Power Transformer Prognostics and Health Management Using Machine Learning: A Review and Future Directions

1. Introduction

Power transformers (PT) are essential links in the electrical power system and have a direct impact on the reliability of the entire network [1]. Being subject to continuous thermal, electrical and mechanical stresses, power transformers, especially aged ones, are prone to various types of failures that degrade their performance and reduce their lifetime [2]. It is therefore necessary to assess their health status, provide a strategic management plan for each transformer and determine the most economical management approach. Without effective management of these assets, it is difficult to make decisions about maintenance and replacement priorities [3]. Poor decisions can result in high maintenance costs and long periods of transformer downtime. The traditional concept of operation and maintenance strategies is often time-based, i.e. systematic maintenance strategies. The transformer is periodically inspected regardless of its condition. This type of maintenance is often very costly to the company and does not promote good asset management.

In general, maintenance strategies can be divided into three types: reactive maintenance, which is carried out after a failure has occurred; systematic maintenance, which is carried out periodically; and condition-based maintenance, where maintenance is conditioned by the state of health of the asset. The development of on-line monitoring sensors offers the possibility of implementing this condition-based maintenance. Real-time monitoring then increases the probability of detecting incipient failures while reducing the probability of failures occurring. It then helps to improve operational safety, control unscheduled maintenance and prioritise the maintenance and replacement schedule based on the condition of each transformer.

The Prognostics and Health Management (PHM) process consists of three modules: Condition Monitoring, Health Assessment and Prognostics. The aim of the condition monitoring module is to compare the online data or extracted descriptors with certain expected or known values that define a threshold for generating alerts. This module is also known as the fault detection level, which aims to detect abnormalities or anomalies in system behavior. Then the Health Assessment module, usually known as the Diagnostics module, must identify the degradation states of the system and assess the causes of the degradation. Finally, the prognostics module aims to predict future trends in the health status of systems in order to estimate the time remaining before systems will be unable to perform their intended function.

In addition, with the increasing use of Internet of Things (IoT), sensors and connectivity between physical assets, PT are now producing large amounts of easily accessible data. The ability to assimilate this data to quickly extract useful information and descriptors for integration into the organizational knowledge chain is required. AI has become one of the most strategic technologies of the 21st century thanks to the growth in computing power, the availability of data and advances in algorithms. Thus, PHM methods for PT are increasingly moving towards artificial intelligence techniques, as evidenced by the number of publications in the literature [4,5,6,7,8]. The literature review conducted here consolidates the scientific production in the field of Power Transformer Prognostics and Health Management (PT-PHM). A comprehensive and detailed literature analysis is given. Subsequently, this literature review is divided into two parts: classical ML techniques and DL techniques. For each part, a formal description of the main ML models used and their application in the field of PT-PHM is detailed. For each part, a table summarizing the literature review is also provided. One of the main observations that can be drawn from this literature review is the conservative nature of the published work. It can be seen that some popular DL models, such as generative models (VAE, GAN), have been successful in other PHM applications, but are hardly used for PT-PHM. Other recently successful popular approaches such as Transformer-based Deep Neural Network [9] or Self-Supervised Learning [10] are completely missing in the PT-PHM domain. An important question for the community of researchers, engineers and students working in the field of PT-PHM is therefore What are the trends in AI and where do we need to go for power transformer prognostics and health management?

The Section 2 gives a brief description of the evolution of ML techniques in order to give the reader some important elements to understand how the ongoing developments on the foundation models will affect the integration of ML techniques in PT-PHM. Then, the main part of this review paper is dedicated to Section 3 and Section 4, which give a complete literature review on the ML techniques for PT-PHM. Finally, Section 5 and Section 6 give some discussion and challenges about the way the research field in PT-PHM needs to go.

2. From Shallow Machine Learning to Foundation Models

2.1. Shallow Machine Learning

The rise of the first ML algorithms began in the 1990s, when the concept of learning from data was introduced. This was the first foundation of AI: a learning algorithm induces the way to solve a task from data, rather than defining how to solve it from prior knowledge. Various prediction, regression and classification applications were then performed on the data. However, for complex data, such as text or images, a step of feature engineering by domain experts is required.

