Modified parity space averaging approaches for online cross-calibration of redundant sensors in nuclear reactors

To maintain safety and reliability of reactors, redundant sensors are usually used to measure critical variables and estimate their averaged time-dependency. Nonhealthy sensors can badly influence the estimation result of the process variable. Since online condition monitoring was introduced, the online cross-calibration method has been widely used to detect any anomaly of sensor readings among the redundant group. The cross-calibration method has four main averaging techniques: simple averaging, band averaging, weighted averaging, and parity space averaging (PSA). PSA is used to weigh redundant signals based on their error bounds and their band consistency. Using the consistency weighting factor (C), PSA assigns more weight to consistent signals that have shared bands, based on how many bands they share, and gives inconsistent signals of very low weight. In this article, three approaches are introduced for improving the PSA technique: the first is to add another consistency factor, so called trend consistency (TC), to include a consideration of the preserving of any characteristic edge that reflects the behavior of equipment/component measured by the process parameter; the second approach proposes replacing the error bound/accuracy based weighting factor ($W^a$) with a weighting factor based on the Euclidean distance ($W^d$), and the third approach proposes applying $W^d$, TC, and C, all together. Cold neutron source data sets of four redundant hydrogen pressure transmitters from a research reactor were used to perform the validation and verification. Results showed that the second and third modified approaches lead to reasonable improvement of the PSA technique. All approaches implemented in this study were similar in that they have the capability to (1) identify and isolate a drifted sensor that should undergo calibration, (2) identify a faulty sensor/s due to long and continuous missing data range, and (3) identify a healthy sensor.