Deep learning shows great potential for bearing fault diagnosis, but its effectiveness is severely limited by the prevalent issue of highly imbalanced data in real-world industrial settings, where fault events are extremely rare. This paper proposes a novel method for imbalanced bearing fault diagnosis that combines class-aware supervised contrastive learning with a quadratic network backbone. This integrated approach, named CCQNet, is designed to counter the effects of highly skewed data distributions by improving feature representation and classification fairness. Comprehensive experiments show that CCQNet substantially outperforms existing methods in handling imbalanced data, particularly at high imbalance ratios like 50:1. This study provides an effective and innovative solution for imbalanced bearing fault diagnosis. Source codes of this paper are available at https://github.com/yuweien1120/CCQNet for public evaluation.

Neural networks that overlook the underlying causal relationships among observed variables pose significant risks in high-stake decision-making contexts due to the concerns about the robustness and stability of model performance. To tackle this issue, we present a general approach for embedding hierarchical causal structure among observed variables into neural network to inform its learning. The proposed methodology, termed causality-informed neural network (CINN), exploits hierarchical causal structure learned from observational data as a structurally informed prior to guide the layer-to-layer architectural design of the neural network while maintaining the orientation of causal relationships in the discovered causal graph. The proposed method involves three steps. First, CINN mines causal relationships from observational data via directed acyclic graph (DAG) learning, where causal discovery is recast as a continuous optimization problem to circumvent the combinatorial nature of DAG learning. Second, we encode the discovered hierarchical causal graph among observed variables into neural network via a dedicated architecture and loss function. By classifying observed variables in the DAG as root, intermediate, and leaf nodes, we translate the hierarchical causal DAG into CINN by creating a one-to-one correspondence between DAG nodes and certain CINN neurons. For the loss function, both intermediate and leaf nodes in the DAG are treated as target outputs during CINN training, facilitating the co-learning of causal relationships among the observed variables. Finally, as multiple loss components emerge in CINN, we leverage the projection of conflicting gradients to mitigate gradient interference among the multiple learning tasks. Computational studies indicate that CINN outperforms several state-of-the-art methods across a broad range of datasets. In addition, an ablation study that incrementally incorporates structural and quantitative causal knowledge into the neural network is conducted to highlight the pivotal role of causal knowledge in enhancing neural network’s prediction performance.

Multi-state systems (MSS) are widely used for modeling the behavior of engineering applications, where the system and its components can have more than two distinct states. Physics-Informed Neural Networks (PINNs) offer a viable solution for characterizing the dynamic state evolution of MSS. However, existing methods predominantly rely on uniformly sampled collocation points across the problem domain when training PINNs. Although some residual-based active learning methods exist, they are inherently static and local, and often fail to capture a crucial aspect of PINN training: identification and accurate modeling of the “critical transition regions” within the problem domain. To address this fundamental challenge, we treat PINN as a dynamic system and introduce a novel active learning method grounded in chaos theory to identify regions within the problem domain that are highly sensitive to initial conditions. Specifically, our method quantifies the degree of chaos at candidate collocation points by introducing small perturbations and using PINN’s forward propagation to simulate the dynamic evolution of both the original and perturbed collocation points. Collocation points that exhibit pronounced chaotic behavior—- where evolutionary trajectories diverge rapidly following perturbation—are identified as the system’s most unstable and valuable regions for PINN training. By prioritizing these dynamically unstable points, our method directs PINN to focus its learning on accurately delineating the boundaries of state transitions, thereby significantly enhancing the accuracy of reliability analysis. Experimental results on multiple benchmark partial differential equations (PDEs) and several MSSs demonstrate that, compared to other PINN learning schemes, our method shows superior accuracy and computational efficiency in MSS reliability assessment.

Understanding causal relationships between traffic states throughout the system is of great significance for enhancing traffic management and optimization in urban traffic networks. Unfortunately, few studies in the literature have systematically analyzed causal structure characterizing the evolution of traffic states over time and gauged the importance of traffic nodes from a causal perspective, particularly in the context of large-scale traffic networks. Moreover, the dynamic nature of traffic patterns necessitates a robust method to reliably discover causal relationships, which are often overlooked in existing studies. To address these issues, we propose a Spatio-Temporal Causal Structure Learning and Analysis (STCSLA) framework for analyzing large-scale urban traffic networks at a mesoscopic level from a causal lens. The proposed framework comprises three main components: decomposition of spatio-temporal traffic data into localized traffic subprocesses; a Bayesian Information Criterion-guided spatio-temporal causal structure learning combined with temporal-dependencies preserving sampling for deriving reliable causal graph to uncover time-lagged and contemporaneous causal effects; establishing several causality-oriented indicators to identify causally critical nodes, mediator nodes, and bottleneck nodes in traffic networks. Experimental results on both a synthetic dataset and the real-world Hong Kong traffic dataset demonstrate that the proposed STCSLA framework accurately uncovers time-varying causal relationships and identifies key nodes that play various causal roles in influencing traffic dynamics. These findings underscore the potential of the proposed framework to improve traffic management and provide a comprehensive causality-driven approach for analyzing urban traffic networks.

It is common for multiple firms\textemdash such as manufacturers, retailers, and third-party insurers\textemdash to coexist and compete in the aftermarket for durable products. In this paper, we study price competition in a partially concentrated aftermarket where one firm offers multiple extended warranty (EW) contracts while the others offer a single one. The demand for EWs is described by the multinomial logit model. We show that, at equilibrium, such an aftermarket behaves like a combination of monopoly and oligopoly. Building upon this base model, we further investigate sequential pricing games for a durable product and its EWs to accommodate the ancillary nature of after-sales services. We consider two scenarios: one where the manufacturer (as the market leader) sets product and EW prices \emph{simultaneously}, and another where these decisions are made \emph{sequentially}. Our analysis demonstrates that offering EWs incentivizes the manufacturer to lower the product price, thereby expanding the market potential for EWs. Simultaneous product-EW pricing leads to a price concession on EWs compared to sequential pricing, effectively reducing the intensity of competition in the aftermarket. Overall, the competitiveness of an EW hinges on its ability to deliver high value to consumers at low marginal cost to its provider. While our focus is on EWs, the proposed game-theoretical pricing models apply broadly to other ancillary after-sales services.