Maintenance models applied to wind turbines. A comprehensive overview

energies Review Maintenance Models Applied to Wind Turbines. A Comprehensive Overview Yuri Merizalde 1, Luis Hernández-Callejo 2,* , Oscar Duque-Perez 3and Víctor Alonso-Gómez 4 1 Faculty of Chemical Engineering, University of Guayaquil, Clemente Ballen 2709 and Ismael Perez Pazmiño, Guayaquil 593, Ecuador; [email protected] 2Department of Agricultural Engineering and Forestry, University of Valladolid (UVA), Campus Universitario Duques de Soria, 42004 Soria, Spain 3Department of Electrical Engineering, University of Valladolid (UVA), Escuela de Ingenierías Industriales, Paseo del Cauce 59, 47011 Valladolid, Spain; oscar[email protected] 4Department of Phisical, University of Valladolid (UVA), Campus Universitario Duques de Soria, 42004 Soria, Spain; victor[email protected] *Correspondence: [email protected]; Tel.: +34-975-129-213 Received: 3 December 2018; Accepted: 8 January 2019; Published: 11 January 2019   Abstract: Wind power generation has been the fastest-growing energy alternative in recent years, however, it still has to compete with cheaper fossil energy sources. This is one of the motivations to constantly improve the efficiency of wind turbines and develop new Operation and Maintenance (O&M) methodologies. The decisions regarding O&M are based on different types of models, which cover a wide range of scenarios and variables and share the same goal, which is to minimize the Cost of Energy (COE) and maximize the profitability of a wind farm (WF). In this context, this review aims to identify and classify, from a comprehensive perspective, the different types of models used at the strategic, tactical, and operational decision levels of wind turbine maintenance, emphasizing mathematical models (MatMs). The investigation allows the conclusion that even though the evolution of the models and methodologies is ongoing, decision making in all the areas of the wind industry is currently based on artificial intelligence and machine learning models. Keywords: strategy and maintenance tactics; maintenance methodologies; mathematical models; failures; prediction 1. Introduction After the investment in the feasibility study and the acquisition and installation of a wind turbine (WT), the main costs incurred during the useful life of a wind power generation project are those corresponding to operation and maintenance (O&M). For this reason, since the United States installed the first wind turbine (between 1887 and 1888) and the feasibility of using wind to generate electrical energy was demonstrated [ 1 ], questions related to O&M arose. The O&M strategy has a direct impact on the cost of energy (COE) produced and on a wind energy project’s profitability [2]. There is a large number of studies that try to optimize the O&M of wind farms (WFs) by applying different approaches and methodologies, but in all cases, the goal is to optimize the cost by determining the exact moment at which maintenance has to be performed; the time interval between each intervention, repair and replacement of a part, maintenance tasks and inspections; the monitoring system; the human resources; the organizational structure; and the redesign of the equipment to improve reliability, maintainability and capability. All of the above are within an environment that includes care for the environment, occupational health, elimination of occupational risks, inventory Energies 2019,12, 225; doi:10.3390/en12020225 www.mdpi.com/journal/energies Energies 2019,12, 225 2 of 41 reduction, failure prognosis and assurance of the continuity of the services without interruption and with high quality standards such that all the people and institutions involved benefit [3]. Jardine and Tsang [ 4 ] defined maintenance as “all activities aimed at keeping an item in, or restoring it to, the physical state considered necessary for the fulfillment of its production function,” for which, according to [ 5 ], there is a need for technical skills, engineering knowledge, methodologies and scientific theories. The comprehensive management of the physical assets of a company is known as physical asset management (PAM) and includes purchases according to technical specifications, planning, operation, performance evaluation, improvements and disposal. When it is decided to perform maintenance, it is necessary to make decisions at various hierarchical levels that go from the management to the operational positions. Hilber [ 6 ] classifies decision making into maintenance strategies, maintenance support organization and maintenance planning. Bertling and Wennerhag [ 7 ] divided the decision-making process regarding maintenance into strategy (long-term decisions), which involves design, location, installation dimensions, maintenance strategy and outsourcing services; tactics (medium-term), which involve the management of inventories (supplies) and organizational structure of the maintenance area; and operations (day-to-day), which involve maintenance scheduling and measurement of its performance. According to the author, the model is “strategic/tactical/operational.” Shafiee [ 8 ] claims that the strategic decisions regarding maintenance include selection of the total replacement and economic life models, consideration of the technological factors and forecasting of resources to ensure competitiveness. The tactical decisions (medium-term maintenance) involve the selection of a correct maintenance policy, such as corrective, via inspection, and based on age or condition. The operational (short-term) level includes maintenance planning and scheduling. To achieve excellence in maintenance, Jardine and Tsang [4] divided decision making into the following: •Strategy: Resource requirements, planning, planning horizon, objectives. • Tactics: Planning; scheduling; inventory management; statistical processing of the information; legal aspects; compliance with the standards; status of the work orders, process and control the processes; selection of the methodology to monitor, detect, diagnose and repair failures; financial indicators; safety; production; etc. • Continuous improvement: This is done through Total Productive Maintenance (TPM) and Reliability-Centered Maintenance (RCM). Despite the classification observed thus far, in some cases, it is not easy to distinguish to which level a decision belongs. It could be that what is strategic for one company corresponds to the tactical part of another company. Within an organization, the tactics of one level usually become the strategy adopted by a lower level. According to [ 9 ], in the field of maintenance management, a strategy refers to the tactical alternatives for managing specific physical assets, whereas decisions regarding applying preventive maintenance (PM) or predictive maintenance considered as maintenance strategies have to be considered as tactical. Regardless of the level at which they are made, the decisions are based on management and mathematical models. Based on the principle that a model is the representation of a system, the models can be physical, schematic, verbal and mathematical. The evolution of the methodologies applied to maintenance have paralleled the constant technological advance of wind turbines, owing to the development and application of a variety of models that try to cover multiple complex and uncertain scenarios that can be presented at any decision level [10,11]. Despite the very large number of publications on models applied to the maintenance of wind turbines, these studies usually cover very specific subjects. For this reason, this review aims to provide a comprehensive view regarding the types of predominant maintenance models in the wind industry, at the different levels of decision making (strategic, tactical and operational), with the goal of determining the appropriate time at which maintenance has to be performed, but without intervening before it is Energies 2019,12, 225 3 of 41 necessary; reducing interruptions; increasing the useful life of the equipment; improving reliability; and minimizing the costs. Due to the large number of models included, their description, analysis and comparison are not within our goals. The interested reader can subsequently deepen their knowledge about some particular model, in addition to identifying the lack of application of certain models, which could lead to new investigations. To achieve the goal of this work, a description and classification of the most important models used at the strategic and tactical levels is performed in Section 2, starting from the general and conceptual to the area specifically related to the wind industry. Section 3addresses the models applied at the operational level, emphasizing MatMs. The fourth section can be considered as a follow-up regarding the models applied at the operational level for the detection, diagnose and prognosis of wind turbine failures. The fifth section includes the conclusions and recommendations. 