An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

Stability mechanism and control of the pumpable supports in longwall recovery room

The load-bearing performance(LBP)of pumpable supports(PPS)is crucial for the stability of longwall pre-driven recovery room(PRR)surrounding rock.However,the unbalanced bearing coefficient(UBC)of the PPS(undertaking unequal load along the mining direction)has not been investigated.A mechanical model of the PRR was established,considering the main roof cantilever beam structure,to derive an assessment formula for the load,the failure criteria,and the UBC of the PPS.Subsequently,the generation mechanisms,and influencing factors of the UBC were revealed.Global sensitivity analysis shows that the main roof hanging length(l_(2))and the spacing between the PPS(r)significantly impact the UBC.A novel design of the PPS and the coupling control technology were proposed and applied to reduce the UBC of the PPS in the adjacent longwall PRR.Monitor results showed no failure of the PPS at the test site,with the UBC(ζ)reduced to 1.1 consistent with the design value(1.15)basically,fully utilizing the collaborative LBP of the PPS.Finally,the maximum roof-to-floor convergence of the PRR was 234 mm,effectively controlling the stability of the surrounding rock of the PRR and ensuring the mining equipment recovery.

Analyzing the Wind-Dominant Electricity Market under Coexistence of Regulated and Deregulated Power Trading

Currently,both regulated and deregulated power trading exist in China’s power system,which has caused imbalanced funds in the electricity market.In this paper,a simulation analysis of the electricity market with wind energy resources is conducted,and the calculation methods of unbalanced funds are investigated systematically.In detail,the calculation formulas of unbalanced funds are illustrated based on their definition,and a two-track electricity market clearing model is established.Firstly,the concept of the dual-track system is explained,and the specific calculation formulas of various types of unbalanced funds are provided.Next,considering the renewable energy consumption,the market clearing model based on DC power flow is constructed and solved;by combining fitting methods of mid-and long-term curves,the unbalanced funds are calculated based on clearing results and formulas.

A Survey of Unbalanced Flow Diagnostics and Their Application

This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high—resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. Key words Unbalanced flow - Geostrophic adjustment - Gravity waves - Nonlinear balance equation - Potential vorticity inversion - Omega equations - Rossby number This research was conducted under support from NSF grant ATM-9700626 of the United States. The numerical computations described herein were performed on the Cray T90 at the North Carolina Supercomputing Center and the Cray supercomputer at the NCAR Scientific Computing Division, which also provided the initialization fields for the MM5. Thanks are extended to Mark Stoelinga at University of Washington for the RIP post-processing package.

Enhanced control of DFIG-used back-to-back PWM VSC under unbalanced grid voltage conditions

This paper presents a unified positive-and negative-sequence dual-dq dynamic model of wind-turbine driven doubly-fed induction generator(DFIG) under unbalanced grid voltage conditions. Strategies for enhanced control and operation of a DFIG-used back-to-back(BTB) PWM voltage source converter(VSC) are proposed. The modified control design for the grid-side converter in the stationary αβ frames diminishes the amplitude of DC-link voltage ripples of twice the grid frequency,and the two proposed control targets for the rotor-side converter are alternatively achieved,which,as a result,improve the fault-ride through(FRT) capability of the DFIG based wind power generation systems during unbalanced network supply. A complete unbalanced control scheme with both grid-and rotor-side converters included is designed. Finally,simulation was carried out on a 1.5 MW wind-turbine driven DFIG system and the validity of the developed unified model and the feasibility of the proposed control strategies are all confirmed by the simulated results.

Modeling and optimization of unbalanced multi-stage logistic system

To decompose an unbalanced multi-stage logistic system to multipleindependent single-stage logistic systems, a new notion of parameterized interface distribution ispresented. For encoding the logistic pattern on each stage, the Pruefer number is used. With theimproved decoding procedure, any Pruefer number produced stochastically can be decoded to a feasiblelogistic pattern, which can match with the capacities of the nodes of the logistic system. Withthese two innovations, a new modeling method based on parameterized interface distribution and thePriifer number coding is put forward. The corresponding genetic algorithm, named as PIP-GA, can findbetter solutions and require less computational time than st-GA. Although requiring a little moreconsumption of memory, PIP-GA is still an efficient and robust method in the modeling andoptimization of unbalanced multi-stage logistic systems.

