On the application of stochastic models in nuclear power plant maintenance

Whereas Philip A. Scarf’s effort [Eur. J. Operat. Res. 99 (1997) 493] can be seen as an “appeal to Maintenance Modelers to work with Maintenance Engineers and Managers on real problems” the current effort can be seen as the start of a program to do just that by using the relatively large 20 year old data bases available at Ontario Power Generation (OPG). A significant portion of the traditional problem areas have been circumvented by combining well known elementary models with input from practitioners in the nuclear maintenance field of over 25 years experience.Case studies of containment airlock seal failures are used here to illustrate the direct applicability of stochastic processes. The application is kept relatively clear and lucid to reflect the often non-stochastically trained audience. The results are displayed via economic alternatives to more easily attract the attention of maintenance managers.The conclusions highlight several dramatic avenues that await the coordinated effort of practitioner and modeler at this particular juncture in time. Pursuit of these avenues could well result in a resurgence of all branches of operational research in large industry.     

Optimizing nuclear power plant refueling with mixed-integer programming

The problem addressed here is scheduling the shutdown for refueling and maintenance of nuclear power plants. The models have up to four reactors requiring of the order of five shutdowns each over a five-year time horizon. The resulting mixed-integer program is large and complex with interesting structure. We show good results using a mixed-integer optimizer taking advantage of a strong linear programming formulation.     

Vibration analysis and optimization of a primary circuit of the nuclear power plant

The mathematical model of the primary circuit of a nuclear power plant VVER 420/213 has been developed. The aim of modelling is a vibration analysis and parameter optimization leading to the decrease of velocity and stress amplitudes of the circuit components. For an assemblage of the mathematical model of the whole primary circuit the modal synthesis method with significant DOF reduction is used.     

Expert system for a nuclear power plant accident diagnosis using a fuzzy inference method

The huge and complicated plants such as nuclear power stations are likely to cause the operators to make mistakes due to a variety of inexplicable reasons and symptoms in case of emergency. That’s why the prevention system assisting the operators is being developed for. First of all, I suggest an improved fuzzy diagnosis. Secondly, I want to demonstrate that a classification system of nuclear plant’s accident investigating the causes of accidents foresees possible problems, and maintains the reliability of the diagnostic reports in spite of improper working in part. In the event of emergency in a nuclear plant, a lot of operational steps enable the operators to find out what caused the problems based on an emergent operating plan. Our system is able to classify their types within twenty to thirty seconds. As so, we expect the system to put down the accidents right after the rapid detection of the damage control-method concerned.     

Lagrangean heuristics applied to a variety of large capacitated plant location problems

A series of performance improving heuristics are developed and embedded into the procedure of Lagrangean heuristics. The principles and ideas of these heuristics are used to build a general framework with which a variety of large Capacitated Plant Location Problems (CPLP) are solved, including the multi-capacitated case. A significant improvement over the results discussed in the literature is recorded. The single-source multi-Capacitated Plant Location Problem, which has not been addressed in the literature, is also tackled with encouraging results.     

Fluctuations of interface statistical physics models applied to a stock market model

In this paper, applying the theory of fluctuations of the interfaces for statistical physics lattice models, we construct a financial model and use this financial model to describe the behavior or fluctuations of a stock price process in a stock market. By using the methods of statistical physics and under some conditions, we show that the finite dimensional distribution of a normalized random process for this financial model converges to the corresponding distribution of the Black–Scholes model.     

A network-related nuclear power plant model with an intelligent branch-and-bound solution approach

This paper presents a network model with discrete requirements for a nuclear power plant. The model determines the batch size and timing for nuclear unit refueling and how much energy should be produced by nuclear and non-nuclear units for each time period to satisfy forecasted demand with minimum total operating costs over the planning horizon. Efficient modeling and solution strategies are developed which constitute a merger of operations research and artificial intelligence. A branch-and-bound solution approach is combined with a pattern recognition component, involving non-parametric discrimination analyses, to select branching variables and directions. By coupling this approach with network optimization techniques to exploit the underlying network structure of the problem, substantial improvements are obtained both in solution quality and solution efficiency.This research was supported in part by the Center for Business Decision Analysis, the Hugh Roy Cullen Centennial Chair in Business Administration, and the Office of Naval Research under contract N00014-87-K-0190. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. CENTER FOR BUSINESS DECISION ANALYSIS Darwin Klingman, Director The University of Texas at Austin Austin, TX 78712, U.S.A.     

Hierarchical Bayesian models applied to air surveillance radars

Evaluation tests for air surveillance radars are often formulated in terms of the probability to detect a target at a specified range. Statistical methods applied in these tests do not explore all data in a full probabilistic model, which is crucial when dealing with small samples. The collected data are arranged longitudinally, in different levels (altitude), indexed both in time and distance. In this context we propose the application of dynamic Bayesian hierarchical models as an efficient way to incorporate the complete data set. Markov Chain Monte Carlo methods (MCMC) are used to make inference and to evaluate the proposed models.     

An example of a nuclear space in infinite dimensional holomorphy

LetU be an open subset of a complex locally convex spaceE, andH(U) the space of holomorphic functions fromU toC. If the dualE′ ofE is nuclear with respect to the topology generated by the absolutely convex compact subsets ofE, then it is shown thatH(U) endowed with the compact open topology is a nuclear space. In particular, ifE is the strong dual of a Fréchet nuclear space, thenH(U) is a Fréchet nuclear space.     

