ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
6 NO.
MAY-2026
Available online at: http://ajet.
Andalas Journal of Electrical and Electronic Engineering Technology ISSN 2777-0079 Remaining Useful Lifetime Prediction of Distribution Transformer Using Dynamic Multi-Scale Attention-based CNN-LSTM Elvis Tamakloe.
Benjamin Kommey.
Jerry John Kponyo.
Daniel Opoku.
Francis Boafo Effah Faculty of Electrical and Computer Engineering.
College of Engineering.
Kwame Nkrumah University of Science and Technology.
Kumasi, 00233.
Ghana
ARTICLE INFORMATION
Received: February 17, 2026
Revised: March 15, 2026
Accepted: March 31, 2026
Available online: May 31, 2026
KEYWORDS
Transformer degradation.
RUL.
Dynamic Multi-Scale Attention.
Data-driven predictive maintenance.
Oil-immersion CORRESPONDENCE Phone: 00233507703286 E-mail: bkommey.
coe@knust.
A B S T R A C T
Oil-immersed transformers are critical assets in the energy industry linking most power utilities to end-users.
Their failure results in prolong outages, leading to huge revenue loss incurred during downtimes and replacement cost.
In extreme cases, transformers in an unhealthy state poses a significant threat to the safety of grid operators.
Interestingly, traditional reactive and preventive methods have been inefficient in determining when legitimate maintenance actions are due, often leading to either early over-maintenance of healthy transformers or late undermaintenance of serviceable and unhealthy transformers.
Predictive maintenance based on determining the remaining useful lifetime (RUL) acts as an actionable step that resolves these challenges by delivering exactly the most appropriate time to undertake maintenance whiles ensuring optimal utilization of resources which saves maintenance cost, reduces downtimes and ensures operator safety and grid reliability.
This work proposed an advanced Dynamic MultiScale Attention (DMSA) model and leverages on multi-modal data fusion from electrical, mechanical, thermal, and environmental sources to provide an improved data-driven solution for accurate prediction of the RUL of distribution transformers.
This technique addressed the drawbacks of employing single modality approaches in capturing complex operational In this work, dynamic scaling model is incorporated to adaptively adjust the attention weights based on the importance of the input features.
For short term predictions, the proposed model experimentally achieved an enhanced performance of 0.
2300 mean absolute error and 0.
9872 coefficient of determination value.
Additionally, the DMSA CNN-LSTM model demonstrated accurate prediction, evidenced by a concordance correlation coefficient value of 0.
These statistical gains were achieved in a computational time of 587.
demonstrating superior scalability in the event of real time deployment.
Furthermore, the longterm prediction was performed using Prophet to fit the data which predicted a RUL of 25 years at 95% confidence interval which corresponded with the reference standard in Ie STD C57.
INTRODUCTION
Maintenance of distribution transformers have played a central role in their management and particularly in ensuring reliable power delivery at economical voltages .
Continuous operation and exposure of distribution transformers to stressors without proper maintenance reduces their performance and accelerates their deterioration over time especially in events of undetected failures .
This unpleasant outcome if left unchecked leads to severe service interruptions, high outages, maintenance downtime and cost.
Thus, to make correct informed decisions regarding the proper management of distribution transformers, it is of utmost necessity to know their remaining useful lifetime (RUL).
This is essential in order to facilitate decisions on transformer maintenance, injections and replacement .
Conventional reactive and preventive practices .
eriodic inspection, schedule maintenance and condition monitorin.
have provided an incomplete understanding of the health of transformers in service.
This shortcoming results in inaccuracies of knowing exactly how long a transformer can https://doi.
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continue operating safely.
RUL addresses this limitation by estimating the time left before the transformer reaches a failure point or an unacceptable level of operation.
In view of this, math or physics-based models were developed to resolve this problem and predict the RUL of transformers using physical properties .
However, this method requires an in-depth domain knowledge to sufficiently model the complex interaction in distribution Furthermore, it is less adaptable to variable transformer operations and requires manual adjustments or calibration which limits the accuracy of their prediction .
The progress in ML and AI has reshaped the terrain of predicting the RUL more accurately compared to physics-based techniques by leveraging on historical operational data sampled from sensor measurements .
In the quest to achieve better performance, several DL models have employed hybrid techniques and incorporated a variety of attention mechanisms in their respective architecture to capture complex machine degradation.
This is intended to capture the intricate dependencies and focus on relevant features that contribute to the deterioration of the transformer in order to make accurate predictions of their RUL ELVIS TAMAKLOE / ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
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The enhanced performance of neural networks models has been attributed to the integrating of an attention mechanism.
However, several types of attentions mechanisms exist and their applications in neural networks vary based on the task requirement, model architecture, and its computational efficiency .
In reference to predicting the RUL of distribution transformers, most deep learning models are unable to captured complex deterioration across different time scales typically in situations where the feature importance varies.
Although the adoption of multi-scale attention mechanism enables DL models focus on the relevant features contributing to transformer deterioration, their performance is suboptimal since they apply fixed weights and are unable to re-weigh vital features to identify sudden changes .
Considering the economic value and productive time that is lost as a result of damaged in-service power transformers, it is imperative to accurately predict the end of useful life in order to put in place the right contingency plans for maintenance action.
This enables proper asset management by making informed decisions at the right time .
Due to aging and fault stress levels, the RUL of power transformers can be thoroughly mapped using features acquired non-intrusively in the data acquisition phase .
, .
This work proposed an innovative DMSA CNN-LSTM model to resolve the problem and improve the accuracy of predicting the RUL of distribution transformer for efficient health management.
proposed an advanced CNN-LSTM model to tackle inaccurate RUL prediction.
The model comprises a multi-level 1D CNN layer and a stacked multi-layer LSTM for extracting deep spatial and time-dependent features, respectively.
That is, the 1D CNN is used to process convolutions along the two dimensions of the input data.
With a time-window ranging from 15-30 and a convolution kernel size of 3 to 7, the input data is processed and transferred into the LSTM network.
The stacked multilayer LSTM network employed dropout regularization to prevent overfitting during training.
Thus, the identified feature vectors from the processed data are transferred to the fully connected layers for prediction.
