Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE...Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.展开更多
Based on the principle of spatial pyramid for signal, a multi-scale transform of two-dimensional （2D） interpolating pyramid is constructed by the nonlinear median operator. The transform properties of error diffuse ...Based on the principle of spatial pyramid for signal, a multi-scale transform of two-dimensional （2D） interpolating pyramid is constructed by the nonlinear median operator. The transform properties of error diffuse halftoning noise on multiple scales are investigated and analyzed through experiments. According to these properties, a robust inverse halftoning method is proposed. The halftoning image is firstly preprocessed by a Gaussian low-pass filter, and decomposed by the one-scale transform. Then a Wiener filter is employed to the detailed coefficients. Finally an inverse image is reconstructed. Experimental results show that the proposed transform has the advantage of separating the halftoning noise and image detail over linear multi-resolution transform. The presented inverse halftoning method performs some excellent abilities on sharp edge, high peak signal-to-noise ratio （PSNR）, and small memory requirement.展开更多
In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background c...In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background.Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.展开更多
The robustness of the subspace method for blind signature waveform estimation with respect to channel order is analyzed in asynchronous DS-CDMA systems theoretically. Theoretical analysis and simulation results show t...The robustness of the subspace method for blind signature waveform estimation with respect to channel order is analyzed in asynchronous DS-CDMA systems theoretically. Theoretical analysis and simulation results show that the overestimating of the channel order will lead to the degradation of the quality of the estimated signature waveform. So we should adopt the channel order as small as possible.展开更多
A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and ...A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and principles contained in the water rocket have much in common with the actual small rocket system, and are suitable as educational and research teaching materials in the field of mechanics. Especially in the field of disaster prevention and mitigation, the use of water rockets is being researched and developed as a rescue tool in the event of a flood or earthquake as a disaster countermeasure. However, since the water rocket is a flying object based on the mechanical principle, it is important to ensure the accuracy and stability of the flight path. In this paper, a mechanical simulator is developed with a numerical calculation program based on the mechanical consideration of water rocket flight performance. In addition, the correlation between the flight distance obtained in the simulation and the estimated flight distance is analyzed by applying a multivariate analysis method and verifying the validity of the flight distance calculated from the result. Based on the verification results, we will apply a statistical optimization method to approach the optimization of flight stability performance conditions for water rockets.展开更多
Background: The robustness is a measurement of an analytical chemical method and its ability to contain unaffected by little with deliberate variation of analytical chemical method parameters. The analytical chemical ...Background: The robustness is a measurement of an analytical chemical method and its ability to contain unaffected by little with deliberate variation of analytical chemical method parameters. The analytical chemical method variation parameters are based on pH variability of buffer solution of mobile phase, organic ratio composition changes, stationary phase (column) manufacture, brand name and lot number variation;flow rate variation and temperature variation of chromatographic system. The analytical chemical method for assay of Atropine Sulfate conducted for robustness evaluation. The typical variation considered for mobile phase organic ratio change, change of pH, change of temperature, change of flow rate, change of column etc. Purpose: The aim of this study is to develop a cost effective, short run time and robust analytical chemical method for the assay quantification of Atropine in Pharmaceutical Ophthalmic Solution. This will help to make analytical decisions quickly for research and development scientists as well as will help with quality control product release for patient consumption. This analytical method will help to meet the market demand through quick quality control test of Atropine Ophthalmic Solution and it is very easy for maintaining (GDP) good documentation practices within the shortest period of time. Method: HPLC method has been selected for developing