Nonlinear Data Reconciliation and Gross Error Detection using Branch-and-Bound Technique

Abstract

Sensor measurements in a process network inherently contain random and/or gross errors. Data are deemed unreliable for process optimization, monitoring, control, and safety. This paper describes a simultaneous data reconciliation (DR) and gross error detection (GED) strategy for adjusting sensor measurements to satisfy mass and energy balances. The problem is modeled as a mixed-integer nonlinearly constrained optimization problem, to be solved by a branch-and-bound technique. The concept of a search tree explains how the technique reduces the search space in optimization. The objective function in each node of the search tree is evaluated using a hybrid Nelder-Mead simplex and particle swarm optimization (NM-PSO) routine from Zahara and Kao (2009). The effectiveness of the method is tested for the highly nonlinear system from Pai and Fisher (1988). In varying number of iterations and number of particles in the NM-PSO routine, the sum-of-squares error (SSE) of the reconciled values from the exact measurements range from 10-6 to 10-1 and the overall power of the DR-GED strategy is a perfect 1.00.