## 7 Conclusions  
Traditionally, condition-based monitoring (CbM) of electric and rotating machines has focused heavily on two primary areas, the _detection_ and the _diagnosis_ of fault modes. More recently, research efforts have investigated the more challenging area of _prognosis_ to determine the remaining useful life (RUL) of the machine under test. This paper introduced a valuable machine learning (ML) approach to estimate the RUL of rolling element bearings, which are a core component of rotating machines.  
The proposed ML recipes and approaches comprise of signal processing techniques and ML algorithms applied to real-world vibration signals, which were acquired from the outer-race of bearings degraded over time using an accelerated ageing test-rig. The paper reports the results for linear and non-linear wear-state models using novel feature engineering derived from Short-Time Fourier Transform (STFT) and Envelope Analysis (EA) representations. In addition, two different classification algorithm approaches, \(k\)-Nearest Neighbour (\(k\)-NN) and Support Vector Machines (SVM), were investigated and compared.  
This work achieved classification accuracy results of up to 74.3% with a mean absolute error (MAE) of 0.08, which demonstrates the method's efficacy for performing the task of RUL. This ultimately offers a robust and low complexity approach that is highly valuable for advanced predictive maintenance purposes in industry.  
The following section details the contributions made by each author to the research that was presented in this journal article submission: E.T.C.: Formal analysis, Methodology, Investigation, Writing--Original Draft and Writing--Review and Editing; V.I.M.: Supervision, Analysis, Results interpretation, Writing--Review and Editing and Visualization; D.F.K.: Supervision, Formal analysis, Methodology, Analysis, Results interpretation, Writing--Review and Editing, Plotting and Visualization. All authors have read and agreed to the published version of the manuscript.  
The research conducted in this publication was funded by the Irish Research Council under award number GOIPG/2021/1744. All authors are with the Faculty of Engineering, Institute of Technology Carlow, Ireland.  
Not applicable.  
Publicly available datasets were analysed in this study. This data can be found here: ([[https://ti.arc.nasa.gov/tech/dash/groups/pceo/prognostic-data-repository/#bearing](https://ti.arc.nasa.gov/tech/dash/groups/pceo/prognostic-data-repository/#bearing)]([https://ti.arc.nasa.gov/tech/dash/groups/pceo/prognostic-data-repository/#bearing](https://ti.arc.nasa.gov/tech/dash/groups/pceo/prognostic-data-repository/#bearing)), accessed on 11 March 2022), also see [62].  
The authors declare no conflict of interest. The Institute of Technology Carlow have endorsed this manuscript to go forward for peer review and publication. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ADC & Analogue-to-digital converter \\ ANN & Artificial neural network \\ CBM & Condition-based monitoring \\ DFT & Discrete Fourier transform \\ EA & Envelope analysis \\ EMD & Empirical mode decomposition \\ FFT & Fast Fourier transform \\ FIR & Finite impulse response \\ \(k\)-NN & \(k\)-Nearest neighbour \\ LSTM & Long short-term memory \\ MA & Moving averaging \\ MAE & Mean absolute error \\ MCSA & Motor Current signal analysis \\ ML & Machine learning \\ RUL & Remaining useful life \\ STFT & Short-Time Fourier transform \\ SVM & Support vector machine \\ WT & Wavelet transform \\ \end{tabular}