Framework for Managing Maintenance of Wind Farms Based on a Clustering Approach and Dynamic Opportunistic Maintenance

energies Article Framework for Managing Maintenance of Wind Farms Based on a Clustering Approach and Dynamic Opportunistic Maintenance Juan Izquierdo 1,2,* , Adolfo Crespo Márquez 2, Jone Uribetxebarria 1and Asier Erguido 1,2 1Ikerlan Technology Research Centre, Operations and Maintenance Technologies Area, 20500 Gipuzkoa, Spain; [email protected] (J.U.); [email protected] (A.E.) 2Industrial Organization and Business Management I, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain; [email protected] *Correspondence: jizquier[email protected] Received: 15 April 2019; Accepted: 20 May 2019; Published: 28 May 2019   Abstract: The growth in the wind energy sector is demanding projects in which profitability must be ensured. To fulfil such aim, the levelized cost of energy should be reduced, and this can be done by enhancing the Operational Expenditure through excellence in Operations & Maintenance. There is a considerable amount of work in the literature that deals with several aspects regarding the maintenance of wind farms. Among the related works, several focus on describing the reliability of wind turbines and many set the spotlight on defining the optimal maintenance strategy. It is in this context where the presented work intends to contribute. In the paper a technical framework is proposed that considers the data and information requisites, integrated in a novel approach a clustering-based reliability model with a dynamic opportunistic maintenance policy. The technical framework is validated through a case study in which simulation mechanisms allow the implementation of a multi-objective optimization of the maintenance strategy for the lifecycle of a wind farm. The proposed approach is presented under a comprehensive perspective which enables the discovery an optimal trade-off among competing objectives in the Operations & Maintenance of wind energy projects. Keywords: maintenance management; wind turbines; clustering; reliability; dynamic opportunistic maintenance; simulation 1. Background and Introduction The attention drawn by renewable energy has increased considerably over recent years. This increasing importance has nurtured an important growth, which is especially prominent in the wind energy sector [ 1 ]. Wind energy is one of the main sources of power generation in Europe with a vast majority of installed capacity in the form of onshore Wind Farms (WFs) [ 2 ]. For the profitability of wind energy projects to be ensured, it is essential to reduce the levelized cost of energy (LCoE) to its minimum [ 2 , 3 ]. Aiming at increasing the energy yield of WFs, the LCoE should be reduced, and this can be done by directly addressing the Capital Expenditure (CAPEX) and the Operational Expenditure (OPEX) of the projects [2]. The scope of the research here presented abides in OPEX reduction; more specifically, this paper is intended to reduce the Operations and Maintenance (O&M) costs. How to reduce the O&M costs has become an ongoing challenge for WFs; the figures associated with these costs are notorious [4,5] and may rise by up to 32% and 12–30% for offshore and onshore WFs, respectively [6,7] . However, aiming at lowering the LCoE by reducing O&M costs is a two-fold challenge since it also entails minimizing the lost energy production [ 8 ] for the entire lifecycle, which oscillates around 20 years perspective [9] . According to the International Renewable Agency, the costs associated with O&M Energies 2019,12, 2036; doi:10.3390/en12112036 www.mdpi.com/journal/energies Energies 2019,12, 2036 2 of 17 account for up to one quarter of the proportion of the LCoE, with 80% of this expenses directly attributed to maintenance [10–12]. In view of the maintenance role in the LCoE and thus in the profitability of WFs, it is important to consider models for optimization of O&M plans and decisions [ 2 ]. The evolution of maintenance models and methodologies have kept pace with the constant technological evolution of Wind Turbines (WTs) [ 3 ]. According to [ 3 ], the goal of all the approaches and methodologies is determining the most adequate maintenance plan, the management of the resources, and the aspects related to Reliability, Availability, and Maintainability (RAM) of the WTs. Within such context, the WF operators are bound to develop new techniques and decision-support tools for optimal maintenance strategies, if they strive to maximize the profitability of the investment [8]. Accordingly, maintenance management discipline acquires a highly significant position since it provides a comprehensive perspective for the management of WTs, allowing for optimal maintenance strategies which reduce maintenance costs while maximizing availability [3,5]. The decision-making process in the asset management