Time-varying Velocity Research Articles

Numerical Study on the Water Entry of a Freely Falling Unmanned Aerial-Underwater Vehicle

The unmanned aerial–underwater vehicle (UAUV) is a new type of vehicle that can fly in the air and cruise in water and is expected to cross the free water surface several times to perform continuous uninterrupted observation and sampling. To analyze the hydrodynamic and motion characteristics of the vehicle, the whole water-entry process of a multi-degree-of-freedom UAUV with various velocity and pitch angle was investigated through a Reynolds-averaged Navier–Stokes method. The computational domain was meshed by trimmer cells. The relative movement between the vehicle and fluid domain was simulated using moving reference frame overset mesh to delineate the interaction region around vehicle body. To reduce the computational cost, adaptive mesh refinement and adaptive time-stepping strategy were used to capture the slamming pressure accurately with reasonable computational effort. First, convergence study is considered. Simulations of the vehicle with various initial velocities and different pitch angles were performed. The variable physical properties were analyzed, and detailed results through the time-varying force and velocity were shown. Initial velocity and pitch angle are found to significantly influence hydrodynamic behavior, including the time-varying force, while thickness ratio has a great impact on added mass and pressure. The results show that higher entry velocity results in greater peak vertical force. The transverse hydrodynamic characteristics for oblique water entry of the vehicle with varies pith angle are quite different.

Impact-Angle-Control Guidance Law with Terminal Constraints on Curvature of Trajectory

This paper presents an impact-angle-control guidance law with terminal constraints on the curvature of the missile trajectory. The formulation takes into account nonlinear kinematics and time-varying velocity, allowing for more general cases in which the flight path angle may not be small throughout the entire trajectory. The proposed optimal guidance law aims to minimize the change rate of pseudo-curvature, which is defined as a curvature with weighting factors based on the flight-path angle and range to go. The analysis shows that the trajectories generated by this nonlinear guidance law have a simple polynomial form with respect to downrange. Numerical simulations demonstrate that the cost function parameter can be used to shape the trajectories along the downrange.

Deep learning-based prediction of intra-cardiac blood flow in long-axis cine magnetic resonance imaging

Purpose: We aimed to design and evaluate a deep learning-based method to automatically predict the time-varying in-plane blood flow velocity within the cardiac cavities in long-axis cine MRI, validated against 4D flow. Methods: A convolutional neural network (CNN) was implemented, taking cine MRI as the input and the in-plane velocity derived from the 4D flow acquisition as the ground truth. The method was evaluated using velocity vector end-point error (EPE) and angle error. Additionally, the E/A ratio and diastolic function classification derived from the predicted velocities were compared to those derived from 4D flow. Results: For intra-cardiac pixels with a velocity > 5 cm/s, our method achieved an EPE of 8.65 cm/s and angle error of 41.27°. For pixels with a velocity > 25 cm/s, the angle error significantly degraded to 19.26°. Although the averaged blood flow velocity prediction was under-estimated by 26.69%, the high correlation (PCC = 0.95) of global time-varying velocity and the visual evaluation demonstrate a good agreement between our prediction and 4D flow data. The E/A ratio was derived with minimal bias, but with considerable mean absolute error of 0.39 and wide limits of agreement. The diastolic function classification showed a high accuracy of 86.9%. Conclusion: Using a deep learning-based algorithm, intra-cardiac blood flow velocities can be predicted from long-axis cine MRI with high correlation with 4D flow derived velocities. Visualization of the derived velocities provides adjunct functional information and may potentially be used to derive the E/A ratio from conventional CMR exams.

Cooperative optimal guidance of hypersonic glide vehicles by real-time optimization and deep learning

This paper investigates the cooperative optimal guidance of hypersonic glide vehicles (HGVs) in the terminal phase with consideration on time-varying velocity, aerodynamic forces, and practical constraints. The cooperative optimal guidance problem is formulated as an optimal control problem with time as the independent variable, which brings great convenience in controlling the impact time. We propose proper convexification techniques to convexify this problem and apply successive convex optimization to get the solution of the original problem. To achieve cooperative guidance of multiple HGVs with time coordination constraint, a deep learning–based approach is proposed to find an optimal common impact time assigned to all the HGVs. The training samples required by deep learning are obtained by convex optimization. An algorithm is then presented to summarize the cooperative optimal guidance strategy. In each guidance loop, the common impact time is updated according to mission conditions, and the guidance commands are generated by the successive solution procedure in real time. Numerical examples will be provided to demonstrate that the proposed cooperative optimal guidance algorithm is effective and efficient, and it can achieve better performance than a popular cooperative proportional navigation guidance law.

