Since the attacks carried out against the United States on September 11, 2001, which involved the commandeering of commercial aircraft, interest has increased in performing trajectory analysis of vehicle types not constrained by roadways or railways, i.e., aircraft and watercraft. Anomalous trajectories need to be automatically identified along with other trajectories of interest to flag them for further investigation. There is also interest in analyzing trajectories without a focus on anomaly detection. Various approaches to analyzing these trajectories have been undertaken with useful results to date. In this research, we seek to augment trajectory analysis by carrying out analysis of the trajectory curvature along with other parameters, including distance and total deflection (change in direction). At each point triplet in the ordered sequence of points, these parameters are computed. Adjacent point triplets with similar values are grouped together to form a higher level of semantic categorization. These categorizations are then analyzed to form a yet higher level of categorization which has more specific semantic meaning. This top level of categorization is then summarized for all trajectories under study, allowing for fast identification of trajectories with various semantic characteristics.
Laky, Daniel; Xu, Shu; Rodriguez, Jose S.; Vaidyaraman, Shankar; Munoz, Salvador G.; Laird, Carl D.
To increase manufacturing flexibility and system understanding in pharmaceutical development, the FDA launched the quality by design (QbD) initiative. Within QbD, the design space is the multidimensional region (of the input variables and process parameters) where product quality is assured. Given the high cost of extensive experimentation, there is a need for computational methods to estimate the probabilistic design space that considers interactions between critical process parameters and critical quality attributes, as well as model uncertainty. In this paper we propose two algorithms that extend the flexibility test and flexibility index formulations to replace simulation-based analysis and identify the probabilistic design space more efficiently. The effectiveness and computational efficiency of these approaches is shown on a small example and an industrial case study.