OPTIMAL SUMMATION INTERVAL AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A DISCRETE SYSTEM

In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/（1 ＋ ｜j｜）^α（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^β,（0.1）vj =∑ k ∈Zn uk^p/（1 ＋ ｜j｜）^β（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^α,where u, v 〉 0, 1 〈 p, q 〈 ∞, 0 〈 λ 〈 n, 0 ≤α ＋ β≤ n- λ,1/p＋1〈λ＋α/n and 1/p＋1＋1/q＋1≤λ＋α＋β/n：=λ^-/n. We first show that positive solutions of（0.1） have the optimal summation interval under assumptions that u ∈ l^p＋1（Z^n） and v ∈ l^q＋1（Z^n）. Then we show that problem（0.1） has no positive solution if 0 〈λˉ pq ≤ 1 or pq 〉 1 and max{（n-λ^-）（q＋1）/pq-1,（n-λ^-）（p＋1）/pq-1} ≥λ^-.

Optimal Failure-Finding Interval through Maximizing Availability

This paper proposes an optimal failure-finding interval （FFI） model based on maximizing expected availability. The model can be viewed as an extension and improvement to the model presented in Moubray （1997）. Numerical results are also included to illustrate the appropriateness of the proposed model.

Grid Integration of Wind Generation Considering Remote Wind Farms:Hybrid Markovian and Interval Unit Commitment

Grid integration of wind power is essential to reduce fossil fuel usage but challenging in view of the intermittent nature of wind.Recently,we developed a hybrid Markovian and interval approach for the unit commitment and economic dispatch problem where power generation of conventional units is linked to local wind states to dampen the effects of wind uncertainties.Also,to reduce complexity,extreme and expected states are considered as interval modeling.Although this approach is effective,the fact that major wind farms are often located in remote locations and not accompanied by conventional units leads to conservative results.Furthermore,weights of extreme and expected states in the objective function are difficult to tune,resulting in significant differences between optimization and simulation costs.In this paper,each remote wind farm is paired with a conventional unit to dampen the effects of wind uncertainties without using expensive utility-scaled battery storage,and extra constraints are innovatively established to model pairing.Additionally,proper weights are derived through a novel quadratic fit of cost functions.The problem is solved by using a creative integration of our recent surrogate Lagrangian relaxation and branch-and-cut.Results demonstrate modeling accuracy,computational efficiency,and significant reduction of conservativeness of the previous approach.

DYNAMIC OPTIMIZATION FOR UNCERTAIN STRUCTURES USING INTERVAL METHOD

An interval optimization method for the dynamic response of structures with inter- val parameters is presented.The matrices of structures with interval parameters are given.Com- bining the interval extension with the perturbation,the method for interval dynamic response analysis is derived.The interval optimization problem is transformed into a corresponding de- terministic one.Because the mean values and the uncertainties of the interval parameters can be elected design variables,more information of the optimization results can be obtained by the present method than that obtained by the deterministic one.The present method is implemented for a truss structure.The numerical results show that the method is effective.

ENVELOPING THEORY BASED METHOD FOR THE DETERMINATION OF PATH INTERVAL AND TOOL PATH OPTIMIZATION FOR SURFACE MACHINING

An enveloping theory based method for the determination of path interval in three axis NC machining of free form surface is presented, and a practical algorithm and the measures for improving the calculating efficiency of the algorithm are given. Not only the given algorithm can be used for ball end cutter, flat end cutter, torus cutter and drum cutter, but also the proposed method can be extended to arbitrary milling cutters. Thus, the problem how to strictly calculate path interval in the occasion of three axis NC machining of free form surfaces with non ball end cutters has been resolved effectively. On this basis, the factors that affect path interval are analyzed, and the methods for optimizing tool path are explored.

