Equilibrium Flow Research Articles

Pareto-improving seat allocation for high-speed railway networks with equilibrium flows

This paper develops optimization models for Pareto-improving seat allocation schemes in high-speed railway (HSR) networks, where time-dependent demand and equilibrium travel choices are incorporated. Under the Pareto-improving seat allocation scheme, at least some passengers are strictly better off, and no passenger is worse off, when compared to the situation with no seat allocation scheme. In particular, two scenarios with fixed and elastic passenger demands are considered. The passenger travel choice equilibrium conditions are taken as constraints for the seat allocation optimization model, which can be further reformulated into a mixed-integer linear programming (MILP) with the help of linearization, relaxation and outer-approximation techniques. The optimal solution then can be obtained by solving the proposed MILP. The numerical examples on two real-world regional HSR systems are presented to illustrate the proposed Pareto-improving seat allocation optimization approach.

Adaptive Control Approach-Based Isolated Microgrid System with Alleviating Power Quality Problems

In this article, a dual third-order generalized integrator-based phase-locked loop (DTOGI-PLL) and an additional degree of freedom-based frequency locked loop (ADF-FLL) control approaches are utilized on a voltage source converter (VSC) to control an isolated microgrid system under different operating conditions. The proposed adaptive approaches provide a fast dynamic response with a precise estimation of frequency, phase angle, and fundamental load current component compared to that of the TOGI-PLL and least mean square (LMS) algorithms. An ADF-FLL allows closed-loop poles to perform more optimally, resulting in faster dynamic performance without compromising filtering capability. Moreover, the proposed adaptive approaches with VSC provide power support, load leveling, harmonic eliminations, and enhance the isolated microgrid’s overall power quality during dynamics in load and energy sources. A solar PV (SPV) array with perturb & observe (P&O) MPPT control is interfaced at the DC link of a bidirectional controller (BDC) to draw maximum solar power. Through dc-link voltage control, the BDC with energy storage system (ESS) ensures the appropriate power flow and power equilibrium between energy sources and load. The Simulation and test results show the dynamic performance of the isolated microgrid is examined under different operational scenarios.

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

With the progress of society and the diversification of transportation modes, people are faced with more and more complicated travel choices, and thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years. A number of multi-criteria traffic network equilibrium problems have been proposed, but most of them do not involve data uncertainty nor computational methods. This paper focuses on the methods for solving robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of the robust vector equilibrium and the robust vector equilibrium with respect to the worst case are introduced, respectively. For the robust vector equilibrium, an equivalent min–max optimization problem is constructed. A direct search algorithm, in which the step size without derivatives and redundant parameters, is proposed for solving this min–max problem. In addition, we construct a smoothing optimization problem based on a variant version of ReLU activation function to compute the robust weak vector equilibrium flows with respect to the worst case and then find robust vector equilibrium flows with respect to the worst case by using the heaviside step function. Finally, extensive numerical examples are given to illustrate the excellence of our algorithms compared with existing algorithms. It is shown that the proposed min–max algorithm may take less time to find the robust vector equilibrium flows and the smoothing method can more effectively generate a subset of the robust vector equilibrium with respect to the worst case.

Effects of NBI-induced energetic ions on internal kink stability in HL-2M

A systematic investigation is carried out, studying the effect of the neutral beam injection induced energetic particles (EPs) on the n = 1 (n is the toroidal mode number) internal kink (IK) instability in the HL-2M tokamak, utilizing the MARS-F/K code [Liu et al., Phys. Plasmas 7, 3681 (2000) and 15, 112503 (2008)]. A high-beta sawteething HL-2M scenario, simulated by the TRANSP code [Breslau et al. Computer Software (2018)], is chosen for this study. Compared to the fluid model, non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid computations with MARS-K show a generally stabilization effect on the IK, due to drift kinetic resonances associated with EPs. The bounce resonance of trapped EPs has minor influence on the mode stability. In the absence of the plasma equilibrium flow and with the assumed particle pitch distribution, the transit resonance of co-current (countercurrent) passing EPs destabilizes (stabilizes) the IK. With plasma flow, both co- and countercurrent passing EPs tend to stabilize the mode, but the effect is stronger with the countercurrent particles. These modeling results provide useful guidance for interpreting MHD instabilities in the future high-performance experiments in HL-2M.

