Stochastic modelling and numerical simulation of fatigue damage

In continuum damage mechanics, fatigue is a phenomenon associated with a continuous material stiffness reduction. Numerically, it can be simulated as an accumulation of damage process. Since the resistance of concrete material reduces drastically after the initiation of macroscopic cracks, fatigue life can be approximated using damage models as the number of cycles by which the material continuity vanishes. The fatigue scatter is an interpretation of material heterogeneity and uncertain external influences. It can be reproduced by treating the damage evolution as a stochastic process. Inspired by the application of the stochastic process in molecular physics, the deterministic damage evolution rate of the Lemaitre model is modified as a stochastic differential equation to characterise the random damage increment. The implicit Euler scheme associated with Monte-Carlo simulation is demonstrated as a practical approach to solve the stochastic integration problem. The stochastic damage model is designed carefully to obey the thermodynamic principles and the deterministic damage law. Particular efforts are addressed to determine suitable random distributions, avoiding negative random damage increments in individual realisations, to have a statistically unbiased mean. To adequately approximate the high-cycle fatigue damage with random noise, the "jumping-cycle" algorithms with different extrapolation strategies are investigated. This damage model is further implemented in the simulation of four-point flexural fatigue of concrete beam, solved by the finite element method. The numerically reproduced fatigue data closely fit the published experimental results and the empirical solution, both in the mean and standard deviation. Compared to the Gaussian white noise, the Weibull random variable has broad applicability to simulate random fatigue damage and other physical processes.Um die Streuung der Messdaten in der Materialermüdung zu beschreiben, wird basierend auf Zufallsprozessen ein phenomenologische Modellierung vorgestellt. Erprobt wird die Modellierung an einem Betonbalken mit ebener Finite Element Diskretisierung, wobei die stochastischen Ermüdungsgleichungen mit der Monte Carlo Methode gelöst werden. Die simulierten Ermüdungsprozesse unter Biegebeanspruchung des quasi-spröden Materialswerden mit experimentellen Daten und etablierten empirischen Gleichungen vergleichen. Um hochzyklische Beanspruchungen zu behandeln, wird ein „jumping-cycle“ Algorithmus angewendet, mit dem die Rechenzeiten stark reduziert werden. Dieser Modellansatz ermöglicht die Simulation von Ermüdungsprozessen mit probabilistischen Information in einem sehr langen Zeitintervall. In derKontinuums-Modellierung geht der Prozess der Materialermüdung mit einer Degeneration der materiellen Integrität einher, die sich z.B. in der Abnahme des elastischen Moduls niederschlägt. Numerisch wird dies als ein kumulativer Schädigungsprozess modelliert. Weil der Materialwiderstand von Beton nach der Entstehung makroskopischer Risse drastisch abnimmt, kann die Ermüdungslebensdauer unter zyklischer Beanspruchung durch ein Schädigungsmodell praktisch sehr gut abgeschätzt werden, sobald das Auftreten makroskopischer Risse prognostiziert wird. Die Streuung in experimentell ermittelten Ermüdungskurven kann durch die mikro-Heterogenität der Materialien und Unsicherheiten in weiteren externen Faktoren verstanden werden, mittels einer Modellierung der Schädigungsentwicklung als stochastische Prozessgleichungen kann diese gut reproduziert werden. In Anlehnung an die Beschreibung stochastischer Prozesse in der theoretischen Physik werden die volutionsgleichungen für die Schädigungsentwicklung des Lemaitre-Modells als stochastische Differentialgleichungen dargestellt. Diese werden mittels impliziter Euler-Verfahren und Monte-Carlo Methoden effizient gelöst. Um die thermodynamische Konsistenz sicherzustellen, insbesondere negative Inkremente der Schädigungsentwicklung zu vermeiden, und unverzerrte statistische Mittel-werte zu erhalten, werden klassische Gaußsche Prozesse durch Weibull-Verteilungen substituiert. Für hochzyklische Belastungen werden „jumping-cycle“ Algorithmen hinsichtlich der Extrapolations-strategien systematisch untersucht. Am Beispiel eines Betonträgers unter Biegebeanspruchung wird das Ermüdungsverhalten simuliert und mit experimentellen Ergebnissen aus der Literatur und empirischen Formeln vergleichen. Der vorgeschlagene Modellierungsansatz zeigt eine gute Übereinstimmung der Mittelwerte und Standardabweichungen mit den publizierten Erkenntnissen. Wenngleich die hier verwendeteWeibull-Statistik im strengen mathematischen Sinne nicht konsistent sein sollte, hat sich diese jedoch als physikalisch konsistent erwiesen, um streuende Ermüdungsschädigung effizient zu beschreiben

