CAJ | 학술논문

为解决时间序列多步预测的高效率、高精度问题，提出一种基于Volterra级数的多重回归仿射投影自适应算法。应用虚假最临近点法算法选择最优嵌入维数，优化模型初始参数。以系统Volterra 核向量增量的模与某约束总和为损失函数，按照最陡下降原理导出各阶Volterra核更新公式，再利用矩阵求逆引理递推求取各阶Volterra子系统自相关逆矩阵导出算法，从而实现了对多输入多输出数据样本的建模，采用该模型对Henon映射产生的时间序列进行多步预测实验，结果表明可以对该时间序列进行准确建模和预测，证明了所提模型的有效性。
위해결시간서렬다보예측적고효솔、고정도문제，제출일충기우Volterra급수적다중회귀방사투영자괄응산법。응용허가최림근점법산법선택최우감입유수，우화모형초시삼수。이계통Volterra 핵향량증량적모여모약속총화위손실함수，안조최두하강원리도출각계Volterra핵경신공식，재이용구진구역인리체추구취각계Volterra자계통자상관역구진도출산법，종이실현료대다수입다수출수거양본적건모，채용해모형대Henon영사산생적시간서렬진행다보예측실험，결과표명가이대해시간서렬진행준학건모화예측，증명료소제모형적유효성。
To improve the efficiency and accuracy of multi-step predicting of the time series,a Volterra series model based on the multi-recursive affine projection (AP)algorithm is proposed.The optimal embedding dimension is identified by false nearest neighbors to optimize the initial parameters of the model.Taking the minimum norm of the Volterra kernel vector increments and certain constraints as the overall cost function,by the steepest descent principle,the adaptive updating formula of the Volterra kernel vector of each order is derived.And the matrix inverse lemma is applied to recursively estimate the inverse of the autocorrelation matrix of Volterra subsystems of each order,thus the algorithm is derived.To illustrate the performance of the method,simulations on Henon time series prediction are performed.The results show that the Henon time series are accurately predicted,which demonstrates the effectiveness of the proposed method.