Abstract: 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.

Key words: pattern recognition, system identification, Volterra series, turbine

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。

关键词: 模式识别, 系统辨识, Volterra级数, 汽轮机