# Modeling a Practical Dual-Fuel Gas Turbine Power Generation System Using Dynamic Neural Network and Deep Learning

^{1}

^{2}

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## Abstract

**:**

^{−9}and the maximum MSE that was recorded for the MISO CNN was 2.9210 × 10

^{−4}, for more than 15 h of GT operation). The results have shown a comparable satisfactory performance for both dynamic NARX ANN and the CNN with a slight superiority of NARX. It can be newly argued that the dynamic ANN is better than the deep learning ANN for the time-based performance simulation of gas turbines (GTs).

## 1. Introduction

#### 1.1. Aims and Motivations

#### 1.2. Related Work and the Paper Contribution

^{−4}and for testing is 0.0055. Rahmoune et al. (2020) [17] have developed a NARX model to identify the dynamic behavior of the gas turbine components under the influence of the vibration phenomena. The results of the proposed NARX model validated the capability of the NARX NN in determining the dynamic behavior of the gas turbine system, with a simulation MSE of 3.8414 × 10

^{−3}for the high pressure (HP) turbine, 1.29152 × 10

^{−1}and 2.12090 × 10

^{−4}for the gas and air control valves, respectively. In terms of deep learning, Cao et al. (2021) [18] have presented different deep learning techniques that have been used to predict the changes in the efficiency and flow capacity of turbomachinery. The degradation predictions have been established via the LSTM approach, with a high accuracy ranging from 81.65% to 93.65%.

^{−9}, and the corresponding testing MSE was 3.4983 × 10

^{−7}. On the other hand, the maximum average MSE was recorded for the MISO CNN as 2.9210 × 10

^{−4}, and both networks worked successfully for more than 15 operating hours of the GT;

## 2. Data Curation and Analysis

#### 2.1. Data Normalization

_{max}) and (x

_{min}) are the maximum and minimum values of the input or output feature to the model, respectively. From the above equation, it can be clearly noticed that the range of features for each variable falls between the 0 and 1 range according to the following three scenarios:

- When $x$ equals the minimum, then $({x}_{norm})$ is 0;
- On the other hand, when $x$ is the maximum point in the array, then (${x}_{norm}$) is 1;
- However, if $x$ is between the minimum and maximum, then (${x}_{norm}$) will be between 0 and 1.

#### 2.2. Data Standardization

## 3. The NARX Model Setup

_{0}to x

_{4}represent the computer representation of the inputs, and w

_{0}to w

_{4}are the connection weights, which will be generalized later in the equations describing the NARX ANN, σ is the sigmoid activation function symbol and S is the linear activation function symbol, Ŷ(t) is the predicted output value. A thorough computer code in the MATLAB programming environment has been developed to set up and configure the NARX models with sophisticated generalization properties. MATLAB is a versatile programming environment that was founded and established by MathWorks for numerical computation in engineering and scientific applications. The generated code includes several hyper-parameters for training and configuring NARX models of a gas turbine generation unit. More precisely, the maximum number of iterations, learning rate, number of hidden layer’s neurons, time delays in the recurrent connections and model structure, i.e., MIMO and MISO configurations, as well as the data type, including normalized, standardized and actual data. All of these have been considered in the developed code as a combination of a variety of settings. Besides, this study employs a feed-forward multilayer dynamic neural network architecture with an input layer, one hidden layer and an output layer with a sigmoid-type transfer function and linear activation function for the output layer. Furthermore, the developed program has been used to train a wide range of NARX topologies, employing three training algorithms in the training step, which are the Levenberg–Marquardt (LM) algorithm, Bayesian regularization algorithm and scaled conjugate algorithm. Eventually, the tweaking of all hyper-parameters, in addition to the training algorithm, results in an indication of the best performance and its relevant NARX model. The mean squared error (MSE), which expresses the average squared error between the network outputs, the default performance function for feed-forward networks can be expressed as [23]:

#### 3.1. The MIMO Model

^{–6}. Figure 8 represents the optimal open-loop MIMO NARX model based on fifteen neurons in the hidden layer.

#### 3.2. The Parallel MISO Model

^{–7}was obtained after 1000 iterations (epochs), since the maximum epochs number was reached. Furthermore, the best regression coefficient was also found in the same NARX network. Figure 9, Figure 10, Figure 11 and Figure 12 show the performance and the regression plot of each developed MISO NARX model that is based on four inputs and one output at a time for the three output variables. These figures illustrate both the mean squared error (MSE) trend for the training and test sets and their regression training coefficient R during the learning procedure.

