Based on the Quick Access Recorder (QAR) data covering over 9000 routes in China, the monthly and intra-day distribution characteristics of aircraft bumpiness at different levels were analyzed, and the relationships between the eddy dissipation rate (EDR) and other aircraft flight status elements during bumpiness occurrence were also analyzed. Afterward, aircraft bumpiness routes were constructed using 19 machine learning models. The analyses show that (1) aircraft bumpiness was mainly concentrated between 0:00 a.m. and 17:00 p.m. Severe aircraft bumpiness occurred more frequently in the early morning in January, especially between 5:00 a.m. and 6:00 a.m., and moderate bumpiness always occurred from 3:00 a.m. to 11:00 a.m. (2) The relationship between the left and right attack angles and aircraft bumpiness on the routes was more symmetrical, with a center at 0 degrees, unlike in the approach area where the hotspots were mainly concentrated in the range of −5 to 0 degrees. In the approach area, the larger the Mach number, the more severe the bumpiness. (3) The performances of the Automatic Relevance Determination Regression (ARD), Partial Least Squares Regression (PLS), Elastic-Net Regression (ENR), Classification and Regression Tree (CART), Passive Aggressive Regression (PAR), Random Forest (RF), Stochastic Gradient Descent Regression (SGD), and Tweedie Regression (TWD) based models were relatively good, while the performances of the Huber Regression (HUB), Least Angle Regression (LAR), Polynomial Regression (PLN), and Ridge Regressor (RR) based models were very poor. The aircraft bumpiness prediction models performed best over the approach area of ZBDT (airport in Datong), ZULS (airport in Lhasa), ZPPP (airport in Kunming), and ZLQY (airport in Qingyang). The model performed best in predicting the ZLLL-ZBDT air route (flight routes for Lanzhou to Datong) with different prediction times.

The idea of experimental design has been widely used in subsampling algorithms to extract a small portion of big data that carries useful information for statistical modeling. Most existing subsampling algorithms of this kind are model-based and designed to achieve the corresponding optimality criteria for the model. However, data generating models are frequently unknown or complicated. Model-free subsampling algorithms are needed for obtaining samples that are robust under model misspecification and complication. This paper introduces two novel algorithms, called the Projection-Uniform Subsampling algorithm and its extension. Both algorithms aim to extract a subset of samples from big data that are space-filling in low-dimensional projections. We show that subdata obtained from our algorithms perform superiorly under the uniform projection criterion and centered $L_2$-discrepancy. Comparisons among our algorithms, model-based and model-free methods are conducted through two simulation studies and two real-world case studies. We demonstrate the robustness of our proposed algorithms in building statistical models in scenarios involving model misspecification and complication.