2. Types of Models Applied at the Strategic and Tactical Levels All decisions (including tactical and operational) involve a strategy that describes the direction to follow to achieve an objective. An example would be the decision of applying maintenance with the intention of reducing costs, increasing reliability, improving safety and respecting the environment. The means and methods to achieve this are the tactics. These strategic decisions have to ensure adequate supply chain management (SCM), performance management, work management and information systems to finally choose the best maintenance methodology, such as RCM, Failure Mode and Effects Analysis (FMEA), Failure Mode, Effects and Criticality Analysis (FMECA) and Preventive Maintenance Optimization (PREMO). Leadership in designing, applying and maintaining an adequate maintenance strategy is the basis for success [12,13]. Generally, the company that installs the WF provides the maintenance during the first years of operation. After this initial step, one of the most important strategic decisions of the owners consists of operating the WFs themselves, whereas the maintenance activities are delegated to another company. Other important strategic decisions include parts inventories, overall repowering to increase the useful life, or replacement, whether it be parts, such as the gearbox, or even the entire WT [14]. The companies that specialize in maintenance will adopt their own tactical and operational strategies to ensure the compliance of the signed contract, which is usually evaluated according to the WF availability. The applied strategies are not very different from the ones used by the industry in general, but the remoteness of the location, difficulty of access, operating height of the wind turbines, particular features of these types of machines, sudden variations of the environmental conditions and loads to which they are exposed cause maintenance in the wind industry to have characteristics that makes it unique, for which there is currently a wide range of models being applied to the O&M of WTs [15] (see Figure 1). The main maintenance strategies are TPM, which is a methodology of continuous improvement based on what has been done by people [ 16 – 20 ]; Total Quality Maintenance (TQMain), whose philosophy is the continuous improvement of processes via empowerment of workers [ 3 ]; Lean Six Sigma (LSS) [ 21 ]; 5S [ 22 ]; E-maintenance [ 23 ]; and lean maintenance, which focuses on reducing the waste in any process, integrating the supply chain and increasing the value for the organization and the customers [ 24 , 25 ]. All these strategies are set within the Japanese philosophy of Total Quality Management (TQM) and are the basis of the tactical and operational strategy of the maintenance system [26,27]. One of the main objectives of any maintenance program is to obtain the highest reliability and availability at the lowest possible cost. With this goal, a variety of methodologies and MatMs have been developed, which have given rise to what is known as RCM. According to [ 28 ], “Reliabilitycentered maintenance is a systematic consideration of system functions, the way functions can fail, and a priority-based consideration of safety and economics that identifies applicable and effective PM tasks”. Energies 2019,12, 225 4 of 41 Energies 2019, 12 FOR PEER REVIEW 4 Figure 1. Comprehensive vision of strategic and tactical models for the maintenance of wind farms (WFs). “Source [5,12–14,16,17], own elaboration”. Figure 1. Comprehensive vision of strategic and tactical models for the maintenance of wind farms (WFs). “Source [5,12–14,16,17], own elaboration”. Energies 2019,12, 225 5 of 41 The goal is to extend the time between failure occurrences, reduce the amount of maintenance, decrease downtime and increase the useful life of the equipment through a methodology that, according to [29], is based on seven questions: • What are the functions and associated desired standards of performance of the asset in its present operating context? •In what manners can it fail to fulfill its functions? •What causes each functional failure? •What happens when each failure occurs? •In what manner does each failure matter? •What should be done to predict or prevent each failure? •What should be done if a suitable proactive task cannot be found? According to the literature, RCM is the predominant methodology in the maintenance of wind turbines [ 30 ]. For this, it is supported by models such as FMEA, FMECA and Root Cause Failure Analysis (RCFA), which in turn include Hazard and Operability Studies (HAZOPs), critical task analysis, quantified risk analysis, the structured what-if technique, fault tree analysis, event tree analysis, cause-effect logic diagrams, the accident evolution and barrier technique, work safety analysis, change analysis and human error probability studies, each with its own subcategories (see Figure 2). FMEA is a methodology in which the components of a system are examined in detail through a systematic process to identify the parts that can fail, the manners in which these failures occur, their origin, their degree of importance and the effects on the equipment performance such that based on this analysis, preventive measures can be adopted before the failure occurs, minimizing the risk and its possible negative effects. In the FMEA methodology, the probability of occurrence of failure, its detection and the magnitude of the effects are weighted according to certain scales and multiplied to obtain the Risk Priority Number (RPN). Given that the failures related to equipment can occur at different stages, there are specific FMEA methodologies for each of them, such as design (DFMEA), manufacture (PFMEA), operation, control and personnel training [ 31 – 34 ]. Another methodology used for determining the causes, consequences and importance of an equipment or system failure is Criticality Analysis (CA). CA uses qualitative and quantitative techniques, such as risk assessment techniques and the Analytical Hierarchy Process (AHP). The level of criticality and importance associated with the failure will be a function of the effects’ magnitude, [ 16 , 35 ]. When FMEA is combined with CA, FMECA is obtained [36–41]. Through the “Relex Reliability Studio 2007 Version 2” software package for FMECA [ 31 ] determines the causes and the manner in which the main failures of a 2-MW turbine with a doubly fed induction generator (DFIG) occur. In [ 36 ], a software package developed in Java Expert Shell System (JESS) is proposed, where the information obtained by FMECA is represented by ontology modeling to obtain an intelligent diagnostic method capable of providing the wind turbine maintenance personnel with the locations and causes of failures. Ref. [ 37 ] uses the operation data of a wind turbine to determine, via FMECA and CA, the main causes of overheating of the gearbox, generator and converter. RCFA includes several methodologies (see Figure 2) that are very similar to each other, even making them seem redundant, since, when analyzed together, they constitute a means of globally considering all the factors that can contribute to the failures of an equipment or system. These techniques usually consist of checklists, which, arranged in increasing order of complexity, include simple lists, lists with cross-referencing systems, simple trees without fault tree logic and trees incorporating fault tree logic [16]. Energies 2019,12, 225 6 of 41 Energies 2019, 12 FOR PEER REVIEW 6 Figure 2. Root Cause Failure Analysis (RCFA) Methods. “Source [16], own elaboration.”