superior method to Compendial method. Both the compendial HPLC method and developed HPLC method was run into the same HPLC system to prove the superiority of developed method. Sensitivity, precision, reproducibility, accuracy parameters were considered for superiority of method. Mobile phase ratio change, pH of buffer solution, change of stationary phase temperature, change of flow rate and change of column were taken into consideration for robustness study of the developed method. Results: The limit of quantitation (LOQ) of developed method was much low than the compendial method. The % RSD for the six sample assay of developed method was 0.4% where the % RSD of the compendial method was 1.2%. The reproducibility between two analysts was 100.4% for developed method on the contrary the compendial method was 98.4%.展开更多
The present study deals with the effects of both tin (Sn) and graphite (Gr) powders on the cold extrudability of Fe-TiC nanocomposites as lubricant. The production process includes low-energy ball milling, powder meta...The present study deals with the effects of both tin (Sn) and graphite (Gr) powders on the cold extrudability of Fe-TiC nanocomposites as lubricant. The production process includes low-energy ball milling, powder metallurgy and cold direct Extrusion. Due to various factors influencing the extrudability of the Fe-TiC nanocomposites, such as milling time, rate of extrusion, type and content of lubricant and etc, Taguchi robust design method of system optimization was used to determine the approximate contribution percent (% ρ) of each factor. In order to investigation of Fe-TiC properties, samples with best quality of extrusion were analyzed by XRD and SEM investigations. The results indicate that, sitting the atomic layers of Sn lubricant between Fe and TiC particles leads to decreasing the friction. In this case sliding the particles on each other is easier and a part of the load is applied on lubricant. The results of extrusion of samples indicate that using 2% Sn admixed and die wall graphite lubrication can improve cold extrudability of Fe-TiC nanocomposites.展开更多
A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inve...A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.展开更多
Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods ar...Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods are based on the assumption that the results affected by gross errors can be found to the left and/or to the right of censoring, or truncated, points. However, as a rule, the (intrinsic) distribution of observations is complex (mixed) consisting of two or more distributions. Then the existing methods, such as ML, Huber’s, etc., yield enlarged estimates for the normal-distribution variance. By studying better estimates the present author has invented new method, called PEROBLS D, based on the Tukeyan mixed-distribution model in which both the contamination rate (percentage) and the parameters of both distributions, forming the mixed one, are estimated, and for the parameters of the basic normal distribution better estimates are obtained than by the existing methods.展开更多
In order to express information on the quality grade of product designed, thetarget value of product quality design was described with a fuzzy number in this paper. Analternative to Taguchi's, the robustness appli...In order to express information on the quality grade of product designed, thetarget value of product quality design was described with a fuzzy number in this paper. Analternative to Taguchi's, the robustness application design method has been recently presented.However, neither Taguchi's method nor the alternative method is capable of dealing satisfactorilywith the frequently encountered situations in which all the noise variables cannot be studiedsimultaneously. Based on the ideas from response surface modeling, linear models theory, and randomeffects models, we provide a method for estimation in the robustness application design method inproduct quality applications. With this new method used, the high-quality ratio of the productdesigned could be increased, and the ability to resist the influence of various disturbing factorsand noise factors could be enhanced.展开更多
A robust airfoil optimization platform is constructed based on the modified particle swarm optimization method （i.e., the second-order oscillating particle swarm method）, which consists of an efficient optimization ...A robust airfoil optimization platform is constructed based on the modified particle swarm optimization method （i.e., the second-order oscillating particle swarm method）, which consists of an efficient optimization algorithm, a precise aerodynamic analysis program, a high accuracy surrogate model, and a classical airfoil parametric method. There are two improvements for the modified particle swarm method compared with the standard particle swarm method. First, the particle velocity is represented by the combination of the particle position and the variation of position, which makes the particle swarm algorithm a second-order precision method with respect to the particle po- sition. Second, for the sake of adding diversity to the swarm and enlarging the parameter searching domain to improve the global convergence performance of the algorithm, an oscillating term is introduced to the update formula of the particle velocity. At last, tak- ing two airfoils as examples, the aerodynamic shapes are optimized on this optimization platform. It is shown from the optimization results that the aerodynamic characteristic of the airfoils is greatly improved in a broad design range.展开更多
