Bootstrapped Gross Error Detection for Efficient and Fault-Tolerant Real-Time Optimization

Real-time optimization (RTO) is a model-based approach for generating economically optimal steady-state process set points. The process model used in RTO requires reconciliation with the plant through parameter estimation, which uses online measurements. In the presence of sensor faults causing measurement bias, the estimation layer can result in suboptimal set points that may violate safety, environmental, or operational constraints. Herein, a gross error detection approach is proposed to determine measurement sets that exclude faults, thus avoiding estimation errors propagating to the set points and ensuring safe operation. This is achieved by computing parameter estimate samples offline using varying measurement combinations and bootstrapping available plant data. The resulting parameter estimates are subjected to single-sample t-tests to determine which estimates are significantly different; these correspond to the measurement that have the highest probability of being faulty. The computational complexity of the algorithm is discussed, whereby it is shown to be related to the observability criteria and number of measurements. A continuously stirred tank reactor with an upper bound on heat generation is used to exemplify the proposed approach in a process safety setting. The incidence of constraint-violating operation is observed to decrease in both frequency and severity when using the proposed framework; thus, the resulting set points are economical while ensuring safe heating limits are respected during operation.