. For identification of the possible failures in a wind turbine, García-Marquez et al. [42] apply a qualitative analysis via Fault Tree Analysis (FTA), along with the Binary Decision Diagram (BDD) method to optimize the FTA quantitative analysis and facilitate the identification of the critical components under different conditions. Fault Tree (FT) consists of top events, basic events and intermediate events connected by AND/OR logic gates. A probability of 0.01 is assigned to each event, and the classification of the basic events with respect to their contribution to the probability of a top event is performed based on the importance measures index, obtained using the heuristic models of Birnbaum, criticality, structural and Fussell Vesely. The number of combinations, events or cut-sets for the type of turbine analyzed was 173. Chou and Tu [43] apply several RCFA methods to determine the causes of the collapse of a wind turbine tower 62 m in height. According to the literature, of the types of maintenances available to meet the RCM objectives, condition based maintenance (CBM) [15,44], along with a Condition Monitoring System (CMS), both online and offline, for the acquisition and treatment of several types of signals from different types of sensors installed throughout the entire wind turbine, is the standard in the wind industry. The use of supervisory control and data acquisition (SCADA) systems for holistic management of the monitoring systems should also be included [45–47]. The database obtained through the CMS is applied for designing proposals at all decision levels (strategic, tactical and operational). Most of the management models discussed thus far, as well as the MatMs that are considered hereinafter, are based on the CMS. It is not surprising that when addressing the maintenance of WTs, CBM and CMS are among the subjects involving the largest number of publications. The final goal of the models discussed thus far (see Figure 1) is to maximize reliability and minimize maintenance costs. With this goal, there are a variety of maintenance models (MMs), which can be classified in several manners. In [16], the authors group the main MMs as total replacement models (constant-interval replacement and age-based replacement), partial replacement models (minimal repairs and normal repairs), replacement models with imperfect maintenance, shock-based replacement models and inspection models. In [48], the authors classify the MMs into inspection, minimal repair, impact and semi-Markov. Given that one of the main objectives is to optimize the main variables through which the maintenance efficiency is measured, one of the manners in which these models can be classified is according to the optimization strategy applied, as shown in Figure 3. From a comprehensive point of view, the models shown in Figure 3 can be considered as a continuation of Figure 1. Figure 2. Root Cause Failure Analysis (RCFA) Methods. “Source [16], own elaboration.”. For identification of the possible failures in a wind turbine, García-Marquez et al. [ 42 ] apply a qualitative analysis via Fault Tree Analysis (FTA), along with the Binary Decision Diagram (BDD) method to optimize the FTA quantitative analysis and facilitate the identification of the critical components under different conditions. Fault Tree (FT) consists of top events, basic events and intermediate events connected by AND/OR logic gates. A probability of 0.01 is assigned to each event, and the classification of the basic events with respect to their contribution to the probability of a top event is performed based on the importance measures index, obtained using the heuristic models of Birnbaum, criticality, structural and Fussell Vesely. The number of combinations, events or cut-sets for the type of turbine analyzed was 173. Chou and Tu [ 43 ] apply several RCFA methods to determine the causes of the collapse of a wind turbine tower 62 m in height. According to the literature, of the types of maintenances available to meet the RCM objectives, condition based maintenance (CBM) [15,44], along with a Condition Monitoring System (CMS), both online and offline, for the acquisition and treatment of several types of signals from different types of sensors installed throughout the entire wind turbine, is the standard in the wind industry. The use of supervisory control and data acquisition (SCADA) systems for holistic management of the monitoring systems should also be included [ 45 – 47 ]. The database obtained through the CMS is applied for designing proposals at all decision levels (strategic, tactical and operational). Most of the management models discussed thus far, as well as the MatMs that are considered hereinafter, are based on the CMS. It is not surprising that when addressing the maintenance of WTs, CBM and CMS are among the subjects involving the largest number of publications. The final goal of the models discussed thus far (see Figure 1) is to maximize reliability and minimize maintenance costs. With this goal, there are a variety of maintenance models (MMs), which can be classified in several manners. In [ 16 ], the authors group the main MMs as total replacement models (constant-interval replacement and age-based replacement), partial replacement models (minimal repairs and normal repairs), replacement models with imperfect maintenance, shock-based replacement models and inspection models. In [ 48 ], the authors classify the MMs into inspection, minimal repair, impact and semi-Markov. Given that one of the main objectives is to optimize the main variables through which the maintenance efficiency is measured, one of the manners in which these models can be classified is according to the optimization strategy applied, as shown in Figure 3. From a comprehensive point of view, the models shown in Figure 3can be considered as a continuation of Figure 1. Energies 2019,12, 225 7 of 41 Energies 2019, 12 FOR PEER REVIEW 7 Figure 3. Maintenance Models according to the optimization method. “Source [48–53], own elaboration.”. Because there is more than one manner of organizing the models, Figure 4 shows an alternative classification that expands and complements Figure 3. In every maintenance strategy and tactic, logistics (inventories and transport) play an important role; therefore, Figure 5 shows a classification of the methodologies used for optimizing inventory management. Regardless of the classification, these models do not usually work in isolation, and in most cases, the proposals are a combination of periodic maintenance (operation time and units produced), CBM (magnitude of the signals obtained by the CMS), inspections and maintenance due to an unexpected failure. In all these cases, there is the alternative of maintaining or replacing the component, but when the failure is unexpected, the strategy is to perform a minimal repair to avoid downtime and to apply, at the end of the next time interval (τ), the maintenance strategy scheduled under normal conditions for each η × τ [54]. When a repair is performed, it is assumed that the component will go back to the initial state that it had prior to the failure; however, there are also MatMs that consider the cases in which the repair or inspection is imperfect [55]. Figure 3. Maintenance Models according to the optimization method. “Source [ 48 – 53 ], own elaboration.”. Because there is more than one manner of organizing the models, Figure 4shows an alternative classification that expands and complements Figure 3. In every maintenance strategy and tactic, logistics (inventories and transport) play an important role; therefore, Figure 5shows a classification of the methodologies used for optimizing inventory management. Regardless of the classification, these models do not usually work in isolation, and in most cases, the proposals are a combination of periodic maintenance (operation time and units produced), CBM (magnitude of the signals obtained by the CMS), inspections and maintenance due to an unexpected failure. In all these cases, there is the alternative of maintaining or replacing the component, but when the failure is unexpected, the strategy is to perform a minimal repair to avoid downtime and to apply, at the end of the next time interval ( τ ), the maintenance strategy scheduled under normal conditions for each η×τ [ 54 ]. When a repair is performed, it is assumed that the component will go back to the initial state that it had prior to the failure; however, there are also MatMs that consider the cases in which the repair or inspection is imperfect [55]. Given that each of the mentioned MMs are based on and explained through one or several MatMs (depending on the conditions under which they are applied), in the next section, a description of the main MMs based on their associated MatMs will be provided. Energies 2019,12, 225 8 of 41 Energies 2019, 12 FOR PEER REVIEW 8 Figure 4. Alternative Classification of maintenance models. “Source [49–53,56–59], own elaboration.”. Figure 5. Inventory models. “Source [16,49–53,56–61], own elaboration.”. Given that each of the mentioned MMs are based on and explained through one or several MatMs (depending on the conditions under which they are applied), in the next section, a description of the main MMs based on their associated MatMs will be provided. The models used to obtain the reliability of a system, diagnose the failures of a component or determine the right time to perform the maintenance are not sufficient to determine the optimal maintenance strategy. Quantification in currency units (costs) of the results obtained through the model applied is necessary to perform an economic and financial analysis [30]. In this context, the costs of an item during its life cycle are divided into Capital Expenditure (CAPEX), which is generated when an item is bought and involves investigation, development, planning and Figure 4. Alternative Classification of maintenance models. “Source [ 49 – 53 , 56 – 59 ], own elaboration.”. Energies 2019, 12 FOR PEER REVIEW 8 Figure 4. Alternative Classification of maintenance models. “Source [49–53,56–59], own elaboration.”