Sofía Carlos

Constrained optimization of test intervals using a steady-state genetic algorithm

Abstract There is a growing interest from both the regulatory authorities and the nuclear industry to stimulate the use of Probabilistic Risk Analysis (PRA) for risk-informed applications at Nuclear Power Plants (NPPs). Nowadays, special attention is being paid on analyzing plant-specific changes to Test Intervals (TIs) within the Technical Specifications (TSs) of NPPs and it seems to be a consensus on the need of making these requirements more risk-effective and less costly. Resource versus risk-control effectiveness principles formally enters in optimization problems. This paper presents an approach for using the PRA models in conducting the constrained optimization of TIs based on a steady-state genetic algorithm (SSGA) where the cost or the burden is to be minimized while the risk or performance is constrained to be at a given level, or vice versa. The paper encompasses first with the problem formulation, where the objective function and constraints that apply in the constrained optimization of TIs based on risk and cost models at system level are derived. Next, the foundation of the optimizer is given, which is derived by customizing a SSGA in order to allow optimizing TIs under constraints. Also, a case study is performed using this approach, which shows the benefits of adopting both PRA models and genetic algorithms, in particular for the constrained optimization of TIs, although it is also expected a great benefit of using this approach to solve other engineering optimization problems. However, care must be taken in using genetic algorithms in constrained optimization problems as it is concluded in this paper.

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

Abstract 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.

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.

Addressing imperfect maintenance modelling uncertainty in unavailability and cost based optimization

Optimization of testing and maintenance activities performed in the different systems of a complex industrial plant is of great interest as the plant availability and economy strongly depend on the maintenance activities planned. Traditionally, two types of models, i.e. deterministic and probabilistic, have been considered to simulate the impact of testing and maintenance activities on equipment unavailability and the cost involved. Both models present uncertainties that are often categorized as either aleatory or epistemic uncertainties. The second group applies when there is limited knowledge on the proper model to represent a problem, and/or the values associated to the model parameters, so the results of the calculation performed with them incorporate uncertainty. This paper addresses the problem of testing and maintenance optimization based on unavailability and cost criteria and considering epistemic uncertainty in the imperfect maintenance modelling. It is framed as a multiple criteria decision making problem where unavailability and cost act as uncertain and conflicting decision criteria. A tolerance interval based approach is used to address uncertainty with regard to effectiveness parameter and imperfect maintenance model embedded within a multiple-objective genetic algorithm. A case of application for a stand-by safety related system of a nuclear power plant is presented. The results obtained in this application show the importance of considering uncertainties in the modelling of imperfect maintenance, as the optimal solutions found are associated with a large uncertainty that influences the final decision making depending on, for example, if the decision maker is risk averse or risk neutral.

Simultaneous and multi-criteria optimization of TS requirements and maintenance at NPPs

Abstract One of the main concerns of the nuclear industry is to improve the availability of safety-related systems at nuclear power plants (NPPs) to achieve high safety levels. The development of efficient testing and maintenance has been traditionally one of the different ways to guarantee high levels of systems availability, which are implemented at NPP through technical specification and maintenance requirements (TS&M). On the other hand, there is a widely recognized interest in using the probabilistic risk analysis (PRA) for risk-informed applications aimed to emphasize both effective risk control and effective resource expenditures at NPPs. TS&M-related parameters in a plant are associated with controlling risk or with satisfying requirements, and are candidate to be evaluated for their resource effectiveness in risk-informed applications. The resource versus risk-control effectiveness principles formally enter in optimization problems where the cost or the burden for the plant staff is to be minimized while the risk or the availability of the safety equipment is constrained to be at a given level, and vice versa. Optimization of TS&M has been found interesting from the very beginning. However, the resolution of such a kind of optimization problem has been limited to focus on only 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 growing interest in the last years to focus on the simultaneous and multi-criteria optimization of TS&M. In the simultaneous optimization of TS&M-related parameters based on risk (or unavailability) and cost, like in many other engineering optimization problems, one normally faces multi-modal and non-linear objective functions and a variety of both linear and non-linear constraints. Genetic algorithms (GAs) have proved their capability to solve these kinds of problems, although GAs are essentially unconstrained optimization techniques that require adaptation for the intended constrained optimization, where TS&M-related parameters act as the decision variables. This paper encompasses, in Section 2 , the problem formulation where the objective function is derived and constraints that apply in the simultaneous and multi-criteria optimization of TS&M activities based on risk and cost functions at system level. Fundamentals of a steady-state GA (SSGA) as an optimization method is given in Section 3 , which satisfies the above requirements, paying special attention to its use in constrained optimization problems. A simple case of application is provided in Section 4 , focussing on TS&M-related parameters optimization for a stand-by safety-related system, which demonstrates how the SSGA-based optimization approach works at the system level, providing practical and complete alternatives beyond only mathematical solutions to a particular parameter. Finally, Section 5 presents our conclusions.

