A tolerance interval based approach to address uncertainty for RAMS+C optimization

This paper proposes an approach based on tolerance intervals to address uncertainty for RAMS+C informed optimization of design and maintenance of safety-related systems using a combined Monte Carlo (MC) (simulation) and Genetic Algorithm (search) procedure. This approach is intended to keep control of the uncertainty effects on the decision criteria and reduce the computational effort in simulating RAMS+C using a MC procedure with simple random sampling. It exploits the advantages of order statistics to provide distribution free tolerance intervals for the RAMS+C estimation, which is based on the minimum number of runs necessary to guarantee a probability content or coverage with a confidence level. This approach has been implemented into a customization of the Multi-Objective Genetic Algorithm introduced by the authors in a previous work. For validation purposes, a simple application example regarding the testing and maintenance optimization of the High-Pressure Injection System of a nuclear power plant is also provided, which considers the effect of the epistemic uncertainty associated with the equipment reliability characteristics on the optimal testing and maintenance policy. This example proves that the new approach can provide a robust, fast and powerful tool for RAMS+C informed multi-objective optimization of testing and maintenance under uncertainty in objective and constraints. It is shown that the approach proposed performs very favourably in the face of noise in the output (i.e. uncertainty) and it is able to find the optimum over a complicated, high-dimensional non-linear space in a tiny fraction of the time required for enumeration of the decision space. In addition, a sensitivity study on the number of generations versus the number of trials (i.e. simulation runs) shows that overall computational resources must be assigned preferably to evolving a larger number of generations instead of being more precise in the quantification of the RAMS+C attributes for a candidate solution, i.e. evolution is preferred to accuracy.     

A model for preventive maintenance planning by genetic algorithms based in cost and reliability

This work has two important goals. The first one is to present a novel methodology for preventive maintenance policy evaluation based upon a cost-reliability model, which allows the use of flexible intervals between maintenance interventions. Such innovative features represents an advantage over the traditional methodologies as it allows a continuous fitting of the schedules in order to better deal with the components failure rates. The second goal is to automatically optimize the preventive maintenance policies, considering the proposed methodology for systems evaluation.Due to the great amount of parameters to be analyzed and their strong and non-linear interdependencies, the search for the optimum combination of these parameters is a very hard task when dealing with optimizations schedules. For these reasons, genetic algorithms (GA) may be an appropriate optimization technique to be used. The GA will search for the optimum maintenance policy considering several relevant features such as: (i) the probability of needing a repair (corrective maintenance), (ii) the cost of such repair, (iii) typical outage times, (iv) preventive maintenance costs, (v) the impact of the maintenance in the systems reliability as a whole, (vi) probability of imperfect maintenance, etc. In order to evaluate the proposed methodology, the High Pressure Injection System (HPIS) of a typical 4-loop PWR was used as a case study. The results obtained by this methodology outline its good performance, allowing specific analysis on the weighting factors of the objective function.     

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.     

RAMS+C informed decision-making with application to multi-objective optimization of technical specifications and maintenance using genetic algorithms

The role of technical specifications and maintenance (TSM) activities at nuclear power plants (NPP) aims to increase reliability, availability and maintainability (RAM) of Safety-Related Equipment, which, in turn, must yield to an improved level of plant safety. However, more resources (e.g. costs, task force, etc.) have to be assigned in above areas to achieve better scores in reliability, availability, maintainability and safety (RAMS). Current situation at NPP shows different programs implemented at the plant that aim to the improvement of particular TSM-related parameters where the decision-making process is based on the assessment of the impact of the change proposed on a subgroup of RAMS+C attributes.This paper briefly reviews the role of TSM and two main groups of improvement programs at NPP, which suggest the convenience of considering the approach proposed in this paper for the Integrated Multi-Criteria Decision-Making on changes to TSM-related parameters based on RAMS+C criteria as a whole, as it can be seem as a decision-making process more consistent with the role and synergic effects of TSM and the objectives and goals of current improvement programs at NPP. The case of application to the Emergency Diesel Generator system demonstrates the viability and significance of the proposed approach for the Multi-objective Optimization of TSM-related parameters using a Genetic Algorithm.     

Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions

This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.     

