# Application of Machine Learning to Express Measurement Uncertainty
## 4 Conclusions  
In this paper, the authors presented a novel \"judgmental\" approach to evaluating the measurement uncertainty of the machine learning model that implements the DART algorithm. The considered method uses the procedure for expressing the type B measurement uncertainty and the maximal value of the empirical absolute loss function of the model. It is related to the testing and monitoring of power equipment and determining partial discharge location by the non-iterative, all-acoustic method. The example uses the dataset representing the correlation of the mean distance of partial discharge and acoustic sensors and the temperature coefficient of sensitivity of the non-iterative algorithm.  
The proposed procedure for uncertainty expression is straightforward and uncomplicated to implement. The results showed that most predictions (>97%) fell into the standard measurement uncertainty interval for both \"seen\" and \"unseen\" data. The advantage of employing the type B measurement uncertainty is that it uses the available data without needing additional optimization (even one input-output pair is sufficient).  
The limitation of the proposed method is that it is applicable only in supervised learning regression techniques. Additionally, the method did not consider other sources of the type B measurement uncertainty of the ML model, such as inadequate rounding of predicted values by the ML model, CPU calculation uncertainty, actuator measurement uncertainty, etc.  
Further research will focus on applying the proposed procedure in various situations and datasets.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Quantity** & **Estimate** & **Standard Uncertainty** & \
\begin{tabular}{c} **Probability** \\ **Distribution** \\ \end{tabular} & **Sensitivity Coefficient** & **Uncertainty Contribution** \\ \hline \(l_{sr}\) &
\begin{tabular}{c} Predicted value by \\ the ML model \\ \end{tabular} & 0.06 m & Uniform & 1.0 & 0.06 m \\ \hline \hline \end{tabular}
\end{table}
Table 2: The example of the row layout in the measurement uncertainty budget of a non-iterative algorithm would correspond to the use of the ML model to estimate \(l_{sr}\).  
**Author Contributions:** Conceptualization, V.P. and B.N.; Data curation, V.P. and U.K.; Formal analysis, V.P. and U.K.; Investigation, V.P. and T.A.R.; Methodology, V.P., U.K., N.B. and S.S.; Resources, V.P. and U.K.; Software, V.P. and S.S.; Supervision, B.N.; Validation, N.B., T.A.R., S.S. and B.N.; Visualization, N.B. and T.A.R.; Writing--original draft, V.P., N.B., S.S. and B.N. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was financially predominantly supported by the Science Fund of the Republic of Serbia, grant no. 6526093, AI-AVANTES (www.fondzanauku.gov.rs accessed on 23 August 2022).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The simulation data presented in this study are available in FigShare at [[https://doi.org/10.6084/m9.figshare.20401953.v1](https://doi.org/10.6084/m9.figshare.20401953.v1)]([https://doi.org/10.6084/m9.figshare.20401953.v1](https://doi.org/10.6084/m9.figshare.20401953.v1)) accessed on 23 August 2022. All other data presented in the study are available on reasonable request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.