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This paper aims to build a neural network model to optimally design two-span continuous reinforced concrete beams. The training and checking data of the neural network are obtained by genetic algorithms, whose constraints are built according to the ACI Building Code and objective function is to find the minimum cost of longitudinal reinforcement, stirrups and concrete. The neural network adopted in this paper is the feed forward back propagation network, whose input vector consists of the span, width and effective depth of the beam, dead load, compressive strength of concrete as well as yield strength of steel and the output vector the positive and negative steel ratios and minimum total cost. The correlation coefficients between the target and network output of the testing data can reach as high as 0.9992, 0.9980 and 0.9999, respectively for the positive and negative steel ratios and minimum cost. Compared with the adaptive neuro-fuzzy inference system, the neural network shows almost the same accuracy but is much easier implemented.

This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the input vector, one hidden layer and output layer. Bayesian regularization is employed to obtain the effective number of neurons in the hidden layer. The input variables and target of the adaptive neuro-fuzzy inference system are the same as those of the neural network. The data clustering technique is used to group data points so that the membership functions will be more tailored to the input data, which in turn greatly reduces the number of fuzzy rules. Numerical results indicate that these two models have almost the same accuracy, while the adaptive neuro-fuzzy inference system takes more time to train. It is also shown that although the effective number of neurons in the hidden layer is less than half the number of the input elements, the neural network can have satisfactory performance

Using a genetic algorithm owing to high nonlinearity of constraints, this paper first works on the optimal design of two-span continuous singly reinforced concrete beams. Given conditions are the span, dead and live loads, compressive strength of concrete and yield strength of steel; design variables are the width and effective depth of the continuous beam and steel ratios for positive and negative moments. The constraints are built based on the ACI Building Code by considering the strength requirements of shear and the maximum positive and negative moments, the development length of flexural reinforcement, and the serviceability requirement of deflection. The objective function is to minimize the total cost of steel and concrete. The optimal data found from the genetic algorithm are divided into three groups: the training set, the checking set and the testing set for the use of the adaptive neuro-fuzzy inference system (ANFIS). The input vector of ANFIS consists of the yield strength of steel, compressive strength of concrete, dead load, span, width and effective depth of the beam; its outputs are the minimum total cost and optimal steel ratios for positive and negative moments. To make ANFIS more efficient, the technique of Subtractive Clustering is applied to group the data to help streamline the fuzzy rules. Numerical results show that the performance of ANFIS is excellent, with correlation coefficients between the three targets and outputs of the testing data being greater than 0.99.