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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Predictive Maintenance for Wind Turbine Bearings: An MLOps Approach with the DIAFS Machine Learning Model</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Nataliya Shakhovska</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jaime Campos</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>College of Engeneering, Design and Phisical Sciences, Brunel University London</institution>
          ,
          <addr-line>Kingston Lane, Uxbridge, Middlesex UB8 3PH</addr-line>
          <country country="UK">United Kingdom</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Informatics, Linnaeus University</institution>
          ,
          <country country="SE">Sweden</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Department of Systems of Artificial Intelligence, Lviv Polytechnic National University</institution>
          ,
          <addr-line>Lviv,79905</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>This article underscores the importance of integrating machine learning analytics to enhance preventive maintenance methodologies, particularly emphasizing condition-based maintenance (CBM) within the wind energy domain. Through empirical evidence derived from wind turbine data, the paper outlines the efficacy and applicability of Machine Learning in Operations (MLOps) for predicting the residual operational life of wind turbine bearings. While the study's principal domain is renewable energy, especially wind power, it employs a specific wind turbine dataset for exhaustive model testing, leading to the proposition of an innovative ensemble model tailored for high-speed wind turbine bearing prognosis. The introduced model, "The Data Interpretation Algorithm for Forecasting Time Series" (DIAFS), crafted for assessing wind turbine bearing conditions, is predicated on an adaptive polynomial model approximation. It emerges as an indispensable asset for maintenance professionals implementing CBM methodologies.</p>
      </abstract>
      <kwd-group>
        <kwd>Condition-based maintenance</kwd>
        <kwd>condition monitoring</kwd>
        <kwd>machine learning</kwd>
        <kwd>MLOps</kwd>
        <kwd>Preventive maintenance</kwd>
        <kwd>wind turbine bearing 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>THE E.U.'s 2050 energy roadmap mandates member states to advance infrastructure for
longterm energy system decarbonization. Estimates suggest a global population increase of 2 billion
by 2050, requiring 47% more energy for a total of 10 billion people. Given the current energy
system's inadequacies and climate goals, there's an urgent need for sustainable energy practices
(energy.ec.europa.eu). In this context, aspects of the wind farms, especially the components,
such as the wind turbines, are critical to investigate. Wind turbines (W.T.) are complex
equipment with a design lifetime of approximately 20 years. However, its life span and
availability can be augmented by the implementation of condition monitoring and preventive
maintenance techniques related to operation and maintenance activities. As a result, this means
that with effective operation and maintenance, these W.T.s are operational to be able to produce
energy. In addition, Operating and maintenance (O&amp;M) costs are part of a large amount of a
wind farm's Levelized Cost of Electricity (LCOE). Thus, the reduction of O&amp;M costs provides
possibilities to control the LCOE in an effective way. Therefore, the optimization of operation
and maintenance are critical factors in controlling the LCOE.</p>
      <p>
        Consequently, one of the few measures of reducing the cost of production is to cut the cost
of operation, including maintenance. It is the second-highest or even the highest element in
operating expenses in some industries. Swanson [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] mentions that companies have started to
undertake more efforts to improve quality and productivity as well as reduce costs to achieve
world-class performance. This has led to examining the activities of the maintenance function.
The author mentions that effective maintenance is crucial for many operations since it extends
the life of the equipment, improves availability, and conserves/retains the equipment in
appropriate conditions. Thus, if a company uses maintenance properly, it increases its
production and revenue by increasing its availability [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. This is so because the availability
change allows the company to vary its production level and output. This, in turn, influences
sales revenue and production costs. At the same time, the maintenance costs are affected since
unplanned and preventive maintenance varies. In addition, the positive impact of the digital
transformation efforts and their respective ICTs on maintenance and, thereby, productivity has
been realized by academia and industry alike [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>Additionally, it's well known that condition-based maintenance (CBM) preventive
maintenance strategy is preferred wherever it is technically feasible and financially viable. The
heart of CBM is condition monitoring (CM), which in principle, involves data acquisition,
processing, analysis, interpretation, and extracting useful information. The information helps to
identify whether asset health has deviated from the normal. If so, then fault diagnosis and
prognosis usually follow. Finally, a decision is taken regarding when and what maintenance
tasks are to be performed.</p>
      <p>
        The CBM is now the most widely employed strategy in the Wind Farm industry [
        <xref ref-type="bibr" rid="ref4 ref5 ref6 ref7">4–7</xref>
        ].
