN-LSTM[J]. Applied Sciences, 2020, 10(19): 6755.

[50] 张术琳, 张亚楠, 田超, 等. 基于CNN的化工园区火灾火焰图像识别研究[J]. 中国安全科学学报, 2024, 34(1): 179-186

[51] Arkin E, Yadikar N, Xu X, et al. A survey: object detection methods from CNN to transformer[J]. Multimedia Tools and Applications, 2023, 82(14): 21353-21383.

[52] Liu Y, Pu H, Sun D W. Efficient extraction of deep image features using convolutional neural network (CNN) for applications in detecting and analysing complex food matrices[J]. Trends in Food Science & Technology, 2021, 113: 193-204.

[53] Wang J, Sun L, Li H, et al. Prediction model of fouling thickness of heat exchanger based on TA-LSTM structure[J]. Processes, 2023, 11(9): 2594.

[54] Al-Selwi S M, Hassan M F, Abdulkadir S J, et al. RNN-LSTM: from applications to modeling techniques and beyond-Systematic review[J]. Journal of King Saud University-Computer and Information Sciences, 2024: 102068.

[55] Lu, W., Li, J., Li, Y., et al. 2020. A CNN-LSTM-based model to forecast stock prices[J]. Complexity, 2020, 2020(1): 6622927.

[56] 马花月. 工程结构化数据预处理技术[J]. 中国科技信息, 2025, (09): 44-47.

[57] 杜林颖, 于鸿彬, 侯立国, 等. 改进的BP神经网络对飞机换热器结垢厚度预测[J]. 计算机仿真, 2020, 37(01): 27-30.

[58] 周梓馨, 张功萱, 寇小勇, 等. 一种基于自注意力机制的深度学习侧信道攻击方法[J]. 信息安全研究, 2022, 8(08): 812-824.

[59] Garbin C, Zhu X, Marques O. Dropout vs. batch normalization: an empirical study of their impact to deep learning[J]. Multimedia Tools and Applications, 2020, 79(19): 12777-12815.

[60] Togun H, Sultan H S, Mohammed H I, et al. A critical review on phase change materials (PCM) based heat exchanger: different hybrid techniques for the enhancement[J]. Journal of Energy Storage, 2024, 79: 109840.

[61] 李建伟, 郭攀, 马俊杰. 矿井开采设备齿轮减速器故障预测模型[J]. 金属矿山, 2025, (03): 175-180.

[62] 杨茂, 张书天, 王勃, 等. 基于混合分位数回归长短期记忆神经网络的风电功率短期区间预测[J]. 太阳能学报, 2025, 46(02): 582-590.

[63] Davoudi E, Vaferi B. Applying artificial neural networks for systematic estimation of degree of fouling in heat exchangers[J]. Chemical Engineering Research and Design, 2018, 130: 138-153.

[64] Asomaning S. The role of olefins in fouling of heat exchangers[D]. University of British Columbia, 1990.

[65] Asomaning S. Heat exchanger fouling by petroleum asphaltenes[D]. University of British Columbia, 1997.

[66] Sundaram B N. The effects of oxygen on synthetic crude oil fouling[D]. University of British Columbia, 1998.

[67] Watkinson A P. Particulate fouling of sensible heat exchangers[D]. University of British Columbia, 1968.

[68] Srinivasan M. Heat exchanger fouling of some Canadian crude oils[D]. University of British Columbia, 2008.

[69] Feiz G. Annular heating probes in oil fouling: effects of wall shear stress[D]. University of British Columbia, 2015.

[70] 郜亚东, 李冠, 赵立峰, 等. 一种四分位数法优化的GM(1,1)模型在高危边坡监测中应用研究[J]. 城市勘测, 2023(3): 171-175.

[71] Agga A, Abbou A, Labbadi M, et al. CNN-LSTM: an efficient hybrid deep learning architecture for predicting short-term photovoltaic power production[J]. Electric Power Systems Research, 2022, 208: 107908.

[72] 解恒星, 张雄, 董锦洋, 等. 基于CNN-Bi LSTM的矿井瓦斯涌出量预测模型[J]. 中国安全生产科学技术, 2024, 20(11): 53-59.

[73] Naseri H R, Mehrdad V. Novel CNN with investigation on accuracy by modifying stride, padding, kernel size and filter numbers[J]. Multimedia Tools and Applications, 2023, 82(15): 23673-23691.

[74] Li G, Hu J, Shan D, et al. A CNN model based on innovative expansion operation improving the fault diagnosis accuracy of drilling pump fluid end[J]. Mechanical Systems and Signal Processing, 2023, 187: 109974.

[75] 陈琨, 王安志. 卷积神经网络的正则化方法综述[J]. 计算机应用研究, 2024, 41(04): 961-969.

[76] Chatfield M D, Cole T J, de Vet H C W, et al. blandaltman: a command to create variants of Bland-Altman plots[J]. The Stata Journal, 2023, 23(3): 851-874.

[77] Fang Y, Yao Y, Lin X, et al. A feature selection based on genetic algorithm for intrusion detection of industrial control systems[J]. Computers & Security, 2024, 139: 103675.

[78] Tian J, Wang Y, Feng X. Simultaneous optimization of flow velocity and cleaning schedule for mitigating fouling in refinery heat exchanger networks[J]. Energy, 2016, 109: 1118-1129.

[79] Katoch S, Chauhan S S, Kumar V. A review on genetic algorithm: past, present, and future[J]. Multimedia Tools and Applications, 2021, 80: 8091-8126.

[80] Alhijawi B, Awajan A. Genetic algorithms: Theory, genetic operators, solutions, and applications[J]. Evolutionary Intelligence, 2024, 17(3): 1245-1256.

[81] Mahmoudinazlou S, Kwon C. A hybrid genetic algorithm for the min-max Multiple Traveling Salesman Problem[J]. Computers & Operations Research, 2024, 162: 106455.

[82] 田佳阳, 贾林权, 王彧斐, 等. 考虑关键换热器备用的原油预热系统清垢周期优化[J]. 化工学报, 2016, 67(12): 5183-5189.

[83] Zhou C, Liu G, Liao S. Probing dominant flow paths in enhanced geothermal systems with a genetic algorithm inversion model[J]. Applied Energy, 2024, 360: 122841.

[84] 叶少华, 杨勇, 饶波, 等. 基于遗传算法的磁压缩电源参数设计方法[J]. 强激光与粒子束, 2025, 37(03): 80-90.

[85] Rahardja U, Sari A, Alsalamy A H, et al. Tribological properties assessment of metallic glasses through a genetic algorithm-optimized machine learning model[J]. Metals and Materials International, 2024, 30(3): 745-755.

[86] Morris J, Wang W, Plaisted T, et al. Optimizing graded metamaterials via genetic algorithm to control energy transmission[J]. International Journal of Mechanical Sciences, 2024, 263: 108775.