Proposing an improved TSK fuzzy model applicable for incomplete data and using it for capacity prediction of RC columns strengthened with NSM or hybrid FRP method

In this article, a method is proposed for modifying the Takagi-Sugeno-Kang (TSK) fuzzy model, which enables the incorporation of incomplete data into the modeling process, extracting valuable information from it. The proposed methodology can prove advantageous in scenarios where experimental data are limited, and the exclusion of incomplete data is not feasible. In order to evaluate the proposed method, experimental data on reinforced concrete (RC) columns strengthened using Near-Surface Mounted (NSM) Fiber-Reinforced Polymer (FRP) bars with (hybrid) or without FRP jackets were collected from the existing literature. Since the mentioned strengthening methods are relatively new and are recommended for cases with eccentric loading or slender columns, the number of conducted tests is limited. Subsequently, fuzzy models were constructed using the conventional and the proposed modified methods. The comparison of the results of the two modeling methods demonstrated a higher accuracy of the proposed approach compared to the conventional one. Furthermore, parametric study of strengthening factors was performed, assessing their influence on capacity. It was found that increasing the axial rigidity of NSM FRP first increases the capacity and then decreases it. Additionally, increasing the confinement-related parameter leads to an increase in the capacity of the strengthened columns.