# Improvement of Marine Steam Turbine Conventional Exergy Analysis by Neural Network Application

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## Abstract

**:**

^{2}> 0.95 for the whole turbine and each of its cylinders.

## 1. Introduction

_{2}power plant emissions detection. Several researchers [49,50,51,52] used MLP for predicting electrical power output from various complex power plants. Wahid et al. [53] applied MLP for the prediction of energy consumption in the buildings. Tahan et al. [54] used MLP for condition-based maintenance of gas turbine, while Lorencin et al. [55] also used MLP for condition-based maintenance, but not for the gas turbine only, then for the entire marine CODLAG (Combined Diesel and Gas) propulsion system. Many other authors also used MLP for the condition-based maintenance problems of various plants and components [56,57].

## 2. Description and Operation Principle of the Analyzed Main Marine Steam Turbine

## 3. Conventional Exergy Analysis of Main Marine Steam Turbine and Each of its Cylinders

#### 3.1. Overall Exergy Analysis Balances and Equations

#### 3.2. Equations for the Exergy Aanalysis of Main Marine Steam Turbine and Its Cylinders

#### 3.2.1. High Pressure Cylinder (HPC)

#### 3.2.2. Low Pressure Cylinder (LPC)

#### 3.2.3. Whole Turbine (WT)

## 4. Exergy Analysis of Main Marine Steam Turbine and Each of its Cylinders by MLP Neural Network Application

- Eliminate the unwanted values such as Rectified linear unit—ReLU ($y=\mathrm{max}\left(0,x\right)$)—used to eliminate negative values [95],
- Map the input files to a certain range such as sigmoid (logistic) function which maps the values to a range of $[0,1$] ($y=\frac{1}{1+{e}^{-x}}$) or hyperbolic tangent function which maps them to the range of [−1, 1] ($y=tanh\left(x\right)$),

^{2}; both of which take the least actual dataset values and a list of predicted values as inputs [99,101].

## 5. Steam Operating Parameters Required for the Exergy Analysis

#### 5.1. Conventional Exergy Analysis

#### 5.2. Exergy Analysis by MLP Neural Network Application

- (1)
- By using all collected data, developed mechanical power, exergy destruction and exergy efficiency of each cylinder are calculated as well as the whole turbine at each of the 24 loads with the conventional exergy analysis.
- (2)
- Results obtained by conventional exergy analysis are then used for MLP training and testing.
- (3)
- MLP is trained for every hyperparameter combination given in Table 5, which results in a total of 442,368 models when the aforementioned cross-validation process is applied.
- (4)
- The results of 442,368 models are compared across 72 input/output parameter combinations, given in Table 5, in order to determine the best possible model architecture for each of the aforementioned combinations.

#### 5.3. Measuring Equipment

## 6. Results and Discussion

#### 6.1. The Results of the Conventional Exergy Analysis

#### 6.2. Exergy Analysis Results by MLP Neural Network Application

## 7. Conclusions

- (1)
- To determine optimal turbine operating points for the measurement of steam temperature, pressure and mass flow rate. The goal will be to find three or four operating points of which the measurement results, along with MLP application, can be used for exergy analysis parameters prediction of the whole turbine and each cylinder at any load, with the lowest possible errors.
- (2)
- Extensive measurements during a long time period will allow determining performance degradation coefficients for the whole analyzed turbine and each of its cylinders. Implementation of such coefficients inside MPL structure will allow accurate and precise predicting of turbine exergy analysis parameters for the entire period of its operation.
- (3)
- Investigate if the same technique can be applied for other main marine steam turbines (especially for newer variants, which consist of three cylinders and steam reheating).

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Specification of Used Measuring Equipment

→ Greisinger GTF 601-Pt100 | |
---|---|

Measuring range: | −200 to +600 °C |

Response time: | approximate 10 s |

Standard: | 1/3 DIN class B |

Error ranges: | $\pm \left(0.10+0.00167\left|\mathrm{Temp}.\mathrm{in}\xb0\mathrm{C}\right|\right)$ |

→ Greisinger GTF 401-Pt100 | |

Measuring range: | −50 to +400 °C |

Response time: | approximate 10 s |

Standard: | DIN class B |

Error ranges: | $\pm \left(0.30+0.00500\xb7\left|\mathrm{Temp}.\mathrm{in}\xb0\mathrm{C}\right|\right)$ |

