Root cause diagnosis of plant-wide oscillations using Granger causality

Introduction

Oscillation

• definition：periodic phenomena with well defined am- plitude and frequency
• cause：Oscillating control loops are very common in industrial processes, which could be due to aggressive controller tuning, valve stiction, external distur- bances, etc.
• result：This kind of plant-wide oscillation will cause poor control performance, low product quality and excessive energy consumption. It is difficult for process engineers to know where original source of the plant-wide oscillation is and do further maintenance or adjustment.

method

1. Thornhill proposed a non-linearity index along with process understanding to find the root cause due to valve stiction.¹
2. Choudhury employ changes in controller gain to distinguish an internally generated oscillation from an external oscillatory disturbance.²
3. Xia proposed multi-resolution spectral ICA to detect and isolate the sources of multiple oscillations, a significance index is utilized to indicate possible root cause.³
4. Jiang incorporate process knowledge into a graph theoretical approach to help diagnosis of root cause. ⁴
5. Bauer proposed a data-driven method to find the propagation direction of disturbance using the idea of transfer entropy. ⁵

main idea

• using a latent variable method with Granger causality both in time-domain and frequency domain to find the root cause of plant-wide oscillations.
• normal operation without any plant interruption

method and implementation

• Time-domain Granger Causality
• Spectral Granger Causality⁶
• conclusion:It is easy to find the plant-wide oscillation frequency through spectrum plot of time-series data. This is will define a frequency range which we most cared about. Then, we could choose a subset of variables which are candi- date root cause, and perform pair-wise spectral Granger causality. If some variable has strong causal effect on other loops and receive negligible contribution from others, then we could infer it to be the root cause of the whole plant oscillation.

Feature Selection

PCA: Each PC(principle component) can be decomposed into a linear combination of a set of original variable. With dimension reduced, we will get several principal components (PC) to represent the raw data sets. Some PCs will carry the plant-wide oscillation pattern and we choose those variables which make strong contribution to those oscillating PCs as features.

criteria: calculate the OSI value:$$\textbf{OSI}_i=\sum_{j \in oscpc} \lambda_j P_{ij}^2$$ $$$\lambda_j$$$ is the eigenvalue of corresponding PC which shows whole plant oscillation.Based on empirical expe- rience, variables with OSI index larger than 1/3 of the max(OSI) are selected to be features and will be included in the causality regression model to do further analysis.