# GA-BP Neural Network-Based Strain Prediction in Full-Scale Static Testing of Wind Turbine Blades

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## Abstract

**:**

## 1. Introduction

## 2. The Method of GA-BPNN

#### 2.1. The Principles of BPNN

_{j}|j = 1,2,…,M} and the dependent variable Y was established using the improved neural network algorithm. Sample X

_{1},…,X

_{M}was used as the input value and Y

_{1},…,Y

_{L}was the output value for training the dependent variable prediction model. The BPNN builds the network structure of the strain–prediction model for the full-scale wind turbine blade static testing, as shown in Figure 1.

#### 2.2. The Principles of GA-BPNN

_{1}, the chromosome x

_{1}is selected. If q

_{k–}

_{1}< r ≤ q

_{k}(2 ≤ k ≤ N), the chromosome x

_{k}is selected, and q

_{i}is called the accumulation probability of chromosome x

_{i}(i = 1,2,…,n), and its calculation formula is as shown in Equation (1). (4) Cross: two chromosomes are selected according to a certain probability, one or more points in the two chromosomes are exchanged with each other randomly to obtain two new chromosomes. (5) Variation: according to a certain mutation probability, in the binary coding of chromosomes, 1 becomes 0, and 0 becomes 1. This operation can effectively avoid premature convergence in the evolution process and thus falling into a local optimum. (6) Repeat steps (3), (4), and (5) until the number of evolutions is reached, then the optimal weights as well as the thresholds will be obtained.

## 3. Full-Scale Static Test of Wind Turbine Blades

#### 3.1. The Wind Turbine Blade Specification

#### 3.2. Testing Procedure

## 4. GA-BPNN-Based Strain Prediction in Full-Scale Static Testing

#### 4.1. GA-BPNN-Based Strain Prediction for the Center of Suction Side

#### 4.2. GA-BPNN-Based Strain Prediction for the Trailing Edge

## 5. Conclusions

- (1)
- Taking advantage of the neural network in dealing with complex problems, this paper established a strain–predictive GA-BPNN model for the center and the trailing edge of the suction side based on the full-scale static testing results of a certain wind turbine blade.
- (2)
- The GA-BPNN had a better performance on strain prediction in full-scale static testing of wind turbine blades than the BPNN. In the training process, the relevant regression coefficient trained by GA-BPNN was closer to 1 than the BPNN. In the test process, all the average errors of GA-BPNN were smaller than those of the BPNN. In the prediction process, the values analyzed by the GA-BPNN were closer to the theoretical values (simulation test values) than those analyzed by the BPNN.
- (3)
- The strain of unmeasured points at the center and the trailing edge of the suction side were predicted by strain–predictive BPNN model, respectively. For strain prediction of the points at the center of the suction side, the relative error rate of the test sample output was within 6.5%. While for strain prediction of the points at the trailing edge of the suction side, the relative error rate of the test sample output was within 18%. Compared with the prediction results of the center of suction side, the error of the trailing edge was relatively larger. For the trailing edge is the faying surface of suction side and pressure side, and the strain is influenced by more factors such as binder type, binder parameters, physical dimension, etc., thus, more inputs are needed to get a more accurate prediction.
- (4)
- The unmeasured points at 33.00 m, 42.00 m, 48.00 m, 52.00 m, 54.00 m, 56.00 m, 58.00 m, 63.00 m, and 65.00 m from the root of the blade were chosen to predict their strain using the BPNN. Comparing the prediction results with the ANSYS simulation data, both the BPNN and GA-BPNN had a high accuracy in predicting the strain, and the GA-BPNN had a smaller error. Thus, the GA-BPNN is more suitable for strain prediction of wind turbine blade static testing.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**(

