基于机器学习的0Cr17Ni4Cu4Nb不锈钢流变应力预测研究

赵礼栋; 张又铭; 张继林; 窦建明; 姚家宝

doi:10.7513/j.issn.1004-7638.2023.04.028

基于机器学习的0Cr17Ni4Cu4Nb不锈钢流变应力预测研究

doi: 10.7513/j.issn.1004-7638.2023.04.028

1.
兰州工业学院计算机与人工智能学院, 甘肃兰州 730050
2.
大连交通大学机车车辆工程学院, 辽宁大连 116000
3.
兰州工业学院机电工程学院, 甘肃兰州 730050
4.
兰州交通大学机电工程学院, 甘肃兰州 730070

基金项目: 甘肃省青年科技基金计划项目（21JR7RA351）；甘肃省自然科学基金（20JR5RA376）；甘肃省重点人才项目（甘组通字 [2022]77 号）；国家级大学生创新创业训练计划项目（202211807007）；兰州交通大学甘肃省重点实验室开放课题（2022051）。

详细信息

作者简介:
赵礼栋，1977年出生，男，硕士，副教授，主要从事计算机软件编程、硬件调试以及模型建立研究，E-mail：40241324@qq.com

通讯作者:
窦建明，1985年出生，男，博士，副教授，主要从事智能制造、切削过程状态监测与故障诊断研究，E-mail：lgy_116@163.com

中图分类号: TG142.7,TP301.6
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- 文章访问数: 79
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- 被引次数: 0
出版历程
- 收稿日期: 2022-11-16
- 刊出日期: 2023-08-30

Research on prediction accuracy of the flow stress of 0Cr17Ni4Cu4Nb stainless steel based on machine learning

1.
School of Computer and Artificial Intelligence, Lanzhou Institute of Technology, Lanzhou 730050, Gansu, China
2.
School of Locomotive and Vehicle Engineering, Dalian Jiaotong University, Dalian 116000, Liaoning, China
3.
School of Electrical and Mechanical Engineering, Lanzhou Institute of Technology, Lanzhou 730050, Gansu, China
4.
College of Electrical and Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

摘要

摘要: 以0Cr17Ni4Cu4Nb不锈钢为例，提出一种基于粒子群优化BP神经网络预测流变应力的新模型。以常温下的准静态（0.001 s⁻¹）压缩试验数据、四种温度（25、350、500、300 ℃）和六种应变率（750、1500、2 000、2600、3500、4500 s⁻¹）的冲击试验数据为基础，构建了 0Cr17Ni4Cu4Nb不锈钢流变应力的随机森林预测模型、粒子群优化随机森林预测模型、Back Propagation（BP）神经网络预测模型以及粒子群优化BP神经网络预测模型，采用统计学的决定系数（R²）、平均绝对误差（MAE）、均方差（MSE）和均方误差平方根（RMSE）四个指标分析评价上述四种模型，得出四种模型预测的综合性能依次是粒子群优化BP神经网络模型、BP神经网络模型、粒子群优化随机森林模型、随机森林模型。粒子群优化BP神经网络模型决定系数R²=0.9997、平均绝对误差MAE=1.5773、均方差MSE=5.5053和均方误差平方根RMSE=2.3463，该模型能够很好预测 0Cr17Ni4Cu4Nb不锈钢流变应力。
- 0Cr17Ni4Cu4Nb不锈钢 /
- 流变应力 /
- 预测模型 /
- 机器学习 /
- 粒子群优化BP神经网络
Abstract: A new model for predicting rheological stresses based on particle swarm optimization BP neural network is proposed for 0Cr17Ni4Cu4Nb stainless steel as an example. Based on the quasi-static (0.001 s⁻¹) compression testing data at room temperature and the impact testing data at four temperatures (25, 350, 500 and 300 ℃) and six strain rates (750, 1500, 2000, 2600, 3500 and 4500 s⁻¹), a random forest prediction model for rheological stress of 0Cr17Ni4Cu4Nb stainless steel, a Particle Swarm Optimized Random Forest prediction model, a Back Propagation (BP) neural network, and a Particle Swarm Optimized BP neural network are constructed. Four indicators including the statistical coefficient of determination (R²), mean absolute error (MAE), mean square error (MSE) and root mean square error (RMSE) are used to analyze and evaluate the four models mentioned above. The comprehensive performance of the prediction models is in sequence of particle swarm optimization BP neural network model, BP neural network model, particle swarm optimization random forest model, and the random forest model. The coefficient of determination R²=0.9997, mean absolute error MAE=1.5773, mean squared error MSE=5.5053 and root mean squared error RMSE=2.3463 are determined for the particle swarm optimized BP neural network model, which can predict the rheological stress of 0Cr17Ni4Cu4Nb stainless steel very well.
- 0Cr17Ni4Cu4Nb stainless steel /
- rheological stress /
- prediction model /
- machine learning /
- particle swarm optimization BP neural network