The model was subsequently trained on 60 iterations with a learning rate set at 0.
01 and tested accordingly to verify its performance by evaluating both the scoring function and the RMSE value.
A root mean squared error value of approximately 18.
2084 was recorded on the test set.
This implies that nearly 18.
2% of error was identified between the actual and predicted values, which suggests a good performance.
However, the scoring results were not provided, and the modelAos performance was not benchmarked.
Although the authors claimed to have conducted a comparative assessment with other traditional data-driven models, no result was shown.
Additionally, the type of dataset used in this experiment was unknown and the issue of data imbalance was not extensively Reducing the estimation error and time is critical for models developed as solutions for estimating the RUL of power In efforts to improve the model performance, .
proposed a Bayesian neural network that evaluates power transformers based on a variety of features.
In achieving this, actual data from about 500 transformers were collected at different periods and external conditions.
The sampled data was preprocessed using wavelet transform (WT) to minimize errors inherent in the dataset.
That is, a scale parameter is employed in this case without the need for a frequency parameter as observed in Fourier transforms.
The resulting features are used as inputs to https://doi.
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train and validate the Bayesian neural network.
Principal Component Analysis (PCA) was primarily utilized to reduce data dimensions which is central for weighting to ensure the best The proposed model achieved a classification accuracy of about 98.
4%, implying that nearly 98% of instances were correctly classified by the model.
This result indicated superiority as compared to other supervised learning models like the KNN.
SVM, and multi-layer perceptron neural network (MLPNN) which achieved accuracies of approximately 92%, 93%, and 96.
4% respectively.
Thus, about 1.
6% of the instances were incorrectly classified, which suggests a reduced error rate compared to the counterpart models.
Although the model recorded a high accuracy, using this metric alone does not fully represent the model's overall performance.
Thus, the F1 score, recall, precision, and hamming loss values were not accounted for and making this work inclined towards classification rather than Furthermore, expressing RUL in the time domain rather than in percentage is more appropriate given the above In .
, two back propagation neural networks (BPNN) models were developed to forecast the degree of polymerization (DP) of a transformer cellulose paper and predict the loss of life (LOL) of the transformer.
This approach utilized concentration data of 2-Furaldehyde .
FAL) collected from dissolve gas analysis (DGA) of the transformer oil.
Based on the forecast result of the DP together with the 2FAL data obtained from the first BPNN algorithm, the LOL was then predicted using the second BPNN algorithm.
The later model achieved a MSE value 58 and correlation coefficient of 0.
Considering this performance, the authors highlighted the success of the model.
However, the high MSE value recorded at the 5 epochs suggests a high difference or variance between the actual and predicted Moreover, the correlation coefficient value of close to unity suggests a high performance between the actual and predicted values.
These two metrics conflicts an in-depth assessment of the performance.
Thus, more metrics are required to comprehensively evaluate the performance of this approach.
Numerous studies have also focused on combining integral sources to predict the loss of life of transformers based on the oil insulations .
However, the models in these studies require extensive multi-modal data to capture intricate details to enhance its predictive performance.
To improve the predictive performance, .
proposed a multi-task model that combined LSTM and GRU models.
After training on an entire dataset that included dissolve gases and oil quality of the transformer, the result revealed a MSE.
MAE.
R2-score and a MedAE of 2.
1346, 0.
985, and 0.
0284 which suggests a significant improvement over other combinations of DL architecture and conventional single regression and ensemble algorithms.
Additionally, the work utilized Shapley Additive Explanations (SHAP), an explainable AI tool which provided a global and instance-level details on features that predominantly influenced the outcome of the modelAos prediction.
Howbeit, numerous iterations over large number of epochs were required to train the model considering the computational resources used in the work.
Furthermore, authors did not sufficiently address the case of data imbalance with regards to their data acquisition system and during preprocessing.
To achieve an equal performance using optimal resources, .
utilized a Support Vector Machine (SVM) to determine the condition of the cellulose insulation in order to estimate the remaining functional lifetime of the transformer.
Although this approach achieved more than 95% accuracy in ELVIS TAMAKLOE / ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
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classifying conditions of the insulation using a variety of SVM models, it nonetheless, did not explicitly describe how this was employed to determine the RUL of the transformer which is a regression study.
METHOD
DL based RUL Estimation Framework Figure 1 presents a prognostic architecture that predicts the duration the transformer in service can continue to effectively operate before failure or breakdown threshold is reached.
The objective of this approach is to estimate this duration based on the features extracted from the transformer data in order to know when to perform maintenance.
Hence, the preprocessed data is used to train the DMSA-based CNN-LSTM model to analyze this regression task using Python.
Figure 1.
DL based RUL Estimation Framework.
After rigorous training, the model is evaluated and its hyperparameters are well-tuned to provide the most suitable result required to accurately predict the RUL of the power The results obtained from this stage are visualized to graphically determine the correlation between the predicted and true .
RUL values.
The goal is to observe possible cases of under-or-over prediction patterns which gives insight into the modelAos performance and discrepancies.
Numerical values of the prediction are then used to make informed decisions with regards to maintenance scheduling either on short-term or long-term Hence, the integration of several features through multimodal data fusion provides a comprehensive platform for accurately predicting transformer RUL.
This is ultimately vital for extending transformer life and enabling reliable power supply.
To a greater extent, by leveraging on the DMSA mechanism offered by the proposed model, the relevant features across the respective time scales .
hort and lon.
are adaptively prioritized to improve the interpretability.
This implies that features with more weights in the modelAos predictions provide insights into the main features influencing the health of the transformer which depicts its RUL.
DL DMSA based CNN-LSTM Block Oil-immersed distribution transformers are complex electrical machines and adopting predictive maintenance offers a huge opportunity to improve their reliability in the power system for a longer period.
However, developing very accurate and robust predictive maintenance models to ensure a comprehensive diagnosis and prognosis of transformers require not only the use of multi-modal datasets but also on the algorithm that handles the associated complexities.
In this work, a DMSA mechanism as presented in Figure 2 was introduced as an innovative and novel approach in an ensembled CNN-LSTM model to capture both the short and long-term dependencies within the complex multimodal dataset.
https://doi.