Torsional vibration analysis of lathe spindle system with unbalanced workpiece

For the purpose of analyzing the torsional vibration caused by the gravitational unbalance torque arisen in a spindle system when it is machining heavy work piece,a 10-DOF lumped parameter model was made for the machine tool spindle system with geared transmission.By using the elementary method and Runge-Kutta method in Matlab,the eigenvalue problem was solved and the pure torsional vibration responses were obtained and examined.The results show that the spindle system cannot operate in the desired constant rotating speed as far as the gravitational unbalance torque is engaged,so it may cause bad effect on machining accuracy.And the torsional vibration increases infinitely near the resonant frequencies,so the spindle system cannot operate normally during these spindle speed ranges.

Influence and determinative factors of ion-to-atom arrival ratio in unbalanced magnetron sputtering systems

Low pressure sputtering with a controlled ratio of ion flux to deposited atom flux at the condensing surface is one of the main directions of development of magnetron sputtering methods. Unbalanced magnetron sputtering, by producing dense secondary plasma around the substrate, provides a high ion current density. The closed-field unbalanced magnetron sputtering system （CFUBMS） has been established as a versatile technique for high-rate deposition high-quality metal, alloy, and ceramic thin films. The＇key factor in the CFUBMS system is the ability to transport high ion currents to the substrate, which can enhance the formation of full dense coatings at relatively low value homologous temperature. The investigation shows that the energy of ions incidenced at the substrate and the ratio of the flux of these ions to the flux of condensing atoms are the fundamental parameters in determining the structure and properties of films produced by ion-assisted deposition processes. Increasing ion bombardment during deposition combined with increasing mobility of the condensing atoms favors the formation of a dense microstructure and a smooth surface.

LINEAR PROVABLE SECURITY FOR A CLASS OF UNBALANCED FEISTEL NETWORK

A structure iterated by the unbalanced Feistel networks is introduced. It is showed that this structure is provable resistant against linear attack. The main result of this paper is that the upper bound of r-round （r≥2m） linear hull probabilities are bounded by q^2 when around function F is bijective and the maximal linear hull probabilities of round function F is q. Application of this structure to block cipher designs brings out the provable security against linear attack with the upper bounds of probabilities.

Dynamic modeling and direct power control of wind turbine driven DFIG under unbalanced network voltage conditions

This paper proposes an analysis and a direct power control (DPC) design of a wind turbine driven doubly-fed induction generator (DFIG) under unbalanced network voltage conditions. A DFIG model described in the positive and negative synchronous reference frames is presented. Variations of the stator output active and reactive powers are fully deduced in the presence of negative sequence supply voltage and rotor flux. An enhanced DPC scheme is proposed to eliminate stator active power oscillation during network unbalance. The proposed control scheme removes rotor current regulators and the decomposition processing of positive and negative sequence rotor currents. Simulation results using PSCAD/EMTDC are presented on a 2-MW DFIG wind power generation system to validate the feasibility of the proposed control scheme under balanced and unbalanced network conditions.

A Nonlinear Control Strategy for Vienna Rectifier Under Unbalanced Input Voltage

The Vienna rectifier with unbalanced input voltage and load transient is analyzed.A nonlinear control strategy for Vienna rectifier under unbalanced input is proposed.From the view of positive and negative sequence components,the proposed nonlinear control strategy suppresses the twice frequency ripple and guarantees the dynamic response characteristic at the same time.Thanks to the proposed nonlinear control strategy,the DC bus capacitor can be reduced a lot since the voltage ripple and drop can be suppressed.A 10 kW Vienna rectifier is built to verify the proposed control strategy.After applying the proposed nonlinear control strategy,the voltage ripple is only7 V and decreases over 75%over the traditional PI control when the unbalanced degree is 20%.The voltage drop can be reduced about 80%than former control strategy which is helpful to reduce the DC bus capacitor and achieve higher power density.The volume of the capacitor can be reduced by 83.3%with the new control method.