HTML全文

图 1 随机森林结构

Figure 1. Random forest structure

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图 2 BP神经网络结构

Figure 2. BP neural network structure

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图 3 基于PSO-RF流程

Figure 3. Flow chart based on PSO-RF

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图 4 基于PSO-BP神经网络流程

Figure 4. Flow chart based on PSO-RF neural network

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图 5 不同模型真应力预测和试验值之间的相关性

Figure 5. Correlation between predicted and experimental values of true stress by different models

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表 1 不锈钢0Cr17Ni4Cu4Nb的化学成分

Table 1. Chemical composition of 0Cr17Ni4Cu4Nb stainless steel %

C	Si	Cr	Ni	Mn	P	S	Cu	Nb	Fe
0.05	0.80	16.25	3.60	0.82	0.03	0.02	3.83	0.28	Bal.

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表 2 随机森林预测能力评价指标

Table 2. Random forest predictive capability evaluation index

ntree	R²	MAE	MSE	ESE
5	0.9477	24.4079	1069.2639	32.3405
10	0.9500	23.9846	1022.4408	31.2505
15	0.9526	23.4958	969.3096	30.9611
20	0.9645	20.9364	725.6117	26.8710
25	0.9629	21.1896	759.2660	27.4315
30	0.9676	19.5587	661.3547	25.6921
35	0.9672	20.1650	671.3218	25.9012
40	0.9664	20.2319	687.3605	26.1867
45	0.9684	19.7709	645.1419	25.3661
50	0.9667	20.0062	680.3112	26.0351
55	0.9666	20.1374	681.8699	26.1012
60	0.9647	20.6059	721.0314	26.8389

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表 3 粒子群优化随机森林预测能力评价指标

Table 3. Particle swarm optimization random forest prediction capability evaluation index

ntree	R²	MAE	MSE	ESE
16	0.9672	20.0205	670.9482	25.8998

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表 4 不同神经元个数训练下的评价指标

Table 4. Evaluation metrics under different training numbers of neurons

神经元数量	R²	MAE	MSE	ESE
3	0.9777	16.5449	455.9399	21.3527
5	0.9802	15.4572	404.0375	20.1007
7	0.9951	7.4794	100.2042	10.0102
9	0.9968	6.0398	65.4811	8.092
11	0.9982	4.4221	36.8969	6.0743
13	0.9978	4.7259	45.1895	6.7223

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表 5 不同隐含层个数训练下的评价指标

Table 5. Evaluation metrics under different training numbers of implied layers

隐含层层数	R²	MAE	MSE	ESE
1	0.9982	4.4194	36.9513	6.0788
2	0.9993	2.5569	14.4780	3.8050
3	0.9996	2.0898	8.9598	2.9933
4	0.9995	2.1464	10.3096	3.2109
5	0.9995	2.0498	9.7388	3.1207
6	0.9997	1.5773	5.5429	2.3543

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表 6 粒子群优化BP神经网络训练下的评价指标

Table 6. Evaluation metrics under particle swarm optimization BP neural network training

