Non-linear Motion Trajectories Research Articles

A novel approach for estimating lung tumor motion based on dynamic features in 4D-CT

Due to the high expenses involved, 4D-CT data for certain patients may only include five respiratory phases (0%, 20%, 40%, 60%, and 80%). This limitation can affect the subsequent planning of radiotherapy due to the absence of lung tumor information for the remaining five respiratory phases (10%, 30%, 50%, 70%, and 90%). This study aims to develop an interpolation method that can automatically derive tumor boundary contours for the five omitted phases using the available 5-phase 4D-CT data. The dynamic mode decomposition (DMD) method is a data-driven and model-free technique that can extract dynamic information from high-dimensional data. It enables the reconstruction of long-term dynamic patterns using only a limited number of time snapshots. The quasi-periodic motion of a deformable lung tumor caused by respiratory motion makes it suitable for treatment using DMD. The direct application of the DMD method to analyze the respiratory motion of the tumor is impractical because the tumor is three-dimensional and spans multiple CT slices. To predict the respiratory movement of lung tumors, a method called uniform angular interval (UAI) sampling was developed to generate snapshot vectors of equal length, which are suitable for DMD analysis. The effectiveness of this approach was confirmed by applying the UAI-DMD method to the 4D-CT data of ten patients with lung cancer. The results indicate that the UAI-DMD method effectively approximates the lung tumor’s deformable boundary surface and nonlinear motion trajectories. The estimated tumor centroid is within 2 mm of the manually delineated centroid, a smaller margin of error compared to the traditional BSpline interpolation method, which has a margin of 3 mm. This methodology has the potential to be extended to reconstruct the 20-phase respiratory movement of a lung tumor based on dynamic features from 10-phase 4D-CT data, thereby enabling more accurate estimation of the planned target volume (PTV).

Experimental investigation on responses characteristics of a mooring line with imposed top-end motions

A series of experiments were performed to investigate the dynamic response of a mooring line based on the catenary configuration with imposed surge and heave motions in a water flume with a considered model scale factor of 1:70. The surge and heave motions with different amplitudes and periods were driven by a programmable electrical motor at the fairlead position, respectively. The dynamic tensions and motion trajectories of the mooring line were measured to illustrate the effects of pretension and motion period on the predominant harmonic components in the dynamic response. The results show that the pretension and motion period have significant effects on the dynamic tensions and nonlinear motion trajectories of the mooring line. Multiple harmonic components of the dynamic tension are observed at the fairlead and the predominant harmonic tensions are found to be changed with variations of the pretension and motion period. A sharp increase of the maximum tension force is observed at large pretension for the mooring line with the surge and heave imposed motions. Such sharp tension increase may result in floating platform and mooring system breakage. The results of this paper revel the foundation of the further studies on the transforming mechanism of the slack and taut state of the mooring line as well as for optimism of the engineering designs in floating offshore devices mooring installations.

Rotation double prisms steered by noncircular gear pairs to scan specified nonlinear trajectories.

In order to scan some specified nonlinear motion trajectories with high accuracy, simple control process, and good stability, we propose a method to design the drive mechanism of the rotation double-prism scanner, which can transfer the nonlinear motor control to the profile design of corresponding noncircular gear pairs. Given a nonlinear target trajectory, this method can successfully change the complicated nonlinear motion of the motor to the more operative uniform rotation. The simulation and experiment results show that the tracking error is less than 0.981mm in the distance of 500mm between the actual tracking trajectory and the original one. The proposed drive mechanical setup offers a perfect alternative to the nonlinear control design of the rotation double-prism scanner.

Modeling and simulation of bearing clearance effects on journal center motion trajectories

A computer aided study to predict the effect of radial clearance on stability parameters and journal center motion trajectories of a hydrodynamic journal bearing is presented. A Reynold’s equation governing fluid-flow in the clearance space is discretized with four noded quadrilateral isoparametric type of elements implementing finite element method technique. The stiffness parameters are obtained using perturbation method, whereas the damping parameters are obtained by differentiating pressure derivative with respect to journal center motion. In the current study, the influence of clearance parameter on critical mass along with threshold speed for different eccentricity ratio is investigated. Linear as well as Nonlinear journal motion trajectories are computed by solving the equations of motion with fourth order Runge Kutta iterative method. It is reported that nonlinear motion trajectories gives enhanced stability margin in terms of the critical mass than that of linear motion trajectories.