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Figure 2.
DL based DSMA CNN-LSTM Block.
In contrast to traditional attention mechanisms, the developed approach incorporates dynamic scaling, enabling the model to adaptively assign weights to both short and long-term temporal This is done in response to changing transformer The design allows the model to selectively emphasize the most valuable time scale during anomaly detection while preserving a broader temporal context for accurate RUL A hybrid CNN-LSTM block is employed, where the CNN component extracts spatial features from the composite multimodal dataset.
The LSTM component models temporal dependencies with the data given its sequential nature.
This combination effectively learns both steady-state and transient behavioural patterns.
The blocks are specifically structured to consist of two 1-D convolutional layers and two LSTM layers with each followed by a 1-D maxpooling layer.
Utilizing 64 and 128 units, a progressive configuration was chosen for the respective CNN and LSTM blocks.
The CNN block employs a kernel size of 3, while a pool size of 2 is used in the maxpooling The output of the final CNN maxpooling layer serves as input to the LSTM block.
The DL based DMSA mechanism is then applied to the LSTM output for adaptive temporal weighting and enhanced predictive capability across multiple timescales.
Figure 3.
Developed DMSA structure The developed DMSA structure shown in Figure 3 is designed to model both short and long-term temporal dependencies as This is accomplished through two complementary attention modules.
One is precisely focused on short-term patterns and the other on long-term sequence data.
In the shortterm attention branch, the input is passed through a single-unit dense layer with a hyperbolic tangent .
activation function.
The resulting output is flattened, and a softmax activation is applied to determine the relative significance of each time step.
The attention weights are repeated across the LSTM units and permuted to match the input dimension, generating an attention weighted representation that projects the short-term dynamics.
The long-term attention mechanism is implemented whereby attention scores are found to take into account broader temporal dependencies in the data.
The attention weights from both short and long-term branches are multiplied element-wise with the ELVIS TAMAKLOE / ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
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corresponding inputs to enhance the most informative features.
The dynamic scaling factor is implemented using two separate lightweight single-unit dense layers with each activated with a tanh-function.
This is to regulate the contributions derived from the attention blocks based on computed scaling coefficients.
The scaling coefficients are multiplied with the respective attention The dynamically scaled attention outputs are combined through element-wise addition to give the unified feature map for the two fully connected layers.
Unlike standard multi-scale attention that applies static or fixed weights and lacks temporal state awareness, the innovation of dynamically scaled attention output enables the model to adaptively reweight the multi-scale temporal features in response to changing transformer condition.
This is derived from the evolving LSTM hidden state which gives the DMSA continuous temporal awareness given the heterogenous nature of transformer data In this manner, accurate RUL prediction in the transformer is captured by emphasizing on the most relevant and informative temporal patterns.
Imperatively, yu is the threshold loss parameter controlling the transition between the MSE and MAE.
Hence, the loss function transitions to MSE given that .
cycnA Oe ycCycn | is small and MAE provided that .
cycnA Oe ycCycn | is huge .
Process Flow Diagram of the RUL Framework The process flow diagram in Figure 4 predicts the continuous RUL of the transformer based on the learned features from the data provided.
This represents a structured regression task where the fused multi-modal data is preprocessed, and the relevant features are extracted accordingly via the data preprocessing and feature extraction stages.
Analytical Representation RUL framework The proposed attention mechanism is applied to enable the model to focus on the significant parts of the transformer data.
To do so, an attention score .
uyc ), attention weights .
uAyc ) and context vector .
are computed using equations .
, .
, and .
This provided the innovative base for this workAos contribution.
yuyc = yc ycN ycycaycuEa.
cOEa Eayc ycaEa ) yceycuycy.
uyc ) .
yuAyc = OcycN yua = OcycNyc=1.
uAyc Eayc ) .
yc = ycycaycuEa.
cOyc Eayc ycayc ) .
yco=1 yceycuycy.
uyc ) The dynamic scaling factor .
is computed accordingly and applied to the context vector to obtain a dynamically scaled result or effective context vector .
uayce ).
This incorporates the individual context vector for the short-term .
uaycEaycuycyc ) and long-term .
uaycoycuycuyci ) as expressed in the following equation:
yuayce = yc Oo .
uaycEaycuycyc yuaycoycuycuyci ) .
Thus, yuayce is then forwarded to the dense layer for final prediction as represented in the equation .
yc = .
cOycuycyc Oo yuayce ycaycuycyc ) .
To predict the RUL which is a regression task, the output and the loss function .
ayu A ) were set accordingly.
Here, linear activation function is employed in the output layer and Huber loss function is used to reduce the difference between predicted and actual target values as expressed in this Equation 7 by leveraging on the merits of MSE and MAE to address the impact outliers that influence the performance of the model .
, .
c A 1 ycA 1 cycnA Oe ycCycn )2 .
c A OeycC |Oyu ycA ycn=1 2 , ycC) = { 1 , .
cycnA OeycC yc.
>yu ycA Oc yu (.
cycn Oe ycCycn | Oe y.
ycn ycn ycA ycn=1 https://doi.
org/10.
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Figure 4.
Process Flow of the RUL Prediction Framework Here, degradation trends that impact the lifetime of the transformer are effectively identified with the innovative proposed DMSA mechanism.
This is achieved through the modelAos adaptive focus on the short-term or long-term patterns.
The model compilation and training are realized with regressionbased loss function .
ean squared erro.
, and metric .
ean absolute erro.
The decision block determines whether the trained model requires further adjustment based on its performance validation.
A AuyesAy means further optimization is required and a AunoAy suggests additional retuning is not required.
The final stage of the flowchart constitutes three different processes that emphasize model evaluation, prediction and error analysis of the predicted RUL.
Therefore, the proposed prognostic approach does not only depict the accuracy of the predictions but also ensures interpretability.
Thus, the attention score of the most vital features and time scale that immensely ELVIS TAMAKLOE / ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
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contribute to the RUL are understood to aid in timely decision making in the phase of maintaining the transformer.
Data Description and Handling To predict the RUL of a power transformer requires a thorough understanding of the trend, patterns and dependencies in the The dataset used in this work represents both electrical and environmental data sampled from a 100kVA rated ONAN distribution transformer at 1s and 15min interval respectively for nearly 10 months .