Reynolds number effects on the bistable flows over a wavy circular cylinder

The wake of wavy cylinder has been shown to exhibit bistability. Depending on the initial condition, the final state of the wake can either develop into steady flow (state I), or periodic shedding (state II). In this paper, we perform numerical simulations to reveal the Reynolds number effects (Re=30 – 300) on these two wake states. With increasing Reynolds number, the steady vortical structures in state I wake sways back and forth in the spanwise direction, resulting in low-frequency fluctuations in drag forces, but not in lift. For state II, the increase in Reynolds number is associated with the emergence of another spectral peak in the lift coefficient. The secondary frequency is associated with highly three-dimensional vortical structures in the wake. For both states, the wakes transition to turbulent flows at higher Reynolds numbers, with the development of small-scale vortices. We further study the streamwise gust flows over the wavy cylinder. The time-varying inflow velocity results in a wide range of instantaneous Reynolds number spanning from the absolutely unstable flow regime to the bistable regime. Depending on the period of the inflow velocity variation, the wake perturbations grown at the absolutely unstable flow regime can be damped out in state I wake, or grow large enough to trigger the transition to state II, resulting in loss of flow control efficacy. The above analyses reveal novel flow physics of the bistable states at unexplored Reynolds numbers, and showcase the complex transition behavior between the two states in unsteady flows. The insights gained from this study improve the understanding of the wake dynamics of the wavy cylinder.

Bearing-Only Formation Maneuvering Control of Multi-agent Systems with Time-Varying Leaders’ Velocity

This paper studies bearing-only formation maneuver control of multi-agent systems modeled as double-integrators. The developed distributed control makes the multi-agent system form a desired geometric pattern in which the target formation is bearing-constrained. The controlled agents are supposed to sense the bearing and bearing rate with respect to several neighboring agents, and the interaction among agents is characterized by a fixed undirected graph. Different from existing control approaches where the target formation or the leaders move at a constant velocity, this paper investigates the case where the leaders’ velocity is time-varying. For each follower agent, a finite-time velocity estimator is used to estimate its desired velocity. Then, a bearing-only control law is designed for the follower using a signum function, which renders the tracking error with respect to the leaders with time-varying velocity to converge to zero. The effectiveness of the control laws is illustrated by simulations.

Identification of modal parameters of long-span bridges under various wind velocities

The modal parameters identification of bridges under non-stationary environmental excitation has caught the attention of researchers. This paper studies the non-stationarity of wind velocity, and extracts the time-varying mean wind velocity based on a discrete wavelet transform and recursive quantitative analysis. The calculated turbulence intensity and turbulence integral scale under the non-stationary model are smaller than those under the stationary model, especially the turbulence integral scale. The empirical wavelet transform is used to identify the modal parameters of long-span bridges, and the power spectral density spectrum is proposed as a replacement for the Fourier spectrum as the basis of the frequency band selection. The bridge modal parameters are then compared using the covariance-driven stochastic subspace system identification method (SSI-COV) and the Hilbert transform method based on an improved empirical wavelet transform (EWT-HT). Both methods can accurately identify the modal frequency, and the absolute difference between these two methods is equal to 0.003 Hz. The wind velocity results in a change of less than 1% in the modal frequency. The absolute difference between the modal damping ratios identified using SSI-COV and EWT-HT is significant and can reach 0.587%. The modal damping ratios are positively correlated with the mean wind velocities, which aligns with the quasi-steady assumption. In addition, the applicability of SSI-COV and EWT-HT is also evaluated using the standard deviation, coefficient of variation, and range dispersion indicators. The results show that the EWT-HT is more applicable to the identification of the modal parameters of long-span bridges under non-stationary wind velocities.

Application scope of equivalent linear technique for across-wind response analysis of tall flexible structures considering nonlinear aero-elastic effect

Large across-wind response of tall flexible structures becomes an increasing concern due to the significant nonlinear aero-elastic effect. The nonlinear aerodynamic damping, which is in phase of time-variant structural velocity, is usually employed to describe nonlinear aero-elastic effect. For the sake of evaluating the across-wind response of tall flexible structures within the framework of linear random vibration theory, equivalent linear aerodynamic damping model is required, which can be deduced from either harmonic balance (HB)- or statistical linearization (SL) technique. This study addressed clarifying application scope of various equivalent linear techniques for evaluating across-wind response of tall flexible structures. By conducting the Monte Carlo simulation and free-vibration wind tunnel test, it is clarified that the root-mean-squared (RMS) response calculated by the HB equivalent linear aerodynamic damping is acceptable, while is not satisfactory with respect to the SL technique especially when the structure is with lower damping level, and in the vicinity of vortex lock-in wind speed. Moreover, it is found that neither HB- nor SL technique can accurately predict the peak response. It is revealed in this study that accuracy of various equivalent linear techniques is essentially affected by probability density function of across-wind response.

