Trade-off between number of constraints and primary-statement robustness in entropy models: the case of the open-channel velocity field.

Antonio Viana Da Silva Filho,José Carlos De Araújo,Armin Raabe

doi:10.1590/0001-3756202020200594

Abstract

In this research, the trade-off between the number of restrictions and the robustness of the primary formulation of entropy models was evaluated. The performance of six hydrodynamic models in open channels was assessed based on 1730 Laser-Doppler anemometry data. It was investigated whether it is better to use an entropy-based model with more restrictions and a weak primary formulation or a model with fewer restrictions, but with a strong formulation. In addition, it was also investigated whether the model performance improves with the insertion of restrictions. Three of the investigated models have a weak formulation (open-channel velocity field represented by Cartesian coordinates); while the other three models have a strong formulation, according to which isovels are represented by curvilinear coordinates. The results indicated that models with two restrictions performed better than those with one restriction, since the additional restriction includes information relevant to the system. Models with three restrictions perform worse than those with two restrictions, because the information lost due to the use of a numerical solution was more substantial than the information gained by the third restriction. In conclusion, a strong primary formulation brought more information to the system than the inclusion of a third constraint.

Highlights

Models are designed to explain physical processes, to which one may assign a probability of event occurrence, considering that each system state has a level of uncertainty
We investigated the performance of six entropy models designed to simulate open-channel velocity fields
Three of the investigated models have a weak primary statement, i.e., they assume that isovels could be well represented by Cartesian coordinates; whereas the remaining three models have a strong statement according to which isovels are better represented by curvilinear coordinates

Summary

Introduction

Models are designed to explain physical processes, to which one may assign a probability of event occurrence, considering that each system state has a level of uncertainty. Welldesigned probabilistic models tend to enhance their capacity of representing reality because they consider the intrinsic uncertainties of the processes, which arise from several sources such as natural randomness, inaccuracy in data measurement, model structure imperfect parameterization, and others Gupta & Govindaraju (2019). Jaynes (1957a, b) physically formulated the informational principle of maximum entropy (PME) using Shannon entropy, which maximizes uncertainty under the given constraints and, avoids. The probability density function associated to a researched process can be obtained by maximizing the constrained entropy function and using the variational calculus and the Lagrange multipliers method

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