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Dynamic probabilistic risk assessment and game theory for cyber security risk analysis in nuclear power plants

Nuclear Power Plants and energy systems have become more prone to cyber-attacks with their digitalization and the increased use of smart equipment. Hence, it is important to quantify the risk associated with cyber-attacks in such systems. Dynamic Probabilistic Risk Assessment which involves studying the evolution of a system due to random events and operator and attacker actions during a cyber-attack by employing a physics-based model of the system is a suitable framework to quantify cybersecurity risk in nuclear power plants. In addition to the plant dynamics, it is also important to model the strategies of the attackers and plant operators for an effective cybersecurity risk assessment. Game theory provides a set of necessary tools to model such strategic interactions. In this research, a framework that integrates dynamic probabilistic risk assessment with game theory for cybersecurity risk analysis in nuclear power plants is presented. The mathematical formulation is derived based on the theory of continuous event trees. We propose a game theory based action model, that utilizes physics-based rewards to define the strategies of attackers and operators at every decision epoch. As a case study, the risk associated with cyber-attacks on the digital components in the secondary side of a pressurized water reactor is studied using a reduced order model. A set of attacker actions and a set of operator actions are defined for the system. The operator and attacker interactions were modelled using simultaneous game, their action policies were computed using the concept of mixed strategy Nash equilibrium and the evolution of the system was studied.

97 MATHEMATICS AND COMPUTING↗

Dynamic probabilistic risk assessment for electric grid cybersecurity

Electric grid cybersecurity risk has become a significant concern of industries and governments. This paper proposes a dynamic probabilistic risk assessment method for electric grid cybersecurity risk analysis. The proposed method helps reduce the reliance on expert judgment, capture a broad range of components and system dynamics, and model the interactions between various contributing entities (e.g., attacker, operator). In addition, the scenarios with multiple events, such as the occurrence of both cyberattacks and failures of physical components, the occurrence of both cyberattacks and operators’ (in)correct reactions, are considered and analyzed. Further, for each cyberattack scenario, Monte Carlo simulations are used to obtain possible sequences of the system's evolution under study and then derive risk estimates. As an application of the proposed method, the risk assessment method serves as the basis of risk-informed defense resource allocation to improve electric grid cybersecurity. The proposed method is verified using the IEEE 14-bus system by evaluating different security resource allocations for selected cyberattack scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP (Presentation)

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. Idaho National Laboratory has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal hydraulics modeling to enhance security planning while reducing costs. A reduced order model for thermal hydraulic simulations performed by the Modular Accident Analysis Program (MAAP) was developed to evaluate reactor core behavior during attack scenarios. MAAP simulations are computationally intensive and must be run in a secure environment, complicating analysis and validation. By pre-computed scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. To address this, Idaho National Laboratory [JL2.1]has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal-hydraulics modeling [JL3.1]to enhance security planning while reducing costs. We developed a tool that produces reduced order models using thermal hydraulic simulations from the Modular Accident Analysis Program (MAAP) [1]. These models can quickly evaluate reactor core behavior during attack simulations, and in so doing, address two barriers of traditional methods: (1) MAAP simulations are computationally intensive, and (2) attack scenarios must be run in a secure environment, which complicates analysis and validation. By precomputing scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Investigation of the Use of Dynamic Probabilistic Risk Assessment Methodologies for Identifying Digital I&C System Common Cause Failures

Digital Instrumentation and Control (I&C) systems have a key role in nuclear power plants in the upgrade of aging analog systems. Digital systems improve plant safety and reliability through features such as increased hardware reliability and stability and improved failure detection capability. There is no consensus on which of the current probabilistic risk assessment methods are most suitable for use in the reliability analysis of digital I&C systems. While the traditional event-tree/fault-tree (ET/FT) approach is still used for their reliability modeling, there are concerns regarding this approach in properly accounting for dynamic interactions among system components since potentially significant dependencies among failure events may not be identified and/or their likelihood may not be properly quantified. Dynamic methodologies are expected to provide a much more accurate representation of probabilistic evolution of the I&C systems in time due to their capability to more properly account for complex interactions than the static approach. The applicability of dynamic PRA methodologies for digital I&C system is investigated using the criteria presented in the NUREG/CR-6901, and the comparisons made in NUREG/CR-6901 are updated in light of the latest studies. The Dynamic Event Tree (DET) approach has been identified as one of the top dynamic methods when evaluated against the requirements for the reliability modeling of digital I&C systems. The DET method is a strong candidate for integration into existing PRA studies, as it bears many similarities to the traditional ET approach. In this study, the DET approach has been applied to the Plant Protection System of the APR1400 design, and the results are compared to results from its available traditional ET/FT analysis. Possible approaches to evaluate and quantify the effects of common cause failures on system safety using dynamic methods are also examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Probabilistic Methods for Cyclical and Coupled Systems with Changing Failure Rates

