Genetic algorithms and Monte Carlo simulation for optimal plant design

We present an approach to the optimal plant design (choice of system layout and components) under conflicting safety and economic constraints, based upon the coupling of a Monte Carlo evaluation of plant operation with a Genetic Algorithms-maximization procedure. The Monte Carlo simulation model provides a flexible tool, which enables one to describe relevant aspects of plant design and operation, such as standby modes and deteriorating repairs, not easily captured by analytical models. The effects of deteriorating repairs are described by means of a modified Brown–Proschan model of imperfect repair which accounts for the possibility of an increased proneness to failure of a component after a repair. The transitions of a component from standby to active, and vice versa, are simulated using a multiplicative correlation model. The genetic algorithms procedure is demanded to optimize a profit function which accounts for the plant safety and economic performance and which is evaluated, for each possible design, by the above Monte Carlo simulation.In order to avoid an overwhelming use of computer time, for each potential solution proposed by the genetic algorithm, we perform only few hundreds Monte Carlo histories and, then, exploit the fact that during the genetic algorithm population evolution, the fit chromosomes appear repeatedly many times, so that the results for the solutions of interest (i.e. the best ones) attain statistical significance.     

Optimizing maintenance and repair policies via a combination of genetic algorithms and Monte Carlo simulation

In this paper we present an optimization approach based on the combination of a Genetic Algorithms maximization procedure with a Monte Carlo simulation. The approach is applied within the context of plant logistic management for what concerns the choice of maintenance and repair strategies. A stochastic model of plant operation is developed from the standpoint of its reliability/availability behavior, i.e. of the failure/repair/maintenance processes of its components. The model is evaluated by Monte Carlo simulation in terms of economic costs and revenues of operation. The flexibility of the Monte Carlo method allows us to include several practical aspects such as stand-by operation modes, deteriorating repairs, aging, sequences of periodic maintenances, number of repair teams available for different kinds of repair interventions (mechanical, electronic, hydraulic, etc.), components priority rankings. A genetic algorithm is then utilized to optimize the components maintenance periods and number of repair teams. The fitness function object of the optimization is a profit function which inherently accounts for the safety and economic performance of the plant and whose value is computed by the above Monte Carlo simulation model. For an efficient combination of Genetic Algorithms and Monte Carlo simulation, only few hundreds Monte Carlo histories are performed for each potential solution proposed by the genetic algorithm. Statistical significance of the results of the solutions of interest (i.e. the best ones) is then attained exploiting the fact that during the population evolution the fit chromosomes appear repeatedly many times. The proposed optimization approach is applied on two case studies of increasing complexity.     

Maintenance and replacement policies under technological obsolescence

The technological obsolescence of a unit is characterized by the existence of challenger units displaying identical functionalities, but with higher performances. This paper aims to define and model in a realistic way, possible maintenance policies of a system including replacement strategies when one type of challenger unit is available. The comparison of these possible strategies is performed based on a Monte Carlo estimation of the costs they incur.     

Variance decomposition-based sensitivity analysis via neural networks

This paper illustrates a method for efficiently performing multiparametric sensitivity analyses of the reliability model of a given system. These analyses are of great importance for the identification of critical components in highly hazardous plants, such as the nuclear or chemical ones, thus providing significant insights for their risk-based design and management. The technique used to quantify the importance of a component parameter with respect to the system model is based on a classical decomposition of the variance. When the model of the system is realistically complicated (e.g. by aging, stand-by, maintenance, etc.), its analytical evaluation soon becomes impractical and one is better off resorting to Monte Carlo simulation techniques which, however, could be computationally burdensome. Therefore, since the variance decomposition method requires a large number of system evaluations, each one to be performed by Monte Carlo, the need arises for possibly substituting the Monte Carlo simulation model with a fast, approximated, algorithm. Here we investigate an approach which makes use of neural networks appropriately trained on the results of a Monte Carlo system reliability/availability evaluation to quickly provide with reasonable approximation, the values of the quantities of interest for the sensitivity analyses. The work was a joint effort between the Department of Nuclear Engineering of the Polytechnic of Milan, Italy, and the Institute for Systems, Informatics and Safety, Nuclear Safety Unit of the Joint Research Centre in Ispra, Italy which sponsored the project.     