Thermal DGA data from .
, .
mapped internal condition of the oil insulation.
This means that similar degradation pattern of the oil insulation exist for transformers with same characteristic and operating conditions .
Featured engineered mechanical vibrations from the current data provided unique contribution highlighted in .
Early fusion was then applied to combine all the modalities into a unified dataset to inherently retain all the original information .
, .
Missing values and outlier were treated and a StandardScaler was then used to normalize the data.
The unified dataset was then divided into 64% training, 16% validation and 20% testing set to ensure representation and robust evaluation.
In the data exploration phase, all conditions were set as features including the health index and the RUL was dedicated as the target or label.
A visual distribution of all the respective features is illustrated in a histogram plot in Figure 5 and a summary of the dataset provided in Table A1 .
ee appendi.
was observed between June 2019 to August 2019 signifying an initialization period due to initial commencement and adjustments in the operating conditions.
From August 2019 onwards, no great variations were recorded as a steady RUL value stood at about 32 years.
However, the slight dips and rises in the RUL under this stable period stemmed from the small variations in the operational features visualized in the composite dataset.
RESULTS AND DISCUSSION
Performance of RUL Prediction or Estimation Model.
The proposed DMSA CNN-LSTM RUL prediction model was trained, tested and validated over a stipulated number of epochs using the new preprocessed composite data.
The paramount objective of the model is to accurately predict or estimate the RUL of the transformer based on the historical data in order to prioritize maintenance actions thereby facilitating efficient asset As discussed in the preceding subsection.
RUL prediction is a prognostic task and in this case the performance of the model is evaluated using standard unique regression metrics .
Table 1 presents the outcome of the proposed model compared with other baseline DNN models.
Table 1.
Initial result of the DMSA CNN-LSTM model against
other DNN models on default parameters MAPE
(%)
c R2score Compt.
Model
MAE
RMSE
Data Investigation before RUL Prediction Assessment
CNN
In this Figure 5, each subplot represents the individual features plotted against the frequency and value on the y-axis and x-axis This is critical to unearth the underlying patterns in the data in order to improve the performance of the DMSA CNNLSTM model for predicting the RUL of the transformer.
The plot reveals that the individual voltage and current features were skewed towards the right with some high values although some values are concentrated on the lower axis.
Other features including the power factor showed narrow distribution indicating that majority of the transformerAos operation are within a normal Moreover, peaks in the fault gases imply a corresponding degradation of insulation materials.
Furthermore, the visualization of the health index provided a holistic representation of the transformerAos health.
Based on this reference, targeted maintenance strategies can then be applied to facilitate in the identification of early signs of abnormalities.
Before that, it is imperative to know that by analyzing how these features affect each other, the proposed model can then effectively and adaptively learn which duration or time scale is essential for predicting the RUL of the transformer.
That is, the variation in the time-series data shows the significance of having both the short-term and long-term attention mechanisms in the model to deal with the complex patterns that results.
Thus, abrupt fluctuations in some features .
emperature or gas concentration.
are addressed with the short-term attentions whereas more slowly evolving changes .
ike gradual rise in water content and gradual depletion of the insulatio.
are captured with the long-term attention mechanism.
Therefore, by visualizing these features, the most influential features that adversely affect the life expectation of the distribution transformer is identified.
A line plot of the life expectation (RUL) is presented over the period (Year_Mont.
See Figure 6 in appendix.
An initial increase in life expectation LSTM
GRU
CNNLSTM
MSA
CNNLSTM
DMSA
CNNGRU
DMSA
CNNLSTM
The performance of these respective models was obtained given a batch size of 32, 50 epochs, a default learning rate of 0.
001 with an Adam optimizer and a default threshold loss parameter .
of Therefore, this table presented the best performance relating to the mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2-scor.
, mean absolute percentage error (MAPE), concordance correlation coefficient .
and computation time required by the model.
The said metrics used in the evaluation process of the model were computed based on their individual unique analytical contributions as given in Equations .
, .
, .
, .
, .
ycAyaya = ycA OcycA Cycn | ycn=.
ycycn Oe yc ycIycAycIya = OoycA OcycA Cycn ) ycn=1.
cycn Oe yc https://doi.
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25077/ajet.
OcycA Cycn ) ycn=1.
cycn Oeyc ycI2 ycycaycuycyce = 1 Oe ycA ycA Ocycn=1.
cycnA OeycI) .
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ycAyaycEya (%) = ycA c OeycCycn | ycn OcycA ycn=1 ( 2yuUyua yua yayaya = ycycn Cycn ycAycn yc yua A yuaycC .
uNycA OeyuNycCycn ) ycycn ) y 100 the DMSA CNN-LSTM architecture resulted in a holistically better performance compared to any of the said DNN models.
yaycuycoycyycycycaycycnycuycuycayco ycycnycoyce .
= ycyceycuycc Oe ycycycycaycyc .
In these equations, ycycnA , ycCycn , ycI, and ycA represent the actual, predicted, mean of the actual value, and the total number of samples present in the dataset respectively.
Furthermore, the variance and means of the actual and predicted values are denoted by yua and yuN Additionally, yuU indicates the Pearsons Correlation Coefficient .
r PCC) which is a measure of the linear correlation between the two variables.
Imperatively, the choice of these performance metrics is to provide a thorough evaluation of the modelAos ability to accurately predict the life expectation of the distribution transformer.
The results of the individual models in Table 1 shows that using DL models achieves more than 97% R2 score in predicting the RUL.
Evaluating the performance in the table, the DMSA CNN-LSTM model recorded the second lowest overall MAE of 0.
2520, and MAPE of 1.
5985 surpassing all the baseline models except the DMSA CNN-GRU model which is used in this ablation study.
A lower MAE value is desirable as it indicates minimum prediction errors.
Additionally, it achieved the second lowest RMSE value of about 1.
4921 after the GRU which obtained a value of 1.
This outcome suggests the proposed modelAos capability in effectively predicting the RUL of the transformer with less deviations from the actual values.
Moreover, a computation time of 595.
