Development of a Statistical Model of Uncertainty in Time-Dependent Channel Power Distribution Predictions

This paper describes the development of a statistical model of uncertainty in channel powers predicted for a 480-channel CANada Deuterium Uranium (CANDU) reactor. It is expressed as the sum of ripple prediction uncertainty and reactor power uncertainty. Ripples are ratios of instantaneous channel powers (prorated to 100% of full power) to reference channel powers. The ripple prediction uncertainty model is a multivariate normal distribution whose covariance matrix captures a unique variance for every channel as well as a unique covariance between every pair of channels. Reactor power uncertainty is common to all 480 channels.

Central to this work is the distinction between apparent uncertainty, measurement uncertainty, and prediction uncertainty. Ripple prediction uncertainty is quantified by removing the contribution of ripple measurement uncertainty to ripple apparent uncertainty (differences between computer code–predicted ripples and measured ripples). This is done because measurement uncertainty causes apparent uncertainty to exceed prediction uncertainty. Measurement uncertainty is quantified using a novel approach referred to as the sister channel approach with time shifting. This approach uses differences between measured ripples in sister channels to quantify actual measurement uncertainty. The time-shifting aspect of the approach accounts for the fact that true ripples in sister channels are not identical at the same time, mainly because sister channels and their neighboring channels are refueled at different times.