A Petri net-based modelling of replacement strategies under technological obsolescence

The technological obsolescence of a unit is characterised by the existence of challenger units displaying identical functionalities, but with higher performances. Though this issue is commonly encountered in practice, it has received little consideration in the literature. Previous exploratory works have treated the problem of replacing old-technology items by new ones, for identical components facing a unique new generation of items. This paper aims to define, in a realistic way, possible replacement policies when several types of challenger units are available and when the performances of these newly available units improve with time.Since no fully generic model can exist in maintenance optimisation, a modular modelling of the problem, allowing easy adaptations to features corresponding to specific applications is highly desirable. This work therefore proposes a modular Petri net model for this problem, underlying a Monte Carlo (MC) estimation of the costs incurred by the different possible replacement strategies under consideration.     

A multiobjective genetic algorithm approach to the optimization of the technical specifications of a nuclear safety system

Systems, structures, and components of Nuclear Power Plants are subject to Technical Specifications (TSs) that establish operational limitations and maintenance and test requirements with the objective of keeping the risk associated to the plant within the limits imposed by the regulatory agencies. Recently, in an effort to improve the competitiveness of nuclear energy in a deregulated market, modifications to maintenance policies and TSs are being considered within a risk-informed viewpoint, which judges the effectiveness of a TS, e.g. a particular maintenance policy, with respect to its implications on the safety and economics of the system operation.In this regard, a recent policy statement of the US Nuclear Regulatory Commission declares appropriate the use of Probabilistic Risk Assessment models to evaluate the effects on the system of a particular TS. These models rely on a set of parameters at the component level (failure rates, repair rates, frequencies of failure on demand, human error rates, inspection durations, and others) whose values are typically affected by uncertainties. Thus, the estimate of the system performance parameters corresponding to a given TS value must be supported by some measure of the associated uncertainty.In this paper we propose an approach, based on the effective coupling of genetic algorithms and Monte Carlo simulation, for the multiobjective optimization of the TSs of nuclear safety systems. The method transparently and explicitly accounts for the uncertainties in the model parameters by attempting to minimize both the expected value of the system unavailability and its associated variance. The costs of the alternative TSs solutions are included as constraints in the optimization. An application to the Reactor Protection Instrumentation System of a Pressurized Water Reactor is demonstrated.     

Availability of K-out-of-N:G systems with non-identical components subject to repair priorities

In this paper, a K-out-of-N:G system with N categories of components is studied. Each component category is characterized by its own failure and repair rates. There are R repair facilities, and repair priorities are specified between the N non-identical components. An algorithm for automatic construction of the system state transition diagram is presented. The stationary availability of each component and that of the system are evaluated by using a multi-dimensional Markov model. We show how this model can be represented as a network of stochastic automata with state-dependent transitions that can be implemented via generalized tensor (or Kronecker) algebra. For the efficiency assessment, an analog Monte Carlo simulation model is developed. Experiments are then conducted and simulation results are compared to those obtained by the proposed approach.     

Reliability and interruption cost prediction using time-dependent failure rates and interruption costs

The main idea presented and discussed in this paper is a model reproducing a time-dependent component failure rate pattern similar to the observed pattern recorded in failure statistics. This pattern includes all types of failures, caused by the weather or by technical and human aspects. Failure causes and mechanisms are not modelled explicitly and the observed pattern is assumed to be representative for the analysis period ahead. Being able to predict and time-tag component failures, the time-dependent variables of load, repair time and customer-specific interruption costs can be adequately combined to calculate annual reliability indices and interruption costs. This fact also permits us to apply an analytical model which will produce expectation values comparable with average values in a Monte Carlo simulation. © 1998 John Wiley & Sons, Ltd.     