The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There ...The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.展开更多
Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio select...Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio selection,and investment strategies,accurate estimates of the relationship among assets are as necessary as are delicate in a time-dependent context.In this regard,fundamental tools that increasingly attract research interests are precision matrix and graphical models,which are able to obtain insights into the joint evolution of financial quantities.In this paper,we present a robust divergence estimator for a time-varying precision matrix that can manage both the extreme events and time-dependency that affect financial time series.Furthermore,we provide an algorithm to handle parameter estimations that uses the“maximization–minimization”approach.We apply the methodology to synthetic data to test its performances.Then,we consider the cryptocurrency market as a real data application,given its remarkable suitability for the proposed method because of its volatile and unregulated nature.展开更多
随着电动汽车和分布式电源接入电网的比例不断提升,虚拟电厂(virtual power plant,VPP)为有效解决电动汽车、分布式电源并网提供了新思路。针对VPP独立运行时面临的运行成本高、电价和源荷不确定性大等挑战,文中提出了一种基于纳什三阶...随着电动汽车和分布式电源接入电网的比例不断提升,虚拟电厂(virtual power plant,VPP)为有效解决电动汽车、分布式电源并网提供了新思路。针对VPP独立运行时面临的运行成本高、电价和源荷不确定性大等挑战,文中提出了一种基于纳什三阶段鲁棒优化的多VPP协同运行的优化方法。为协调VPP运营商与电动汽车用户的经济利益冲突,采用主从博弈理论刻画VPP运营商和电动汽车上下层之间的互动关系,上层VPP运营商充分考虑到电力市场购售电价以及源荷功率波动带来的不确定性影响,由三阶段鲁棒优化模型构造上层主体,三阶段鲁棒优化模型较以往的传统模型不同,文中采用了min-maxmin-maxmin的构造刻画模型内部关系;构建了基于纳什谈判理论的多VPP协同优化模型,为解决复杂非凸非线性优化的求解问题,将模型等效转化为多VPP合作成本最小化和电能谈判支付两个子问题;考虑到各VPP间信息隐私安全,采用交替方向乘子法(alternating direction method of multipliers,ADMM)对上述两个子问题进行分布式求解。算例验证表明,所提方法不仅在多重不确定性影响的情况下为参与合作的各VPP提供了可行且鲁棒性强的调度方案,而且为各VPP制定了合理的能源交互策略和利益分配方案,参与合作的各VPP均实现了经济效益的提升。展开更多
基金the National Natural Science Foundation of China (Nos.52304123 and 52104077)the Postdoctoral Fellowship Program of CPSF (No.GZB20230914)+1 种基金the China Postdoctoral Science Foundation (No.2023M730412)the National Key Research and Development Program for Young Scientists (No.2021YFC2900400)。
文摘Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.
基金This work was supported by the Pre-Research Foundation of Ministries and Commissions(No.51416050205DZ0144)Natural Science Foundation of Shaanxi Province (No.2004F32)the Scientific Research Program from the Education Department of Shaanxi Province (No.04JK244).
文摘Based on the principle of spatial pyramid for signal, a multi-scale transform of two-dimensional （2D） interpolating pyramid is constructed by the nonlinear median operator. The transform properties of error diffuse halftoning noise on multiple scales are investigated and analyzed through experiments. According to these properties, a robust inverse halftoning method is proposed. The halftoning image is firstly preprocessed by a Gaussian low-pass filter, and decomposed by the one-scale transform. Then a Wiener filter is employed to the detailed coefficients. Finally an inverse image is reconstructed. Experimental results show that the proposed transform has the advantage of separating the halftoning noise and image detail over linear multi-resolution transform. The presented inverse halftoning method performs some excellent abilities on sharp edge, high peak signal-to-noise ratio （PSNR）, and small memory requirement.
基金supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2019QD018)National Natural Science Foundation of China(Grant Nos.11975143,12105161,61602188)+1 种基金CAS Key Laboratory of Science and Technology on Operational Oceanography(Grant No.OOST2021-05)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents(Grant Nos.2017RCJJ068,2017RCJJ069)。
文摘In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background.Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.
文摘The robustness of the subspace method for blind signature waveform estimation with respect to channel order is analyzed in asynchronous DS-CDMA systems theoretically. Theoretical analysis and simulation results show that the overestimating of the channel order will lead to the degradation of the quality of the estimated signature waveform. So we should adopt the channel order as small as possible.
