Abstract
Synchronization of variable trajectories from batch process data is a delicate operation that can induce artifacts in the definition of multivariate statistical process control (MSPC) models for real-time monitoring of batch processes. The current paper introduces a new synchronization-free approach for online batch MSPC. This approach is based on the use of local MSPC models that cover a normal operating conditions (NOC) trajectory defined from principal component analysis (PCA) modeling of non-synchronized historical batches. The rationale behind is that, although non-synchronized NOC batches are used, an overall NOC trajectory with a consistent evolution pattern can be described, even if batch-to-batch natural delays and differences between process starting and end points exist. Afterwards, the local MSPC models are used to monitor the evolution of new batches and derive the related MSPC chart. During the real-time monitoring of a new batch, this strategy allows testing whether every new observation is following or not the NOC trajectory. For a NOC observation, an additional indication of the batch process progress is provided based on the identification of the local MSPC model that provides the lowest residuals. When an observation deviates from the NOC behavior, contribution plots based on the projection of the observation to the best local MSPC model identified in the last NOC observation are used to diagnose the variables related to the fault. This methodology is illustrated using two real examples of NIR-monitored batch processes: a fluidized bed drying process and a batch distillation of gasoline blends with ethanol.
Highlights
Industrial sectors often rely on batch processes to produce their intermediate or final products
This step was followed by k-means analysis on the overlapped individual normal operating conditions (NOC) batch trajectories to define the clusters used to build the local multivariate statistical process control (MSPC) models covering the overall NOC process trajectory
The present work introduces a new approach for online monitoring of spectroscopic-monitored batch process evolution through the design of local MSPC models covering an overall NOC batch process trajectory, defined from the principal component analysis (PCA) modeling of non-synchronized NOC batches
Summary
Industrial sectors often rely on batch processes to produce their intermediate or final products. Most data-driven modeling strategies aiming at building online MSPC charts to monitor process evolution require that data from several NOC batches, I, that have the same batch length, i.e. batch data matrices with the same numbers of rows K, and follow the same and synchronized process dynamics. The number of clusters used to set the local MSPC models will be closely related to the process progress resolution desired to study the batch evolution and will be limited by the number of available NOC observations. Once the local MSPC models and their related multivariate control charts limits are set, the online process evolution of new batches can be tracked based on the local models defined. For every new online observation, xk (a NIR spectrum in XNEW), its scores values, tk,m, are obtained for each local MSPC model using its related PCA loadings, Pm, as follows, tk,m xkPm (2). This visualization approach will be provided for the real process applications studied in this work
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