→ Yamatake JTG960A | |
---|---|

Measuring span: | 0.7 to 14 MPa |

Setting range: | −0.1 to 14 MPa |

Working pressure range: | 2.0 kPa to 14 MPa |

Accuracy: | $\pm 0.15\%\mathrm{for}\psi \ge 2.1\mathrm{MPa}$ $\pm \left(0.05+0.1\xb7\frac{2.1}{\psi}\right)\%\mathrm{for}\psi 2.1\mathrm{MPa}$ |

→ Yamatake JTG940A | |

Measuring span: | 35 to 3500 kPa |

Setting range: | −100 to 3500 kPa |

Working pressure range: | 2.0 kPa to 3500 kPa |

Accuracy: | $\pm 0.1\%\mathrm{for}\psi \ge 0.14\mathrm{MPa}$ $\pm \left(0.025+0.75\xb7\frac{0.14}{\psi}\right)\%\mathrm{for}\psi 0.14\mathrm{MPa}$ |

→ Yamatake JTD960A | |
---|---|

Measuring span: | 0.25 to 14 MPa |

Setting span: | −100 to 14 MPa |

Working pressure range: | 2.0 kPa to 14 MPa |

Accuracy: | $\pm 0.15\%\mathrm{for}\psi \ge 3.5\mathrm{MPa}$ $\pm \left(0.1+0.05\xb7\frac{3.5}{\psi}\right)\%\mathrm{for}\psi 3.5\mathrm{MPa}$ |

→ Yamatake JTD930A | |

Measuring span: | 35 to 700 kPa |

Setting span: | −100 to 700 kPa |

Working pressure range: | 2.0 kPa to 14 MPa |

Accuracy: | $\pm 0.1\%\mathrm{for}\psi \ge 140\mathrm{kPa}$ $\pm \left(0.025+0.075\xb7\frac{140}{\psi}\right)\%\mathrm{for}\psi 140\mathrm{kPa}$ |

→ Yamatake JTD920A | |

Measuring span: | 0.75 to 100 kPa |

Setting span: | −100 to 100 kPa |

Working pressure range: | 2.0 kPa to 14 MPa |

Accuracy: | $\pm 0.1\%\mathrm{for}\psi \ge 5.0\mathrm{kPa}$ $\pm \left(0.025+0.075\xb7\frac{5.0}{\psi}\right)\%\mathrm{for}\psi 5.0\mathrm{kPa}$ |

→ Yamatake JTD910A | |

Measuring span: | 0.1 to 2 kPa |

Setting span: | −1 to 1 kPa |

Working pressure range: | up to 210 kPa |

Accuracy: | $\pm \left(0.15+0.15\xb7\frac{1.0}{\psi}\right)\%$ |

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**Figure 1.**Scheme of the main marine steam turbine along with operating points required for the exergy analysis. HPC: High Pressure Cylinder; LPC: Low Pressure Cylinder; PP1: The first Propulsion Propeller; PP2: The second Propulsion Propeller.

**Figure 2.**The illustration of the Multilayer Perceptron (MLP) process used in the research, starting with the parameter search performed using a grid search (GS), yielding the MLP model, which is then applied on separate K-Fold splits and evaluated using ${R}^{2}$ and $MAE$ metrics.

**Figure 4.**The ranges of measured values used as inputs into the MLP for (

**a**) temperature, (

**b**) pressure and (

**c**) mass flow rate in each operating point, along with the environmental values for temperature and pressure (labeled as Env.).

**Figure 5.**The range of measured values used as outputs into the MLP for (

**a**) exergy efficiency and (

**b**) exergy loss measured for HPC, LPC and WT.

**Figure 6.**Mechanical power developed by the main turbine and each of its cylinders at three observed loads.

**Figure 7.**Exergy destruction and exergy efficiency of the main turbine and each of its cylinders at three observed loads.

**Figure 20.**$MAE$ and $MRE$ values of the selected input combination (1,4,7) for exergy destruction (exergy loss).

**Figure 21.**${R}^{2}$ values of the selected input combination (1,4,7) for exergy destruction (exergy loss).

Operating Point * | Temperature (°C) | Pressure (MPa) | Mass Flow Rate (kg/h) |
---|---|---|---|

1 | 487 | 6.2 | 9622 |

2 | - | - | 0 |

3 | 235 | 0.097 | 9622 |

4 | - | - | 0 |

5 | 235 | 0.097 | 9622 |

6 | - | - | 0 |

7 | 62.13 | 0.00511 | 9622 |

Operating Point * | Temperature (°C) | Pressure (MPa) | Mass Flow Rate (kg/h) |
---|---|---|---|

