# Neural Network Optimization Algorithms to Predict Wind Turbine Blade Fatigue Life under Variable Hygrothermal Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Hygro-Thermo-Mechanics of Wind Turbine Blades

- Mechanical (wind gust, storms...);
- Thermal (temperature variation);
- Hygrometric (moisture variation).

## 3. Data and Method

#### 3.1. Fatigue Data

_{s}, fiber contents (35–36%), and many stitched fabrics.

#### 3.2. Backpropagation Neural Network BPNN

_{i}is the synaptic weight matrix linking the input with the hidden layer, and w

_{s}is the synaptic weight matrix linking the hidden layer with the output, according to Equation (2) [6,12,13,14]:

_{i,j,k}represents the weight connection strengths for node j in the (k − 1)th layer to node i in the kth layer; out

_{j,k}is the output of node i in the kth layer and θ

_{i,k}is the threshold associated with node i in the kth layer.

_{d}is the desired output.

#### 3.3. Particle Swarm Optimization PSO

_{b}) as well as the best position of its neighbors (P

_{g}), and then computes a new position [14]. Figure 3 briefly illustrates the concept of PSO.

^{T}the transpose of a matrix A. The quality of its position is determined by the value of the objective function at this point. This particle keeps in memory the best position by which it has already passed, which we note ${\overrightarrow{p}}_{i}={\left({p}_{i1},{p}_{i2},\dots {p}_{id}\right)}^{T}$. The best position reached by its neighboring particles is noted ${\overrightarrow{g}}_{i}={\left({g}_{i1},{g}_{i2},\dots {g}_{id}\right)}^{T}$. At time t, the velocity vector is calculated from Equation (4):

_{id}and p

_{id}are the velocity and position of particle i (i = 1, 2, … n), where n is the number of particles; d = 1, 2, … m, and m is the number of input variables to be optimized; w is usually a constant, called the “inertia weight factor”; c

_{1}and c

_{2}are cognitive and social acceleration factors, respectively, that scale the old velocity and increase new velocity toward P

_{best}(local best result) or G

_{best}(global best result); r

_{1}and r

_{2}represent random numbers that are uniformly distributed in the interval [0,1] [8,14].

#### 3.4. Cuckoo Search Algorithm

- Every cuckoo lays solely one egg at a time, and the eggs are exactly set in a nest (randomly selected nest);
- The nest has better quality eggs, which are carried onto the next round;
- The number of the nest is fixed, and the quality of the nest is static and not alterable.

_{i}= (x

_{i}

_{1}, x

_{i}

_{2}, … x

_{id}), where d is the dimension of the problem. The fitness of each nest can be determined according to their own location information [17,18]. The nests are updated according to Equation (6):

_{a}) to be abandoned. If a nest is abandoned, a new nest will be created according to Equation (7):

#### 3.5. Data Preparation

## 4. Proposed Hybrid Models for Fatigue Life Prediction

_{max}, and one output, the normalized number of cycles to failure N. The network consists of a single hidden layer of 10 neurons using a sigmoid activation function, while the output uses a linear activation function with one computation neuron. It is a fixed architecture for all our proposed combinations, and we try each time to replace the BP algorithm (Levenberg-Marquardt) with one of the suggested algorithms (PSO and CS). Since we have only one input and one output, data scaling was achieved by normalizing/standardizing real-valued input and output variables.

