APPLICATION OF RECENT DEVELOPMENTS IN INTEGRAL DATA ASSIMILATION TO IN-DEPTH ANALYSIS OF UH1.2 EXPERIMENT AND TRANSPOSITION TO WHOLE PWR CORE

Recent developments in the Integral Data Assimilation (IDA) methods within Bayesian framework have been achieved at CEA to tackle the problem of correlated experiments (through technological uncertainties) and neutron transport model numerical effects. Hence, reference Monte-Carlo and deterministic calculations (TRIPOLI4® and APOLLO3®) are used together to solve neutron transport equations and get the sensitivity profiles. Furthermore, the analysis of the mock-up experiments technological parameters is performed to get accurate uncertainties and correlations between the experiments (finally the covariance experimental matrix required for IDA). We apply here the IDA approach with a new, extend set of statistical indicators (Cook’s distance, Bayesian and Aikike Information criteria (BIC, AIC)) implemented in the nuclear physics CEA CONRAD code, to the integral experiments UH1.2 in reference and voided configurations (standard PWR fuel assembly in the EOLE mock-up reactor). The adjusted multigroup cross-sections and posterior covariances are compared by choosing different ingredients in the assimilation process. Finally, the investigated key neutron parameters; reactivity, reactivity worth (void effects) and fissions rates are transposed (with the same CONRAD code) to a standard PWR core. This in-depth analysis enables us to predict the residual uncertainties and biases due to the multigroup cross-section adjustments assessing at the same time the similarity of these integral experiments for the main PWR neutronic safety parameters. In addition, technological parameters uncertainties and their impact on Bayesian adjustment process are taken into account through a global experimental covariance matrix. We point out that the UH1.2 experiments bring relevant additional information to PWR keff calculations reducing significantly the posterior results but are less relevant for fission rate distribution in reference and voided configurations.

Nuclear data adjustment using Bayesian inference, diagnostics for model fit and influence of model parameters

The mathematical models used for nuclear data evaluations contain a large number of theoretical parameters that are usually uncertain. These parameters can be calibrated (or improved) by the information collected from integral/differential experiments. The Bayesian inference technique is used to utilize measurements for data assimilation. The Bayesian approximation is based on the least-square or Monte-Carlo approaches. In this process, the model parameters are optimized. In the adjustment process, it is essential to include the analysis related to the influence of model parameters on the adjusted data. In this work, some statistical indicators such as the concept of Cook’s distance; Akaike, Bayesian and deviance information criteria; effective degrees of freedom are developed within the CONRAD platform. Further, these indicators are applied to a test case of 155Gd to evaluate and compare the influence of resonance parameters.

Influence of nuclear data parameters on integral experiment assimilation using Cook’s distance

Nuclear data used in designing of various nuclear applications (e.g., core design of reactors) is improved by using integral experiments. To utilize the past critical experimental data to the reactor design work, a typical procedure for the nuclear data adjustment is based on the Bayesian theory (least-square technique or Monte-Carlo). In this method, the nuclear data parameters are optimized by the inclusion of the experimental information using a Bayesian inference. The selection of integral experiments is based on the availability of well-documented specifications and experimental data. Data points with large uncertainties or large residuals (outliers) may affect the accuracy of the adjustment. Hence, in the adjustment process, it is very important to study the influence of experiments as well as of the prior nuclear data on the adjusted results. In this work, the influence of each individual reaction (related to nuclear data) is analyzed using the concept of Cook’s distance. First, JEZEBEL (Pu239, Pu240 and Pu241) integral experiment is considered for data assimilation and then the transposition of results on ASTRID fast reactor concept is discussed.