An example of a nuclear space in infinite dimensional holomorphy

LetU be an open subset of a complex locally convex spaceE, andH(U) the space of holomorphic functions fromU toC. If the dualE′ ofE is nuclear with respect to the topology generated by the absolutely convex compact subsets ofE, then it is shown thatH(U) endowed with the compact open topology is a nuclear space. In particular, ifE is the strong dual of a Fréchet nuclear space, thenH(U) is a Fréchet nuclear space.     

BELENE nuclear power plant numerical and experimental bedrock,layers and surface signals

An investigation of BELENE Nuclear Power Plant (NPP) free field signal is presented in the current study. An SH wave propagation trough multilayer geological media in the region is considered. An original structural model of the geological column has been developed. The investigated layers are isotropic, with constant depth and skyline parallel. The SH rays are with an arbitrary angle as far as the layers are concerned. The seismic SH waves have been generated by a special detonation device. The main results of the study are graphically illustrated. A comparison between the original BELENE NPP experimental and the numerical surface (free field) signals (obtained by the formulated direct problem) for the investigated geological column has been carried out and its results are hereby shown.     

Comparison of two different models to account for induced flow anisotropy during complex loading processes

Some metals exhibit an increase of the yield stress after orthogonal strain path changes, i.e. so–called cross hardening. Two approaches are discussed in this work which are capable of taking that effect into account in an appropriate manner. The first approach is closely related to that of Teodosiu and Hu. The second model considers besides the movement of the center of the yield surface and its proportional expansion also the change of its shape and is able to describe the induced anisotropic behavior with regard to complicated loading histories. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An assessment of turbulence models applied to the simulation of a two-dimensional submerged jet

This paper is concerned with the investigation of the performance of different turbulence models in the numerical prediction of transient flow caused by a confined submerged jet. Several widely used models, i.e., the standard k–ε, RNG k–ε, low Reynolds number k–ε models and the differential Reynolds stress model, as included in CFD codes, were compared with each other for a two-dimensional, incompressible, turbulent jet flow and with reported experimental data. A flapping oscillation was predicted regardless of the model used. A chosen Strouhal (St) number definition brought the fundamental frequencies from both the experiments and computations into close proximity. However, different turbulence models have exhibited quite different behaviours in terms of the frequency and regularity of the oscillation and in terms of the scale and duration of the vortices generated. All versions of the k–ε model yielded regular oscillations, which agree with experimental observations. On the other hand, the Reynolds stress (RS) model produced a complex pattern but a slower dissipation of vortices. In addition, some aspects of gridding and inflow representation are also discussed.     

Stochastic dual dynamic programming applied to nonconvex hydrothermal models

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented.     

Comparison of two models for managing reliability growth during product design

Relying on reliability growth testing to improve system designis neither usually effective nor efficient. Instead it is importantto design in reliability. This requires models to estimate reliabilitygrowth in the design that can be used to assess whether goalreliability will be achieved within the target timescale forthe design process. Many models have been developed for analysisof reliability growth on test, but there has been much lessattention given to reliability growth in design. This paperdescribes and compares two models: one motivated by the practicalengineering process; the other by extending the reasoning ofstatistical reliability growth modelling. Both models are referencedin the recently revised edition of international standard IEC61164. However, there has been no reported evaluation of theirproperties. Therefore, this paper explores the commonalitiesand differences between these models through an assessment oftheir logic and their application to an industrial example.Recommendations are given for the use of reliability growthmodels to aid management of the design process and to informproduct development.     

Comparison principles applied to obstacle problems with penalties

Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L _∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved.

For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem.

The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters.     

An algorithm based on a sequence of linear complementarity problems applied to a walrasian equilibrium model: An example

The Walrasian equilibrium problem is cast as a complementarity problem, and its solution is computed by solving a sequence of linear complementarity problems (SLCP). Earlier numerical experiments have demonstrated the computational efficiency of this approach. So far, however, there exist few relevant theoretical results that characterize the performance of this algorithm. In the context of a simple example of a Walrasian equilibrium model, we study the iterates of the SLCP algorithm. We show that a particular LCP of this process may have no, one or more complementary solutions. Other LCPs may have both homogeneous and complementary solutions. These features complicate the proof of convergence for the general case. For this particular example, however, we are able to show that Lemke's algorithm computes a solution to an LCP if one exists,and that the iterative process converges globally.     

The natural hedge of a gas-fired power plant

Electricity industries worldwide have been restructured in order to introduce competition. As a result, decision makers are exposed to volatile electricity prices, which are positively correlated with those of natural gas in markets with price-setting gas-fired power plants. Consequently, gas-fired plants are said to enjoy a “natural hedge.” We explore the properties of such a built-in hedge for a gas-fired power plant via a stochastic programming approach, which enables characterisation of uncertainty in both electricity and gas prices in deriving optimal hedging and generation decisions. The producer engages in financial hedging by signing forward contracts at the beginning of the month while anticipating uncertainty in spot prices. Using UK energy price data from 2006 to 2011 and daily aggregated dispatch decisions of a typical gas-fired power plant, we find that such a producer does, in fact, enjoy a natural hedge, i.e., it is better off facing uncertain spot prices rather than locking in its generation cost. However, the natural hedge is not a perfect hedge, i.e., even modest risk aversion makes it optimal to use gas forwards partially. Furthermore, greater operational flexibility enhances this natural hedge as generation decisions provide a countervailing response to uncertainty. Conversely, higher energy-conversion efficiency reduces the natural hedge by decreasing the importance of natural gas price volatility and, thus, its correlation with the electricity price.