#### 4.1. PSO-Based ANN

#### 4.2. CS-Based NN (CSNN)

## 5. Results and Discussion

_{max}) and the number of cycles to failure (N). For illustration and comparative purposes, we have presented in the same figure and for each studied temperature, four plots for different experimental and predicted values obtained with BPNN, PSO-ANN, and CSNN, where they show typical fatigue life predictions. We did not have enough data to predict scenarios for 50 °C wet conditions. All the data originates from SNL, who performed the experiments and made their database publicly available. Therefore, we have not being able to test the 50 °C wet with the following materials: Derakane 8084, CoRezyn 75-AQ-010 and Derakane 411C-50.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Nijssen, R.P.L. Fatigue Life Prediction and Strength Degradation of Wind Turbine Rotor Blade Composites. Ph.D. Dissertation, Delft University, Delft, The Netherlands, 2006. [Google Scholar]
- Li, M. Temperature and Moisture Effects on Composite Materials for Wind Turbine Blades. Master’s Thesis, Montana State University, Bozeman, MT, USA, 2000. [Google Scholar]
- Mandell, J.; Samborsky, D.D.; Li, M. Selection of fiberglass matrix resins for increased toughness and environmental resistance in wind turbine blades. AIAA J.
**2000**, 57, 354–366. [Google Scholar] [CrossRef][Green Version] - SNL/MSU/DOE. Composite Material Fatigue Database. Mechanical Properties of Composite Materials for Wind Turbine Blades; Montana State University-Bozeman: Bozeman, MT, USA, 2016; Version 25.0. Available online: http://energy.sandia.gov/ (accessed on 20 October 2016).
- Samborsky, D.D.; Mandell, J.; Cairns, D.S. Selection of reinforcing fabrics for wind turbine blades. AIAA J.
**1999**, 24, 32–42. [Google Scholar] [CrossRef][Green Version] - Ziane, K.; Zebirate, S.; Zaitri, A. Fatigue strength prediction in composite materials of wind turbine blades under dry–wet conditions: An artificial neural network approach. Wind Eng.
**2016**, 40, 189–198. [Google Scholar] [CrossRef] - Attaf, B. Eco-conception et développement des pales d’éoliennes en matériaux composites. In Revue des Energies Renouvelables SMEE’10 Bou Ismail Tipaza; 2010; pp. 37–48. Available online: https://docplayer.fr/12968847-Eco-conception-et-developpement-des-pales-d-eoliennes-en-materiaux-composites.html (accessed on 3 July 2021).
- Ziane, K. Analyse, Évaluation et Réduction des Risques d’un Parc Éolien. Ph.D. Dissertation, Université d’Oran 2 Mohamed Ben Ahmed, Oran, Algeria, 2017. [Google Scholar]
- Samborsky, D.D.; Agastra, P.; Mandell, J.F. Fatigue trends for wind blade infusion resins and fabrics. In Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, USA, 12–15 April 2010. [Google Scholar] [CrossRef][Green Version]
- Agastra, P.; Samborsky, D.D.; Mandell, J.F. Fatigue resistance of fiberglass laminates at thick material transitions. In Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA, USA, 4–7 May 2009; pp. 1–23. [Google Scholar] [CrossRef][Green Version]
- Mandell, J.F.; Samborsky, D.D.; Agastra, P.; Sears, A.T.; Wilson, T.J. Analysis of SNL/MSU/DOE Fatigue Database Trends for Wind Turbine Blade Materials; SANDIA National Laboratories: Albuquerque, NM, USA, 2010; SAND2010-7052.
- Al-Assaf, Y.; El-Kadi, H. Fatigue life prediction of unidirectional glass fiber/epoxy composite laminae using neural networks. Compos. Struct.
**2001**, 53, 65–71. [Google Scholar] [CrossRef] - Vassilopoulos, A.P.; Georgopoulos, E.F.; Dionysopoulos, V. Artificial neural networks in spectrum fatigue life prediction of composite materials. Int. J. Fatigue
**2007**, 29, 20–29. [Google Scholar] [CrossRef] - Ziane, K.; Zebirate, S.; Zaitri, A. Particle swarm optimization-based neural network for predicting fatigue strength in composite laminates of wind turbine blades. Compos. Mech. Comput. Appl. Int. J.
**2015**, 6, 321–338. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995; pp. 1942–1948. [Google Scholar] [CrossRef]
- Zhang, J.R.; Zhang, J.; Lok, T.M.; Lyu, M.R. A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training. Appl. Math. Comput.
**2007**, 185, 1026–1037. [Google Scholar] [CrossRef] - Yang, X.S.; Deb, S. Cuckoo search via Lévy flights. In Proceedings of the World Congress on Nature & Biologically Inspired Computing, Coimbatore, India, 9–11 December 2009. [Google Scholar] [CrossRef]
- Ding, J.; He, X.; Jiang, B. Wu, Y. Parameter identification for area-specific resistance of direct methanol fuel cell using cuckoo search algorithm. In Bio-Inspired Computing—Theories and Applications; Gong, M., Linqiang, P., Tao, S., Tang, K., Zhang, X., Eds.; Springer: Heidelberg, Germany, 2015; Volume 562, pp. 107–112. [Google Scholar] [CrossRef]
- Anga, J.Y.; Abdul Majida, M.S.; Mohd Norb, A.; Yaacobc, S.; Ridzuana, M.J.M. First-ply failure prediction of glass/epoxy composite pipes using an artificial neural network model. Compos. Struct.
**2018**, 15, 579–588. [Google Scholar] [CrossRef] - Gudise, V.G.; Venayagamoorthy, G.K. Comparison of particle swarm optimization and back-propagation as training algorithms for neural networks. In Proceedings of the IEEE Swarm Intelligence Symposium SIS’03, Indianapolis, IN, USA, 26 April 2003; pp. 110–117. [Google Scholar] [CrossRef]
- Yi, J.; Xu, W.; Chen, Y. Novel back propagation optimization by cuckoo search algorithm. Sci. World J.
**2014**, 2014, 1–8. [Google Scholar] [CrossRef][Green Version] - Nawi, N.M.; Khan, A.; Rehman, M.Z. A new back-propagation neural network optimized with cuckoo search algorithm. In Computational Science and Its Applications—ICCSA 2013, 7971; Murgante, B., Misra, S., Carlini, M., Torre, C., Nguyen, H.-Q., Taniar, D., Apduhan, B.O., Gervasi, O., Eds.; Springer: Berlin/Heidelberg, Germany, 2013. [Google Scholar] [CrossRef][Green Version]
- Ziane, K.; Zebirate, S.; Khan, A.; Ilinca, A. A cuckoo search based neural network to predict fatigue life in rotor blade composites. J. Mech. Eng. Sci.
**2020**, 14, 6430–6442. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Blade subjected to a hygro-thermomechanical loading [7].

