基于KPCA残差方向梯度的故障检测方法及应用

针对核主元分析(KPCA)在应用过程中非线性映射不存在原像、故障变量无法辨识、工程应用困难等问题,提出了一种改进的KPCA残差方向梯度故障检测方法。利用主元统计量和残差统计量的偏微分之间存在着相关性这一性质,对与主元统计量相关的格拉姆矩阵偏微分中间计算过程进行优化,提出一种新的KPCA残差方向梯度算法,在此基础上结合统计量形成系统故障检测的新方法。非线性系统仿真表明,改进的KPCA残差方向梯度法不仅具有较优的故障变量辨识能力,还极大地减小了计算量,缩短了计算时间。大型热力系统的应用进一步表明,无论对于单故障和多故障的情况,方法均具有较好的故障检测能力,并且不存在残差污染,易于工程实现。

Fault detection method based on KPCA residual direction gradient and its application

Aiming at the fact that there is no preimage in nonlinear mapping and fault variable cannot be identified which result in that it is difficult for engineering application of kernel principle analysis, an improved KPCA residual direction gradient algorithm is proposed to overcome the above drawbacks in this paper. By use of the correlation between the partial differential of principle statistic and residual statistic, the gram matrix partial differential intermediate computation process is simplified and the KPCA residual direction gradient index is obtained, combined with residual statistic a new fault detection method is proposed. Nonlinear system simulation computation shows that improved KPCA residual direction gradient method has excellent capability of fault variable identification while computational complexity is greatly decreased and the calculation time is shortened. Furthermore, large scale thermodynamic system application shows that the proposed method has better capability in fault detection whenever in case of single fault or multiple faults and there is no residual contamination while it is very suitable for engineering realization.