Risk-averse Robust Interval Economic Dispatch for Power Systems with Large-scale Wind Power Integration

This paper presents a robust interval economic dispatch(RIED)model for power systems with large-scale wind power integration.Differing from existing interval optimization(IO)approaches that merely rely on the upper and lower boundaries of random variables,the distribution information retained in the historical data is introduced to the IO method in this paper.Based on the available probability distribution function(PDF),wind power curtailment and load shedding are quantified as the operational risk and incorporated into the decision-making process.In this model,we need not rely on the forecasted value of wind power,which is randomly fluctuating and quite unpredictable.Furthermore,when the PDFs of wind power are taken into account,the resulting dispatch solution makes a good tradeoff between the generation cost and the operational risk.Finally,the RIED model yields an optimal dispatch solution for thermal units and the allowable intervals of wind power for the wind farms,which efficiently mitigates the uncertainty in wind power generation and provides more practical suggestions for system operators.Simulation studies are conducted on a modified IEEE-118 bus system and the results verify the effectiveness of the proposed RIED model.

An improved window opening behavior model involving the division of the dummy variable’s interval level:Case study of an office building in Xi’an during summer

Window opening behavior significantly impacts indoor air quality,thermal comfort,and energy consumption.A field measurement was carried out in three typical rooms(a standard office,a meeting room and a smoking office)within an office building.The window state and the physical environment were continuously recorded during the measured periods.Three typical window opening behaviors were found in the measured samples,namely,active,moderate,and passive.The common logistic regression coefficient indicated that solar radiation exhibited the greatest effect on window opening behavior in the smoking office and standard office.Typically,window opening behavior in the meeting room was the most strongly correlated with time of the day,mainly because of the meeting schedule for occupants in the meeting room.This study discussed the dividing principles involved in setting the dummy variable interval level(discretizing continuous variables and dividing them into different intervals),and proposed a method to determine the optimal interval level of each variable.The improved model led to the increase in the prediction accuracy rate of the window being opened by 2.0%and 3.3%according to the comparison with the original model based on dummy variables and the common model based on continuous variables,respectively.This study can provide a reference value for simulating energy consumption in office buildings in the future.

Geological characteristics and co-exploration and co-production methods of Upper Permian Longtan coal measure gas in Yangmeishu Syncline, Western Guizhou Province, China

Coal measure gas(also known as coal-bearing unconventional gas)is the key field and development direction of unconventional natural gas in recent years.The exploration and evaluation of coal measure gas(coalbed methane,coal shale gas and coal measure tight sandstone gas)from single coalbed methane has greatly expanded the field and space of resource evaluation,which is of positive significance for realizing the comprehensive utilization of coal resources,maximizing the benefits and promoting the innovation of oil and gas geological theory and technological advances in exploration and development.For the first time,in Yangmeishu Syncline of Western Guizhou Province,the public welfare coalbed methane geological survey project of China Geological Survey has been carried out a systematic geological survey of coal measure gas for the Upper Permian Longtan Formation,identified the geological conditions of coal measure gas and found high quality resources.The total geological resource quantity of coalbed methane and coal shale gas is 51.423×109 m3 and the geological resource abundance is up to 566×106 m3/km2.In this area,the coal measures are characterized by many layers of minable coal seams,large total thickness,thin to the medium thickness of the single layer,good gas-bearing property of coal seams and coal measure mudstone and sandstone,good reservoir physical property and high-pressure coefficient.According to the principle of combination of high quality and similarity of key parameters of the coal reservoir,the most favorable intervals are No.5-2,No.7 and No.13-2 coal seam in Well YMC1.And the pilot tests are carried out on coal seams and roof silty mudstone,such as staged perforation,increasing hydraulic fracturing scale and"three gas"production.The high and stable industrial gas flow with a daily gas output of more than 4000 m3 has been obtained,which has realized the breakthrough in the geological survey of coal measure gas in Southwest China.Based on the above investigation results,the geological characteristics of coal measure gas in the multi-thin-coal-seam-developed area and the coexploration and co-production methods,such as the optimization method of favorable intervals,the highefficiency fracturing and reservoir reconstruction method of coal measures,and the"three gas"drainage and production system,are systematically summarized in this paper.It will provide a reference for efficient exploration and development of coal measure gas in similar geological conditions in China.