2953s indicates the proposed modelAos scalability in efficiently utilizing the available computational resource thus ensuring its real-time application in practical scenarios.
Interestingly, aside the MAE.
MAPE and computational time, the baseline GRU model performed slightly ahead of the DMSA CNN-LSTM model in terms of the R2 score, and c performance metrics indicating slightly better correlation with the true or actual values of the RUL.
Notably, the closer the metrics are to a value of 1, the better the performance of the model.
The ensembled CNN-LSTM model achieved the highest RMSE value of 1.
8826 which is undesirable since it produces the largest deviations between predicted and actual It also has the lowest R2 score of 0.
9774 suggesting the least correlation compared to its counterpart models.
Though this result is below the proposed model, it is however achieved with a slightly lower computation time of 425.
The MSA CNNLSM.
LSTM and CNN models obtained an R2 score of 0.
9804, and 0.
9806 with comparatively good c values of 9913, 0.
9899, and 0.
9896 respectively.
Evidently, the CNN model produced the minimum overall computation time of 6341s while recording the highest MAE and MAPE values 0236 and 4.
4959 respectively.
Comparing the results between the DMSA CNN-LSTM and DMSA CNN-GRU architecture, it is noticeable that the former generally performed better on four critical evaluation metrics which includes the RMSE, c.
R2 score, and computational time than the latter.
this context, the statistical significance of the proposed model obtained about 11.
3%, 0.
39%, 0.
20% and 7.
9% improvement in terms of RMSE.
R2 score, c and computational time respectively over the DMSA CNN-GRU model.
From this perspective, it is largely important to highlight that leveraging on https://doi.
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Figure 7.
Initial Training and Validation loss and MAE curves of the proposed RUL model on default parameters The learning outcome of the proposed RUL model was visualized over 50 epochs of the training and validation process as shown in Figure 7.
In this figure, both the training and validation loss decreased substantially as the number epochs .
In other words, the training loss decreased smoothly from over 2.
00 and eventually a value close to 0.
The validation loss fluctuated in the early stages of the training process from 1.
37 and finally stabilized to approximately 0.
This graphical outcome shows that the model learned effectively on the training data and partly generalized well on the validation data despite some degree of recorded fluctuations.
Similar to the training loss, the training MAE of the DMSA CNN-LSTM model reduced gradually and steadily as number of epochs increased indicating consistent learning for improved predictions.
Unlike the training MAE, the validation MAE experienced an unsmooth downward trend with pronounced fluctuations over the epochs.
To improve the performance of the proposed model, hyperparameter tuning was applied and the result was compared with the individually tuned baseline DNN models.
Table 2 highlights the hyperparameters applied to achieve the improved performance of the DMSA CNN-LSTM model in Table 3.
Table 2.
Tuned hyperparameter elements in the RUL prediction Hyperparameter Value /Designation Loss function r Huber Threshold parameter .
Optimizer Adam Learning rate Batch size Epoch Table 3.
Result of the DMSA CNN-LSTM model against other DNN models on hyperparameters MAPE
(%)
c R2score Compt.
Model
MAE
RMSE
CNN
LSTM
GRU
CNNLSTM
MSA
CNNLSTM
DMSA
CNNGRU
DMSA
CNNLSTM
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Analyzing the result of the various hyperparameter tuned models in Table 3 suggests that the DMSA CNN-LSTM model outperforms its counterpart by achieving the lowest error rate of 2300 MAE value whiles realizing a robust generalization with high R2 score and c value of 0.
9872 and 0.
9936 respectively.
Furthermore, the MAPE value of 1.
8205% .
he second lowest valu.
achieved by the model demonstrates minimum relative error which implies high accuracy.
Considering a tradeoff between computational efficiency and overall model performance, although the DMSA CNN-LSTM model achieved a computational time of 587.
3387s which is appreciably higher 3042s and 432.
2007s recorded from CNN and CNNLSTM models respectively.
However, it is significantly faster than the baseline LSTM and GRU models.
Analytical study of the results on both the DMSA CNN-LSTM and DMSA CNN-GRU architecture shows that utilizing the LSTM as the backbone of the proposed model achieved the lowest errors values, and fit better with stronger agreement between predicted and actual RUL Moreover, the faster computational time recorded with the proposed model suggests approximately 5% edge over the GRU supported DMSA architecture.
This outcome reveals that the simplified gating inherent in the GRU combined with the DMSA architecture made it less suitable for real-time deployment especially given the involvement of much longer sequences within the data.
A chronological approach was introduced to find the most suitable optimizer in the hyperparameter tuning stage.
On this ground, the proposed model was trained on the Adam.
AdamW.
Nadam.
Root Mean Squared RMSprop, and Adadelta optimizers with a default learning rate of 0.
001 respectively.
Table 4 presents the result of these five optimizers after training on 50 epochs and 32 batch sizes.
Table 4.
Performance of proposed model on different optimizers RMSprop R2score Compt.
Adadelta
AdamW
Nadam
Adam
Optimizer MAE
RMSE
MAPE
(%)
c Examining the outcome in the Table 4, demonstrates that Adam optimizer produced the best overall result achieving the lowest MAE.
RMSE, and MAPE of 0.
2520, 1.
4921 and 1.
respectively while maintaining high R2-score and c of 0.
9930 respectively at an efficient computation time of 2953s compared to the recorded values by the other Numerically, the low error rates (MAE.
RMSE, and MAPE suggests that the Adam optimizer minimizes errors between predicted and actual values and explains inherent variance better than its counterparts.
Hence, this provided an invaluable insight in the accuracy of predicting the RUL in distribution power transformers.
Other variants of Adam specifically AdamW and Nadam performed equally well across the respective performance metrics.
Additionally, the RMSprop optimizer being the fastest with a computational time of 491.
also recorded values close to AdamW optimizer although weaker than Adam and Nadam.
On the contrary, the Adadelta optimizer performed the least across most of the performance metrics https://doi.
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excluding the computational time.
Hence, this practical analysis reiterates or affirms the Adam optimizer as the most suited optimizer for the proposed RUL prediction model.
Furthermore, various learning rates were evaluated with the Adam whiles other parameters maintained accordingly.