TrackCam

Panning and tracking shots are popular photography techniques in which the camera tracks a moving object and keeps it at the same position, resulting in an image where the moving foreground is sharp but the background is blurred accordingly, creating an artistic illustration of the foreground motion. Such shots however are hard to capture even for professionals, especially when the foreground motion is complex (e.g., non-linear motion trajectories). In this work we propose a system to generate realistic, 3D-aware tracking shots from consumer videos. We show how computer vision techniques such as segmentation and structure-from-motion can be used to lower the barrier and help novice users create high quality tracking shots that are physically plausible. We also introduce a pseudo 3D approach for relative depth estimation to avoid expensive 3D reconstruction for improved robustness and a wider application range. We validate our system through extensive quantitative and qualitative evaluations.

Autonomous framework for segmenting robot trajectories of manipulation task

In manipulation tasks, motion trajectories are characterized by a set of key phases (i.e., motion primitives). It is therefore important to learn the motion primitives embedded in such tasks from a complete demonstration. In this paper, we propose a core framework that autonomously segments motion trajectories to support the learning of motion primitives. For this purpose, a set of segmentation points is estimated using a Gaussian Mixture Model (GMM) learned after investigating the dimensional subspaces reduced by Principal Component Analysis. The segmentation points can be acquired by two alternative approaches: (1) using a geometrical interpretation of the Gaussians obtained from the learned GMM, and (2) using the weights estimated along the time component of the learned GMM. The main contribution of this paper is the autonomous estimation of the segmentation points based on the GMM learned in a reduced dimensional space. The advantages of such an estimation are as follows: (1) segmentation points without any internal parameters to be manually predefined or pretuned (according to the types of given tasks and/or motion trajectories) can be estimated from a single training data, (2) segmentation points, in which non-linear motion trajectories can be better characterized than by using the original motion trajectories, can be estimated, and (3) natural motion trajectories can be retrieved by temporally rearranging motion segments. The capability of this autonomous segmentation framework is validated by four experiments. In the first experiment, motion segments are evaluated through a comparison with a human expert using a publicly available kitchen dataset. In the second experiment, motion segments are evaluated through a comparison with an existing approach using an open hand-writing database. In the third experiment, the segmentation performance is evaluated by retrieving motion trajectories from the reorganization of motion segments. In the fourth experiment, the segmentation performance is evaluated by clustering motion segments.

Effects of turbulence on dynamic performance of accelerated/decelerated hydrodynamic journal bearing system

The hydrodynamic journal bearing system has found the wide spread application in high speed rotating machines such as compressors, gas turbines, steam turbines, etc. The rotors generally operate at high speed; therefore the lubricant flow in the clearance space of journal bearing does not remain laminar for accelerated/decelerated journals. Then, study of the dynamic response of the hydrodynamic journal bearing system considering superlaminar flow is needed. In this paper, the analysis is done for the fluid-low-field in the clearance space of hydrodynamic journal bearing system using short bearing assumption under laminar, transition and turbulent flow conditions. The positive pressure zone is established after deleting sub-ambient pressure around clearance space. Linear and non-linear motion trajectories at constant speed are obtained using the fourth order Runge-Kutta method. The non-linear motion trajectories during acceleration and deceleration are also obtained. Journal centre trajectories at constant speed and laminar flow, show the expected trend, i.e., system is stable below threshold speed curve, unstable above it, whereas for superlaminar flow, stable behaviour is found at some distance away from the stability curve. The behaviour during stopping/starting of journal centre trajectories is also obtained by non-linear equations of motion. The results also show the expected trend.

A comprehensive study of stability in an electro-statically actuated micro-beam

This paper studies the mechanical and bifurcation behavior of a capacitive micro-beam suspended between two conductive stationary plates, which can be used as a micro-switch or as a RF resonator. The equation of dynamic motion of the micro-switch is obtained using Euler–Bernoulli beam theorem. The equilibrium positions or the fixed points of the micro-switch are obtained by solving the equation of the static deflection using the step-by-step linearization method (SSLM) and discretizing by Galerkin weighted residual method. In order to study the global stability of the obtained fixed points a modified non-linear mass–spring model is used. Non-linear motion trajectories in phase portraits are given and regions of bounded and unbounded solutions separated by a homoclinic or heteroclinic orbits and positions of the stationary conductive plates are illustrated. Critical values of the applied voltage leading to qualitative changes in the micro-beam behavior through a saddle node or pitch fork bifurcations for different values of the gap and voltage ratios are obtained. The effects of different gaps and voltage ratios also are investigated.