As a critical structure of aerospace equipment, aluminum alloy stiffened plate will influence the stability of spacecraft in orbit and the normal operation of the system. In this study, a GWO-ELM algorithm-based impact damage identification method is proposed for aluminum alloy stiffened panels to monitor and evaluate the damage condition of such stiffened panels of spacecraft. Firstly, together with numerical simulation, the experimental simulation to obtain the damage acoustic emission signals of aluminum alloy reinforced panels is performed, to establish the damage data. Subsequently, the amplitude-frequency characteristics of impact damage signals are extracted and put into an extreme learning machine (ELM) model to identify the impact location and damage degree, and the Gray Wolf Optimization (GWO) algorithm is employed to update the weight parameters of the model. Finally, experiments are conducted on the irregular aluminum alloy stiffened plate with the size of 2200 mm × 500 mm × 10 mm, the identification accuracy of impact position and damage degree is 98.90% and 99.55% in 68 test areas, respectively. Comparative experiments with ELM and backpropagation neural networks (BPNN) demonstrate that the impact damage identification of aluminum alloy stiffened plate based on GWO-ELM algorithm can serve as an effective way to monitor spacecraft structural damage.

In recent years, the rapidly developing aerospace industry and activities have led to a surge in space debris [

Time difference localization and intelligent algorithm are employed to identify the impact location [

The booming computer technology witnesses prominent progress in intelligent algorithms [

Considering the complex characteristics of impact stress wave in aluminum alloy reinforced structure, the traditional ways of damage identification could not be accurate, following the insufficient stability and poor classification effect due to the randomly generated weights in the standard ELM algorithm-based methodology. To solve this problem, an impact damage identification for aluminum alloy stiffened plate based on GWO-ELM algorithm is proposed. Firstly, an aluminum alloy stiffened plate was employed as the carrier, and the acquisition system of impact damage signal was established by combining the ground simulation with the numerical one. Afterwards, based on the analysis of the propagation characteristics of impact acoustic emission signal, the acquired signals were utilized to establish the impact damage sample library. Finally, the parameters of the ELM model were optimized with the Gray Wolf algorithm, and the obtained impact damage intelligent identification model of the aluminum alloy stiffened plate was verified for performance via experiments.

As for the framework of this paper,

The complex structure of aluminum alloy stiffened plate will make changes in impact stress wave, such as reflection, scattering, attenuation and superposition. Therefore, to understand the propagation characteristics of stress waves in the aluminum alloy stiffened plate, the impact simulation model of the spacecraft bulkhead aluminum alloy stiffened plate was established based on ANSYS, as depicted in

Parameter name | Value | Unit | Parameter name | Value | Unit |
---|---|---|---|---|---|

Plate material | Al 2017 | Stiffener height | 5 | mm | |

Plate density | 2.79 | g/cm^{3} |
Stiffener width | 4/7/15/18/25/37 | mm |

Plate length | 2200 | mm | Projectile material | Al 7075 | |

Plate width | 500 | mm | Projectile density | 2.82 | g/cm^{3} |

Plate thickness | 10 | mm | Finite element | 3D164 unit |

As the impact velocity increases, the damage by the projectile to aluminum alloy stiffened plate changes from cratering damage to perforation damage, as illustrated in

Extreme learning machine serves as an algorithm to solve single hidden layer feedforward neural network [

For the single hidden layer feedforward neural network, assuming the length of the sample data set as

Assume that the connection weight between the hidden layer and the output layer is

The above N equations are pieced together into a matrix form, denoted as:

wherein,

For the desired output value

According to the least square method, the parameter

Therefore, a given test sample

In 2014, Mirjalili et al. firstly proposed Gray Wolf Optimization algorithm, which works by means of the imitation of the predation process of the strictly hierarchical natural gray wolf population. The gray wolf population involves four grades, namely

wherein,

After obtaining the relative distance, the individual will update the position according to