**a**) Regression curve of the BPNN model error; (

**b**) regression curve of the GA-BPNN model error; (

**c**) GA iteration curve graph of mean square error; (

**d**) GA iteration curve graph of fitness function value. (

**e**) The fitting results comparison of the training set about BPNN; (

**f**) The fitting results comparison of the training set about GA-BPNN.

**Figure 9.**(

**a**) Regression curve of the BPNN model error; (

**b**) regression curve of the GA-BPNN model error; (

**c**) GA-iteration curve graph of mean square error; (

**d**) GA-iteration curve graph of fitness function value. (

**e**) The fitting results comparison of the training set about BPNN; (

**f**) The fitting results comparison of the training set about GA-BPNN.

Items | The Distance of Loading Positions from the Blade Root (m) | ||||
---|---|---|---|---|---|

18.0 | 30.0 | 42.0 | 50.0 | 60.0 | |

target load (kN) | 94.6 | 143.0 | 59.8 | 104.4 | 68.0 |

The Applied Load (kN) | |||||
---|---|---|---|---|---|

The Distance of Loading Positions from the Blade Root (m) | 0 | 40% | 60% | 80% | 100% |

18.00 | 0 | 37.85 | 57.48 | 75.76 | 94.74 |

30.00 | 0 | 57.42 | 86.17 | 114.60 | 143.15 |

42.00 | 0 | 24.09 | 35.85 | 48.16 | 60.15 |

50.00 | 0 | 42.34 | 62.75 | 83.04 | 104.67 |

60.00 | 0 | 27.25 | 40.98 | 54.51 | 68.07 |

Items | The Location of Strain Gauge | Load (kN) | The Distanceto the Blade Root (m) | ||||

F1 | F2 | F3 | F4 | F5 | l1 | ||

1 | 2000 | 37.85 | 57.42 | 24.09 | 42.34 | 27.25 | 0 |

2 | 6000 | 57.48 | 86.17 | 35.85 | 62.75 | 40.98 | 1.16 |

3 | 9000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

… | … | … | … | … | … | … | … |

… | … | … | … | … | … | … | … |

50 | 48,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

Items | The Displacement of Loading Positions (m) | ||||||

s1 | s2 | s3 | s4 | s5 | s6 | s7 | |

1 | 159 | 755 | 2159 | 3717 | 6384 | 7900 | −1186 |

2 | 264 | 1158 | 3257 | 5596 | 9605 | 11,876 | −1898 |

3 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −2383 |

… | … | … | … | … | … | … | … |

… | … | … | … | … | … | … | … |

50 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −2971 |

Items | The Location of Strain Gauge | Load (kN) | The Distanceto the Blade Root (m) | ||||

F1 | F2 | F3 | F4 | F5 | l1 | ||

1 | 2000 | 57.48 | 86.17 | 35.85 | 62.75 | 40.98 | 1.16 |

2 | 15,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

3 | 24,000 | 37.85 | 57.42 | 24.09 | 42.34 | 27.25 | 0 |

4 | 36,000 | 94.74 | 143.15 | 60.15 | 104.67 | 68.07 | 8.51 |

5 | 51,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

6 | 33,000 | 57.48 | 86.17 | 35.85 | 62.75 | 40.98 | 1.16 |

Items | The Displacement of Loading Positions (m) | ||||||

s1 | s2 | s3 | s4 | s5 | s6 | s7 | |

1 | 264 | 1158 | 3257 | 5596 | 9605 | 11,876 | −1790 |

2 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −2748 |

3 | 159 | 755 | 2159 | 3717 | 6384 | 7900 | −1964 |

4 | 477 | 1976 | 5490 | 9405 | 16,019 | 19,741 | −4849 |

5 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −2490 |

6 | 264 | 1158 | 3257 | 5596 | 9605 | 11,876 | −3047 |

−1.624 | −0.512 | −0.417 | −0.084 | −0.001 | 0.320 | 0.260 | 0.712 | 0.008 | 0.111 | −0.382 | −0.780 | 0.660 |

−0.444 | −0.136 | 0.609 | −0.492 | −0.509 | −0.182 | −0.598 | −0.761 | −0.186 | −0.243 | −0.786 | −0.296 | −0.198 |

