分布式反应器模型的小波逼近辨识方法

Identification of wavelet approximation distributed reactor model

小波变换作为一种有效的函数逼近工具,为其应用于分布参数系统的逼近提供了理论根据。以一大类复杂化学反应器分布参数模型为研究对象,采用Haar正交小波函数逼近非线性分布参数模型,然后采用多变量最小二乘递推辨识算法求解集总化的多变量状态空间模型参数。不仅考虑实际过程中状态量、控制量或变参数的乘积非线性特征,而且将反应过程的传质系数当作空间变参数进行辨识,为此,提出了一种便于逼近计算的新的Haar小波运算矩阵——平方积分运算矩阵,并得到了计算通式。通过仿真实例说明了通过提高Haar小波逼近阶数可极大地改善辨识效果,同时运用变尺度分段逼近方法,以较低的阶数较好地逼近平稳过程,说明了该方法的有效性。

Wavelet transform, as an efficient function approximation tool, proves its feasibility while applied to distributed parameter systems. This work was engaged in a large category of distributed parameter models of complicated chemical reactors. Haar ortbogonal wavelet was applied to the approximate nonlinear distributed parameter model, followed by multivariable recursive least square algorithm to solve the unknown parameters of lumped state space model. This work not only involved that nonlinear feature as a result of the product of state variables, control variables and varying parameters in the actual process, but also considered the mass transfer coefficients as variable spatial parameters to identify. Therefore, a new Haar wavelet operational matrix called square integral operational matrix was proposed as well as its calculation method. It is proved by simulation that the identification effect can be greatly improved by increasing the Haar wavelet expansion rank. And varying-scale wavelet expansion can preferably approximate the process with a lower rank. Thus, prove the efficiency of that method.