In power plants, flue gases can cause severe corrosion damage in metallic parts such as flue ducts, heat exchangers, and boilers. Coating is an effective technique to prevent this damage. A robust fuzzy model of the surface roughness (_{a} and _{z}) of flue gas ducts coated by protective composite coating from epoxy and nanoparticles was constructed based on the experimental dataset. The proposed model consists of four nanoparticles (ZnO, ZrO_{2}, SiO_{2}, and NiO) with 2%, 4%, 6%, and 8%, respectively. Response surface methodology (RSM) was used to optimize the process parameters and identify the optimal conditions for minimum surface roughness of this coated duct. To prove the superiority of the proposed fuzzy model, the model results were compared with those obtained by ANOVA, with the coefficient of determination and the root-mean-square error (RMSE) used as metrics. For _{a}, for the first output response, using ANOVA, the coefficient-of-determination values were 0.9137 and 0.4037, respectively, for training and prediction. Similarly, for _{z}, the second output response, the coefficient-of-determination results were 0.9695 and 0.4037, respectively, for training and prediction. In the fuzzy modeling of _{a}, for the first output response, the RMSE values were 0.0 and 0.1455, respectively, for training and testing. The values for the coefficient of determination were 1.00 and 0.9807, respectively, for training and testing. The results prove the superiority of fuzzy modeling. For modeling the second output response _{z}, the RMSE values were 0.0 and 0.0421, respectively, for training and testing, and the coefficient-of-determination values were 1.00 and 0.9959, respectively, for training and testing.

The two main cycles in steam power plants are the water-steam cycle and the air-gas cycle [

The corrosion caused by flue gases of power plant equipment has been studied [

In a related study, the corrosion in the flue gas cleaning system of a biomass-fired power plant was investigated [_{2}O_{3}, Fe_{3}O_{4}, and FeO (OH), with an oxidation gradient shown in depth.

Much research has been devoted to overcoming corrosion formation due to flue gases in the aerospace industry [

In this work, the author’s previous experimental results will be used to model and optimize the surface roughness of epoxy/nanoparticles coating composites. These composite coatings are used as a protective layer against the formation of corrosion by performing two roles: preventing the flue gases from reacting with the duct material, and minimizing the surface roughness, thereby leading to less friction with these gases.

For decades, fuzzy logic (FL) has demonstrated its efficacy in both modeling and control of linear as well as nonlinear systems. In the system’s modeling, the advantage of using FL emerges when the available data has some sort of uncertainty or is superimposed with noise, which is the case in most real-life application measurements.

The main contribution of the current research is to present a robust fuzzy model of the surface roughness (_{a} and _{z}) of a flue gas duct coated by protective composite coating from epoxy and nanoparticles based on the experimental dataset. The proposed model consists of four nanoparticles (ZnO, ZrO_{2}, SiO_{2}, and NiO) with 2%, 4%, 6%, and 8%. Response surface methodology (RSM) was used to optimize the process parameters and identify the optimal conditions for minimum surface roughness of this coated duct. To prove the superiority of the proposed fuzzy model, the model results were compared with those obtained by ANOVA, with the coefficient of determination and root-mean-square error (RMSE) as metrics.

The experimental data for this research was obtained from our previous research [

Input | Output | |||
---|---|---|---|---|

(Parameters of surface roughness profile) | ||||

Coating type | Nano particle (%) | Fe (%) | Ra | Rz |

CS (Cortensteel) | 0 | 98.79 | 1.9684 | 12.7243 |

C1 | 0 | 70.35 | 0.4419 | 2.3003 |

C2 | 2 | 35.6 | 0.28 | 1.9287 |

4 | 68.08 | 0.773 | 2.1199 | |

6 | 36.94 | 0.9373 | 3.7222 | |

8 | 67.05 | 1.2891 | 4.1147 | |

C3 | 2 | 90.43 | 0.9146 | 6.4432 |

4 | 93.74 | 1.1101 | 7.9508 | |

6 | 86.21 | 3.9205 | 18.238 | |

8 | 88.05 | 2.9831 | 22.5906 | |

C4 | 2 | 76.08 | 0.2028 | 1.6214 |

4 | 91.38 | 0.3384 | 2.0798 | |

6 | 71.62 | 1.2324 | 5.2231 | |

8 | 59.56 | 1.112 | 7.5193 | |

C5 | 2 | 7.31 | 0.2857 | 1.8146 |

4 | 57.64 | 0.9427 | 4.1588 | |

6 | 71.63 | 0.9329 | 4.2712 | |

8 | 19.26 | 0.7426 | 4.0682 |

The materials used in this study were Corten Steel, Belzona 1391T epoxy, and nanoparticles, such as zinc oxide (ZnO, 99%, 35–45 nm), zirconium oxide (ZrO_{2}, 99+%, 40 nm), silicon dioxide (SiO_{2}, 99+%, 20–30 nm), and nickel oxide (NiO, 99%, 10–20 nm) [

