Control-loop diagnosis using continuous evidence through kernel density estimation

• Proposed kernel density estimation for control loop monitoring.
• Developed control loop diagnosis with continuous probability density function.
• Proved performance limit of discrete monitors in diagnosis.

While most previous work in the subject of Bayesian Fault diagnosis and control loop diagnosis use discretized evidence for performing diagnosis (an example of evidence being a monitor reading), discretizing continuous evidence can result in information loss. This paper proposes the use of kernel density estimation, a non-parametric technique for estimating the density functions of continuous random variables. Kernel density estimation requires the selection of a bandwidth parameter, used to specify the degree of smoothing, and a number of bandwidth selection techniques (optimal Gaussian, sample-point adaptive, and smoothed cross-validation) are discussed and compared. Because kernel density estimation is known to have reduced performance in high dimensions, this paper also discusses a number of existing preprocessing methods that can be used to reduce the dimensionality (grouping according to dependence, and independent component analysis). Bandwidth selection and dimensionality reduction techniques are tested on a simulation and an industrial process.