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Abstract JA253Full Paper + Presentation
Simple Bayesian Updating by Cross-Entropy Minimization: Application at Leibstadt NPP
A novel method for performing Bayesian updates was developed for applications in Probabilistic Risk Assessment (PRA) at Leibstadt NPP (KKL). The approach is based on the conversion of generic industry priors into conjugate distributions, yielding simple formulas for posterior distribution parameters. While this general idea is established in PRA guidelines (see NUREG/CR-6823 and EPRI TR-1002936), the new approach is based on minimizing cross-entropy between the generic and approximating prior, rather than matching mean and variance (moment matching).
According to the Swiss PRA guideline ENSI-A05, KKL is required to perform Bayesian updates of component failure rates and frequencies of certain initiating events (e.g., internal fires and flooding), combining generic industry data with plant-specific evidence. Most generic data sources used in KKL PRA employ lognormal distributions, which are not conjugate to the Poisson likelihood. Thus, a numerical integration routine for Bayesian updates had previously been developed. The new approach retains the simplicity of moment matching and can easily be implemented in a spreadsheet. It simplifies code maintenance, avoids numerical issues and is more transparent. Unlike moment matching, the resulting posteriors closely resemble those obtained through numerical integration.
To evaluate the new approach, Bayesian updated component failure rates in the KKL PRA model were replaced by those derived from the new method. Results show no significant risk impact: mean component failure rates decreased by an average of 2.5 percent and total core damage frequency increased by 3.7 percent. Posterior credible intervals tend to be wider. The largest deviations from the numerical posteriors occur at low percentiles, but are considerably smaller than with moment matching. A complementary study on synthetic data - covering realistic prior-evidence combinations for KKL PRA applications - confirmed these results.
The use of Gamma distributions also resolves a mathematical issue when generic priors are split into multiple distributions (e.g., to match component boundaries in the PRA model). This also addresses an issue raised during the 2014 IAEA IPSART mission at KKL.
Based on properties of Beta and Gamma distributions, the method can be extended to a variety of prior distribution types as well as probability parameters (Binomial likelihood).
The new method will serve as a basis for the next Bayesian updates of KKL component failure rates and is intended to be used for all future Bayesian updates in KKL PRA.
← Check another abstractAccording to the Swiss PRA guideline ENSI-A05, KKL is required to perform Bayesian updates of component failure rates and frequencies of certain initiating events (e.g., internal fires and flooding), combining generic industry data with plant-specific evidence. Most generic data sources used in KKL PRA employ lognormal distributions, which are not conjugate to the Poisson likelihood. Thus, a numerical integration routine for Bayesian updates had previously been developed. The new approach retains the simplicity of moment matching and can easily be implemented in a spreadsheet. It simplifies code maintenance, avoids numerical issues and is more transparent. Unlike moment matching, the resulting posteriors closely resemble those obtained through numerical integration.
To evaluate the new approach, Bayesian updated component failure rates in the KKL PRA model were replaced by those derived from the new method. Results show no significant risk impact: mean component failure rates decreased by an average of 2.5 percent and total core damage frequency increased by 3.7 percent. Posterior credible intervals tend to be wider. The largest deviations from the numerical posteriors occur at low percentiles, but are considerably smaller than with moment matching. A complementary study on synthetic data - covering realistic prior-evidence combinations for KKL PRA applications - confirmed these results.
The use of Gamma distributions also resolves a mathematical issue when generic priors are split into multiple distributions (e.g., to match component boundaries in the PRA model). This also addresses an issue raised during the 2014 IAEA IPSART mission at KKL.
Based on properties of Beta and Gamma distributions, the method can be extended to a variety of prior distribution types as well as probability parameters (Binomial likelihood).
The new method will serve as a basis for the next Bayesian updates of KKL component failure rates and is intended to be used for all future Bayesian updates in KKL PRA.