Method for encoding and decoding variables in engineering problems. Issue 17 (November 2022) - Chevalier, Philippe A.J.G.; Constales, Denis
Highlights: An efficient and effective method for creating trial functions is presented. The method is exemplified for a measurement function for future power grids. A measurement function that connects 19 dimensional variables is presented. Connectives are found between quantity equations and their geometric properties. Method generalization results in the classification of the kind of quantities. Abstract: Dimensional analysis can be used in those cases, where the system of equations describing the problem to solve is unknown. The setup of the trial function F ( Q 1, …, Q M ) = 0 relies on the expertise of the researcher. The researcher is confronted with the questions: which Q m is the dependent variable; what is the value of M ; are the chosen Q m effective. The new encoding-decoding method disclosed has the goal to answer these three questions and belongs to dimensional exploration techniques that can help in discovering the governing equations. This new method is based on low complexity, high performing, and well-established computer algorithms of number theoretic functions. The encoding-decoding method is exemplified on a real-world problem by searching for the positively homogeneous measurement function that models wave phenomena, electromagnetic phenomena, electromechanical phenomena, and thermodynamic phenomena of the future power grids. The temporal variation of the power density is considered in its form of the kind of quantity called second order partial derivative of the energy density with respect to time denoted ∂ 2 W ( r, t ) ∂ t 2 . The new method generates a trial function F ( ∂ 2 W ( r, t ) ∂ t 2, Q 2, …, Q 19 ) = 0 and a positively homogeneous measurement function u ( π 1, …, π 9 ) = 0 for the design of experiments. The validation of this new method is performed through its application on two cases: the simple pendulum and the kind of quantity energy. The efficiency, effectiveness, and completeness of the encoding-decoding method are compared with classical and modern dimensional analysis. The new method has the advantage over those state-of-the-art methods in requiring less dimensionless quantities π k as arguments of the measurement function u ( π 1, …, π K ) = 0 when modeling real-world problems. The encoding-decoding method is based on lattice theory while classical and modern dimensional analysis are based on linear algebra.