Condition monitoring and maintenance can be performed with, for instance, vibration analysis,
acoustic emission, sensory signals and signal processing methods, statistical methods, trend
analysis, time-domain analysis, fast-Fourier transform (FFT), wavelet transforms, fault tree
analysis (FTA) [
        <xref ref-type="bibr" rid="ref8 ref9">8-9</xref>
        ].
      </p>
      <p>
        When it comes to renewable energy sources, such as wind farms, the efficiency
improvement in energy production goes hand in hand with the possibility of providing
predictive maintenance to the different energy production equipment. For instance, to provide
service to various equipment, the level of energy production is stable and can utilize its full
potential without fluctuations due to equipment breakdowns. Although, a disadvantage of using
wind farms is that they do not always produce energy. It requires storing energy when
production diminishes because of changed weather conditions. Therefore, battery storage
systems offer the possibility of having a more stable output of power to match the required
demand. Obtaining energy while minimizing pollution/contamination and costs is worrying
many due to climate change and global warming. In this aspect, renewable energy is an
excellent alternative. Continuously, the fluctuations in energy production as a result of different
weather conditions have led to the option of moving the wind turbines offshore since the
conditions are better suited, i.e., higher and stable wind speeds are experienced [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. The
importance of renewable energy in the future is a fact; for instance, Balischewski et al. [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]
mention that renewable energy production in the case of wind power accounted for
approximately 12% of Germany's total power production in 2015. In addition, in 2019, wind
energy generated enough electricity to cover 15% of Europe's power demand (windeurope.org).
Thus, the wind-energy sector has grown significantly among renewable energy sources in the
last two decades. The most common fault in wind turbines is linked to gearbox failures, though
the bearing errors are overrepresented [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
      </p>
      <p>
        Furthermore, it is well known that difficulties arise when implementing the entire cycle of
condition-based maintenance (CBM). It is connected with specific issues regarding CBM
characteristics, such as the amount of data produced, data integrations, and the lack of experts.
Consequently, these issues have been tried to be solved over time, namely with the support of
various ICTs, such as expert systems, decision support systems, artificial intelligence, and
distributed intelligence [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ].
      </p>
      <p>Consequently, the main contributions of this paper are connected with the use of machine
learning (ML) algorithms supported with MLOps, e.g., machine learning in operations. Its
contributions are the following:</p>
      <p>•A Machine Learning (ML) pipeline that uses training data from wind turbines. This design
identifies patterns and creates a model that can handle new data without breaking.</p>
      <p>• A new ML model for predictive maintenance for wind turbine bearings. This model
monitors the condition of wind turbine bearings using an adaptive polynomial model to
approximate time series data. The data is split into two: level and trend. For forecasting, it
considers past data trends. We also employed the Holt-Winters Exponential Smoothing method
for more precise forecasting. The high R-Squared values of proposed model suggest it
effectively predicts new data.</p>
      <p>• In addition, two ML stacking models were developed. One combines regression and
knearest neighbors (knn) with a regression tree, while the other combines regression with support
vector regression (svr) and a regression tree. These combinations reduce predictor correlation
and enhance model generalization. Notably, the second model has a low Root Mean Square
Error, indicating minimized errors in predictions.</p>
      <p>Overall, the approach described in this article is comprehensive and provides an effective
solution for wind turbine-bearing data analysis and forecasting. The research methodology is
built as follows:
1. Dataset preprocessing.
2. Models' development.
3. Results evaluation.
4. System architecture development.
5. System development and testing.</p>
      <p>The contribution mentioned above is presented further in section 4 of the paper.
