基于主元独立性分析与混合核RVM的复杂过程区间预测方法研究及应用

近年来，随着化工过程日趋复杂，对过程监控及关键变量预测提出了更高的要求。传统意义上的点预测已不能满足化工过程上的实际需求，且点预测无法描述过程上的不确定性问题，因此不能很好地把握预测变量的趋势。由此，提出了一种基于主元独立性分析（principal component independent analysis，PCIA）与混合核相关向量机（RVM）的区间预测方法。首先，结合核主元成分分析（KPCA）和独立元分析（ICA）对复杂过程原始变量进行主元成分提取和独立性分析，形成独立主元；其次，将高斯核函数与多项式核函数相结合形成混合核，与RVM结合对得到的独立主元进行回归建模预测，并运用T分布对预测值进行区间估计；然后，构造区间评价综合函数对区间估计结果进行优劣分析，在分析预测区间覆盖率（PICP）及预测区间宽度（NMPIW）的基础上，引入累积偏差（AD）提高区间评判的合理性。最后，将所提方法应用到TE仿真过程进行区间预测分析，仿真结果表明，提出的区间预测方法对实际生产过程具有较高的预测精度和区间估计质量，可以有效地预测关键变量的趋势。

Research and application of interval prediction method for complex processes based on principal component independent analysis and mixed kernel RVM

In recent years, higher requirements have been put forward to process monitoring and key variable prediction with increasing complexity of chemical processes. Traditional point predictions do not meet these actual needs nor describe uncertainty concern, so that they could not predict variable trending well. An interval prediction method was proposed from principal component independent analysis and mixed kernel RVM. First, kernel principal component analysis (KPCA) and independent element analysis (ICA) were combined to extract principal components from original variables in complex process and to form independent principal components by independent analysis. Second, mixed kernel from Gauss and polynomial kernel functions and RVM were combined to generate a regression prediction model for the independent principal components, and T distribution was used to make interval estimation on predicted values of the model. Third, comprehensive interval evaluation function was constructed to analyze quality of the interval estimation results. Based on prediction interval coverage probability (PICP) and normal mean prediction interval width (NMPIW), accumulative deviation (AD) was introduced to improve rationality of the interval evaluation. The interval prediction analysis on TE simulation process showed that the proposed interval prediction method had better prediction accuracy and interval estimation quality, which could effectively predict trending of key variables in actual production process.