Bayesian method for simultaneous gross error detection and data reconciliation

Abstract

Process measurements collected from daily industrial plant operations are essential for process monitoring, control and optimization. However, those measurements are generally corrupted by errors, which include gross errors and random errors. Conventionally, those two types of errors were addressed separately by gross error detection and data reconciliation.This work focuses on solving the simultaneous gross error detection and data reconciliation problem using the hierarchical Bayesian inference technique. The proposed approach solves the following problems in a unified framework. First, it detects which measurements contain gross errors. Second, the magnitudes of the gross errors are estimated. Third, the covariance matrix of the random errors is estimated. Finally, data reconciliation is performed using the maximum a posteriori estimation. The proposed algorithm is applicable to both linear and nonlinear systems. For nonlinear case, the algorithm does not involve any linearization or approximation steps. Numerical case studies are provided to demonstrate the effectiveness of the proposed method.

A critical review of statistical calibration/prediction models handling data inconsistency and model inadequacy

“…Recently, metrologists have developed statistical methods enabling to preserve all data, notably through the use of bayesian hierarchical models. 39,41,42 • Model inadequacy results from approximations at various stages of model development and is responsible for systematic errors in predictions. 43 It should be identified and quantified by comparison with reference data.…”

Estimation of Feeding Composition of Industrial Process Based on Data Reconciliation

“…Zhang et al [ 18 ] used a novel particle filter (PF) algorithm based on the measurement test (MT) to solve the dynamic simultaneous gross error detection and data reconciliation. Yuan et al [ 19 ] established a new hierarchical Bayesian framework, which can simultaneously estimate the real value of process variables and obtain the magnitudes of gross errors. The last strategy is robust data reconciliation.…”

Tighter Mixed-Integer Quadratic Programming Model for Process Data Rectification

“…Several novel robust estimators, such as quasi-weighted leastsquares 15 and correntropy, 16 have also been proposed in recent decades. A disadvantage of robust data reconciliation is that the cutoff point for a bias needs to be tuned with the true values of measurements via Monte Carlo simulations; however, recently, Llanos et al 11 devised a robust measurement test and Yuan et al 17 presented a hierarchical Bayesian inference technique to avoid the need for tuning. Sańchez and Maronna 18 combined the strengths of monotone and redescending robust estimators to reduce the influence of sporadic outliers, which occur in real chemical plants due to a complex and poor electromagnetic environment.…”