Modelling and optimizing sequential imperfect preventive maintenance

This paper deals with the problem of scheduling imperfect preventive maintenance (PM) of some equipment. It uses a model due to Kijima in which each application of PM reduces the equipment's effective age (but without making it as good as new). The approach presented here involves minimizing a performance function which allows for the costs of minimal repair and eventual system replacement as well as for the costs of PM during the equipment's operating lifetime. The paper describes a numerical investigation into the sensitivity of optimum schedules to different aspects of an age-reduction model (including the situation when parts of a system are non-maintainable—i.e., unaffected by PM).     

Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes

In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements and that systems or objects are, therefore, brought back into an as good as new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption cannot be made. The quintessential problem with imperfect maintenance is how to model it. In many cases it is very difficult to assess by how much a partial repair will improve the condition of a system or object and it is equally difficult to assess how such a repair influences the rate of deterioration. In this paper, a superposition of renewal process is used to model the effect of imperfect maintenance. It constitutes a different modelling approach than the more common use of a virtual age process.     

A hybrid genetic based optimization procedure for aircraft conceptual analysis

The problem to define a methodology for the analysis of aircraft performances, in the phase of conceptual design, is addressed. The proposed approach is based on a numerical optimization procedure where a scalar objective function, the take-off weight, is minimized. Deterministic and stochastic approaches as well as hybridizations between these two search techniques are considered. More precisely, we consider two-stage strategies where the optimum localization is performed by a genetic algorithm, while a gradient-based method is used to terminate the optimization process. Also, another type of hybridization strategy is investigated where a partially converged gradient-based method is incorporated in the genetic algorithm as a new operator. A detailed discussion is made and various different solutions are critically compared. The proposed methodology is consistent and capable of giving fundamental information to the designer for further investigating towards the directions identified by the procedure. A basic example is described, and the use of the methodology to establish the effects of different geometrical and technological parameters is discussed.     

Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

A new modeling approach to the safety evaluation of N-modular redundant computer systems in presence of imperfect maintenance

A large number of safety-critical control systems are based on N-modular redundant architectures, using majority voters on the outputs of independent computation units. In order to assess the compliance of these architectures with international safety standards, the frequency of hazardous failures must be analyzed by developing and solving proper formal models. Furthermore, the impact of maintenance faults has to be considered, since imperfect maintenance may degrade the safety integrity level of the system. In this paper, we present both a failure model for voting architectures based on Bayesian networks and a maintenance model based on continuous time Markov chains, and we propose to combine them according to a compositional multiformalism modeling approach in order to analyze the impact of imperfect maintenance on the system safety. We also show how the proposed approach promotes the reuse and the interchange of models as well the interchange of solving tools.     

Multi-objective optimization of generalized reliability design problems using feature models—A concept for early design stages

Reliability optimization problems such as the redundancy allocation problem (RAP) have been of considerable interest in the past. However, due to the restrictions of the design space formulation, they may not be applicable in all practical design problems. A method with high modelling freedom for rapid design screening is desirable, especially in early design stages. This work presents a novel approach to reliability optimization. Feature modelling, a specification method originating from software engineering, is applied for the fast specification and enumeration of complex design spaces. It is shown how feature models can not only describe arbitrary RAPs but also much more complex design problems. The design screening is accomplished by a multi-objective evolutionary algorithm for probabilistic objectives. Comparing averages or medians may hide the true characteristics of this distributions. Therefore the algorithm uses solely the probability of a system dominating another to achieve the Pareto optimal set. We illustrate the approach by specifying a RAP and a more complex design space and screening them with the evolutionary algorithm.     

Alternatives and challenges in optimizing industrial safety using genetic algorithms

Safety (S) improvement of industrial installations leans on the optimal allocation of designs that use more reliable equipment and testing and maintenance activities to assure a high level of reliability, availability and maintainability (RAM) for their safety-related systems. However, this also requires assigning a certain amount of resources (C) that are usually limited. Therefore, the decision-maker in this context faces in general a multiple-objective optimization problem (MOP) based on RAMS+C criteria where the parameters of design, testing and maintenance act as decision variables. Solutions to the MOP can be obtained by solving the problem directly, or by transforming it into several single-objective problems. A general framework for such MOP based on RAMS+C criteria is proposed in this paper. Then, problem formulation and fundamentals of two major groups of resolution alternatives are presented. Next, both alternatives are implemented in this paper using genetic algorithms (GAs), named single-objective GA and multi-objective GA, respectively, which are then used in the case of application to solve the problem of testing and maintenance optimization based on unavailability and cost criteria. The results show the capabilities and limitations of both approaches. Based on them, future challenges are identified in this field and guidelines provided for further research.     