Advancements in nuclear system designs with automated control features provide many benefits, but can lead to complex coupled systems and dynamic failure scenarios. This is especially true for microreactor designs where components are not expected to be replaced during the reactor’s lifetime. Hence, the life of the system, in addition to the safety, needs to be evaluated. Modeling these sequences of time-dependent events requires addressing cyclical processes and changing failure rates in ways that represent the actual system dynamics in contrast to a single sampling for a component’s time to failure. This research presents two distinct analytical methods for several failure distributions that evaluate a final time to failure used for different scenarios where the time to failure must be sampled multiple times. The first method is used when evaluating a component whose failure rate increases due to an outside event after the initial sampling but before the initially sampled time to failure. The second method is used when evaluating multiple identical components or a component that has been replaced with a new identical version before the second sampling. The two methods were implemented in a few representative case studies developed in the dynamic probabilistic risk assessment tool Event Modeling Risk Assessment using Linked Diagrams. Overall, this paper provides guidelines on how these approaches give a more realistic and accurate dynamic probabilistic risk assessment of complex systems.

97 MATHEMATICS AND COMPUTING↗

Light Water Reactor Sustainability Program: Upgrade of EMRALD to a Modern JavaScript-based Framework

Event Modeling Risk Assessment using Linked Diagrams (EMRALD) is a software tool developed at Idaho National Laboratory for researching the capabilities of dynamic probabilistic risk assessment. It provides a simple interface to represent complex interactions often seen when developing dynamic models. EMRALD can also interface with other applications by modifying inputs, running, and using their results within EMRALD for dynamic and integrated assessment. This report goes over the work performed as part of the Risk-Informed Systems Analysis Pathway under the Light Water Reactor Sustainability program to upgrade the EMRALD software.

97 MATHEMATICS AND COMPUTING↗

EMRALD Technology Advancements for Commercial Grade Dedication Readiness

Event Modeling Risk Assessment using Linked Diagrams (EMRALD) is a software tool developed at Idaho National Laboratory for researching the capabilities of dynamic probabilistic risk assessment. It provides a simple interface to represent complex interactions often seen when developing dynamic models. EMRALD can also interface with other applications by modifying inputs as well as running and using their results within EMRALD for dynamic and integrated assessment. To enable wider industry use cases, collaborative work between Idaho National Laboratory and FPoliSolutions was performed through the technology commercialization fund TCF-20-21448. This report covers the additional features and capabilities developed under this work.

97 MATHEMATICS AND COMPUTING↗

Simulation-Based Recovery Action Analysis Using the EMRALD Dynamic Risk Assessment Tool

Recovery human action is defined as the action that prevents deviant conditions from producing unwanted effects. Analyzing recovery actions has been a critical part in human reliability analysis (HRA). However, there are a couple of limitations to treating recovery actions using only the current HRA methods available. Representatively, the existing recovery analysis does not specifically consider recovery actions as they have occurred in actual nuclear power plants (NPPs). To handle the challenges in the existing recovery analyses, this study suggests a way to analyze recovery actions under a dynamic HRA method, the Procedure-based Risk Investigation MEthod-Human Reliability Analysis (PRIME-HRA) method. The PRIME-HRA method suggests a way on how to develop dynamic simulation models using dynamic risk assessment tools such as the Event Modeling Risk Assessment Using Linked Diagram (EMRALD) [1] and the Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER) [2]. EMRALD and HUNTER are the dynamic probabilistic risk assessment and HRA tools developed at Idaho National Laboratory. In this paper, differences on analyzing recovery actions in the Technique for Human Error-Rate Prediction (THERP), the Cause-Based Decision Tree (CBDT) and the Korean Standard HRA (K-HRA) and challenges of these approaches are introduced. How we have developed the PRIME-HRA is also introduced in this paper. Then, the proposed approach to analyzing recovery human actions in dynamic context is partially discussed with an example.