The Effect of Unbalanced Coefficient of Magnetron on the Structure and Properties of CN_x Coatings

The effect of unbalanced coefficient of magnetron （UCM） on the structure and tribological properties of CrNx hard coatings was studied.The CrNx coatings were deposited on both Si wafer and hardened tool steel substrates using a closed-field unbalanced magnetron sputtering ion plating technique in a gas mixture of Ar＋N2 under different unbalanced magnetron conditions.The coatings were characterized by means of XRD,XPS,SEM,microhardness tester and pin-on-disc tribometer to study respectively their structure,chemical bonding state,microstructure,hardness and tribological properties.The experimental results show that the UCM has a profound effect on the structure,hardness and tribological properties of the CrNx coatings.With increasing the values of UCM,the dominant phases in the deposited coatings evolved from Cr＋Cr2N to Cr2N＋CrN,the microstructure became denser and the hardness increased;in addition,reduced coefficient of friction and improved wear resistance of CrNx coatings were also observed under a larger UCM.

Gyroscope Fault Diagnosis Using Fuzzy SVM to Unbalanced Samples

A novel fuzzy support vector machine based on unbalanced samples(FSVM-US)is proposed to solve the high false positive rate problem since the gyroscope output is susceptible to unmanned aerial vehicle(UAV)airborne electromagnetic environment and the gyroscope abnormal signal sample is rather rare.Firstly,the standard deviation of samples projection to normal vector for SVM classifier hyper plane is analyzed.The imbalance feature expression reflecting the hyper plane shift for the number imbalance between samples and the dispersion imbalance within samples is derived.At the same time,the denoising factor is designed as the exponential decay function based on the Euclidean distance between each sample and the class center.Secondly,the imbalance feature expression and denoising factor are configured into the membership function.Each sample has its own weight denoted the importance to the classifier.Finally,the classification simulation experiments on the gyroscope fault diagnosis system are conducted and FSVM-US is compared with the standard SVM,FSVM,and the four typical class imbalance learning(CIL)methods.The results show that FSVM-US classifier accuracy is 12% higher than that of the standard SVM.Generally,FSVM-US is superior to the four CIL methods in total performance.Moreover,the FSVMUS noise tolerance is also 17% higher than that of the standard SVM.

Energy-balanced clustering protocol for data gathering in wireless sensor networks with unbalanced traffic load

Energy-efficient data gathering in multi-hop wireless sensor networks was studied,considering that different node produces different amounts of data in realistic environments.A novel dominating set based clustering protocol (DSCP) was proposed to solve the data gathering problem in this scenario.In DSCP,a node evaluates the potential lifetime of the network (from its local point of view) assuming that it acts as the cluster head,and claims to be a tentative cluster head if it maximizes the potential lifetime.When evaluating the potential lifetime of the network,a node considers not only its remaining energy,but also other factors including its traffic load,the number of its neighbors,and the traffic loads of its neighbors.A tentative cluster head becomes a final cluster head with a probability inversely proportional to the number of tentative cluster heads that cover its neighbors.The protocol can terminate in O(n/lg n) steps,and its total message complexity is O(n2/lg n).Simulation results show that DSCP can effectively prolong the lifetime of the network in multi-hop networks with unbalanced traffic load.Compared with EECT,the network lifetime is prolonged by 56.6% in average.

Fabrication of Diamond-like Carbon Films by Ion Assisted Middle Frequency Unbalanced Magnetron Sputtering

Diamond-like carbon （DLC） films are deposited by the Hall ion source assisted by the mid-frequency unbalanced magnetron sputtering technique. The effects of the substrate voltage bias, the substrate temperature, the Hall discharging current and the argon/nitrogen ratio on the DLC film＇s performance were studied. The experimental results show that the film＇s surface roughness, the hardness and the Young＇s modulus increase firstly and then decrease with the bias voltage incrementally increases. Also when the substrate temperature rises, the surface roughness of the film varies slightly, but its hardness and Young＇s modulus firstly increase followed by a sharp decrease when the temperature surpassing 120 ℃. With the Hall discharging current incrementally rising, the hardness and Young＇s modulus of the film decrease and the surface roughness of the film on 316L stainless steel firstly decreased and then remains constant.

