The Master Curve methodology, standardized ASTM E1921, provides a direct characterization of the reference temperature T0. Guaranteeing an accurate estimation of T0 is a major challenge due to its sensitivity to various parameters, including test matrix (number of specimens, test temperatures) and geometry configuration (dimensions, precrack front). This dependence is all the more significant with the new miniaturized mini-CT specimens. This paper discusses requirements of ASTM E1921 standard and gives recommendations for different specimen sizes. The analyses are based on finite element analysis and Beremin cleavage fracture model to replicate physical fracture toughness tests, followed by Monte Carlo sampling to quantify the statistical dispersion of T0 estimates. The main conclusions provide recommendations for a more accurate estimation of T0 and suggestions for updating the standard requirements. These include recommendations on the number of tests, the estimation of standard deviation, a suggested new test temperature range for mini-CTs, an extended range of dimensional imperfections, and updates to precrack front specifications.

In a context of uncertainty quantification, the probabilistic model of a random vector at the input of a computational code is not always known. An identification of the joint distribution on a restricted sample of experimental data can lead to a bad calibration of the model. The quantity of interest estimated at the output of the code is then subject to a bi-level epistemic uncertainty that must be properly quantified. A first level arises from the statistical estimation whilst a second one comes from the identification of the probabilistic model. Each epistemic uncertainty can thus be reduced by an enrichment with new data, either by increasing the size of the estimation sample or by increasing the size of the identification sample. When gathering data is costly, it is then interesting to know which uncertainty source to reduce first, thus introducing a trade-off between simulation and physical experiment. This paper aims at presenting a sensitivity-analysis-guided enrichment procedure in a small data context to improve the estimation quality of a quantity of interest. The proposed methodology is shown to be both low cost and adaptive by introducing importance-sampling-based methods. The performance of the guided enrichment procedure is assessed on three examples.

Understanding the environment is crucial for autonomous robots to perform navigation and manipulation tasks. Never-seen-before objects may have complex appearances and dynamics, where only physical interactions can help to identify visually hidden properties like mass or friction. In this work we propose a baseline for the newly defined problem of using physical interactions to discover unknown properties of objects, without prior knowledge of them or any supervision. The agent first uses intrinsically motivated unsupervised reinforcement learning to learn how to interact with objects, so as to get observations with a level of information which eases the physical properties estimation. A self-supervised predictive task is then set up while following the learned behaviour to extract a latent representation of the physical properties of an object. When applied to a simulated mobile robot in presence of varying objects, the proposed baseline identifies and differentiates categorical properties, e.g. shape, and quantifies continuous properties, e.g. mass and friction, with excellent correlations to their true values even from noisy observations. It achieves significantly better results than simple interactions of a policy that performs poor exploration. This work provides an implementation of a functional, object-oriented action-perception cycle for embodied robotic agents.

With the European Union legislative push to phase out internal combustion engines by 2035, the demand for electric vehicles and efficient energy storage solutions, particularly lithium-ion batteries, is set to rise. Addressing this demand necessitates both the optimization of battery lifespan and the development of robust methodologies for real-time assessment of state of health and prediction of remaining useful life. This study introduces a novel hybrid grey-box prognostic and health management framework that combines a physical battery model with a multi-layer perceptron particle filter (MLP-PF) for real-time estimation of degradation parameters. The approach leverages an electrochemical model developed in Modelica to simulate battery voltage and track degradation parameters, thereby capturing the battery dynamic behavior over time. By integrating a data-driven MLP-PF, this method adapts the physical degradation parameters, ensuring ongoing and precise estimation of remaining useful life. Experimental validation, in terms of accuracy and confidence interval coverage, confirms the framework capability in prediction and relative quantification of uncertainties. These results underscore the framework practical utility for battery management systems in electric vehicles, providing an adaptable and accurate tool for decision-makers in battery maintenance and replacement.

The simulation of random spatial variation in the mechanical properties of composite materials using random fields derived from their microstructure can be computationally demanding, since it often requires numerical homogenization of a large number of stochastic volume elements (SVEs). These SVEs are usually extracted from an initial image of the composite microstructure by using a moving window technique and their homogenized properties constitute the discrete data points of the random field at the centroid of each SVE. By replacing the expensive and highly repetitive homogenization procedure with a convolutional neural network (CNN), it is possible to perform nearly instant computations of random property fields. In this work, a CNN is proposed, that takes as input an SVE image and returns its apparent mechanical properties, and can therefore be applied along with the moving window technique. Training is performed on randomly generated SVEs with varying volume fractions and inclusion positions, which are representative of the SVEs obtained during processing of the initial large composite image. It is shown that the proposed CNN can accurately predict the mechanical properties of SVEs and it is subsequently applied for the prediction of random property fields derived from computer simulated and real microstructure images. Results show that, with the proposed methodology, it is possible to make accurate predictions of random fields within a few seconds, a procedure which could potentially require hours of computation time with the finite element based approach.

