Defining Regression Polynomials with Process Similarity Criteria

Abstract

Highly accurate monitoring and prediction is essential in detecting abnormality events and forecasting demands in supply chains. This investigation provides a computational procedure for defining polynomials that satisfy similarity criteria in the monitoring process for a polynomial of any degree. It provides an example of using algorithms to predict transient thermal processes in electronic devices. The second-degree polynomial defined with this algorithm is compared with a polynomial defined using a minimum least square algorithm. This regression method can be applied to a wide variety of data sets, creating actionable metrics that inform risk analysis, failure prediction, and optimization strategies. Applications include grid stabilization, battery optimization in Electric Vehicles (EVs), and failure prediction in electronic components. As an example, this paper shows superior prediction capabilities through thermal analysis of a circuit board. The proposed method of the data prediction provides an alternative to the neural network diagnostics for the processes when real-time rapid identification is required. Such diagnostics is most critical for detecting electronic devices, battery grids, toxic ingredients intrusion in water or air systems and clean technology processes. Because the method can predict future data in milliseconds, it satisfies the requirements for such processes. The choice in defining the analytical approach in predicting events should be taken by analyzing required estimation time. The forecasting demands in the supply chain do not require high computational speed. However, when the amount of the predicted item is big, using the proposed method would benefit in decreasing computational complexity. The known method of using multiple polynomials does not provide high accuracy in prediction. The computational procedure for calculating polynomial coefficients includes the solution of the nonlinear operator equations. It is proposed to use hypernumber theory for solving such equations. The method provides an efficient solution for the complex nonlinear equations.