To avoid the aerodynamic performance loss of airfoil at non-design state which often appears in single point design optimization, and to improve the adaptability to the uncertain factors in actual flight environment, ...To avoid the aerodynamic performance loss of airfoil at non-design state which often appears in single point design optimization, and to improve the adaptability to the uncertain factors in actual flight environment, a two-dimensional stochastic airfoil optimization design method based on neural networks is presented. To provide highly efficient and credible analysis, four BP neural networks are built as surrogate models to predict the airfoil aerodynamic coefficients and geometry parameter. These networks are combined with the probability density function obeying normal distribution and the genetic algorithm, thus forming an optimization design method. Using the method, for GA（W）-2 airfoil, a stochastic optimization is implemented in a two-dimensional flight area about Mach number and angle of attack. Compared with original airfoil and single point optimization design airfoil, results show that the two-dimensional stochastic method can improve the performance in a specific flight area, and increase the airfoil adaptability to the stochastic changes of multiple flight parameters.展开更多
Background： Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to bi...Background： Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Methods： Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms. Results： Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses. Conclusions： Adaptive optimization and management led to 6%-14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.展开更多
After suffering from a grid blackout, distributed energy resources(DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s ...After suffering from a grid blackout, distributed energy resources(DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s resilience. In this study, a multi-source coordinated load restoration strategy was investigated for a distribution network with soft open points(SOPs). Here, the flexible regulation ability of the SOPs is fully utilized to improve the load restoration level while mitigating voltage deviations. Owing to the uncertainty, a scenario-based stochastic optimization approach was employed,and the load restoration problem was formulated as a mixed-integer nonlinear programming model. A computationally efficient solution algorithm was developed for the model using convex relaxation and linearization methods. The algorithm is organized into a two-stage structure, in which the energy storage system is dispatched in the first stage by solving a relaxed convex problem. In the second stage, an integer programming problem is calculated to acquire the outputs of both SOPs and power resources. A numerical test was conducted on both IEEE 33-bus and IEEE 123-bus systems to validate the effectiveness of the proposed strategy.展开更多
This article presents a novel approach to integrate a throughput prediction model for the ball mill into short-term stochastic production scheduling in mining complexes.The datasets for the throughput prediction model...This article presents a novel approach to integrate a throughput prediction model for the ball mill into short-term stochastic production scheduling in mining complexes.The datasets for the throughput prediction model include penetration rates from blast hole drilling(measurement while drilling),geological domains,material types,rock density,and throughput rates of the operating mill,offering an accessible and cost-effective method compared to other geometallurgical programs.First,the comminution behavior of the orebody was geostatistically simulated by building additive hardness proportions from penetration rates.A regression model was constructed to predict throughput rates as a function of blended rock properties,which are informed by a material tracking approach in the mining complex.Finally,the throughput prediction model was integrated into a stochastic optimization model for short-term production scheduling.This way,common shortfalls of existing geometallurgical throughput prediction models,that typically ignore the non-additive nature of hardness and are not designed to interact with mine production scheduling,are overcome.A case study at the Tropicana Mining Complex shows that throughput can be predicted with an error less than 30 t/h and a correlation coefficient of up to 0.8.By integrating the prediction model and new stochastic components into optimization,the production schedule achieves weekly planned production reliably because scheduled materials match with the predicted performance of the mill.Comparisons to optimization using conventional mill tonnage constraints reveal that expected production shortfalls of up to 7%per period can be mitigated this way.展开更多
To investigate the equilibrium relationships between the volatility of capital and income, taxation, and ance in a stochastic control model, the uniqueness of the solution to this model was proved by using the method ...To investigate the equilibrium relationships between the volatility of capital and income, taxation, and ance in a stochastic control model, the uniqueness of the solution to this model was proved by using the method of dynamic programming under the introduction of distributive disturbance and elastic labor supply. Furthermore, the effects of two types of shocks on labor-leisure choice, economic growth rate and welfare were numerically analyzed, and then the optimal tax policy was derived.展开更多
A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modem risky theory, a unique positive solution to the dynamic ...A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modem risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.展开更多
Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmis...Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.展开更多
In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible...In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage;this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.展开更多
文摘To avoid the aerodynamic performance loss of airfoil at non-design state which often appears in single point design optimization, and to improve the adaptability to the uncertain factors in actual flight environment, a two-dimensional stochastic airfoil optimization design method based on neural networks is presented. To provide highly efficient and credible analysis, four BP neural networks are built as surrogate models to predict the airfoil aerodynamic coefficients and geometry parameter. These networks are combined with the probability density function obeying normal distribution and the genetic algorithm, thus forming an optimization design method. Using the method, for GA（W）-2 airfoil, a stochastic optimization is implemented in a two-dimensional flight area about Mach number and angle of attack. Compared with original airfoil and single point optimization design airfoil, results show that the two-dimensional stochastic method can improve the performance in a specific flight area, and increase the airfoil adaptability to the stochastic changes of multiple flight parameters.
