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极限学习机是近年来提出的一种前向单隐层神经网络训练算法，具有训练速度快、不会陷入局部最优等优点，但其性能会受到随机选取的输入权值和阈值的影响. 针对这一问题，提出一种基于多目标优化的改进极限学习机，将训练误差和输出层权值的均方最小化同时作为优化目标，采用带精英策略的快速非支配排序遗传算法对极限学习机的输入层到隐层的权值和阈值进行优化. 将该算法应用于摇摆工况下自然循环系统不规则复合型流量脉动的多步滚动预测，分析了训练误差和输出层权值对不同步长预测效果的影响. 仿真结果表明，优化极限学习机预测误差可以用较小的网络规模获得很好的泛化能力. 为流动不稳定性的实时预测提供了一种准确度较高的途径，其预测结果可以作为核动力系统操作员的参考.Extreme learning machine (ELM) is a recently proposed learning algorithm for single-hidden-layer feedforward neural networks, which has a fast learning speed while avoiding the problem of local optimal solution. However, the performance of ELM may be affected due to the random determination of the input weights and hidden biases. In this paper, a multi-objective optimized extreme learning machine (MO-ELM) is proposed to solve this problem. The algorithm uses the no-dominated sorting genetic algorithm II algorithm to select input weights and hidden biases. Both the learning errors and the mean square value of output weights are used as optimization objects. The MO-ELM algorithm is used in the multi-step forecast of irregular complex flow oscillations of natural circulation system in rolling motion, and the influences of learning errors and output weights on forecast results are analyzed. Experimental results show that MO-ELM can achieve good generalization performance with much more compact networks and provide a relatively accurate forecast method of flow rate, and the forecast results can be used as reference to nuclear power system operators.
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Keywords:
- flow instability /
- extreme learning machine /
- multi-objective optimization /
- no-dominated sorting genetic alorithm Ⅱ
[1] Huang G B, Zhu Q Y, Siew C K 2004 Proceedings of the International Joint Conference on Neural Networks Budapest, Hungary, July 25-29, 2004 p985
[2] Li M B, Huang G B, Saratchandran P, Sundararajan N 2005 Neurocomputing 68 306
[3] Rong H J, Ong Y S, Tan A H, Zhu Z 2008 Neurocomputing 72 359
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[5] Feng G, Huang G B, Lin Q, Gay R 2009 IEEE Trans. Neural Networ. 20 1352
[6] Cao J, Lin Z, Huang G B 2010 Neurocomputing 73 1405
[7] Cao J, Lin Z, Huang G B 2011 Neural Process. Lett. 33 251
[8] Javed K, Gouriveau R, Zerhouni N 2014 Neurocomputing 123 299
[9] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese) [高光勇, 蒋国平 2012 物理学报 61 040506]
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[12] Deb K, Pratap A, Agarwal S, Meyarivan T 2002 IEEE Trans. Evolut. Comput. 6 182
[13] Huang B, Buckley B, Kechadi T M 2010 Expert Syst. Appl. 37 3638
[14] Ak R, Li Y, Vitelli V, Zio E, Droguett E L, Jacinto C M C 2013 Expert Syst. Appl. 40 1205
[15] He B Y, Li H Y, Zhang B 2013 Acta Phys. Sin. 62 190505 (in Chinese) [贺波勇, 李海阳, 张波 2013 物理学报 62 190505]
[16] Tan S C, Su G H, Gao P Z 2009 Ann. Nucl. Eng. 36 103
[17] Tan S C, Su G H, Gao P Z 2009 Appl. Therm. Eng. 29 3160
[18] Tan S C, Pang F G 2005 Nucl. Power Engineer. 26 140 (in Chinese) [谭思超, 庞凤阁 2005 核动力工程 26 140]
[19] Tan S C, Gao P Z, Su G H 2008 Atom. Energy Sci. Technol. 42 1007 (in Chinese) [谭思超, 高璞珍, 苏光辉 2008 原子能科学技术 42 1007]
[20] Jiang H, Li T, Zeng X L, Zhang L P 2014 Chin. Phys. B 23 010501
[21] Zhang W, Tan S, Gao P, Wang Z, Zhang L, Zhang H 2014 Ann. Nucl. Energy 65 1
[22] Srinivas N, Deb K 1994 Evolutionary Comput. 2 221
[23] Bartlett P L 1998 IEEE Trans. Inform. Theory 44 525
[24] Lee W S, Bartlett P L, Williamson R C 1996 IEEE Trans. Inform. Theory 42 2118
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[1] Huang G B, Zhu Q Y, Siew C K 2004 Proceedings of the International Joint Conference on Neural Networks Budapest, Hungary, July 25-29, 2004 p985
[2] Li M B, Huang G B, Saratchandran P, Sundararajan N 2005 Neurocomputing 68 306
[3] Rong H J, Ong Y S, Tan A H, Zhu Z 2008 Neurocomputing 72 359
[4] Miche Y, van Heeswijk M, Bas P, Simula O, Lendasse A 2011 Neurocomputing 74 2413
[5] Feng G, Huang G B, Lin Q, Gay R 2009 IEEE Trans. Neural Networ. 20 1352
[6] Cao J, Lin Z, Huang G B 2010 Neurocomputing 73 1405
[7] Cao J, Lin Z, Huang G B 2011 Neural Process. Lett. 33 251
[8] Javed K, Gouriveau R, Zerhouni N 2014 Neurocomputing 123 299
[9] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese) [高光勇, 蒋国平 2012 物理学报 61 040506]
[10] Bhat A U, Merchant S S, Bhagwat S S 2008 Ind. Eeg. Chem. Res. 47 920
[11] Zhu Q Y, Qin A K, Suganthan P N, Huang G B 2005 Pattern Rrcogn. 38 1759
[12] Deb K, Pratap A, Agarwal S, Meyarivan T 2002 IEEE Trans. Evolut. Comput. 6 182
[13] Huang B, Buckley B, Kechadi T M 2010 Expert Syst. Appl. 37 3638
[14] Ak R, Li Y, Vitelli V, Zio E, Droguett E L, Jacinto C M C 2013 Expert Syst. Appl. 40 1205
[15] He B Y, Li H Y, Zhang B 2013 Acta Phys. Sin. 62 190505 (in Chinese) [贺波勇, 李海阳, 张波 2013 物理学报 62 190505]
[16] Tan S C, Su G H, Gao P Z 2009 Ann. Nucl. Eng. 36 103
[17] Tan S C, Su G H, Gao P Z 2009 Appl. Therm. Eng. 29 3160
[18] Tan S C, Pang F G 2005 Nucl. Power Engineer. 26 140 (in Chinese) [谭思超, 庞凤阁 2005 核动力工程 26 140]
[19] Tan S C, Gao P Z, Su G H 2008 Atom. Energy Sci. Technol. 42 1007 (in Chinese) [谭思超, 高璞珍, 苏光辉 2008 原子能科学技术 42 1007]
[20] Jiang H, Li T, Zeng X L, Zhang L P 2014 Chin. Phys. B 23 010501
[21] Zhang W, Tan S, Gao P, Wang Z, Zhang L, Zhang H 2014 Ann. Nucl. Energy 65 1
[22] Srinivas N, Deb K 1994 Evolutionary Comput. 2 221
[23] Bartlett P L 1998 IEEE Trans. Inform. Theory 44 525
[24] Lee W S, Bartlett P L, Williamson R C 1996 IEEE Trans. Inform. Theory 42 2118
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