In Table 5, the default learning rate of 0.
001 emerged as the best choice, showing higher accuracy and efficiency compared to other investigated learning Table 5.
Performance of proposed model on different learning MAPE
(%)
c R2score Compt.
Learning MAE
RMSE
From the table, learning rates specifically 0.
01, 0.
00001, and 000001 resulted in high error rates (MAE.
RMSE, and MAPE value.
which practically makes them unsuitable for training the proposed model due to their poor convergence.
Conversely, an optimal learning rate of 0.
001 provided the lowest MAE.
RMSE, and MAPE as highlighted in the table.
Additionally, the highest R2 score and c values recorded by this default learning rate suggests the best balance between accurate predictions and error minimization Moreover, the DMSA CNN-LSTM RUL prediction model was trained on four separate epochs .
, 100, 150 and 200 epoch.
whiles keeping the other parameters constant.
Therefore, their respective performance is presented accordingly in Table 6.
Table 6 Performance of proposed model on different epochs MAPE
(%)
c R2score Compt.
Epoch
MAE
RMSE
Detailed evaluation of the result in Table 6 indicates that at 50 epochs, the proposed model performed best which is evident by the low MAE.
RMSE, and MAPE together with the highest R2score and c values.
This optimal performance was recorded at a desirable training time of 595.
2953s showing computational However, increasing the number of epochs beyond 50 significantly increased the computational time to approximately 2039s, 1638.
8936s and 2589.
5685s for 100, 150 and 200 epochs respectively.
Additional analysis of the result suggested that the performance of the proposed model on the error and correlation metrics slightly declined after 50 epochs suggesting that possible overfitting.
Thus, considering this analysis, training the proposed model for 50 epochs gave the best overall performance, balancing predictive accuracy with computational Various batch sizes were explored in the tuning stage of the proposed modelAos hyperparameters to enhance training efficiency, obtain better results, and optimize the use of computational resources.
Table 7 summarized the performance of the proposed model on five different batch sizes.
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Table 7 Performance of proposed model on different batch sizes MAPE
(%)
c R2score Compt.
Batch
MAE
RMSE
Interestingly, as the batch size increases by factor of two, a corresponding decrease in the computation time was observed during the training process.
In other words, the proposed model converged faster on larger batch sizes than for smaller batch sizes.
Noticeably, the 32-batch size produced the minimum errors values across the MAE.
RMSE, and MAPE.
It also provided the highest correlations (R2-score, and .
at an optimal computation time of 595.
Evaluating the other respective batch sizes reveal that the batch size of 128 performed relatively well on key error metrics (MAE and MAPE) compared to 16, 64, and 256 batch sizes.
Hence, the overall assessment immensely validated the 32-batch size as the most appropriate in providing a balance between the proposed modelAos accuracy and computational speed or efficiency.
Furthermore, the threshold parameter .
of the Huber loss function was investigated to identify the most effective value suitable to enhance the performance of the proposed model as shown in Table 8.
In view of this, different threshold parameter values were experimented 5 interval starting from the default value 1.
Table 8 Performance of proposed model on different threshold
Threshold
MAE
RMSE
R2score
MAPE
(%)
c Compt.
The various threshold parameter values in the table denote how the tuning factors affect the proposed modelAos training and prediction of outputs.
It is imperative to note that at yu = 9.
5, the proposed model achieves the best overall performance.
This is evident by the lowest MAE.
RMSE, and MAPE values of 0.
4175, and 1.
8205 which implies minimal prediction error, reduced deviations from actual RUL values and reliable overall https://doi.
org/10.
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predictions respectively.
More so, the highest R2-score and c values of 0.
9872, and 0.
9936 depicts significant correlation and prediction which aligns better with the actual or true data values.
Achieving this outcome within an optimal computation time 0f 3387s indicates that the threshold value of 9.
5 is most preferable for achieving improved result during hyperparameter The overall performance of the hyperparameter tuned DMSA CNN-LSTM RUL prediction model is summarized in Table 9.
Additionally, a comparative assessment of the proposed tuned DMSA CNN-LSTM model was performed to evaluate its performance against the hyperparameter tuned baseline GRU
Table 9 Overall performance of the best performing models after hyperparameter tuning MAPE
(%)
c R2 score Compt.
Tuned Model
GRU
MAE
RMSE
DMSA
CNNGRU
DMSA
CNNLSTM
This result show that the proposed DMSA CNN-LSTM model merged strong predictive accuracy with computational efficiency.
That is, it achieved a lower MAE, and MAPE of 0.
2300, and 8205 respectively.
Even though, the RMSE is slightly higher than the tuned GRU model by a margin of 0.
2238, the overall error minimization indicates that the proposed model dominated in this aspect.
Furthermore, the high R2-score and c value of 9872 and 0.
9936 obtained by the proposed model suggests a close performance with the tuned baseline GRU model.
This implies close similarity in terms of thoroughly identifying the underlining patterns inherent in the data.
Remarkably, the proposed model achieved this result approximately 55% faster than the GRU model and 5% faster than the DMSA CNN-GRU model thus indicating its superiority and preferability for reliable prediction of distribution transformer maintenance periods.
The six subplots .
ee Appendi.
in the respective Figures 8.
, 8.
, and 8.
demonstrates how the proposed modelAos Huber loss evolved across different hyperparameter settings taking into consideration the learning rate, batch size and epochs.
It is observed from the result in Figure 8.
that applying a 0.
learning rate produced a much faster and stable convergence of the loss curves in tuning 1-3 compared to those outside the bracket .
01 and 0.
which resulted in much slower convergence.
A batch size of 64 and 128 produced more stable curves within the 10th epoch in tuning 2 and 3 of Figure 8.
However, considering faster convergence and computational efficiency, the batch size of 32 enabled the DMSA CNN-LSTM model achieve similar result using less memory requirements per iteration.
The justification on 50 epochs enabled the proposed model to substantially reduce training time without overfitting compared to training on larger epochs.
That is, in realtime RUL prediction, rapid convergence was selected over extended training which yields lower losses.
Hence, unlike other tunings in Figure 8.
, 8.
, and 8.
