(703c) Quality-Relevant Fault Detection and Identification for Batch Processes Based on Stochastic Programming

Batch processes play an important role in modern industry, producing high-value products such as food, plastics, pharmaceuticals, and semiconductors [1]. Since the products of batch processes often require extremely high quality, it is necessary to develop quality-relevant monitoring methods for process safety and quality enhancement [2]. Over the past years, various methods have been proposed to solve the problem using multivariate statistical monitoring methods, such as multiway partial least squares [3] and other output related methods [4-6]. However, most of these methods are based on the assumption that batch-to-batch variations are not obvious, which means that quality-relevant variables in each historical batch are identical and follow a similar trajectory. With the increased complexity and integrated nature of modern industrial processes, the quality variables of different batches may behave rather differently, primarily due to the stochastic nature of process parameters and other process uncertainties. Based on existing methods, the historical quality-relevant variables are calculated directly on the basis of historical process variables and mechanistic models with fixed coefficients. Thus, the quality-relevant data collected during actual operation may not quite agree with the historical monitoring model. When faced with the problem of online batch process monitoring, the stochastic features of different batch runs need to be taken into consideration.

To address this challenge, we propose a batch process monitoring method based on stochastic programming, which can make the monitoring model more robust and reliable. Based on historical process data, quality-relevant variables are generated with stochastic model coefficients and other model uncertainties, such as varying set-points and sensor noise. Then the stochastic programming model is introduced to classify historical batches into different scenarios by solving a constrained optimization problem [7,8]. According to this model, all batches are considered normal, and similar batches are integrated into the same scenario. A discrete probability density function is obtained to reveal the probability of each scenario. Then a mean trajectory is extracted from the quality-relevant variables of different scenarios and the residuals of each scenario can be obtained at the same time. For monitoring purposes, the control limit of the historical data is developed by the stochastic residuals. Once the residuals of online data are obtained, it can be compared with the control limit to detect quality-relevant faults. Following detection, this method can achieve online model updating by integrating a new normal batch into historical scenarios. Meanwhile, the information of faulty batches is extracted as well, including the abnormal residuals and the exact detection time to help fault classification and identification. The proposed approach is illustrated using a simulated penicillin fed-batch fermentation process.

 References:

[1] F. Shen and Z. Song, "Multivariate trajectory-based local monitoring method for multiphase batch processes, Ind. Eng. Chem. Res., 54, 1313-1325, 2015.

[2] W. Sun, Y. Meng, A. Palazoglu, J. Zhao, H. Zhang and J. Zhang "A method for multiphase batch process monitoring based on auto phase identification," J. Process Control, 21, 627-638, 2011.

[3] P. Nomikos and J.F. MacGregor, "Multi-way partial least squares in monitoring batch processes," Chemom. Intell. Lab. Syst., 30, 97−108, 1995.

[4] Z. Ge, Z. Song and F. Gao, "Review of recent research on data-based process monitoring," Ind. Eng. Chem. Res., 52, 3543-3562, 2013.

[5] N. Lu and F. Gao, "Stage-based process analysis and quality prediction for batch processes," Ind. Eng. Chem. Res., 44, 3547-3555, 2005.

[6] C. Zhao, F. Wang, Z. Mao, N. Lu, and M. Jia, "Improved batch process monitoring and quality prediction based on multiphase statistical analysis,'' Ind. Eng. Chem. Res., 47, 835-849, 2008.

[7] J.R. Birge and F. Louveaux. Introduction to stochastic programming. Springer-Verlag, New York, 2011.

[8] C. Liu, Y. Fan and F. Ordonez, " A two-stage stochastic programming model for transportation network protection," Comput. Oper. Res., 36, 1582-1590,2009.