In the first integration of shallow ML architectures in PHM applications, the raw measurements provided by the sensors cannot be easily linked to the health state of the systems. In fact, the data is often affected by a significant amount of noise or imperfect signal transmission. In addition, these data are often represented by complex time series, typically characterized by a high redundant information content, which tends to hide the relatively limited discriminative features of interest. For these reasons, once the data are acquired, a set of candidate features must be extracted and then only the most informative among them must be properly selected. Once these steps are completed, the final set of extracted features can be used to train an ML algorithm to perform the desired diagnostic or prognostic task (Figure 1). The powerfulness of shallow ML techniques can be quite limited, and their input often consists of high-level features manually extracted from raw data by human experts.

2.2. Deep Machine Learning

The emergence of DML in the 2010s revitalized the field of AI. Several ingredients made this resurgence possible: 1) the availability of massive data, 2) the advent of GPU resources, and 3) the tenacity of many AI researchers. DNNs are then trained on the raw input data, and high-level features emerge through training. This has led to great performance gains by several DML architectures on standard benchmarks.

Thus, in the PHM process, DML architectures emerge as an extension of classical shallow ML architectures. Once DNNs are trained, their inputs pass through a nested series of successive computations, resulting in the extraction of a set of complex features across different engineering domains that are highly informative for the task of interest. This property is one of the hallmarks of DML and can be seen as one of its key success factors for automated end-to-end feature extraction from different data structures. The main power of DML is then the automated feature learning from low-level elementary features to high-level abstract features [11] (Figure 1). Nevertheless, DML models perform well when trained on specific data to solve a specific task in a specific context. This constraint limits their use for complex power systems, which require a high degree of model explainability, and robust generalization.

2.3. The Emergence of a New Concept, the Foundation Models

At the end of the 2020s, important AI concepts have been developed that form the basic ingredients of the foundation models. In fact, recent advances in AI research have led to the emergence of a new paradigm: foundation models. These recent advances are: Modular Learning, Transformer architecture, SSL, MMF, MTL, and graph-oriented approaches.

A foundation model is described as a general-purpose AI model that has been trained to solve a wide range of general-purpose tasks such as text synthesis, image manipulation, and audio generation. It can be a stand-alone system or can be used as a basis for many other applications or models. The idea of foundation models was first introduced by Bommasani et al, [12]. Some of the best known foundation models are BERT [13], GPT [14] and CLIP [15]. It is important to note that the Foundation Models define a new concept in AI rather than a new structure or algorithm of a ML model. The power of the foundation models lies in their scale, which requires improvements in computer hardware and the availability of much more training data. The modular DL is at the heart of the scalability of foundation models (Figure 1). Thus, foundation models overcome the limitations of DL models by providing better generalization performance on large multimodal datasets. However, building a foundation model is often very resource intensive. The most expensive models cost hundreds of millions of dollars for the underlying data and computation required. In contrast, it is much less expensive to adapt or directly use an existing foundation model for a specific use case.

3. Classic ML Techniques

This section mainly discusses the use of classical ML methods for the PT-PHM. A total of 149 papers have been reviewed and analysed for this section. The Figure 2 shows the density distribution of these papers in the year of publication. As can be seen from the Figure 3, a first main group, representing more than 50% of the papers analyzed, concerns the Fuzzy Inference Systems, the SVM and the ANN. A second group, representing 19% of the papers, deals with other ML techniques such as the ANFIS, the Gaussian Process, the Feed-forward Wavelet Network and two clustering techniques, the Fuzzy c-means and the K-NN. In the third group, several ML techniques were used together for some comparative studies in 13% of the papers. For example, in [16,17,18,19] several ML techniques such as ANN, SVM and ANFIS were compared for HI assessment. Finally, a last group, representing almost 10% of the papers analyzed, concerns some marginal applications of the following ML techniques: Bayesian inference (2.70%), ELM (2.70%), ensemble learning (2%), decision tree (2%), random forest (1.35%) and hidden Markov models (0.68%).

3.1. Artificial Neural Networks

Recent papers have used ANNs for monitoring and asset management of PT [28,29,30,34,42]. In these papers, shallow structures of the feed-forward MLP are trained by the back-propagation algorithm. In [42], a BPNN enhanced with the AdaBoost algorithm is used to estimate moisture content. The results show superior performance compared to other techniques such as SVM, RF and k-NN. Mousavi et al., [34] propose a method based on an Artificial Neural Network (ANN) integrated genetic algorithm to modify the effect of temperature variation in the results of polarisation and depolarisation current (PDC) tests. The purpose of ANN is to transfer parameters related to higher temperatures to target parameters. In [30], an artificial neural network based approach is proposed to assign the weight for several independent DGA methods in the fusion procedure according to the fault type detection accuracy for the range of input gas concentrations.