, tuning 1 in Figure 8.
provided the much-needed balance of speed and accuracy which is more suitable and in events where the model requires additional ELVIS TAMAKLOE / ANDALAS JOURNAL OF ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY - VOL.
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Figure 9.
Histogram plot of the distribution of the actual and predicted RUL values continuously spread across three main categorizes .
, 30 and 50 In contrast to the results in Figure 8.
, very strong However, the dominant distributions fell within 10 years oscillations, unstable and divergent loss curves were obtained in and 30 years as indicated by their level of frequency in the test Figure 8.
particularly for tuning 1-4 given the high learning rate Imperatively, the predicted RUL values matched closely Furthermore, training the proposed model on lower with the actual RUL values showing high degree of overlaps learning rate typically 0.
000001 resulted in very slow learning indicative of the strong performance by the proposed model as and severe underfitting as seen in hyperparameter tuning 5-6.
numerically validated in Table 10.
This outcome made these sections of tuning parameters inappropriate for the proposed DMSA CNN-LSTM model.
An outlook of the prediction error was visualized in Figure 10 to Interestingly, the loss curves in the individual subplot of Figure buttress the strong predictive performance of the DMSA CNN8.
showed stable characteristics but at the expense of slower LSTM RUL estimation model.
In this figure, the error distribution convergence and risk of potential underfitting.
Hence, this is centered around a value of zero without any significant requires significant tradeoffs which made them unreliable for skewness towards either the extreme positive or negative values.
predicting transformer RULs in real-time sensitive scenarios.
This suggests that the model is unbiased and captures the relevant trend in the data without given preference to a particular error Therefore, based on this performance, it is evident that the The histogram plot in Figure 9 represents the distribution of the proposed model does not significantly overpredicts or actual and predicted values in the test data.
It shows the actual underpredicts the RUL values in the entire test data.
Given the RUL .
arked in orang.
which denotes the ground-truth life strength of the proposed model, the performance of its future expectancy distribution and the predicted RUL .
arked in blu.
RUL predictions was established for short term predictions only.
which also represents the distribution of the predicted life expectancy values by the DMSA CNN-LSTM model.
Based on the results in this figure, it is noticeable that the RUL values are Figure 10.
Distribution of RUL prediction errors between actual and predicted values https://doi.
org/10.
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Long-Term RUL Predictions with Prophet The significance of accurately predicting the RUL of the distribution transformer is an indispensable prognostic approach for reliable asset management.
In this regard, a prediction of the RUL for the next 10 years was performed and illustrated in Figure 11 indicating trends from 2020 to 2030 using Prophet forecasting May to December 2028 the RUL fell below 1 year suggesting an accelerated decline in the transformer useful lifetime.
Moreover, in the early period of 2029 the RUL reached zero indicating that the transformer has failed, nonoperational and its end of predicted lifespan has been realized.
Holistically, the decline in RUL values was initially gradual but became accelerated towards the end of the transformerAos life expectancy.
Table 11 Long-term RUL predictions for 2027, 2028, and 2029 Date .
/y.
Figure 11.
Prediction of the trend of the RUL of the distribution The downwards trend in the RUL plot as seen in Figure 11 shows a gradual and continuous deterioration in the life expectancy of the distribution oil immersed transformer over the period on the condition that no maintenance interventions are carried out.
This steady linear degradation implies that the deterioration pattern of the transformer starts from about 25 years and predictably declines to zero considering the impacts of all the stressors involved in the transformerAos operation.
Based on rate of decline, it is expected that the transformer reaches it end of life between That is, at this point the life expectancy value reaches zero provided the operating conditions remain the same and no unexpected failures occur.
Furthermore, in the early years of the forecast, the 95% confidence interval visibly appear large however, its outlook narrowed as the years progressed.
This implies that in the early prediction of the RUL value.
Prophet exhibited a sizeable uncertainty but this uncertainty reduced as its approached 2028, and 2029.
The reduction in the uncertainty means more confidence in long term RUL predictions.
The mean RUL values predicted from 2027 to the end of life in 2029 is presented in Table 11.
Table 10 Numerical difference between actual and predicted values in the test and validation data Test Actual Predicted Difference A A A A From the table, the predicted RUL of the distribution transformer indicates a generally steady degradation with respect to time.
Notably, the RUL value of the transformer in the period of 2027 remained over a year until early 2028.
This implies that the transformer is still operational despite the continuous deterioration pattern.
This steady pattern was followed in the early period from January 2028 to April 2028 nonetheless, after https://doi.
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Date
1/2027
RUL
Predictions .
A Date
1/2028
RUL
A 1/2029 RUL
A 2/2027 A 2/2028 A 3/2027 2/2029 A 3/2028 A
3/2029
4/2027
4/2028
4/2029
5/2027
5/2028
5/2029
6/2027
6/2028
6/2029
7/2027
7/2028
7/2029
8/2027
8/2028
8/2029
9/2027
9/2028
9/2029
10/2027
10/2028
10/2029
11/2027
11/2028
11/2029
12/2027
12/2028
12/2029
Noticeably, this characteristic trend is typical of distribution transformers given the cumulative stress experienced.
Therefore, based on this result, the long-term prediction using Prophet suggests that identified maintenance activities including transformer replacement can be undertaken as the last resort before the year 2028.
Thus, the RUL in 2029 is undesirable for reliable power distribution as the transformer is at risk of run-tofailure.
Hence, taking into account the prediction made regarding the distribution oil-immersed transformer as evident in Figure 11, it is clear that the RUL of the transformer is expected to be approximated 25 years considering its current operational Interestingly, this outcome aligned with the expected degradation pattern of distribution transformers as referenced in Ie STD C57.
91, which represents a standard that estimates the life expectancy of a transformer to be approximately 20.
55 years .
Thus, considering the objective of this research, predicting both the short and long-term RUL of distribution transformers provides a comprehensive guide for improved decision making to enhance their effective management.
Comparative Assessment of the RUL Prediction or Estimation Model The current industrial revolution has led to the development of innovative models aimed at improving the limitations of the existing oneAos whiles taking notice of the enormous implications that could occur in the event of failing to accurately predict the RUL of the transformer.