DiffKendall: A Novel Approach for Few-Shot Learning with Differentiable Kendall's Rank Correlation

Few-shot learning aims to adapt models trained on the base dataset to novel tasks where the categories are not seen by the model before. This often leads to a relatively uniform distribution of feature values across channels on novel classes, posing challenges in determining channel importance for novel tasks. Standard few-shot learning methods employ geometric similarity metrics such as cosine similarity and negative Euclidean distance to gauge the semantic relatedness between two features. However, features with high geometric similarities may carry distinct semantics, especially in the context of few-shot learning. In this paper, we demonstrate that the importance ranking of feature channels is a more reliable indicator for few-shot learning than geometric similarity metrics. We observe that replacing the geometric similarity metric with Kendall's rank correlation only during inference is able to improve the performance of few-shot learning across a wide range of datasets with different domains. Furthermore, we propose a carefully designed differentiable loss for meta-training to address the non-differentiability issue of Kendall's rank correlation. Extensive experiments demonstrate that the proposed rank-correlation-based approach substantially enhances few-shot learning performance

AutoEval-Video: An Automatic Benchmark for Assessing Large Vision Language Models in Open-Ended Video Question Answering

We propose a novel and challenging benchmark, AutoEval-Video, to comprehensively evaluate large vision-language models in open-ended video question answering. The comprehensiveness of AutoEval-Video is demonstrated in two aspects: 1) AutoEval-Video constructs open-ended video-questions across 9 skill dimensions, addressing capabilities of perception, comprehension, and generation. 2) AutoEval-Video contains newly collected videos that cover over 40 distinct themes. To efficiently evaluate responses to the open-ended questions, we employ an LLM-based evaluation approach, but instead of merely providing a reference answer, we annotate unique evaluation rules for every single instance (video-question pair). To maximize the robustness of these rules, we develop a novel adversarial annotation mechanism. By using instance-specific rules as prompt, GPT-4, as an automatic evaluator, can achieve a stable evaluation accuracy of around 97.0\%, comparable to the 94.9\% - 97.5\% accuracy of a human evaluator. Furthermore, we assess the performance of eight large vision-language models on AutoEval-Video. Among them, GPT-4V(ision) significantly outperforms other models, achieving an accuracy of 32.2\%. However, there is still substantial room for improvement compared to human accuracy of 72.8\%. By conducting an extensive case study, we uncover several drawbacks of GPT-4V, such as limited temporal and dynamic comprehension, and overly general responses. Code is available at \href{https://github.com/Xiuyuan-Chen/AutoEval-Video}{\color{magenta}https://github.com/Xiuyuan-Chen/AutoEval-Video}

FILM: How can Few-Shot Image Classification Benefit from Pre-Trained Language Models?

Few-shot learning aims to train models that can be generalized to novel classes with only a few samples. Recently, a line of works are proposed to enhance few-shot learning with accessible semantic information from class names. However, these works focus on improving existing modules such as visual prototypes and feature extractors of the standard few-shot learning framework. This limits the full potential use of semantic information. In this paper, we propose a novel few-shot learning framework that uses pre-trained language models based on contrastive learning. To address the challenge of alignment between visual features and textual embeddings obtained from text-based pre-trained language model, we carefully design the textual branch of our framework and introduce a metric module to generalize the cosine similarity. For better transferability, we let the metric module adapt to different few-shot tasks and adopt MAML to train the model via bi-level optimization. Moreover, we conduct extensive experiments on multiple benchmarks to demonstrate the effectiveness of our method

Information Flow in Self-Supervised Learning

In this paper, we provide a comprehensive toolbox for understanding and enhancing self-supervised learning (SSL) methods through the lens of matrix information theory. Specifically, by leveraging the principles of matrix mutual information and joint entropy, we offer a unified analysis for both contrastive and feature decorrelation based methods. Furthermore, we propose the matrix variational masked auto-encoder (M-MAE) method, grounded in matrix information theory, as an enhancement to masked image modeling. The empirical evaluations underscore the effectiveness of M-MAE compared with the state-of-the-art methods, including a 3.9% improvement in linear probing ViT-Base, and a 1% improvement in fine-tuning ViT-Large, both on ImageNet