Contribution rate plot for nonlinear quality-related fault diagnosis with application to the hot strip mill process

A Quality-Based Nonlinear Fault Diagnosis Framework Focusing on Industrial Multimode Batch Processes

“…Since, this part may include theỹ related part [5], a further PCA decomposition on it is needed. To this end, the PCA model is developed below:…”

“…Let a single process measurement be φ ∈ Rm, which is an abbreviation of φ(z), by the convenience of kernel trick, K = ΦΦ T ∈ R N ×N and k = Φφ ∈ R N are satisfied. Actually, they are the normalized value based on the raw mapped data in a way [5]:…”

“…Of them, contribution plot method was broadly used, as it is free of a prior process knowledge [29]. Considering KPLS model with the kernel function involved, a contribution rate plot approach was proposed by Peng et al [5] It was also proved that this approach can be promoted to any kernel methods [5].…”

“…Recently, such kind of models have been extended to batch processes for QFDD [23], [24], [25]. However, KPLS has drawbacks such as low fault detection rate (FDR) and high false alarm rate (FAR) [5]. Thus, some improvements should be derived based on KPLS model to let it more efficient.…”

“…Another handicap for ensuring the product quality is the strong nonlinearity in HSMR, in this case the traditional linear theory will not be sensible. In recent years, to solve such kinds of problem, quality-related fault detection and diagnosis (QFDD) methods have been raised and proved to be useful for quality control [1], [5], [6], [7], [8].…”