Use of dynamic Bayesian networks for life extension assessment of ageing systems
Introduction
Most technical systems are subject to ageing and deterioration, which implies that their reliability and availability degrade in time. When ageing systems reach their design lifetime, important decisions must be made if the aim is to keep them in operation for some additional years. This is the case for many oil and gas (O&G) facilities on the Norwegian Continental Shelf, which were built in the 70s and 80s with a design lifetime typically of 20–30 years, and are expected to remain in operation for another 10 or 20 years. Extending the lifetime of these facilities requires identifying and selecting optimal decision alternatives which allow operating the various systems and components beyond their design lifetime in a safe and economic manner. Typical decision alternatives may include replacement, overhauling, modification, or keeping the system in operation without any changes (denominated use-up in this article). In addition, other measures can be taken in order to decrease the probability of failure of the systems during the life extension period, such as performing more maintenance and inspections. Extending the system lifetime may be a challenging task, and the decision making process should be supported by quantitative analyses that are capable of predicting the future performance of the system, taking into account relevant factors influencing the system behavior and the uncertainty in the results.
A quantitative analysis should consist of a model that considers reliability, maintenance and safety aspects, as well as associated costs and uncertainties. Such a model requires much data, which may not be available. Another challenge may be the limited knowledge and information available about the physical degradation mechanisms and technical condition of the ageing system. In addition, few systems have been operated beyond their design lifetime in O&G facilities yet, which means that there is limited or no recorded data and experience. All this may lead to making several assumptions in the model and analyses, increasing the uncertainty in the results.
Given the large uncertainties that most likely will be involved in quantitative analyses for life extension assessments, Bayesian networks (BN) are a possible approach for modeling and predicting the system performance. BN are powerful tools for reasoning under uncertainty, using well-established theoretical foundations of probability calculus as the base for performing inference and handling uncertainty [1]. BNs can be extended to dynamic Bayesian networks (DBN) by introducing temporal dependencies in the network, which allows modeling the dynamic behavior of a system. Several BN and DBN models have been proposed for assessing reliability and maintenance of technical systems [2], [3], [4], [5]. They have also been applied to assess and predict the performance of degrading repairable systems, for instance Weber et al. [6] proposed a method for developing DBNs and predicting the reliability of a degrading system; Nielsen and Sørensen [7] presented a DBN for modeling deterioration processes and assist in decision making for maintenance planning of offshore wind turbines; Straub [8] used a DBN for assessing the condition and reliability of structural elements subject to deterioration; Hu et al. [9] presented a DBN for safety prognosis and assessment of fault propagation paths in complex degrading systems; Neil and Marquez [10] proposed a hybrid BN for modeling renewable systems subject to repairs and delays, and assessing the system availability; and Ferreiro et al. [11] presented a BN for prognosis and decision making on aeroplane maintenance actions. However, most of the literature applying BNs to degrading repairable systems focuses on failure diagnostics, prognostics, and optimization of intervals for inspections and condition based maintenance, which do not capture many of the factors that are important for assessing the life extension of ageing systems (e.g., operational costs, availability and safety throughout the life extension period).
The main objective of this article is to propose a DBN model for decision support regarding life extension of ageing repairable systems. The DBN is used to compute relevant variables for the decision making process, for instance number of failures, unavailability, and costs (i.e. investment, maintenance and down time costs), in addition to the probability of failure on demand (PFD) for safety systems. Furthermore, the model includes variables which describe the technical condition of the system at the time of analysis, and its evolution throughout the additional years of operation depending on the decision alternatives and maintenance actions performed. The model provides relevant information of the system not only at present time, but also during its operation throughout the life extension period. The model can be updated with data observed during operation (e.g., number of failures, number of maintenance actions, and costs derived from maintenance), hence improving the prediction of the system performance and reducing the uncertainty of the results. This allows the re-evaluation and optimization of planned maintenance actions (e.g., functional tests, overhauls and renewals) during operation.
In this article, imperfect corrective maintenance (CM) refers to maintenance actions performed after the occurrence of a failure to bring the equipment back to operation and partially restore its condition. Imperfect condition-based maintenance (CBM) comprises a combination of condition monitoring, inspection, analysis, and the ensuing maintenance actions which are performed based on the condition of the equipment, and partially restore its condition. The equipment׳s condition is revealed by condition monitoring and/or inspections. Functional tests (FT) detect whether an equipment in stand-by (e.g., safety system) is functioning or failed, but cannot reveal the equipment׳s condition (i.e., cannot measure the degradation). CBM actions only refer to the maintenance actions that are performed at a specific time in order to fix some degradation in the equipment before it leads to a failure. Condition monitoring, inspections and FTs are considered different actions than CBM actions, although they are used to assess the equipment׳s condition and support the need for performing a CBM action. Furthermore, imperfect time-based maintenance (TBM) refers to maintenance actions carried out with an established time schedule and which restore to some extent the equipment׳s condition.
The structure of the article is as follows: Section 2 gives a brief introduction to DBNs and their application for modeling ageing repairable systems. Section 3 describes the proposed DBN model for decision making support. Section 4 presents a real case study where the life extension of a firewater pump system is assessed, and conclusions are given in Section 5.
Section snippets
Dynamic Bayesian networks
BNs are probabilistic models based on directed acyclic graphs which are used for representing and reasoning with uncertain knowledge [12]. A BN is composed of a set of nodes representing the system variables (which can be discrete or continuous), and a set of directed arcs representing the dependencies or influence among the variables. In discrete BNs, variables are defined over a set of mutually exclusive states, and a probability is associated to each state. The quantification of
Model
The proposed approach for decision support consists of building and applying a DBN for assessing different decision alternatives for the life extension, based on the predicted performance of the system. There are three approaches normally used to construct DBNs and define the CPTs: based on underlying parametric models, using expert knowledge, and building the model with empirical data. For the life extension of O&G facilities, the available data from the system is limited in most cases, and
Application of the model to a firewater pump system
The proposed DBN model has been applied to a real system installed in an O&G facility in order to assess life extension possibilities. The system under study consists of two firewater pumps driven by diesel engines and working in parallel. Since this is a safety system operated on demand, functional tests are performed to verify whether the components are functioning or failed. A constraint in the analysis is that the system has to comply with the regulations regarding SIL. For firewater pump
Conclusions
This article presents a DBN model for assessing the life extension of ageing repairable systems. This model is a decision support tool that can be used for (i) selecting optimal alternatives for extending the lifetime of the system; (ii) identifying and minimizing the factors that have a negative impact on the system performance; and (iii) reassessing and adjusting the selected alternatives based on new information gathered during the operation of the system in the life extension period. The
Acknowledgments
The authors are grateful to Gassco and MARINTEK for the cooperation and support facilitated through the Gassco research programme on ageing management.
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