Accordingly, section 2 highlights some aspects of the domain of interest. Then, later in section
3, the machine learning analytical capabilities are explained, and the term MLOps, i.e., machine
learning in operations, is presented; hence, the section discusses what would be needed to
achieve analytical capabilities supported by the MLOps in the field. Further on, in section 4, a
case example using Wind turbine failure data is provided, namely for a bearing fault considering
the essential aspects of implementing MLOps in the domain. Finally, in section 5, the
discussions and conclusions are given.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Preventive Maintenance of Wind Turbines</title>
      <p>Despite the widespread adoption of wind turbines, the effective prediction of bearing failures
remains a significant challenge, leading to unplanned downtimes and reduced turbine
availability. Therefore, operation and maintenance, and specially condition-based maintenance,
become key aspects to consider in this context.</p>
      <p>
        Thus, one of the most common faults in wind turbines is connected with gearbox failures,
but where the bearing errors are overrepresented [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. It is known that the main bearing failures
are vital factors to consider when it comes to increasing wind farms' reliability and availability
[
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. Furthermore, it is one of the critical reasons that condition monitoring on the bearings is
crucial. Hence, the failures of rolling element bearings (REBs) considerably influence the entire
machinery; therefore, it is of primary importance to perform effective condition monitoring of
REBs not to incur lost production time and economic losses. Moreover, it is crucial to be able to
decide when to perform maintenance actions to the equipment based on condition monitoring
and its connected CBM approach. In this respect, diminishing energy costs, especially those
connected with unplanned stoppages, faults, support delays, etc., is crucial.
      </p>
      <p>
        Consequently, all the former aspects are related to operation and maintenance practices,
with considerable potential for cost reductions and innovations. Therefore, it is essential to
consider the operation and maintenance of the wind industry, especially when it is believed to
drastically cover a significant part of the E.U.'s total electricity consumption. Further, the
domain's state of the art and challenges and its wind turbine bearing condition monitoring
methods can be found in [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. In addition, a review of the use of machine learning methods for
wind farm turbines is also highlighted in [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. The remaining useful life (RUL) is the length of
time a machine is likely to operate before it requires repair or replacement. By taking RUL into
account, engineers can schedule maintenance, optimize operating efficiency, and avoid
unplanned downtime. For this reason, estimating RUL is a top priority in predictive
maintenance programs. The paper calculates RUL based on methodology from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]. In this
case, the availability of wind farms, as mentioned above, is vital to produce energy. Their
availability can be seen as technical availability, which involves the percentage of time that a
wind turbine/wind farm is available to generate energy. It is stated as the percentage of the
theoretical maximum of its availability [
        <xref ref-type="bibr" rid="ref18 ref19">18, 19</xref>
        ]. The equation below is from the IEC Standard
61400-26, highlighting the percentage of the theoretical maximum, as mentioned above. This
formula is widely used in the wind industry and indicates the operational performance of wind
turbines/wind farms.
      </p>
      <p>Availability = 1 – (Unavailable Time)/(Available Time + Unavailable Time)</p>
      <p>Thus, low availability can be poor wind farm reliability performance or a below-standard
maintenance action. Therefore, an effective operation and maintenance approach (O&amp;M ) is
crucial to be able to make the conditions of optimal availability of the wind turbine, which at the
same time can produce the expected amount of energy.</p>
      <p>
        Consequently, the efficiency improvement in energy production goes in hand with the
possibility of providing predictive maintenance to the different energy production equipment.
