Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivari...Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.展开更多
Algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a kind generalization of the classical algebraic variety. Th...Algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a kind generalization of the classical algebraic variety. This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.展开更多
Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and...Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.展开更多
目的比较不同算法对桂枝茯苓胶囊内容物吸湿性预测模型性能的影响,确定最优建模算法。方法以54个物理性质参数为输入,胶囊内容物吸湿性为输出,对比偏最小二乘算法(partial least squares,PLS)、决策树算法(classification and regressio...目的比较不同算法对桂枝茯苓胶囊内容物吸湿性预测模型性能的影响,确定最优建模算法。方法以54个物理性质参数为输入,胶囊内容物吸湿性为输出,对比偏最小二乘算法(partial least squares,PLS)、决策树算法(classification and regression tree,CART)、多元自适应回归样条算法(multivariate adaptive regression splines,MARS)和广义路径追踪算法(generalized path seeker,GPS)对建立吸湿性预测模型性能的影响。结果MARS算法建立的预测模型性能最佳,预测能力最强,模型的校正集决定系数(R2c)为0.843,预测集决定系数(R2p)为0.808,校正集均方根误差(root mean square error of calibration,RMSEC)为0.391,预测集均方根误差(root mean square error of prediction,RMSEP)为0.472,平均相对预测误差为2.69%,小于5%。结论MARS算法建立的吸湿性预测模型更适合桂枝茯苓胶囊的生产应用,该算法可嵌入在线控制系统,为生产过程的质量控制智能化提供技术支持。展开更多
基金Supported by the National Natural Science Foundation of China （Grant Nos. 10271022 and 60373093）.
文摘Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.
基金Supported by National Natural Science Foundation of China (Grant Nos. U0935004, 11071031 and 10801024)Fundamental Research Funds for the Central Universities (Grant Nos. DUT10ZD112, DUT11LK34)National Engineering Research Center of Digital Life, Guangzhou 510006, China
文摘Algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a kind generalization of the classical algebraic variety. This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
文摘Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.
文摘目的比较不同算法对桂枝茯苓胶囊内容物吸湿性预测模型性能的影响,确定最优建模算法。方法以54个物理性质参数为输入,胶囊内容物吸湿性为输出,对比偏最小二乘算法(partial least squares,PLS)、决策树算法(classification and regression tree,CART)、多元自适应回归样条算法(multivariate adaptive regression splines,MARS)和广义路径追踪算法(generalized path seeker,GPS)对建立吸湿性预测模型性能的影响。结果MARS算法建立的预测模型性能最佳,预测能力最强,模型的校正集决定系数(R2c)为0.843,预测集决定系数(R2p)为0.808,校正集均方根误差(root mean square error of calibration,RMSEC)为0.391,预测集均方根误差(root mean square error of prediction,RMSEP)为0.472,平均相对预测误差为2.69%,小于5%。结论MARS算法建立的吸湿性预测模型更适合桂枝茯苓胶囊的生产应用,该算法可嵌入在线控制系统,为生产过程的质量控制智能化提供技术支持。