A Non-Stationary 6G UAV Channel Model With 3D Continuously Arbitrary Trajectory and Self-Rotation

In this paper, based on the geometric stochastic modeling method, a space-time-frequency (S-T-F) non-stationary model with three-dimensional (3D) continuously arbitrary trajectory and self-rotation is proposed for sixth generation (6G) massive multiple-input multiple-output (MIMO) millimeter wave (mmWave) unmanned aerial vehicle (UAV) channels. It is the first 6G massive MIMO mmWave UAV channel model that considers the 3D continuously arbitrary trajectory of UAV in practice and models S-T-F non-stationarity of 6G UAV channels. In the proposed model, the calculation of channel impulse response (CIR) is developed, which considers the 3D time-varying accelerations and self-rotations of transceivers and clusters. To further model the S-T-F non-stationarity of UAV channels, a novel UAV-related birth-death (BD) algorithm based on correlated clusters is developed. In the developed algorithm, the impact of typical UAV-related parameters, e.g., the UAV’s moving direction, altitude, and time-varying velocity, on the setting of correlated clusters and the BD process is sufficiently considered. Important channel statistical properties are derived and investigated. Some numerical results and interesting observations are given, which can provide some assistance for the design of 6G massive MIMO mmWave UAV communication systems. Finally, the utility of the proposed model is verified by the close agreement between simulation results and ray-tracing-based results.

Dynamic analysis of moving beams featuring time-varying velocity under self-excited force moving along with the end

Dynamic analysis of moving beams featuring time-varying velocity under self-excited force moving along with the end

A time-varying distributed unit hydrograph method considering soil moisture

Abstract. The distributed unit hydrograph (DUH) method has been widely used for flow routing in a watershed because it adequately characterizes the underlying surface characteristics and varying rainfall intensity. Fundamental to the calculation of DUH is flow velocity. However, the currently used velocity formula assumes a global equilibrium of the watershed and ignores the impact of time-varying soil moisture content on flow velocity, which thus leads to a larger flow velocity. The objective of this study was to identify a soil moisture content factor, which, based on the tension water storage capacity curve, was derived to investigate the response of DUH to soil moisture content in unsaturated areas. Thus, an improved distributed unit hydrograph, based on time-varying soil moisture content, was obtained. The proposed DUH considered the impact of both time-varying rainfall intensity and soil moisture content on flow velocity, assuming the watershed to be not in equilibrium but varying with soil moisture. The Qin River basin and Longhu River basin were selected as two case studies, and the synthetic unit hydrograph (SUH), the time-varying distributed unit hydrograph (TDUH) and the current DUH methods were compared with the proposed method. Then, the influence of time-varying soil moisture content on flow velocity and flow routing was evaluated, and results showed that the proposed method performed the best among the four methods. The shape and duration of the unit hydrograph (UH) were mainly related to the soil moisture content at the initial stage of a rainstorm, and when the watershed was approximately saturated, the grid flow velocity was mainly dominated by excess rainfall. The proposed method can be used for the watersheds with sparse gauging stations and limited observed rainfall and runoff data.

Simultaneous localization and formation using angle-only measurements in 2D

This paper solves the simultaneous localization and formation (SLAF) problem for a multi-agent system moving in 2D plane. The multi-agent system consists of leaders who have the knowledge of their absolute positions in the global coordinate frame, and followers who do not know their absolute positions but have angle-only measurements and communication with respect to their neighboring agents. The aim of SLAF is to simultaneously localize and control the followers such that a desired formation among the leaders and followers can be achieved by using locally available sensing and communication information. To handle the challenging situation where the formation becomes unlocalizable at some nongeneric configurations, a perturbation-based SLAF algorithm is proposed such that the SLAF task can be achieved with an asymptotic convergence. To meet different tasks’ requirements, three types of distributed SLAF algorithms are designed for the followers when the leaders are static, move with constant, or time-varying velocities, respectively. The effect of measurement noises, extension to other types of sensor measurements, requirement on agents’ coordinate frames, collision and collinearity avoidance are also discussed. To validate the theoretical results, simulation examples corresponding to the discussed scenarios are carried out.