Sample code | Composite coating | Percentages | No. of samples |
---|---|---|---|

CS | Corten steel | 1 | |

C1 | Epoxy | Pure epoxy | 1 |

C2 | Epoxy with nanoparticles ZnO | 2%, 4%, 6% and 8% with Epoxy | 4 |

C3 | Epoxy with nano-particles ZrO_{2} |
2%, 4%, 6% and 8% with Epoxy | 4 |

C4 | Epoxy with nano-particles SiO_{2} |
2%, 4%, 6% and 8% with Epoxy | 4 |

C5 | Epoxy with nanoparticles NiO | 2%, 4%, 6% and 8% with Epoxy | 4 |

To measure the surface roughness of all the samples, the stylus-based tester from Taylor Hobson [_{a}), the average absolute deviation of the profile points from a mean line, and the 10-point height method (_{z}), the distance between the average of the five highest points and the average of the five lowest points on a digitized profile.

Modeling by fuzzy logic involves three phases. The first phase consists of fuzzifying the values of the input signals. This is performed by mapping the crisp values, through their corresponding membership functions (MFs), to fuzzy values. This phase is called fuzzification. These MFs can take either gaussian or triangular shapes, depending on the application. The fuzzified inputs are logically processed to obtain the fuzzy output according to the pre-set fuzzy rules [

IF a is MFa and b is MFb, THEN c is MFc, where MFa and MFb denote the fuzzy membership functions of the two inputs a and b, respectively, and MFc is the fuzzy membership function of the output c.

_{a} and _{z}, respectively. The data from

Source | Sum of squares | df | Mean square | F-value | p-value significant |
---|---|---|---|---|---|

Model | 2.26 | 9 | 0.2514 | 7.05 | 0.0137 |

A-coating | 0.6469 | 1 | 0.6469 | 18.16 | 0.0053 |

B-percent | 0.3414 | 1 | 0.3414 | 9.58 | 0.0212 |

AB | 0.0341 | 1 | 0.0341 | 0.9559 | 0.3660 |

A² | 0.2675 | 1 | 0.2675 | 7.51 | 0.0337 |

B² | 0.0993 | 1 | 0.0993 | 2.79 | 0.1461 |

A²B | 0.0908 | 1 | 0.0908 | 2.55 | 0.1615 |

AB² | 0.0104 | 1 | 0.0104 | 0.2906 | 0.6093 |

A³ | 0.6813 | 1 | 0.6813 | 19.12 | 0.0047 |

B³ | 0.0666 | 1 | 0.0666 | 1.87 | 0.2207 |

Residual | 0.2138 | 6 | 0.0356 | ||

Cor total | 2.48 | 15 |

Regarding the second output response _{z}, the ANOVA data shown in

Source | Sum of squares | df | Mean square | F-value | p-value significant |
---|---|---|---|---|---|

Model | 14.61 | 9 | 1.62 | 21.20 | 0.0007 |

A-coating | 4.57 | 1 | 4.57 | 59.74 | 0.0002 |

B-percent | 1.44 | 1 | 1.44 | 18.82 | 0.0049 |

AB | 0.0382 | 1 | 0.0382 | 0.4996 | 0.5062 |

A² | 3.85 | 1 | 3.85 | 50.34 | 0.0004 |

B² | 0.0031 | 1 | 0.0031 | 0.0399 | 0.8483 |

A²B | 0.9934 | 1 | 0.9934 | 12.98 | 0.0113 |

AB² | 0.0624 | 1 | 0.0624 | 0.8156 | 0.4013 |

A³ | 5.30 | 1 | 5.30 | 69.19 | 0.0002 |

B³ | 0.1438 | 1 | 0.1438 | 1.88 | 0.2196 |

Residual | 0.4593 | 6 | 0.0765 | ||

Cor total | 15.07 | 15 |

The statistical analysis of the ANOVA model for both output responses can be seen in

First ANOVA model of _{a} |
Second ANOVA model of _{z} |
|||||||
---|---|---|---|---|---|---|---|---|

Std. dev. | 0.1888 | R² | 0.9137 | Std. dev. | 0.2767 | R² | 0.9695 | |

Mean | 0.9849 | Adjusted R² | 0.7842 | Mean | 2.27 | Adjusted R² | 0.9238 | |

C.V.% | 19.16 | Predicted R² | 0.4037 | C.V.% | 12.16 | Predicted R² | 0.6350 | |