field has been divided into strategic (long-term), tactic (medium-term), and operational (short-term) to achieve excellence in maintenance [13–15] . It is the purpose of the research in this paper to address the different aspects of the maintenance decision-making process. This is done by answering the research question of whether it is possible to achieve maintenance excellence for the lifecycle of WFs by a maintenance strategy which considers the different behaviors of the WTs and integrated business-related objectives. Aiming at providing an answer for the aforementioned research question, a technical framework for managing maintenance is proposed in the paper. The framework is a comprehensive proposal that considers different aspects regarding the maintenance of a WF. Within the possibilities offered by the current trend for big data, certain key aspects to create a failure database are integrated in the framework, which enables a clustering approach based on the failure behaviors of the different failure modes of each WT. This approach supports an opportunistic maintenance policy with dynamic thresholds that regard not only to the reliability of the assets but also business considerations. Besides, the framework also incorporates the strategic view through a Life-Cycle Cost (LCC) perspective integrated by means of a multi-objective optimization and supported by simulation techniques that provide valuable information to find an attractive trade-off between cost and performance. 1.1. Related Works In the context of maintenance, several studies have proven the utility of reliability approaches to optimize it [ 5 , 16 , 17 ]. If seeking to take forward a reliability study, the information needed as an input to the decision should be at hand, in the right format, and on time [ 18 ]. The idea of a common database in the wind energy sector is not novel. In [ 19 ] the objectives of a RAM database can be seen and in [ 10 ] different sources of WT data are analyzed. The challenges faced when building such database with quality data have been addressed by the integration of data coming from different sources [ 4 , 10 , 19 , 20 ]. Nonetheless, to translate the data into information and exploit its inherent value, it is essential a correct assessment of the failure process and therefore the selection of the proper time-to-failure model, which will enable optimization of the maintenance plan [21]. The reliability study of a WF and the creation of the failure database involves combining data from similar assets, in this case WTs. This combination of data is known as data-pooling, and in [ 21 ], as well as in [ 22 ], several conditions to be met by the equipment subject to data-pooling are stated. Nonetheless, this may lead to combining data from assets with unlike behaviors. The heterogeneity in the failure behavior among WTs may be caused by the presence of different models of WTs, which entail different technical solutions [ 23 ]. Moreover, this multiplicity in the failure frequencies may also be the result of the different operational conditions of the assets [16,17,24,25]. To deal with the diversity in failure behaviors when managing a considerable number of assets, similarity-based approaches have been proposed in recent research works [ 26 – 28 ]. The work in [ 27 ] where a spectral clustering approach is proposed to later address the maintenance optimization Energies 2019,12, 2036 3 of 17 problem to all the assets belonging to the same cluster is especially interesting. Another interesting work is the research in [ 29 ], which provides a very similar approach using a different clustering algorithm. In the wind energy sector, and with the purpose of enhancing maintenance management, approaches based on clustering concepts and algorithms can also be found in the recent literature. A fuzzy clustering approach based on Mahalanobis distance is proposed in [ 30 ] for warnings and failure detection and it is applied to a real WF. Another interesting proposal is the cluster analysis combined with Frequent Pattern Mining presented in [ 31 ] for WT fault detection. In addition, it has also been proposed along with Artificial Neural Networks in [ 32 ] for developing optimal maintenance strategies. The selected approach highly conditions the adequacy of the maintenance strategy [ 33 ]. In the case of WTs, it is important to select one that takes into account the multi-component nature of the turbines [34,35] . The WTs are composed of several subsystems with dependencies among them that can be classified as (i) economic, where the simultaneous performance of maintenance activities implies different economic consequences that implement them individually [ 36 ]; (ii) structural, where maintenance actions on one system may imply maintenance activities on others [ 37 ]; and (iii) stochastic, where the failure hazard of two