Cu Films Deposited by Unbalanced Magnetron Sputtering Enhanced by ICP and External Magnetic Field Confinement

Metallic copper（Cu） films were deposited on a Si （100） substrate by unbalanced magnetron sputtering enhanced by radio-frequency plasma and external magnetic field confinement. The morphology and structure of the films were examined by scanning electron microscopy （SEM）, atomic force microscope （AFM） and X-ray diffraction （XRD）. The surface average roughness of the deposited Cu films was characterized by AFM data and resistivity was measured by a four-point probe. The results show that the Cu films deposited with radio-frequency discharge enhanced ionization and external magnetic field confinement have a smooth surface, low surface roughness and low resistivity. The reasons may be that the radio-frequency discharge and external magnetic field enhance the plasma density, which further improves the ion bombardment effect under the same bias voltage conditions. Ion bombardment can obviously influence the growth features and characteristics of the deposited Cu films.

Novel control scheme for 3-phase PWM current-source converters under unbalanced source voltage conditions

Under unbalanced source voltage supply, considerable output second harmonics and input low-order harmonics in 3-phase PWM current-source converters (PWM-CSC) are generated. This paper proposes a new deadbeat controller based on compensation for unbalanced source voltage and current. With the proposed scheme, the second harmonics of the output current are eliminated and low-order harmonics of the source current are reduced effectively. Simulation and experimental results con- firmed the feasibility of the proposed method.

Flexible Power Regulation and Limitation of Voltage Source Inverters under Unbalanced Grid Faults

This paper develops a flexible power regulation and limitation strategy of voltage source inverters(VSIs)under unbalanced grid faults.When the classical power theory is used under unbalanced grid faults,the power oscillations and current distortions are inevitable.In the proposed strategy,the extended power theory is introduced to compute the power feedbacks together with the classical power theory.Based on the combination of the classical and extended power theory,the proposed strategy can achieve the sinusoidal current provision and the flexible regulation between three common targets,i.e.,constant active power,balanced current,and constant reactive power.Meanwhile,the proposed strategy is associated with a power limiter,which is capable to keep the currents under the pre-defined threshold and to compute the maximum apparent power for better utilization of the inverter capacity.With this power limiter,the rated inverter capacity is fully used for both the active and reactive power provisions under unbalanced grid faults.Using the proposed power regulation and limitation,the VSI can avoid overcurrent tripping and flexibly regulate its power under unbalanced grid faults.All the conclusions are verified by the real-time hardware-in-loop tests.

Experimental study of suppressing the unbalanced response vibration of rotor system with a G-type integral squeeze film damper

Conventional squeeze film dampers have numerous challenges including lock up,bistable response and incoordinate precession.In order to resolve these nonlinear problems,a novel G-type integral squeeze film damper(GISFD)is proposed in this research.The experimental test rig is provided to investigate the rotor system with an unbalanced single disk.Numerical simulation results show that the structural design of GISFD is reasonable,which can ensure its safe and stable operation.The influence of different support stiffnesses on the first-order speed of the rotor system is analyzed.Experimental results show that GISFD can effectively suppress the unbalanced response vibration of the rotor.In a certain range,it is found that the suppression effect of GISFD increases with the increase in the kinematic viscosity of the damping fluid.When the silicone oil with kinematic viscosity coefficients v=30.0 cm^(2)/s is employed,the vibration reduction of GISFD is approximately 71.51%.Furthermore,the experimental results show that with the increase of the unbalance,there is a linear relationship between the unbalance and the corresponding amplitude of the unbalanced response.It is concluded that GISFD has excellent linear damping characteristics and reduces the sensitivity of the rotor system to the unbalanced mass.

Analysis of Variance in an Unbalanced Two-Way Mixed Effect Interactive Model

The expected mean squares for unbalanced mixed effect interactive model were derived using Brute Force Method. From the expected mean squares, there are no obvious denominators for testing for the main effects when the factors are mixed. An expression for F-test for testing for the main effects was derived which was proved to be unbiased.