Research on Soft-Sensing Method Based on Adam-FCNN Inversion in Pichia pastoris Fermentation
Abstract
1. Introduction
2. Methods
2.1. Non-Deterministic Mechanism Model of the Fermentation Process
2.1.1. Volume Change Equation
2.1.2. Cell Growth Kinetics Equation
2.1.3. Substrate Consumption Equation
2.1.4. Enzyme Production Dynamics
2.1.5. Dissolved Oxygen Dynamics
2.1.6. pH Dynamic
2.1.7. “Grey-Box” Dynamic Model
2.2. Reversibility Analysis
- Solve the inverse model of the virtual subsystem;
- Combine the model with the virtual subsystem to form a complete system that works as a dynamic compensator;
- Reconstruct the inputs of the virtual sensor based on the outputs of this complete system.
2.3. Improved FCNN
3. Adam-FCNN Inversion-Based Soft-Sensing
3.1. Data Collection
- Microbial Cultivation: The GS115 strain was cultured on YPD agar plates at 30 °C for 48 h. A single colony was inoculated into BMGY liquid medium and cultivated at 30 °C and 250 rpm for 24 h. The culture was sequentially transferred to a 5 L seed bioreactor, followed by a 50 L secondary seed bioreactor (inoculation volume: 5–10%). When the cell density in the secondary bioreactor reached OD600 = 120 ± 15, the culture was transferred to the main fermentation tank.
- Sterilization: The air pipeline was sterilized at 130 °C for 40 min across three cycles. The bioreactor was sterilized with saturated steam at 0.15 MPa for 30 min. After cooling, sterilized culture medium was introduced into the tank.
- Data Collection and Sample Processing: Auxiliary variables (dissolved oxygen Do, fermentation broth volume, pH, ammonia flow rate, methanol flow rate, antifoaming agent flow rate, and phosphate flow rate) were recorded every 4 h. Meanwhile, methanol consumption was documented, 5 mL fermentation samples were centrifuged (8000 rpm, 10 min), and Pichia pastoris concentration was measured offline via the wet weight method. Supernatants were filtered through 0.22 μm membranes and analyzed for inulinase concentration using HPLC (Agilent 1260, Santa Clara, CN, USA) with a detection limit of 0.01 g/L.
- Batch Cultivation Phase: Pichia pastoris is cultured in mineral medium under batch conditions to accumulate biomass.
- Glycerol Fed-Batch Accumulation Phase: A glycerol-supplemented feeding medium is gradually added to further increase Pichia pastoris concentration, preparing for the subsequent high-density induction phase.
- Methanol Induction Phase: A methanol-supplemented feeding medium is slowly introduced while maintaining the methanol concentration at about 1%. During this phase, Pichia pastoris begins synthesizing inulinase.
3.2. Model Training and Online Correction
3.3. Adam-FCNN Inversion Soft-Sensing Model
- (1)
- If , the input data are processed using a moving average filter. Specifically, the input data over a defined period are averaged as
- (2)
- If , the current input is temporarily set to , followed by reprocessing using the moving average algorithm to mitigate abrupt fluctuations.
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Environmental Parameter | Unit | Measuring Method |
---|---|---|
Agitation Speed | rpm | Rotational Speed Sensor |
Fermentation Temperature | °C | Temperature Sensor |
Inlet Airflow Rate | L/min | Flowmeter |
Dissolved Oxygen Do | % | Dissolved Oxygen Analyzer |
Fermentation Liquid Volume | L | Differential Pressure Sensor |
Ammonia Water Flow Rate | L/min | Flow Velocity Sensor |
Methanol Flow Rate | L/min | Flow Velocity Sensor |
Antifoaming Agent Flow Rate | L/min | Flow Velocity Sensor |
Phosphate Flow Rate | L/min | Flow Velocity Sensor |
Pressure in Tank | Mpa | Diaphragm Pressure Gauge |
Fermentation Time | h | Timer |
pH Value of Fermentation Liquid | - | pH Electrode |
Dataset | MSE (FCNN Inversion) | MSE (Adam-FCNN Inversion) |
---|---|---|
Training | 0.5127 | 0.0315 |
Testing | 0.4981 | 0.0371 |
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Wang, B.; Ma, W.; Jiang, H.; Huang, S. Research on Soft-Sensing Method Based on Adam-FCNN Inversion in Pichia pastoris Fermentation. Sensors 2025, 25, 4105. https://doi.org/10.3390/s25134105
Wang B, Ma W, Jiang H, Huang S. Research on Soft-Sensing Method Based on Adam-FCNN Inversion in Pichia pastoris Fermentation. Sensors. 2025; 25(13):4105. https://doi.org/10.3390/s25134105
Chicago/Turabian StyleWang, Bo, Wenyu Ma, Hui Jiang, and Shaowen Huang. 2025. "Research on Soft-Sensing Method Based on Adam-FCNN Inversion in Pichia pastoris Fermentation" Sensors 25, no. 13: 4105. https://doi.org/10.3390/s25134105
APA StyleWang, B., Ma, W., Jiang, H., & Huang, S. (2025). Research on Soft-Sensing Method Based on Adam-FCNN Inversion in Pichia pastoris Fermentation. Sensors, 25(13), 4105. https://doi.org/10.3390/s25134105