隐含层结构	R²	MAE	MSE	ESE
12	0.9969	5.8513	63.677	7.9798
12×12	0.9995	2.1863	10.9691	3.312
12×12×8	0.9997	1.4770	5.5053	2.3463
9×11×12×12	0.9997	1.6695	6.6039	2.5698
12×11×10×12×11	0.9996	1.7680	7.3263	2.7067
12×12×12×12×12×12	0.9997	1.5030	5.6700	2.3812

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参考文献(38)

[1]	Wang Jianxing, Yang Gang, Zhang Zhongmo, et al. Effect of ECAP deformation on microstructure and mechanical properties of 0Cr17Ni4Cu4Nb stainless steel[J]. Journal of Plasticity Engineering, 2018,25(1):119−124. (王剑星, 杨钢, 张忠模, 等. ECAP变形对0Cr17Ni4Cu4Nb不锈钢组织与力学性能的影响[J]. 塑性工程学报, 2018,25(1):119−124. Wang Jianxing , Yang Gang , Zhang Zhongmo, et al. Effect of ECAP deformation on microstructure and mechanical properties of 0 Cr17 Ni4 Cu4 Nb stainless steel[J]. Journal of Plasticity Engineering, 2018, 25(1): 119-124.
[2]	Wang Jianxing, Yang Gang, Liu Tianmo, et al. Effect of Ni content on mechanical properties of 0Cr17Ni4Cu4Nb stainless steel[J]. Transactions of Materials and Heat Treatment, 2010,31(12):56−60. (王剑星, 杨钢, 刘天模, 等. Ni含量对0Cr17Ni4Cu4Nb不锈钢力学性能的影响[J]. 材料热处理学报, 2010,31(12):56−60. Wang Jianxing, Yang Gang, Liu Tianmo, et al. Effect of Ni content on mechanical properties of 0 Cr17 Ni4 Cu4 Nb stainless steel[J]. Transactions of Materials and Heat Treatment, 2010, 31(12): 56-60
[3]	Wang Hanxiao, Bai Bing, Zhang Changyi, et al. Micro-structure and properties analysis of nuclear power stem material 17-4PH stainless steel at different service time[J]. Nuclear Science and Engineering, 2018,38(2):318−325. (王瀚霄, 白冰, 张长义, 等. 核电阀杆材料17-4PH不锈钢服役不同时间的组织性能分析[J]. 核科学与工程, 2018,38(2):318−325. doi: 10.3969/j.issn.0258-0918.2018.02.022 Wang Hanxiao, Bai Bing, Zhang Changyi, et al. Micro-structure and properties analysis of nuclear power stem material 17-4 PH stainless steel at different service time[J]. Nuclear Science and Engineering, 2018, 38(2): 318-325. doi: 10.3969/j.issn.0258-0918.2018.02.022
[4]	Huang Jing, Ma Yuan, Wang Mingjie, et al. Investigation and optimization of investment casting 0Cr17Ni4Cu3Nb stainless steel parts aero-engines[J]. Special Casting & Nonferrous Alloys, 2019,39(2):159−162. (黄静, 马原, 王明杰, 等. 精密铸造0Cr17Ni4Cu3Nb不锈钢航空发动机零件[J]. 特种铸造及有色合金, 2019,39(2):159−162. Huang Jing, Ma Yuan, Wang Mingjie, et al. Investigation and optimization of investment casting 0 Cr17 Ni4 Cu3 Nb stainless steel parts aero-engines[J]. Special Casting & Nonferrous Alloys, 2019, 39(2): 159-162
[5]	Sun Jianxin, Liu Yongsheng, Guo Baofeng, et al. Hot deformation behavior and hot processing map of 17-4PH stainless steel for oil fracturing valve box[J]. Journal of Plasticity Engineering, 2022,29(4):112−118. (孙建新, 刘永胜, 郭宝峰, 等. 石油压裂阀箱用17-4PH不锈钢热变形行为及热加工图[J]. 塑性工程学报, 2022,29(4):112−118. Sun Jianxin, Liu Yongsheng, Guo Baofeng, et al. Hot deformation behavior and hot processing map of 17-4 PH stainless steel for oil fracturing valve box [J]. Journal of Plasticity Engineering, 2022, 29(4): 112-118.
