一种用于数据校正的最小二乘与准最小二乘组合方法

Weighted least squares and quasi-weighted least squares combined method for data rectification

过程系统的控制与优化要求可靠的过程数据。通过测量得到的过程数据含有随机误差和过失误差,采用数据校正技术可有效地减小过程测量数据的误差,从而提高过程控制与优化的准确性。针对传统基于最小二乘的数据校正方法:和基于准最小二乘的鲁棒数据校正方法:,分析了它们的优缺点,并提出了一种最小二乘与准最小二乘组合方法:。该方法:先采用准最小二乘估计器检测过失误差并剔除,然后再采用最小二乘估计器进行数据校正,可以综合前两种方法:各自的优点,使得数据校正结果:更加准确。将提出最小二乘与准最小二乘组合方法:应用于线性与非线性系统的数据校正中,通过校正结果:的比较说明此方法:的具有较好的过失误差检测能力和较准确的数据校正结果:。最后将此方法:应用于实际过程系统空气分离流程的数据校正中,结果:说明了此方法:的有效性。

Reliable process data are required for process control and optimization. As a result of random and gross errors existing in the measured process data, data rectification is needed to minimize the measurement errors. Therefore, the results of process control and optimization are more accurate. The advantages and disadvantages of methods for data rectification based on weighted least squares and quasi-weighted least squares are analyzed. An efficient method, weighted least squares and quasi-weighted least squares combined method, is proposed in this paper. This method uses quasi-weighted least squares estimator for gross error detection, and then weighted least squares estimator is used for data reconciliation. The proposed method, considering the advantages of previous two methods, is used for both linear and nonlinear systems. Results of comparisons show that the performance of gross error detection is improved and the results of data reconciliation are more accurate by using the proposed method. Finally, the proposed method is used for air separation process system. The effectiveness of the proposed method is demonstrated by the results of numerical simulations .