Online monitoring of multi-phase batch processes using phase-based multivariate statistical process control

Real time phase detection based online monitoring of batch fermentation processes

“…Hence, the problem of phase change detection is treated to be equivalent to that of detection of changes in statistical properties of the data. To be consistent with earlier work [9,12], we refer to a point where phase change is detected as a singular point (SP).…”

“…To capture such dynamic relationships, appropriately lagged data can be added to the current measurement [12]. Let the data at current time be related to data up to d samples in the past, where d is known as the lag, then the current data x k is modified as:…”

“…While searching through the parameter space, the following values for these parameters have been considered regardless of the organism: d [0, 4,8,12,16], t [5,10,15,20] min, j [4,5,6,7,8] and h [2,3,4,5,6,7,8]. We first construct the receiver operating characteristic (ROC) curve for all possible models (i.e.…”

“…Evolution of a batch fermentation process can then be conceptualized as a sequence of such phases, each with its own duration and dynamics. It is expected that batch-to-batch variability would therefore, among other things, translate to variations in switching times between the phases [12]. Hence, effective monitoring can be achieved by detecting the time of occurrence of these various phases.…”

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

“…The new index can be bounded by kernel density estimation (KDE)-based method with J th,ϕ , and then the final detection decision logic is ϕ y ≤ J th,ϕ ⇒ Quality is fault − free ϕ y > J th,ϕ ⇒ Quality is faulty (16) Regarding the method, it is worth noting: (1) it can deliver higher fault detection performances, as it avoids the qualityorthogonal part inΦ, which is the completely quality-related part in KPLS; (2) it further includes the possible qualityrelated parts inΦ, while this part was left by KPLS modelling; (3) it involves a simplified computation process compared with the method in [5]. The method involves an extra PCA model on an N × N (O(N 3 ))matrix than KPLS model, however, in [5], the method includes one extra PCA on an l × l matrix and two additional PCA models on N × N matrices.…”