different systems are not independent [ 38 ]. In this context , opportunistic maintenance policies are the most suitable, and therefore they have been widely researched [33]. Opportunistic maintenance policy makes the most of short-term situations to perform the maintenance of non-failed systems when a failure has already happened in another one, grounding its decision on a threshold regarding a system’s age, reliability or health condition [ 5 ]. Opportunistic maintenance has proven its utility in the sector through several works in the recent literature [ 39 ], and it has been highly related to multi-criteria approaches [ 40 ]. The consideration of opportunistic maintenance under a multi-criteria perspective allows the handling of some main conflicting objectives such as maintenance cost, availability, or manager preferences [ 41 ]. This advantage is especially beneficial in the wind energy sector where it is important to bear in mind the maximization of revenue, power, and reliability, and the minimization of Operations and Maintenance costs [ 42 ]. Some of the latest research in the wind energy sector is in this area. The application of opportunistic maintenance in [ 43 ] takes advantage of low wind-speed periods to perform corrective actions. The research in [ 44 ] provides an opportunistic maintenance policy based on remaining useful life estimation according to condition-monitoring data. The opportunistic maintenance is also proposed with different types of maintenance actions, e.g., the works in [ 34 , 45 – 47 ]. In addition, the authors of [ 48 , 49 ] integrate the opportunistic maintenance policy with multi-objective optimization. 1.2. Overview Given the importance of the reviewed works in the literature of the Wind Energy sector, it is the scope of this paper to provide a managing framework that supports the maintenance management of WF operators. The proposed framework is a cross-functional value proposition that starts by considering the requisites of the failure database to later define a maintenance policy. The opportunistic maintenance policy will be supported by a clustering approach that allows the addressing of different behaviors of the WTs within the same WF. Besides, the framework is considered under a lifecycle perspective integrated through simulation techniques and multi-objective optimization algorithms. The proposed framework is presented in the following Section 2. An initial and brief introduction is first provided along with a representation according to IDEF0 methodology, then every function is explained in detail in each corresponding subsection. The principles of the creation of a failure data base for the study is explained in Section 2.1, the reliability considerations of WTs are presented in Section 2.2, and finally, the opportunistic maintenance policy is explained in Section 2.3. In Section 3 the case study is presented, Section 3.1 describes the development of the case study and the initial assumptions and then Section 3.2 consists of the results obtained in the implementation of the framework. Finally, Section 4summarizes the main conclusions obtained through the research Energies 2019,12, 2036 4 of 17 process, its output represented as the framework, and the application to a real case study in the wind energy sector. 2. Framework and Methods The proposed technical framework, Figure 1, is a comprehensive integration of different technical solutions and methods to ease maintenance management. The framework proposes an initial data treatment, considering different information sources, to create a RAM database that will enable modeling of the reliability of WTs. To undertake the reliability modeling, a clustering algorithm is proposed along with the Kullback–Leibler Divergence measure, which approach addresses the difficulty derived from the heterogeneity in the failure behaviors of the WTs. The reliability models, which describe the failure behaviors within the WF, as well as data from the RAM database and information regarding the cost structure, will serve as input for the methods proposed for defining an optimal maintenance strategy. These methods regard multi-objective optimization algorithms and simulation software under both a lifecycle perspective and governed by the principles of opportunistic maintenance. Figure 1. Technical framework. The technical framework is represented in Figure 1following the IDEF0 methodology [ 50 ], it consists of three functions: RAM database creation, Reliability modeling, and Maintenance strategy definition. The functions are associated with interfaces represented by arrows, which have been referred to as INCOMs [ 51 ]: Inputs (I) of the function box enter from the left, they are transformed into Outputs (O) leaving the box by means of the Mechanisms (M), which enter though the bottom and refer to tools, algorithms, or resources that enable