diff --git a/2-state-of-the-art/v2.tex b/2-state-of-the-art/v2.tex new file mode 100644 index 0000000..06c3185 --- /dev/null +++ b/2-state-of-the-art/v2.tex @@ -0,0 +1,200 @@ +\section{State of the Art and Limits of Current Practice} + +The principal aim of this research is to create autonomous reactor control +systems that are tractably safe. To understand what is being automated, we must +first understand how nuclear reactors are operated today. This section examines +reactor operators and the operating procedures we aim to leverage, then +investigates limitations of human-based operation, and concludes with current +formal methods approaches to reactor control systems. + +\subsection{Current Reactor Procedures and Operation} + +Nuclear plant procedures exist in a hierarchy: normal operating procedures for +routine operations, abnormal operating procedures for off-normal conditions, +Emergency Operating Procedures (EOPs) for design-basis accidents, Severe +Accident Management Guidelines (SAMGs) for beyond-design-basis events, and +Extensive Damage Mitigation Guidelines (EDMGs) for catastrophic damage +scenarios. These procedures must comply with 10 CFR 50.34(b)(6)(ii) and are +developed using guidance from NUREG-0900~\cite{NUREG-0899, 10CFR50.34}, but their +development relies fundamentally on expert judgment and simulator validation +rather than formal verification. Procedures undergo technical evaluation, +simulator validation testing, and biennial review as part of operator +requalification under 10 CFR 55.59~\cite{10CFR55.59}. Despite this rigor, +procedures fundamentally lack formal verification of key safety properties. No +mathematical proof exists that procedures cover all possible plant states, that +required actions can be completed within available timeframes, or that +transitions between procedure sets maintain safety invariants. + +\textbf{LIMITATION:} \textit{Procedures lack formal verification of correctness +and completeness.} Current procedure development relies on expert judgment and +simulator validation. No mathematical proof exists that procedures cover all +possible plant states, that required actions can be completed within available +timeframes, or that transitions between procedure sets maintain safety +invariants. Paper-based procedures cannot ensure correct application, and even +computer-based procedure systems lack the formal guarantees that automated +reasoning could provide. + +Nuclear plants operate with multiple control modes: automatic control, where the +reactor control system maintains target parameters through continuous reactivity +adjustment; manual control, where operators directly manipulate the reactor; and +various intermediate modes. In typical pressurized water reactor operation, the +reactor control system automatically maintains a floating average temperature +and compensates for power demand changes through reactivity feedback loops +alone. Safety systems, by contrast, operate with implemented automation. Reactor +Protection Systems trip automatically on safety signals with millisecond +response times, and engineered safety features actuate automatically on accident +signals without operator action required. + +The division between automated and human-controlled functions reveals the +fundamental challenge of hybrid control. Highly automated systems handle reactor +protection---automatic trips on safety parameters, emergency core cooling +actuation, containment isolation, and basic process +control~\cite{WRPS.Description, gentillon_westinghouse_1999}. Human operators, +however, retain control of strategic decision-making: power level changes, +startup/shutdown sequences, mode transitions, and procedure implementation. + +\subsection{Human Factors in Nuclear Accidents} + +Current-generation nuclear power plants employ over 3,600 active NRC-licensed +reactor operators in the United States~\cite{operator_statistics}. These +operators divide into Reactor Operators (ROs), who manipulate reactor controls, +and Senior Reactor Operators (SROs), who direct plant operations and serve as +shift supervisors~\cite{10CFR55}. Staffing typically requires at least two ROs +and one SRO for current-generation units~\cite{10CFR50.54}. Becoming a reactor +operator requires several years of training. + +The persistent role of human error in nuclear safety incidents---despite decades +of improvements in training and procedures---provides the most compelling +motivation for formal automated control with mathematical safety guarantees. +Operators hold legal authority under 10 CFR Part 55 to make critical decisions, +including departing from normal regulations during emergencies. The Three Mile +Island (TMI) accident demonstrated how a combination of personnel error, design +deficiencies, and component failures led to partial meltdown when operators +misread confusing and contradictory readings and shut off the emergency water +system~\cite{Kemeny1979}. The President's Commission on TMI identified a +fundamental ambiguity: placing responsibility for safe power plant operations on +the licensee without formal verification that operators can fulfill this +responsibility does not guarantee safety. This tension between operational +flexibility and safety assurance remains unresolved: the person responsible for +reactor safety is often the root cause of failures. + +Multiple independent analyses converge on a striking statistic: 70--80\% of +nuclear power plant events are attributed to human error, versus approximately +20\% to equipment failures~\cite{WNA2020}. More significantly, the root cause of +all severe accidents at nuclear power plants---Three Mile Island, Chernobyl, and +Fukushima Daiichi---has been identified as poor safety management and safety +culture: primarily human factors~\cite{hogberg_root_2013}. A detailed analysis +of 190 events at Chinese nuclear power plants from +2007--2020~\cite{zhang_analysis_2025} found that 53\% of events involved active +errors, while 92\% were associated with latent errors---organizational and +systemic weaknesses that create conditions for failure. + + +\textbf{LIMITATION:} \textit{Human factors impose fundamental reliability limits +that cannot be overcome through training alone.