文摘Background： Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Methods： Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms. Results： Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses. Conclusions： Adaptive optimization and management led to 6%-14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.
基金supported by the State Grid Tianjin Electric Power Company Science and Technology Project (Grant No. KJ22-1-45)。
文摘After suffering from a grid blackout, distributed energy resources(DERs), such as local renewable energy and controllable distributed generators and energy storage can be used to restore loads enhancing the system’s resilience. In this study, a multi-source coordinated load restoration strategy was investigated for a distribution network with soft open points(SOPs). Here, the flexible regulation ability of the SOPs is fully utilized to improve the load restoration level while mitigating voltage deviations. Owing to the uncertainty, a scenario-based stochastic optimization approach was employed,and the load restoration problem was formulated as a mixed-integer nonlinear programming model. A computationally efficient solution algorithm was developed for the model using convex relaxation and linearization methods. The algorithm is organized into a two-stage structure, in which the energy storage system is dispatched in the first stage by solving a relaxed convex problem. In the second stage, an integer programming problem is calculated to acquire the outputs of both SOPs and power resources. A numerical test was conducted on both IEEE 33-bus and IEEE 123-bus systems to validate the effectiveness of the proposed strategy.
基金the National Sciences and Engineering Research Council of Canada(NSERC)under CDR Grant CRDPJ 500414-16NSERC Discovery Grant 239019the COSMO mining industry consortium(AngloGold Ashanti,BHP,De Beers,AngloAmerican,IAMGOLD,Kinross Gold,Newmont Mining,and Vale).
文摘This article presents a novel approach to integrate a throughput prediction model for the ball mill into short-term stochastic production scheduling in mining complexes.The datasets for the throughput prediction model include penetration rates from blast hole drilling(measurement while drilling),geological domains,material types,rock density,and throughput rates of the operating mill,offering an accessible and cost-effective method compared to other geometallurgical programs.First,the comminution behavior of the orebody was geostatistically simulated by building additive hardness proportions from penetration rates.A regression model was constructed to predict throughput rates as a function of blended rock properties,which are informed by a material tracking approach in the mining complex.Finally,the throughput prediction model was integrated into a stochastic optimization model for short-term production scheduling.This way,common shortfalls of existing geometallurgical throughput prediction models,that typically ignore the non-additive nature of hardness and are not designed to interact with mine production scheduling,are overcome.A case study at the Tropicana Mining Complex shows that throughput can be predicted with an error less than 30 t/h and a correlation coefficient of up to 0.8.By integrating the prediction model and new stochastic components into optimization,the production schedule achieves weekly planned production reliably because scheduled materials match with the predicted performance of the mill.Comparisons to optimization using conventional mill tonnage constraints reveal that expected production shortfalls of up to 7%per period can be mitigated this way.
文摘To investigate the equilibrium relationships between the volatility of capital and income, taxation, and ance in a stochastic control model, the uniqueness of the solution to this model was proved by using the method of dynamic programming under the introduction of distributive disturbance and elastic labor supply. Furthermore, the effects of two types of shocks on labor-leisure choice, economic growth rate and welfare were numerically analyzed, and then the optimal tax policy was derived.
基金The Social Science Foundation of China(No06BJY011)
文摘A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modem risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.
基金supported by the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(Grant No.34000-31610293)。
文摘Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.
基金supported by the NSF of China(11931018, 12271274)the Tianjin Natural Science Foundation (19JCYBJC30400)。
文摘In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties' utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a deductible and coverage;this is done by modelling the problem as a stochastic game in a continuous-time framework. A numerical example is provided to illustrate the results of the paper.
