一种泛函级数建模的新方法及其应用  

New modeling method and application based on functional series

作　　者：王海涛[1] 段哲民[1] 司伟 

机构地区：[1]西北工业大学电子信息学院,西安710072 [2]陕西省电力设计院,西安710032

出　　处：《计算机工程与应用》2012年第35期11-14,142,共5页Computer Engineering and Applications

基　　金：国家电网综合计划项目(No.ZDK048-2010);西北工业大学基础研究基金(No.JC201013)

摘　　要：针对非线性动态系统较难做任意精度逼近的这一问题,提出了使用Volterra级数高阶核估算的全新估计方法。该方法在核函数理论基础上,构造特殊线性空间,将求解Volterra级数的各阶核的问题转化为求用输出观测向量在希尔伯特空间中某一子空间上的投影的问题,使原本复杂、难于计算的非线性系统的Volterra级数的逼近问题在所构建的线性空间中巧妙地以向量内积的方式解决。给出了具体计算方法。相比于其他时域或频域估计Volterra核的方法,该算法的优点在于理论体系严密、计算量不会随着阶数增高而成几何级数增加,辨识精度高,理论上能够辨识出任意阶的核,改善了现有的估计Volterra核的方法难以估计超过4阶或更高阶核的缺点,特别能够应用在对动态系统和强非线性系统的建模上。通过对电厂汽轮机轴系统的辨识和仿真,证明了该方法的有效性。Aiming at nonlinear dynamic system is more difficult to arbitrary precision approximation, it proposes a new estimation method using the Volterra series high-end nuclear estimates. This method is based on the theory of the kernel function, constructs special linear space, the solution of the Volterra series order of the nuclear problem is transformed with the output vector of observations for the sake of the projection on a subspace in the Hilbert space, difficult calculation of nonlinear systems of Volterra series in the linear space builds skillfully way to solve the vector inner product. By specific calculation method, compared with other time domain or frequency domain to estimate the Volterra kernel method, the advantage of this algorithm is tight theoretical system, the computation is not with the increased order made of an increase in geometric progression, it has high identification accuracy, in theory, it is able to identify any order kernel, improve that the existing estimate of the Volterra kernel of the method is difficult to estimate the 4 order or higher kernel, in particular, it can be used in the modeling of dynamic systems and strongly nonlinear systems. Identification and simulation of power plant steam turbine system prove the effectiveness of the method.

关 键 词：模式识别 系统辨识 VOLTERRA级数 汽轮机 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]