Unified Approach to Modeling Equilibrium Flows of Detonating Gases

Unified Approach to Modeling Equilibrium Flows of Detonating Gases

A new source finding and tracking analysis approach for the active reflector of five-hundred-meter aperture spherical telescope

The FAST (Five-hundred-meter Aperture Spherical Telescope) is the world’s largest single-aperture radio telescope. During operation, FAST needs to follow the observed celestial body to adjust displacements, which can be divided into two processes: the source finding and tracking. In this paper, a new numerical method based on Vector Form Intrinsic Finite Element (VFIFE) is proposed to simulate the source finding and tracking process for FAST’s active reflector. The basic principle of static equilibrium and calculation flow of the sourcing and tracking analysis is proposed, and the finite element program is compiled to analyze the displacement process of the reflector cable-net structure. Then, six typical test conditions are selected to simulate the sourcing and tracking displacement process. The obtained final form in the equilibrium state adheres to the target configuration, demonstrating the applicability of the suggested approach and the correctness of calculation findings. In addition, the change in the actuator length and the structural force distribution can be simultaneously derived. These values serve as a vital theoretical foundation for FAST’s practical operation and regulation.

Vertical Distribution of Suspended Sediment Concentration in the Unsaturated Jingjiang Reach, Yangtze River, China

The Rouse formula and its variants have been widely used to describe the vertical distribution of the sediment concentration in sediment-laden flows in equilibrium. Han’s formula extends the Rouse formula to non-equilibrium regimes, where the diffusive flux is still assumed to be Fickian. The turbulent flow and suspension regimes downstream of a mega-reservoir, e.g., the Three Gorges Reservoir, usually exhibit fractal and unsaturated properties, respectively. To characterize the non-Fickian dynamics of suspended sediment and the non-equilibrium regime in natural dammed rivers, this study proposes a new formula for the concentration profile of unsaturated sediment based on the Hausdorff fractal derivative advection–dispersion equation. In addition, we find that the order of the Hausdorff fractal derivative is related to the sizes of the sediment and the degrees of non-equilibrium. Compared to Rouse and Han’s formulae, the new formula performs better in describing the sediment concentration profiles in the Jingjiang Reach, approximately 100 km below the Three Gorges Dam.

Metamodel-Based Optimization Method for Traffic Network Signal Design under Stochastic Demand

Traffic network design problems (NDPs) play an important role in urban planning. Since there exist uncertainties in the real urban traffic network, neglecting the uncertainty factors may lead to unreasonable decisions. This paper considers the transportation network signal design problem under stochastic origin-destination (OD) demand. In general, solving this stochastic problem requires a large amount of computational budget to calculate the equilibrium flow corresponding to a certain demand distribution, which limits its real applications. To reduce the computational time in calculating the equilibrium flow under stochastic demand, this paper proposes a metamodel-based optimization method. First, a combined metamodel that integrates a physical modeling part and a model bias generic part is developed. The metamodel is used to approximate the time-consuming average equilibrium flow solution process, hence to improve the computational efficiency. To further improve the convergence and the solution optimality performance of the metamodel-based optimization, the gradient information of traffic flow with respect to the signal plan is incorporated in the optimization model. A gradient-based metamodel algorithm is then proposed. In the numerical example, a six-node test network is used to examine the proposed metamodel-based optimization method. The proposed combined metamodel is compared with the benchmark method to investigate the importance of incorporating a model bias generic part and the traffic flow gradient information in the combined metamodel. Although there is a reduction in solution optimality since the metamodel is an approximation of the original model, the metamodel methods greatly improve the computational efficiency (the computational time is reduced by 4.84 to 13.47 times in the cases of different initial points). By incorporating the model bias, the combined metamodel can better approximate the original optimal solution. Moreover, incorporating the gradient information of the traffic flow in the optimization search algorithm can further improve the solution performance. Numerical results show that the gradient-based metamodel method can effectively improve the computation efficiency while slightly reducing the solution optimality (with an increase of 0.09% in the expected total travel cost).

Diagnosis of wind turbine systematic yaw error through nacelle anemometer measurement analysis

The power produced by a wind turbine can be considerably affected by the presence of systematic errors, which are particularly difficult to diagnose. This study deals with wind turbine systematic yaw error and proposes a novel point of view for diagnosing and quantifying its impact on the performance. The keystone is that, up to now in the literature, the effect of the yaw error on the nacelle wind speed measurements of the affected wind turbine has been disregarded. Given this, in this work a new method based on the general principle of flow equilibrium is proposed for the diagnosis of such type of error. It is based on recognizing that a misaligned wind turbine measures the wind speed differently with respect to when it is aligned. The method is shown to be effective for the diagnosis of two test cases, about which an independent estimate of the yaw error is available from upwind measurements (spinner anemometer). A data-driven generalization of the concept of relative performance is then formulated and employed for estimating how much the systematic yaw error affects wind turbine performance. It is shown that the proposed method is more appropriate than methods employing wind speed measurements (like the power curve), which are biased by the presence of the error. The results of this study support that SCADA-collected data can be very useful to diagnose wind turbine systematic yaw error, provided that a critical analysis about their use is done.