The integration of particle or Kalman filters with machine learning tools like support vector machines, Gaussian processes, or neural networks has seen extensive exploration in the context of prognostic and health management, particularly in model-based applications. This paper focuses on the Multi-Layer Perceptron Particle Filter (MLP-PF), a data-driven approach that harnesses the non-linearity of MLP to describe degradation trajectories without relying on a physical model. The Bayesian nature of the particle filter is utilized to update MLP parameters, providing flexibility to the method and accommodating unexpected changes in the degradation behavior. To showcase the versatility of MLP-PF, this work demonstrates its seamless integration into diverse use cases, such as lithium-ion battery analysis, virtual health monitoring for turbofans, and the assessment of fatigue crack growth. We illustrate how it effortlessly accommodates various contexts through slight parameter modifications. Adjustment includes variation in the number of neurons or layers in the MLP, threshold adjustments, initial training refinements and the adaptation of the process noise. Addressing different degradation processes across these applications, MLP-PF proves its adaptability and utility in various contexts. These findings highlight the method’s versatility in adapting to diverse use cases and its potential as a robust prognostic tool across various industries. MLP-PF offers a practical and efficient means of estimating remaining useful life and predicting degradation in complex systems, with implications for advancing prognostic tools in diverse applications.

Traditional remaining useful life (RUL) prediction methods based on particle filter (PF) require the manual tuning of hyperparameters, such as process or measurement noise, which poses challenges, particularly in real-life applications where external and operating conditions may change, potentially leading to large errors in the predictions. We address this issue by replacing the measurement equation of a PF with a mean variance estimation neural network that estimates the mean and the variance of the output distribution. As a result, the measurement noise is automatically estimated by the neural network and does not require manual setting. Through simulations and comparative analyses with state-of-the-art methods, the proposed mean variance estimation neural network particle filter (MVENN-PF) is shown to provide more stable and accurate RUL predictions, thereby potentially enhancing the robustness of battery health management systems based on it. Additionally, by eliminating the need to manually set a model hyperparameter (the measurement noise) the proposed method simplifies the modeling process, making it more accessible and adaptable to various battery systems.

In the automotive industry, sensors collect data that contain valuable driving information. The collected datasets are in multivariate time series (MTS) format, which are noisy, non-stationary, lengthy, and unlabeled, making them difficult to analyze and model. To understand the driving behavior at specific times of operation, we employ an unsupervised representation learning method. We present Temporal Neighborhood Coding for Maneuvering (TNC4maneuvering), which aims to understand maneuverability in smart transportation data via a use-case of bivariate accelerations from three operation days out of 2.5 years of driving. Our method proves capable of extracting meaningful maneuver states as representations. We evaluate them in various downstream tasks, including time-series classification, clustering, and multi-linear regression. Moreover, we propose methods for pruning the sizes of representations along with a window-size optimizing algorithm. Our results show that TNC4maneuvering has the capacity to generalize over longer temporal dependencies, although scalability and speedup present challenges.

The accurate estimation of the remaining useful life plays a crucial role in ensuring the reliability and efficiency of turbofan engines. In this study we address this objective by resorting to a virtual health indicator, previously developed by the authors for the estimation of the turbofan state of health, which is propagated in the future for estimating the engine end of life. The proposed approach consists in a combination of a multi-layer perceptron whose parameters are identified by a particle filter, in which the network act as a surrogate model for the hidden degradation state. The model is initialized on the basis of known degradation trajectories, and is recursively updated by the particle filter when new observations are available, providing flexibility to the method. To assess the effectiveness of the proposed approach, a comparison is made with a commonly used combination in the literature, which utilises a particle filter and a sum of two exponential functions. The results of the comparison demonstrate that the new approach achieves at least comparable results, and in the majority of cases, it outperforms the usual combination.