[6]	Zhang Jilin, Jia Haishen, Yi Xiangbin, et al. Effect of high temperature and high strain rate on the dynamic mechanical properties of 06Cr19Ni10 austenitic stainless steel[J]. Iron Steel Vanadium Titanium, 2022,43(1):145−151. (张继林, 贾海深, 易湘斌, 等. 高温高应变率对06Cr19Ni10奥氏体不锈钢动态力学性能的影响[J]. 钢铁钒钛, 2022,43(1):145−151. Zhang Jilin, Jia Haishen, Yi Xiangbin, et al. Effect of high temperature and high strain rate on the dynamic mechanical properties of 06 Cr19 Ni10 austenitic stainless steel[J]. Iron Steel Vanadium Titanium, 2022, 43(1): 145-151.
[7]	Jia Haishen, Zhang Jilin, Yi Xiangbin, et al. Experimental study on rheological behavior of 022Cr18Ni14Mo2 stainless steel at high temperature and high strain rate[J]. Journal of Mechanical Strength, 2022,44(3):600−606. (贾海深, 张继林, 易湘斌, 等. 高温、高应变率下022Cr18Ni14Mo2不锈钢流变行为的试验研究[J]. 机械强度, 2022,44(3):600−606. Jia Haishen, Zhang Jilin, Yi Xiangbin, et al. Experimental study on rheological behavior of 022 Cr18 Ni14 Mo2 stainless steel at high temperature and high strain rate[J]. Journal of Mechanical Strength, 2022, 44(3): 600-606
[8]	Jia Haishen, Luo Wencui, Zhang Jilin, et al. Study on dynamic mechanical properties and constitutive model of 022Cr18Ni14Mo2 stainless steel under impact load[J]. Iron Steel Vanadium Titanium, 2022,43(2):178−185. (贾海深, 罗文翠, 张继林, 等. 冲击载荷下022Cr18Ni14Mo2不锈钢动态力学特性及其本构模型研究[J]. 钢铁钒钛, 2022,43(2):178−185. doi: 10.7513/j.issn.1004-7638.2022.02.027 Jia Haishen, Luo Wencui, Zhang Jilin, et al. Study on dynamic mechanical properties and constitutive model of 022 Cr18 Ni14 Mo2 stainless steel under impact load[J]. Iron Steel Vanadium Titanium, 2022, 43(2): 178-185. doi: 10.7513/j.issn.1004-7638.2022.02.027
[9]	Duan Xinmin, Sun Peiqiu, Xu Zhiqiang, et al. Study on the integral forming technology of front /rear interfacering for 0Cr17Ni4Cu4Nb[J]. Forging & Stamping Technology, 2016,41(5):44−48. (段新民, 孙培秋, 徐志强, 等. 0Cr17Ni4Cu4Nb前/后接口套圈整体成形技术研究[J]. 锻压技术, 2016,41(5):44−48. Duan Xinmin , Sun Peiqiu , Xu Zhiqiang, et al. Study on the integral forming technology of front /rear interfacering for 0 Cr17 Ni4 Cu4 Nb[J]. Forging & Stamping Technology, 2016, 41(5): 44-48.
[10]	Ding Jun, Gu Yuchuan, Huang Xia, et al. Research on prediction accuracy of flow stress of 304 stainless steel based on artificial neural network optimized by improved genetic algorithm[J]. Journal of Mechanical Engineering, 2022,58(10):78−86. (丁军, 古愉川, 黄霞, 等. 基于改进遗传算法优化人工神经网络的304不锈钢流变应力预测准确性研究[J]. 机械工程学报, 2022,58(10):78−86. Ding Jun , Gu Yuchuan , Huang Xia, et al. Research on prediction accuracy of flow stress of 304 stainless steel based on artificial neural network optimized by improved genetic algorithm[J]. Journal of Mechanical Engineering, 2022, 58(10): 78-86.