For instance, to provide service to the various equipment by doing so is the level of energy
production stable and can utilize its full potential without fluctuations because of equipment
breakdowns. It is, therefore, crucial to optimize the O&amp;M. Thus, preventive maintenance based
on the CBM approach provides an understanding of when it is suitable to maintain the
equipment to avoid unplanned stoppages; in this case, the energy production and try to keep the
wind turbines available so they can be operational and receive service when it is needed. It is,
therefore, key to understand the various offshore wind turbine operation and maintenance
approaches and how they might impact O&amp;M [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. Consequently, it is essential to find tools,
such as machine learning algorithms supported with Mlops, to support the preventive
maintenance of wind turbines..
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Machine Learning Analytical Capabilities via Mlops</title>
      <p>
        In the application of machine learning methodologies, it is imperative to source appropriate
datasets and subsequently undergo rigorous data preprocessing. This involves the acquisition of
relevant data, subsequent cleansing procedures, and preparation for analytical diagnosis.
Periodic retraining of models is essential to ensure their robustness and accuracy. Furthermore,
for optimal performance, it's paramount that models autonomously adapt their parameters based
on data-driven insights, especially in response to dynamic changes in the input dataset [
        <xref ref-type="bibr" rid="ref21 ref22">21,22</xref>
        ].
This self-adjustment capability ensures the model's relevance and precision across varying data
landscapes, which are all key aspects. ML is used where it can be applied to learn by comparing
and correlating numerous similar patterns from various data sources to develop models to
understand and foresee different things of interest [
        <xref ref-type="bibr" rid="ref23 ref24">23-24</xref>
        ]. ML learning learns from experience
based on big data or specific datasets. It can detect different patterns in the labeled and not
labeled data, i.e., supervised and unsupervised learning, and from where the results are not
known [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ]. The role of the ML in industrial asset management is to provide further information
about when to provide services to the production equipment to keep production running and
avoid unplanned stoppages. The increase in the use of A.I. and ML depends on, for instance,
emergent technologies, such as new sensor technologies, the Internet of Things (IoT), and big
data, which goes hand in hand while intending to reach industry 4.0 and all that it involves in
the digitization process. The characteristics of these technologies are that they increase the
amount of data that is created, gathered, and possible to analyze. Several different
machinelearning algorithms have been tested and suggested [
        <xref ref-type="bibr" rid="ref23 ref24 ref25">23-25</xref>
        ]. However, in the domain of
industrial asset management, i.e., condition monitoring and maintenance and its related CBM
approach, the specific tools and techniques have been successfully used for several years.
Hence, they are slow and rather conservative and belong to a vertical market, e.g., to
acquire/adopt new emerging technologies. However, the domain still leans on its well-accepted
signal processing technologies, among others, for the CBM approach. Therefore, it is essential
to understand if those suggested ML algorithms have a place in a running CBM strategy, i.e., if
they are suitable for operation, namely the so-called MLOps (Machine learning in operations).
      </p>
      <p>
        Nevertheless, there are efforts to use machine learning methods for wind farms turbine,
especially for blade fault detection or generator temperature monitoring [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. The use of
machine learning for wind turbine bearing fault detection in [
        <xref ref-type="bibr" rid="ref26 ref27">26, 27</xref>
        ] is reported. However, the
implementation and use of the MLOps approach are not considered. Thus, these new ICTs, such
as the IoT, big data, and machine learning, involve substantial modifications in several aspects
for their successful implementation and use, i.e., how the maintenance department creates, uses,
and manages their different Information Systems (I.S) &amp; digital capabilities. The current work
considers the use of the bearings faults as a case to highlight the use of ML in the domain of
interest. MLOps come into the picture to provide organizations with the capabilities embedded
in those technologies, in this case, machine learning into MLOps for industrial asset
management. The term MLOps was coined by Sculley et al. [
        <xref ref-type="bibr" rid="ref28">28</xref>
        ] in the article titled "Hidden
technical debt in machine learning systems." In this case, the needs of MLOps emerge, i.e.,
machine learning in operations, e.g., a term that is derived from the DevOps for machine
learning. It highlights critical issues in machine learning and the gap from the pilot development
into the actual deployment, which needs to consider many more aspects. This is highlighted in
Figure 1 below. As seen in Figure 1, there is a need to cover several elements to implement ML
successfully into operations in the domain.
