Fault detection with improved principal component pursuit method

• The traditional low rank representation (LRR) idea is introduced into the PCP method to get an improved PCP (IPCP) method.
• A low-rank coefficient matrix is constructed, and it represents explicit relationships between the variables.
• The obtained coefficient matrix is potentially useful to derive a powerful fault detection statistic.
• The power of the proposed method is evaluated in numerical simulation, the TE process and implemented in blast furnace.

In modern industries, principal component analysis (PCA) is one of the most popular data-driven methods. Since the directions of loading vectors can be severely affected by samples distribution, PCA is known for its sensitivity to outliers. In this paper, a robust principal component analysis method, improved principal component pursuit (IPCP), is proposed. Based on this IPCP method, a process model and an online monitoring statistic is developed. The traditional low rank representation (LRR) idea is introduced into PCP method. By applying this IPCP method, a low-rank coefficient matrix is constructed, and it represents explicit relationships between the variables as well as contains other useful information of the processes. Moreover, the obtained coefficient matrix is potentially useful to derive a powerful fault detection statistic. In order to test and evaluate the effectiveness of coefficient matrix constructed by IPCP and the power of proposed monitoring statistic, all algorithms are first tested in numerical simulation. Then they are illustrated in the TE process, which simulates the practical field condition. Finally the proposed methods are implemented in a blast furnace process.