the function; and the Controls (C) enter the box from the top and constrain the function. In particular, Inputs and Outputs of the herein-depicted framework pertain to data and decisions, whereas Mechanisms correspond to specific algorithms, models, and means that allow creation of the RAM database, to model the reliability of WTs and to select the optimal maintenance strategy. The function application is constrained by the Controls, which in this research represents business aspects, data requisites, or maintenance process specificities. By defining the INCOMs in such manner, the technical framework flow can be conceived as a flow in which the output of a function constitutes the input of another until an optimal maintenance strategy is reached. In the successive subsections, each one of the functions with their corresponding INCOMs is thoroughly explained, besides Table 1 gathers all the mathematical symbols utilized in the subsections. Energies 2019,12, 2036 5 of 17 Table 1. Nomenclature. Reliability Modeling βShape parameter of Weibull distribution diDiagonal entries of Degree matrix αScale parameter of Weibull distribution IIdentity matrix γEuler–Mascheroni constant Lsym Graph Laplacian matrix ΓGamma function λ1, ..., λCGraph Laplacian matrix eigenvalues WSimilarity matrix ¯ u1, ..., ¯ uCGraph Laplacian matrix eigenvectors wij Entries of the similarity matrix UMatrix of eigenvectors dKL(µikµj)Kullback–Leibler Divergence among two distributions uic Entries of Umatrix dsym KL Symmetric Kullback–Leibler Divergence TTransformed Umatrix DDegree matrix tic Entries of Tmatrix Maintenance Strategy Definition kaTime value for money constant GPtGenerated power in t qcRestoration factor of CM NT Number of MTs qpr Restoration factor of PM cdisp Cost of dispatching a team ccCorrective cost θt Binary variable for corrective dispatch of MT cpr Preventive cost γtBinary variable for preventive dispatch of MT cna Opportunity cost for not-produced energy cteam Cost of MT cpPenalty cost DRT Dynamic reliability threshold zhikt Binary variable for CM SRT Static reliability threshold yhikjt Binary variable for PM Twt Available working time of MTs mcMaintainability of corrective actions tTime period (days) mpr Maintainability of preventive actions 2.1. RAM Database Creation Information is an essential pillar in every decision-making process and it is highly conditioned by the characteristics of the data it comes from. In the decision-making process, to select the optimal maintenance strategy herein presented, the information utility will be highly conditioned by the quantity and quality of the available data (Constraints C1 and C2). As stated by [ 21 ], many data are recorded for maintenance management purposes rather than reliability; hence, the information content may be misleading without the proper scrutiny and cleaning. In the proposed technical framework, building up the RAM database from the data coming from the SCADA (Supervisory Control And Data Acquisition) and the CMMS (Computerized Maintenance Management Software) systems is considered. • SCADA Data (Input I1): this data is intended to provide feedback of a high-level overview of the performance of the WTs. The data coming from the SCADA system can be categorized into three types of information recorded in time intervals: operational data, availability data, and alarms data. The operational data usually pertains to different variables which characterize the operation of the WTs, e.g., power output, wind speed, temperature of components, or environmental conditions. Availability is a measure of the total time the WT is operational and ready to produce power, independently of external factors such as the weather, the grid state, or maintenance activities. In addition, the data coming from the alarms is sensor information which indicates the state of the WTs and have an associated severity level and usually are responsible for triggering corrective maintenance actions. Energies 2019,12, 2036 6 of 17 • CMMS Data (Input I2): generally the operators of WFs keep track of the maintenance actions performed in the WTs in a variety of forms. This record of maintenance activities is usually known as Work Orders or Maintenance Logs. The work orders may be handwritten in predefined forms, but presently it is more common to find the data as digital work order inputs which have detailed information regarding the materials and resources consumed. To construct a proper RAM database from this data, it is essential to invest a considerable amount of effort in filtering the data, bearing in mind the objective of the data. Therefore, a proper determination of failure modes underpins the data-quality enhancement (Mechanism M1). As the data comes from two different sources, it is essential to match the information contained in both. With that aim , the identification of the patterns that link SCADA information with the maintenance work orders of the CMMS (Mechanism M2) is proposed. Once the data is properly filtered according to the failure mode definition and the coherence among the two sources of data is ensure, it is possible to calculate the Time Between Failures (TBF) for the failure modes of the WTs (Mechanism M3). 