Accurate assessment of Remaining Useful Lifetime (RUL) of power transformers plays an essential role in improving the reliability of power grid while reducing operating costs. A dynamical RUL prediction technique is proposed in this article through analyzing the individual difference by multi-dimensional fusion of condition monitoring data. Firstly, the on-site Dissolved Gas Analysis (DGA) measurements and the calculated Degree of Polymerization (DP) are fused with the method of Analytic Hierarchy Process (AHP) and Variable Weight Principle (VWP) to construct the power transformer Life Correlation Index (LCI). Secondly, the parameters of Wiener model are updated iteratively by Bayesian rule and Expectation Maximization (EM) algorithm, to obtain the distribution and prediction of residual transformer lifetime. The residual lifetimes of four 500 kV power transformers in operation are calculated, and the predicted remaining lifetimes are 24.73 years, 30.66 years, 2.79 years, and 0.07 years, respectively. The effectiveness and reliability are demonstrated by the worst transformer case with the predicted RUL of 0.07 years, in which a short circuit fault of that transformer happened immediately after power-off maintenance. In particular, this method is able to predict the residual lifetime of transformers in a dynamic way, which provides significant practical implications for the assessment management of power transformers.

In this article, an errors-in-variables regression model in which the errors are negatively superadditive dependent (NSD) random variables is studied. First, the Marcinkiewicz-type strong law of large numbers for NSD random variables is established. Then, we use the strong law of large numbers to investigate the asymptotic normality of least square (LS) estimators for the unknown parameters. In addition, the mean consistency of LS estimators for the unknown parameters is also obtained. Some results for independent random variables and negatively associated random variables are extended and improved to the case of NSD setting. At last, two simulations are presented to verify the asymptotic normality and mean consistency of LS estimators in the model.

This paper focuses on the density estimation problem that occurs when the sample is negatively associated and biased. We constructed a block thresholding wavelet estimator to recover the density function from the negatively associated biased sample. The pointwise optimality of this wavelet density estimation is shown as $L^p$ ( $1\le p<\infty$ ) risks over Besov space. To validate the effectiveness of the block thresholding wavelet method, we provide some examples and implement the numerical simulations. The results indicate that our block thresholding wavelet density estimator is superior in terms of the mean squared error (MSE) when comparing with the nonlinear wavelet density estimator.

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.