The terminal airspace that surrounds an airport is the area with high flight density and complex structure. Aircraft are asked to follow the standard arrival and departure routes in terminal airspace, yet the actual trajectories may deviate due to air traffic control (ATC) instructions, pilots' decisions, surveillance and flying performance variations, etc. Predicting aircraft trajectories considering such uncertainties plays a crucial role in evaluating a redesign of the standard routes. Traditional simulation approaches for generating aircraft trajectories in a terminal airspace are cumbersome to use as it requires a detailed setup for each new scenario, while most existing data-driven methods can only be used in an airspace with historical trajectories, not applicable to new structure designs or other terminal areas. To fill in gap, in this paper, we develop a new model based on Multilayer Perceptron Neural Network (MLPNN) to predict aircraft trajectories with uncertainties for terminal airspace design evaluations. A key feature of the proposed model is that it is trained on existing standard routes yet it can be applied to new standard routes to generate trajectories. The enabler of the model's transferability is a novel input-and-output construction method for feature representations of raw trajectory data based on domain knowledge, including trajectory reconstruction, feature engineering, and output designing. After the input-and-output construction, a supervised learning model based on MLPNN is built to predict the standard deviations from the extracted features using historical trajectory data of existing standard routes. Once the model is built, trajectories with uncertainty can be simulated, through applying Gaussian distribution and exponential moving average algorithms, even on newly designed standard routes, where no aircraft have flown yet. Subsequently, new terminal airspace designs could be evaluated for their safety, efficiency, and environmental implications based on the simulated trajectories. The proposed model was tested on real-world operational data. Results showed that the model can quantify the characteristics of aircraft trajectories that are transferable across standard routes, and generate trajectories for new standard routes. We also demonstrated the proposed model on evaluating deficiencies on fuel consumption of actual arrival trajectories compared with the designed arrival routes. The generated trajectories showed 23%–37% more fuel consumption on average than the standard arrival routes in the terminal airspace of Hong Kong International Airport, which was validated with actual flight data.

In the above article [1], Table I, III, and IV should show 'N/m' instead of 'kN/m' and they should also show 'Ns/m' instead of 'kNs/m.' The revised tables are shown below. Also, in (1), “k_pw ” should be changed to “k_pw.” And on page 2952, first line, in the left column, “They also found…” should be changed to “We also found…”.

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.