      </p>
      <p>
        At the same time, the prerequisite surrounding infrastructure is vast and multifaceted. The
different business needs to organize continuous cooperation and interaction between all
participants in the processes of working with machine learning models, from business to
engineers and Big Data developers, including Data Scientists and ML specialists. MLOps is
important for industries with needs of streaming data processing, such as wind turbines
remaining useful life forecasting. Thus, MLOps provides organizational and business
capabilities, i.e., automation, engagement, insight/decision-making, and innovation [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ]. Hence,
one of the main challenges in connection with Artificial Intelligence and machine learning, in
this case, is that many of the systems are in the experimental phases, and few of them are
deployed in production because of their complexities. Furthermore, deployment entails multiple
factors, such as data and system integration with existing technologies, architectures, and legacy
infrastructure. In addition, modification of business processes and the organizational culture,
adequate employee skills, data engineering, organizational change management, etc. [
        <xref ref-type="bibr" rid="ref29">29</xref>
        ].
Consequently, as a result, the total production deployment is a lengthier process than pilot
projects and has higher costs. It is, therefore, crucial to have a clear strategy, vision, and purpose
for taking advantage of the inherent organizational intellectual skills and material resources
[
        <xref ref-type="bibr" rid="ref29">29</xref>
        ]. Thus, digital transformation and its solutions must be combined with people and a smart
approach to successfully digitalizing the area of interest. Hence, the focus should be on
optimizing maintenance throughout the asset life and based on the operations' needs with
suitable digital solutions.
      </p>
    </sec>
    <sec id="sec-4">
      <title>IV. Creating analytics capabilities for wind farms supported by the</title>
    </sec>
    <sec id="sec-5">
      <title>MLOps approach</title>
      <p>This section outlines the process of implementing MLOps for wind turbines equipped with
sensors on their bearings. Initially, the MLOps framework facilitates the integration of resources
from diverse origins. Additionally, the selection of an appropriate model may vary based on the
source of data. A schematic representation of the MLOps pipeline is provided in Figure 2.</p>
      <p>The reason for monitoring the ML model is to understand how it solves the business
problem. Concerning wind farms, data quality is crucial. Often this data is presented as a time
series. In addition, seasonality may be different for different data sources because wind farms
are situated in different places with various conditions. Despite its "flexibility" in finding
relationships in large datasets, the ML model has many vulnerabilities.</p>
      <p>Therefore, effective monitoring of machine learning models is essential for several reasons.
First, the quality and structure of input data play a pivotal role in the accuracy of the model.
Second, as models evolve, their performance can degrade over time, necessitating consistent
evaluations. Third, there are challenges related to interdependent models and unique pipeline
configurations. Fourth, there may be instances of abnormal values or predictions that the model
has not previously encountered, emphasizing the need for robust outlier detection mechanisms.
Additionally, understanding the model's inner workings and decision-making process is vital,
particularly in contexts where interpretability is crucial. In many scenarios, there's ambiguity
regarding the true values in queries a priori, leading to uncertainty about the precise class or
cluster to which a particular component belongs. Furthermore, the time required for model
computations, potential unavailability of deployment endpoints, alterations in the application's
business logic, susceptibility to cyberattacks, and potential data losses all underscore the
importance of rigorous monitoring. Such considerations are fundamental in ensuring the model's
accuracy and reliability throughout its lifecycle.</p>
      <p>
        In the present study, we analyzed a dataset obtained from a 2MW wind turbine's high-speed
shaft driven by a 20-tooth pinion gear [
        <xref ref-type="bibr" rid="ref30">30</xref>
        ]. Vibration signals, each lasting 6 seconds, were
captured daily over a span of 50 consecutive days. Notably, on March 17, two measurements
were taken and are considered as separate days for this analysis. Over these 50 days, an inner
race fault emerged, leading to the bearing's failure. In its compact form, the dataset has a
measurement time step of 5 days. The Remaining Useful Life (RUL) computed using the
methodology from [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] is utilized as a time series. Various models have been employed for data
analysis, and a novel ensemble has been explicitly introduced for prognostics and RUL
forecasting of wind turbine high-speed bearings. The structure of this research is outlined as
follows:
1. Time Series Analysis: Classic time series models are employed for a primary data
investigation.
