Neural Nonlinear Autoregressive Model with Exogenous Input (NARX) for Turboshaft Aeroengine Fuel Control Unit Model^{ †}
Abstract
:1. Introduction
- Increased performance with the reduction in engine weight due to digital signaling, lower wire/connector count, reduced cooling need. 5% increase in thrust-to-weight ratio;
- Improved Mission Success: System availability improvement due to automated fault isolation, reduced maintenance time, and modular line-replaceable unit (LRU). 10% increase in system availability;
- Lower Life Cycle Cost: Reduced cycle time for design and manufacturing; reduced component and maintenance costs.
2. Materials and Methods
2.1. Gas Turbine Modelling
2.1.1. Design Point
2.1.2. Transient Simulations
2.1.3. Deteriorated Model
2.2. Neural Network Application to Transient Simulations
NARX Neural Network
- Mean-Square-Error (MSE) defined as follows:$$MSE=\frac{{\displaystyle \sum _{i}{\left({Y}_{GSP}(i)-{Y}_{NN}(i)\right)}^{2}}}{n}$$
- The Root-Mean-Square-Error (RMSE) defined as follows:$$RMSE=\sqrt{\frac{{\displaystyle \sum _{i}{\left({Y}_{GSP}(i)-{Y}_{NN}(i)\right)}^{2}}}{n}}$$
- The coefficient of determination R^{2} is defined as follows:$${R}^{2}=\frac{{{\displaystyle {\sum}_{i}({Y}_{GSP}(i)-Y}}_{NN}(i){)}^{2}}{{\displaystyle {\sum}_{i}({Y}_{GSP}(i)}{)}^{2}-\frac{{\displaystyle \sum _{i}{\left({Y}_{NN}(i)\right)}^{2}}}{n}}$$
3. Results
- Engine parameters: shaft speed (Nc), turbine inlet total temperature (TIT), fuel mass flow rate (Wf_b), and compressor pressure ratio (PRc);
- Environment parameters: Mach number (M), atmospheric total temperature (TT1), and total pressure (PT1).
3.1. NARX Neural Networks Prediction Results
3.1.1. Healthy Results
3.1.2. NARX Neural Networks Prediction Results Degraded Model
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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Description | Value |
---|---|
Power | 200–400 (kW) |
Weight | 110 (kg) |
Pressure Ratio | 8:1 |
Turbine Inlet Temp | 1173.15 (K) |
SFC (Specific Fuel Consumption) | 0.426–0.33 (kg/kWh) |
Compressor Configuration | 1 centrifugal |
Turbine Configuration (one stage) | HPT, LPT |
Description | Value | Unit |
---|---|---|
Power (POW) | 266 | (kW) |
Intake Pressure ratio (PR) | 0.988 | (-) |
Air Flow rate (W_{a}) | 2 | (kg/s) |
Combustion efficiency (η_{b}) | 0.985 | (-) |
Fuel Flow rate (Wfb) | 0.0315 | (kg/s) |
Compressor Rotor Speed (n_{1}) | 40,891 | (rpm) |
Compressor Efficiency (η_{c}) | 0.825 | (-) |
LPT Rotor Speed (n_{2}) | 6000 | (rpm) |
Turbine efficiency (η_{t}) | 0.88 | (-) |
Spool Mechanical Efficiency (η_{m}) | 0.99 | (-) |
h [m] | Mach Number | |
---|---|---|
TO (Take-Off) | 0 | 0 |
CR1 (Cruise1) | 313.5 | 0.45 |
CR2 (Cruise2) | 400 | 0.12 |
CR3 (Cruise3) | 800 | 0.09 |
CR4 (Cruise4) | 313.5 | 0.21 |
Physical Fault | Flow Capacity Change | Isentropic Efficiency Change |
---|---|---|
Compressor Fouling | ${\dot{m}}_{c}\downarrow $ | η_{c}↓ |
Compressor Erosion | ${\dot{m}}_{c}\downarrow $ | η_{c}↓ |
Compressor Corrosion | ${\dot{m}}_{c}\downarrow $ | η_{c}↓ |
Compressor Blade Rubbing | ${\dot{m}}_{c}\downarrow $ | η_{c}↓ |
Turbine Fouling | ${\dot{m}}_{t}\downarrow $ | η_{t}↓ |
Turbine Erosion | ${\dot{m}}_{t}\uparrow $ | η_{t}↓ |
Turbine Corrosion | ${\dot{m}}_{t}\downarrow $ | η_{t}↓ |
Turbine Blade Rubbing | ${\dot{m}}_{t}\uparrow $ | η_{t}↓ |
Thermal Distortion | ${\dot{m}}_{t}\uparrow $ | η_{t}↓ |
FOD (Foreign Object Damage) | ${\dot{m}}_{c}\downarrow $ and ${\dot{m}}_{t}\downarrow $ | η_{c}↓ and η_{t}↓ |
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De Giorgi, M.G.; Strafella, L.; Ficarella, A. Neural Nonlinear Autoregressive Model with Exogenous Input (NARX) for Turboshaft Aeroengine Fuel Control Unit Model. Aerospace 2021, 8, 206. https://doi.org/10.3390/aerospace8080206
De Giorgi MG, Strafella L, Ficarella A. Neural Nonlinear Autoregressive Model with Exogenous Input (NARX) for Turboshaft Aeroengine Fuel Control Unit Model. Aerospace. 2021; 8(8):206. https://doi.org/10.3390/aerospace8080206
Chicago/Turabian StyleDe Giorgi, Maria Grazia, Luciano Strafella, and Antonio Ficarella. 2021. "Neural Nonlinear Autoregressive Model with Exogenous Input (NARX) for Turboshaft Aeroengine Fuel Control Unit Model" Aerospace 8, no. 8: 206. https://doi.org/10.3390/aerospace8080206