The failure rate is an important indicator to assess the reliability of substation equipment, and the failure rate prediction is an effective way to master the operation status of substation equipment. According to the characteristics of failure rate data, such as failure period segmentation and stochastic variation, this paper proposes a combined prediction method by the data decomposition of failure rate time series and the segmentation theory of failure periods, and then establishes a new failure rate prediction model of substation equipment based on Weibull distribution and time series analysis. Compared with the traditional Weibull distribution function model which can’t describe the stochastic variation of failure rate data and can’t identify failure period automatically, the proposed model in this paper uses the minimum sum algorithm of residual squares obtained by the Weibull distribution to accurately identify the demarcation point between different failure periods, and then establishes Autoregressive Moving Average (ARMA) model to achieve combined prediction. Finally, the effectiveness of the proposed model is verified by the engineering example and comparison with traditional failure rate prediction methods.

The measurements of the diameter of different layers, the thickness of different layers and the eccentricity of insulation layer in the cross-section of power cables are important items of power cable test, which currently depend on labor-intensive manual operations. To improve efficiency, automatic measurement methods are in urgent need. In this paper, a monocular vision-based framework for automatic measurement of the diameter, thickness, and eccentricity of interest in the cross-section of power cables is proposed. The proposed framework mainly consists of three steps. In the first step, the images of cable cross-section are captured and undistorted with the camera calibration parameters. In the second step, the contours of each layer are detected in the cable cross-section image. In order to detect the complete and accurate contours of each layer, the structural edges in the cross-section image are firstly detected and divided into individual layers, then unconnected edges are connected by arc-based method, and finally contours are refined by the proposed break detection and grouping (BDG) and linear trend-based correction (LTBC) algorithm. In the third step, the monocular vision-based cross-section dimension measurement is accomplished by placing a chessboard coplanar with the power cable cross-section plane. The homography matrix mapping pixel coordinates to chessboard world coordinates is estimated, and the diameter, thickness and eccentricity of specific layers are calculated by homography matrix-based measurement method. Simulated data and actual cable data are both used to validate the proposed method. The experimental results show that diameter, minimum thickness, mean thickness and insulation eccentricity of simulated image without additive noise are measured with root mean squared error (RMSE) of 0.424, 0.103 and 0.063 mm, and 0.002, respectively, those of simulated image with additive Gaussian noise and salt and pepper noise are measured with RMSE of 0.502, 0.243 and 0.058 mm and 0.001. Diameter, minimum thickness and mean thickness of actual cable images are measured with average RMSE of 0.768, 0.308 and 0.327 mm. The measurement error of insulation eccentricity of actual cable image is comparatively large, and the measurement accuracy should be improved.