Fault detection and diagnosis strategy based on a weighted and combined index in the residual subspace associated with PCA

Process monitoring and diagnosis are crucial for efficient and optimal operation of a chemical plant. Most multivariate statistical process monitoring strategies, such as principal component analysis, kernel principal component analysis, and dynamic principal component analysis, take advantage of the squared prediction error statistic to monitor the state of samples in a residual subspace (RS). Squared prediction error is defined as the square of the 2‐norm of a residual vector, and it is calculated as the squared norm of the residual components. When the distributions of variables in an RS are quite different from one another, the detection ability of squared prediction error visibly declines. To accurately monitor the faults occurring in the RS, a new fault detection index based on a weighted combination of Hotelling's T2 and squared Euclidean distance is developed in this paper. Principal component analysis is first introduced for dividing the original input space into a principal component subspace and an RS. Next, a weighted and combined index is implemented to monitor the variability of samples in the RS. In addition, a corresponding fault diagnosis strategy based on the contribution plot is also developed in this paper. The proposed method is tested on a numerical example and the Tennessee Eastman process. Simulation results show that the new index is effective in both fault detection and diagnosis. Most multivariate statistical process monitoring strategies, such as principal component analysis (PCA), take advantage of the squared prediction error statistic (SPE) to monitor the state of samples in a residual subspace. When the distributions of variables in a residual subspace are quite different from one another, the detection ability of SPE visibly declines. To accurately monitor the faults occurring in the residual subspace, a new fault detection index based on a weighted combination of T2 and squared Euclidean distance is developed in this paper.