The control of an induction motor (IM) drive is a complex process and requires speed estimation, which is dependent on various machine parameters. The linear regression approach reduces this dependency by eliminating the need for flux computation and gain adjustment of the PI controllers. The performance of the linear regression model deteriorates when data is noisy, the best fit deviates from the desired value. The Gaussian Process (GP) model is a non-parametric model, that can incorporate these noisy measurements and model uncertainties. In this paper, the speed of the IM drive with vector control is estimated using Gaussian Process Regression (GPR). The fictitious quantity$X$= ū*×$I$is used to eliminate the calculation of flux in the stator or rotor and its characteristic of stable drive in all four quadrants. The GP is viewed as a surrogate model, the prediction distribution obtained gives a confidence interval, used for usefulness validation that also distinguishes GP model from other black-box models. Furthermore, the Bayesian approach of GPR involves lesser complex evaluations making this approach simple and agile.

In transmission and distribution substations, power transformers account for the majority of capital investment. As they are expensive, effective thermal performance monitoring is necessary for life extension. The hot-spot temperature value is among the most significant factors affecting a transformer's life expectancy. As HST evaluation require some Top-oil Temperature model parameters, accurate estimations of TOT are required to analyze the thermal performance and lifespan of transformers. Conventionally, the TOT parameters from the Resistance-Capacitance network are determined using the input-output data. While the regressor signals meet the Persistence of Excitation criterion in the Gradient Estimator a parametric estimate error approaches zero and the parameter converges to their true value. The Design of Experiment is often carried out in the test center to meet the PE requirement. As a consequence, actual operating transformer data is utilized for the identification and estimation of the parameters associated with the TOT model by using finite-time estimators. The detected PE issue, the impact of DoE, and the efficiency of FTEs with different filters for non-PE data obtained from the actual operating transformers' thermal model are demonstrated by experimental analysis using MATLAB.