. Figure 5. Inventory models. “Source [16,49–53,56–61], own elaboration.”. Given that each of the mentioned MMs are based on and explained through one or several MatMs (depending on the conditions under which they are applied), in the next section, a description of the main MMs based on their associated MatMs will be provided. The models used to obtain the reliability of a system, diagnose the failures of a component or determine the right time to perform the maintenance are not sufficient to determine the optimal maintenance strategy. Quantification in currency units (costs) of the results obtained through the model applied is necessary to perform an economic and financial analysis [30]. In this context, the costs of an item during its life cycle are divided into Capital Expenditure (CAPEX), which is generated when an item is bought and involves investigation, development, planning and Figure 5. Inventory models. “Source [16,49–53,56–61], own elaboration.”. The models used to obtain the reliability of a system, diagnose the failures of a component or determine the right time to perform the maintenance are not sufficient to determine the optimal maintenance strategy. Quantification in currency units (costs) of the results obtained through the model applied is necessary to perform an economic and financial analysis [ 30 ]. In this context, the costs of an item during its life cycle are divided into Capital Expenditure (CAPEX), which is generated when an item is bought and involves investigation, development, planning and production, and Operating Expenditure (OPEX), which includes operation, maintenance and disposal. According to [16], a method of summarizing these concepts is presented in Equation (1): LCC =Cinv +Ccm +Cpm +Cpl +Crem (1) where LCC = life cycle cost, C inv = cost of the investment, C cm = cost for corrective maintenance, Cpm = cost for preventive maintenance, Cpl = cost for production loss and Crem = remainder value. Energies 2019,12, 225 9 of 41 The methodology based on the analysis of the costs during the useful life cycle is known as Life Cycle Cost Analysis (LCCA). In an environment of high uncertainty, aiming to include a large number of variables in different scenarios, LCCA uses most of the models seen in this section, quantifying in currency units the results of the models used [47]. Applying FMEA and modeling the reliability through the Weibull distribution, [ 33 ] determines the main causes of failures of the subsystems of a WT (2–3 MW), average annual failures and the costs expected for each failure. Contrary to the conventional FMEA procedure, in this proposal, the criticality of a failure is calculated as the total expected failure cost multiplied by the relative failure rate. According to the analysis, wear is the main cause of failure, with the gearbox and the rotor-blades being the most critical subsystems, which agrees with the results of studies that apply other methodologies. A very similar proposal, but comparing onshore and offshore wind turbines, is presented in [ 34 ]. Reference [ 47 ] finds the Net Present Value (NPV) from the sum of the annual maintenance costs during the life cycle of the project to demonstrate that the use of the CMS is justified as long as a reduction in the production and corrective maintenance costs is obtained. LCCA that is individually applied to WTs or to WFs, both onshore and offshore, allows determination of the optimal strategies that include the CMS. It can be said that each of the MMs has an associated costs model, as we will see in the following section. 3. Maintenance Types and Associated Mathematical Models A MatM is a set of equations that represent a physical system. The equation that defines the model is called an equation of state, and its solution allows knowing the evolution of the independent variable, both in time and space [ 10 , 11 ]. MatMs can be classified in different manners, starting with a conventional and simple form shown in Figure 6. Energies 2019, 12 FOR PEER REVIEW 9 production, and Operating Expenditure (OPEX), which includes operation, maintenance and disposal. According to [16], a method of summarizing these concepts is presented in Equation (1): LCC = C inv + C cm + C pm + C pl + C rem (1) where LCC = life cycle cost, C inv = cost of the investment, C cm = cost for corrective maintenance, C pm = cost for preventive maintenance, C pl = cost for production loss and C rem = remainder value. The methodology based on the analysis of the costs during the useful life cycle is known as Life Cycle Cost Analysis (LCCA). In an environment of high uncertainty, aiming to include a large number of variables in different scenarios, LCCA uses most of the models seen in this section, quantifying in currency units the results of the models used [47]. Applying FMEA and modeling the reliability through the Weibull distribution, [33] determines the main causes of failures of the subsystems of a WT (2–3 MW), average annual failures and the costs expected for each failure. Contrary to the conventional FMEA procedure, in this proposal, the criticality of a failure is calculated as the total expected failure cost multiplied by the relative failure rate. According to the analysis, wear is the main cause of failure, with the gearbox and the rotorblades being the most critical subsystems, which agrees with the results of studies that apply other methodologies. A very similar proposal, but comparing onshore and offshore wind turbines, is presented in [34]. Reference [47] finds the Net Present Value (NPV) from the sum of the annual maintenance costs during the life cycle of the project to demonstrate that the use of the CMS is justified as long as a reduction in the production and corrective maintenance costs is obtained. LCCA that is individually applied to WTs or to WFs, both onshore and offshore, allows determination of the optimal strategies that include the CMS. It can be said that each of the MMs has an associated costs model, as we will see in the following section. 3. Maintenance Types and Associated Mathematical Models A MatM is a set of equations that represent a physical system. The equation that defines the model is called an equation of state, and its solution allows knowing the evolution of the independent variable, both in time and space [10,11]. MatMs can be classified in different manners, starting with a conventional and simple form shown in Figure 6. Figure 6. General classification of mathematical models. “Source [11], own elaboration.”. Veltem [10] proposed a classification according to the space formed by the orthogonal axes S, Q and M, where S represents the type of system (social, economic, chemical, mechanical or electrical), Figure 6. General classification of mathematical models. “Source [11], own elaboration.”. Veltem [ 10 ] proposed a classification according to the space formed by the orthogonal axes S,Q and M, where Srepresents the type of system (social, economic, chemical, mechanical or electrical), Qis the objectives axis (speculation, prediction, analysis, design or control), and Mcorresponds to the mathematical structure (algebraic equations, differential equations, continuous processes, discrete processes, linear processes and black, gray and white box models). Here, the psychological, economic and social systems belong to the black box model, whereas the electrical and mechanical systems correspond to the white box model. Depending on the level of knowledge that there is in how they are constructed, MatMs can also be classified into white, gray and black box models. White box models are characterized by their relative ease of interpretation, as their deduction is based on knowledge of physical or Energies 2019,12, 225 16 of 41 where y= Time elapsed until a defect appears after an inspection and β = Probability of identifying a certain defect during an inspection. 