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• An overview of the DT initiatives and research developments for the design optimization and intelligent transformation of nuclear energy systems in many nations is provided to give a trend of Digital Twin for Nuclear Reactor System (DTNRS) development. • Four properties of DTNRS are summarized, which are given by the block definition diagram of Model-Based System Engineering (MBSE) philosophy. • A systematic and hierarchical "V" architecture based on the MBSE philosophy, which reflects the digital-related technologies of the DTNRS throughout the whole life cycle is proposed to bridge the gap between thermal-hydraulic numerical simulation and theoretical research of DT. • A prospective application scenario of DT in nuclear energy is pictured. A four-layered decomposition construction model is developed, and the five-step instructive demonstration of the DTNRS is given based on a Generation III (GEN-III) reactor with its visualized condition map. Digital Twin (DT) technology has gained significant attention in various areas, including nuclear energy. Technologies such as machine learning, artificial intelligence, and high-fidelity modeling and simulation have been studied to further the digitalization of the nuclear industry. In this paper, an overview of the DT initiatives and developments for the design optimization and intelligent transformation of nuclear energy systems is described to provide a development trend of DT technology for nuclear reactors. For the design of DT for complex systems such as nuclear reactors, Model Based Systems Engineering (MBSE) technology offers requirements models, design processes, and system verification that are clearer, more precise, and more comprehensive. Four properties of Digital Twin for Nuclear Reactor System (DTNRS) are summarized, which are given by the block definition diagram of MBSE philosophy. Then, to bridge the gap between numerical models and theoretical research of DT, a systematic and hierarchical "V" architecture is proposed, which reflects the digital-related technologies of the DTNRS throughout the whole life cycle. Furthermore, a four-layered decomposition construction model is developed and a prospective application scenario of DTNRS is pictured. Finally, the five-step instructive demonstration of the DTNRS is given based on a Generation III (GEN-III) reactor with its visualized condition map. [ABSTRACT FROM AUTHOR]

• Digital-twin approach with physics-based models for fault detection and diagnosis. • Direct inference of fault severity distributions via Bayesian probabilistic network. • Provide improved fault probability estimations over traditional discrete treatment of model-based diagnosis. • Demonstrative results with a BWR motor-pump set using real-time plant data. For applications in condition-based maintenance of nuclear systems, the assessment of fault severity is crucial. In this work, we developed a framework that allows for direct inference of the probability distributions of possible faults in a system. We employed a model-based approach with model residuals generated from analytical redundancy relations provided by physics-based models of the system components. From real-time sensor readings, the values of the model residuals can be calculated, and the posterior probability distributions of the faults can be computed directly using the methods of Bayesian networks. From the posterior distribution of each fault, one can estimate the fault probability based on a chosen threshold and assess the severity of the fault. By eliminating the discretization and simplifications in middle steps, this approach allows us to leverage the available computational resources to provide more accurate fault probability estimates and severity assessments. [ABSTRACT FROM AUTHOR]

In a recently developed Nearly Autonomous Management and Control (NAMAC) system, neural networks (NNs) are used to develop digital twins for diagnosis (DT-Ds). However, NNs are not usually considered extrapolation models and may result in large errors if they are applied to unseen data outside the training data (uncovered). In this study, we propose a data coverage assessment (DCA) to determine if the NN-based DT-Ds are extrapolated based on their epistemic uncertainty. The uncertainty quantification algorithms and uncertainty thresholds are selected based on the confusion matrix of classifying evaluation data into covered or uncovered data. To demonstrate the adaptability of the proposed framework, we applied it to a basic feedforward neural network and a more advanced recurrent neural network based on a more nonlinear database. Case studies show that the proposed framework can distinguish unseen data for both basic and advanced applications with proper uncertainty quantification algorithms and thresholds. • Assess the data coverage of NN-based DTs to determine if they are extrapolated. • Test cases on FNNs and RNNs to demonstrate the adaptability of the framework. • The framework can distinguish unseen data with proper UQ algorithms and thresholds. [ABSTRACT FROM AUTHOR]

Reactor Operation Digital Twin (RODT) is now receiving increasing attention and investment in nuclear engineering domain. A prototype of a RODT was first brought out by Gong et al. at Nuclear Power Institute of China. The RODT contains a forward solver for online real-time simulation and an inverse problem solver for parameter identification and state estimation. To further improve the efficiency and accuracy of RODT and promote the practical deployment of RODT (i) we first propose an advanced differential evolution algorithm to upgrade the inverse solver; (ii) then we bring out a systematical uncertainty quantification of RODT considering assimilation noisy observations. The accuracy and validity of the proposed RODT are tested along one cycle operating stage of HPR1000, at various operating temperatures, control rod steps, general power level and the inlet temperature of a practical nuclear reactor core. Numerous numerical results confirm its potential for practical engineering applications for on-line parameter identification and state estimation. • An advanced differential evolution algorithm is implemented into the proposed RODT. • Observation denoising is realized with PCA followed by a normalization process. • Numerical tests on HPR1000 proof its efficiency and accuracy of the improved RODT. [ABSTRACT FROM AUTHOR]

• Development of prognosis digital twin with LSTM recurrent network. • Improvement of prognosis digital twin for better prediction and decision-making. • Investigation of manual search, Bayesian approach, and physics-guided ML. The nearly autonomous management and control (NAMAC) system is a comprehensive control system to assist plant operations by furnishing control recommendations to operators. Prognosis digital twin (DT-P) is a critical component in NAMAC for predicting action effects and supporting NAMAC decision-making during normal and accident scenarios. To quantifying and reducing uncertainty of machine-learning-based DT-Ps in multi-step predictions, this work investigates and derives insights from the application of three techniques for optimizing the performance of DT-P by long short-term memory recurrent neural networks, including manual search, sequential model-based optimization, and physics-guided machine learning. Sequential model-based optimization and physics-guide machine learning result in smallest errors when the predicting transients are similar to the training data. [ABSTRACT FROM AUTHOR]