Industrial application of RAM modeling: Development and implementation of a RAM simulation model for the Lexan plant at GE Industrial, Plastics

A RAM (reliability, availability and maintenance) model has been built for the GE Industrial, Plastics Lexan^® plant in Bergen op Zoom, The Netherlands. It was based on a Reliability Block Diagram with a Monte Carlo simulation engine. The model has been validated against actual plant data from two different sources, and against local expert opinions, resulting in a satisfactory simulation model. The model was used to assess two key decisions that were (to be) made by GE Industrial, Plastics concerning operation and shutdown policies of the plant. The model results showed that the operation and maintenance could be further improved, and that in doing so the annual production loss could be reduced further.     

Age-related maintenance versus reliability centred maintenance: a case study on aero-engines

Reliability Centred Maintenance (RCM) is a procedure carried out as part of the logistic support analysis (LSA) process and is described in the US Department of Defence Military Standards (Mil Std 2173). RCM allows logisticians the opportunity to determine the best maintenance policy for each component within a system. However, the only data that are available to carryout RCM using Mil Std 2173 are of MTBF. This implies that all the necessary mathematical models need to be based on the exponential distribution. This is a serious drawback to the whole concept of RCM as the exponential distribution cannot be used to model items that fail due to wear, or any other mode that is related to their age. In this paper, a new approach to RCM is proposed using the concepts of soft life and hard life to optimise the total maintenance cost. For simplicity, only one mode of failure is considered for each component. However, the model can be readily applied to multiple failure modes. The proposed model is applied to find the optimal maintenance policies in the case of military aero-engines using Monte Carlo simulation. The case study shows a potential benefit from setting soft lives on relatively cheap components that can cause expensive, unplanned engine rejections.     

Simulation modelling of repairable multi-component deteriorating systems for ‘on condition’ maintenance optimisation

The main purpose of this work is to model continuously monitored deteriorating systems by using Monte Carlo simulation and embedding the resulting model within an ‘on condition’ maintenance optimisation scheme that aims at minimising the expected total system cost over a given mission time. The simulation model is first introduced by considering a non-repairable single component subjected to stochastic degradation. The modelling is then generalised to multi-component repairable systems. To find the optimal degradation thresholds of maintenance intervention, the cost optimisation procedure employed is a simple search in the space of the maintenance thresholds. The sensitivity of the results to some of the driving cost parameters has also been examined.     

Monte Carlo-based assessment of system availability. A case study for cogeneration plants

The complexity of the modern engineering systems besides the need for realistic considerations when modeling their availability and reliability render analytic methods very difficult to be used. Simulation methods, such as the Monte Carlo technique, which allow modeling the behavior of complex systems under realistic time-dependent operational conditions, are suitable tools to approach this problem.The scope of this paper is, in the first place, to show the opportunity for using Monte Carlo simulation as an approach to carry out complex systems' availability/reliability assessment. In the second place, the paper proposes a general approach to complex systems availability/reliability assessment, which integrates the use of continuous time Monte Carlo simulation. Finally, this approach is exemplified and somehow validated by presenting the resolution of a case study consisting of an availability assessment for two alternative configurations of a cogeneration plant.In the case study, a certain random and discrete event will be generated in a computer model in order to create a realistic lifetime scenario of the plant, and results of the simulation of the plant's life cycle will be produced. After that, there is an estimation of the main performance measures by treating results as a series of real experiments and by using statistical inference to reach reasonable confidence intervals. The benefits of the different plant configurations are compared and discussed using the model, according to their fulfillment of the initial availability requirements for the plant.     

