The Application of Convex Optimization to Load Optimal Allocation in a Single Workstation System

The service quality of a workstation depends mainly on its service load, ifnot taking into account all kinds of devices' break-downs. In this article, an optimization modelwith inequality constraints is proposed, which aims to minimize the service load. A noveltransformation of optimization variables is also devised and the constraints are properly combinedso as to make this model into a convex one, whose corresponding Lagrange function and the KKTconditions are established afterwards. The interior-point method for convex optimization ispresented here as an efficient computation tool. Finally, this model is evaluated by a real example,from which conclusions are reached that the interior-point method possesses advantages such asfaster convergeoce and fewer iterations and it is possible to make complicated nonlinearoptimization problems exhibit convexity so as to obtain the optimum.

Total Maximum Allocated Loads on Stoichiometry of Nitrogen and Identification of Critical Form in Jiaozhou Bay, China

Total pollutant load control management for total dissolved nitrogen(TDN) is an urgent task required to gain a good water quality status in Jiaozhou Bay(JZB), China. In this paper, the stoichiometry of multiform TDN on land-ocean interactions associated with marine biogeochemical reaction(LOIMBR) was studied by modeling the load-response relationship based on a three-dimensional water quality model of nitrogen in JZB. The results showed that the stoichiometry on LOIMBR of dissolved organic nitrogen(DON), NO3-N and NH4-N was 3:1:1, with one-third of the contribution on the concentration of dissolved inorganic nitrogen(DIN) in JZB for the land-based DON loads to DIN loads. Based on the stoichiometric relationship of nitrogen forms, the total maximum allocated load(TMAL) of equivalent TDN(ETDN) was approximately 5300 t a^-1 in JZB, equivalent to the TMAL of 5700, 5800 and 15600 t a^-1 for NH4-N, NO3-N and DON, respectively. According to the loads of ETDN, there were four outfalls overloaded in JZB in 2015, which lie in the head of the bay. In the four overloaded outfalls, besides NO3-N, NH4-N was the critical nitrogen control form for Moshui River, while DON for Dagu River and Haibo River. The results of numerical experiments further showed that JZB will achieve good water quality after 7 years by implementation of the 'different emission reduction' based on TMAL of ETDN, which is significantly better than 'equal percent removal'.

Nonlinear optimization of load allocation in a manufacturing system

Based on the queuing theory, a nonlinear optimization model is proposed in this paper. A novel transformation of optimization variables is devised and the constraints are properly combined so as to make this model into a convex one, from which the Lagrangian function and the KKT conditions are derived. The interiorpoint method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are drawn that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method for convex optimization needs fewer iterations with significant computational savings. It appears that many non-linear ootimization oroblems in the industrial engineering field would be amenable to this method of solution.

Load Allocation Research in a Manufacturing System

Based on queuing theory, a nonlinear optimization model is proposed in this paper, which has the service load as its objective function and includes three inequality constraints of Work In Progress （WIP）. A novel transformation of optimization variables is also devised and the constraints are properly combined so as to make this model into a convex one from which the Lagrangian function and the Karurh Kuhn Tucker （KKT） conditions are derived. The interior-point method for convex optimization is presented here as a computationaUy efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are reached that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method needs fewer iterations with significant computational savings and it is possible to make nonlinear and complicated optimization problems convexified so as to obtain the optimum.

Application of Convex Optimization to Queuing Systems

On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.

An approach to calculating allowable watershed pollutant loads

To improve the management of discharge pollutants loads in the reservoirs＇ watershed, an approach of the allowable pollutants loads calculation and its allocation, based on the water environment model, was proposed. Establishment of the approach framework was described at first. Under the guidance of this framework, two major steps were as follows： modeling and scenario analysis were involved and should be applied to support the decision of discharge loads management; Environ- mental Fluid Dynamic Code （EFDC） model was selected as the kernel model in this framework. In modeling step, spatial discretization for establishing cell map in model, data preprocessing, parameter calibration and uncertainty analysis （which is considered as the significantly relevant factor of the margin of safety （MOS））, were conducted. As a result of the research, the model-based approach presented as a combination of estimation and precise calculation, which contributed to scenario analysis step. Some integrated modules, such as scenario simulation, result analysis and plan optimization were implemented as cycles in the scenario analysis. Finally, allowable pollutant loads under various conditions were calculated. The Chaihe Reservoir in Liaoning Province, China was used as a case study for an application of the approach described above. Results of the Chaihe reservoir water quality simulation, show good agreement with field data and demonstrated that the approach used in the present study provide an efficient and appropriate methodology for pollutant load allocation.

URBAN STORMWATER MANGEMENT-AN MS4 SUCCESS STORY FOR WESTERN MICHIGAN UNIVERSITY

Regulation of stormwater runoff is increasing throughout the United States.The Environmental Protection Agency(EPA)and state agencies are beginning to move toward effluent and/or load limits for pollutants in stormwater.Compliance costs for treating urban stormwater runoff,especially in highly-developed areas where retrofits are required,will only continue to increase.

EXPERIMENTAL INVESTIGATION OF CHARACTERISTIC FREQUENCY IN UNSTEADY HYDRAULIC BEHAVIOUR OF A LARGE HYDRAULIC TURBINE

The features of unsteady flow such as pressure variation and fluctuation in a large hydraulic turbine usually lead to the instability of operation. This article reports the recent in site investigation concerning the characteristic frequencies in pressure fluctuation, shaft torsional oscillation and structural vibration of a prototype 700 MW Francis turbine unit. The investigation was carried out for a wide load range of 200 MW-700 MW in the condition of water head 57 m-90 m. An extensive analysis of both time-history and frequency data of these unsteady hydraulic behaviours was conducted. It was observed that the pressure fluctuation in a draft tube is stronger than that in upstream flow passage. The low frequency with about one third of rotation frequency is dominative for the pressure fluctuation in part load range. Also the unsteady features of vibration of head cover and torsional oscillation of shaft exhibited the similar features. Numerical analysis showed that the vibration and oscillation are caused by vortex rope in the draft tube. In addition, a strong vibration with special characteristic frequency was observed for the head cover in middle load range. The pressure fluctuation in the draft tube with the same frequency was also recorded. Because this special vibration has appeared in the designed normal running condition, it should be avoided by carefully allocating power load in the future operation.