## 4. The Deep Learning Convolutional Neural Network (CNN) Model Setup

^{–3}learning rate. We shall avoid confusion in mentioning all trials that have been made, so we have mentioned only the ultimate parameters that have attained the lowest possible MSE. Then, the final CNN architectures with MIMO and MISO structures, and final optimal MSE value for each, are mentioned in Table 7.

## 5. Time-Based Simulation Results and Discussion

^{–9}and maximum MSE of 2.9210 × 10

^{–4}) for the adopted long operation time of the GT (more than 15 h of continuous operation), which indicate the robustness of deep learning and shallow dynamic ANNs. Such accuracies in the responses of GTs are difficult to attain by physics-informed or other system identification techniques because the power plant noises and uncertainties are high, and increasingly vary with the changes in the operating conditions. In addition, the differences in the nature of the responses make the simulation far more challenging; for instance, the power variations appear to be slower than the changes in the temperature and frequency, whereas the later responses change more severely, which makes the problem computationally over-complicated for the models to track all these variation trends simultaneously. Nevertheless, the proposed techniques in this paper have easily handled such computational burdens and prediction capabilities for a longer time than what has been previously published, which covers more than 15 h (or more than 54,000 sec) of operation.

- Its simplified structure that implicates the direct effect of inputs and outputs; therefore, there are more realistic reflections of the inputs on the outputs;
- The use of feedback delayed outputs as additional inputs, which increase the number of inputs utilized to depict the output more accurately. This important feature has no equivalence in CNN, despite its sophistication in the variety and number of its layers.

## 6. Conclusions

- It is generally highly recommended to normalize the data of GTs rather than dealing with actual quantities in using ANNs in models;
- The training algorithm of BR outperforms other training algorithms because of its late ultimate termination criteria, unlike other aforementioned earlier ones (LM and SCG);
- The prediction capabilities of NARX ANN and CNN for the GTs time-based dynamic performance are satisfactory, with very small negligible errors for both techniques.

- There was a slight superiority of the dynamic NARX type in terms of its accuracy. A new conclusion can be suggested by stating that the main computational reason, which is the feedback delay element in NARX despite the shallow structure, is capable of providing additional information with other direct inputs in order to improve the accuracy over the deep CNN, in which there is no delay feedback element;
- Based on the aforementioned results, deep learning can act as an alternative choice of modeling GTs in real applications, but cannot be a substitutional tool for the shallow dynamic ANN. This is because both have shown successful performances and can be used reliably in real applications;
- Despite the achieved targets of the paper, there are still some deep learning techniques that have not been investigated in the literature; these techniques might have a comparable performance, and this motivates the mentioning of some future research opportunities;
- One of the clearer future trends is to use other deep learning techniques and to compare them appropriately with developed/published ones. This may include the advanced deep recurrent neural network and locally connected neural networks;
- Another possible future outcome is to include the fuel preparation system, especially for biogas firing for such turbines, and the process of (gasification/digestion), in order to quantify the amount of materials used to be converted to biogas and to link those with an enhanced control strategy with new objectives;
- Another feasible future point is designing a supervisory controller for the developed ANN models and applying it to regulate the diffusion and premix modes, together with the objectives of a higher efficiency and lower emissions. A comparative study with other modeling philosophies may be useful, such as physics-based models and other black-box and grey-box models, with emphasis on many performance criteria rather than the mere numeric value of the accuracies.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADGTE | Aero-derivative gas turbine engine |

ANNs | Artificial neural networks |

BPNN | Back-propagation Neural Network |

BR | Bayesian regularization |

CCGT | Combined cycle gas turbine unit |

CR | Compression ratio |

COP | Compressor outlet pressure |

COT | Compressor outlet temperature |

CNN | Convolutional neural network |

EXT | Exhausted temperature |

FF | Feed-forward |

Freq | Frequency |

GT | Gas turbine |

GE | General electric |

HRSG | Heat recovery steam generator |

LM | Levenberg-–Marquardt |

LSTM | Long short term memory |

MSE | Mean squared error |

MIMO | Multi-input multi-output |

MISO | Multi-input single-output |

NG | Natural gas |

NGV | Natural gas control valve position |

NARX | Nonlinear autoregressive network with exogenous inputs |

Norm | Normalized data |

1D | One-dimension |

P | Output power |

PSO | Particle swarm optimization |

PILTV | Pilot gas valve position |

R | Regression parameter |

RMSE | Root mean squared error |

SCG | Scaled conjugate |

Stand | Standardized data |

TDL | Tapped delay line |

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**Figure 6.**Performance plot of the developed MIMO NARX model designed for the gas turbine power plant.