文摘A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and principles contained in the water rocket have much in common with the actual small rocket system, and are suitable as educational and research teaching materials in the field of mechanics. Especially in the field of disaster prevention and mitigation, the use of water rockets is being researched and developed as a rescue tool in the event of a flood or earthquake as a disaster countermeasure. However, since the water rocket is a flying object based on the mechanical principle, it is important to ensure the accuracy and stability of the flight path. In this paper, a mechanical simulator is developed with a numerical calculation program based on the mechanical consideration of water rocket flight performance. In addition, the correlation between the flight distance obtained in the simulation and the estimated flight distance is analyzed by applying a multivariate analysis method and verifying the validity of the flight distance calculated from the result. Based on the verification results, we will apply a statistical optimization method to approach the optimization of flight stability performance conditions for water rockets.
文摘Background: The robustness is a measurement of an analytical chemical method and its ability to contain unaffected by little with deliberate variation of analytical chemical method parameters. The analytical chemical method variation parameters are based on pH variability of buffer solution of mobile phase, organic ratio composition changes, stationary phase (column) manufacture, brand name and lot number variation;flow rate variation and temperature variation of chromatographic system. The analytical chemical method for assay of Atropine Sulfate conducted for robustness evaluation. The typical variation considered for mobile phase organic ratio change, change of pH, change of temperature, change of flow rate, change of column etc. Purpose: The aim of this study is to develop a cost effective, short run time and robust analytical chemical method for the assay quantification of Atropine in Pharmaceutical Ophthalmic Solution. This will help to make analytical decisions quickly for research and development scientists as well as will help with quality control product release for patient consumption. This analytical method will help to meet the market demand through quick quality control test of Atropine Ophthalmic Solution and it is very easy for maintaining (GDP) good documentation practices within the shortest period of time. Method: HPLC method has been selected for developing superior method to Compendial method. Both the compendial HPLC method and developed HPLC method was run into the same HPLC system to prove the superiority of developed method. Sensitivity, precision, reproducibility, accuracy parameters were considered for superiority of method. Mobile phase ratio change, pH of buffer solution, change of stationary phase temperature, change of flow rate and change of column were taken into consideration for robustness study of the developed method. Results: The limit of quantitation (LOQ) of developed method was much low than the compendial method. The % RSD for the six sample assay of developed method was 0.4% where the % RSD of the compendial method was 1.2%. The reproducibility between two analysts was 100.4% for developed method on the contrary the compendial method was 98.4%.
文摘The present study deals with the effects of both tin (Sn) and graphite (Gr) powders on the cold extrudability of Fe-TiC nanocomposites as lubricant. The production process includes low-energy ball milling, powder metallurgy and cold direct Extrusion. Due to various factors influencing the extrudability of the Fe-TiC nanocomposites, such as milling time, rate of extrusion, type and content of lubricant and etc, Taguchi robust design method of system optimization was used to determine the approximate contribution percent (% ρ) of each factor. In order to investigation of Fe-TiC properties, samples with best quality of extrusion were analyzed by XRD and SEM investigations. The results indicate that, sitting the atomic layers of Sn lubricant between Fe and TiC particles leads to decreasing the friction. In this case sliding the particles on each other is easier and a part of the load is applied on lubricant. The results of extrusion of samples indicate that using 2% Sn admixed and die wall graphite lubrication can improve cold extrudability of Fe-TiC nanocomposites.
文摘A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.
文摘Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods are based on the assumption that the results affected by gross errors can be found to the left and/or to the right of censoring, or truncated, points. However, as a rule, the (intrinsic) distribution of observations is complex (mixed) consisting of two or more distributions. Then the existing methods, such as ML, Huber’s, etc., yield enlarged estimates for the normal-distribution variance. By studying better estimates the present author has invented new method, called PEROBLS D, based on the Tukeyan mixed-distribution model in which both the contamination rate (percentage) and the parameters of both distributions, forming the mixed one, are estimated, and for the parameters of the basic normal distribution better estimates are obtained than by the existing methods.
