مدل های مبتنی بر رگرسیون بردار پشتیبانی برای پیش بینی ویژگی های شکست مقاومت بالا و قدرت فوق العاده بالای تیرهای بتن

This paper examines the applicability of support vector machine (SVM) based regression to predict fracture characteristics and failure load (Pmax) of high strength and ultra high strength concrete beams. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described briefly. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Support Vector Regression (SVR) is the extension of SVMs to solve regression and prediction problems. The main characteristics of SVR includes minimizing the observed training error, attempts to minimize the generalized error bound so as to achieve generalized performance. Four Support Vector Regression (SVR) models have been developed using MATLAB software for training and prediction of fracture characteristics. It is observed that the predicted values from the SVR models are in good agreement with those of the experimental values.

Concrete has been one of the most commonly used construction materials in the world. One of the major problems civil engineers face today is concerned with preservation, maintenance and retrofitting of structures. The historical development of concrete material may be marked and divided into several stages. The first is the traditional normal strength concrete followed by high strength concrete, high performance concrete and reactive powder concrete/UHSC. Since UHSC is a relatively new material, the fracture behavior of this material is not well understood [1], [2], [3] and [4]. UHSC is successfully applied in the field for the construction of Sherbrook Pedestrian Bridge, Canada, The Glenmore/Legs by Pedestrian, Alberta, Canada and Π shaped UHPC beams installed in footbridges in Auckland, New Zealand [5] and [6]. Concrete is a quasi-brittle material, which means its fracture process zone (FPZ) size is not small compared with the typical specimen or structural dimension. Classical linear elastic fracture mechanics (LEFM) approach is unable to predict the progressive failure of concrete specimens due to the presence of large FPZ of variable size ahead of the crack tip and the cohesive stress transferred within FPZ of the quasi-brittle materials like concrete [7]. The LEFM based modeling approach assumes that once a crack propagates by a distance, this part of the material loses its load carrying capacity suddenly and completely. The complex nonlinear phenomena that take place in FPZ can be idealized and approximated using nonlinear fracture approaches to predict the localized physical behavior in the vicinity of a crack and at the crack tip. Nonlinear fracture mechanics based approach recognizes that FPZ exists in front of the crack tip, in which the material can still carry loadings by mechanisms such as aggregate interlocking, surface friction and material bonding. As the crack propagates and opens, the material in FPZ softens with gradual energy dissipation, which can be accurately modeled by the fictitious crack model. The crack propagation direction is assumed to be perpendicular to the direction of the maximum stress at the cohesive crack tip. The cohesive crack model is one of such simplified nonlinear fracture models that can simulate satisfactorily the behavior of concrete fracture. Inspired by the early stage of development of the fracture models [7], [8] and [9]. Hillerborg et al. [10] initially applied cohesive crack method (or fictitious crack model) as a suitable nonlinear model for mode I fracture to simulate the softening damage of concrete structures. Support Vector Machines (SVM) are leaning machines implementing the structural risk minimization inductive principle to obtain good generalization on a limited number of learning patterns. Support vector regression attempts to minimize the generalization error bound so as to achieve generalized performance. In SVR, the loss function is used to penalize errors that are greater than the threshold value-ε. These loss functions usually lead to the sparse representation of the decision rule, giving significant algorithmic and representational advantages. It is observed that, the support vector machine (SVM) was applied to various pattern recognition applications such as text classification and image recognition [11] and [12] and was extended to regression analysis [13], [14], [15] and [16]. SVM was proved to be successful in various field of engineering [17], [18], [19], [20] and [21]. Lee et al. [17] successfully predicted the concrete strength based on its mix proportion data by using SVR technique and neural networks (NN) against the experimental results and concluded SVR method can predict the compressive strength of concrete with higher estimation accuracy and in a shorter computation time. Samui [18] used SVM to determine the settlement of shallow foundations on cohesionless soil and it was found that SVM has potential to be a useful and practical tool for prediction of settlement. Chen et al. [19] estimated the exposed temperature for fire-damaged concrete using SVM. It was concluded that the accuracy of estimation for the SVM model increases with the increase of effective parameter and the ratio of training samples to the total samples was considered in the analysis of SVM model. Maity et al. [20] verified the potential of SVR for prediction of monthly stream-flow using endogenous property. Shi and Dong [21] predicted strength of cement using support vector machine. The results of SVM were compared with that of the artificial neural network (ANN) model results. It was found that the SVM has achieved better accuracy and generalization than the ANN method. From the above literature, it is observed that the SVR is one of the recent advanced statistical methods to predict the responses and its potential applicability is not verified in the field of structural engineering. In the present study, the support vector machine for regression (Support Vector Regression, SVR) is applied to predict fracture characteristics and failure load of high strength concrete (HSC) and ultra high strength concrete (UHSC) beams. Training and test patterns for the SVR are based on the test results obtained using three point bending test. This paper presents the details of characterization and casting of high strength and ultra high strength concrete beams. Procedure for evaluation of failure load and fracture characteristics such as critical stress intensity factor (KIC), facture energy (GF) and critical crack tip opening displacement (CTODc) have been explained in brief. Finally the applicability of SVR to predict fracture characteristics and failure load of high strength and ultra high strength concrete beams is examined.

Fracture mechanics based SVM model has been developed to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). SVM model has also been developed to predict the failure loads under the three point bending test for HSC and UHSC beam specimens. Characterization of mix of high strength and ultra strength concrete has been described. An overview of experimental details of beams tested under static loading has been shown and methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Four SVM models have been developed using MATLAB software for training and prediction of the three fracture parameters. SVM has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed that the predicted values of failure load, facture energy, critical stress intensity factor and critical crack tip opening displacement are in good agreement with those of the experimental values. The R2 values for all four developed models is found to be closer to 1 indicating better predictability of the models.