偏最小二乘相关算法在系统建模中的两类典型应用

Two Typical Applications of the Related Partial Least Square Algorithms in the Field of System Modeling

讨论了偏最小二乘回归(PLSR)的相关算法对两类典型实际系统建模的有效应用。分析了传统的偏最小二乘回归批处理算法及由此产生的一种简化算法的基本原理和技术特点。在此基础上,对原有的递推算法进行了一定程度的改进,直接采用自变量主元t的回归系数矩阵P和R来取代旧的数据信息,从而进一步简化了计算过程。针对上述两种算法的特点,分别对无人机费用模型(少样本,多变量)和切削力峰值模型(多样本,少变量)参数进行了估计计算,说明了各自算法的应用优势。

Two typical system modeling applications, based on related methods about the partial least squares regression (PLSR) are discussed under the different practical conditions. The main principle and techniques of the traditional batch method and its simplified algorithm are introduced in details. Furthermore, the paper presents a simplified recursive PLS algorithm including the advantages of both the ordinary recursive algorithm and the simplified batch algorithm, which simplifies the recursive computations by using the regression coefficient matrix P and R of the principal component t to replace the previous data directly. The two related PLSR methods are implemented successfully to estimate the parameters of two kinds of models, the life cycle cost assessment model for unmanned aerial vehicle (with less samples and more variables) and the maximal resultant cutting force model of an NC machining process (with more samples and less variables). The simulation results demonstrate that algorithms discussed in the paper are effective and practical for the relevant applications.