Passively adaptive wind energy harvester featuring a double-airfoil bluff body with adjustable attack angles

In nature, the wind always fluctuates in magnitude. Hence, it is essential to consider the adaptability and durability of wind energy harvesters. This paper proposes a passively adaptive piezoelectric wind energy harvester with a double-airfoil bluff body to enhance performance subjected to time-varying wind velocity. The proposed double-airfoil bluff body is inspired by the fact that the attack angle can significantly affect the aerodynamic characteristics of the airfoil. An associated aero-electromechanical model is numerically developed to investigate the influence of the attack angle on the energy harvesting performance. Based on the aero-electromechanical model, the numerical results demonstrate three typical working modes that appear under different attack angles: vortex-induced vibration, galloping, and vibration suppression. These working modes can promise the proposed harvester to effectively and safely scavenge ambient wind energy. The physical mechanisms behind the three working modes are thoroughly explored given the work-energy principle and evolution of the vortex structure. The performance enhancement of the proposed harvester can be attributed to the positive aerodynamic work and an airfoil dynamic stall. Experiments are thereafter conducted to validate the theoretical results. Compared to the conventional galloping-based harvester with a square prism, the maximum voltage improvement percentage of the proposed harvester is over 62.3% within the investigated wind speed range when the attack angle is set to 10°.

Synthesis of patient-specific multipoint 4D flow MRI data of turbulent aortic flow downstream of stenotic valves.

We propose to synthesize patient-specific 4D flow MRI datasets of turbulent flow paired with ground truth flow data to support training of inference methods. Turbulent blood flow is computed based on the Navier–Stokes equations with moving domains using realistic boundary conditions for aortic shapes, wall displacements and inlet velocities obtained from patient data. From the simulated flow, synthetic multipoint 4D flow MRI data is generated with user-defined spatiotemporal resolutions and reconstructed with a Bayesian approach to compute time-varying velocity and turbulence maps. For MRI data synthesis, a fixed hypothetical scan time budget is assumed and accordingly, changes to spatial resolution and time averaging result in corresponding scaling of signal-to-noise ratios (SNR). In this work, we focused on aortic stenotic flow and quantification of turbulent kinetic energy (TKE). Our results show that for spatial resolutions of 1.5 and 2.5 mm and time averaging of 5 ms as encountered in 4D flow MRI in practice, peak total turbulent kinetic energy downstream of a 50, 75 and 90% stenosis is overestimated by as much as 23, 15 and 14% (1.5 mm) and 38, 24 and 23% (2.5 mm), demonstrating the importance of paired ground truth and 4D flow MRI data for assessing accuracy and precision of turbulent flow inference using 4D flow MRI exams.

CFD Simulation of a Submersible Passive Rotor at a Pipe Outlet under Time-Varying Water Jet Flux

During the past two decades, passive rotors have been proposed and introduced to be used in a number of different water sector applications. One of these applications is the use of a passive rotor at the outlets of pipe outfalls to enhance mixing. The main objective of this study is to develop a CFD computational workflow to numerically examine the feasibility of using a passive rotor downstream of the outlet of pipe outfalls to improve the mixing properties of the near flow field. The numerical simulation for a pipe outlet with a passive rotor is a numerical challenge because of the nonlinear water-structure interactions between the water flow and the rotor. This study utilizes a computational workflow based on the ANSYS FLUENT to simulate that water-structure interaction to estimate the variation in time of the angular speed (ω) of a passive rotor initially at rest and then subjected to time-varying water velocity (υ). Two computational techniques were investigated: the six-degrees-of-freedom (6DOF) and the sliding mesh (SM). The 6DOF method was applied first to obtain a mathematical relation of ω as a function of the water velocity (υ). The SM technique was used next (based on the deduced ω-υ relation by the 6DOF) to minimize the calculation time considerably. The study has shown that the 6DOF technique accurately determines both maximum and temporal angular speeds, with discrepancies within 3% of the measured values. A number of numerical runs were conducted to investigate the effect of the gap distance between the passive rotor and the pipe outlet and to examine the effect of using the passive rotor on the near flow field downstream of the rotor. The model results showed that as the gap distance of the pipe outlet to the passive rotor increases, the rotor’s maximum angular speed decreases following a decline power-law trend. The numerical model results also revealed that the passive rotor creates a spiral motion that extends downstream to about 15 times the pipe outlet diameter. The passive rotor significantly increases the turbulence intensity by more than 500% in the near field zone of the pipe outlet; however, this effect rapidly vanishes after four times the pipe diameter.