Variable | Abbreviation | Unit | Actual Operational Range |
---|---|---|---|

Pilot gas valve position Natural gas control valve position Compressor outlet pressure Compressor outlet temperature | PILTV NGV COP COT | % % bar °C | [41.06–44.79%] [27.18–39.45%] [11.45–16.75] [366.5–439.90] |

Variable | Abbreviation | Unit | Actual Operational Range |
---|---|---|---|

Output power Frequency Exhausted temperature | P Freq EXT | MW Hz $\mathbb{C}$ | [241.57–124.89] [49.91–50.14] [558.72–559.47] |

Hidden Layer Neurons | Time Delay | Training Algorithm | Data Format | Performance Average MSE | Regression | ||||
---|---|---|---|---|---|---|---|---|---|

Training | Validation | Test | Training | Validation | Test | ||||

5 | 2 | LM | Actual | 3.4998 × 10^{–6} | 4.3858 × 10^{–6} | 6.1132 × 10^{–6} | 0.99997 | 0.99996 | 0.99994 |

11 | 15 | LM | Stand | 3.1147 × 10^{–6} | 4.2107 × 10^{–6} | 8.6999 × 10^{–6} | 0.99998 | 0.99996 | 0.99991 |

20 | 20 | LM | Norm | 3.4393 × 10^{–6} | 4.5559 × 10^{–6} | 3.8095 × 10^{–6} | 0.99997 | 0.99995 | 0.99996 |

11 | 15 | BR | Stand | 2.3191 × 10^{–6} | 6.050 × 10^{–6} | 0.99998 | 0.99994 | ||

15 | 30 | BR | Norm | 1.0732
× 10^{–6} | 3.2062
× 10^{–6} | 0.99998 | 0.99997 | ||

20 | 20 | BR | Norm | 2.7990 × 10^{–6} | 3.2469 × 10^{–6} | 0.99997 | 0.99996 | ||

9 | 5 | SCG | Actual | 4.5996 × 10^{–5} | 4.4098 × 10^{–5} | 3.1814 × 10^{–5} | 0.99993 | 0.99993 | 0.99993 |

15 | 15 | SCG | Norm | 1.4164 × 10^{–4} | 1.6761 × 10^{–4} | 2.6512 × 10^{–4} | 0.99992 | 0.99994 | 0.99993 |

Hidden Layer Neurons | Time Delay | Training Algorithm | Data Format | Performance MSE | Regression | ||||
---|---|---|---|---|---|---|---|---|---|

Training | Validation | Test | Training | Validation | Test | ||||

9 | 5 | LM | Actual | 1.9266 × 10^{–7} | 2.0124 × 10^{–7} | 3.2844 × 10^{–6} | 0.99997 | 0.99996 | 0.99997 |

11 | 15 | LM | Stand | 2.8425 × 10^{–7} | 4.3205 × 10^{–7} | 3.4621 × 10^{–6} | 0.99996 | 0.99997 | 0.99991 |

20 | 30 | LM | Norm | 2.6179 × 10^{–7} | 3.0105 × 10^{–7} | 1.2145 × 10^{–6} | 0.99996 | 0.99997 | 0.99996 |

9 | 5 | BR | Actual | 2.5613 × 10^{–8} | 6.7436 × 10^{–6} | 0.99996 | 0.99989 | ||

11 | 15 | BR | Stand | 1.7642 × 10^{–8} | 3.3149 × 10^{–7} | 1 | 1 | ||

15 | 25 | BR | Norm | 1.4258 × 10^{–8} | 1.4642 × 10^{–7} | 1 | 1 | ||

20 | 30 | BR | Norm | 6.2626
× 10^{–9} | 3.4983
× 10^{–7} | 1 | 1 | ||

9 | 5 | SCG | Actual | 4.4996 × 10^{–5} | 4.2032 × 10^{–5} | 2.3214 × 10^{–5} | 0.99272 | 0.99097 | 0.99505 |

