非线性多项式模型结构与参数一体化辨识

针对非线性系统领域具有更广泛意义的线参数多项式组合模型，提出一种非线性多项式模型结构辨识和参数辨识一体化算法。该算法将结构辨识中基于贡献项的择优过程与基于冗余项的劣汰过程结合。在择优过程中，根据输出向量投影残差下降的最大化，采用基于输出向量残差化的递归改进Gram-Schmidt（RMGS）算法，在向量空间的全集中择优，并允许部分冗余非模型项选入。在劣汰过程中，为平等对待正交化向量的贡献，采用基于改进正交化次序的模型结构劣汰策略，在优选集合里逐个删除对实际输出贡献相对较小的结构项，以系统完备性指标为约束，确认结构与参数。2类典型非线性多项式模型辨识仿真算例对比验证了算法的有效性。

Nonlinear polynomial model's structure and parameter integration identification

An integration algorithm of nonlinear polynomial model structure identification and parameter identification was proposed for the linear parametric polynomial assembled model,which had wider signifi-cance in the field of nonlinear systems.The algorithm combined optimal-selecting process based on contribu-tion items with poor-eliminating process based on redundant items in structure identification.In the optimal-se-lecting process,the recursive modified Gram-Schmidt (RMGS)algorithm based on output vector residual was used to select the better terms in the vector space,and some redundant non-model terms were allowed to be selected,according to the maximizing drop of the output vector projection residual.In the poor-eliminating process,the algorithm adopted the model structure poor-eliminating strategy based on modified orthogonal se-quence to deal with the contribution of the orthogonal vector equally.The structure items with small contribu-tion to the actual output were deleted from the optimal set.The structure and parameters were determined by the system completeness index.Two examples of typical nonlinear polynomial model identification simulation demonstrate the effectiveness of the algorithm.