Abordagem simultânea na reconciliação de dados e estimação de parâmetros: avaliação da matriz de covariância e regiões de abrangência das variáveis de decisão

Abstract

Data reconciliation (DR) and parameter estimation (PE) problems require measured or estimated quantities that intrinsically have uncertainty which is propagated to the decision variables of the optimization problem. In the same way that the quality of the measured data is evaluated, the quality of the results obtained after solving the optimization problem must be evaluated, which is often neglected. Thus, the objective of this dissertation is to show the importance and discuss ways to evaluate reconciled quantities and parameters of models obtained in DR problems and in problems that apply the simultaneous approach in data reconciliation and parameter estimation (SDRPE), as well as the characteristics of the residues. Three routes were explored: (i) proposal of a method for evaluating the covariance matrix of the decision variables, which was able not only to reproduce results similar to the methods in the literature, but also to calculate the covariance matrix in cases where these were not were successful; (ii) proposal of a method for the construction of the coverage regions, based on the bootstrap technique, which proved to be useful to evaluate the quality of the model and the phenomenological coherence of the reconciled quantities obtained; and (iii) analysis of residuals through graphs and statistical tests, which showed the importance of validating the hypotheses adopted in the construction of the objective function as well as the need to use adequate analysis tools depending on the type of case, univariate or multivariate. In addition, the use of coverage regions to choose the best model was suitable for cases in which the analysis using the quantitative criteria AIC, AICc, BIC, 𝑅2 and 𝑅2𝑎𝑑𝑗 was not effective.