RKRLS及在混炼胶质量建模与预报中的应用研究

对递推最小二乘(RLS)进行了非线性的核(kernel)变换,并采用正则化技术改写了目标范函,提出了一种正则核变换递推最小二乘(regularized kernel,RLS)算法.获得了RKRLS模型的系数和误差表达式,分析了算法的推广能力并证明了KeYnel RLS算法为其特例,进而导出了RKRLS算法在限定、增长和缩减记忆三种不同模式下的递推公式均无需进行求逆计算.RKRLS算法具有三个特性:小样本、可控的推广能力和速度快,因而非常适合于工业应用场合.通过对橡胶混炼质量的门尼指标进行建模和预测分析表明,本算法具有较好的跟踪预测性能.

RKRLS and its application to modeling and prediction of rubber compound quality

The regularized kernel recursive least square (RKRLS) algorithm proposed here applies "Kenel Trick" to recursive least square (RLS) and adopts a regularized method to perfect the target function. The coefficient and error formulas of RKRLS model were obtained and the generalization ability was analyzed. Kernel RLS was proved to be a special case of RKRLS. Furthermore, three different recursive algorithms of RKRLS were deduced involving the restricted, increased and decreased modes, which all dispense with the need for calculating the matrix inversion. It was shown RKRLS has three properties: small samples, rapidity and controllable generalization ability, which makes it very suitable for real industry modeling issue. The industrial experiment on quality data modeling and prediction for rubber compound verified the obtained results and advantages of RKRLS algorithm.