In reference to this, the performance of the proposed model is benchmarked against current state-of-theart models to understand its overall contribution and highlight its Imperatively, the complementary use of Prophet as a statistical tool in this domain of RUL prediction provides the baseline benchmark for better validation and assessment of results .
, .
Hence, the performance of the DMSA CNNLSTM RUL prediction model was benchmarked against other recent works in this domain.
In view of this, a comparative assessment and evaluation was presented in Table 12 and Table 13 to thoroughly underline the importance of this work.
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Table 12.
Comparative assessment of the proposed work with current benchmarks Author Algorithm.
Spatio-Temporal Complete Graph Convolution Network
(STCGCN)
Extreme
Gradient
Boosting (XGB) Back propagation (BPNN) Random Forest (RF) Adaptive Network-Based Fuzzy Inference System
(ANFIS)
Physics-Informed Neural
Network
(PINN)
Features DGA Electrical load Electrical and temperature Ambient current, and degree of polymerization Electrical Degree (DP) Purpose Remaining Useful Lifetime Prediction Remaining Useful Lifetime Prediction Remaining Useful Lifetime Prediction Useful Lifetime Estimation Estimating Transformer Loss of Life Remaining Useful Lifetime Prediction Performance MAE: 0.
RMSE: 0.
MAPE: 21.
RMSE(TOTav.
etrain: 1.
67A1.
etest: 6.
23A2.
trn : 50ts.
& .
trn : 100ts.
MSEavg: 4.
Accavg:93.
Load .
ith HMM) RMSE:0.
0172 and .
o HMM) RMSE:0.
RMSE:2.
946y10-10 R2-score: 0.
Compt.
time: 25.
MSE: 26.
RMSE: 5.
MAE: 3.
At .
110oC) Electrical and temperature Ambient humidity, load and Electrical Oil .
trn : 25ts.
MSEavg: 11.
Accavg:88.
Electrical load
Dataset
Dissolve gas
Data Availability Open access
N/A
Simulation N/A N/A N/A Origin Multi- sourced Multi- sourced From 01-05-2012 to 13-012017.
(>60month.
1 day for DGA dataset and 1 hour for oil temperature.
3years and 10months (Nov.
2012-Sep.
1 hour Multi- sourced (Ira.
1 year Simulation (MATLAB) 1 year Synthetic generation Duration Simulation (MATLAB) N/A N/A 1 hour 1 day Sampling Degree (DP) Table 13.
Comparative assessment of proposed work with current benchmarks .
ontinued from table .
Author This work Algorithm Nguyen.
Widrow Neural
Network
Time Series Decomposition Decomposition-based Neural
Controlled Differential Equation (DNCDE) Dynamic Multi-Scale Attention
CNN-LSTM
(DMSA CNN-LSTM) and Prophet Features Electrical Electrical load and ambient temperature Vibrations Electrical.
DGA .
Transformer .
, and Ambient .
xternal temperatur.
Purpose Distribution Transformer Lifetime Prediction Distribution Transformer Remaining Useful Lifetime Estimation Fault localization .
ulti-label classificatio.
Performance MAE: 0.
trn:25ts.
H MAE:
trn:25ts.
M MAE:
trn:25ts.
D TSD .
oad kVA) MAE: 2.
RMSE: 3.
TSD (Ambien.
MAE: 2.
RMSE: 3.
RULerr:2.
2062A0.
Forecasting Power Transformer Remaining Service Life Accuracy: 92A1 R: 0.
9721A0.
MAE: 0.
0318A0.
Running time: 0.
Electrical load and ambient temperature Vibration data MAE: 0.
RMSE: 1.
R2-score: 0.
MAPE: 1.
c: 0.
Training time: 587.
Dataset H-Haar wavelet M-Meyer wavelet D-Daubechies wavelet Electrical data Data Availability N/A Private Private (Hubei DC Compan.
Fused multi-modal dataset (Electrical.
DGA .
, and vibration Open access Origin Multi- sourced (Surabaya cit.
Multi- sourced Single-sourced Multi- sourced Duration 12 hours N/A Approximately 10 months .
lectrical and environmental dat.
and others N/A Sampling N/A N/A 1s-15min environmental dat.
others N/A https://doi.
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The comparative assessment seen in both Table 12 and Table 13, indicates that the DMSA CNN-LSTM model with Prophet proved advantageous compared to the other baseline models evaluated as The value of thoroughly extracting both the temporal and spatial dependencies via the CNN and LSTM layers provided a huge lead in accurately predicting the RUL both in the short-term and long-term respectively.
Thus, employing DMSA mechanism gave the required adaptability to enable the model focus on only the important features that contributes most to the transformerAos life expectancy.
Therefore, fusing the rich multimodal dataset ensured an efficient prediction of both the short term and long term of the remaining useful lifetime.
CONCLUSIONS
With reference to the outcome achieved in this work, it is noteworthy that using the proposed DMSA CNN-LSTM model combined with multi-modal fusion is a highly effective datadriven approach for short-term prediction of the RUL in predictive maintenance of distribution power transformers.
Importantly, this research analysis highlights the need for combining diverse data sources in predictive maintenance since single-modality techniques lacks efficiency in terms of capturing complex interactions between different operational conditions necessary for accurate RUL prediction.
The fusion of multimodal datasets enabled the DMSA CNN-LSTM to correlate several sensor readings, facilitating accurate short-term predictions with minimal errors.
That is, it achieved a performance of 0.
2300 MAE, 1.
4175 RMSE, 0.
9872 R2-score 8205 MAPE.
Moreover, the proposed DMSA CNN-LSTM model demonstrated accurate prediction, evidenced by a c value of 0.
which is preferably closer to unity and achieved a computational time of 587.
Furthermore, the long-term prediction performed with Prophet predicted a RUL of 25 years at 95% confidence interval which agrees with the reference standard in Ie STD C57.
91 as expected.
This sets a new benchmark for future research and development in this domain.
Therefore, the use of the proposed solution together with Prophet library tool in predictive maintenance supports fast and proactive interventions which facilitates informed decision making, and ensures effective management of transformers in energy sector leading to reliable power distribution.
REFERENCES