A spectral simulation approach to evaluate probabilistic measurement precision of a reactor coolant pump torsional vibration shaft crack monitoring system

A prototype torsional vibration monitoring system has been installed on two reactor coolant pumps at Tennessee Valley Authority Sequoyah Power Plant Unit 1 nuclear reactor for shaft crack monitoring. The system uses a change in torsional natural frequencies as a diagnostic feature since as a crack grows the shaft line torsional dynamics change commensurately. For effective diagnostic monitoring, it is critical to know the inherent feature variation resulting from the instrumentation and data processing. The integrated nature of the prototype hardware/software system and the inaccessibility of the equipment inside the reactor containment building make it impossible to evaluate the measurement capability in a traditional instrumentation chain approach. Hence, a simulation-based evaluation was performed to determine the cumulative effect of the measurement system on the uncertainty in the torsional natural frequency estimation. The identification algorithm operates on the measured torsional spectrum to estimate a natural frequency. All of the inherent measurement and data processing uncertainties ultimately affect the spectrum in some manner. Therefore, if the characteristics of the reactor coolant pump torsional spectrum can be replicated via a model; it can be used to assess the overall prototype system measurement uncertainty. The underlying premise is that the line shaft dynamics remain constant, in the absence of a fault, and hence any natural frequency variation is due strictly to the measurement system uncertainty. To this end, a single degree of freedom simulation model was first developed which matched the natural frequency and damping of a crack sensitive torsional mode in the reactor coolant pump. The model input was carefully selected such that the averaged spectral amplitude and variance from the ensembles matched the measured reactor coolant pump torsional vibration. The model was then used to create one hundred sample responses that replicated pump spectral response in a statistical sense. The same data processing routines used in the prototype system were applied to the simulation data thus creating sample populations of the natural frequency and damping. Statistical tolerance limits containing 99.9% of the sample population with a 99.9% probability were used to quantify the system's measurement uncertainty. The limits for the crack sensitive mode 3 of the reactor coolant pump were (1) natural frequency: ±0.04740 Hz and (2) damping ratio: ±0.00036.