Estimating system reliability with fully masked data under Brown-Proschan imperfect repair model

This article presents a statistical procedure for estimating the lifetime distribution of a repairable system based on consecutive inter-failure times of the system. The system under consideration is subject to the Brown-Proschan imperfect repair model. The model postulates that at failure the system is repaired to a condition as good as new with probability p, and is otherwise repaired to its condition just prior to failure. The estimation procedure is developed in a parametric framework for incomplete set of data where the repair modes are not recorded. The expectation-maximization principle is employed to handle the incomplete data problem. Under the assumption that the lifetime distribution belongs to the two-parameter Weibull family, we develop a specific algorithm for finding the maximum likelihood estimates of the reliability parameters, the probability of perfect repair (p), as well as the Weibull shape and scale parameters (α, β) The proposed algorithm is applicable to other parametric lifetime distributions with aging property and explicit form of the survival function, by just modifying the maximization step. We derive some lemmas which are essential to the estimation procedure. The lemmas characterize the dependency among consecutive lifetimes. A Monte Carlo study is also performed to show the consistency and good properties of the estimates. Since useful research is available regarding optimal maintenance policies based on the Brown-Proschan model, the estimation results will provide realistic solutions for maintaining real systems.     

Application of the state transition sampling technique to system reliability evaluation

Monte Carlo simulation is becoming an attractive alternative to analytical approaches for reliability evaluation in large electric power systems. Monte Carlo simulation is generally more flexible than an analytical technique when complex operating conditions and system considerations such as multi-derated states, chronology, reservoir operating rules, bus load uncertainty and weather effects need to be incorporated. Monte Carlo techniques are usually classified as being either a sequential or non-sequential method. The basic non-sequential Monte Carlo approach is known as the state sampling method in which the actual frequency of failure is estimated from the number of failures encountered during the simulation process. The actual frequency of failure can be more accurately obtained by using a sequential approach which models the component up and down cycles together with the system load. This paper presents and illustrates the application of the state transition sampling technique. This method can be used to estimate the actual frequency index without requiring an additional enumeration procedure or sampling the component up and down cycles and storing chronological information on the overall state of the system. In this approach the next system state is obtained by allowing a component to undergo transitions from its present state. The procedure focuses on transitions of the whole system rather than on component states or state durations. This technique is usually much faster than the traditional sequential simulation approach. The state transition sampling technique will be illustrated by application to generating capacity and composite generation and transmission system reliability assessment in a representative electric power system. © 1997 John Wiley & Sons, Ltd.     

A Tolerance Design Method for Electronic Circuits Based on Performance Degradation

Due to the effects of manufacturing tolerances and environmental conditions, component parameters vary and degrade with time. This may cause performance measures of electronic circuits to deviate from design specifications. Therefore, a tolerance design method based on performance degradation is proposed for electronic circuits, so as to improve the robustness of output characteristics. First, sensitive components causing output fluctuation are determined via orthogonal experiment and PSpice simulation. Then, degradation path models are established to describe the degradation process of sensitive components. The predicted values worked out by the degradation path models are substituted into the simulation model for Monte Carlo analysis. Besides, output characteristics and performance reliability are evaluated according to Monte Carlo simulation. Finally, optimum allocation is carried out for component tolerances as per minimum life cycle cost. The proposed method is illustrated by a case study of light‐emitting diode (LED) driver. Copyright © 2013 John Wiley & Sons, Ltd.     

Monte Carlo reliability model for microwave monolithic integrated circuits

A Monte Carlo simulation is reported for analog integrated circuits and is based on the modification of the failure rate of each component due to interaction effects of the failed components. The Monte Carlo technique is the methodology used to treat such circuits, since they are independent of the number of components and the degree of system complexity. The reliability model is applicable over a wide temperature and bias range and may be used to predict reliability of microwave systems. The model is compared with accelerated test results of two analog microwave circuits. Excellent agreement has been obtained for a low noise amplifier as well as for a transimpedence amplifier. Copyright © 2007 John Wiley & Sons, Ltd.     