1 | 511 | 6.065 | 51,419 |

2 | - | - | 0 |

3 | 259 | 0.401 | 51,419 |

4 | - | - | 0 |

5 | 259 | 0.401 | 51,419 |

6 | 158 | 0.085 | 2985 |

7 | 28.85 | 0.00397 | 48,434 |

Operating Point * | Temperature (°C) | Pressure (MPa) | Mass Flow Rate (kg/h) |
---|---|---|---|

1 | 500 | 5.795 | 95,570 |

2 | 354 | 1.558 | 3398 |

3 | 250 | 0.590 | 92,172 |

4 | 250 | 0.590 | 13,172 |

5 | 250 | 0.590 | 79,000 |

6 | 154 | 0.120 | 4636 |

7 | 34.80 | 0.00557 | 74,364 |

**Table 4.**Operating points used for regression models for each set of outputs. For each operating point, trained models use steam mass flow rate, temperature and pressure—in addition to ambient pressure and temperature.

Operating Points Combination | HPC * (Outputs: $\dot{\mathit{E}}{\mathit{x}}_{\mathbf{D}\mathbf{E}\mathbf{S},\mathbf{H}\mathbf{P}\mathbf{C}}$$,{\mathit{\eta}}_{\mathbf{E}\mathbf{X},\mathbf{H}\mathbf{P}\mathbf{C}}$) | LPC * (Outputs: $\dot{\mathit{E}}{\mathit{x}}_{\mathbf{D}\mathbf{E}\mathbf{S},\mathbf{L}\mathbf{P}\mathbf{C}}$$,{\mathit{\eta}}_{\mathbf{E}\mathbf{X},\mathbf{L}\mathbf{P}\mathbf{C}}$) | WT * (Outputs: $\dot{\mathit{E}}{\mathit{x}}_{\mathbf{D}\mathbf{E}\mathbf{S},\mathbf{W}\mathbf{T}}$$,{\mathit{\eta}}_{\mathbf{E}\mathbf{X},\mathbf{W}\mathbf{T}}$) |
---|---|---|---|

1 | - | - | - |

2 | 1,2,3,4,5,6,7 | 1,2,3,4,5,6,7 | 1,2,3,4,5,6,7 |

3 | 1,2,3,4,5 | 3,4,5,6,7 | 1,2,3,5 |

4 | 1,2,3 | 4,6,7 | 2,6,7 |

5 | 1,2 | 5,6,7 | 1,2,3 |

6 | 1,3 | 6,7 | 5,6,7 |

7 | 2,3 | 5,6 | 4,6,7 |

8 | 3,4 | 4,6 | 3,6,7 |

9 | 1,4 | 5,7 | 1,2,3,4,5 |

10 | 2,4 | 4,7 | 2,4,6,7 |

11 | - | - | 1,3,7 |

12 | - | - | 1,4,7 |

13 | - | - | 1,5,7 |

14 | - | - | 2,4,6 |

15 | - | - | 2,6,7 |

16 | - | - | 1,3,5,7 |

Count | 10 | 10 | 16 |

**Table 5.**Possible values of hyperparameters used in grid search, with the number of the possible hyperparameter values being given in the column titled Total Count.

Hyperparameter | Possible Hyperparameter Values | Total Count |
---|---|---|

Hidden Layer Sizes | (84,84,84,84) (84,84,84) (84,84) (84) (42,42,42,42) (42,42,42) (42,42) (42) (21,21,21,21) (21,21,21) (21,21) (21) (84,42,42,21) (42,21,21) (84,42,21) (42,21) | 16 |

Activation Function | ‘relu’ ‘identity’ ‘logistic’ ‘tanh’ | 4 |

Solver | ‘adam’ ‘lbfgs’ | 2 |

Learning Rate Type | ‘constant’ ‘adaptive’ ‘inverse scaling’ | 3 |

Initial Learning Rate Value | 0.5 0.1 0.01 0.00001 | 4 |

L2 Regularization parameter | 0.1 0.01 0.001 0.0001 | 4 |

**Table 6.**Steam operating parameters range (min–max) in each operating point for all 24 measured turbine loads.

Operating Point * | Temperature (°C) | Pressure (MPa) | Mass Flow Rate (kg/h) |
---|---|---|---|

