In the present study, Deep Learning (DL) algorithm or Deep Neural Networks (DNN), one of the most powerful techniques in Machine Learning (ML), is employed for estimation of ultimate load factor of nonlinear inelastic steel truss. Datasets consisting of training and test data are created based on advanced analysis. In datasets, input data are the member cross-sections of the truss members and output data is the ultimate load factor of the whole structure. An example of a planar 39-bar steel truss is studied to demonstrate the efficiency and accuracy of the DL method. Five optimizers such as Adadelta, Adam, Nadam, RMSprop and SGD and five activation functions such as ELU, LeakyReLU, Sigmoid, Softplus, and Tanh are considered. Based on analysis results, it is proven that DL algorithm shows very high accuracy in the regression of the ultimate load factor of the planar 39-bar nonlinear inelastic steel truss. The number of layers can be selected with a small value such as 1, 2 or 3 layers and the number of neurons in each layer can be chosen in the range [N i , 3N i ] with N i is the number of input variables of the model. The activation functions ELU and LeakyReLU have better convergence speed of the training process compared to Sigmoid, Softplus and Tanh. The optimizer Adam works well with all activation functions considered and produces better MSE values regarding both training and test data.
113Hung, T. V., et al. / Journal of Science and Technology in Civil Engineering the load-carrying capacity of whole structure that allows elimination of the tedious individual member check approach used in the classical methods. However, advanced analysis methods are excessive computing times to solve the design problems which require lots of structural analyses such as optimization or reliability analysis of the structure [5][6][7][8]. In such cases, using metamodels based on machine learning (ML) techniques are considered as an efficient solution.Metamodel is an approximate mathematical representation used to perform the complicated relationship between input and output data. In light of this, nonlinear inelastic responses of the structure are predicted without performing advanced analysis. Some popular ML methods are Support Vector Machine (SVM) [9], Kriging [10], Random Forest (RF) [11], Gradient Tree Boosting (GTB) [12], Decision Tree (DT) [13], and so on. The applications of ML methods into structural design are quite diverse but focused primarily on damage detection [14,15] and health monitoring [16,17]. Besides, researchers have been applying ML methods for structural optimization [18], reliability analysis [19], prediction of structural ultimate strength [20], etc.The performance of traditional ML methods largely depends on the data representation choice of the users since these methods cannot automatically detect the representations or features needed for classification or detection from the raw input data. The pattern-recognition often requires complex techniques with high expertise. Therefore, using ML methods is c...