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    • 1. 发明申请
    • STOCHASTIC STATE ESTIMATION FOR SMART GRIDS
    • 智能网格的STOCHASTIC状态估计
    • US20140032187A1
    • 2014-01-30
    • US13880449
    • 2011-11-04
    • Motto Alexis LegbedjiAndrey TorzhkovAmit Chakraborty
    • Motto Alexis LegbedjiAndrey TorzhkovAmit Chakraborty
    • G06F17/50
    • G06F17/5009G05B13/042G05B17/02G06F17/10
    • A method of approximating a solution of a stochastic state estimation (SSE) model of an electric grid, includes choosing (70) starting anchor points in an SSE model of an electric grid, relaxing (71) constraints of an SSE objective function to solve for a feasible solution of the SSE model, calculating (72) updated dual variables and infeasibility reduction directions from the feasible solution, generating (73) a linear cut for the chosen starting anchor points, choosing (74) a step size toward the reduction directions, and updating (75) the anchor points through branching by making the chosen step, wherein each anchor point defines a rectangle that at least partially covers a feasible solution set of the SSE model and the set of rectangles covering the feasible solution set of the SSE model define an approximate solution of the SSE model of said electric grid.
    • 一种近似电网随机状态估计(SSE)模型解的方法包括选择(70)在电网SSE模型中启动锚点,放松(71)SSE目标函数的约束,以求解 从可行解中计​​算(72)更新的双变量和不可行性减少方向,对所选择的起始锚点产生(73)线性切割,选择(74)向减小方向的步长, 以及通过进行所选择的步骤来通过分支来更新(75)所述锚定点,其中每个锚点定义至少部分地覆盖所述SSE模型的可行解集合的矩形,并且覆盖所述SSE模型的可行解集的矩形集合 定义所述电网的SSE模型的近似解。
    • 8. 发明授权
    • System and method for energy plant optimization using mixed integer-linear programming
    • 使用混合整数线性规划的能源工厂优化的系统和方法
    • US08396572B2
    • 2013-03-12
    • US12691909
    • 2010-01-22
    • Andrey TorzhkovAmit Chakraborty
    • Andrey TorzhkovAmit Chakraborty
    • G05B13/02
    • G05B17/02G05B13/042
    • A method for optimizing operational settings for a plurality of energy devices includes representing each of the plurality of energy devices in terms of a set of decision variables and operational parameters. The decision variables and operational parameters are constrained based on operational conditions and interrelationship within the plurality of energy devices. A two-tiered model of the plurality of energy devices is generated wherein a top tier of the model represents interaction of various sub-models and a bottom tier of the model includes a set of the sub-models that form the top tier, each sub-model representing detailed operation of the plurality of energy devices. The two-tiered model is optimized to provide either a schedule of operation for the plurality of energy devices or real-time control for the plurality of energy devices.
    • 用于优化多个能量设备的操作设置的方法包括根据一组决策变量和操作参数来表示多个能量设备中的每一个。 决定变量和操作参数基于多个能量设备内的操作条件和相互关系来约束。 生成多个能量装置的两层模型,其中模型的顶层表示各种子模型的交互作用,模型的底层包括形成顶层的子模型集合,每个子模型 - 表示多个能量装置的详细操作的模型。 双层模型被优化以提供多个能量装置的操作计划或者用于多个能量装置的实时控制。
    • 9. 发明申请
    • System and Method for Energy Plant Optimization Using Mixed Integer-Linear Programming
    • 使用混合整数线性规划的能源工厂优化的系统和方法
    • US20110066258A1
    • 2011-03-17
    • US12691909
    • 2010-01-22
    • Andrey TorzhkovAmit Chakraborty
    • Andrey TorzhkovAmit Chakraborty
    • G05B13/02
    • G05B17/02G05B13/042
    • A method for optimizing operational settings for a plurality of energy devices includes representing each of the plurality of energy devices in terms of a set of decision variables and operational parameters. The decision variables and operational parameters are constrained based on operational conditions and interrelationship within the plurality of energy devices. A two-tiered model of the plurality of energy devices is generated wherein a top tier of the model represents interaction of various sub-models and a bottom tier of the model includes a set of the sub-models that form the top tier, each sub-model representing detailed operation of the plurality of energy devices. The two-tiered model is optimized to provide either a schedule of operation for the plurality of energy devices or real-time control for the plurality of energy devices.
    • 用于优化多个能量设备的操作设置的方法包括根据一组决策变量和操作参数来表示多个能量设备中的每一个。 决定变量和操作参数基于多个能量设备内的操作条件和相互关系来约束。 生成多个能量装置的两层模型,其中模型的顶层表示各种子模型的交互作用,模型的底层包括形成顶层的子模型集合,每个子模型 - 表示多个能量装置的详细操作的模型。 双层模型被优化以提供多个能量装置的操作计划或者用于多个能量装置的实时控制。
    • 10. 发明授权
    • Hybrid interior-point alternating directions algorithm for support vector machines and feature selection
    • 用于支持向量机和特征选择的混合内点交替方向算法
    • US08719194B2
    • 2014-05-06
    • US13611528
    • 2012-09-12
    • Zhiwei QinXiaocheng TangIoannis AkrotirianakisAmit Chakraborty
    • Zhiwei QinXiaocheng TangIoannis AkrotirianakisAmit Chakraborty
    • G06N99/00
    • G06N99/005
    • A method for training a classifier for selecting features in sparse data sets with high feature dimensionality includes providing a set of data items x and labels y, minimizing a functional of the data items x and associated labels y L ⁡ ( w , b , a , c , γ 1 , γ 2 ) := 1 N ⁢ ∑ i = 1 N ⁢ a i + λ 1 ⁢  c  1 + λ 2 2 ⁢  w  2 2 + γ 1 T ⁡ ( e - Y ⁡ ( Xw + be ) - a ) + γ 2 T ⁡ ( w - c ) + μ 1 2 ⁢  e - Y ⁡ ( Xw + be ) - a  2 2 + μ 2 2 ⁢  w - c  2 2 to solve for hyperplane w and offset b of a classifier by successively iteratively approximating w and b, auxiliary variables a and c, and multiplier vectors γ1 and γ2, wherein λ1, λ2, μ1, and μ2 are predetermined constants, e is a unit vector, and X and Y are respective matrix representations of the data items x and labels y; providing non-zero elements of the hyperplane vector w and corresponding components of X and Y as arguments to an interior point method solver to solve for hyperplane vector w and offset b, wherein w and b define a classifier than can associate each data item x with the correct label y.
    • 用于训练用于在具有高特征维度的稀疏数据集中选择特征的分类器的方法包括提供一组数据项x和标号y,使数据项x和相关标签y L⁡(w,b,a, c,γ1,γ2):= 1NΣi = 1 N ai +λ1c1 +λ2 2w2 2 +γ1 T⁡(e-Y⁡(Xw + be)-a)+γ2 T⁡(w-c)+μ1 2e -Y⁡(Xw + be)-a22 +μ2 2w -c2 2求解 对于分类器的超平面w和偏移量b,通过连续迭代地近似w和b,辅助变量a和c以及乘数向量γ1和γ2,其中λ1,λ2,μ1和μ2是预定常数,e是单位矢量, X和Y是数据项x和标签y的相应矩阵表示; 提供超平面矢量w的非零元素和X和Y的对应分量作为内点方法求解器的参数来求解超平面矢量w和偏移b,其中w和b定义分类器,可以将每个数据项x与 正确的标签y。