Aiming at the shortcomings of the Golden Jackal optimization algorithm, such as low convergence accuracy and easy falling into the optimal local solution, an improved Golden Jackal optimization algorithm was proposed. First, sine and piecewise linear (SPM) chaotic mapping was introduced to increase the population number to achieve the purpose of initial population diversity. The self-adaptive weight and sine–cosine algorithm improved the position update formula of the Golden Jackal optimization algorithm, so the global search ability of the golden jackal algorithm is improved, and avoid the algorithm that fell into local optimality. Second, simulation experiments with eight standard test functions are performed to prove that the algorithm has excellent optimization ability. The improved Golden Jackal optimization algorithm was applied to optimize the kernel parameters of hybrid kernel principal component analysis. A fault diagnosis model is proposed to improve the golden jackal algorithm to optimize the kernel principal component analysis. Finally, the proposed method is used to fault diagnosis in the hot strip mill process. According to the study of simulation results, the faulty data can be identified effectively by this method, the accuracy is up to 100%, and the fault false alarm rate is greatly reduced.