3.5. Maintenance Models Based on Markov Models Unlike most of the models that assume that a system can only be in two states (operating or out of service due to a failure), the Markov models assume that a system can transit between several states, following a continuous-time stochastic process [ 33 ]. When the model assumes that the process can only transit between three states (operating, with failures and out of service due to a failure), the model is called semi-Markov [ 45 , 49 , 55 ]. Figure 7shows a classification alternative for variants that can include Markov chains. Considering the stochastic behavior of the weather, the difficult accessibility conditions and the constraints on the maintenance resources, study [ 71 ] uses Markov chains for modeling the corrective maintenance and its impact on the turbine availability of an offshore WF. The transition between the three states assumed by the model is obtained through an algorithm based on a Poisson process. The average availability is obtained by solving the transition matrix of the model. In [ 92 ], the authors propose a six-state Markov model for quantifying the impact of maintenance of the components of a wind turbine on the downtime and the failure risk. The transition and the failure risk during the life cycle stages of the equipment, in addition to during the failure and maintenance stages, are determined by a survivability index, whereas the performance and the failure risk probability at different maintenance intervals are modeled by the transition rate probabilities. To construct the model, the failure rate and the downtime data are used. In [ 93 ], the use of the weather conditions and the downtime data is proposed for forecasting the availability of a wind turbine through a model based on cyclic non-homogenous Markov chains consisting of 16 states. Based on the conditions revealed during the inspections and using the semi-Markov model, the study [ 94 ] proposes a strategy that minimizes the maintenance cost of a wind turbine gearbox. To determine the optimal strategy, on top of the inspections, the model also considers the equipment deterioration, minimal repairs and PM. In [ 95 ], the authors define a stochastic model based on the Partially Observed Markov Decision Process (POMDP) with heterogeneous parameters and solved by the backward dynamic programming method to determine the strategy that minimizes the gearbox maintenance costs, considering the variable weather conditions under which the wind turbine operates. According to the authors, the model demonstrates the advantages of dynamic CBM over a static CBM strategy. Energies 2019, 12 FOR PEER REVIEW 16 𝑅(𝑥) =  𝑓 (ℎ)𝑑ℎ   (24) where y = Time elapsed until a defect appears after an inspection and β = Probability of identifying a certain defect during an inspection 3.5. Maintenance Models Based on Markov Models Unlike most of the models that assume that a system can only be in two states (operating or out of service due to a failure), the Markov models assume that a system can transit between several states, following a continuous-time stochastic process [33]. When the model assumes that the process can only transit between three states (operating, with failures and out of service due to a failure), the model is called semi-Markov [45,49,55]. Figure 7 shows a classification alternative for variants that can include Markov chains. Considering the stochastic behavior of the weather, the difficult accessibility conditions and the constraints on the maintenance resources, study [71] uses Markov chains for modeling the corrective maintenance and its impact on the turbine availability of an offshore WF. The transition between the three states assumed by the model is obtained through an algorithm based on a Poisson process. The average availability is obtained by solving the transition matrix of the model. In [92], the authors propose a six-state Markov model for quantifying the impact of maintenance of the components of a wind turbine on the downtime and the failure risk. The transition and the failure risk during the life cycle stages of the equipment, in addition to during the failure and maintenance stages, are determined by a survivability index, whereas the performance and the failure risk probability at different maintenance intervals are modeled by the transition rate probabilities. To construct the model, the failure rate and the downtime data are used. In [93], the use of the weather conditions and the downtime data is proposed for forecasting the availability of a wind turbine through a model based on cyclic non-homogenous Markov chains consisting of 16 states. Based on the conditions revealed during the inspections and using the semi-Markov model, the study [94] proposes a strategy that minimizes the maintenance cost of a wind turbine gearbox. To determine the optimal strategy, on top of the inspections, the model also considers the equipment deterioration, minimal repairs and PM. In [95], the authors define a stochastic model based on the Partially Observed Markov Decision Process (POMDP) with heterogeneous parameters and solved by the backward dynamic programming method to determine the strategy that minimizes the gearbox maintenance costs, considering the variable weather conditions under which the wind turbine operates. According to the authors, the model demonstrates the advantages of dynamic CBM over a static CBM strategy. Figure 7. Markov models. “Source [16], own elaboration”. 3.6. Models Applied to the Logistics of Operation and Maintenance Figure 7. Markov models. “Source [16], own elaboration”. 3.6. Models Applied to the Logistics of Operation and Maintenance An important factor in making decisions about the maintenance strategy is related to logistics, which according to [ 96 ] is responsible for “the flow of materials from suppliers into an organisation, Energies 2019,12, 225 17 of 41 through operations within the organisation, and then out to customers.” From the conceptual point of view, to understand the effect of transport on production costs, we can refer to [ 97 ], where the problem of minimizing costs when transporting a product from certain production plants to different points of distribution or consumption is analyzed. As far as the wind industry is concerned, for [ 98 ], logistics refers to the planning, acquisition, storage and transportation of WTs or individual components, for which it may be necessary to use trailers, helicopters, rubber boats, jack-up and crane vessels. Wind turbine equipment is large and heavy, so, for land transport it is necessary roads that support heavy trucks. If roads are in poor condition, the transport equipment will be damaged, increasing maintenance costs. Rail is cheaper than moving tonnage by road, but this type of transport is limited by low railway penetration, in addition, road transport for the initial and final part of the trip, could be used. The maritime alternative is used for international transport and offshore WF. Air transport is faster, however, it is the most expensive, cannot be used for all components and its use depends a lot on weather conditions [ 98 ]. In this context, one of the reasons why the block maintenance strategy is preferred, is precisely to take advantage of the availability of transport and technical personnel, which gains more relevance when it comes to offshore WF, where in addition to the necessary resources (facilities, spare parts, transportation and human resources) that are used in onshore WFs, the planning and use of maritime and air transport is necessary. In order to optimize the supply chain, logistics, maintenance programming and costs in the wind industry, there are some approach that use several MatMs. Thus, as in offshore WFs, O&M operations depend on weather conditions, in the work of [ 99 ], maintenance and climate statistics are used in a Monte Carlo simulation model to determine the availability (weather windows) of an offshore WF based on wind speed, wave height and visibility. Transport alternatives used are helicopter and rubber boat. In [ 100 ] a Mixed Integer Linear Programming (MILP) model is proposed, through which the supply chain (location and plant size) is determined, as well as the use of the vessels, depending on the weather periods, in such a way that the accumulation and underutilization of resources during periods of inactivity is minimized. In the work of [ 101 ], Generalized Stochastic Petri nets (GSPN) coupled with Monte Carlo, is used to simulate O&M planning when several types of maintenance are applied and considering weather windows, age reduction, logistics times and costs. This research concludes that Preventive Maintenance (PM), both CBM and age dependent with imperfect repair maintenance, decreases wind turbine failures rates and reduces almost all mean costs compared to corrective maintenance (CM). The logistics related to the WFs is a very specialized and extensive field, to deepen on this topic it is suggested to consult the references [102–104]. A very important complement related to the operational part of maintenance is the planning of activities. According to [ 16 ], the models for optimizing planning include Material Requirements Planning (MRP), the critical path method (CPM), and Program Evaluation and Review Techniques (PERT). The application of each model depends on the planning horizon, as reported in Table 1. Table 1. Maintenance scheduling models. Term Time Model Long 3 months–1 year MRP, CPM Medium Weekly PERT, CPM Short Daily - 4. Methodologies and Mathematical Models Applied to the Detection, Diagnosis and Prognosis of Failures Among the models used in the tactical and operational strategy, the ones focused on failure diagnosis and prediction occupy a very important place; therefore, Section 4.1 is dedicated to the models used for failure prediction and diagnosis in the different WT components, whereas Section 4.2 is focused on the failure