Aiming at the problem that the accelerometer is prone to fault under the harsh working environment of the health monitoring system， a principal weighted statistic method for principal components analysis （PCA） residual space is proposed. Firstly， the sensor fault response is characterized by the fault direction and the fault magnitude vector， and the projection of the sensor fault in the residual space is obtained. Secondly， through theoretical derivation， the squared prediction error （SPE） statistic is squared with the elements in the residual space main vector， these elements are used as nonlinear weighting coefficients of SPE statistic. Then the cumulative contribution rate as an indicator of sensor fault location is calculated by Bayesian inference. The applicability of the proposed method is verified by simulating common sensor gain and bias fault. The three-span continuous beam model is used as a numerical example. The calculation results show that the traditional principal component analysis method has a diagnostic rate of 5.45% and 3.43% respectively for common gain failure and deviation fault， however， the proposed method in this paper increases its diagnostic rate to 69.8% and 100%. At the same time， the faulty sensor can be accurately located under both sensor faults. The real bridge example of the Lamberti Bridge in Parma shows that the proposed method has a diagnostic rate of 77.58% for gain fault and can correctly locate the faulty sensor channel.