Availability and cost functions for periodically inspected preventively maintained units

Unavailability and cost rate functions are developed for components whose failures can occur randomly but they are detected only by periodic testing or inspections. If a failure occurs between consecutive inspections, the unit remains failed until the next inspection. Components are renewed by preventive maintenance periodically, or by repair or replacement after a failure, whichever occurs first (age-replacement). The model takes into account finite repair and maintenance durations as well as costs due to testing, repair, maintenance and lost production or accidents. For normally operating units the time-related penalty is loss of production. For standby safety equipment it is the expected cost of an accident that can happen when the component is down due to a dormant failure, repair or maintenance. The objective of maintenance optimization is to minimize the total cost rate by proper selection of two intervals, one for inspections and one for replacements. General conditions and techniques are developed for solving optimal test and maintenance intervals, with and without constraints on the production loss or accident rate. Insights are gained into how the optimal intervals depend on various cost parameters and reliability characteristics.     

Computational strategy for the crash design analysis using an uncertain computational mechanical model

The framework of this paper is the robust crash analysis of a motor vehicle. The crash analysis is carried out with an uncertain computational model for which uncertainties are taken into account with the parametric probabilistic approach and for which the stochastic solver is the Monte Carlo method. During the design process, different configurations of the motor vehicle are analyzed. Usual interpolation methods cannot be used to predict if the current configuration is similar or not to one of the previous configurations already analyzed and for which a complete stochastic computation has been carried out. In this paper, we propose a new indicator that allows to decide if the current configuration is similar to one of the previous analyzed configurations while the Monte Carlo simulation is not finished and therefore, to stop the Monte Carlo simulation before the end of computation.     

Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment

Traditional fault tree (FT) analysis is widely used for reliability and safety assessment of complex and critical engineering systems. The behavior of components of complex systems and their interactions such as sequence- and functional-dependent failures, spares and dynamic redundancy management, and priority of failure events cannot be adequately captured by traditional FTs. Dynamic fault tree (DFT) extend traditional FT by defining additional gates called dynamic gates to model these complex interactions. Markov models are used in solving dynamic gates. However, state space becomes too large for calculation with Markov models when the number of gate inputs increases. In addition, Markov model is applicable for only exponential failure and repair distributions. Modeling test and maintenance information on spare components is also very difficult. To address these difficulties, Monte Carlo simulation-based approach is used in this work to solve dynamic gates. The approach is first applied to a problem available in the literature which is having non-repairable components. The obtained results are in good agreement with those in literature. The approach is later applied to a simplified scheme of electrical power supply system of nuclear power plant (NPP), which is a complex repairable system having tested and maintained spares. The results obtained using this approach are in good agreement with those obtained using analytical approach. In addition to point estimates of reliability measures, failure time, and repair time distributions are also obtained from simulation. Finally a case study on reactor regulation system (RRS) of NPP is carried out to demonstrate the application of simulation-based DFT approach to large-scale problems.     

Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues

Two efficient Monte Carlo models are described, facilitating predictions of complete time-resolved fluorescence spectra from a light-scattering and light-absorbing medium. These are compared with a third, conventional fluorescence Monte Carlo model in terms of accuracy, signal-to-noise statistics, and simulation time. The improved computation efficiency is achieved by means of a convolution technique, justified by the symmetry of the problem. Furthermore, the reciprocity principle for photon paths, employed in one of the accelerated models, is shown to simplify the computations of the distribution of the emitted fluorescence drastically. A so-called white Monte Carlo approach is finally suggested for efficient simulations of one excitation wavelength combined with a wide range of emission wavelengths. The fluorescence is simulated in a purely scattering medium, and the absorption properties are instead taken into account analytically afterward. This approach is applicable to the conventional model as well as to the two accelerated models. Essentially the same absolute values for the fluorescence integrated over the emitting surface and time are obtained for the three models within the accuracy of the simulations. The time-resolved and spatially resolved fluorescence exhibits a slight overestimation at short delay times close to the source corresponding to approximately two grid elements for the accelerated models, as a result of the discretization and the convolution. The improved efficiency is most prominent for the reverse-emission accelerated model, for which the simulation time can be reduced by up to two orders of magnitude.