Passive safety systems analysis: A novel approach for inverse uncertainty quantification based on Stacked Sparse Autoencoders and Kriging metamodeling

In passive safety system analysis, it is important to provide the uncertainty quantification of the Thermal-Hydraulic (T-H) code output (e.g., the amount of energy exchanged by the passive safety system during an accidental transient). This requires setting proper Probability Density Functions (PDFs) to represent the uncertainty of selected code inputs and the propagation of this uncertainty through the code. One way to obtain the PDF is by Inverse Uncertainty Quantification (IUQ) methods, which rely directly on experimental data and code simulation results. In this work, we present an innovative IUQ method based on: (i) Stacked Sparse Autoencoders (SSAEs) to reduce the problem dimensionality; and (ii) Kriging metamodels to lower the computational burden associated with the sampling of the uncertain input parameters posterior PDF by Markov Chain Monte Carlo (MCMC) (for which many model simulations are typically required). The novelty stands in the use of SSAEs for dimensionality reduction: this allows using directly the raw data available from experimental facilities or computer codes (typically characterized by small signal-to-noise ratios) without having to resort to filtering techniques, whose choice and setting are nontrivial and bias the results. The proposed approach is applied to the power exchanged by the Heat Exchanger (HX) predicted by the RELAP5-3D model of the PERSEO facility, characterized by a small signal-to-noise ratio (SNR) value. Principal Component Analysis (PCA) and SSAE are compared to explain the application of these methodologies in the context of IUQ and highlight the main advantages and drawbacks while also showing the suitability to deal with non-filtered (raw) data.