Flow velocity and implication on particle size of bottom sediment in the commodore channel lagos, southwestern nigeria

Flow velocity generally influences the erosion, transport and deposition of sediments. Flow velocity and in relation to particle size distribution in the Commodore channel was investigated with the Acoustic doppler current profiler (ADCP), echosounder and veen van grab. Those equipment were deployed through a low draft survey boat to acquire acoustic and sediment data covering the study area. The ADCP measured the current velocity along fourteen established transect lines while twenty surface sediments samples were collected along the banks and center of the channel respectively. Sediment samples were analyzed for grain size distributions and mineralogicaly composition while the acoustics data were analyzed with Matlab software to produce velocity profiles for the channel area. The study aimed to determine the magnitude and direction of flow of water along the channel with a view to ascertain the sediment transport process. Results indicated no significant difference in flow velocities along the different channel points. The flow velocity was however slightly higher around the channel mouth than in mid and upper reaches of the channel. The flow velocities showed negative correlation of (– 0.54 and – 0.28) with the sediment characteristics indicating that the sediment particle size distributions is unrelated to the flow velocity. This anomaly in the equilibrium flow velocity suggest the impact of dredging and the continuous ebbing and flooding of tidal water which resulted to reworking of the sediment particle sizes prior to deposition. The sediment distributions were fine sand, moderately sorted, fine skewed with leptokurtic peaked. Significant fractions of the sediments were deposited in fluvial and shallow marine environments while a few were deposited in the beach and turbidity environment. Sediments and acoustic data interpreted from the study suggest that sediment supply to the area was by fluvial processes through the barrier lagoon drainage basin.

Experimental study on electrochemical machining of TC11 titanium alloy blades based on cylindrical array microstructure cathodes

Titanium alloys have a wide range of applications in aerospace, however, this material is very sensitive to changes in the flow field during electrochemical machining (ECM) and suffers from frequent short-circuiting and poor surface quality. Studies have shown that optimization and improvement of the cathode structure often improve the processing properties of the material. To process titanium alloy under a steady state, the laser processing system was used to prepare cylindrical array microstructure on the end surface of cathode. The comparison between the original and improved cathode was conducted in ECM experiments. The experimental results showed that serious flow marks existed on the original cathode processing surface. Within the range of processable voltage, short circuits occurred at the processing heights of 1.823 mm and 1.655 mm. The improved cathode can process a bright finish surface without flow marks and there were no short circuits. The influence of two microstructure arrangements on the blade surface quality was also investigated. Compared to inline cylindrical array (ICA) cathode. The processing gap equilibrium flow rate of the staggered cylindrical array (SCA) cathode is about 0.3 L/min higher. The average surface roughness of the blade hub was reduced from 1.632 µm to 0.574 µm. Additionally, there are multiple layers of electrolysis products adhering to the non-machined surface and the machined sidewall of the blade. The oxygen content of the outer layer is higher than that of the inner layer, and the oxygen content of the non-machined surface is significantly higher than that of the machined sidewall. The microstructure cathode designed in this paper realizes the stable processing of titanium alloy in passivation electrolyte.

Boundary Guidance Strategy and Method for Urban Traffic Congestion Region Management in Internet of Vehicles Environment

Accelerated urbanization has increased regional traffic congestion. To alleviate traffic congestion in a homogeneous road network, combined with the advantage of real-time traffic information obtained by the Internet of Vehicles (IoVs), a boundary guidance strategy for traffic congestion region is proposed. The strategy considers the optimal operation state of traffic congestion region and is divided into two categories according to different destinations of traffic demands. Meanwhile, a method for the boundary guidance strategy is presented in which the macroscopic fundamental diagram (MFD) is used to determine the optimal accumulation, a traffic flow equilibrium model is established to calculate the real-time accumulation, and a fuzzy adaptive PID control algorithm is designed to calculate the optimal traffic inflow of the traffic congestion region. Furthermore, an example is selected for simulation. The results show that the boundary guidance strategy can effectively improve the operational state of the road network and alleviate traffic congestion. Finally, the influence of connected vehicle penetration rate on the strategy is discussed. The simulation results show that the strategy can improve the operation state of the road network under mixed traffic flow, and the higher the penetration rate, the more significant its effect on alleviating traffic congestion.

