## 4 Case Study
### Fermentation Process for Penicillin Production  
#### 4.1.1 Process Description  
The penicillin fermentation process is a typical biochemical batch benchmark for soft sensor and fault diagnosis algorithms. The penicillin fermentation industrial process simulation platform, which can comprehensively reflect the actual process of penicillin fermentation, etc., and provides standardized biochemical reaction data, was developed by a process modeling and monitoring research group led by Professor [PERSON] at the Illinois Institute of Technology (IIT) from 1998 to 2002. This simulation platform considers the effects of control variables such as the pH value, temperature, aeration rate, agitator power, and substrate acceleration rate on bacterial and penicillin production and comprehensively includes factors such as bacterial growth, carbon dioxide concentration, penicillin production, and generation of heat at the same time. The technological process of the penicillin fermentation process is shown in Figure 4, and the detailed process description and dynamic model are referred to [45].  
Different reaction results can be obtained for different application requirements by adjusting the initial values of some process variables in the fermentation tank. In the construction of the soft sensor model in this study, penicillin concentration is used as the output variable, and 14 process variables are used as the input variables. See Table 1 for the meaning of specific variables.  
Figure 4: Flow sheet of the process.  
Based on the simulation platform, the fermentation cycle was set to 400 h, the sampling interval was 1 h, and the initial value of the substrate concentration for each process was increased or decreased by 0.1-0.2 from the default value. Eight batches of fermentation process data were counted, and five batches of process data were randomly selected as training samples (62.5% of the total data volume) for model training. Two batches of process data were used as the validation set (25% of the total data volume) for model parameter optimization and integration pruning. Two batches of process data were used as the validation samples (25% of the total data volume) for model parameter optimization and integration pruning, and one batch of process data was used as the test set samples (12.5% of the total data volume) for soft measurement model performance evaluation.  
The model parameters affect the prediction performance of the model. In this study, the parameters in the base model were optimized adaptively using the GWO algorithm with the objective of minimizing the RMSE criteria, and the specific content and search range of the parameter optimization included the following:  
(1) The number of supervised latent variables \(n_{l}\) in EPLS and VSEPLS, where \(n_{l}=[1,2,\cdots m]\), and \(m\) represents the characteristic dimension of the input variable.  
(2) Three kernel function parameters in LV-VSEPLS and MLV-VSEPLS, where \(\sigma\in[0.5,0.7,0.9,1,2]\) for the Gaussian kernel function, \(d\in[2,3,4,5,6]\) for polynomial kernel functions, and \(\delta=[0.1,0.3,0.5,0.7,0.9,1,2,3]\) for the Cauchy kernel function.  
(3) In the MOGWO algorithm, the number of populations is set to 200, the number of iterations is 100, and the one with the best performance among the Pareto optimal solutions is selected as the final screening combination of the base model.