Development of an intelligent moving horizon estimator integrated with fault diagnosis for automated model maintenance

Abstract

Fidelity of the dynamic or steady-state model used for making economic decisions in real-time optimization (RTO) or economic nonlinear model predictive control (ENMPC) is critical in achieving the desired economic benefits in the face of fast changing and uncertain market conditions. Since the model parameters/ unmeasured disturbances keep changing with changes in the operating regime, online updating of the model parameters using recent operating data is essential for accruing the benefits of RTO or ENMPC over a long period of time. In practice, a large number of model parameters/ unmeasured disturbances are susceptible to change and adjusting all of them without discrimination can result in over-fitting and/or erroneous parameter estimates. Automating the task of finding the “active subset of parameters/ disturbances” that need to be adjusted while carrying out the online model update can eliminate the need for an expert intervention for online maintenance of a dynamic/ steady-state model. This can be achieved by developing an automated decision-making system that performs the active subset selection task by diagnosing the root cause(s) of departures from the normal behavior by analyzing transient data. In this work, fault tolerant moving horizon estimator (MHE) approaches have been proposed that integrate fault diagnosis and identification (FDI) with the conventional MHE formulation for carrying out automated online model maintenance. Diagnosis and compensation for bias and drift-type faults in sensors, actuators, model parameters, and unmeasured disturbances have been considered in the development. Statistical properties of decision variables of the unconstrained MHE formulation for linear systems are derived and further used for fault detection and estimation of the time of occurrence of a fault. Subsequently, fault identification step is derived using the generalized likelihood ratio framework. Since the magnitude of the isolated fault may drift with time, the fault magnitude estimates are refined by including the isolated fault magnitude as an additional parameter in the MHE decision variable set. A hypothesis test is developed to stop the magnitude refinement when the fault magnitudes converge. The model used in MHE is subsequently modified to accommodate persistent faults so that multiple faults occurring sequentially in time can be diagnosed. Further, to facilitate the application of the proposed approach to systems exhibiting nonlinear dynamics, trajectory linearization-based and nonlinear MHE-based approaches are developed for carrying out FDI. The efficacy of the proposed approaches is demonstrated by conducting stochastic simulations using the benchmark Williams–Otto reactor system. Analysis of the simulation results reveals that the proposed MHE-based FDI approaches outperform the Kalman filter and extended Kalman filter-based FDI approaches in terms of diagnostic performance. Moreover, the proposed MHE-FDI approaches are able to isolate and compensate for multiple single faults occurring sequentially in time and have embedded capability to carry out self-diagnosis and auto-correction only when required.