[11]	Zhong Mingjun, Wang Kelu, Lu Shiqiang, et al. Study on high temperature deformation behavior and BP neural network constitutive model of MoNb alloy[J]. Journal of Plasticity Engineering, 2020,27(12):177−182. (钟明君, 王克鲁, 鲁世强, 等. MoNb合金高温变形行为及BP神经网络本构模型研究[J]. 塑性工程学报, 2020,27(12):177−182. doi: 10.3969/j.issn.1007-2012.2020.12.025 Zhong Mingjun, Wang Kelu, Lu Shiqiang, et al. Study on high temperature deformation behavior and BP neural network constitutive model of MoNb alloy[J]. Journal of Plasticity Engineering, 2020, 27(12): 177-182. doi: 10.3969/j.issn.1007-2012.2020.12.025
[12]	Luo Rui, Cao Yun, Qiu Yu, et al. Investigation of constitutive model of as-extruded spray-forming 7055 aluminum alloy based on BP artificial neural network[J]. Journal of Aeronautical Materials, 2021,41(1):35−44. (罗锐, 曹赟, 邱宇, 等. 基于BP人工神经网络喷射成形7055铝合金的本构模型[J]. 航空材料学报, 2021,41(1):35−44. Luo Rui , Cao Yun , Qiu Yu, et al. Investigation of constitutive model of as-extruded spray-forming 7055 aluminum alloy based on BP artificial neural network[J]. Journal of Aeronautical Materials, 2021, 41(1): 35-44.
[13]	Wu Xiongxi. Model of constitutive relationship and processing map for 7050 aluminum alloy based on BP neural network[J]. Special Casting & Nonferrous Alloys, 2014,34(10):1011−1015. (吴雄喜. 基于BP神经网络的7050铝合金本构关系模型及加工图[J]. 特种铸造及有色合金, 2014,34(10):1011−1015. doi: 10.15980/j.tzzz.2014.10.001 Wu Xiongxi. Model of constitutive relationship and processing map for 7050 aluminum alloy based on BP neural network[J]. Special Casting & Nonferrous Alloys, 2014, 34(10): 1011-1015. doi: 10.15980/j.tzzz.2014.10.001
[14]	Zhou Feng, Wang Kelu, Lu Shiqiang, et al. Flow behavior and BP neural network high temperature constitutive model of Ti-22Al-24Nb-0.5Y alloy[J]. Journal of Materials Engineering, 2019,47(8):141−146. (周峰, 王克鲁, 鲁世强, 等. Ti-22Al-24Nb-0.5Y合金流变行为及BP神经网络高温本构模型[J]. 材料工程, 2019,47(8):141−146. doi: 10.11868/j.issn.1001-4381.2017.001548 Zhou Feng , Wang Kelu , Lu Shiqiang, et al. Flow behavior and BP neural network high temperature constitutive model of Ti-22 Al-24 Nb-0.5 Y alloy[J]. Journal of Materials Engineering, 2019, 47(8): 141-146. doi: 10.11868/j.issn.1001-4381.2017.001548
[15]	Zhang Qing, Li Ping, Xue Kemin. Model of constitutive relationship for TB8 alloy based on BP neural network[J]. Forging & Stamping Technology, 2010,35(1):130−133. (张青, 李萍, 薛克敏. 基于BP神经网络的TB8合金高温本构关系模型[J]. 锻压技术, 2010,35(1):130−133. Zhang Qing , Li Ping , Xue Kemin. Model of constitutive relationship for TB8 alloy based on BP neural network[J].
[16]	Wang Tianxiang, Lu Shiqiang, Wang Kelu, et al. Flow stress behavior and artificial neural network constitutive model of Ti60 alloy[J]. Special Casting & Nonferrous Alloys, 2020,40(9):1019−1023. (王天祥, 鲁世强, 王克鲁, 等. Ti60合金的流变应力行为及人工神经网络本构模型[J]. 特种铸造及有色合金, 2020,40(9):1019−1023. doi: 10.15980/j.tzzz.2020.09.022 Wang Tianxiang, Lu Shiqiang, Wang Kelu, et al. Flow stress behavior and artificial neural network constitutive model of Ti60 alloy[J]. Special Casting & Nonferrous Alloys, 2020, 40(9): 1019-1023 doi: 10.15980/j.tzzz.2020.09.022