The Lithium-Ion Batteries (LIB) industry is rapidly growing and is expected to continue expanding exponentially in the next decade. LIBs are already widely used in everyday life, and their demand is expected to increase further, particularly in the automotive sector. The European Union has introduced a new law to ban Internal Combustion Engines from 2035, pushing for the adoption of electric vehicles and increasing the need for more efficient and reliable energy storage solutions such as LIBs. As a result, the establishment of Gigafactories in Europe and the United States is accelerating to meet the growing demand and partially reduce dependencies on China, which is currently the main producer of LIBs. To fully realize the potential of LIBs and ensure their safe and sustainable use, it is crucial to optimize their useful life and develop reliable and robust methodologies for estimating their state of health and predicting their remaining useful life. This requires a comprehensive understanding of LIB behavior and the development of effective prognostic and health management approaches that can accurately predict battery degradation, plan for maintenance and replacements, and improve battery performance and lifespan. This work, funded by the GREYDIENT project, a European consortium aiming to advance the state of the art in the grey-box approach, combines physical modeling (white box) and machine learning (black box) techniques to demonstrate the grey-box effectiveness in the Prognostic and Health Management. The grey-box approach here proposed consist in a combination of a physical battery model whose degradation parameters are estimated online at every cycle by a Multi-Layer Perceptron Particle Filter (MLP-PF). An electrochemical degradation model of a Lithium-Ion battery cell has been derived by use of Modelica. The model simulates the output voltage of the cell, while the degradation over time is simulate through the variation of 3 parameters: qMax (maximum number of Lithium-Ions available), R0 (Internal Resistance) and D (Diffusion Coefficient). To validate the model we resorted to the well-known NASA Battery Dataset, which has also been used to infer the optimal values of the three hidden degradation parameters at every cycle, to obtain their Run-to-Failure history. Then, the physical model is combined the MLP-PF: a MLPArtificial Neural Network is firstly trained on the Run-to-Failure degradation processes of the model parameters, allowing the propagation of the parameters in the future and the corresponding estimation of the battery Remaining Use ful Life (RUL). The MLP is then updated online by a Particle Filter every time a new measurement is available from the Battery Management System (BMS), providing flexibility to this method, needed for the electrochemical nature of the batteries, and allowing the propagation of uncertainties.

Multivariate time-series data contains valuable information, but are challenging to analyze and model. This study uses unsupervised representation learning approaches to extract meaningful representations from unlabeled data, which are used to identify patterns of underlying states. These representations can be later utilized as inputs in downstream tasks for prognosis and health management (PHM) of complex physical systems, with the aim of quantifying system's reliability and efficiency, and measuring the potential for failure, reducing downtime, and improving overall safety. We evaluate the performance of three advanced methods, namely Temporal Neighborhood Coding (TNC), Triplet Loss, and Contrastive Predictive Coding (CPC), on three simulated scenarios that mimic real-world situations. Key Performance Indicators are used as evaluation metrics for clustering and classification tasks. Our objective is to demonstrate the practicality of these approaches in multiple scenarios while remaining domain agnostic.

Quantifier l’influence globale de variables d’entrée sur l’estimation de la fiabilité d’un système relève d’un intérêt majeur pour garantir la robustesse de cette mesure et la sécurité du système. Pour ce faire, cette étude décline une formulation des indices de Sobol sur la fonction indicatrice et une stratégie d’estimation à moindre coût dans le contexte où les distributions des variables aléatoires d’entrée sont entachées d’incertitudes épistémiques.

This chapter considers a probabilistic framework for the input uncertainty modeling assuming sufficient information is available to construct a relevant input probabilistic model. It focuses on a specific class of reliability-oriented sensitivity analysis (ROSA) methods and its extension to reliability problems involving two uncertainty levels in input. The chapter presents the Sobol' indices on the indicator function. It proposes an extension of the previous indices to the case of a bi-level input uncertainty. The chapter analyses an efficient strategy based on both simulation and kernel density estimation so as to get efficient estimators for the indices. It illustrates the benefits of such a methodology on different test cases. The chapter also presents a class of global variance-based sensitivity indices adapted to ROSA. It also considers a disaggregated version of the augmented input vector to separate both types of uncertainty. The chapter then presents a simplified, but representative, fallout trajectory simulation model.

This chapter considers a finite set of uncertain scalar parameters modeled by a random vector. It introduces copulas for their practical use in the modeling of dependencies between random inputs. The chapter presents a brief review of some scalar and bivariate measures of dependence. The main computational task of the first-order reliability method is to search for the supposedly unique most probable failure point using a suitable optimization algorithm. Several methods are available to solve the optimization problem in equation, including general algorithms, such as the usual sequential quadratic programming algorithm, and others which have been specifically tailored to solve equation. The chapter also presents the main basis of some popular sampling methods, which are often used for the reliability assessment of rare events. The cross-entropy method is a generic approach that addresses a variety of problems, such as the probability estimation of rare events and the optimization of discrete or continuous problems.

Ce chapitre aborde l’estimation de probabilités faibles utiles pour l’analyse de la fiabilité de systèmes à fortes exigences de sûreté. La présentation inclut les méthodes FORM et SORM connues en fiabilité structurale, mais également les méthodes basées sur un échantillonnage naïf (Monte-Carlo) ou préférentiel (tirage d’importance, subset simulation). La sensibilité de la probabilité de défaillance calculée est également introduite.