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KONG, FANCHAO The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument
Fanchao Kong 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this paper, the prescribed mean curvature Rayleigh $p$-Laplacian equation with a deviating argument $$\Big{(}\varphi_p(\frac{u'(t)}{\sqrt{1+(u'(t))^{2}}})\Big{)}'+f( u'(t))+g(t,u(t-\tau(t)))=e(t) $$ is studied. By using Mawhin's continuation theorem and some analysis methods, we obtain the existence of a set with $2kT$-periodic solutions for this equation and then a homoclinic solution is obtained as a limit of a certain subsequence of the above set.
Fanchao Kong,Tao Tian,Dechun Lu,Bing Xu,Weipeng Lin,Xiuli Du 대한토목학회 2023 KSCE Journal of Civil Engineering Vol.27 No.11
Four hybrid intelligent methods are developed to predict the maximum ground surface settlement (Smax) induced by shallow underground excavation method (SUEM). Particle swarm optimization (PSO) algorithm with k-fold cross validation is used to determine the optimal hyperparameters or random parameters in the four machine learning (ML) methods, namely that, back-propagation neural network (BPNN), extreme learning machine (ELM), support vector regression (SVR) and random forest (RF). 100 field engineering samples are collected from published papers. In each data sample, the effect of stratum mechanical conditions, tunnel geometric parameters and construction parameters on Smax is considered. Correlation laws among parameters are investigated through Pearson correlation coefficient, data distribution histogram and correlation confidence ellipse. The performance of four PSO-based ML methods is comprehensively compared by fitness function, time cost and prediction accuracy in the training and test processes. PSO-RF outperforms PSO-SVR, PSO-ELM and PSO-BPNN in the prediction accuracy for Smax owing to larger R2, smaller MAE and RMSE. Calculation time that the optimal hyperparameters are determined is the fastest for PSO-RF, and PSO-ELM has the smallest fitness function. The prediction performance of PSO-RF method for construction parameters is also discussed. This work can provide theoretical guidance for design and construction of SUEM.