prognosis and RUL, emphasizing soft computing models. Energies 2019,12, 225 18 of 41 4.1. Detection and Diagnosis It is possible to perform a failure diagnosis in WTs using models included in the following techniques: signal analysis, model-based and data-based classes [ 105 ]. Figure 8includes some models corresponding to the first two options; the third will be addressed in Section 4.2. Energies 2019, 12 FOR PEER REVIEW 18 4.1. Detection and Diagnosis It is possible to perform a failure diagnosis in WTs using models included in the following techniques: signal analysis, model-based and data-based classes [105]. Figure 8 includes some models corresponding to the first two options; the third will be addressed in Section 4.2. Figure 8. Models Applied for the Detection and Diagnosis of Failures. Source [105–108], own elaboration. Because wind turbines are located in remote areas and at considerable heights, failure monitoring, detection and diagnosis are usually performed via the analysis of the signals obtained from the sensors that are part of the CMS. References can be found on the application of many MatMs (white, gray and black box) for the detection and diagnosis of failures in the different parts of a wind turbine (see Table 2). However, despite the variety of available signals, the use of vibration predominates in the wind industry, as not only is vibration produced in all the wind turbine parts (from the blades to the tower), but also, it provides early signs of failures; therefore, there is more time to plan and execute the corrective actions [46]. Table 2. References on Applications of mathematical models (MatMs) for Failure Diagnosis in Wind Turbines. Part of the Wind Turbine Signal Model Blades Shaft Bearing Gearbox Braking System Electric Generator Converter Tower Current Finite elements [109] Artificial neural network (ANN) [110] Electromechanical model [111] [111] [111] [111] [112] [111] [111] Vibration Rule induction ANN [113] Fast Fourier transform (FFT) Wavelets [114,115] [114] Mahalanobis distance ANN [116] Morlet continuous Wavelet Wigner-Ville distribution [117,118] Wavelets Immune genetic algorithm [119] Spectral kurtosis [120] Fuzzy logic [121] k-Nearest neighbor (k-NN) [122] Support vector machine (SVM) [119,122] k-Means [122] Nonlinear state estimation technique [123] Figure 8. Models Applied for the Detection and Diagnosis of Failures. Source [ 105 – 108 ], own elaboration. Because wind turbines are located in remote areas and at considerable heights, failure monitoring, detection and diagnosis are usually performed via the analysis of the signals obtained from the sensors that are part of the CMS. References can be found on the application of many MatMs (white, gray and black box) for the detection and diagnosis of failures in the different parts of a wind turbine (see Table 2). However, despite the variety of available signals, the use of vibration predominates in the wind industry, as not only is vibration produced in all the wind turbine parts (from the blades to the tower), but also, it provides early signs of failures; therefore, there is more time to plan and execute the corrective actions [46]. Table 2. References on Applications of mathematical models (MatMs) for Failure Diagnosis in Wind Turbines. Part of the Wind Turbine Signal Model Blades Shaft Bearing Gearbox Braking System Electric Generator Converter Tower Current Finite elements [109] Artificial neural network (ANN) [110] Electromechanical model [111] [111] [111] [111] [112] [111] [111] Vibration Rule induction ANN [113] Fast Fourier transform (FFT) Wavelets [114,115] [114] Mahalanobis distance ANN [116] Morlet continuous Wavelet Wigner-Ville distribution [117,118] Wavelets Immune genetic algorithm [119] Spectral kurtosis [120] Fuzzy logic [121] k-Nearest neighbor (k-NN) [122] Support vector machine (SVM) [119,122] k-Means [122] Nonlinear state estimation technique [123] Energies 2019,12, 225 19 of 41 Table 2. Cont. Thermal Data mining [124,125] [125] [41,124,125] [125] Autoregressive model ANN [126] Bagging, ANN, kNN Genetic programming [127] Continuous time Markov chain Monte Carlo [128] Autoassociative Kernel Regression (AAKR) Moving window statistic [129] ANN [130] Acoustic Continuous time Markov chain Monte Carlo [127] Wavelet transforms Wigner-Ville distribution Hilbert transforms [131] [132] Support vector regression (SVR) [133] Due to the variability of the weather conditions under which wind turbines operate, the methods for transient signal analysis are the norm, especially with the use of wavelets. The study of the spectrum by the models included in Figure 8allows detection and diagnosis of failures according to the magnitude of the components of the fundamental wave of the signal. As an example, several types of failures and their associated components according to the cause and the part of the electrical generators can be found in [ 134 – 137 ]. In addition, each of the WT parts can require a specific methodology. An example is the gearbox, whose maintenance is also based on online and offline analysis of the oil conditions [ 14 ]. Another example is the electric generator, for which there is a variety of specific methods for the detection and diagnosis of failures according to each of the parts [ 105 , 135 – 139 ]. The followed procedure is similar for all the signal types and is shown in Figure 9. Energies 2019, 12 FOR PEER REVIEW 19 Table 2. Cont. Thermal Data mining [124,125] [125] [41,124,125] [125] Autoregressive model ANN [126] Bagging, ANN, kNN Genetic programming [127] Continuous time Markov chain Monte Carlo [128] Autoassociative Kernel Regression (AAKR) Moving window statistic [129] ANN [130] Acoustic Continuous time Markov chain Monte Carlo [127] Wavelet transforms Wigner- Ville distribution Hilbert transforms [131] [132] Support vector regression (SVR) [133] Due to the variability of the weather conditions under which wind turbines operate, the methods for transient signal analysis are the norm, especially with the use of wavelets. The study of the spectrum by the models included in Figure 8 allows detection and diagnosis of failures according to the magnitude of the components of the fundamental wave of the signal. As an example, several types of failures and their associated components according to the cause and the part of the electrical generators can be found in [134–137]. In addition, each of the WT parts can require a specific methodology. An example is the gearbox, whose maintenance is also based on online and offline analysis of the oil conditions [14]. Another example is the electric generator, for which there is a variety of specific methods for the detection and diagnosis of failures according to each of the parts [105,135–139]. The followed procedure is similar for all the signal types and is shown in Figure 9. Figure 9. Schematic of the processes for failure detection, diagnosis and prognosis. Modified from [107,140]. 4.2. Prognosis of Failures The MatMs applied at the tactical level and analyzed in the previous sections (most of them being white box models) assume many idealizations (materials, design, labor, working conditions, and contingencies), so it is difficult to expect that the results obtained by the model coincide with the real behavior. In addition, the models considered until now are not capable of addressing the lack of Figure 9. Schematic of the processes for failure detection, diagnosis and prognosis. Modified from [107,140]. 4.2. Prognosis of Failures The MatMs applied at the tactical level and analyzed in the previous sections (most of them being white box models) assume many idealizations (materials, design, labor, working conditions, and contingencies), so it is difficult to expect that the results obtained by the model coincide with the real behavior. In addition, the models considered until now are not capable of addressing the lack of information and uncertainty that accompanies any process, much less learning autonomously. Currently, to obtain these characteristics, the tendency is to resort to the models grouped as soft computing or computational intelligence, which are a set of AI techniques, most of them being black Energies 2019,12, 225 20 of 41 box or hybrid models that use a large amount of MatMs and computational programs that aim to emulate the manner in which living organisms (bees, ants, fish, cells and humans) learn, reason, behave in groups, transmit traits from generation to generation and make optimal decisions [141–143]. In the area of WT maintenance, the prognosis usually refers to failures, RUL, availability, energy demand and production [ 144 – 155 ]. Based on the division of soft computing into approximate reasoning techniques and optimization techniques, which is done in [ 156 ], presented in Figures 10–12 is an alternative classification of the most-used MatMs for such purposes [ 142 , 157 – 163 ]. Currently, the use