3.2. Fuzzy Inference System

In [48], the risk index for power transformers is assessed from the aggregation of three fuzzy inference systems. The expert criteria are exploited to create the rules and the definitions of the input membership functions. The HI is predicted by the FIS based on the results of the physico-chemical tests normally performed on the insulating liquid of the units. This paper shows that the proposed methodology, based on the FIS, for assessing the condition of power allows the integration of values commonly available to asset managers in electrical systems. Through this integration, it is possible to rank the units in order to define maintenance strategies for the analysed units. With the same objective of decision making for PT asset management, a combined approach of FIS and fuzzy clustering means is used by [51] as an expert system for diagnosis and prognosis of incipient faults of power transformers along with critical parameters such as dissolved gas analysis, moisture content, furans, interfacial tension, degree of polymerisation.

In the majority of the papers analyzed, the FIS have been applied mainly to FDD based on dissolved gas analysis, as detailed in the Table 1. However, this type of method can also be found in other fields such as partial discharge analysis [44,107], Frequency Response Analysis [106,108] thermal analysis [106,111] and heat dissipation [106], Frequency spectroscopy [112], insulation resistance [106] and insulation paper analysis [51,109].

3.3. Support Vector Machine (SVM)

The SVM method is one of the most popular techniques used in power transformers for FDD, where the function $f\left(x\right)$ is used to classify conditions such as discharge faults ($f\left(x\right)=+1$) from thermal faults ($f\left(x\right)=-1$). SVMs have the advantage of using a small amount of training data, which reduces the training time [163,164]. The accuracy of the SVM technique depends on its parameters and the kernel function used [165].

As for the other ML techniques, SVM has mainly been used in power transformer diagnostics based on dissolved gas analysis, as shown in the Table 1. The simplest way to use SVM for FDD based on a set of dissolved gas concentrations as input is binary classification. The most common are hydrogen (H2), methane (CH4), acetylene (C2H2), ethylene (C2H4), ethane (C2H6), carbon monoxide (CO) and carbon dioxide (CO2). In [62] a multi-stage SVM classification was proposed for FDD. The first stage consists of separating a faulty condition from a non-faulty condition. The following stages are successively used to separate the faulty conditions, e.g. the thermal fault from the discharge fault. A method based on Kernel Principal Component Analysis (KPCA) and a hybrid improved Seagull Optimization Algorithm is proposed by [60] to optimise the parameters of the SVM. Furthermore, the KPCA technique was used by [58] for feature extraction and dimension reduction, and reduce the dimension of the feature vector. In order to obtain the optimal classification model in high-dimensional space, a Genetic Algorithm (GA) introduced in Whale Optimization Algorithm (WOA) was used to optimise two important parameters of SVM: Penalty Factor and Kernel Function Parameter.

Furthermore, the SVM techniques have been used in the detection of partial discharges [2,72,76], in frequency response analysis [71] in the analysis of vibro-acoustic signals [74], thermal analysis [21,161] and infrared analysis [70], in polarisation-depolarisation current analysis [65,82] in spectroscopy [75] in the prediction of the degree of polymerisation [73] and for the differential protection [77].

3.4. Summary of Work Using Classic ML methods

Table 1 summarizes the analysis of all the papers considered in this section in terms of the classic ML techniques used. Three tasks are then highlighted, the fault detection and diagnosis (FDD), the health index assessment and the prediction of some condition monitoring data such as the prediction of top oil temperature [20] or the thermal modeling for condition monitoring [21]. The main part of the analyzed paper deals with dissolved gas analysis, alone or in combination with other monitoring parameters (marked with a + sign). In the next three subsections we will have a closer look at the main ML techniques used by the first group shown in the Figure 3, i.e. ANNs, FIS and SVMs.

4. Deep Learning Architectures

Nowadays, due to the development of several heuristics for training large architectures and the use of GPU hardware [166,167,168], the size of ANNs can reach several hidden layers with more than 650 thousand neurons and 630 million trained parameters (e.g. alexNet [169]). In recent years, deep learning methods based on neural networks have attracted the attention of many researchers for dissolved gas analysis [170], infrared image analysis [171] for differential protection [172], or for the prediction of dibenzyl disulphide concentration[173]. In this section we discuss the use of Deep ML methods for PT-PHM. A total of 42 articles have been reviewed and analysed for the purpose of this section. The Figure 4 shows the density distribution of these papers in the year of publication. As shown in the Figure 5, the most popular DML architecture is the convolutional neural network, which is used in more than 50% of the published papers. Recurrent Neural Networks and AE architectures are two other DL models that are also proving successful. Finally, two new concepts are emerging in the field of PT: attention mechanics and GNNs.