[17]	An Zhen, Li Jinshan, Feng Yong, et al. Modeling constitutive relationship of Ti-555211 alloy by artificial neural network during high-temperature deformation[J]. Rare Metal Materials and Engineering, 2015,44(1):62−66. doi: 10.1016/S1875-5372(15)30013-8
[18]	Wang Chunhui, Sun Zhihui, Zhao Jiaqing, et al. Creep deformation constitutive model of BSTMUF601 superalloy using BP neural network method[J]. Rare Metal Materials and Engineering, 2020,49(6):1885−1893.
[19]	He Long, Zhang Ranyang, Zhao Gangyao, et al. Constitutive model of GH5188 superalloy based on BP neural network[J]. Special Casting & Nonferrous Alloyss, 2021,41(2):223−226. (何龙, 张冉阳, 赵刚要, 等. 基于BP神经网络的GH5188高温合金本构模型[J]. 特种铸造及有色合金, 2021,41(2):223−226. doi: 10.15980/j.tzzz.2021.02.020 He Long , Zhang Ranyang, Zhao Gangyao, et al. Constitutive model of GH5188 superalloy based on BP neural network[J]. Special Casting & Nonferrous Alloyss, 2021, 41(2): 223-226. doi: 10.15980/j.tzzz.2021.02.020
[20]	Qiu Qian, Wang Kelu, Li Xin, et al. Constitutive relationship of SP700 titanium alloy based on BP neural network[J]. Journal of Plasticity Engineering, 2021,28(11):167−172. (邱仟, 王克鲁, 李鑫, 等. 基于BP神经网络的SP700钛合金本构关系[J]. 塑性工程学报, 2021,28(11):167−172. Qiu Qian, Wang Kelu, Li Xin, et al. Constitutive relationship of SP700 titanium alloy based on BP neural network[J]. Journal of Plasticity Engineering, 2021, 28(11): 167-172.
[21]	Lei Jinwen, Xue Xiangyi, Zhang Siyuan, et al. High-precision constitutive model of Ti6242s alloy hot deformation based on artificial neural network[J]. Rare Metal Materials and Engineering, 2021,50(6):2025−2032. (雷锦文, 薛祥义, 张思远, 等. 基于人工神经网络的高精度Ti6242s合金热变形本构模型[J]. 稀有金属材料与工程, 2021,50(6):2025−2032. Lei Jinwen, Xue Xiangyi, Zhang Siyuan, et al. High-precision constitutive model of Ti6242 s alloy hot deformation based on artificial neural network[J]. Rare Metal Materials and Engineering, 2021, 50(6): 2025-2032.
[22]	Zhang Pin, Yin Zhenyu, Jin Yinfu, et al. A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest[J]. Engineering Geology, 2020,265:628−638.
[23]	Wang Jie, Cheng Xuexin, Peng Jinzhu. A weighted random forest model based on particle swarm optimization[J]. Journal of Zhengzhou University(Natural Science Edition), 2018,50(1):72−76. (王杰, 程学新, 彭金柱. 一种基于粒子群算法优化的加权随机森林模型[J]. 郑州大学学报(理学版), 2018,50(1):72−76. doi: 10.13705/j.issn.1671-6841.2017006 Wang Jie, Cheng Xuexin, Peng Jinzhu. A weighted random forest model based on particle swarm optimization[J]. Journal of Zhengzhou University(Natural Science Edition), 2018, 50(1): 72-76. doi: 10.13705/j.issn.1671-6841.2017006
[24]	Breiman L. Random forests[J]. Machine Learning, 2001,45(1):5−32. doi: 10.1023/A:1010933404324