of AI models is the norm in the wind industry, and they are applied at all levels, from the strategic and tactical models (RCM, FMEA, FMECA, etc.) discussed in Section 2[ 36 , 164 , 165 ] to failure detection, diagnosis and prognosis and RUL determination [ 17 , 166 ]. AI techniques represent a new step in the evolution of MatMs such that once they are trained, they learn autonomously, have a life of their own and are capable of performing prognoses based on the natural behavioral pattern of the analyzed data, whether historical or obtained in real time. This is known as machine learning, [ 167 , 168 ]. The application of these methodologies has been greatly facilitated owing to software packages such as LabView, Python, SPSS, R and MATLAB. Of the large amounts of models included in Figures 10–13, not all have obtained the same degree of attention, with the models based on SVMs, ANNs, fuzzy logic and Bayesian networks and the hybrid models highlighted, which are briefly described in the remainder of this section. Figure 13 shows the manner in which MATLAB [ 160 ] classifies the models used for its machine learning application, in addition, for space reasons, several references regarding the application of AI models have been included in Table 2, according to the WT component to which they are applied. Energies 2019, 12 FOR PEER REVIEW 20 information and uncertainty that accompanies any process, much less learning autonomously. Currently, to obtain these characteristics, the tendency is to resort to the models grouped as soft computing or computational intelligence, which are a set of AI techniques, most of them being black box or hybrid models that use a large amount of MatMs and computational programs that aim to emulate the manner in which living organisms (bees, ants, fish, cells and humans) learn, reason, behave in groups, transmit traits from generation to generation and make optimal decisions [141–143]. In the area of WT maintenance, the prognosis usually refers to failures, RUL, availability, energy demand and production [144–155]. Based on the division of soft computing into approximate reasoning techniques and optimization techniques, which is done in [156], presented in Figures 10– 12 is an alternative classification of the most-used MatMs for such purposes [142,157–163]. Currently, the use of AI models is the norm in the wind industry, and they are applied at all levels, from the strategic and tactical models (RCM, FMEA, FMECA, etc.) discussed in section two [36,164,165] to failure detection, diagnosis and prognosis and RUL determination [17,166]. AI techniques represent a new step in the evolution of MatMs such that once they are trained, they learn autonomously, have a life of their own and are capable of performing prognoses based on the natural behavioral pattern of the analyzed data, whether historical or obtained in real time. This is known as machine learning, [167,168]. The application of these methodologies has been greatly facilitated owing to software packages such as LabView, Python, SPSS, R and MATLAB. Of the large amounts of models included in Figures 10–13, not all have obtained the same degree of attention, with the models based on SVMs, ANNs, fuzzy logic and Bayesian networks and the hybrid models highlighted, which are briefly described in the remainder of this section. Figure 13 shows the manner in which MATLAB [160] classifies the models used for its machine learning application, in addition, for space reasons, several references regarding the application of AI models have been included in Table 2, according to the WT component to which they are applied. Figure 10. Approximate reasoning models. “Source [142,157–163], own elaboration”. Figure 10. Approximate reasoning models. “Source [142,157–163], own elaboration”. Energies 2019,12, 225 21 of 41 Energies 2019, 12 FOR PEER REVIEW 21 Figure 11. Optimization models. “Source [142,157–163], own elaboration.”. Figure 11. Optimization models. “Source [142,157–163], own elaboration.”. Energies 2019,12, 225 22 of 41 Energies 2019, 12 FOR PEER REVIEW 22 Figure 12. Optimization models. “Source [142,157–163], own elaboration.”. Figure 13. Classification of models used for machine learning. Taken from [169]. Figure 12. Optimization models. “Source [142,157–163], own elaboration.”. Energies 2019, 12 FOR PEER REVIEW 22 Figure 12. Optimization models. “Source [142,157–163], own elaboration.”. Figure 13. Classification of models used for machine learning. Taken from [169]. Figure 13. Classification of models used for machine learning. Taken from [169]. 4.2.1. Support Vector Machines (SVMs) Belonging to the nonparametric models and to supervised learning techniques, SVMs are based on statistical learning theory (SLT) and structural risk minimization (SRM). These models can be used Energies 2019,12, 225 23 of 41 for classification problems (support vector classification) and for regression problems (support vector regression, SVR). Regarding the first option, SVMs classify a set of data according to a certain subset or class to which they belong, and the most basic model assumes two classes, labeled − 1 and 1. If each element of the data set can be correctly assigned to one of these labels, it is said that the samples can be classified by a set of functions. Generalization of the model is only possible if no significant errors are made in terms of the precision obtained with the training data and the capability of the model to learn with other data sets. The separation of classes or subsets can be performed using linear or nonlinear hyperplanes (linear and nonlinear learning). For the first option, it is assumed that there is a linear hyperplane H (also called the decision hyperplane) of the largest possible margin such that Equation (25) is satisfied. The data subset (class 1) is located on one side of the hyperplane H, whereas the second subset (class − 1) is located on the opposite side. The hyperplane H is located between hyperplanes H1 and H2 (Equations (26) and (27)). The points located on H 1 and H 2 , which are also characterized as being the points closest to H, are called support vectors. Each of the subsets obtained after the first classification can be divided again into subsets: H:w·x−b=0 (25) H1:w·xi−b≥1, yi=1 (26) H2:w·xi−b≤ −1, yi=−1 (27) When the data cannot be linearly classified in their original space, an SVM creates a nonlinear separation hypersurface, in which the linear classification can be applied again. The nonlinear transformation can be performed by sigmoidal and polynomial functions, among others. Given that there will be an error ( ε ) between each sample and the ideal hyperplane, the goal is to find the support vector for which the sum of the classification errors is minimized. Considering the error ε Equation (26) becomes Equation (28). Construction of the separation hyperplanes by nonlinear functions (such as polynomials of degree greater than two) could lead to obtaining decision hyperplanes in spaces with many dimensions, in which it would be very complicated to perform the operations with vectors. Fortunately, the hypothetical decision space can be determined by an adequate kernel function, given in [ 170 , 171 ]. The use of the kernel allows finding a linear solution in the higher-dimensional feature space that is equivalent to a nonlinear solution in the original input space, whose dimensions are lower [119]: H1:w·xi−b≥1−εi,εi≥0 (28) In the wind industry, the SVM method is used to develop solution proposals for problems in different areas. The study [ 133 ] estimates and predicts the noise level produced by a WT as a function of wind speed via SVR. The kernel functions used were polynomials and the Radial Basis Function (RBF) since, according to the author, they are more efficient. [ 122 ] applies SVM to the vibration signal to identify the failure patterns of the bearings in WTs. In [ 172 ], the authors process the vibration signal through the Hilbert–Huang transform (HHT) method and apply SVM to detect and diagnose the bearing failures. The bearing degradation and RUL are obtained via SVR. To obtain a failure classifier, the SVM model is trained with historical observations. When the vibration signal is measured in real time, the SVM classifies the magnitudes of the frequencies corresponding to the inner and outer tracks and the balls; in this manner, failures are detected and diagnosed. 