Three-dimensional enclosing control for stratospheric airship to circumnavigate a moving target

This paper addresses the problem of a stratospheric airship flying around a time-varying velocity moving target in a three-dimensional space under external disturbance. In order to achieve a spiral shape circumnavigation around the moving target, it is necessary to keep the same altitude as the moving target with time-varying height vertically while keeping a fixed circle radius around the moving target at the horizontal plane. First, based on the air current estimator, we design different guidance laws for different target tracking methods on the horizontal and vertical planes respectively, which can obtain the expected velocity and the expected angular velocity. Second, an adaptive backstepping attitude controller to track the desired yaw rate is introduced by estimating the boundaries of dynamic couplings and unknown disturbance. Finally, a velocity controller is added to track the desired velocity. Numerical simulations show the validity of this algorithm.

Bearing-Based Distributed Formation Control of Unmanned Aerial Vehicle Swarm by Quaternion-Based Attitude Synchronization in Three-Dimensional Space

Most of the recent research on distributed formation control of unmanned aerial vehicle (UAV) swarms is founded on position, distance, and displacement-based approaches; however, a very promising approach, i.e., bearing-based formation control, is still in its infancy and needs extensive research effort. In formation control problems of UAVs, Euler angles are mostly used for orientation calculation, but Euler angles are susceptible to singularities, limiting their use in practical applications. This paper proposed an effective method for time-varying velocity and orientation leader agents for distributed bearing-based formation control of quadcopter UAVs in three-dimensional space. It combines bearing-based formation control and quaternion-based attitude control using undirected graph topology between agents without the knowledge of global position and orientation. The performance validation of the control scheme was done with numerical simulations, which depicted that UAV formation achieved the desired geometric pattern, translation, scaling, and rotation in 3D space dynamically.

Numerical Investigation of an Unsteady Blade Surface Blowing Method to Reduce Rotor Blade-Vortex Interaction Noise

This paper presents a numerical investigation of unsteady surface blowing using periodic variations of jet velocity with azimuthal angle to reduce helicopter rotor blade-vortex interaction (BVI) noise. The unsteady blowing is modeled as the mass flow outlet boundary condition of time-varying jet velocity on the blade surface grid using computational fluid dynamics. The same high-resolution overset grid system and flow/noise solver are used to perform a detailed flow field simulation and noise prediction for the nonblowing baseline case and the steady/unsteady blowing cases under the rotor BVI condition, and a grid convergence study for the steady and unsteady blowing cases is carried out. The BVI noise reduction and rotor thrust coefficient results of the unsteady blowing method and the previously published steady blowing with constant jet velocity are then compared. The noise reduction level of unsteady blowing is approximately equivalent to that of steady blowing (noise reduction is more than 3 dB). However, the loss in rotor thrust coefficient caused by unsteady blowing (3.3%) is only half of that by steady blowing (6.3%); the air mass cost by unsteady blowing is only 63.7% of that by steady blowing per rotation revolution. The results show that unsteady blowing can effectively reduce BVI noise with lower cost and less thrust loss.

Maneuvering Angle Rigid Formations With Global Convergence Guarantees

Angle rigid multi-agent formations can simultaneously undergo translational, rotational, and scaling maneuvering, therefore combining the maneuvering capabilities of both distance and bearing rigid formations. However, maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are available. Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra, this paper aims to solve this challenging problem in both 2D and 3D under a leader-follower framework. For the 2D case where the leaders have constant velocities, by using local relative position and velocity measurements, a formation maneuvering law is designed for the followers governed by double-integrator dynamics. When the leaders have time-varying velocities, a sliding mode formation maneuvering law is proposed by using the same measurements. For the 3D case, to establish an angle-induced linear equation for each tetrahedron, we assume that all the followers' coordinate frames share a common <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> direction. Then, a formation maneuvering law is proposed for the followers to globally maneuver <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> -weakly angle rigid formations in 3D. The extension to Lagrangian agent dynamics and the construction of the desired rigid formations by using the minimum number of angle constraints are also discussed. Simulation examples are provided to validate the effectiveness of the proposed algorithms.

Adaptive Bearing-Only Formation Tracking Control for Nonholonomic Multiagent Systems

In this article, we consider the formation tracking problem of nonholonomic multiagent systems only using relative bearing measurements between the agents. Such a practical and important yet challenging issue has been taken into limited consideration by existing approaches, which usually requires additional measurements such as relative positions. The contributions of this article are two-fold. First, a fully distributed reference velocity estimator is proposed. Under the proposed adaptive estimator, each agent can estimate the time-varying reference velocity asymptotically. Second, an input-to-state stable controller is designed according to the bearing rigid theory. Under the proposed controller, the formation with bearing-only constraints can be achieved. Finally, the proposed scheme is demonstrated and its effectiveness is verified by presenting some simulation and experimental tests.