基于核映射极限学习机的入口氮氧化物预测
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摘要
针对在线贯序极限学习机(OS-ELM)算法隐含层输出不稳定、易产生奇异矩阵和在线贯序更新时没有考虑训练样本时效性的问题,提出一种基于核函数映射的正则化自适应遗忘因子(FFOS-RKELM)算法.该算法利用核函数代替隐含层,能够产生稳定的输出结果.在初始阶段加入正则化方法,通过构造非奇异矩阵提高模型的泛化能力;在贯序更新阶段,通过新到的数据自动更新遗忘因子.将FFOS-RKELM算法应用到混沌时间序列预测和入口氮氧化物时间序列预测中,相比于OS-ELM、FFOS-RELM、OS-RKELM算法,可有效地提高预测精度和泛化能力.
To solve the problem that the hidden layer output of an online sequential extreme learning machine(OS-ELM)algorithm is not stable, the singular matrix is easy to produce, and the OS-ELM has no consideration about the training sample timeliness during the sequential updating process, an improved OS-ELM algorithm online sequential extreme learning machine based on adaptive forgetting factor of kernel function mapping(FFOS-RKELM) is presented based on the regularization and adaptive forgetting factor of kernel function mapping. In the FFOS-RKELM algorithm, the kernel function replaces the hidden layer to produce the stable output results. In the initialization phase, the regularization method can improve the generalization ability of the model by constructing a nonsingular matrix. During the sequential updating phase, the forgetting factor can be adjusted automatically according to new data. The FFOS-RKELM algorithm is applied to the prediction of the chaotic time series and the time series of Inlet NOx. Compared with the OS-ELM algoyithm, the FFOS-RELM algorithm and the OS-RKELM algorithm, the proposed algorithm can improve the prediction accuracy and generalization ability more effectively.
To solve the problem that the hidden layer output of an online sequential extreme learning machine(OS-ELM)algorithm is not stable, the singular matrix is easy to produce, and the OS-ELM has no consideration about the training sample timeliness during the sequential updating process, an improved OS-ELM algorithm online sequential extreme learning machine based on adaptive forgetting factor of kernel function mapping(FFOS-RKELM) is presented based on the regularization and adaptive forgetting factor of kernel function mapping. In the FFOS-RKELM algorithm, the kernel function replaces the hidden layer to produce the stable output results. In the initialization phase, the regularization method can improve the generalization ability of the model by constructing a nonsingular matrix. During the sequential updating phase, the forgetting factor can be adjusted automatically according to new data. The FFOS-RKELM algorithm is applied to the prediction of the chaotic time series and the time series of Inlet NOx. Compared with the OS-ELM algoyithm, the FFOS-RELM algorithm and the OS-RKELM algorithm, the proposed algorithm can improve the prediction accuracy and generalization ability more effectively.
引文
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[2] Huang G B, Zhu Q Y, Siew C K, et al. Extreme learning machine:Theory and applications[J]. Neurocomputing,2006, 70(1):489-501.
[3] Liang N Y, Huang G B, Saratchandran P, et al. A fast and accurate online sequential learning algorithm for feedforward networks[J]. IEEE Trans on Neural Networks, 2006, 17(6):1411-1423.
[4] Huang G B, Zhou H M, Ding X J, et al. Extreme learning machine for regression and multiclass classification[J].IEEE Trans on Systems, Man, and Cybernetics, Part B:Cybernetics, 2012, 42(2):513-529.
[5] Huynh H T, Won Y. Regularized online sequential learning algorithm for singlehidden layer feedforward neural networks[J]. Pattern Recognition Letters, 2011,32(14):1930-1935.
[6] Deng W Y, Ong Y S, Tan P S, et al. Online sequential reduced kernel extreme learning machine[J].Neurocomputing, 2016, 174:72-84.
[7] Soares S G, Araujo R. An adaptive ensemble of online extreme learning machines with variable forgetting factor for dynamic system prediction[J]. Neurocomputing,2016, 171:693-707.
[8] Javed K, Gouriveau R, Zerhouni N. SWELM:Asummation wavelet extreme learning machine algorithm with a priori parameter initialization[J].Neurocomputing, 2014, 123:299-307.
[9]杜占龙,李小民,郑宗贵,等.基于正则化与遗忘因子的极限学习机及其在故障预测中的应用[J].仪器仪表学报, 2015, 36(7):1546-1553.(Du Z L, Li X M, Zheng Z G, et al. Extreme learning machine based on regularization and forgetting factor and its application in fault prediction[J]. Chinese J of Scientific Instrument, 2015, 36(7):1546-1553.)
[10] You C X, Huang J Q, Lu F. Recursive reduced kernel based extreme learning machine for aeroengine fault pattern recognition[J]. Neurocomputing, 2016, 214:1038-1045.
[11] Shao Z F, Meng Joo Er. An online sequential learning algorithm for regularized extreme learning machine[J].Neurocomputing, 2016, 173:778-788.
[12] Lan Y, Soh Y C, Huang G B. Ensemble of online sequential extreme learning machine[J].Neurocomputing, 2009, 72:3391-3395.
[13] Jerome M, Rui A, Francisco S. Adaptive fuzzy identification and predictive control for industrial processes[J]. Expert Systems with Applications, 2013,40(17):6964-6975.
[14]李军,李大超.基于优化核极限学习机的风电功率时间序列预测[J].物理学报, 2016, 65(13):39-48.(Li J, Li D C. Wind power time series prediction based onoptimized online kernal extreme learning machine[J].Physics J, 2016, 65(13):39-48.)
[15]刘伟,王科俊,邵克勇.混沌时间序列的混合粒子群优化预测[J].控制与决策, 2007, 22(5):562-565.(Liu W, Wang K J, Shao K Y. Predicting chaotic time series using hybrid particle swarmoptimization algorithm[J]. Control and Decision, 2007, 22(5):562-565.)