4.1. Convolutional Neural Networks

CNNs have been successfully applied to the detection and diagnosis of power transformers, as shown in the Table 4, mainly for DGA, but also for partial discharge source detection [182,183,184] and vibration and acoustic signal analysis [181]. In [174], the difficulty of applying the CNN model to a small vector size is addressed. In fact, existing dissolved gas analysis methods use five gases as features ($H_2$, $C{H}_4$, $C_2{H}_6$, $C_2{H}_4$, $C_2{H}_2$). Compared to image type data, such as thermal image data, only five features are too few to serve as input to the CNN model during training. A reduced number of input features combined with the deep layers of the CNN slows down the learning process and makes it too oscillatory, leading to overfitting. Features are then reconstructed to overcome this problem, as shown in Figure 6. Permutations and combinations of the five gases allow the features of the model input vector to be increased.

With the same objective of increasing the size of the input vector of dissolved gas concentration, the method proposed by [178] uses an input vector of 35 features containing three categories: 1) seven raw dissolved gas concentration data including $H_2$, $C{H}_4$, $C_2{H}_2$, $C_2{H}_4$, $C_2{H}_6$, $CO$ and $C{O}_2$; 2) the fraction of each gas relative to the total concentration of the seven gases; and 3) 21 proportions calculated from the ratio of two gas concentrations. All features are normalised to the interval $[0,1]$ to reduce the scale differences of the input features.

A total of 28 dissolved gas fractions are considered in [176] (listed by Table 2). To overcome the problem of over-fitting from a reduced set of data available for training, the gcForest algorithm is optimised by a combination of CNN and CasXGBoost (cascade extreme gradient boosting). A total of five output classes are used: LE-D (Low Energy Discharge), HE-D (High Energy Discharge), LM-T (Low Temperature Overheating), HT (High Temperature Overheating) and NC (Normal Condition).

4.2. Recurrent Neural Network

In order to take into account the dynamics of the training data, a particular architecture of recurrent neural networks (RNNs) is specially adapted for the analysis of time signals. RNNs contain feedback loops to memorize information from previous units and are best suited to time series analysis. Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM) cells are popular variants of RNNs that attempt to alleviate the vanishing gradient problem. LSTM has recently been used for dissolved gas analysis and power transformer prediction [192,197,198,199]. Thus, models have been developed and tested by [192] and [198] for predicting the concentration of the following gases $H_2$, $C{H}_4$, $C_2{H}_6$, $C_2{H}_4$, $C_2{H}_2$ from a concentration history. In [198] a simple structure of a LSTM neural network was tested and compared with other models such as a Support Vector Regression, Regression Tree and Gaussian Process Regression. According to the results published by the authors, the LSTM model outperforms other models in predicting gas concentrations over a seven-week horizon. In addition, a more complex hybrid structure combining a Highly Attentional Tracking Network (HATT) model and a Recurrent Long Short-Term Memory Network (RLSTM) model has been proposed by [192] for predicting dissolved gas concentrations.

In order to improve the reliability of the diagnosis obtained from a fault classification model listed in Table 3, several configurations of LSTM and bi-LSTM models, illustrated by Figure 7, were tested by [197]. According to the results published by the authors, the performance of the LSTM model in terms of accuracy, recall and precision is $99.01\%$, $98.79\%$ and $99.12\%$ respectively.

4.3. Auto-Encoders

The AEs have recently been applied to dissolved gas analysis [180,200,201,202,203]. In [202], the AE is used to extract some relevant features from a set of several concentrations of dissolved gases such as $H_2$, $C_2{H}_2$, $C_2{H}_4$, $C_2{H}_6$, $C{H}_4$ and $CO$. Thus, the features extracted from the encoder are used to detect and identify two types of faults: thermal and electrical. As shown in Figure 8, health indicators are thus defined for the detection and identification of faults from the latent space obtained by the encoder. Four degradation sequences are illustrated by [202]: two thermal degradation sequences and two electrical sequences.