11 | 15 | SCG | Stand | 1.5093 × 10^{–4} | 2.6054 × 10^{–4} | 2.4232 × 10^{–4} | 0.99562 | 0.99341 | 0.99598 |

15 | 25 | SCG | Norm | 1.3164 × 10^{–4} | 2.7791 × 10^{–4} | 1.6512 × 10^{–4} | 0.95759 | 0.94021 | 0.95058 |

**Table 5.**Samples of the trials of the results of MISO NARX structures for the system frequency (Freq).

Hidden Layer Neurons | Time Delay | Training Algorithm | Data Format | Performance MSE | Regression | ||||
---|---|---|---|---|---|---|---|---|---|

Training | Validation | Test | Training | Validation | Test | ||||

9 | 5 | LM | Actual | 6.0188 × 10^{–6} | 2.0124 × 10^{–7} | 3.2844 × 10^{–6} | 0.99997 | 0.99996 | 0.99997 |

11 | 15 | LM | Stand | 7.5393 × 10^{–6} | 4.3205 × 10^{–7} | 3.4621 × 10^{–6} | 0.99996 | 0.99997 | 0.99991 |

20 | 30 | LM | Norm | 8.4340 × 10^{–6} | 3.0105 × 10^{–7} | 1.2145 × 10^{–6} | 0.99996 | 0.99997 | 0.99996 |

9 | 5 | BR | Actual | 3.7643 × 10^{–6} | 6.7436 × 10^{–6} | 0.99996 | 0.99989 | ||

11 | 15 | BR | Stand | 3.7362 × 10^{–6} | 3.3149 × 10^{–7} | 1 | 1 | ||

15 | 25 | BR | Norm | 1.5820
× 10^{–6} | 1.4642
× 10^{–7} | 1 | 1 | ||

20 | 30 | BR | Norm | 2.1999 × 10^{–6} | 3.4983 × 10^{–7} | 1 | 1 | ||

5 | 2 | SCG | Actual | 2.4112 × 10^{–4} | 3.1053 × 10^{–4} | 2.2242 × 10^{–4} | 0.99332 | 0.99379 | 0.99023 |

11 | 15 | SCG | Stand | 2.4386 × 10^{–4} | 2.6054 × 10^{–4} | 2.4232 × 10^{–4} | 0.99341 | 0.99341 | 0.99588 |

15 | 25 | SCG | Norm | 3.4042 × 10^{–5} | 2.7791 × 10^{–4} | 1.6512 × 10^{–4} | 0.95658 | 0.96020 | 0.95038 |

**Table 6.**Samples of the trials of the results of MISO NARX structures for the exhausted temperature (EXT).

Hidden Layer Neurons | Time Delay | Training Algorithm | Data Format | Performance MSE | Regression | ||||
---|---|---|---|---|---|---|---|---|---|

Training | Validation | Test | Training | Validation | Test | ||||

5 | 2 | LM | Actual | 1.8337 × 10^{–6} | 1.3246 × 10^{–6} | 6.1132 × 10^{–6} | 0.99997 | 0.99996 | 0.99994 |

20 | 30 | LM | Norm | 1.8947 × 10^{–6} | 1.5678 × 10^{–6} | 3.8095 × 10^{–6} | 0.99997 | 0.99995 | 0.99996 |

5 | 2 | BR | Actual | 1.4468 × 10^{–6} | 2.7617 × 10^{–6} | 0.99990 | 0.99979 | ||

15 | 25 | BR | Norm | 4.2333 × 10^{–6} | 2.9041 × 10^{–6} | 0.99998 | 0.99997 | ||

20 | 30 | BR | Norm | 3.3177
× 10^{–7} | 1.4889
× 10^{–6} | 1 | 1 | ||

9 | 5 | SCG | Actual | 1.1165 × 10^{–4} | 1.2062 × 10^{–4} | 2.1814 × 10^{–4} | 0.99219 | 0.99002 | 0.99108 |

10 | 10 | SCG | Stand | 7.8369 × 10^{–5} | 9.0913 × 10^{–5} | 7.1945 × 10^{–5} | 0.99444 | 0.99215 | 0.99519 |

15 | 25 | SCG | Norm | 7.4106 × 10^{–4} | 6.9733 × 10^{–4} | 7.01950 × 10^{–4} | 0.94648 | 0.94070 | 0.94048 |

