Implementation of the Uncertainty Estimation of the Measurement of a Complex Quantity by Various Methods

The evaluation of metrological characteristics of measuring equipment is an important aspect of production automation. Automated information-measuring systems are widely used in manufacturing and are responsible for the operational monitoring of energy consumption in technological processes. Many aspects of quality management utilize measurement uncertainty and statistical distribution of the measured quantity. A particularly challenging issue is the assessment of uncertainty in the measurement of complex-valued quantities due to small sample sizes, which hinder reliable estimation of the sample correlation coefficient. Numerical simulation with predefined properties in the MATLAB environment is performed to select the optimal method for uncertainty estimation of total power. Covariance matrices of amplitude and phase in polar coordinates are obtained based on the law of uncertainty propagation in matrix form. Three scenarios of the relationship between active and reactive power inputs have been analyzed and assessed using numerical simulations in the MATLAB environment. Geometric representations of the modeled complex quantities are used to understand the principles of uncertainty transformation. Estimation of the upper bound of measurement uncertainty using boundary intervals has been proposed. Estimation of uncertainty through the root mean square circular range has demonstrated a reduced coverage probability of 92.8%. Estimation using the maximum circular range has shown a high coverage probability of 98.5%, regardless of the correlation between active and reactive power. In conclusion, the article emphasizes that for assessing the conformity of metrological characteristics of measuring equipment, repeated measurement modeling can be employed. In limited information scenarios of the measured quantity, its uncertainty should be estimated as an upper bound using the maximum circular range.