2. Data Interpretation Algorithm Development: A novel Data Interpretation Algorithm
for Forecasting Time Series is crafted based on the modified adaptive
monoparameter Braun model. Data is segmented into levels and trends. The Holt-Winters
Exponential Smoothing method, tailored for time series data with both trends and
seasonal variations, is employed. This method facilitates forecasting by leveraging
previously observed weighted changes.
3. Predictive Modeling: Classical predictive machine learning models are utilized
alongside the development of a new ensemble schema. The innovative stacking
model we developed suggests deforming meta-features based on pairwise
multiplication results. These are then integrated with the training dataset in a
metamodel.
4. Result Analysis and MLOps Architecture Development: A comparative analysis of
the results is conducted, leading to the formulation of an MLOps architectural
framework.
      </p>
      <p>Initially, classical time series models are applied. The polynomial trend model essentially
functions as a multiple regression equation, making the methods and procedures of regression
analysis, as discussed in the initial segment of this publication, largely relevant for its
delineation. The AutoRegressive Integrated Moving Average (ARIMA) constructed time series
is illustrated in Fig. 3. It begins with a visualization of the vibration signals in the time domain.
Forecasts are generated for the subsequent five values (depicted by the red line). This
visualization offers forecasted data without any smoothing.</p>
      <p>For time-series forecasts, Root Mean Squared Error (RMSE) measure is used. It is equal to
17.93.</p>
      <p>Next, based on vibration level, RUL is calculated.</p>
      <p>To decrease RMSE, smoothing is proposed. The adaptive mono-parameter Braun model is
used for stationary time series based on simple exponential smoothing:
y ̂_(t+1)=S_t,S_t=αy_t+(1-α) S_(t-1),t=1,2,3,…,
(1)
where y ̂_(t+1) is the prognostic value of time series level in time (t+1), S_t is the exponential
mean, α is the adaptation coefficient, and y_t is the current time series value.</p>
      <p>In this context, the model's value is derived from a weighted average of the current actual
value and preceding model values. This weight is commonly referred to as the smoothing factor.
It dictates the rate at which the most recent observable data point diminishes in influence. A
lower weight ensures that prior model values exert a stronger influence, leading to a smoother
data series. Taking the adaptation coefficient α and the warning period τ, it is necessary to
approximate the series using an adaptive polynomial model.</p>
      <p>The novel method for predictive maintenance of wind turbine bearing is developed in the
paper.</p>
      <p>This method consists of the following steps:
1. Zero-order time series analysis (р = 0);
2. First order time series analysis (р = 1);
3. Assess the accuracy and quality of forecasts;
4. Make a forecast.</p>
      <sec id="sec-5-1">
        <title>The first two steps of proposed method are presented below.</title>
        <p>Step 1.</p>
        <p>The procedure for Step 1 was developed as a sequence of the following steps:
Let y ̂_0= y_0.</p>
        <p>Append array y ̂ using the following formula:</p>
        <p>y ̂_(t )= α*y_t+(1-α)* y ̂_(t-1) ,
where y ̂_(t ) is an actual value, and y _̂(t-1) is the previous number from the prediction array.</p>
        <p>Repeat step 2 for all values in the dataset.</p>
        <p>Step 2.
