一种改进的子空间辨识方法在热工过程中的应用

A Modified Subspace Identification Method and Its Application in Thermal Process

针对现有MOESP(multiple-input multiple-output output-error state space model identification)和N4SID(numerical algorithm for subspace state space systemidentification)算法在计算状态空间模型系统矩阵(A、B、C、D)时的不足,提出1种改进的子空间辨识方法。该方法利用MOESP算法可以根据系统观测矩阵直接计算出系统矩阵A和输出矩阵C的优点,先计算矩阵A和C,然后采用N4SID算法计算输入矩阵B和前馈矩阵D。该方法既能够避免MOESP算法在计算矩阵B和D时需要构建大矩阵的缺点,又能避免N4SID算法在计算矩阵A和C时需要求解线性最小二乘的问题,降低了算法的复杂性。将该算法应用于某天然气电站和Alstom气化炉模型的辨识中,通过考核算法的CPU运算时间、CPU浮点数运算次数(floating-pointoperations,FLOPS)和相对误差等指标,将该算法与原有MOESP和N4SID算法进行了比较。计算结果表明,改进的子空间辨识算法能够在保证较好辨识精度的前提下,提高原有算法的计算效率,特别是在大容量数据样本条件下,能够有效降低CPU运算时间和FLOPS。

A modified subspace identification method（SIM） was proposed according to the drawbacks of MOESP（multiple-input multiple-output output-error state space model identification） and N4SID（numerical algorithm for subspace state space system identification） in capturing system matrices（A,B,C,and D） of a state-space model.Taking the advantage that the matrices A and C could be directly calculated from the observation matrix,the proposed method calculated the matrices A and C earlier using MOESP,and then the matrices B and D were calculated by N4SID later.Accordingly,the method not only need not to construct large matrices needed in MOESP for calculating B and D,but also can reduce the computational complexity,due to avoidance of solving the linear least square problem needed in N4SID for calculating A and C.Then,the method was applied to the identification of a gas fired power plant and Alstom gasifier model.Some performance criteria such as CPU runtime,floating-point operations（FLOPS） and model relative error of the method were introduced to the comparison between the modified SIM,MOESP and N4SID.The simulation results show that the modified SIM could both promise the identification precision and improve the calculation efficiency.Especially under large data condition,the FLOPS and CPU runtime could be effectively reduced.