**Table 7.**The effect of learning rate during attempts towards optimal solution (parallel MISO and MIMO).

Parallel MISO CNN | MIMO CNN All Outputs | ||||||
---|---|---|---|---|---|---|---|

Normalized EXT | Normalized Freq | Normalized P | |||||

Learning Rate | Average MSE | Learning Rate | Average MSE | Learning Rate | Average MSE | Learning Rate | Average MSE |

1 | 0.1000023029 | 1 | 0.0486324 | 1 | 0.1000023029 | 1 | 0.0623 |

1 × 10^{–2} | 0.0009281756 | 1 × 10^{–1} | 0.0461746 | 1 × 10^{–2} | 0.0000920723 | 1 × 10^{–2} | 0.0010 |

1 × 10^{–3} | 0.0000754316 | 1 × 10^{–3} | 0.0059033 | 1 × 10^{–3} | 0.0000502320 | 1 × 10^{–3} | 0.0012 |

1 × 10^{–5} | 0.0009873912 | 1 × 10^{–6} | 0.0052704 | 1 × 10^{–5} | 0.0008763900 | 1 × 10^{–5} | 0.0142 |

1 × 10^{–7} | 0.3573216283 | 1 × 10^{–9} | 0.2094497 | 1 × 10^{–7} | 0.1232704280 | 1 × 10^{–7} | 0.1450 |

3 × 10^{–1} | 0.0987941528 | 3
× 10^{–3} | 0.0015080 | 3 × 10^{–1} | 0.0957923018 | 3 × 10^{–1} | 0.0616 |

3 × 10^{–2} | 0.0041973211 | 4 × 10^{–3} | 0.0018637 | 3 × 10^{–2} | 0.0011962601 | 3 × 10^{–2} | 0.00412842 |

3
× 10^{–3} | 0.0000452316 | 5 × 10^{–3} | 0.0026439 | 3
× 10^{–3} | 0.0000384926 | 3
× 10^{–3} | 0.00074576 |

3 × 10^{–5} | 0.0004128134 | 5 × 10^{–4} | 0.0022009 | 3 × 10^{–5} | 0.0003279034 | 1 | 0.01075099 |

3 × 10^{–7} | 0.0083392732 | 6 × 10^{–3} | 0.0035000 | 3 × 10^{–7} | 0.0040356721 | 1 × 10^{–2} | 0.03599427 |

**Table 8.**Final version of the adjustable CNN with the final MSEs (normalized data, 1000 epoch and batch size 32).

Parallel MISO CNN | MIMO CNN | |||
---|---|---|---|---|

CNN Adjustable Design Parameter | Normalized EXT Performance | Normalized Freq Performance | Normalized Power Performance | All Outputs |

No. of convolutional layers | 3 | 2 | 3 | 3 |

Filter size for each convolutional layer | 2 | 2 | 2 | 2 |

No. of filters in the convolutional layer | 64_32_256 | 100_200 | 64_32_256 | 256_32_32 |

No. of hidden layers | 1 | 1 | 1 | 1 |

No. of neurons in the hidden layer | 70 | 100 | 64 | 70 |

Max-pooling layers | 2 | 2 | 2 | 2 |

Filter size in each max-pooling layer | 2 | 2 | 2 | 2 |

Final MSE | 8.6124826
× 10^{–6} | 2.9210
× 10^{–4} | 8.3504346
× 10^{–6} | 1.6581
× 10^{–4} |

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## Share and Cite

**MDPI and ACS Style**

Alsarayreh, M.; Mohamed, O.; Matar, M. Modeling a Practical Dual-Fuel Gas Turbine Power Generation System Using Dynamic Neural Network and Deep Learning. *Sustainability* **2022**, *14*, 870.
https://doi.org/10.3390/su14020870

**AMA Style**

Alsarayreh M, Mohamed O, Matar M. Modeling a Practical Dual-Fuel Gas Turbine Power Generation System Using Dynamic Neural Network and Deep Learning. *Sustainability*. 2022; 14(2):870.
https://doi.org/10.3390/su14020870

**Chicago/Turabian Style**

Alsarayreh, Mohammad, Omar Mohamed, and Mustafa Matar. 2022. "Modeling a Practical Dual-Fuel Gas Turbine Power Generation System Using Dynamic Neural Network and Deep Learning" *Sustainability* 14, no. 2: 870.
https://doi.org/10.3390/su14020870