# Prediction of the Yield Strength of RC Columns Using a PSO-LSSVM Model
## 3 Data Collection and Pre-Processing  
In this work, a quantity of data adopted for the following calculations is collected from the PEER database [49; 50] and the relevant literature [22; 44]. The PEER database covers extensive hysteretic curves of the RC columns with various material properties obtained by pseudo-static cyclic test. As for the collected original experimental data, relevant preprocessing should be conducted to obtain the corresponding yield point whose values are used to compare with predictive values (see Section 4 for details). The steps of data pre-processing are as follows: Firstly, determine the skeleton curve of each hysteretic curve according to the rule seen in Section 2.1; secondly, determine the yield point on the obtained skeleton curve according to the method seen in Section 2.2, and the yield strength and displacement are obtained. However, the amount of data involved in the data collection and pre-processing is enormous. To improve the data-processing efficiency, the above two steps are implemented via programming calculation. Thus, a program script was written for plotting the skeleton curves, and then the yield strength and yield displacement are both outputted. Thereafter, a total of 382 test results were selected and organized in bulk according to the parameter types, and then all the types of the parameter were categorized into two parts: input parameters and output properties. The input parameters are the influencing factors including the basic parameters of the RC column. The output properties denote performances of the RC column, e.g., yield strength and displacement, which are codetermined by the influence factors. In the present model, nine representative influence factors are identified as the input parameters of the proposed model for the prediction of output properties. The set of influence factors can be expressed as \(\{D_{c},\,\rho_{r},\,SecT,f_{c},f_{yl},f_{ygr},\,\rho_{l},\,\rho_{v},\,\rho_{n}\}\), where \(D_{c}\) is the section size; \(\rho_{r}\) is the span-to-depth ratio defined as \(L/D_{c}\), in which \(L\) is length; \(SecT\) is the section type, \(SecT=1\) or \(SecT=2\) denotes the square or circle section type; \(f_{c}\) is the strength of concrete; \(f_{yl}\) is the yield strength of longitudinal bars; \(f_{ygr}\) is the yield strength of transverse bars; \(\rho_{l}\) is the longitudinal reinforcement ratio; \(\rho_{v}\) is the transverse reinforcement ratio; \(\rho_{n}\) is the axial load ratio defined by \(\rho_{n}=P/(A_{g}f_{c})\), in which \(P\) is the constant axial load and \(A_{g}\) is the gross section area. These input parameters, i.e., influence factors mentioned above, are summarized in Table 2.  
The focus of the developed model is a prediction of the yield strength (\(F_{y}\)) and yield displacement (\(\Delta_{y}\)) of RC columns, which are considered as the output properties in the present study. The ranges of the input parameters and output properties are presented in Table 3 in detail. It can be seen that the input parameters and output properties are well-distributed over a wide range. Thus, each specimen in the test database can be written as \(\{\{D_{c},\,\rho_{r},\,SecT,f_{c},f_{yl},f_{ygr},\,\rho_{l},\,\rho_{v},\,\rho_{n }\},\,\{F_{y},\,\Delta_{y}\}\}\), which involves the input parameters and output properties. Figure 3 displays the histograms of the input parameters and output properties. Figure 2: The yield point judgment methods: (**a**) Geometric Graphic Method; (**b**) R. Park Method; (**c**) Equivalent Elasto-Plastic Energy Method.