Poster Session 1

Although the shock wave propagation in the dusty gas medium is widely used in research, astrophysics, military, and industrial applications, the shock wave in a self-gravitating mixture of van der Waals gas and a pseudo-fluid of inert solid particles in a rotating medium, is not well understood. In the present paper, the strong exponential shock wave propagation in a self-gravitating mixture of non-ideal gas and a pseudo-fluid of small solid particles is modelled for unsteady adiabatic and isothermal flows in a rotating medium. In our model, the solid particles are considered as chemically inert pseudo-fluid, and the equilibrium flow conditions hold in the entire flow field region. The similarity solutions are derived for isothermal and adiabatic flows. The vorticity vector components, and isothermal and adiabatic compressibility's are also taken into account. It is shown that the zero-temperature gradient supposition brings the reflective changes in pressure, axial vorticity vector, density, and compressibility distributions in contrast to the adiabatic flow. The shock strength decreases, and the compressibility increases due to the zero-temperature gradient consideration. Also, the effects of the problem parameters on shock waves and the distributions of the flow variables velocity, density, etc., are discussed in detail. It is remarkable to note that due to the consideration of a self-gravitating mixture or with an increase in the ratio of the density of solid particles to the initial density of the gas, the shock strength increases; whereas due to the consideration of non-idealness of the gas or rotating medium the shock strength decreases.

Time and toll trade-off with heterogeneous users: A continuous time surplus maximization bi-objective user equilibrium model

This paper presents a continuous time surplus maximization bi-objective user equilibrium (C-TSmaxBUE) model, in which the users’ variability toward the time and toll trade-off in a tolled road network is explicitly considered. Different users are assigned with different ratios of the time saved per unit of money (RTSMs), the values of which represent the different expectations to trade more money for less travel time. Infinite indifference curves are then generated by considering continuously distributed RTSMs in the population. Accordingly, we extend the definition of the path-based time surplus for the C-TSmaxBUE model, which can be formulated as a Beckmann-type mathematical program operating in the space of RTSM boundaries. To solve the problem, we develop a path-based single-boundary adjustment (SBA) algorithm that fits the non-additive structure of the model. The algorithm involves a Newton-type flow equilibration procedure that simultaneously adjusts RTSM boundaries and path flows, as well as a column generation scheme that firstly enumerates all efficient paths and then identifies the paths that have the potential to reduce generalized travel times. Numerical results on a small network show the feature of the equilibrium flow pattern, whereas instances of practical size confirm that SBA is an efficient tool to obtain high-quality equilibrium solutions. Compared to the original TSmaxBUE problem, we found that a larger set of efficient paths will be used when the users’ heterogeneity is considered.

The Impact of Automated Vehicles on Road and Intersection Capacity

With the rapid development of autonomous driving technology, future road traffic must be composed of autonomous vehicles and artificial vehicles. Although autonomous vehicles have greatly improved road capacity, few studies have involved capacity at signal-controlled intersections, and most of the studies are based on experimental simulation. As such, there is a need to more scientifically analyze the impact of autonomous vehicles on road and intersection capacity. Based on three theories of flow-density relationships, traffic flow equilibrium analysis, and the following model, this paper firstly deduces the flow-density relationship of different vehicle types in a single environment. Secondly, flow-density relationships under different proportions of self-driving vehicles are derived. Through the derivation of these two models, the basic road saturation flow rates under different permeabilities of self-driving vehicles, can be obtained. Based on these results, a revised calculation model for the capacity of signalized intersections with different proportions of autonomous vehicles is proposed, which is essentially to revise the basic saturation flow rate under different permeabilities of autonomous vehicles. By using SUMO 1.15.0 traffic simulation software, the theoretical models are individually tested. The results show that the error rate between the theoretical calculation results and the SUMO simulation results, is less than 16%. This study can provide a basis for the calculation of basic capacity of roads and intersections in a future man-machine hybrid driving environment, and provide theoretical guidance for traffic management and control.

Global gyrofluid simulations of turbulence in tokamak plasmas

We develop a tokamak plasma turbulence simulation code based on a fluid model using the BOUT++ framework. The model corresponds to a global extension of the local gyrofluid model (Beer and Hammett, 1996 [11]), where external sources and neoclassical equilibrium flows are included but some higher-order kinetic effect terms are ignored for the global nonlinear simulation. Hyper-viscous damping terms are introduced to compensate for the stabilizing effect of the missing kinetic terms. With an appropriate hyper-viscosity, we obtain reasonable linear and nonlinear results on ion temperature gradient modes compared to global gyrokinetic simulations. We perform global flux-driven simulations with self-consistently evolving profiles with external heat sources/sinks. A spectral analysis of heat flux in flux-driven turbulence exhibits a broad 1/f (f is the frequency) spectrum observed in gyrokinetic simulations, indicating the prevalence of self-organized criticality-like heat avalanches. We also investigate the effect of an externally imposed vorticity source on turbulence suppression and transport barrier formation. It is shown that internal transport barrier can form even for a monotonic safety factor profile when a sufficiently strong vorticity source is applied.

