In view of the problem that it's difficult for the sum of squares double exponentially weighted moving average(SS-DEWMA) chart to select appropriate parameters, which satisfy multiple optimal indexes of data monitoring, a multi-objective optimization of SS-DEWMA(MO-SS-DEWMA) chart data monitoring method is proposed and applied to sensor fault detection of nonlinear systems. Firstly, a composite embedded square-root cubature Kalman filter(CESCKF) is used to estimate the states of systems and generate residuals. Then, by constructing the function between missed detection rate(MDR) and false alarm rate(FAR) of the residual assessment (data monitoring) index and parameters of the SS-DEWMA chart, and taking the MDR and FAR as the minimum cost objective functions, a multi-objective particle swarm optimization(MO-PSO) algorithm is employed to offline optimize the control width and smoothing parameter, and the output results of the optimized SS-DEWMA chart are compared with the threshold value to detect the faults online, in which, a wavelet analysis algorithm is used in order to reduce the influence of noise on SS-DEWMA chart. Finally, the proposed algorithm is applied to the fault detection of the displacement sensor of the continuous casting mold system driven by servo motors. Simulated and experimental results show that the proposed method can effectively reduce the MDR and FAR.