Distributed model predictive control based on adaptive sampling mechanism

In this work,an adaptive sampling control strategy for distributed predictive control is proposed.According to the proposed method,the sampling rate of each subsystem of the accused object is determined based on the periodic detection of its dynamic behavior and calculations made using a correlation function.Then,the optimal sampling interval within the period is obtained and sent to the corresponding sub-prediction controller,and the sampling interval of the controller is changed accordingly before the next sampling period begins.In the next control period,the adaptive sampling mechanism recalculates the sampling rate of each subsystem’s measurable output variable according to both the abovementioned method and the change in the dynamic behavior of the entire system,and this process is repeated.Such an adaptive sampling interval selection based on an autocorrelation function that measures dynamic behavior can dynamically optimize the selection of sampling rate according to the real-time change in the dynamic behavior of the controlled object.It can also accurately capture dynamic changes,meaning that each sub-prediction controller can more accurately calculate the optimal control quantity at the next moment,significantly improving the performance of distributed model predictive control(DMPC).A comparison demonstrates that the proposed adaptive sampling DMPC algorithm has better tracking performance than the traditional DMPC algorithm.

面向多任务的船舶舱室布局区间优化设计研究

Searching for the optimal cabin layout plan is an efective way to improve the efciency of the overall design and reduce a ship’s operation costs.The multitasking states of a ship involve several statuses when facing diferent missions during a voyage,such as the status of the marine supply and emergency escape.The human fow and logistics between cabins will change as the state changes.An ideal cabin layout plan,which is directly impacted by the above-mentioned factors,can meet the diferent requirements of several statuses to a higher degree.Inevitable deviations exist in the quantifcation of human fow and logistics.Moreover,uncontrollability is present in the fow situation during actual operations.The coupling of these deviations and uncontrollability shows typical uncertainties,which must be considered in the design process.Thus,it is important to integrate the demands of the human fow and logistics in multiple states into an uncertainty parameter scheme.This research considers the uncertainties of adjacent and circulating strengths obtained after quantifying the human fow and logistics.Interval numbers are used to integrate them,a two-layer nested system of interval optimization is introduced,and diferent optimization algorithms are substituted for solving calculations.The comparison and analysis of the calculation results with deterministic optimization show that the conclusions obtained can provide feasible guidance for cabin layout scheme.

Economic Dispatch of Power Systems with Virtual Power Plant Based Interval Optimization Method

Load prediction and power prediction uncertainties are inevitable aspects of a virtual power plant(VPP).In power system economic dispatch(ED)modeling,the interval is used to describe prediction uncertainties.An ED model with interval uncertainty is established in this paper.The probability degree definition is adopted to convert the interval-based economic dispatch model into a deterministic model for the purposes of solving the modeling problem.Simulation tests are performed on a 10-machine system using professional optimization software(LINGO).The simulation results verify the validity of the proposed interval-based scheme for the economic dispatch of a power system with VPP.

Impacts of Optimization Interval on Home Energy Scheduling for Thermostatically Controlled Appliances

Home energy management systems(HEMS)have attracted much attention in recent years for energy efficiency and cost savings.Home energy scheduling is an important function of the HEMS,especially for thermostatically controlled appliances(TCAs).Optimization interval is a basic parameter in home energy scheduling,a topic that has been seldom studied before.This paper studies the impacts of optimization interval on home energy scheduling taking into consideration four scheduling strategies for TCAs.A tracking strategy is developed to arrive at a suboptimal solution while avoiding unacceptable solving time.The impact mechanism of optimization interval is analyzed.The optimization interval takes into account the scheduling ability of HEMS,flexibility of TCAs,the feasibility of scheduling,scheduling performances,user experiences,and model accuracy.The flexibility of TCAs,which depends on optimization interval,is defined and modeled.Two time division methods are proposed,namely,consistent interval division method(CIDM)and inconsistent interval division method(IIDM).Numerical simulation is carried out to verify the analysis.The results show that optimization interval impacts the flexibility,feasibility,and performance of scheduling.The proposed tracking strategy is seen as an effective method for HEMS.