1. Let x=1, y ̂_0= y_0, l_0= y_0, and .b_0= y_1-y_0, where y is our initial dataset.
2. Define new level value using the formula: l_x= αy_x+(1- α)(l_(x-1)+b_(x-1) ).
3. Define new trend value: b_x=β(l_x-l_(x-1) )+(1-β)b_(x-1).
4. Define our prediction y ̂_(x+1)=l_x+b_x.
5. Define x=x+1 and repeat steps 2-5 until x&lt;n.
(2)</p>
      </sec>
      <sec id="sec-5-2">
        <title>The results of proposed method are given in Table 1.</title>
        <p>The performance of the time series models on the presented testing data is given below:
1. Exponential Smoothing: MAPE is appr. 8.5 %
2. Proposed method: MAPE is appr. 2.2 %
3. Holt's Trend Method: MAPE is appr. 6.6 %
4. ARIMA: MAPE is appr. 3.1 %
5. TBATS: MAPE is appr. 3.2 %</p>
        <p>The Exponential Smoothing model did well by achieving a lower MAPE of 8.5 percent. All
the other models outperformed them by producing lower MAPE. However, the DIAFS model
emerged as the winner based on its test data with MAPE performance, which was close to 2.2
%.</p>
      </sec>
      <sec id="sec-5-3">
        <title>Next, machine learning predictive models are used for data analysis.</title>
        <p>First of all, kurtosis was calculated. The kurtosis measure describes the tail of distribution –
how similar are the outlying values of the distribution to the standard normal distribution? For
example, the standard normal distribution has a kurtosis of 0.</p>
        <p>Stochastic variables and numerous uncertainties can substantially complicate the problem.
To circumvent these challenges, various ensembles are proposed. An ensemble method in both
statistics and machine learning leverages multiple trained algorithms to achieve superior
predictive performance than what could be attained by any single algorithm alone. In contrast to
a statistical ensemble, a machine learning ensemble encompasses a distinct finite set of
alternative models but typically allows for much more flexible structures. The central premise is
to employ fundamentally diverse models to enhance the capability of processing unfamiliar
data. The results derived from regression, KNN, ANN models, and the proposed ensemble of
predictive models were subsequently compared.</p>
        <p>Bagging is an ensemble technique where models are trained in parallel on different random
subsets of the training data. The final decision is derived from the majority voting of the
ensemble classifiers, selecting the class predicted by the majority.</p>
        <p>Boosting involves training an ensemble of models sequentially, where each subsequent
model focuses on instances that the preceding classifier misclassifies. While boosting typically
yields more accurate results than bagging, it can be susceptible to overfitting.</p>
        <p>Stacking involves partitioning the training set into N blocks. N-1 blocks are used to train a
set of base models, while the Nth block, paired with outputs from the base classifiers (referred
to as meta-features), trains another model. One limitation of the traditional stacking approach is
the disparity between the meta-features in the training sample and the actual responses from
specific regressors. In classical stacking, non-overlapping unique values may exist between
training and testing meta-features. Our developed stacking model seeks to address this by
deforming meta-features based on pairwise multiplication outcomes. These transformed
features, combined with the training dataset, feed into a meta-model, mitigating weak predictor
result correlations and enhancing model generalization.</p>
        <p>Regression analysis utilized three condition indicators: RMS, Kurtosis, and E.I. Performance
of each regression model was assessed using RMSE, R^2, and adjusted-R^2. Among the models
tested, SVR, polynomial regression, and a single-hidden layer ANN with 12 neurons emerged
as the superior weak predictors. Conversely, the tuned KNN model underperformed, as shown
in Table 1.</p>
        <p>
          The results derived from our proposed ANN model showcase its capability to predict the
remaining useful life of a bearing, a feat attributed to the synergy between the regression and
ANN models through the optimal condition indicator. The DIAFS model also exhibits
promising results, boasting the highest R-Squared and Adjusted R-Squared values, suggesting
its potential in forecasting novel observations. Although the ANN model provides accurate
predictions and is corroborated by other research [
          <xref ref-type="bibr" rid="ref12 ref16">12, 16</xref>
          ], its performance remains reliant on
the regression model. This dependency underlines why ensemble models typically surpass
standalone ANN models. The second stacking model boasts the lowest RMSE, signifying
minimal residuals. However, its R^2 value doesn't mirror this superiority, underscoring the
necessity of the regression model in optimizing the ANN's predictive efficacy.