2.2. Reliability Modeling Considering that the database contains the failure information (output from previous functional box O1) with certain quality (Constraint C3), it is possible to address the modeling of the reliability following a spectral cluster approach, which is proposed to address the differences in the failure behaviors of the same failure mode in each WT (Constraints C4 and C5). The methodological process followed in this functional unit is represented in Figure 2. Figure 2. Methodological process of the Reliability Modeling functional box. For every failure mode, the process considers fitting a Weibull distribution to the TBF data for each WT (Mechanism M4). With the Weibull distributions of each WT and failure mode, it is the purpose of the algorithms herein presented to cluster them following a similarity-based approach inspired by the work in [26,27]. It is possible to measure how similar two probability distributions are according to the Kullback–Leibler Divergence (Mechanism M5), which can be calculated by Equation (1) in the case of two Weibull distributions being γ≈ 0.5772 the Euler–Mascheroni constant and Γ=R+∞ −∞tz−1e−tdt z ≥0 the Energies 2019,12, 2036 7 of 17 gamma function. Nonetheless the Kullback–Leibler Divergence is a non-symmetric measure which can be converted to symmetric by Equation (2) and therefore the similarity among two Weibull distributions can be described in a generic and symmetric form by Equation (3). Expressing similarities in such way allows the definition of a similarity matrix Win which each element is wij. dKL(µikµj) = log βiαβj j βjαβi i!−(βi−βj) log(αi)−γ βi!+ αi αj!βj Γ βj βi +1!−1 (1) dsym KL =1 2(dKL(µikµj) + dKL(µjkµi)) (2) wij =1 1+dsym KL (3) From the similarity matrix W of size [N , N] it is possible to construct the graph G= (V , E) where each of the nodes vi represents the baseline Weibull distribution of certain failure mode of each turbine, and each edge eij is the similarity between two distributions based on the Kullback–Leibler Divergence. Having defined such a graph, the problem is finding the partition of the graph such that the weights of the edges are small and large for intercluster and intracluster connections, respectively. To fulfil such an aim, the spectral clustering approach is proposed, therefore it is necessary to compute the normalized Graph Laplacian matrix. From W the degree matrix D is calculated, which is a diagonal matrix whose diagonal entries are defined according to Equation (4), and then the normalized Graph Laplacian matrix is calculated as described in Equation (5), where L=D−W and I is the identity matrix of size [N,N]. di= N ∑ j=1 wij,i=1, ..., N(4) Lsym =D−1/2L D−1/2 =I−D−1/2W D−1/2 (5) To extract the information of the graph, the C smallest eigenvalues λ1 , ..., λC are selected along with their corresponding eigenvectors ¯ u1 , ..., ¯ uC , with C the desired number of clusters. The relevant information is considered by transforming matrix W into a reduced matrix U of size [N , C] . The columns of U are the C eigenvectors ¯ u1 , ..., ¯ uC which contain the information regarding the similarities among the i-th baseline distribution and others. It has been proven that it is possible to enhance cluster properties of the data by normalizing the rows of the matrix U and forming matrix T[52], where every element is computed following Equation (6). tic =uic C ∑ c=1 u2 ic!0.5 ,i=1, ..., N,c=1, ..., C(6) Once the matrix T is obtained, a k-medoids algorithm (Mechanism M6) is proposed as an unsupervised clustering to partition the dataset into C clusters, which has proven to perform better for large datasets and to be more stable against possible outliers [53]. By repeating these calculations for every failure mode, it is possible to address the definition of the maintenance strategy of a WF. The effectiveness of the maintenance strategy is expected to increase since the WF is now characterized by different clusters (Output O4) of every failure mode, with their corresponding reliability model (Output O5) which directly tackles the issue of heterogeneity in the failure frequencies. Energies 2019,12, 2036 8 of 17 2.3. Maintenance Strategy Definition The clustering and their corresponding reliability models will support the definition and optimization of the maintenance strategy. In line with the insights provided in the literature review, opportunistic maintenance management is especially suitable for the wind energy sector, since it takes advantage of short-term information and dependencies among