**Figure 2.**Feedforward neural network with one hidden layer [14].

**Figure 3.**Displacement of a particle [8].

**Figure 6.**Use of PSO to train a feedforward NN [14].

**Figure 10.**Flowchart of CSNN combination [21].

**Figure 11.**Experimental and predicted values of ortho-polyester resin fatigue life (CoRezyn 63-AX-051). (

**a**): T = 50 °C wet; (

**b**): T = 50 °C dry; (

**c**): T = 20 °C wet; (

**d**): T = 20 °C dry.

**Figure 12.**Experimental and predicted values of vinyl ester resin fatigue life (Derakane 8084). (

**a**): T = 50 °C wet; (

**b**): T = 20 °C dry; (

**c**): T = 20 °C wet.

**Figure 13.**Experimental and predicted values of iso-polyester resin fatigue life (CoRezyn 75-AQ-010). (

**a**): T = 50 °C wet; (

**b**): T = 20 °C dry; (

**c**): T = 20 °C wet.

**Figure 14.**Experimental and predicted values of vinyl ester resin fatigue life (Derakane 411C-50). (

**a**): T = 50 °C wet; (

**b**): T = 20 °C dry; (

**c**): T = 20 °C wet.

Laminate | Matrix Materials | |||||||
---|---|---|---|---|---|---|---|---|

General Material Name | Lay-Up | Volume Fiber (%) | Resin | Description | Resin Trade Name | Supplier | ||

MD-DD5P-UP2 | [0/±45/0]_{S} | 35–36 | Ortho-polyester | Orthophthalic | CoRezyn 63-AX-051 | Interplastics Corporation | ||

Iso-polyester | Isophthalic | CoRezyn 75-AQ-010 | ||||||

MD-DD5P-VE | [0/±45/0]_{S} | 35–36 | Vinyl ester 411C-50 | Unmodified | Derakane 411C-50 | Dow Chemical | ||

Vinyl ester 8084 | Rubber toughened | Derakane 8084 | ||||||

Fiber reinforcing fabrics | ||||||||

E-glass fabric | Fabric orientation | Type | Areal weight (g/m^{2}) | Supplier | ||||

Knytex D155 | 0° unidirectional fabrics | Stitched unidirectional | 527 | Owens corning fabrics | ||||

Knytex DB120 | ±45 fabrics | Bias, stitched | 393 | Owens corning fabrics |

Testing Temperature T (°C) | Stress Ratio R | UCS * (MPa) | Hygrometric Conditions |
---|---|---|---|

50 °C Wet | 10 | −34.5 | Wet coupons (1.0% distilled water) |

50 °C Dry | 10 | −34.5 | |

20 °C Wet | 10 | −31 | |

50 °C Dry | 10 | −37.9 |

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

Normalized maximum compressive stress σ_{max} | Normalized number of cycles to failure N |

Parameters | Values |
---|---|

Number of particles | 20 |

Number of generations (max iterations) | 1000 |

Maximum velocity V_{max} | 0.9 |

Minimum velocity V_{min} | 0.4 |

Cognitive and social acceleration factors c_{1} and c_{2} | 2 |

Search space range | [−100, 100] |

Inertia weight factor w | 0.72 |

Material | Environmental Conditions | BPNN | PSO-ANN | CSNN | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | Epochs | CPU Time (s) | Accuracy (%) | RMSE | MAE | Epochs | CPU Time (s) | Accuracy (%) | RMSE | MAE | Epochs | CPU Time (s) | Accuracy (%) | ||

