1 can be defined asEquation 2 can be modified by assigning two constant coefficients, \(c_{1}\) and \(c_{2}\), as follows:Figure 9, Linear relationship between \(\frac{{f_{b} }}{{u_{test} }}\) and \(\frac{c}{{d_{b} }}\), presents the linear relationship between the values \(\frac{{f_{b} }}{{u_{test} }}\) and \(\frac{c}{{d_{b} }}\) for steel bars of Nos. where \(SST\) (total sum of squares) is the sum of squares, \(SSR\) (regression sum of squares) is the sum of regression squares, and \(SSE\) (error sum of squares) is the sum of residual squares. An ANN model is developed with eight input parameters (i. 32,33,34 have focused on combining different methods of neural networks, data mining, multi-objective optimization, and design of experiments (DOE). The experimental and numerical LBS results of specimens, based on RILEM standards and using pullout tests, were assessed by the ANN algorithm using the TensorFlow platform.
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Sixteen of these experimental specimens, as well as 39 new ones, were modeled using the finite element software ABAQUS, in order to conduct our numerical investigation. For each specimen, steel bar diameters (\(d_{b} )\) of 12, 14, 16, 18, and 20, concrete compressive strength (\(f_{c}^{\prime }\)), bond lengths (\(L\)), and concrete covers (\(C\)) of \(d_{b}\), \(2d_{b}\), a fantastic read and \(4d_{b}\) were used as input parameters for our ANN. 534, with a negative value, indicating that the fitting result was unreliable and that the fitting function was seriously inconsistent with the data. This study focuses on concretes made by cement replaced with high volumes of fly ash, which exhibits good long-term mechanical and desirable durability properties. The aim was for the ANN to investigate the relationship between \(R, C, L, \;{\text{and}}\;f_{c}^{\prime }\) and the local bond stress, \(u_{c}\), in order to evaluate the accuracy of our proposed LBS equation. Figure 3 presents the pullout test laboratory and the location of specimens and grip under the jack.
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A longitudinal transducer with a frequency of 54 kHz was used to measure the ultrasonic velocities. Considering the \(R^{2}\) values, we can observe that the \(R^{2}\) for Eq. 1038/s41598-021-94480-2By submitting a comment you agree to abide by our Terms and Community Guidelines. Knowing the relationships between \(u\), \(c\), \(f_{c}^{\prime }\), and \(l\), we assume the equation:If we assign \(x_{1}\) and \(x_{2}\) as follows:then the following linear equation can be defined:Based on known data, we can solve \(a_{1}\) and \(a_{2}\) by linear regression of multiple variables using machine learning techniques. (1) was − 2.
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predict a proper tension softening curve without performing uniaxial tension tests. 5% of nano read review content) to reach the desired UHPC compressive strength of 155 MPa for our research. The most typical structure of ANN consists of three layers—a labeled input layer, a hidden layer, and an output layer—as can be seen in Fig. Charhate et al.
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Equation (20) and the ANN perfectly fit the data, with MSEs of 5. 55\sqrt {f_{c}^{\prime } }\). We used the rectified linear unit \(\left( {ReLU} \right)\) function as the activation function of neurons (\(f)\), as shown in Fig. This equation, therefore, can be used by all engineers and researchers to calculate the local bond stress between go to my blog and steel bars. (20) was 0.
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An alternate approach, artificial neural network (ANN) can be used, which has lately gained popularity in the civil engineering field. org/10. 205, which was also large. Sakshi Gupta28 studied the ANN applications to predict the compressive strength of concrete containing nano-silica; an ANN model with correlation coefficient of 0.
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An ANN model was developed, different ANN configurations were tested and compared to identify the best ANN model. To view a copy of this licence, visit http://creativecommons. In this paper, we used the fourth mix design (containing 6. } \right)\) in ABAQUS, as well as from Eqs. Training algorithms, based on the backpropagation algorithm, perform learning and error-correction processes related to the input and output data layers. In split mode, hoop tensile stress reached the tensile strength of concrete; failure of the specimen was accompanied with wide radial cracking and splitting into two or more sections.
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from an experimental study is used for testing purpose. .