0.752 | 0.050 | −0.181 | 0.496 | 0.566 | 0.578 | −0.792 | −0.285 | −0.212 | −0.684 | −0.236 | −0.142 | −0.203 |

0.958 | −0.057 | 0.577 | −0.194 | 0.442 | 0.591 | −0.815 | −0.558 | −0.676 | 0.162 | 0.675 | 0.206 | 0.091 |

−0.635 | −0.264 | 0.651 | −0.449 | 0.632 | 0.333 | 0.226 | 0.340 | −0.109 | −0.219 | 0.298 | −0.844 | 0.505 |

0.217 | 0.182 | 0.478 | −0.769 | 0.072 | −0.530 | 0.283 | −0.203 | −0.106 | 0.436 | 0.570 | −0.286 | −0.373 |

1.450 | −0.685 | 0.204 | 0.173 | 0.117 | −0.745 | −0.620 | 0.052 | 0.535 | −0.263 | 0.598 | −0.487 | −0.182 |

−3.288 | 0.581 | −0.291 | −0.754 | −0.506 | 0.911 | 0.032 | −0.245 | 0.185 | −0.532 | −0.308 | 0.648 | 0.230 |

−2.997 | 0.292 | −0.991 | −0.479 | 0.125 | 0.2931 | −0.114 | −0.357 | −0.606 | 1.1067 | −0.465 | 0.768 | 0.473 |

0.188 | −0.658 | −0.602 | −0.798 | 0.145 | −1.308 | −0.993 | −0.486 | −0.466 | −1.517 | 0.0098 | 0.063 | 0.233 |

0.115 | 0.649 | −0.239 | −0.401 | 0.574 | −0.624 | −0.898 | −0.949 | −0.045 | 0.681 | −0.834 | −0.593 | −0.559 |

−0.840 | 0.154 | −0.366 | 1.023 | 0.784 | −0.651 | −0.378 | 0.3140 | 0.922 | 0.233 | −0.807 | −0.184 | −0.164 |

−2.537 | 0.575 | −0.386 | 0.625 | 0.151 | −0.056 | −0.062 | −0.721 | −0.067 | −0.654 | 0.579 | −0.715 | 0.440 |

0.415 | 1.046 | 0.047 | −0.508 | 1.002 | −0.638 | −0.023 | −0.274 | −0.669 | −0.590 | 0.483 | 0.112 | 0.636 |

Items | The Location of Strain Gauge | Load (kN) | The Distanceto the Blade Root (m) | ||||

F1 | F2 | F3 | F4 | F5 | l1 | ||

1 | 2000 | 37.85 | 57.42 | 24.09 | 42.34 | 27.25 | 0 |

2 | 6000 | 57.48 | 86.17 | 35.85 | 62.75 | 40.98 | 1.16 |

3 | 9000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

… | … | … | … | … | … | … | … |

… | … | … | … | … | … | … | … |

50 | 48,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

Items | The Displacement of Loading Positions (m) | ||||||

s1 | s2 | s3 | s4 | s5 | s6 | s7 | |

1 | 159 | 755 | 2159 | 3717 | 6384 | 7900 | −146 |

2 | 264 | 1158 | 3257 | 5596 | 9605 | 11,876 | −418 |

3 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −497 |

… | … | … | … | … | … | … | … |

… | … | … | … | … | … | … | … |

50 | 477 | 1976 | 5490 | 9405 | 16,019 | 19,741 | −396 |

Items | The Location of Strain Gauge | Load (kN) | The Distanceto the Blade Root (m) | ||||