Ortho-polyester (CoRezyn 63-AX-051) | 50 °C wet | 0.0175 | 0.0259 | 277 | 9.371 | 94.443 | 0.0181 | 0.0316 | 228 | 227.73 | 94.394 | 0.0141 | 0.0079 | 62 | 6.632 | 94.761 |

50 °C dry | 0.0316 | 0.0342 | 54 | 7.453 | 92.006 | 0.0331 | 0.0284 | 112 | 111.50 | 93.115 | 0.0309 | 0.0282 | 23 | 2.961 | 92.138 | |

20 °C wet | 0.036 | 0.0387 | 18 | 5.820 | 92.878 | 0.0206 | 0.0235 | 32 | 31.71 | 93.618 | 0.0199 | 0.0165 | 3 | 0.267 | 94.204 | |

20 °C dry | 0.0374 | 0.0298 | 14 | 5.158 | 92.867 | 0.0374 | 0.0295 | 11 | 10.95 | 92.869 | 0.0387 | 0.0271 | 10 | 1.292 | 92.655 | |

Iso-polyester (CoRezyn 75-AQ-010) | 50 °C wet | 0.1256 | 0.0917 | 1000 | 28.886 | 81.330 | 0.1256 | 0.0961 | 1000 | 909.09 | 81.333 | 0.1256 | 0.083 | 1000 | 32.490 | 81.322 |

20 °C dry | 0.2996 | 0.206 | 152 | 8.674 | 63.117 | 0.2886 | 0.188 | 381 | 379.32 | 63.975 | 0.0412 | 0.0361 | 144 | 8.769 | 91.630 | |

20 °C wet | 0.0519 | 0.0375 | 5 | 2.051 | 87.675 | 0.0447 | 0.0323 | 16 | 15.54 | 91.052 | 0.04 | 0.0282 | 16 | 1.39 | 91.750 | |

Vinyl ester (Derakane 411C-50) | 50 °C wet | 0.1126 | 0.0825 | 98 | 7.903 | 82.366 | 0.064 | 0.058 | 157 | 152.09 | 88.088 | 0.0424 | 0.0397 | 131 | 7.277 | 91.243 |

20 °C dry | 0.0655 | 0.0694 | 1000 | 28.760 | 86.078 | 0.0479 | 0.0431 | 1000 | 991.07 | 90.894 | 0.0469 | 0.046 | 1000 | 32.327 | 90.113 | |

20 °C wet | 0.0979 | 0.0637 | 133 | 8.342 | 84.611 | 0.0655 | 0.0429 | 416 | 414.17 | 87.879 | 0.0196 | 0.0257 | 327 | 11.168 | 94.131 | |

Vinyl ester (Derakane 8084) | 50 °C wet | 0.019 | 0.0253 | 122 | 8.197 | 94.248 | 0.0186 | 0.0241 | 169 | 158.43 | 94.312 | 0.0184 | 0.0151 | 112 | 8.023 | 94.344 |

20 °C dry | 0.0529 | 0.0524 | 195 | 8.847 | 87.141 | 0.0608 | 0.0554 | 217 | 210.21 | 88.496 | 0.0314 | 0.0293 | 259 | 10.806 | 92.018 | |

20 °C wet | 0.1558 | 0.1268 | 599 | 17.299 | 77.753 | 0.1392 | 0.1144 | 627 | 621.40 | 79.504 | 0.1268 | 0.0759 | 1000 | 32.112 | 81.102 |

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**MDPI and ACS Style**

Ziane, K.; Ilinca, A.; Karganroudi, S.S.; Dimitrova, M. Neural Network Optimization Algorithms to Predict Wind Turbine Blade Fatigue Life under Variable Hygrothermal Conditions. *Eng* **2021**, *2*, 278-295.
https://doi.org/10.3390/eng2030018

**AMA Style**

Ziane K, Ilinca A, Karganroudi SS, Dimitrova M. Neural Network Optimization Algorithms to Predict Wind Turbine Blade Fatigue Life under Variable Hygrothermal Conditions. *Eng*. 2021; 2(3):278-295.
https://doi.org/10.3390/eng2030018

**Chicago/Turabian Style**

Ziane, Khaled, Adrian Ilinca, Sasan Sattarpanah Karganroudi, and Mariya Dimitrova. 2021. "Neural Network Optimization Algorithms to Predict Wind Turbine Blade Fatigue Life under Variable Hygrothermal Conditions" *Eng* 2, no. 3: 278-295.
https://doi.org/10.3390/eng2030018