Spatiotemporal modeling and forecasting is an essential task for many real-world problems, especially in the field of transportation and public health. The complex and dynamic patterns with dual attributes of time and space create unique challenges for effective modeling and forecasting. With the advancement of data collection, storage, and sharing technologies, the amount of data and the types of data available for spatiotemporal modeling research in transportation and public health are rapidly increasing. Some traditional spatiotemporal methods become obsolete. There is a need to review existing methods and propose new ones to harness the power of newly available data. Therefore, in this chapter, we conduct a comprehensive survey of methods and algorithms for spatiotemporal monitoring and forecasting, focusing on applications in transportation and public health. Then, we propose a systematic framework to incorporate three different approaches: statistical methods, machine learning methods, and mechanistic simulation methods. The proposed framework is expected to help researchers in the field to better formulate spatiotemporal problems, construct appropriate models, and facilitate new developments that combine the strengths of mechanistic approaches and data-driven ones. The proposed general framework is illustrated via examples of spatiotemporal methods developed in transportation and public health.

A novel data-driven framework to monitor the health status of high-speed rail suspension system by measuring train vibrations is proposed herein. Unlike existing methods, this framework does not rely on sophisticated dynamic models or high-fidelity simulations; it combines the power of data and domain knowledge to generate a model that can be trained quickly and adapted easily to different rail systems. In addition, the framework includes a module to generate a training dataset, tackling a typical challenge in real-world system monitoring, namely, the lack of labeled data due to practical limits. Based on the multi-output support vector regression (MSVR), the proposed framework can monitor the stiffness and damping coefficients of the suspension system using vibration signals measured on trains in real time. The framework comprises three modules. First, a simple suspension system dynamics model is built to generate a training dataset. Furthermore, key features are extracted from frequency response curves to reflect the impact of spring and damper degradation. Subsequently, a supervised learning model based on the MSVR is built to predict the stiffness and damping coefficients of suspension systems from features extracted in the second module. Once the model is built, real-time monitoring can be achieved by feeding the vibration signals as they are collected during operations. The proposed framework was evaluated on simulation data for its accuracy and tested on real-world operational data for its practicability.