} The persistent human +error contribution despite four decades of improvements demonstrates that these +limitations are fundamental rather than a remediable part of human-driven control. + +\subsection{Formal Methods} +\subsubsection{HARDENS} + +The High Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS) +project represents the most advanced application of formal methods to nuclear +reactor control systems to date~\cite{Kiniry2024}. + +HARDENS aimed to address a fundamental dilemma: existing U.S. nuclear control +rooms rely on analog technologies from the 1950s--60s. This technology is +obsolete compared to modern control systems and incurs significant risk and +cost. The NRC contracted Galois, a formal methods firm, to demonstrate that +Model-Based Systems Engineering and formal methods could design, verify, and +implement a complex protection system meeting regulatory criteria at a fraction +of typical cost. The project delivered a Reactor Trip System (RTS) +implementation with full traceability from NRC Request for Proposals and IEEE +standards through formal architecture specifications to verified software. + +HARDENS employed formal methods tools and techniques across the verification +hierarchy. High-level specifications used Lando, SysMLv2, and FRET (NASA Formal +Requirements Elicitation Tool) to capture stakeholder requirements, domain +engineering, certification requirements, and safety requirements. Requirements +were analyzed for consistency, completeness, and realizability using SAT and SMT +solvers. Executable formal models used Cryptol to create a behavioral model of +the entire RTS, including all subsystems, components, and limited digital twin +models of sensors, actuators, and compute infrastructure. Automatic code +synthesis generated verifiable C implementations and SystemVerilog hardware +implementations directly from Cryptol models---eliminating the traditional gap +between specification and implementation where errors commonly arise. + +Despite its accomplishments, HARDENS has a fundamental limitation directly +relevant to hybrid control synthesis: the project addressed only discrete +digital control logic without modeling or verifying continuous reactor dynamics. +The Reactor Trip System specification and verification covered discrete state +transitions (trip/no-trip decisions), digital sensor input processing through +discrete logic, and discrete actuation outputs (reactor trip commands). The +project did not address continuous dynamics of nuclear reactor physics. Real +reactor safety depends on the interaction between continuous +processes---temperature, pressure, neutron flux---evolving in response to +discrete control decisions. HARDENS verified the discrete controller in +isolation but not the closed-loop hybrid system behavior. + +\textbf{LIMITATION:} \textit{HARDENS addressed discrete control logic without +continuous dynamics or hybrid system verification.} Verifying discrete control +logic alone provides no guarantee that the closed-loop system exhibits desired +continuous behavior such as stability, convergence to setpoints, or maintained +safety margins. + +HARDENS produced a demonstrator system at Technology Readiness Level 2--3 +(analytical proof of concept with laboratory breadboard validation) rather than +a deployment-ready system validated through extended operational testing. The +NRC Final Report explicitly notes~\cite{Kiniry2024} that all material is +considered in development, not a finalized product, and that ``The demonstration +of its technical soundness was to be at a level consistent with satisfaction of +the current regulatory criteria, although with no explicit demonstration of how +regulatory requirements are met.'' The project did not include deployment in +actual nuclear facilities, testing with real reactor systems under operational +conditions, side-by-side validation with operational analog RTS systems, +systematic failure mode testing (radiation effects, electromagnetic +interference, temperature extremes), NRC licensing review, or human factors +validation with licensed operators in realistic control room scenarios. + +\textbf{LIMITATION:} \textit{HARDENS achieved TRL 2--3 without experimental +validation.} While formal verification provides mathematical correctness +guarantees for the implemented discrete logic, the gap between formal +verification and actual system deployment involves myriad practical +considerations: integration with legacy systems, long-term reliability +under harsh environments, human-system interaction in realistic +operational contexts, and regulatory acceptance of formal methods as +primary assurance evidence. + +\subsubsection{Sequent Calculus and Differential Dynamic Logic} +There has been additional work to do verification of hybrid systems by extending +the temporal logics directly. The result has been the field of differential +dynamic logic (dL). dL introduces two additional operators +into temporal logic: the box operator and the diamond operator. The box operator +\([\alpha]\phi\) states that for some region \(\phi\), the hybrid system +\(\alpha\) always remains within that region. In this way, it is a safety +ivariant being enforced for the system. The second operator, the diamond +operator \(<\alpha>\phi\) says that for the region \(\phi\), there is at least +one trajectory of \(\alpha\) that enters that region. This is a declaration of a +liveness property. + +%source: https://symbolaris.com/logic/dL.html + +While dL allows for the specification of these liveness and safety properties, +actually proving them for a given hybrid system is quite difficult. Automated +proof assistants such as KeYmaera X exist to help develop proofs of systems +using dL, but so far have been insufficient for reasonably complex hybrid +systems. The main issue behind creating system proofs using dL is state space +explosion and non-terminating solutions. +%Source: that one satellite tracking paper that has the problem with the +%gyroscopes overloding and needing to dump speed all the time +Approaches have been made to alleviate +these issues for nuclear power contexts using contract and decomposition based +methods, but are far from a complete methodology to design systems with. +%source: Manyu's thesis. +Instead, these approaches have been used on systems that have been designed a +priori, and require expert knowledge to create the system proofs. + +%Maybe a limitation here? 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