1 | 485–513 | 5.795–6.2 | 3835–96,789 |

2 | 283–365 | 0.08–1.565 | 0–3398 |

3 | 229–279 | 0.048–0.593 | 3835–93,521 |

4 | 229–279 | 0.048–0.593 | 0–13,202 |

5 | 229–279 | 0.048–0.593 | 3835–80,319 |

6 | 121–169 | 0.009–0.121 | 0–4772 |

7 | 28.616–100.02 | 0.00392–0.00561 | 3835–75,547 |

Operating Point * | Temperature (Immersion Probes) [116] | Pressure (Pressure Transmitters) [117] | Mass Flow Rate (Differential Pressure Transmitters) [118] |
---|---|---|---|

1 | Greisinger GTF 601-Pt100 | Yamatake JTG960A | Yamatake JTD960A |

2 | Yamatake JTG940A | ||

3 | Greisinger GTF 401-Pt100 | Yamatake JTD930A | |

4 | |||

5 | |||

6 | Yamatake JTD920A | ||

7 | Yamatake JTD910A |

Operating Point | ${\mathit{R}}^{2}$ | +/- | $\mathit{M}\mathit{A}\mathit{E}$ | +/- |
---|---|---|---|---|

1,4 (HPC) | 0.9914541639 | 0.02378781401 | 51.27713297 | 36.21271356 |

4,7 (LPC) | 0.9712139368 | 0.09161658705 | 36.22307872 | 50.75836187 |

1,4,7 (WT) | 0.9992643028 | 0.00172978046 | 20.44955009 | 12.32598431 |

**Table 9.**Hyperparameters used for best solutions achieved in selected operating points, for modeling of exergy destruction.

Operating Point | 1,4 (HPC) | 4,7 (LPC) | 1,4,7 (WT) |
---|---|---|---|

Activation Function | ReLU | ReLU | ReLU |

L2 Regularization | 0.001 | 0.01 | 0.1 |

Hidden Layer Sizes | (84) | (84, 84, 84, 84) | (84, 84, 84, 84) |

Learning Rate Type | Adaptive | Constant | Adaptive |

Initial learning rate | 0.1 | 0.01 | 1e-05 |

Solver | LBFGS | LBFGS | LBFGS |

Operating Point | ${\mathit{R}}^{2}$ | +/- | $\mathit{M}\mathit{A}\mathit{E}$ | +/- |
---|---|---|---|---|

1,4 (HPC) | 0.9894154031 | 0.03141286439 | 0.3393632265 | 0.3058120431 |

4,7 (LPC) | 0.9906770758 | 0.02055184947 | 0.6985228666 | 1.1429986910 |

1,4,7 (WT) | 0.9951798924 | 0.01330619104 | 1.6066829045 | 0.0133061910 |

**Table 11.**Hyperparameters used for best solutions achieved in selected operating points, for modeling of exergy efficiency.

Operating Point | 1,4 (HPC) | 4,7 (LPC) | 1,4,7 (WT) |
---|---|---|---|

Activation Function | ReLU | ReLU | ReLU |

L2 Regularization | 0.1 | 0.1 | 0.1 |

Hidden Layer Sizes | (84,42,21) | (84,84,84) | (84,84,84,84) |

Learning Rate Type | Constant | Constant | Adaptive |

Initial learning rate | 0.1 | 0.01 | 1e-5 |

solver | LBFGS | LBFGS | LBFGS |

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**MDPI and ACS Style**

Baressi Šegota, S.; Lorencin, I.; Anđelić, N.; Mrzljak, V.; Car, Z.
Improvement of Marine Steam Turbine Conventional Exergy Analysis by Neural Network Application. *J. Mar. Sci. Eng.* **2020**, *8*, 884.
https://doi.org/10.3390/jmse8110884

**AMA Style**

Baressi Šegota S, Lorencin I, Anđelić N, Mrzljak V, Car Z.
Improvement of Marine Steam Turbine Conventional Exergy Analysis by Neural Network Application. *Journal of Marine Science and Engineering*. 2020; 8(11):884.
https://doi.org/10.3390/jmse8110884

**Chicago/Turabian Style**

Baressi Šegota, Sandi, Ivan Lorencin, Nikola Anđelić, Vedran Mrzljak, and Zlatan Car.
2020. "Improvement of Marine Steam Turbine Conventional Exergy Analysis by Neural Network Application" *Journal of Marine Science and Engineering* 8, no. 11: 884.
https://doi.org/10.3390/jmse8110884