the WTs to make optimal maintenance decisions. Accordingly, the framework proposes to implement a reliability-based dynamic opportunistic maintenance policy (C8) summarized in Figure 3, which as well as considering the economic dependencies of WTs, enables taking advantage of more favorable weather conditions to enhance WF production outcome. To fulfil this aim, based on the concept of dynamic reliability thresholds—acting as decision variables of the maintenance model—maintenance activities are fostered at low wind-speed periods, and hindered at high wind-speed periods, thus limiting the production losses caused by maintenance downtimes. While the interested reader may address the dynamic opportunistic maintenance policy in [ 5 ], the building blocks of the multi-level maintenance optimization model developed for this research are summarized as follows (the definition of the intermediate variables of the model is in Table 2): •Problem definition. The wind farm (WF) to be considered in the case study involves the maintenance of H wind turbines (WTs) and their systems (i = 1,2,...,N), connected in series. Each of the systems might fail in k different failure modes (FMs), which are classified according to their consequences and require different corrective maintenance (CM) activities (k = 1,2,...,K). Likewise, WF managers may decide to maintain the WTs’ system before failure occurrence, where per-FM different preventive maintenance (PM) levels can be performed (j = 1,2,...,J). This classification depends on the restoration factor ( q ). If the PM activity restores the system to a state in which its operating and reliability behavior is as good as new, i.e., replacement activities, it is considered to be perfect maintenance ( j=J). On the contrary, when PM activity partially restores the condition of the system to an operational condition worse than the new one but better than just before the performance of maintenance, it is considered to be imperfect maintenance (see [ 54 ] for further information), with j=1the most imperfect repair. •Objective functions. The main objectives pursued by the maintenance strategy are defined. They should be aligned with the objectives of the business (C9) and should consider the whole lifecycle of the assets. In the case of WFs, special emphasis is placed on optimizing the OPEX (considering time value of money by means of ka ) and production losses entailed by the maintenance strategy (See Equations (12) and (13)). The core parts of these indicators are: – Corrective and preventive cost (I3), subjected to the restoration effect (q) of the maintenance activity carried out, as in [ 34 , 49 ]. They consider the materials and tools needed to perform them ( cc ik , cpr ik ), as well as the opportunity cost that they entail, represented by the amount of power that could not be produced because of performing such maintenance activities (cna) . Likewise, in the case of CM, failures usually avoid distribution of the committed energy, entailing a penalty cost (cp). zhikt·hcc ik ·(qc ik)2+mc ik ·GPt·(cna +cp)i(7) yhikjt·cpr ikj·qpr ikj2+mpr ikj ·GPt·cna(8) – Maintenance resources cost (I3). They consider the number of maintenance teams hired (NT) and the cost entailed by dispatching them to the WFs cdisp either preventively (γt) or correctively (θt). (γt+θt)·cdisp (9) NT ·cteam (10) Energies 2019,12, 2036 9 of 17 – Production losses. They consider the maintainability (O3) of PM and CM activities ( mc ik , mpr ik ) as well as the power that would have been generated (GPt). GPt·mc ik ·zhikt +mpr ikj ·yhikjt(11) •Maintenance strategy. An imperfect maintenance strategy where decisions are triggered by dynamic reliability thresholds is defined (see Equation (14)): 1. DRTikt , if the reliability of any of the FMs (O5) is below this threshold, a maintenance team is compulsorily dispatched to the WFs to perform PM. 2. SRTikjt , once a maintenance team is dispatched to the WF, either preventively or correctively, and according to the reliability of the specific FM (O5), it determines whether PM level j should be performed during period tfor preventing FM kof system i. •Capacity constrains (C8). Maintenance teams’ availability and their working time Twt is defined (see Equation (15)). •Maintenance process constraints (C7). Only one maintenance task per WT and time period is allowed (see Equation (16)). Once the building block of the model has been defined, the mathematical formulation of the model is expressed in the following equations regarding the objective functions (OF), the constraints of the model, and the intermediate binary variables (in Table 2). OFOpex =min "∑ t (γt+θt)·cdisp +∑ h ∑ i ∑ k ∑ t zhikt hcc ik (qc ik)2+mc ik ·GPt(cna +cp)i+ ∑ h ∑ i ∑ k ∑ j ∑ t yhikjt cpr ikj qpr ikj2+mpr ikj ·GPt·cna+∑ t NT ·cteam#·(1+ka)−t (12) OFLP =min ∑ t GPt· ∑ h ∑ i ∑ k mc ik ·zhikt +∑ h ∑ i ∑ k ∑ j mpr ikj ·yhikjt!