Due to the complex operating condition of the transformer, its faults are with the characteristic of multi-class faults, class imbalance, and limited diagnostic data availability, the VAE has been used as a generative model for data augmentation [180,200,201]. The results presented in these papers show that the performance of the diagnostic model was improved after data augmentation by VAE.

4.4. Attention Mechanism

The attention mechanism has recently been used for PT asset management by the following papers [177,179,188,192,196] The attention mechanism has been used to improve the prediction of the model by further mining the temporal relationship of the different time points in [192] and to improve the power transformer fault diagnosis based on DGA [177,179]. In transformer fault diagnosis, dissolved gas in oil data have a wide variety of types, and the main gas data of some faults are similar. Therefore, it is more difficult to obtain important characteristic data. To solve this problem, a channel space-time attention network is used by [177] to fully extract the significant features from the dissolved gas in oil. Furthermore, current transformer diagnostics methods focus on discrete dissolved gas analysis, neglecting deep feature extraction from multi-channel sequential data. The unused consecutive data contains the significant temporal information reflecting the transformer condition. To solve this problem, multichannel consecutive data cross-extraction is proposed by [179] to extract the significant information on time sequence and channel successively, as shown in Figure 9. The multichannel sequential data, including hydrogen (H2), methane (CH4), ethane (C2H6), ethylene (C2H4) and acetylene (C2H2). The output shows the probability distribution of the condition of the power transformer, with the highest being selected as the final diagnostic result. The transformer states include Normal Condition (NC), Low Overheating (LT), Medium Overheating (MT), High Overheating (HT), Partial Discharge (PD), Low Energy Discharge (LD) and High Energy Discharge (HD). The experimental tests carried out by the authors show that the MCDC model, based on the attention mechanism, outperforms other models such as HMM, GRU and DBN.

Finally, another interesting application of the attention mechanism is multimodal fusion. This technique has been used by [188] to fuse two modalities: dissolved gas data and infrared images. The experimental diagnostic results presented by the authors show the superiority of multi-modal fusion over other techniques such as DBN, HMM, ANN.

4.5. Graph Neural Networks

In many scientific fields, some important objects and problems can be expressed naturally, or better, with a complex structure. In fact, structural and semantic information from the original data (images, sequential text or time series) can be used to incorporate domain-specific knowledge to capture finer relationships between data. Graph-based approaches, associated with the concept of ANN, represent a new paradigm in the field of ML that highlights semantic causal inference relationships [211,212], such as the interdependence between systems and components in a predictive maintenance [213]. Furthermore, these methods can achieve promising performances in reasoning tasks, while promoting their explainability and interpretability. In recent years, GNN [214,215,216,217] has attracted increasing interest from the scientific community [213,218,219,220,221,222], and several variants have been developed, such as convolutional GNN [223], recurrent GNN [224], and auto-encoder GNN [225]. The goal of a GNN is to learn effective node representations by iteratively combining the structure of the graph with the representation of the node attributes.

The data processing capabilities of GNNs have been explored in recent publications for assessing the condition of power transformers [175,193,205,206]. A model based on GCN has been proposed by [206] to predict the dissolved gas concentration. As shown in Figure 10, the input vector of the prediction model is defined by ${\mathbf{X}}_t=(X_t^1,X_t^2,...,X_t^N)$, where each input variable $X_t^i=(x_{tT}^i,...,x_{t-1}^i,x_t^i)$ represents the history of the concentration of dissolved gas $i^{th}$, and each element $x_j^i$ gives the concentration of dissolved gas $i^{th}$ at time j. The output of the model is the prediction of the dissolved gas concentration at time $t+h$. ${\widehat{\mathbf{Y}}}_{t+h}=({\widehat{x}}_{t+h}^1,{\widehat{x}}_{t+h}^2,...,{\widehat{x}}_{t+h}^N,)$.

The concentration of the following five gases ($H_2$, $C{H}_4$, $C_2{H}_6$, $C_2{H}_4$, $C_2{H}_2$), is used for a 500 KV power transformer to predict one step ahead. The predictions made by GCN are better than those made by other architectures such as LSTM.

4.6. Summary of Work Using Deep Learning Architectures

Table 4 summarizes the analysis of all the papers considered in this section in terms of the Deep learning architectures used. Three tasks are then highlighted, the fault detection and diagnosis (FDD), the health index assessment and the prediction of some condition monitoring data.

Table 4. Summary of work using Deep learning architectures.

