Abstract
To implement the quality-relevant monitoring scheme for batch processes with multiple output modes, this paper presents a novel methodology based on stochastic programming. Bringing together tools from stochastic programming and ensemble learning, the developed methodology focuses on the robust monitoring of process quality-relevant variables by taking the stochastic nature of batch process parameters explicitly into consideration. To handle the problem of missing data and lack of historical batch data, a bagging approach is introduced to generate individual quality-relevant sub-datasets, which are used to construct the corresponding monitoring sub-models. For each model, stochastic programming is used to construct an optimal quality trajectory, which is regarded as the reference for online quality monitoring. Then, for each sub-model, a corresponding control limit is obtained by computing historical residuals between the actual output and the optimal trajectory. For online monitoring, the current sample is examined by all sub-models, and whether the monitoring statistic exceeds the control limits is recorded for further analysis. The final step is ensemble learning via Bayesian fusion strategy, which is under the probabilistic framework. The implementation and effectiveness of the developed methodology are demonstrated through two case studies, including a numerical example, and a simulated fed-batch penicillin fermentation process.
Highlights
With the combination of stochastic programming and an ensemble learning strategy, an integrated individual monitoring framework can solve some of the important issues pertaining to complicated batch process monitoring
Baggingfor forbatch batch processes processes with and According to the bagging strategy with the original process dataset X ∈ R I × J × K, quality trajectories are established as Y ∈ R I ×K × N, where I represents batch numbers, J represents the number of process variables, K represents sample numbers in one batch and N is the number of output mode
The main purpose of the methodology developed in this work is to achieve quality-relevant monitoring for batch processes based on stochastic programming and ensemble learning strategy
Summary
Batch processes are widely used in modern industrial applications due to the growing requirements of producing high-value products, such as food, plastics, pharmaceuticals, and biological and semiconductor materials [1,2,3,4]. Methods, such as multiway principal component analysis (MPCA) and multiway partial least squares (MPLS) [8,9] These traditional data-based methods are developed for monitoring purposes based on historical batch data [10,11]. The lack of historical data, for example, is an important problem that is encountered when data-based modeling is implemented. This problem is commonly the result of the missing data problem, the insufficiency of historical batches, and the lack of quality variables [14,15]. A feasible compromise is to use process data together with only partial process knowledge to construct a quality-relevant monitoring model [22,23]
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