Expectation Maximization Approach for Simultaneous Gross Error Detection and Data Reconciliation Using Gaussian Mixture Distribution

Abstract

Process measurements play a significant role in process identification, control, and optimization. However, they are often corrupted by two types of errors, random and gross errors. The presence of gross errors in the measurements affects the reliability of optimization and control solutions. Therefore, in this work, we characterize the measurement noise model using a Gaussian mixture distribution, where each mixture component denotes the error distribution corresponding to random error and gross error, respectively. On the basis of this assumption, we propose a maximum likelihood framework for simultaneous steadystate data reconciliation and gross error detection. Since the proposed framework involves the noise mode as a hidden variable denoting the existence of gross errors in the data, it can be solved using the expectation maximization (EM) algorithm. This approach does not require the parameters of the error distribution model to be preset, rather they are determined as part of the solution. Several case studies are presented to demonstrate the effectiveness of the proposed approach.

A New Data Reconciliation Strategy Based on Mutual Information for Industrial Processes

“…More details about STA can be found in references. 49,50 The nonlinear example is applied to demonstrate the effectiveness of the proposed data reconciliation method by Tjoa and Biegler 51 and Alighardashi et al 52 This nonlinear system contains five measured variables, three unmeasured variables, and six nonlinear constraint equations. The setting of the nonlinear simulation can be described as eq 12.…”

“…The nonlinear example is applied to demonstrate the effectiveness of the proposed data reconciliation method by Tjoa and Biegler and Alighardashi et al This nonlinear system contains five measured variables, three unmeasured variables, and six nonlinear constraint equations. The setting of the nonlinear simulation can be described as eq . where x = [ x 1 , x 2 ,···, x 5 ] is the measured variable vector; u = [ u 1 , u 2 , u 3 ] is the unmeasured variable vector.…”

Estimation of Feeding Composition of Industrial Process Based on Data Reconciliation

“…Through the comparative analysis of various methods like Welsch, quasi-weighted least squares and comentropy M-estimators, the feasibility and effectiveness of robust estimators in simultaneous gross error detection and data reconciliation were demonstrated [ 28 ]. Alighardashi et al [ 29 ] proposed a maximum likelihood framework for simultaneous data reconciliation and gross error detection for steady-state data. Xie et al [ 30 ] utilized a novel robust estimator to improve the robustness of data reconciliation.…”

Location Estimation-Based Mixed Integer Linear Programming Approach for Multiple Gross Error Identification

“…To obtain reliable process data routinely, Tjoa and Biegler 10 proposed a contaminated normal objective function instead of a least-squares function, following which Alighadashi et al 11 characterized the measurement error with a Gaussian mixture model and proposed a maximum likelihood framework for simultaneous GEI and DR. Johnston and Kramer 12 introduced a robust estimator for data reconciliation, which reduces the influence of large magnitude error during reconciliation, and several other types of robust estimators have been reported since this contribution, which were summarized and evaluated by O ̈zyurt and Pike. 13 After that, several novel robust estimators have also been presented, such as quasi-weighted least-squares (QWLS) 14 and correntropy.…”