Dual Interval Optimization Based Trading Strategy for ESCO in Day-ahead Market with Bilateral Contracts

Being capable of aggregating multiple energy resources, the energy service company(ESCO) has been regarded as a promising alternative for improving power system flexibility and facilitating the consumption of renewable resources in the electricity market. Considering the uncertain variables in day-ahead(DA) market trading, an ESCO can hardly determine their accurate probability distribution functions. Traditional interval optimization methods are used to process these uncertain variables without specific probability distribution functions.However, the lower and upper bounds of the intervals may change due to extreme weather conditions and other emergent events. Hence, a dual interval optimization based trading strategy(DIOTS) for ESCO in a DA market with bilateral contracts(BCs) is proposed. First, we transfer the dual interval optimization model into a simple model consisting of several interval optimization models. Then, a pessimistic preference ordering method is applied to solve the derived model. Case studies illustrating an actual test system corroborate the validity and the robustness of the proposed model, and also reveal that ECSO is critical in improving power system flexibility and facilitating the ability of absorbing renewable resources.

MPC-based interval number optimization for electric water heater scheduling in uncertain environments

In this paper,interval number optimization and model predictive control are proposed to handle the uncertain-but-bounded parameters in electric water heater load scheduling.First of all,interval numbers are used to describe uncertain parameters including hot water demand,ambient temperature,and real-time price of electricity.Moreover,the traditional thermal dynamic model of electric water heater is transformed into an interval number model,based on which,the day-ahead load scheduling problem with uncertain parameters is formulated,and solved by interval number optimization.Different tolerance degrees for constraint violation and temperature preferences are also discussed for giving consumers more choices.Furthermore,the model predictive control which incorporates both forecasts and newly updated information is utilized to make and execute electric water heater load schedules on a rolling basis throughout the day.Simulation results demonstrate that interval number optimization either in day-ahead optimization or model predictive control format is robust to the uncertain hot water demand,ambient temperature,and real-time price of electricity,enabling customers to flexibly adjust electric water heater control strategy.

Realization of error correction and reconciliation of continuous quantum key distribution in detail

The efficiency of reconciliation in the continuous key distribution is the main factor which limits the ratio of secret key distribution. However, the efficiency depends on the computational complexity of the algorithm. This paper optimizes the two main aspects of the reconciliation process of the continuous key distribution： the partition of interval and the estimation of bit. We use Gaussian approximation to effectively speed up the convergence of algorithm. We design the estimation function as the estimator of the SEC （sliced error correction） algorithm. Therefore, we lower the computational complexity and simplify the core problem of the reconciliation algorithm. Thus we increase the efficiency of the reconciliation process in the continuous key distribution and then the ratio of the secret key distribution is also increased.

Risk management for sulfur dioxide abatement under multiple uncertainties

In this study, interval-parameter programming, two-stage stochastic progranaming （TSP）, and conditional value-at-risk （CVaR） were incorporated into a general optimization framework, leading to an interval-parameter CVaR-based two-stage programming （ICTP） method. The ICTP method had several advantages： （i） its objective function simultaneously took expected cost and risk cost into consideration, and also used discrete random variables and discrete intervals to reflect uncertain properties; （ii） it quantitatively evaluated the right tail of distributions of random variables which could better calculate the risk of violated environmental standards; （iii） it was useful for helping decision makers to analyze the trade-offs between cost and risk; and （iv） it was effective to penalize the second-stage costs, as well as to capture the notion of risk in stochastic programming. The developed model was applied to sulfur dioxide abatement in an air quality management system. The results indicated that the ICTP method could be used for generating a series of air quality management schemes under different risk-aversion levels, for identifying desired air quality management strategies for decision makers, and for considering a proper balance between system economy and environmental quality.

Energy Management System Design and Testing for Smart Buildings Under Uncertain Generation (Wind/Photovoltaic) and Demand

This study provides details of the energy management architecture used in the Goldwind microgrid test bed. A complete mathematical model, including all constraints and objectives, for microgrid operational management is first described using a modified prediction interval scheme. Forecasting results are then achieved every 10 min using the modified fuzzy prediction interval model, which is trained by particle swarm optimization.A scenario set is also generated using an unserved power profile and coverage grades of forecasting to compare the feasibility of the proposed method with that of the deterministic approach. The worst case operating points are achieved by the scenario with the maximum transaction cost. In summary, selection of the maximum transaction operating point from all the scenarios provides a cushion against uncertainties in renewable generation and load demand.