Comparing effectiveness and efficiency in technical specifications and maintenance optimization

Optimization of technical specification requirements and maintenance (TS&M) has been found interesting from the very beginning at Nuclear Power Plants (NPPs). However, the resolution of such a kind of optimization problem has been limited often to focus only on individual TS&M-related parameters (STI, AOT, PM frequency, etc.) and/or adopting an individual optimization criterion (availability, costs, plant risks, etc.). Nevertheless, a number of reasons exist (e.g. interaction, similar scope, etc.) that justify the interest to focus on the coordinated optimization of all of the relevant TS&M-related parameters based on multiple criteria.The purpose of this paper is on signifying benefits and improvement areas in performing the coordinated optimization of TS&M through reviewing the effectiveness and efficiency of common strategies for optimizing TS&M at system level. A case of application is provided for a stand-by safety-related system to demonstrate the basic procedure and to extract a number of conclusions and recommendations from the results achieved. Thus, it is concluded that the optimized values depend on the particular TS&M-related parameters being involved and the solutions with the largest benefit (minimum risk or minimum cost) are achieved when considering the simultaneous optimization of all of them, although increased computational resources are also required. Consequently, it is necessary to analyze not only the value reached but also the performance of the optimization procedure through effectiveness and efficiency measures which lead to recommendations on potential improvement areas.     

Optimal condition based maintenance with imperfect information and the proportional hazards model

Condition based maintenance (CBM) is based on collecting observations over time, in order to assess equipment's state, to prevent its failure and to determine the optimal maintenance strategies. In this paper, we derive an optimal CBM replacement policy when the state of equipment is unknown but can be estimated based on observed condition. We use a proportional hazards model (PHM) to represent the system's degradation. Since equipment's state is unknown, the optimization of the optimal maintenance policy is formulated as a partially observed Markov decision process (POMDP), and the problem is solved using dynamic programming. Practical advantages of combining the PHM with the POMDP are shown.     

Multi-objective design optimization of electrostatically actuated microbeam resonators with and without parameter uncertainty

Electrostatically actuated microbeam resonators are widely used components in microelectromechanical systems for sensing and signal filtering purposes. Due to the uncertainties resulting from manufacturing processes, material properties, and modeling assumptions, microbeam resonators may exhibit significant variations in their performance compared to nominal designs. There has been limited research on the performance prediction and the design optimization of such microsystems while accounting for relevant uncertainties. In this study, such uncertainties are considered in terms of the variability of parameters that define the dimensions, the material properties, and the operating conditions of the device. In addition, uncertainties with respect to a two-dimensional model of a microbeam resonator subject to electrostatic actuation are considered. A finite element model consisting of both the microbeam and the substrate is developed. The actuation forces are predicted by a reduced order electrostatic model, which accounts for the electromechanical interaction. A computationally efficient procedure is presented for simulating the steady-state dynamic response under electrostatic forces. The probabilistic performance of the microresonator is investigated using Monte Carlo simulation. A genetic algorithm is used to optimize the stochastic behavior of the microbeam resonator. The design is posed as combinatorial multi-objective optimization problem. Two design criteria describing the filter performance in terms of the shape of the frequency–response curve are simultaneously considered. The numerical results demonstrate the effectiveness of this procedure for the multi-objective optimization design of microbeam resonators and the importance of considering parameter uncertainty in the design of these devices.     

Fuzzy regression approach to process modelling and optimization of epoxy dispensing

Epoxy dispensing is one of the popular processes to perform microchip encapsulation for chip-on-board (COB) packages. However, determination of proper process parameters setting for optimal quality of the encapsulation is difficult due to the complex behaviour of the encapsulant during dispensing and the uncertainties caused by fuzziness of epoxy dispensing systems. In conventional regression models, deviations between the observed values and the estimated values are supposed to be in probability distribution. However, when data is irregular, the obtained regression model has an unnaturally wide possibility range. In fact, these deviations in some processes such as epoxy dispensing can be regarded as system fuzziness that can be dealt with properly using fuzzy regression method. In this paper, a fuzzy regression approach with fuzzy intervals to process modelling of epoxy dispensing for microchip encapsulation is described. Two fuzzy regression models relating three process parameters and two quality characteristics respectively for epoxy dispensing were developed. They were then introduced to formulate a fuzzy multi-objective optimization problem. A fuzzy linear programming technique was employed to formulate the optimization model. By solving the model, an optimal setting of process parameters can be obtained. Validation experiments were conducted to evaluate the effectiveness of the proposed approach to process modelling and optimization of epoxy dispensing for microchip encapsulation.     

Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation

Efficient maintenance policies are of fundamental importance in system engineering because of their fallbacks into the safety and economics of plants operation. When the condition of a system, such as its degradation level, can be continuously monitored, a Condition-Based Maintenance (CBM) policy can be implemented, according to which the decision of maintaining the system is taken dynamically on the basis of the observed condition of the system.In this paper, we consider a continuously monitored multi-component system and use a Genetic Algorithm (GA) for determining the optimal degradation level beyond which preventive maintenance has to be performed. The problem is framed as a multi-objective search aiming at simultaneously optimizing two typical objectives of interest, profit and availability. For a closer adherence to reality, the predictive model describing the evolution of the degrading system is based on the use of Monte Carlo (MC) simulation. More precisely, the flexibility offered by the simulation scheme is exploited to model the dynamics of a stress-dependent degradation process in load-sharing components and to account for limitations in the number of maintenance technicians available. The coupled (GA[plus ]MC) approach is rendered particularly efficient by the use of the ‘drop-by-drop’ technique, previously introduced by some of the authors, which allows to effectively drive the combinatorial search towards the most promising solutions.     

Reliability and cost optimization of electronic devices considering the component failure rate uncertainty

The objective of this paper is to present an efficient computational methodology to obtain the optimal system structure of electronic devices by using either a single or a multiobjective optimization approach, while considering the constraints on reliability and cost. The component failure rate uncertainty is taken under consideration and it is modeled with two alternative probability distribution functions. The Latin hypercube sampling method is used to simulate the probability distributions. An optimization approach was developed using the simulated annealing algorithm because of its flexibility to be applied in various system types with several constraints and its efficiency in computational time. This optimization approach can handle efficiently either the single or the multiobjective optimization modeling of the system design. The developed methodology was applied to a power electronic device and the results were compared with the results of the complete enumeration of the solution space. The stochastic nature of the best solutions for the single objective optimization modeling of the system design was sampled extensively and the robustness of the developed optimization approach was demonstrated.     

多目标进化算法的一种基于生成树的分布性维护方法

针对多目标进化算法的种群维护和运行效率相矛盾的问题,提出了一种基于生成树的分布性维护方法,即对整个种群构造一棵生成树,定义一种密度估计指标--树聚集距离,并结合树中的最短树枝和个体度数对种群进行维护.由于树聚集距离和度数具有动态性,每移出一个个体,种群中与之相连个体的信息都会发生相应的变化,因而可即时反映出种群的分布情况.与三个著名的算法NSGA-Ⅱ、SPEA2和C-NSGA-Ⅱ的比较实验表明,该方法能在得到良好分布性解集的同时,能以较快的速度对种群进行维护,具有较好的时间效率.     

Integrated optimization of structure and control for piezoelectric intelligent trusses with uncertain placement of actuators and sensors

The finite element modeling of truss structures with piezoelectric members is presented. Based on the approach of independent modal space control, the controllability and observability indices of the system related to the positions of actuators/sensors are demonstrated. Consequently, the effective damping response time is evaluated. The object of the optimization model is to minimize a specified performance index of the intelligent truss subjected to constraints on the natural frequency and the amplitude of displacement response as well as the applied voltages under a given disturbance. Structural sizing variables, control parameters and actuator/sensor placements are treated as the independent design variables. Coding, the calculation of fitness and the optimization procedure of Genetic Algorithms are discussed so as to solve the integrated optimization with two different types of design variable space: discrete and continuous. Numerical examples are presented to show the effectiveness and usefulness of integrated optimization of structure and control for piezoelectric intelligent trusses.The authors would like to thank for the support by Natural Science Foundation of China under grant 10072050 and the Doctorate Creation Foundation of Northwestern Polytechnical University under grant 200236.