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DOE OSTI2020

Markov Process to Evaluate the Value Proposition of a Risk-Informed Predictive Maintenance Strategy

To achieve high-capacity factors, the nuclear fleet has relied on labor-intensive and time-consuming operation and preventive maintenance programs for plant systems. Manually performed inspection, calibration, testing, and maintenance of plant assets at periodic frequencies, along with time-based replacement of assets irrespective of condition, have resulted in a costly, labor-centric business model. Fortunately, there are technologies that can eliminate unnecessary preventive maintenance activities by deploying risk-informed predictive maintenance, enabling the transition to a technology-centric business model. The technology-centric business model will enable plants to optimize and automate maintenance activities, leading to cost reductions since labor is a rising cost and technology is a declining cost. The implementation of scalable technologies and methodologies across plant systems and across the nuclear fleet is critical for successful deployment of a risk-informed predictive maintenance strategy at commercial nuclear power plants. The work presented in the report is being developed as part of a collaborative research effort between Idaho National Laboratory and Public Service Enterprise Group Nuclear, LLC. This report describes the technical basis using the Markov Process to evaluate the value proposition for the risk-informed predictive maintenance strategy for the circulating water system. The plant process data from the Salem nuclear plant’s circulating water system is utilized to develop a Markov chain risk models and formulation to estimate the loss and gain in revenue based on plant availability. The outcomes presented in this report provides the technical basis for extensive quantitative evaluation of a scalable risk-informed predictive maintenance strategy as part of future research.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Unfolding of the Villin Headpiece Domain: Revealing Structural Heterogeneity with Time‐Resolved X‐Ray Solution Scattering and Markov State Modeling

Understanding protein folding pathways is crucial to deciphering the principles of protein structure and function. Here, the unfolding dynamics of the 35‐residue villin headpiece (HP35) and a norleucine‐substituted variant (2F4K) using a combination of experimental and computational techniques is investigated. Time‐resolved X‐ray solution scattering coupled with equilibrium molecular dynamics simulations and Markov state modeling reveals distinct unfolding mechanisms between the two variants: HP35 and 2F4K. Specifically, HP35 exhibits a two‐state unfolding process, whereas an intermediate state is identified for the 2F4K mutant. A Markov state model constructed from simulations is used to map atomic‐level transitions to experimental observations, providing insights into the role of sequence variations in modulating folding pathways. The findings underscore the importance of integrating experimental and computational approaches to unravel protein unfolding mechanisms between heterogenous structural ensembles.

Nijhawan, Adam K. [Department of Chemistry Northwe↗

DOE OSTI2021

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

Zhu, Jin↗

DOE OSTI2024

Spiking Markov Reward Process v.0.1

SAND2024-11150O The Spiking Markov Reward Process software is a spiking neural network that streams binary arithmetic and computes the state value function of a Markov reward process. The software will be released to the SpiNNcloud group for development of neuromorphic acceleration. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Wang, Felix↗

DOE OSTI2020

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Transitional Markov Chain Monte Carlo Sampler in UQTk

Transitional Markov Chain Monte Carlo (TMCMC) is a variant of a class of Markov Chain Monte Carlo algorithms known as tempering-based methods. In this report, the implementation of TMCMC in the Uncertainty Quantification Toolkit is investigated through the sampling of high-dimensional distributions, multi-modal distributions, and nonlinear manifolds. Furthermore, the Bayesian model evidence estimates obtained from TMCMC are tested on problems with known analytical solutions and shown to provide consistent results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Markov Chain Monte Carlo Parameter Estimation of Deflagration Losses in a Rotating Detonation Engine

One of the practical challenges of the studies of rotating detonation engines (RDEs) is the direct estimation of losses from experimental measurements. This study attempts at resolving this limitation by combining a reduced order model (ROM) of the detonation wave characteristics with a Markov chain Monte Carlo parameter estimation framework. The model considers simple deflagration losses and the overall impact of deflagration on RDE performance. To evaluate this model, a Markov Chain Monte Carlo (MCMC) sampling technique was applied to estimate the loss parameters within the model for a set of conditions operated in hydrogen-air over a range of mass flow rates and equivalence ratios. The MCMC parameter estimation framework allowed for the determination of a posterior distribution of the loss parameters for each test condition, an examination of the correlation between the loss parameters and measured performance metrics of the RDE, and an uncertainty propagation of these parameters. The predicted model loss parameters were then compared to indirect experimental measurements of the deflagration combustion fractions to evaluating the validity of the approach, and shed light on the benefits and drawbacks of the model, measurement techniques, and the estimation framework.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1973

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗

NASA NTRS1974

A Markov model for NASA's Ground Communications Facility

A 'natural' way of constructing finite-state Markov chains (FSMC) is presented for those noise burst channels that can be modeled by them. In particular, a five-state Markov chain is given as a model of errors occurring at the Ground Communications Facility (GCF). A maximum likelihood procedure applicable to any FSMC is developed for estimating all the model parameters starting from the data of error runs. A few of the statistics important for estimating the performance of error control strategies on the channel are provided.

Adeyemi, O.↗

NASA NTRS1975

Strong scintillations in astrophysics. I - The Markov approximation, its validity and application to angular broadening

The Markov approximation to the propagation of waves in an extended, irregular medium is discussed in an astrophysical context. A new derivation is presented which is simple and which shows that the assumption of Gaussian statistics used by previous authors is irrelevant. We discuss the relevance of the approximation and show that it may apply in many situations of interest, including interstellar scintillations of pulsar signals. The approximation does not require the assumption of weak scattering or Gaussian correlation functions. The Markov equation for the angular spectrum is particularly simple, and solutions are discussed for typical turbulence spectra. It is found that the equation for the angular spectrum is very nearly that used by previous authors, and the present discussion shows that these results are much more general than previously thought. A possible observational test for distinguishing between Gaussian and power-law interstellar density spectra is discussed.

Lee, L. C.↗

NASA NTRS1978

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗

NASA NTRS1979

An 'adding' algorithm for the Markov chain formalism for radiation transfer

An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.

Esposito, L. W.↗

NASA NTRS1982

A Markov chain model for reliability growth and decay

A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.

Siegrist, K.↗

NASA NTRS1988

Semi-Markov Unreliability-Range Evaluator

Reconfigurable, fault-tolerant systems modeled. Semi-Markov unreliability-range evaluator (SURE) computer program is software tool for analysis of reliability of reconfigurable, fault-tolerant systems. Based on new method for computing death-state probabilities of semi-Markov model. Computes accurate upper and lower bounds on probability of failure of system. Written in PASCAL.

Butler, Ricky W.↗

NASA NTRS1989

Markov reliability models for digital flight control systems

The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.

Mcgough, John↗

NASA NTRS1989

Optimal q-Markov COVER for finite precision implementation

The existing q-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced order model. All q-Markov COVERs allow some freedom in the choice of parameters. Here, researchers exploit this freedom in the existing theory to optimize the models with respect to these finite wordlength effects.

Williamson, Darrell↗

NASA NTRS1989

A non-homogeneous Markov model for phased-mission reliability analysis

Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation.

Smotherman, Mark↗