[25]	Wang Weitong, Fan Haidong, Liang Chengsi, et al. Predictive modeling of NO_x outlet of hedged boiler based on random forest[J]. Thermal Power Generation, 2022,51(4):96−104. (王伟同, 范海东, 梁成思, 等. 基于随机森林算法的对冲锅炉出口NO_x排放量预测模型研究[J]. 热力发电, 2022,51(4):96−104. Wang Weitong, Fan Haidong, Liang Chengsi, et al. Predictive modeling of NO_x outlet of hedged boiler based on random forest[J]. Thermal Power Generation, 2022, 51(4): 96-104.
[26]	Wu Xianguo, Liu Pengcheng, Chen Hongyu, et al. Prediction of concrete strength based on random forest[J]. Concrete, 2022,(1):17−20,24. (吴贤国, 刘鹏程, 陈虹宇, 等. 基于随机森林的高性能混凝土抗压强度预测[J]. 混凝土, 2022,(1):17−20,24. Wu Xianguo, Liu Pengcheng, Chen Hongyu, et al. Prediction of concrete strength based on random forest[J]. Concrete, 2022(1): 17-20, 24.
[27]	Yan Liangming, Shen Jian, Li Zhoubing, et al. Modelling for flow stress and processing map of 7055 aluminum alloy based on artificial neural networks[J]. The Chinese Journal of Nonferrous Metals, 2010,20(7):1296−1301. (闫亮明, 沈健, 李周兵, 等. 基于神经网络的7055铝合金流变应力模型和加工图[J]. 中国有色金属学报, 2010,20(7):1296−1301. doi: 10.19476/j.ysxb.1004.0609.2010.07.008 Yan Liangming, Shen Jian, Li Zhoubing, et al. Modelling for flow stress and processing map of 7055 aluminum alloy based on artificial neural networks[J]. The Chinese Journal of Nonferrous Metals, 2010, 20(7): 1296-1301. doi: 10.19476/j.ysxb.1004.0609.2010.07.008
[28]	Lv Zhe, He Lile, Lin Yuyang, et al. Parameters prediction of BP neural network based on constitutive model of aluminum alloy powder forming[J]. Hot Working Technology, 2022,51(4):46−50. (吕哲, 贺利乐, 林育阳, 等. 基于铝合金粉末成形本构模型的BP神经网络参数预测[J]. 热加工工艺, 2022,51(4):46−50. Lv Zhe, He Lile, Lin Yuyang, et al. Parameters prediction of BP neural network based on constitutive model of aluminum alloy powder forming[J]. Hot Working Technology, 2022, 51(4): 46-50.
[29]	Feng Xi, Li Qing, Quan Wei, et al. Overview of multiobjective particle swarm optimization algorithm[J]. Chinese Journal of Engineering, 2021,43(6):745−753. (冯茜, 李擎, 全威, 等. 多目标粒子群优化算法研究综述[J]. 工程科学学报, 2021,43(6):745−753. Feng Xi, Li Qing, Quan Wei, et al. Overview ofmultiobjective particle swarm optimization algorithm[J]. Chinese Journal of Engineering, 2021, 43(6): 745-753.
[30]	Li Hejian, Xu Xiaowei, Wang Ke, et al. Transformer fault diagnosis model based on particle swarm optimization and random forest[J]. Journal of Kunming University of Science and Technology(Natural Sciences), 2021,46(3):94−101. (李鹤健, 徐肖伟, 王科, 等. 基于粒子群优化随机森林的变压器故障诊断模型[J]. 昆明理工大学学报(自然科学版), 2021,46(3):94−101. doi: 10.16112/j.cnki.53-1223/n.2021.03.451 Li Hejian, Xu Xiaowei, Wang Ke, et al. Transformer fault diagnosis model based on particle swarm optimization and random forest[J]. Journal of Kunming University of Science and Technology(Natural Sciences), 2021, 46(3): 94-101. doi: 10.16112/j.cnki.53-1223/n.2021.03.451
