The degree of polymerization (DP) is one of the methods for estimating the aging of polymer-based insulation systems, such as cellulose insulation in power components. The main degradation mechanisms in polymers are hydrolysis, pyrolysis, and oxidation. These mechanisms combined cause a reduction of the DP. However, the data availability for these types of problems is usually scarce. This study analyzes insulation aging using cellulose degradation data from power transformers. The aging problem for the cellulose immersed in mineral oil inside power transformers is modeled with ordinary differential equations (ODEs). We recover the governing equations of the degradation system using Physics-Informed Neural Networks (PINNs) and symbolic regression. We apply PINNs to discover the Arrhenius equation's unknown parameters in the Ekenstam ODE describing cellulose contamination content and the material aging process related to temperature for synthetic data and real DP values. A modification of the Ekenstam ODE is given by Emsley's system of ODEs, where the rate constant expressed by the Arrhenius equation decreases in time with the new formulation. We use PINNs and symbolic regression to recover the functional form of one of the ODEs of the system and to identify an unknown parameter.

This paper focuses on the thermal modelling of power transformers using physics-informed neural networks (PINNs). PINNs are neural networks trained to consider the physical laws provided by the general nonlinear partial differential equations (PDEs). The PDE considered for the study of power transformer’s thermal behaviour is the heat diffusion equation provided with boundary conditions given by the ambient temperature at the bottom and the top-oil temperature at the top. The model is one dimensional along the transformer height. The top-oil temperature and the transformer’s temperature distribution are estimated using field measurements of ambient temperature, top-oil temperature and the load factor. The measurements from a real transformer provide more realistic solution, but also an additional challenge. The Finite Volume Method (FVM) is used to calculate the solution of the equation and further to benchmark the predictions obtained by PINNs. The results obtained by PINNs for estimating the top-oil temperature and the transformer’s thermal distribution show high accuracy and almost exactly mimic FVM solution.

Physics-Informed Neural Networks (PINNs) are a novel approach to the integration of physical models into Neural Networks when solving supervised learning problems. PINNs have shown potential in mapping spatio-temporal input and the solution of a partial differential equation (PDE). However, despite their advantages for many applications, they often fail to train when target PDEs contain high frequencies or multiscale features. Thermal modelling of power transformers is fundamental for improving their efficiency and extending their lifetime. In this work, we investigate the performance of different PINN architectures applied to a 1D heat diffusion equation with a specific heat source representing the heat distribution inside a transformer. Measurements, which include the top-oil temperature, the ambient temperature and the load factor are taken from a transformer in service. We demonstrate the limitations of PINNs, propose possible remedies, and provide an overall assessment of the potential of using PINNs for transformer thermal modelling.

Our work aims at simulating and predicting the temperature conditions inside a power transformer using Physics-Informed Neural Networks (PINNs). The predictions obtained are then used to determine the optimal placement for temperature sensors inside the transformer under the constraint of a limited number of sensors, enabling efficient performance monitoring. The method consists of combining PINNs with Mixed Integer Optimization Programming to obtain the optimal temperature reconstruction inside the transformer. First, we extend our PINN model for the thermal modeling of power transformers to solve the heat diffusion equation from 1D to 2D space. Finally, we construct an optimal sensor placement model inside the transformer that can be applied to problems in 1D and 2D.

Power transformers are subjected to electrical currents and temperature fluctuations that, if not properly controlled, can lead to major deterioration of their insulation system. Therefore, monitoring the temperature of a power transformer is fundamental to ensure a long-term operational life. Models presented in the IEC 60076-7 and IEEE standards, for example, monitor the temperature by calculating the top-oil and the hot-spot temperatures. However, these models are not very accurate and rely on the power transformers' properties. This paper focuses on finding an alternative method to predict the top-oil temperatures given previous measurements. Given the large quantities of data available, machine learning methods for time series forecasting are analyzed and compared to the real measurements and the corresponding prediction of the IEC standard. The methods tested are Artificial Neural Networks (ANNs), Time-series Dense Encoder (TiDE), and Temporal Convolutional Networks (TCN) using different combinations of historical measurements. Each of these methods outperformed the IEC 60076-7 model and they are extended to estimate the temperature rise over ambient. To enhance prediction reliability, we explore the application of quantile regression to construct prediction intervals for the expected top-oil temperature ranges. The best-performing model successfully estimates conditional quantiles that provide sufficient coverage.

As the quest for more sustainable and environmentally friendly materials has increased in the last decades, cellulose nanofibrils (CNFs), abundant in nature, have proven their capabilities as building blocks to create strong and stiff filaments. Experiments have been conducted to characterize CNFs with a rheo-optical flow-stop technique to study the Brownian dynamics through the CNFs’ birefringence decay after stop. This paper aims to predict the initial relaxation of birefringence using Principal Component Analysis (PCA) and Long Short-Term Memory (LSTM) networks. By reducing the dimensionality of the data frame features, we can plot the principal components (PCs) that retain most of the information and treat them as time series. We employ LSTM by training with the data before the flow stops and predicting the behavior afterward. Consequently, we reconstruct the data frames from the obtained predictions and compare them to the original data.

Cellulose Nanofibrils (CNFs), highly present in nature, can be used as building blocks for future sustainable materials, including strong and stiff filaments. A rheo-optical flow-stop technique is used to conduct experiments to characterize the CNFs by studying Brownian dynamics through the CNFs' birefringence decay after stop. As the experiments produce large quantities of data, we reduce their dimensionality using Principal Component Analysis (PCA) and exploit the possibility of visualizing the reduced data in two ways. First, we plot the principal components (PCs) as time series, and by training LSTM networks assigned for each PC time series with the data before the flow stop, we predict the behavior after the flow stop (Bragone et al., 2024). Second, we plot the first PCs against each other to create clusters that give information about the different CNF materials and concentrations. Our approach aims at classifying the CNF materials to varying concentrations by applying unsupervised machine learning algorithms, such as k-means and Gaussian Mixture Models (GMMs). Finally, we analyze the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF) of the first principal component, detecting seasonality in lower concentrations.

Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is still limited compared to numerical methods, mainly when used in applications that model realistic systems. The network initialization follows a random distribution of the initial weights, as in the case of traditional neural networks, which could lead to severe model convergence bottlenecks. To overcome this problem, we follow current studies that deal with optimal initial weights in traditional neural networks. In this paper, we use a convex optimization model to improve the initialization of the weights in PINNs and accelerate convergence. We investigate two optimization models as a first training step, defined as pre-training, one involving only the boundaries and one including physics. The optimization is focused on the first layer of the neural network part of the PINN model, while the other weights are randomly initialized. We test the methods using a practical application of the heat diffusion equation to model the temperature distribution of power transformers. The PINN model with boundary pre-training is the fastest converging method at the current stage.

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric uncertainties in big multi-scale problems remains challenging. We propose $PINN a novel method of computing global uncertainty in PDEs using a Bayesian framework, by combining local Bayesian Physics-Informed Neural Networks (BPINN) with domain decomposition. The solution continuity across subdomains is obtained by imposing the flux continuity across the interface of neighboring subdomains. To demonstrate the effectiveness of $PINN, we conduct a series of computational experiments on PDEs in 1D and 2D spatial domains. Although we have adopted conservative PINNs (cPINNs), the method can be seamlessly extended to other domain decomposition techniques. The results infer that the proposed method recovers the global uncertainty by computing the local uncertainty exactly more efficiently as the uncertainty in each subdomain can be computed concurrently. The robustness of $PINN is verified by adding uncorrelated random noise to the training data up to 15% and testing for different domain sizes.