Boundary layer flow over a bump and the three-dimensional law of the wall

Many turbulence theories in use today are based on two-dimensional equilibrium flows and have limitations when applied to three-dimensional flows. A three-dimensional law of the wall would help to improve simulation fidelity, but while several versions have been proposed, none have been widely accepted. In this study, the three-dimensional attached boundary layer flow over the windward side of the BeVERLI (Benchmark Validation Experiments for RANS/LES Investigations) Hill bump model was measured using near-wall laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel to study the mean flow and turbulence structure. These mean velocity measurements are compared with the predictions of the proposed three-dimensional (3D) law of the wall of van den Berg [A three-dimensional law of the wall for turbulent shear flows. J Fluid Mech. 1975;70(1):149–160.], which incorporates pressure gradients and inertial effects but assumes alignment of the mean flow gradient and shear-stress angles, and to the sublayer momentum equations, which are exact in the limit of wall-normal . In regions with mild stress/strain misalignment, the van den Berg model compares favourably with the experimental data up to a maximum of , and the sublayer momentum relationship compares favourably with the experimental data in the linear sublayer.

End-to-end learning of user equilibrium with implicit neural networks

This paper intends to transform the transportation network equilibrium modeling paradigm via an “end-to-end” framework that directly learns travel choice preferences and the equilibrium state from multi-day link flow observations. The centerpiece of the proposed framework is to use deep neural networks to represent travelers’ route choice preferences and then encapsulate the neural networks in a variational inequality that prescribes the user equilibrium flow distribution. The proposed neural network architecture ensures the existence of equilibrium and accommodates future changes in road network topology. The variational inequality is then embedded as an implicit layer in a learning framework, which takes the context features (e.g., road network and traveler characteristics) as input and outputs the user equilibrium flow distribution. By comparing computed equilibrium flows with observed flows, the neural networks can be trained. The proposed end-to-end framework is demonstrated and validated using synthesized data for the Sioux Falls network.

Work Zone Scheduling Problem in the Urban Traffic Networks

Abstract A significant part of highway and street congestion is produced by work zones. Depending on the type of construction and/or rehabilitation activity, street capacity could be significantly decreased, or the street could be completely closed. The work zone generates traffic delays in the street where maintenance is performed. Additionally, the work zone generates additional traffic on the neighboring streets, since many drivers change their routes. There are numerous possible work zone schedules. The total travel time of all network users highly depends on the chosen work zones schedule. Work zones scheduling problem has a natural nested structure that requires to be modeled as a bi-level problem. We considered the bi-level work zones scheduling problem. The objective function in the upper level, which we try to minimize, represents the total travel time of all network users. Relations in the lower level, help us to compute User Equilibrium flows. The proposed solution to the problem is based on the combination of Integer Programming and a heuristic traffic assignment algorithm. The output of the developed model consists of the start time of each work zone. The Sioux Falls benchmark network is used to illustrate the proposed procedures and the achieved performances.

Negative Effect Prediction and Refueling Traffic Flow Equilibrium of Urban Energy Supply Network during Weekends and Holidays

With the continuous improvement of people’s living standards, the travel demand for vehicles increases rapidly during weekends and holidays. This situation leads to a number of negative impacts on the transport network, such as traffic congestion, carbon emissions, and long queues at refueling stations. The impact of vehicles requiring energy replenishment on the negative effect is nonlinear. Therefore, the negative effect data of working days cannot be directly used to evaluate the cost, and the traffic equilibrium allocation problem also needs to be solved. An equilibrium allocation model of hybrid vehicles considering the energy replenishment demand in holidays is established, aiming at minimizing the total time cost and energy consumption cost. The Frank–Wolfe algorithm is used to solve the traffic allocation problem in advance, and the negative effect of the urban energy network during holidays is predicted by the Genetic Algorithm—Back Propagation (GA-BP) algorithm. Then, the energy-replenishing vehicles in the traffic network are induced to reduce the total cost. Finally, taking the actual road network in Jiulongpo District of Chongqing City, southwest of China, as an example, the negative effects of multiple stations are predicted. The results show that the prediction method proposed in this paper is effective during holiday periods. In addition, as the market share of electric vehicles increases, the negative cost can decrease gradually. The predicted results can provide a reference for traffic managers.