99 GENERAL AND MISCELLANEOUS↗

An Approach to Dynamic Human Reliability Analysis and Its Data Collection Framework

Human reliability analysis (HRA) is a method for evaluating human errors in a variety of complex systems such as nuclear power plants, military systems, aircraft, and chemical plants. Most HRA methods currently used by regulatory institutes or utilities are called static HRA and are carried out by simple worksheets or simple calculators. To date, there are many unsolved or intrinsic challenges in static HRA. For example, existing static HRA does not realistically model and evaluate human actions as they would be performed at actual systems. There is no method with HRA to objectively estimate the time required for human actions despite being essential to HRA processes. In addition, many HRA methods still rely on a dataset generated prior to the 1980s, from unrelated industry experience or simply from expert judgment. Accordingly, this study attempted to research how to overcome the challenges of existing HRA via dynamic risk assessment (a.k.a., simulation-based or computation-based risk assessment) techniques. First, this study developed a dynamic HRA method, named as PRocedure-based Investigation Method of EMRALD Risk Assessment – HRA (PRIMERA-HRA). The PRIMERA-HRA mainly concentrates on providing HRA analysts with specific guidelines on how to reasonably model human actions, assign human reliability data and evaluate output of simulation within a dynamic probabilistic risk assessment tool, called as Event Modeling Risk Assessment using Linked Diagrams (EMRALD). Second, this study also developed a module for performance shaping factors (i.e., the key concept in HRA quantification) applicable to dynamic HRA, then implemented it based on PRIMERA-HRA within the EMRALD tool. Third, this study developed an HRA data collection framework to support dynamic HRA, called as Simplified Human Error Experimental Program (SHEEP). Originally, the SHEEP study aimed to support static HRA and its data collection, but recently extended the scope to the new technologies such as dynamic HRA or HRA for advanced reactors. SHEEP focuses on the use of data collected from simplified simulators to complement—but not replace—data collection studies using full-scope simulators and actual operators. To date, many experiments were conducted under the SHEEP framework. Multiple analyses, such as human performance analysis, human error analysis, task complexity analysis, learning effect analysis and time distribution analysis, were also carried out using the collected data. Then, based on the major insights, an approach to inferring full-scope data based on simplified simulator data was proposed. The PRIMERA-HRA and SHEEP research are expected to evaluate human actions more realistically than existing static HRA, provide an opportunity to collect more HRA data with reasonable cost and labor, then contribute to enhance the quality of HRA.

99 - GENERAL AND MISCELLANEOUS↗

An Approach to Dynamic Human Reliability Analysis and Its Data Collection Framework

Human reliability analysis (HRA) is a method for evaluating human errors in a variety of complex systems such as nuclear power plants, military systems, aircraft, and chemical plants. Most HRA methods currently used by regulatory institutes or utilities are called static HRA and are carried out by simple worksheets or simple calculators. To date, there are many unsolved or intrinsic challenges in static HRA. For example, existing static HRA does not realistically model and evaluate human actions as they would be performed at actual systems. There is no method with HRA to objectively estimate the time required for human actions despite being essential to HRA processes. In addition, many HRA methods still rely on a dataset generated prior to the 1980s, from unrelated industry experience or simply from expert judgment. Accordingly, this study attempted to research how to overcome the challenges of existing HRA via dynamic risk assessment (a.k.a., simulation-based or computation-based risk assessment) techniques. First, this study developed a dynamic HRA method, named as PRocedure-based Investigation Method of EMRALD Risk Assessment – HRA (PRIMERA-HRA). The PRIMERA-HRA mainly concentrates on providing HRA analysts with specific guidelines on how to reasonably model human actions, assign human reliability data and evaluate output of simulation within a dynamic probabilistic risk assessment tool, called as Event Modeling Risk Assessment using Linked Diagrams (EMRALD). Second, this study also developed a module for performance shaping factors (i.e., the key concept in HRA quantification) applicable to dynamic HRA, then implemented it based on PRIMERA-HRA within the EMRALD tool. Third, this study developed an HRA data collection framework to support dynamic HRA, called as Simplified Human Error Experimental Program (SHEEP). Originally, the SHEEP study aimed to support static HRA and its data collection, but recently extended the scope to the new technologies such as dynamic HRA or HRA for advanced reactors. SHEEP focuses on the use of data collected from simplified simulators to complement—but not replace—data collection studies using full-scope simulators and actual operators. To date, many experiments were conducted under the SHEEP framework. Multiple analyses, such as human performance analysis, human error analysis, task complexity analysis, learning effect analysis and time distribution analysis, were also carried out using the collected data. Then, based on the major insights, an approach to inferring full-scope data based on simplified simulator data was proposed. The PRIMERA-HRA and SHEEP research are expected to evaluate human actions more realistically than existing static HRA, provide an opportunity to collect more HRA data with reasonable cost and labor, then contribute to enhance the quality of HRA.

