The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from t...The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini- mum-area ellipse with arc length, and avoids the occurrence of ＇oscillation＇ and ＇loops＇. We compare the new method with the uni- form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.展开更多
城市轨道交通TOD区域中,各组成部分之间存在相互作用和依赖关系,导致碳排放数据之间呈现出非线性耦合特性,难以精准捕捉其内在规律,易在碳排放量化过程中引入显著误差。故研究提出基于长期能源替代规划(Long-range Energy Alternatives ...城市轨道交通TOD区域中,各组成部分之间存在相互作用和依赖关系,导致碳排放数据之间呈现出非线性耦合特性,难以精准捕捉其内在规律,易在碳排放量化过程中引入显著误差。故研究提出基于长期能源替代规划(Long-range Energy Alternatives Planning,LEAP)技术的城市轨道交通TOD区域碳排放测算方法。首先,应用LEAP技术获取城市轨道交通TOD区域的能源数据,以自下而上的系统动力学视角,有效整合能源供应、消费及转换过程中的各类数据,精准刻画能源消费与碳排放之间的非线性映射关系。同时,利用偏最小二乘(Partial least squares regression,PLS)回归与最小残差回归检测并修复数据,并采用最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)填补能源数据中的缺失值,提高能源信息数据的质量;然后,引入密度峰值聚类算法对能源信息数据展开聚类分析;最后,根据不同类型的能源信息数据计算货物运输、轨道交通以及普通机动车的能源消耗,根据计算结果获得城市轨道交通TOD区域的碳排放量。仿真结果表明:上述方法具有较高的数据修复精度与碳排放测算精度。展开更多
基金Supported by the National Research Foundation for the Doctoral Program of Higher Education of China(20110131130004)Independent Innovation Foundation of Shandong University,IIFSDU(2012TB013)Ji’nan Science and Technology Development Project(No.201202015)
文摘The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini- mum-area ellipse with arc length, and avoids the occurrence of ＇oscillation＇ and ＇loops＇. We compare the new method with the uni- form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.
文摘城市轨道交通TOD区域中,各组成部分之间存在相互作用和依赖关系,导致碳排放数据之间呈现出非线性耦合特性,难以精准捕捉其内在规律,易在碳排放量化过程中引入显著误差。故研究提出基于长期能源替代规划(Long-range Energy Alternatives Planning,LEAP)技术的城市轨道交通TOD区域碳排放测算方法。首先,应用LEAP技术获取城市轨道交通TOD区域的能源数据,以自下而上的系统动力学视角,有效整合能源供应、消费及转换过程中的各类数据,精准刻画能源消费与碳排放之间的非线性映射关系。同时,利用偏最小二乘(Partial least squares regression,PLS)回归与最小残差回归检测并修复数据,并采用最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)填补能源数据中的缺失值,提高能源信息数据的质量;然后,引入密度峰值聚类算法对能源信息数据展开聚类分析;最后,根据不同类型的能源信息数据计算货物运输、轨道交通以及普通机动车的能源消耗,根据计算结果获得城市轨道交通TOD区域的碳排放量。仿真结果表明:上述方法具有较高的数据修复精度与碳排放测算精度。