4.2.2. Bayesian Networks Rule-based systems have limitations in representing knowledge and in reasoning under conditions of uncertainty. Therefore, it was necessary to replace the inferences and assumptions characteristic of the traditional logical reasoning with a probabilistic interpretation of the relationship between the propositional variables and causes, giving rise to Bayesian Networks (BNs). To solve such problems, there can be several alternatives, each of which (according to the BN model) is assigned a probability Energies 2019,12, 225 24 of 41 (which can be obtained via statistical analysis of the available data); they are treated according to probability theory (Bayes’ rules), which is why this AI model is also known as a probabilistic network, as presented by [173,174]. The BN structure follows the Markov chain properties [175]. BNs are part of the models known as knowledge-based or model-based systems. Their structure is represented by a type of graph known as a Directed Acyclic Graph (DAG), in which the nodes symbolize the prepositional variables and the dependency between variables (cause-effect relationship) is represented by an arrow along with the corresponding probability of occurrence. The language by which the events and their probabilities are expressed is Boolean algebra, and therefore, each variable will have a conditional probability table, as presented in [173,174]. Based on previously collected data, visual inspections and data obtained in real time, ref. [ 176 ] proposes a model that replaces the semiannual scheduled maintenance and considers periodic inspections and repair to control the degradation induced by fatigue. The proposed model for planning and learning in uncertain dynamic systems is based on the Bayes-adaptive partially observable Markov decision process model and is capable of learning from the environment, updating the distribution of the model parameters and selecting the optimal strategy under conditions of uncertainty. In [ 177 ], the authors apply maximum the likelihood method of BNs to obtain the transition probabilities between the states of a semi-Markov model used for estimating the RUL of the blades of a WT. Using the real and observed values of the wind turbulence intensity and RPM of the electrical generator, [ 178 ] constructs a BN model that can calculate the failure probability at any point in time and the impact of the possible maintenance actions and quantify the deterioration level during a time period for the gearbox of a WT. The strength of the dependence of the variables used was quantified via a Kalman filter. To predict the failures of the wind turbine components (blades, gearbox, generator, main bearing, pitch and yaw), in [ 179 ], the BN model is used, trained with the available data on meteorological variables, failure records and the technology used in WTs. In [ 175 ], the authors perform a specific study regarding BNs and include a section in which a considerable amount of applications to different areas of the wind industry can be found. 4.2.3. Artificial Neural Networks (ANNs) ANNs are MatMs that aim to emulate the physical structure, operation and capability of biological neurons to establish relationships between the input and output signals. If for the magnitude of the linear combination (weighted sum) of each input (dendrites), multiplied by a factor or weight (synapsis), the activation function (linear, stepped, triangular, Gaussian, sigmoidal, etc.) reaches a value equal to or higher than the threshold, then the neuron’s output (axon) will be activated. An ANN is a set of neurons (equivalent to a biological nervous system) organized into input layers, hidden layers and output layers. The network analyzed as a whole has a very similar structure to a neuron. The output of the neurons of a layer is converted into the input of the neurons of the following layer by connecting links multiplied by a factor or weight. Through the use of a large amount of previously collected data, the neurons are entered in the manner in which they have to proceed (“think”) such that the ANN can then generalize and perform reliable predictions based on the reading of data in real time, as presented in [ 180 – 183 ]. When the ANNs have a large number of layers, these models are called deep learning models [ 184 ]. The higher the numbers of variables and layers are, the higher the computational effort required. There are several types of ANNs, which can be classified according to several criteria. Presented in Figure 14 is a possible classification, leaving references [ 180 – 186 ] for further insight into the vast theory and practice of these types of models. According to [ 186 ], highlighted among the advantages of ANNs are adaptive learning, self-organization, tolerance to incomplete data or presence of noise and easy implementation, as there are even chips specialized for ANNs. However, ref. [ 183 ] also mention same disadvantages, such as training being needed for each problem, the need to perform multiple tests to achieve an adequate architecture, the training being long and possibly consuming several hours, the need for a Energies 2019,12, 225 25 of 41 large amount of data to train the network, the lack of a specific model being followed, and the internal dynamics of the system being unknown such that the results appear complex for an outside observer. In recent years, these types of MatMs have been widely used to make use of the database of the SCADA system, through which the records of temperature, vibration and current can be accessed, in addition to the atmospheric variables and energy production of the WTs. Based on the data collected by the CMS, ref. [ 44 ] proposes a CBM strategy (based on the failure probability) in which, due to the dependency between the components of a WT, they are considered as a single unit, and the presence of the maintenance team in a WF for performing maintenance on multiple turbines instead of a single WT is also considered. The distribution of the time to failure is predicted by a feedforward neural network, composed of an input layer, two hidden layers and an output layer. The ANN input data are the ages of the components at the moment of the inspection and in the previous inspections, whereas the output is the life percentage of the component, on which the time to failure is based on. With the time interval between maintenances, the age of the component at the moment of the inspection, the time to failure and the standard deviation of the time to failure distribution (a normal distribution is assumed) predicted by the ANN, the failure probability at a certain instant is obtained. Contrary to the models that use the life cycle to predict the RUL of a component, study [ 187 ] proposes the prediction of the RUL of the gearbox bearings of a WT through the combination of the short-term prediction by an ANN with the estimation of the long-term tendency based on polynomial fits. For the prediction by the ANN, a three-layer network is used (input, hidden and output), and the number of outputs is the same as the inputs and depends on how many variables (characteristics) should be predicted. For the referred to study, 8 time characteristics were used (mean, RMS, variance, square root of amplitude, skewness factor, kurtosis factor, waveform factor and margin indicator), as were the energy of the first four bands of the vibration signal frequency spectrum. Ref. [ 186 ] presents the specific state of the art regarding the different types of ANNs combined with other MatMs applied to the different areas involved in the wind industry, that is, design optimization (WTs and wind farms), forecasting and prediction (wind speed, wind power, noise, torque and power factor), WT control and failure diagnosis and prediction (gearbox, bearings, generator, rotor, blades and electrical and electronic control). 4.2.4. Fuzzy Logic By using MatMs with different probability distributions and extending the classical digital logic theory, fuzzy logic aims to emulate the human behavior capable of making decisions under conditions of uncertainty due to there being few data, incomplete data or heterogeneous data, as in the case of big data. When facing phenomena whose truthfulness and falseness cannot be completely defined, it is not possible to apply classic logic; consequently, there has arisen an alternative of constructing diffusive control systems, which through a set of IF-THEN propositions, combine fuzzy variables to obtain a response or output. For this, based on the concept that when a property that identifies the elements of a set is clear, the absolute belonging, or not, of an element to such a set is perfectly defined, and according to the traditional mathematical logic, values of 1 and 0 will be assigned to it, respectively. When the property is not clear, according to the fuzzy logic theory, the membership is given by a characteristic function or membership function, whose magnitude (membership degree) ranges from 0 to 1. Depending on the relationship between the variables of the analyzed phenomenon, the membership of an element to a set can be obtained by several functions (triangular, trapezoidal, Gaussian, double Gaussian, bell, S,Z, π , sigmoidal, singleton or fuzzy point), whose names refer to the graph of the function used, as presented in [89,124,133,134,188]. 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