Understanding Long-Term Dynamics of Individual Metro Usage: A Hidden Semi-Markov State Framework with Survival Analysis

Understanding how individual metro usage evolves over multi-year horizons is essential for transit planning and passenger retention. However, existing approaches typically characterize mobility patterns as static clusters or short-term variability, leaving the lifecycle dynamics of transit participation underexplored. This study proposes a state-based lifecycle modeling framework that integrates Hidden Semi-Markov Models (HSMM) with discrete-time survival analysis to characterize the evolution of individual metro mobility. The HSMM infers latent mobility states with explicit duration distributions and a transition matrix governing regime changes, while the survival component models exit and re-entry events via state-dependent hazard functions conditioned on mobility-state trajectories and behavioral history. Applied to four years of smart card data from the Shanghai metro system (2021-2024), the framework enables the identification of interpretable mobility states, the characterization of transition dynamics, and the quantification of state-dependent exit and re-entry processes. The analysis reveals five robust mobility states with a directional transition hierarchy centered on an occasional-usage gateway state, and fundamentally different temporal mechanisms governing disengagement and return: exit hazard is state-dependent but duration-independent, whereas re-entry hazard decays sharply with inactivity length. These findings provide a methodological foundation for lifecycle-oriented mobility analysis and practical guidance for transit operators to identify at-risk users and time retention interventions.

A Blind Source Separation Framework to Monitor Sectoral Power Demand from Grid-Scale Load Measurements

As we are moving towards decentralized power systems dominated by intermittent electricity generation from renewable energy sources, demand-side flexibility is becoming a critical issue. In this context, it is essential to understand the composition of electricity demand at various scales of the power grid. At the regional or national scale, there is however little visibility on the relative contributions of different consumer categories, due to the complexity and costs of collecting end-users consumption data. To address this issue, we propose a blind source separation framework based on a constrained variant of non-negative matrix factorization to monitor the consumption of residential, services and industrial sectors at high frequency from aggregate high-voltage grid load measurements. Applying the method to Italy's national load curve between 2021 and 2023, we reconstruct accurate hourly consumption profiles for each sector. Results reveal that both households and services daily consumption behaviors are driven by two distinct regimes related to the season and day type whereas industrial demand follows a single, stable daily profile. Besides, the monthly consumption estimates of each sector derived from the disaggregated load are found to closely align with sample-based indices and be more precise than forecasting approaches based on these indices for real-time monitoring.