DL techniques	Task	Data	Ref
CNN	FDD	DGA	[174,175,176,177,178,179,180]
	FDD	Other	[172,181,182,183,184,185,186,187,188]
	HI	DGA	[189]
	HI	DGA+	[190,191]
	Pred.	DGA	[192,193]
	Pred.	Other	[194,195,196]
RNN	FDD	DGA	[197]
	Pred.	DGA	[192,193,198,199]
	FDD	Other	[172,188]
	Pred.	Other	[195,196]
AE-VAE	FDD	DGA	[180,200,201,202,203]
	Pred.	DGA	[204]
Attention	FDD	DGA	[177,179]
	FDD	Other	[188]
	Pred.	DGA	[192]
	Pred.	Other	[196]
GNN	FDD	DGA	[175]
	HI	DGA+	[205]
	Pred.	DGA	[193,206]
DBN	FDD	DGA	[207,208]
GAN	FDD	DGA	[209]
PINNs	Pred.	Other	[210]

Table 4. Summary of work using Deep learning architectures.

DL techniques	Task	Data	Ref
CNN	FDD	DGA	[174,175,176,177,178,179,180]
	FDD	Other	[172,181,182,183,184,185,186,187,188]
	HI	DGA	[189]
	HI	DGA+	[190,191]
	Pred.	DGA	[192,193]
	Pred.	Other	[194,195,196]
RNN	FDD	DGA	[197]
	Pred.	DGA	[192,193,198,199]
	FDD	Other	[172,188]
	Pred.	Other	[195,196]
AE-VAE	FDD	DGA	[180,200,201,202,203]
	Pred.	DGA	[204]
Attention	FDD	DGA	[177,179]
	FDD	Other	[188]
	Pred.	DGA	[192]
	Pred.	Other	[196]
GNN	FDD	DGA	[175]
	HI	DGA+	[205]
	Pred.	DGA	[193,206]
DBN	FDD	DGA	[207,208]
GAN	FDD	DGA	[209]
PINNs	Pred.	Other	[210]

5. What are the trends in AI and where do we need to go for the prognostics and the health management?

5.1. Modular Learning

The development of a ML model that can perform multiple tasks without experiencing negative inter-task interference phenomena while maintaining good generalization performance on non-identically distributed data is less well controlled [226]. Negative interference is characterized by the phenomenon of catastrophic forgetting, well known in the field of ML. The ability to transfer knowledge to new tasks is enhanced by Modular learning. Modular neural networks (MNN) architectures are emerging solutions for positive learning transfer while avoiding negative interference [226]. Several MNN architectures have been developed in the literature, such as the modular architecture proposed by Rahaman et al. for an application to geospatial data [227], the Perceiver IO architecture proposed by Jaegle et al. [228], or the Neural Attentive Circuits architecture proposed by Rahaman [229]. In a Modular learning process, three main phases must be considered [226]:

• The learning module management phase which must meet the training, management and storage objectives of the modules.
• The routing phase which aims to define the way in which the modules are chosen and activated in order to meet a specific objective.
• The aggregation phase whose objective is to construct the final response from the responses of the various modules requested by the routing.

5.2. Self-Supervised Learning

In most industrial processes monitored under real operating conditions, a large amount of data is collected daily by the various sensors. However, only a part of this data can be properly used, and a very negligible part of the data is labeled by experts. In fact, labeling is generally a very time-consuming process that is usually performed by human experts. In addition, most of the data comes from normal asset behavior. As a result, the data collected is generally not representative of the different degradation mechanisms.

Learning techniques can be divided into two main families: supervised and unsupervised learning. Learning deep neural networks with supervised techniques requires a large amount of labeled data to achieve an acceptable level of performance. For the reasons mentioned above, these techniques are not suitable for industrial applications. Furthermore, unsupervised techniques, which do not require labeled data, can be effective for fault detection applications, but lack knowledge of degradation to effectively perform more sophisticated tasks such as diagnosis or prognosis.

SSL is an unsupervised learning paradigm that explores effective feature representations from unlabeled data [10]. Unlike conventional supervised learning, which requires an abundance of labeled data, SSL exploits the underlying information of unlabeled data, reducing the dependence on the annotation phase, which is very time consuming. The general principle of SSL is to create pretext tasks to allow the model to acquire efficient and relevant representations during the task solving phase. For example, learning to reconstruct noisy or partially hidden input allows the model to extract relevant features that could be used by another classification model. SSL has the advantage of exploiting the inherent properties of the data to allow the model to learn to extract high-level global descriptors from a large amount of unlabeled data. Therefore, a significant number of research papers on SSL have been published recently [230,231,232,233,234,235,236].

