Support vector regression based modelling approach was used to predict the shear strength of reinforced and prestressed concrete deep beams. To compare its performance, a back-propagation neural network and the three empirical relations was used with reinforced concrete deep beams. For prestressed deep beams, one empirical relation was used. Results suggest an improved performance by the SVR in terms of prediction capabilities in comparison to the empirical relations and back propagation neural network. Parametric studies with SVR suggest the importance of concrete cylinder strength and ratio of shear span to effective depth of beam on strength prediction of deep beams.
Various modelling approaches are being used to predict the behaviour of structures and their components by civil engineers. The traditional modelling approaches are based on empirical relationships derived using experimental data. Number of models has been proposed to predict the compressive strength and shear strength of beams and columns depending on different experimental conditions and assumptions. Several studies suggest the data specific nature of these models. As the design of a structure or a structural component may requires an iterative process in which the assumed model behaviour converges with the experimental behaviour, thus requiring a cost efficient computational technique.
Within last decade, researchers have explored the potential of back-propagation artificial neural networks (ANN) to solve various civil engineering problems. In structural engineering, neural networks have successfully been applied to several areas such as structural analysis and design [1], [2] and [3], structural damage assessment [4], [5] and [6], prediction of compressive strength of concrete mixes [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] and [18], shear strength prediction of reinforced concrete beams [19], [20], [21], [22], [23] and [24] and compressive strength of columns [25], [26], [27] and [28] as well as in non destructive strength assessment [29].
Determination of suitable architecture and various user-defined parameters has been a major issue in the design of an ANN [30]. ANN based modelling algorithm requires setting up of different learning parameters (like learning rate, momentum), the optimal number of nodes in the hidden layer and the number of hidden layers. In most of the reported applications, selection of number of hidden layers and the nodes in hidden layer is done by using a rule of thumb or trying several arbitrary architectures to select one that gives the best performance with test dataset. A suitable value of parameters like learning rate and momentum is also required for selected hidden layers and nodes. Design of a back-propagation neural network also involves in using a non-linear optimisation problem that may results in a local minima. During training process a large number of training iterations may force ANN to over train, which may affect the predicting capabilities of the model. Several studies suggested using a validation dataset (i.e. a dataset other than the training dataset) to have an idea about the suitable number of iterations for a specific dataset. This may be a problem for studies where number of dataset is limited, like one of concrete strength prediction. Recent studies [31], [32] and [33] suggest the usefulness of genetic algorithm to find the optimal architecture of ANN.
An alternative modelling technique, called Support Vector Machines [34], has recently been applied to the field of civil engineering and provides improved performance in comparison to empirical relations and back-propagation neural network [35], [36], [37], [38], [39], [40], [41] and [42]. Keeping in view the better performance by the support vector machines, present study examines its potential in predicting the shear strength of reinforced concrete deep beams and prestressed deep beams. The results obtained by the support vector machines were compared with the [43] and [44] codes and strut-and-tie methods. The results were also compared with a back-propagation neural network to highlight the efficiency of the proposed method.
This study suggests that SVR is a powerful computational tool and can effectively be used to analyse the complex relationship between various parameter used in predicting shear strength of deep beams. Comparisons between the SVR and strut-and-tie as well as ACI approaches indicate that SVR results are better. In spite of the fact that determination of C and kernel specific parameters still requires a heuristic process, this paper shows the potential of SVR with a suitable kernel function as an alternative modelling technique for shear strength predication of deep beams in place of back-propagation neural network and other empirical approaches.
The SVR model is also used to perform parametric studies and found to be successful in modelling physical processes. The parametric studies suggest that the shear strength of deep beams increases as the concrete strength increases and the shear span-to-depth-ratio decreases. The shear strength of deep beams is not affected by the variation in horizontal web reinforcement for a/d > 1 while the influence of variation in horizontal web reinforcement on shear strength is more predominant for a/d < 1. The results of the parametric studies using SVR were in agreement with the work carried out by Smith and Vantsiotis [50].