Use of multiple objective evolutionary algorithms in optimizing surveillance requirements

This paper presents the development and application of a double-loop Multiple Objective Evolutionary Algorithm that uses a Multiple Objective Genetic Algorithm to perform the simultaneous optimization of periodic Test Intervals (TI) and Test Planning (TP). It takes into account the time-dependent effect of TP performed on stand-by safety-related equipment. TI and TP are part of the Surveillance Requirements within Technical Specifications at Nuclear Power Plants. It addresses the problem of multi-objective optimization in the space of dependable variables, i.e. TI and TP, using a novel flexible structure of the optimization algorithm. Lessons learnt from the cases of application of the methodology to optimize TI and TP for the High-Pressure Injection System are given. The results show that the double-loop Multiple Objective Evolutionary Algorithm is able to find the Pareto set of solutions that represents a surface of non-dominated solutions that satisfy all the constraints imposed on the objective functions and decision variables. Decision makers can adopt then the best solution found depending on their particular preference, e.g. minimum cost, minimum unavailability.

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.

Maintenance modeling and optimization integrating human and material resources

Maintenance planning is a subject of concern to many industrial sectors as plant safety and business depend on it. Traditionally, the maintenance planning is formulated in terms of a multi-objective optimization (MOP) problem where reliability, availability, maintainability and cost (RAM+C) act as decision criteria and maintenance strategies (i.e. maintenance tasks intervals) act as the only decision variables. However the appropriate development of each maintenance strategy depends not only on the maintenance intervals but also on the resources (human and material) available to implement such strategies. Thus, the effect of the necessary resources on RAM+C needs to be modeled and accounted for in formulating the MOP affecting the set of objectives and constraints. In this paper RAM+C models to explicitly address the effect of human resources and material resources (spare parts) on RAM+C criteria are proposed. This extended model allows accounting for explicitly how the above decision criteria depends on the basic model parameters representing the type of strategies, maintenance intervals, durations, human resources and material resources. Finally, an application case is performed to optimize the maintenance plan of a motor-driven pump equipment considering as decision variables maintenance and test intervals and human and material resources.

Comparing effectiveness and efficiency in technical specifications and maintenance optimization

Abstract 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.

Genetic algorithm-based optimization of testing and maintenance under uncertain unavailability and cost estimation: A survey of strategies for harmonizing evolution and accuracy

Abstract This paper presents the results of a survey to show the applicability of an approach based on a combination of distribution-free tolerance interval and genetic algorithms for testing and maintenance optimization of safety-related systems based on unavailability and cost estimation acting as uncertain decision criteria. Several strategies have been checked using a combination of Monte Carlo (simulation)––genetic algorithm (search-evolution). Tolerance intervals for the unavailability and cost estimation are obtained to be used by the genetic algorithms. Both single- and multiple-objective genetic algorithms are used. In general, it is shown that the approach is a robust, fast and powerful tool that performs very favorably in the face of noise in the output (i.e. uncertainty) and it is able to find the optimum over a complicated, high-dimensional nonlinear space in a tiny fraction of the time required for enumeration of the decision space. This approach reduces the computational effort by means of providing appropriate balance between accuracy of simulation and evolution; however, negative effects are also shown when a not well-balanced accuracy–evolution couple is used, which can be avoided or mitigated with the use of a single-objective genetic algorithm or the use of a multiple-objective genetic algorithm with additional statistical information.