Figure 11 shows a classic diagram of the use of SSL in industrial monitoring applications. In a first phase, SSL pre-trains learning models using simple pretext tasks. This phase allows the model to extract complex features from the data without the need for human expertise. In a second phase, the model is refined by supervised learning with a minimum of labeled data, reducing the cost of human intervention.

5.3. Multimodal Fusion

Industrial systems can generate many types of data from different sensors, such as time signals, images, videos, and also a significant amount of textual information, such as maintenance work orders, maintenance reports, and so on. Therefore, the field of PHM is gradually beginning to emphasis multi-sensor data fusion to better understand physical phenomena and various degradation mechanisms. This is reflected in the recent publication of several papers that have explored the principle of information fusion [237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261].

MMF requires some prior processing of each of the modalities before they can be fused. Indeed, two different modalities will have two different digital representations, e.g. an image and an acoustic signal. Their fusion cannot be done directly in the data space, but requires a descriptor extraction phase. The Figure 12 shows a typical example of fusion of two different modalities. Each modality has its own neural network that extracts the relevant features, which are then fused. The same classifier can then be trained directly on the shared feature space.

The MMF involves three main steps. The first is to train the neural networks that extract the features of each modality. This can be done using methods such as self-learning. Next, the obtained pre-trained models are frozen and used for the next step. The features of each modality are then extracted from one of the hidden layers before the output layer. Their fusion can be done either directly, e.g. by concatenation [256], or by using newer techniques such as transformers or attention mechanisms [238,245,249,254,260]. Finally, the last step is to learn a classifier from the obtained feature space.

5.4. Towards the Foundation Models

Foundation models offer a potentially effective solution to the PHM process for complex industrial systems, as their advanced cognitive abilities allow them to solve certain complex reasoning tasks [262]. Therefore, the success of these foundation models marks the transformation of the research paradigm in AI, where we move from a mono-modal, single-task research paradigm with limited data to a multimodal, MTL research paradigm with big data and large-scale foundation models [262]. Looking at the evolution of the last few years, there is a gradual move from a collection of monolithic architectures for narrow and unique tasks to a set of modular and reconfigurable architectures that can handle different types of tasks [262,263].

This new class of foundation models is composed of billions of parameters [263,264] and is trained on massive amounts of data. The concept of modular learning, which is a new paradigm in ML [226,265,266], is at the core of the foundation models. In addition, the recent development of Transformer architectures [266,267,268], has provided great opportunities for extracting complex features from foundation models. Furthermore, the concept of SSL has enabled neural networks to have a robust capacity for unsupervised representation of features and descriptors [10]. Finally, MMF algorithms, MTL combined with the attention mechanism, have allowed foundation models to interact between the different modalities of the learning data [269,270].

However, integrating an foundation model based solely on data-driven learning into a PHM process requires a high level of AI expertise and rigorous methodology. Three main aspects need to be considered: the modularity, reliability and explainability of the foundation models. In fact, a modular AI structure with knowledge distributed across multiple AI models is better suited to the PHM process of complex industrial system than a single monolithic model. Thanks to this modularity, the AI models will be more explainable, transferable from one asset to another and easily upgradeable without the constraint of catastrophic forgetting.

6. What Are the Challenges?

6.1. Modularity of the LSF Models

A major drawback of large-scale models is that they are based on monolithic structures. This leads to several undesirable consequences related to adaptability. First, it is very difficult to refine the model after the appearance of a new target task. Second, the explainability of the model is a real challenge when the justification of a given response is important for decision making. For several years, some research efforts have been directed towards the learning of disentangled representations [271,272], the learning of causal representations with the hypothesis of independent causal mechanisms [273], and more explicitly, the learning of modular representations [265,274]. Modular architectures try to take advantage of this structure by allowing the learning of systems of sparse interacting neural modules. If we observe the developments of the last decade along this axis, we are gradually moving from a collection of monolithic architectures for narrow tasks to a modular and re-configurable architecture to handle different types of tasks.

Another expected benefit of modular deep learning is a better ability to transfer to new tasks. Transfer learning involves taking the "knowledge" learned from one specific task and applying it to another task in a different context. However, developing a model that can perform multiple tasks without suffering from negative interference between tasks and with good generalization performance on non-identically distributed data remains a significant challenge. Modular NN architectures represent emerging solutions for positive transfer learning while avoiding negative interference (catastrophic forgetting phenomenon).

