Some Improvements in State/Parameter Estimation Using the Cell-to-Cell Mapping Technique

The cell-to-cell-mapping technique (CCMT) models system evolution in terms of probability of transitions within a user-specified time interval (e.g., data-sampling interval) between sets of user-defined parameter/state variable magnitude intervals (cells). The cell-to-cell transition probabilities are obtained from the given linear or nonlinear plant model. In conjunction with monitored data and the plant model, the Dynamic System Doctor (DSD) software package uses the CCMT to determine the probability of finding the unmonitored parameter/state variables in a given cell at a given time recursively from a Markov chain. The most important feature of the methodology with regard to model-based fault diagnosis is that it can automatically account for uncertainties in the monitored system state, inputs, and modeling uncertainties through the appropriate choice of the cells, as well as providing a probabilistic measure to rank the likelihood of faults in view of these uncertainties. Such a ranking is particularly important for risk-informed regulation and risk monitoring of nuclear power plants. The DSD estimation algorithm is based on the assumptions that (a) the measurement noise is uniformly distributed and (b) the measured variables are part of the state variable vector. A new theoretical basis is presented for CCMT-based state/parameter estimation that waives these assumptions using a Bayesian interpretation of the approach and expands the applicability range of DSD, as well as providing a link to the conventional state/parameter estimation schemes. The resulting improvements are illustrated using a point reactor xenon evolution model in the presence of thermal feedback and compared to the previous DSD algorithm. The results of the study show that the new theoretical basis (a) increases the applicability of methodology to arbitrary observers and arbitrary noise distributions in the monitored data, as well as to arbitrary uncertainties in the model parameters; (b) leads to improvements in the estimation speed and accuracy; and (c) allows the estimator to be used for noise reduction in the monitored data. The connection between DSD and conventional state/parameter estimation schemes is shown and illustrated for the least-squares estimator, maximum likelihood estimator, and Kalman filter using a recently proposed scheme for directly measuring local power density in nuclear reactor cores.