F1 | F2 | F3 | F4 | F5 | l1 | ||

1 | 24,000 | 37.85 | 57.42 | 24.09 | 42.34 | 27.25 | 0 |

2 | 21,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

3 | 33,000 | 37.85 | 57.42 | 24.09 | 42.34 | 27.25 | 0 |

4 | 36,000 | 94.74 | 143.15 | 60.15 | 104.67 | 68.07 | 8.51 |

5 | 21,000 | 94.74 | 143.15 | 60.15 | 104.67 | 68.07 | 8.51 |

6 | 24,000 | 75.76 | 114.6 | 48.16 | 83.04 | 54.51 | 5.69 |

Items | The Displacement of Loading Positions (m) | ||||||

s1 | s2 | s3 | s4 | s5 | s6 | s7 | |

1 | 159 | 755 | 2159 | 3717 | 6384 | 7900 | −189 |

2 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −532 |

3 | 159 | 755 | 2159 | 3717 | 6384 | 7900 | −147 |

4 | 477 | 1976 | 5490 | 9405 | 16,019 | 19,741 | −652 |

5 | 477 | 1976 | 5490 | 9405 | 16,019 | 19,741 | −717 |

6 | 368 | 1557 | 4350 | 7469 | 12,773 | 15,770 | −598 |

0.182 | 0.134 | −0.272 | −1.017 | −1.216 | −0.874 | −1.074 | −0.827 | −0.489 | −0.865 | −0.668 | 0.041 | 0.167 |

−0.216 | 1.769 | 2.422 | 1.784 | 1.773 | 2.682 | 1.436 | 1.961 | 1.403 | 1.449 | 1.070 | 1.780 | 2.273 |

0.0524 | −0.305 | 0.762 | −0.029 | −0.317 | −0.078 | −0.368 | 0.324 | −0.364 | 0.009 | −0.116 | 0.725 | −0.416 |

−0.317 | 2.778 | 1.776 | 3.031 | 1.922 | 3.017 | 2.795 | 2.940 | 2.743 | 2.104 | 2.824 | 2.203 | 2.066 |

0.115 | −1.131 | −0.772 | −0.829 | −0.806 | −0.417 | −1.82 | −0.654 | −1.715 | −1.022 | −1.058 | −0.487 | −1.129 |

41.803 | −0.991 | −1.52 | −0.70 | 2.601 | −1.894 | 0.510 | 1.772 | 1.574 | 0.787 | 0.038 | −1.27 | −1.056 |

0.763 | −0.671 | −0.05 | 0.95 | −1.021 | −0.596 | 11.960 | −0.777 | 0.365 | −0.601 | −1.262 | −1.40 | 0.277 |

−1.333 | 2.607 | 1.381 | 1.42 | 3.559 | 0.850 | −15.57 | 3.153 | 3.654 | 2.847 | 2.374 | 3.27 | 2.519 |

−28.76 | 5.738 | 4.997 | 4.46 | 6.254 | 5.188 | 5.005 | 5.217 | 6.533 | 5.527 | 5.109 | 4.64 | 5.508 |

1.322 | 3.529 | 3.600 | 2.85 | −8.248 | 3.232 | 3.252 | −4.561 | −4.716 | −3.261 | −2.641 | 1.17 | 1.212 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Z.; Liu, X.; Wang, K.; Liang, Z.; Correia, J.A.F.O.; De Jesus, A.M.P.
GA-BP Neural Network-Based Strain Prediction in Full-Scale Static Testing of Wind Turbine Blades. *Energies* **2019**, *12*, 1026.
https://doi.org/10.3390/en12061026

**AMA Style**

Liu Z, Liu X, Wang K, Liang Z, Correia JAFO, De Jesus AMP.
GA-BP Neural Network-Based Strain Prediction in Full-Scale Static Testing of Wind Turbine Blades. *Energies*. 2019; 12(6):1026.
https://doi.org/10.3390/en12061026

**Chicago/Turabian Style**

Liu, Zheng, Xin Liu, Kan Wang, Zhongwei Liang, José A.F.O. Correia, and Abílio M.P. De Jesus.
2019. "GA-BP Neural Network-Based Strain Prediction in Full-Scale Static Testing of Wind Turbine Blades" *Energies* 12, no. 6: 1026.
https://doi.org/10.3390/en12061026