[31]	Li Le, Shu Yuechao, Wu Jianpeng, et al. A damage prediction model of wet friction elements based on PSO-BP neural network[J]. Transactions of Beijing Institute of Technology, 2022,42(12):1246−1255. (李乐, 舒越超, 吴健鹏, 等. 基于PSO-BP神经网络湿式摩擦元件损伤预测模型[J]. 北京理工大学学报, 2022,42(12):1246−1255. doi: 10.15918/j.tbit1001-0645.2021.347 Li Le, Shu Yuechao, Wu Jianpeng, et al. A damage prediction model of wet friction elements based on PSO-BP neural network[J]. Transactions of Beijing Institute of Technology, 2022, 42(12): 1246-1255. DOI: 10.15918/j.tbit1001-0645.2021.347.
[32]	Fan Shengxu, Yang Chunxi, Yang Qiliang, et al. Prediction model of Panax notoginseng leaf area growth based on particle swarm-optimization random forest algorithm and meteorological data[J]. Chinese Traditional and Herbal Drugs, 2022,53(10):3103−3110. (范升旭, 杨春曦, 杨启良, 等. 基于粒子群-随机森林算法和气象数据的三七叶面积生长预测模型[J]. 中草药, 2022,53(10):3103−3110. doi: 10.7501/j.issn.0253-2670.2022.10.021 Fan Shengxu, Yang Chunxi, Yang Qiliang, et al. Prediction model of Panax notoginseng leaf area growth based on particle swarm-optimization random forest algorithm and meteorological data[J]. Chinese Traditional and Herbal Drugs, 2022, 53(10): 3103-3110. doi: 10.7501/j.issn.0253-2670.2022.10.021
[33]	程学新. 粒子群优化加权随机森林算法研究[D]. 郑州: 郑州大学, 2017. Cheng Xuexin. Research on particle swarm optimization weighted random forest algorithm[D]. Zhengzhou: Zhengzhou University, 2017.
[34]	李超. 粒子群优化算法改进策略及其应用研究[D]. 无锡: 江南大学, 2021. Li Chao. Improvement strategies for particle swarm optimization algorithms with applications[D]. Wuxi: Jiangnan University, 2021.
[35]	Chang Ruohan, Cai Zhongyi, Cheng Liren, et al. Flow stress prediction model and processing map of Mg-Zn-Zr alloy based on GA-BP network[J]. Materials Reports, 2017,31(6):136−139,146. (常若寒, 蔡中义, 程丽任, 等. 基于遗传BP网络的Mg-Sm-Zn-Zr合金应力预测模型及加工图[J]. 材料导报, 2017,31(6):136−139,146. doi: 10.11896/j.issn.1005-023X.2017.06.027 Chang Ruohan, Cai Zhongyi, Cheng Liren, et al. Flow stress prediction model and processing map of Mg-Zn-Zr alloy based on GA-BP network[J]. Materials Reports, 2017, 31(6): 136-139, 146. doi: 10.11896/j.issn.1005-023X.2017.06.027
[36]	Zhang Jilin, Jia Haishen, Yi Xiangbin, et al. Dynamic mechanical properties and comparison of two constitutive models for martensitic stainless steel 0Cr17Ni4Cu4Nb[J]. Materials Research Express, 2021,8(10):106501. doi: 10.1088/2053-1591/ac29f5
[37]	Hu Yi, Zhang Lushan, Yuan Fuyin, et al. Prediction of concrete strength based on random forest[J]. Construction Technology, 2020,49(17):89−94. (胡毅, 张陆山, 袁福银, 等. 基于随机森林的混凝土强度预测研究[J]. 施工技术, 2020,49(17):89−94. Hu Yi, Zhang Lushan, Yuan Fuyin, et al. Prediction of concrete strength based on random forest[J]. Construction Technology, 2020, 49(17): 89-94.
[38]	Zou Dafang, Wang Zidong, Zhang Leimin, et al. Deep field relation neural network for click-through rate prediction[J]. Information Sciences, 2021,577:128−139. doi: 10.1016/j.ins.2021.06.079