        </p>
        <p>In the implemented system, forecasts are pre-calculated using a pre-trained ML model for
incoming data and stored in a dedicated database. Subsequent input requests access this
database for predictions. Architecturally, this mirrors the Lambda pattern, blending "hot"
realtime data processing with "cold" historical data processing, typically residing in a Data Lake on
Apache Hadoop (Fig. 4).</p>
        <p>The Lambda Architecture encompasses both a conventional batch data pipeline for
faststreaming real-time data and a serving layer designated for query responses. Ingressed batch
data populates a batch layer, prepping it for indexing. Several pre-trained ML models then
analyze this data concurrently. The models listed in Table 1 are incorporated. The serving layer
facilitates the pre-result voting process, selecting the best model or a suitable combination for
the given data. The selected model subsequently processes incoming stream data.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>5. Conclusions</title>
      <p>This research introduces a predictive model rooted in MLOps methodology to determine wind
turbine bearings' Remaining Useful Life (RUL). The model efficiently detects degradation
patterns in real time, adjusting its parameters in response to new data, and offers a fully
automated configuration, enabling its deployment across multiple wind turbines. As such, it
emerges as an indispensable tool for condition-based maintenance.</p>
      <p>Our ensemble stacking model, incorporating regression, SVR, and random forest techniques,
has demonstrated commendable generalization capabilities. The model's effectiveness is
underscored by its proficiency in leveraging condition indicators, which were appraised using
criteria like monotonicity and trendability.</p>
      <p>The incorporation of MLOps in this research has facilitated the following: Enhanced
innovation through holistic machine learning lifecycle management; Reproducible and robust
model iterations tailored for enterprise settings; Efficient tracking using advanced dataset and
model registries; Improved traceability and accountability through detailed logging;
Streamlined model workflows ensuring consistent delivery; Generation of unbiased models
emphasizing feature importance, assessed using uniform distribution metrics.</p>
      <p>Our research further proposes new model for monitoring wind turbine bearing conditions.
DIAFS's adaptability, anchored in an adaptive polynomial model, facilitates real-time
refinement, promising accurate and timely predictions. This algorithm not only refines the
precision of forecasting but also augments maintenance strategies. Through DIAFS, potential
issues can be preemptively identified, optimizing resource allocation and reducing operational
downtimes. Such a data-driven approach, focusing on empirical evidence, leads to significant
cost savings, increasing wind turbines' overall efficiency and lifespan. Furthermore, the
scalability inherent to DIAFS ensures its applicability within the expanding world of wind
energy.</p>
      <p>While the primary application of the ensemble model is in wind turbines, its adaptable
architecture ensures relevance across varied industrial maintenance scenarios, such as managing
Rolling Element Bearings (REBs) failures. Beyond the technical abilities mentioned above as a
digital transformation driver, this study recognizes the pivotal role of workforce adaptation to
these evolving digital tools.</p>
      <p>Lastly, future research will focus on adapting the developed models to analyze raw data in
real time. Additionally, it would be interesting to extend the MLOps pipeline to facilitate
realtime monitoring of wind turbines, thereby enabling faster fault detection and the potential
implementation of predictive maintenance strategies.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <sec id="sec-7-1">
        <title>The paper was prepared as part of H2020 project ZEBAI, # 101138678</title>
      </sec>
    </sec>
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