6.2. Reliability of the LSF Models

When designing a ML model, it is common to focus on performance metrics based on the accuracy obtained on a test set drawn from the same distribution as the training set: this is called the Identical and Independent Distribution assumption. However, this does not take into account the deployment of ML systems in the real world, such as modern power grid systems, where the test environment is often very different from the learning environment. To improve the reliability of ML systems, three main conditions must be considered: models must represent their own uncertainty, they must generalize robustly to new scenarios and they must be able to adapt effectively to new data [275].

• Quantifying uncertainty. Quantifying prediction uncertainty allows practitioners to know when to trust model predictions. Various metrics can be used to quantify the quality of uncertainty, such as expected calibration error, which measures how well confidence in the model matches its accuracy. Quantifying uncertainty also helps improve decision making; a popular framework is selective prediction, where a model can refer its prediction to human experts when it is uncertain. Another popular task is open-set recognition, where the model encounters inputs from new classes at test time that were not seen during training, and the goal is to reliably detect that these inputs belong to one of the training classes.
• Robust generalization. Robust generalization involves making an estimate or prediction about something that is not seen. Prediction quality is typically measured in terms of accuracy (e.g., top-1 error for classification problems and root mean square error for regression problems) and appropriate scoring rules such as log-likelihood and Brier score. In the real world, we are interested not only in measurements on new data from the same distribution on which the model was trained, but also in robustness, measured by measurements on data subject to non-distributional changes, such as changes in covariates or subpopulations.
• Adaptation. Adaptation consists of testing the capabilities of the model during its learning process. Benchmarks typically evaluate static datasets with a predefined split between training and testing. In many applications, however, we are interested in models that can quickly adapt to new data and learn efficiently with as few labeled examples as possible. Examples include few-shot learning, where the model learns from a small set of examples; active learning, where the model not only learns but also participates in the acquisition of the data from which it learns; and lifelong learning, where the model learns during a sequence of tasks and must not forget information relevant to previous tasks.

6.3. Explainability of the LSF Models

ML models are considered black boxes because it is very difficult to understand how these models work in practice, despite their widespread use and exceptional performance. Therefore, it is difficult for experts to trust and justify the decisions and recommendations made by these models in the field of power systems, where a high level of responsibility is required.

In recent years, eXplainable Artificial Intelligence (XAI) techniques have been developed to improve the explainability of ML models so that their results can be better understood [276,277,278,279,280,281]. There are several challenges and limitations that must be addressed when implementing XAI for power system applications. One of the main challenges is to use models that are both efficient and transparent. In general, accurate models are more complex and harder to understand. This general compromise is especially important in the field of electric power systems, where a typical user generally requires both high performance and precise exposition in order to enjoy a high level of trust.

In addition, the lack of standardization and clear definitions are one of the main limitations of XAI. Currently, while some works and studies define what explainability is, there is still no consensus on a specific definition of XAI and explainability. Some works focus on visualization methods, while others use the concept of feature importance or relevance. Another limitation of XAI techniques is the lack of metrics for evaluating the quality of the explanation. Although a clear definition of explainability can be provided, it is desirable to have a metric for evaluating the degree of explainability of a model. These metrics should measure an explainability score for each XAI technique, on each model.

7. Conclusion

This paper presents the integration of ML techniques in the field of PT-PHM. It provides a comprehensive review of the state of the art in PT-PHM by analysing more than 200 papers, mostly published in scientific journals. This analysis is divided into two parts: a part dealing with classical ML techniques, such as shallow ANN architectures, SVM, fuzzy inference systems, KNN; and a second part dealing with DL architectures, such as CNN, AE, attention mechanism and GNN.

After the first revolution in ML models, moving from simple ML models requiring significant feature extraction (AI 1.0) to deeper models with complex learning (AI 2.0), a new paradigm is emerging: Large-scale foundation models (AI 3.0). Despite the fact that scientific research in the field of PT-PHM is still very conservative, mainly in AI 1.0 and gradually moving towards AI 2.0, all the ingredients are in place for the transition to AI 3.0 techniques: more and more multimodal PT monitoring data are being collected such as DGA, infrared images, vibration analysis or thermal monitoring. New techniques such as Transformer-based Deep Neural Networks, Self-Supervised Learning or Multimodal Fusion should be used to optimize the PT-PHM process.