(13) S.T. 0≤DRTikt ≤SRTik1t≤... ≤SRTikjt ≤ ≤... ≤SRTikJt ≤1ieI,keK,jeJ;teT(14) ∑ i ∑ k ∑ j mpr ikj ·yikjt +∑ i ∑ k mc ik ·zikt ≤NT ·Twt ∀teT(15) ∑ j yhikjt +zhikt ≤1heH,ieI,keK,teT(16) zhikt,yhikjte{0, 1}heH,ieI,keK,teT,∀j=1, 2 Table 2. Intermediate binary variables used in the model. zhikt =     1i f CM k is per f ormed in system i o f WT h in period t 0otherwise θt=     1i f a MT is correctively dispatched to WF in period t 0otherwise yhikjt =     1i f PM j is per f ormed in FM k o f system i o f WT h in period t 0otherwise γt=     1i f a MT is preventively dispatched to WF in period t 0otherwise Energies 2019,12, 2036 16 of 17 11. IRENA, I.R.E.A. Renewable Power Generation Costs in 2012: An Overview; International Renewable Energy Agency (IRENA): Abu Dhabi, UAE, 2012. 12. PowerTech eV, V. Levelised Cost of Electricity (LCOE 2015); Verfugbar unter; VGB PowerTech e.V.: Essen, Germany, 2015. 13. Jardine, A.K.; Tsang, A.H. Maintenance, Replacement, and Reliability: Theory And Applications, 1st ed.; CRC Press: Boca Raton, FL, USA, 2005; doi:10.1201/9781420044614. 14. Bertling, L.; Wennerhag, P. Wind Turbine Operation and Maintenance; Technical Report; Elforsk: Stockholm, Sweden, 2012. 15. Shafiee, M. Maintenance logistics organization for offshore wind energy: Current progress and future perspectives. Renew. Energy 2015,77, 182–193. [CrossRef] 16. Izquierdo, J.; Márquez, A.C.; Uribetxebarria, J. Dynamic artificial neural network-based reliability considering operational context of assets. Reliabil. Eng. Syst. Saf. 2019,188, 483–493. [CrossRef] 17. Izquierdo, J.; Crespo, A.; Uribetxebarria, J.; Erguido, A. Assessing the impact of operational context variables on rolling stock reliability. A real case study. In Safety and Reliability—Safe Societies in a Changing World; CRC Press, Ed.; Taylor & Francis Group: London, UK; Trondheim, Norway, 2017; Proceedings of ESREL 2018, pp. 571–578. 18. Rausand, M.; Höyland, A. System Reliability Theory: Models, Statistical Methods, and Applications; John Wiley & Sons Hoboken, NJ, USA, 2004; Volume 396. 19. Hameed, Z.; Vatn, J.; Heggset, J. Challenges in the reliability and maintainability data collection for offshore wind turbines. Renew. Energy 2011,36, 2154–2165. [CrossRef] 20. Nguyen, T.H.; Prinz, A.; Friisø, T.; Nossum, R.; Tyapin, I. A framework for data integration of offshore wind farms. Renew. Energy 2013,60, 150–161. [CrossRef] 21. Louit, D.; Pascual, R.; Jardine, A. A practical procedure for the selection of time-to-failure models based on the assessment of trends in maintenance data. Reliabil. Eng. Syst. Saf. 2009,94, 1618–1628. [CrossRef] 22. Stamatelatos, M.; Veseley, W.; Dugan, J.; Fragola, J.; Minarik, J.; Rialsback, J. Fault Tree Handbook with Aerospace Applications; NASA Office of Safety and Mission Assurance: Washington, DC, USA, 2002. 23. Li, H.; Yang, C.; Zhao, B.; Wang, H.; Chen, Z. Aggregated models and transient performances of a mixed wind farm with different wind turbine generator systems. Electric Power Syst. Res. 2012 ,92, 1–10. [CrossRef] 24. Cao, L.; Qian, Z.; Zareipour, H.; Wood, D.; Mollasalehi, E.; Tian, S.; Pei, Y. Prediction of Remaining Useful Life of Wind Turbine Bearings under Non-Stationary Operating Conditions. Energies 2018,11, 3318. [CrossRef] 25. Zimroz, R.; Bartelmus, W.; Barszcz, T.; Urbanek, J. Diagnostics of bearings in presence of strong operating conditions non-stationarity—A procedure of load-dependent features processing with application to wind turbine bearings. Mech. Syst. Signal Process. 2014,46, 16–27. [CrossRef] 26. Cannarile, F.; Compare, M.; Di Maio, F.; Zio, E. Handling reliability big data: A similarity-based approach for clustering a large fleet of assets. In Safety and Reliability of Complex Engineered Systems-Proceedings of the 25th European Safety and Reliability Conference; ESREL: Zurich,Switzerland, 2015; Volume 2015, pp. 891–896. 27. Cannarile, F.; Compare, M.; Di Maio, F.; Zio, E. A clustering approach for mining reliability big data for asset management. Proc. Inst. Mech. Eng. Part O J. Risk Reliabil. 2018,232, 140–150. [CrossRef] 28. Baraldi, P.; Di Maio, F.; Rigamonti, M.; Zio, E.; Redouane, S. Unsupervised clustering of vibration signals for identifying anomalous conditions in a nuclear turbine. J. Intell. Fuzzy Syst. 2015,28, 1723–1731. [CrossRef] 29. Jiang, B.; Pei, J.; Tao, Y.; Lin, X. Clustering uncertain data based on probability distribution similarity. IEEE Trans. Knowl. Data Eng. 2013,25, 751–763. [CrossRef] 30. Ruiz de la Hermosa, R. Wind farm monitoring using Mahalanobis distance and fuzzy clustering. Renew. Energy 2018,123, 526–540. [CrossRef] 31. Elijorde, F.; Kim, S.; Lee, J. A Wind Turbine Fault Detection Approach Based on Cluster Analysis and Frequent Pattern Mining. KSII Trans. Internet Inf. Syst. 2014,8, 664–677. [CrossRef] 32. Hameed, Z.; Wang, K. Development of optimal maintenance