99 - GENERAL AND MISCELLANEOUS↗

Automatic Generation of Event Trees and Fault Trees: A Model-Based Approach

In the past few decades, the increasing complexity of modern engineering systems has been driven by the integration of a large number of components whose operations may involve many disciplines (e.g., thermal hydraulics, plant operations, cybersecurity). Most computational tools used by industry and regulators for system safety and reliability assessments are still based on the traditional fault tree (FT) and event tree (ET) approach, which may not be able to capture complex interactions among system constituents. The use of simulation tools has widely increased in the past few decades to improve the fidelity of the reliability and safety analyses. However, the direct use of simulation tools as part of dynamic probabilistic risk assessment (DPRA) methods is not getting traction since (1) modeling the whole system under consideration with DPRA methods may be computationally expensive and unnecessary, and (2) the manual integration of DPRA models into existing state-of-practice probabilistic risk assessment models (i.e., based on FTs and ETs) can be time consuming and prone to errors. Here, in this paper we propose a procedure to overcome this limitation by presenting several algorithms designed to automatically construct subsystem ETs and FTs from DPRA methods for integration into an existing ET/FT system model.

97 MATHEMATICS AND COMPUTING↗

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

Success Path Method: Introduction to the Success Path Method Software Tool©

As part of its commitment to advancing safety and reliability assessment methodologies, Argonne National Laboratory pioneered the use of an evaluation method called the Success Path Method (SPM) to improve risk management for offshore oil and gas operations. The development of the SPM at Argonne has been driven by the need to improve existing risk assessment methodologies by focusing on the steps necessary for success rather than failure modes alone. This is particularly important for industrial environments like offshore facilities that perform multiple functions under a continuously evolving set of operational conditions – such as water depth and temperature, currents, and weather conditions. In these dynamic environments, the traditional Probabilistic Risk Assessment (PRA) approach is far too complex as it focuses on what can go wrong – which comprises an infinite failure space that must be fully explored and understood. By shifting the focus to a finite space of success paths, the SPM enables operators and decision makers to prioritize a manageable number of steps that must go right to ensure success. Building on its five decades of experience in safety assessments for the nuclear industry, Argonne made major adaptations to existing risk assessment methods utilizing features similar to fault trees that are traditionally used in PRA to map all pathways in which the system can malfunction. In contrast, SPM identifies the components and processes that must function correctly to achieve specific outcomes – such as preventing the uncontrolled release of hydrocarbons during drilling operations. The SPM framework integrates equipment, procedures, software, processes, and human actions to ensure that physical barriers meet critical safety functions in dynamic operational conditions. This approach helps identify failure modes and improve operational risk management by narrowing the focus to key success elements, which in turn reduces uncertainty and helps users understand, manage, and respond to failures.

97 MATHEMATICS AND COMPUTING↗

Safety Benefits Assessment for Accident Tolerant Fuels in Consideration of Steam Generator Tube Degradation Using Dynamic Event Tree Analysis

Accident tolerant fuel (ATF) is expected to delay or prevent core damage by providing additional coping time under accidents involving loss of core cooling. The effect of extended coping time may vary depending on the plant response to accidents. Age-related component degradation that deteriorates plant performance over time could have an impact on the actual advantages of ATF. The potential safety benefits of two near-term ATF candidates, including Cr-coated Zr cladding and FeCrAl cladding, are assessed for a 2-in. loss-of-coolant accident with failed high-pressure safety injection using the dynamic event tree (DET) approach considering possible stress corrosion cracking of steam generator (SG) tubing under aging. The DET approach allows likelihood quantification of accident sequences leading to core damage, including stochastic variation of system response and human actions during accident mitigation. The safety benefits of the selected ATF claddings in terms of additional coping time and the core damage frequency reduction rate under specified accident situations were quantitatively estimated. The results show that the deployment of the two selected ATF claddings is expected to lead to longer coping times and lower core damage frequency due to the wider safety margin to peak cladding temperature they provide. The safety advantages would be greater as SG tube degradation proceeds. Thus, the two ATF candidates would lead to less severe consequences in terms of likelihood of core damage and susceptibility to the SG tube degradation than UO 2 -Zr fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

An Approach to Dynamic Human Reliability Analysis Using the EMRALD Dynamic Risk Assessment Tool

There is a need for research into dynamic human reliability analysis (HRA) (i.e., simulation- or computation-based HRA), as many researchers have emphasized the importance of applying dynamic approaches to probabilistic safety assessments (PSAs). This study proposes the Procedure-based Investigation Method of EMRALD Risk Assessment – Human Reliability Analysis (PRIMERA-HRA), a dynamic HRA approach based on the Event Modeling Risk Assessment Using Linked Diagram (EMRALD) software developed by Idaho National Laboratory (INL). This study suggests how this software can be used to model human actions and evaluate error probabilities. The applicability of this approach is also be investigated in light of an extended loss of AC power (ELAP) scenario. This paper then discusses the major insights derived by comparing this dynamic HRA approach against the static one.

99 GENERAL AND MISCELLANEOUS↗