Toward a Digital Twin of a Solid Oxide Fuel Cell Microcogenerator: Data-Driven Modelling
Abstract
:1. Introduction
2. SOFC Digital Twin Methodology
2.1. SOFC Digital Twin Scope and Architecture
2.2. SOFC Deep and Machine Learning Models
2.2.1. ML Algorithms
2.2.2. DL Algorithms
2.3. Validation Methods
- Mean absolute error (MAE)
- Mean absolute percentage error (MAPE)
- Mean squared error (MSE)
- Root mean square error (RMSE)
- R2 Score
- Weighted score (WS)
- n is the total number of observations or data points.
- represents the actual observed values in the dataset.
- represents the predicted values corresponding to .
- is the mean of the observed values (.
3. Discussion and Results
3.1. Experimental Setup and Data Analysis
3.2. Model Validation
4. Conclusions
- The experimental setting of the study considered the measurement data acquisition during 3935 h of SOFC operation, with parameters like electric power output, gas flow rates, and system efficiency, whose correlation revealed strong dependencies used to conceptualise the models’ features.
- Validation results, including the MAE, MAPE, and RMSE, revealed that XGBoost, GBoost, and RF algorithms were accurate and fast enough for real-time efficiency prediction within a DT framework.
- RF Regressor was found to be the best regression, with R2 almost equal to 0.99 and an RMSE equal to 0.31 using the entire dataset. Such high accuracy of the model potentially supports the integration of SOFCs into energy management systems, improving operational efficiency.
- Additionally, the potential of having a DT was demonstrated by observing how the most accurate model evolved over time based on the data collected, transitioning from XGBoost to GBoost, and finally to RF.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Nominal electric power in AC [kW] | 1.3 |
Minimum power output in AC [kW] | 0.5 |
Maximum power output in AC [kW] | 1.5 |
Electric efficiency in nominal condition on NG LHV | 57% |
Cogeneration efficiency in nominal condition on NG LHV | 88% |
Nominal thermal power output [kW] | 0.75 |
Nominal NG consumption [m3/h] | 0.24 |
NG supply pressure [mbar] | 17–25 |
Start-up time [h] | 24 |
Model | MSE | MAE | RMSE | MAPE | R2 | WS | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Total | Test | Total | Test | Total | Test | Total | Test | Total | Test | Total | Test | |
XGBoost | 0.13 | 0.27 | 0.16 | 0.25 | 0.36 | 0.52 | 0.04 | 0.04 | 0.98 | 0.96 | 0.03 | 0.04 |
RF | 0.10 | 0.14 | 0.17 | 0.24 | 0.31 | 0.38 | 0.04 | 0.04 | 0.99 | 0.98 | 0.03 | 0.03 |
LSTM | 0.29 | 0.24 | 0.36 | 0.36 | 0.54 | 0.49 | 0.07 | 0.07 | 0.96 | 0.96 | 0.06 | 0.05 |
GBoost | 0.11 | 0.17 | 0.20 | 0.25 | 0.33 | 0.41 | 0.04 | 0.04 | 0.98 | 0.97 | 0.03 | 0.03 |
ANN | 0.28 | 0.26 | 0.34 | 0.34 | 0.53 | 0.51 | 0.04 | 0.04 | 0.96 | 0.95 | 0.04 | 0.04 |
Polynomial Regression | 0.41 | 0.36 | 0.45 | 0.44 | 0.64 | 0.60 | 0.09 | 0.09 | 0.94 | 0.94 | 0.07 | 0.07 |
Model | 500 h | 1000 h | 1500 h | 2000 h | 2500 h | |||||
---|---|---|---|---|---|---|---|---|---|---|
R2 | WS | R2 | WS | R2 | WS | R2 | WS | R2 | WS | |
XGBoost | 0.998 | 0.004 | 0.876 | 0.067 | 0.941 | 0.038 | 0.957 | 0.035 | 0.975 | 0.035 |
RF | 0.837 | 0.085 | 0.929 | 0.041 | 0.943 | 0.037 | 0.969 | 0.028 | 0.983 | 0.031 |
LSTM | 0.957 | 0.030 | 0.872 | 0.081 | 0.883 | 0.090 | 0.914 | 0.080 | 0.953 | 0.060 |
GBoost | 0.938 | 0.034 | 0.966 | 0.022 | 0.958 | 0.029 | 0.971 | 0.027 | 0.974 | 0.036 |
ANN | 0.845 | 0.081 | 0.961 | 0.025 | 0.892 | 0.062 | 0.911 | 0.057 | 0.950 | 0.047 |
Polynomial Regression | 0.993 | 0.009 | 0.878 | 0.079 | 0.859 | 0.105 | 0.888 | 0.099 | 0.941 | 0.074 |
Model | Advantages | Disadvantages | Limitations |
---|---|---|---|
XGBoost | High accuracy (MAPE = 0.04) | Requires a lot of memory | Possible overfitting if not properly regularised |
Fast training times (0.19 s) | |||
RF | Highest R2 (0.99) and WS (0.03) | Poor performance on small dataset (R2500 h = 0.84) | Not always suitable for sequential or temporal data |
Fast training times (0.54 s) | |||
LSTM | Excellent for time series | Very long training times (6.47 s) | Large amounts of data required |
GBoost | Robustness as the number of data variates (R2 > 0.93) | Many iterations needed to fine-tune hyperparameters | Can overfit with too many iterations |
ANN | Ability to capture complex patterns | High training times (3.72 s) | Large amounts of data for training needed |
Polynomial Regression | Very fast training times (0.008 s) | Not as accurate as other models | Sensitive to outliers |
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Share and Cite
Testasecca, T.; Maniscalco, M.P.; Brunaccini, G.; Airò Farulla, G.; Ciulla, G.; Beccali, M.; Ferraro, M. Toward a Digital Twin of a Solid Oxide Fuel Cell Microcogenerator: Data-Driven Modelling. Energies 2024, 17, 4140. https://doi.org/10.3390/en17164140
Testasecca T, Maniscalco MP, Brunaccini G, Airò Farulla G, Ciulla G, Beccali M, Ferraro M. Toward a Digital Twin of a Solid Oxide Fuel Cell Microcogenerator: Data-Driven Modelling. Energies. 2024; 17(16):4140. https://doi.org/10.3390/en17164140
Chicago/Turabian StyleTestasecca, Tancredi, Manfredi Picciotto Maniscalco, Giovanni Brunaccini, Girolama Airò Farulla, Giuseppina Ciulla, Marco Beccali, and Marco Ferraro. 2024. "Toward a Digital Twin of a Solid Oxide Fuel Cell Microcogenerator: Data-Driven Modelling" Energies 17, no. 16: 4140. https://doi.org/10.3390/en17164140