Methods for a longitudinal quantitative outcome with a multivariate Gaussian distribution multi-dimensionally censored by therapeutic intervention

2013 ◽  
Vol 33 (8) ◽  
pp. 1288-1306 ◽  
Author(s):  
Wanjie Sun ◽  
Michael D. Larsen ◽  
John M. Lachin
Keyword(s):  
Gaussian Distribution ◽  
Therapeutic Intervention ◽  
Multivariate Gaussian Distribution ◽  
Multivariate Gaussian

Process Monitoring and Fault Diagnosis of Penicillin Fermentation Based on Improved MICA

2012 ◽  
Vol 591-593 ◽  
pp. 1783-1788 ◽  
Author(s):  
Zhi Yang Jia ◽  
Pu Wang ◽  
Xue Jin Gao
Keyword(s):  
Fault Diagnosis ◽  
Process Monitoring ◽  
Gaussian Distribution ◽  
Component Analysis ◽  
Higher Order ◽  
Process Variables ◽  
Multivariate Gaussian Distribution ◽  
Independent Components ◽  
Multivariate Gaussian ◽  
Penicillin Fermentation

In the process monitoring and fault diagnosis of batch processes, traditional principal component analysis (PCA) and least-squares (PLS), are assuming that the process variables are multivariate Gaussian distribution. But in the practical industrial process, the data observed of process variables do not necessarily be the multivariate Gaussian distribution. Independent component analysis (ICA), as a higher-order statistical method, is more suitable for dynamic systems. Observational data are decomposed into a linear combination of the independent components under statistical significance. The higher order statistics will be extracted and the mixed signals are decomposed into independent non-Gaussian components. Traditional method of ICA has to predefine the number of independent components. This paper proposed an improved MICA method of realizing the automatically choosing the independent components through setting the threshold value of the negentropy. The method can solve the problem of predefining the number of independent components in traditional methods and meanwhile it reduces the complexity of the monitoring model. The proposed method is used to do the process monitoring and fault diagnosis of penicillin fermentation and the results verify the feasibility and effectiveness of the method.

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