文摘In order to express information on the quality grade of product designed, thetarget value of product quality design was described with a fuzzy number in this paper. Analternative to Taguchi's, the robustness application design method has been recently presented.However, neither Taguchi's method nor the alternative method is capable of dealing satisfactorilywith the frequently encountered situations in which all the noise variables cannot be studiedsimultaneously. Based on the ideas from response surface modeling, linear models theory, and randomeffects models, we provide a method for estimation in the robustness application design method inproduct quality applications. With this new method used, the high-quality ratio of the productdesigned could be increased, and the ability to resist the influence of various disturbing factorsand noise factors could be enhanced.
文摘A robust airfoil optimization platform is constructed based on the modified particle swarm optimization method （i.e., the second-order oscillating particle swarm method）, which consists of an efficient optimization algorithm, a precise aerodynamic analysis program, a high accuracy surrogate model, and a classical airfoil parametric method. There are two improvements for the modified particle swarm method compared with the standard particle swarm method. First, the particle velocity is represented by the combination of the particle position and the variation of position, which makes the particle swarm algorithm a second-order precision method with respect to the particle po- sition. Second, for the sake of adding diversity to the swarm and enlarging the parameter searching domain to improve the global convergence performance of the algorithm, an oscillating term is introduced to the update formula of the particle velocity. At last, tak- ing two airfoils as examples, the aerodynamic shapes are optimized on this optimization platform. It is shown from the optimization results that the aerodynamic characteristic of the airfoils is greatly improved in a broad design range.
基金partially supported by the Russian Foundation for Basic Research(grant No.07-01-00729)the Singapore Academic Research Funds R-146-000-064-112 and R-146-000-099-112the Boole Centre for Research in Informatics at the National University of Ireland,Cork and by the Mathematics Applications Consortium for Science and Industry in Ireland(MACSI)under the Science Foundation Ireland Mathematics Initiative.
文摘The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.
文摘Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio selection,and investment strategies,accurate estimates of the relationship among assets are as necessary as are delicate in a time-dependent context.In this regard,fundamental tools that increasingly attract research interests are precision matrix and graphical models,which are able to obtain insights into the joint evolution of financial quantities.In this paper,we present a robust divergence estimator for a time-varying precision matrix that can manage both the extreme events and time-dependency that affect financial time series.Furthermore,we provide an algorithm to handle parameter estimations that uses the“maximization–minimization”approach.We apply the methodology to synthetic data to test its performances.Then,we consider the cryptocurrency market as a real data application,given its remarkable suitability for the proposed method because of its volatile and unregulated nature.
文摘随着电动汽车和分布式电源接入电网的比例不断提升,虚拟电厂(virtual power plant,VPP)为有效解决电动汽车、分布式电源并网提供了新思路。针对VPP独立运行时面临的运行成本高、电价和源荷不确定性大等挑战,文中提出了一种基于纳什三阶段鲁棒优化的多VPP协同运行的优化方法。为协调VPP运营商与电动汽车用户的经济利益冲突,采用主从博弈理论刻画VPP运营商和电动汽车上下层之间的互动关系,上层VPP运营商充分考虑到电力市场购售电价以及源荷功率波动带来的不确定性影响,由三阶段鲁棒优化模型构造上层主体,三阶段鲁棒优化模型较以往的传统模型不同,文中采用了min-maxmin-maxmin的构造刻画模型内部关系;构建了基于纳什谈判理论的多VPP协同优化模型,为解决复杂非凸非线性优化的求解问题,将模型等效转化为多VPP合作成本最小化和电能谈判支付两个子问题;考虑到各VPP间信息隐私安全,采用交替方向乘子法(alternating direction method of multipliers,ADMM)对上述两个子问题进行分布式求解。算例验证表明,所提方法不仅在多重不确定性影响的情况下为参与合作的各VPP提供了可行且鲁棒性强的调度方案,而且为各VPP制定了合理的能源交互策略和利益分配方案,参与合作的各VPP均实现了经济效益的提升。