strategies for offshore wind turbine by using artificial neural network. Wind Eng. 2012,36, 353–364. [CrossRef] 33. Wang, H.; Pham, H. Optimal Preparedness Maintenance of Multi-unit Systems with Imperfect Maintenance and Economic Dependence. In Springer Series in Reliability Engineering; Springer Science + Business Media, Berlin, Germany: 2006; pp. 135–150. [CrossRef] 34. Ding, F.; Tian, Z. Opportunistic maintenance optimization for wind turbine systems considering imperfect maintenance actions. Int. J. Reliabil. Q. Saf. Eng. 2011,18, 463–481. [CrossRef] Energies 2019,12, 2036 17 of 17 35. Nicolai, R.; Dekker, R. A review of multi-component maintenance models. In Proceedings of the European Safety and Reliability Conference, Stavanger, Norway, 25–27 June 2007; pp. 289–296. 36. Dekker, R.; Wildeman, R.E.; van der Duyn Schouten, F.A. A review of multi-component maintenance models with economic dependence. Math. Methods Oper. Res. 1997,45, 411–435. [CrossRef] 37. Sasieni, M.W. A Markov Chain Process in Industrial Replacement. OR 1956,7, 148. [CrossRef] 38. Nakagawa, T.; Murthy, D. Optimal replacement policies for a two-unit system with failure interactions. RAIRO-Oper. Res. 1993,27, 427–438. [CrossRef] 39. De Almeida, A.T.; Ferreira, R.J.P.; Cavalcante, C.A.V. A review of the use of multicriteria and multi-objective models in maintenance and reliability. IMA J. Manag. Math. 2015,26, 249–271. [CrossRef] 40. Cavalcante, C.A.; Lopes, R.S. Multi-criteria model to support the definition of opportunistic maintenance policy: A study in a cogeneration system. Energy 2015,80, 32–40. [CrossRef] 41. Cavalcante, C.; Lopes, R. Opportunistic Maintenance Policy for a System with Hidden Failures: A Multicriteria Approach Applied to an Emergency Diesel Generator. Math. Probl. Eng. 2014 ,2014, 157282. [CrossRef] 42. Iqbal, M.; Azam, M.; Naeem, M.; Khwaja, A.; Anpalagan, A. Optimization classification, algorithms and tools for renewable energy: A review. Renew. Sustain. Energy Rev. 2014,39, 640–654. [CrossRef] 43. Besnard, F.; Patrikssont, M.; Strombergt, A.B.; Wojciechowskit, A.; Bertling, L. An optimization framework for opportunistic maintenance of offshore wind power system. In Proceedings of the 2009 IEEE Bucharest PowerTech, Bucharest, Romania, 28 June–2 July 2009; [CrossRef] 44. Tian, Z.; Jin, T.; Wu, B.; Ding, F. Condition based maintenance optimization for wind power generation systems under continuous monitoring. Renew. Energy 2011,36, 1502–1509. [CrossRef] 45. Ding, F.; Tian, Z. Opportunistic maintenance for wind farms considering multi-level imperfect maintenance thresholds. Renew. Energy 2012,45, 175–182. [CrossRef] 46. Sarker, B.R.; Faiz, T.I. Minimizing maintenance cost for offshore wind turbines following multi-level opportunistic preventive strategy. Renew. Energy 2016,85, 104–113. [CrossRef] 47. Zhu, W.; Fouladirad, M.; Bérenguer, C. A multi-level maintenance policy for a multi-component and multifailure mode system with two independent failure modes. Reliab. Eng. Syst. Saf. 2016 ,153, 50–63. [CrossRef] 48. Atashgar, K.; Abdollahzadeh, H. Reliability optimization of wind farms considering redundancy and opportunistic maintenance strategy. Energy Convers. Manag. 2016,112, 445–458. [CrossRef] 49. Abdollahzadeh, H.; Atashgar, K.; Abbasi, M. Multi-objective opportunistic maintenance optimization of a wind farm considering limited number of maintenance groups. Renew. Energy 2016 ,88, 247–261. [CrossRef] 50. IEEE, C.S. IEEE Standard for Functional Modeling Language—Syntax and Semantics for IDEF0; IEEE Std 1320.1-1998; IEEE Computer Society: Washington DC, USA, 1998; p. i, [CrossRef] 51. Kusiak, A.; Larson, T.N.; Wang, J.R. Reengineering of design and manufacturing processes. Comput. Ind. Eng. 1994,26, 521–536. [CrossRef] 52. Von Luxburg, U. A tutorial on spectral clustering. Stat. Comput. 2007,17, 395–416. [CrossRef] 53. Velmurugan, T.; Santhanam, T. Computational complexity between K-means and K-medoids clustering algorithms for normal and uniform distributions of data points. J. Comput. Sci. 2010,6, 363. [CrossRef] 54. Pham, H.; Wang, H. Imperfect maintenance. Eur. J. Oper. Res. 1996,94, 425–438. [CrossRef] 55. Zille, V.; Bérenguer, C.; Grall, A.; Despujols, A. Modelling multicomponent systems to quantify reliability centred maintenance strategies. Proc. Inst. Mech. Eng. Part O J. Risk Reliabil. 2011,225, 141–160. [CrossRef] 56. Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002,6, 182–197. [CrossRef] 57. Salazar, D.; Rocco, C.M.; Galván, B.J. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms. Reliabil. Eng. Syst. Saf. 2006,91, 1057–1070. [CrossRef] 58. Martin-Tretton, M.; Reha, M.; Drunsic, M.; Keim, M. Data collection for current us wind energy projects: Component costs, financing, operations, and maintenance. Contract 2012,303, 275–300. [CrossRef] c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).