Adeq Precision | 9.5972 | Adeq precision | 16.6070 |

In addition to p and f-values, other statistical parameters such as coefficient of determination or ^{2}, adjusted ^{2}, predicted ^{2}, and coefficient of variation (C.V.%) were used to evaluate the effectiveness of the developed models [_{a}, the first output response, the coefficient-of-determination values were 0.9137 and 0.4037, respectively, for training and prediction, whereas for the second output response, _{z}, the coefficient-of-determination values were 0.9695 and 0.4037, respectively, for training and prediction. The predicted

For the adequate precision and the signal-to-noise ratio, values for both the output responses were 9.597 and 16.6070, respectively. A signal-to-noise ratio greater than 4 indicates an adequate signal, confirming that each model can be used to navigate the design space.

As shown in _{a} and _{z} from the RSM optimization method can be seen in

A fuzzy system is used to simulate and model the surface roughness of the flue gas duct coated by nanoparticles. To detect the minimum values of surface roughness parameters such as _{a} and _{z}, different materials and percentages of nanoparticles were used. The system inputs are epoxy with varying percentages of nanoparticles, and the outputs of fuzzy logic system are surface roughness parameters values.

A plot of the system’s I/O data showed a nonlinear relationship that requires a robust tool to handle this kind of data. Fuzzy logic is one of the best tools for building an efficient and robust model for the data under consideration. Therefore, each of the experiment used a dual-input single-output data sample to construct the fuzzy model. This set of data was divided into two portions with a ratio of 70:30 for the training and testing phases. In system modeling, the most appropriate fuzzy model structure is the Takagi–Sugeno adaptive neuro-fuzzy inference system (ANFIS), which can track the nonlinear data accurately, and this was the artificial neural network used in this work. Furthermore, the subtractive clustering (SC) technique was utilized to construct the fuzzy rules, which produced seven and 10 fuzzy rules, respectively, for _{a} and _{z}. However, the minimum, maximum, and Wavg were selected for the implication, aggregation, and defuzzification methods, respectively. In addition, the inputs’ MFs were selected as the Gaussian shape for the fuzzification process, and only 10 epochs were found to be sufficient for the current training phase. The statistical measures were used for the assessment of model performance during the training and testing phases. These measures include the RMSE and the covariance, ^{2}, between the model’s output and the experimental data.

MSE | RMSE | Coefficient of determination (R^{2}) |
||||||
---|---|---|---|---|---|---|---|---|

Train | Test | All | Train | Test | All | Train | Test | All |

First fuzzy model of _{a} |
||||||||

1.4E-13 | 0.0212 | 0.0047 | 0.0000 | 0.1455 | 0.0686 | 1.0000 | 0.9807 | 0.9947 |

Second fuzzy model of _{z} |
||||||||

7.0E-11 | 0.0018 | 0.0004 | 0.0000 | 0.0421 | 0.0188 | 1.0000 | 0.9959 | 0.9996 |

As shown in _{a}, the RMSE values are 0.0 and 0.1455, respectively, for training and testing. The coefficient-of-determination values are 1.00 and 0.9807, respectively, for training and testing. This proves the superiority of fuzzy modeling. For modeling the second output of _{z}, the RMSE values are 0.0 and 0.0421, respectively, for training and testing. The coefficient-of-determination values are 1.00 and 0.9959, respectively, for training and testing.

The training and testing data for predicted and experimental results are plotted in

_{a} and _{z} surface changing values related to percent (%) and nanoparticles for the fuzzy system.

Optimization and robust fuzzy modeling were performed for the surface roughness of the protective composite coating of flue ducts in power plants. These composites consisted of epoxy reinforced by four nanoparticles, namely, Zno, ZrO_{2}, SiO, and NiO, in percentages of 2%, 4%, 6%, and 8%, respectively. These nano-epoxy composite coatings showed significant improvements in corrosion resistance, which were obtained by optimizing and modeling their surface roughness due to low Ra and Rz values compared with those of Corten Steel. The experimental results revealed that the surface roughness profile at 2% showed a dramatic improvement in all four types of nano-epoxy composite coatings (C2–C5), compared to the original Corten Steel. Moreover, increasing the intensity of the nanoparticles in the composite coating resulted in an increase of the surface roughness. The conclusion is that an increase in these valuable minerals will improve the resistance to corrosion and will strengthen the coating layer. In the future work, modern optimization algorithm will be considered to determine the optimal system parameters.

The authors acknowledge the support of King Fahd University of Petroleum & Minerals, Saudi Arabia.