This paper is concerned with the data-driven realization of fault detection approach with performance optimization. For our purpose, the datadriven realization form of linear kernel representations is studied first, which is essential in our work. It is followed by a data-driven realization of kernel representation and its implementation in the design scheme of fault detection systems. Nevertheless, the basic idea behind this approach lies in the one-step identification of kernel representation using LQ-decomposition. Then, the recursive kernel representation is introduced and the so-called gradient descent algorithm is applied to optimize the performance of the proposed data-driven fault detection system. The effectiveness of the proposed approaches is illustrated by a numerical example and a case study on laboratory setup of a three-tank system.