Based on

After the location model is obtained, the position of

To optimize the performance of the algorithm, the gray wolf

where,

To summarize the above mentioned analysis, the impact damage identification algorithm flow of aluminum alloy stiffened plate based on GWO-ELM can be depicted as

(1) The aluminum alloy stiffened plate of the spacecraft cabin wall has 68 regions for identification. An electric simulation gun launched the plastic projectile with a diameter of 7 mm to simulate low-speed impact, and the generated acoustic emission signals were collected by the acoustic emission acquisition system as the original non-damage signals. By utilizing ANSYS software and Lagrange algorithm, the simulation model of aluminum alloy stiffened plate of a spacecraft bulkhead was established, and the original signals of cratering and perforation damage were obtained.

(2) The amplitude-frequency of the original signals obtained by FFT transform was applied to construct the data sample set, including the training set and test set with the ratio of 7:3.

(3) Depending on the training set and GWO algorithm, the impact damage identification model of the aluminum alloy stiffened plate was established based on GWO-ELM.

(4) The performance of damage identification model was verified in the test set.

(5) The algorithm outstood ELM and BPNN methods.

Impact damage signal acquisition systems have low-speed impact system as well as the high-speed one, as shown in

The high-speed impact signal acquisition system obtains the impact acoustic emission signals by numerical simulation under cratering and perforation. Although more accurate high-speed impact acoustic emission signal can be acquired by the two-stage light gas gun in a high-speed impact experiment, it is challenging to design the damage data set due to the high expenditure. Target size is limited by the target cabin size, and it is difficult for projectile velocity and trajectory to accurately control, and experimental process to measure. Therefore, the selected data simulation methods are employed to achieve accurately control on experimental parameters and various impact conditions. Based on the numerical simulation platform of NVIDA Tesla V100 high performance computing GPU, the ANSYS is utilized to establish the numerical simulation model of aluminum alloy stiffened plate to simulate the process of cratering and perforation damage.

Taking the low-speed impact experiment as an example, the electric gun is adopted to shoot 68 areas on the aluminum alloy stiffened plate (as shown in

(1) Determine the first impact area

(2) Carry out the same test on the 5 points in the second impact area

(3) The data acquisition process of cratering and perforation in high-speed impact is continuously carried out to the low-speed one, and 51000 groups of cratering and perforation data are obtained, respectively.

The data samples of each damage degree are divided into training sets and test sets in a ratio of 7:3, namely 35700 groups and 15300 groups, respectively, as listed in

Degree of damage | Training set | Test set | Total |
---|---|---|---|

No damage | 35700 | 15300 | 51000 |

Cratering damage | 35700 | 15300 | 51000 |

Perforation damage | 35700 | 15300 | 51000 |

Total | 107100 | 45900 | 153000 |

Under three damage degrees, the FFT transform is to convert time-domain impact signals into frequency-domain signals. To clearly explore the relationship of amplitude-frequency with impact areas,

To estimate the frequency characteristics with different damage degrees in the same impact area, the amplitude-frequency of the three damage degrees is represented in the same coordinate system. The amplitude-frequency characteristics of area 1, 32 and 65 are depicted in

The optimizing idea of the Gray Wolf algorithm is to initialize ELM from the population parameter and avoid the limitation of ELM, in order to make the model with randomly generated initial weight matrices and bias matrix. The wolves are updated by spatial position error feedback to achieve the continuously optimized fitness of the Gray Wolf until getting a qualified global optimal solution, that is, obtaining the optimal weight matrix and deviation matrix of ELM impact damage identification, and the optimal damage identification model.

(1) Parameter initialization. The coordinate and displacement parameters of the Gray Wolf population are randomly set, following a random initialization of the weight matrix and bias matrix of ELM.

(2) Fitness calculation and prey search. The fitness value is calculated as the training error of the initial ELM network, and the lowest error network object rounded up as the prey.

(3) Update of ELM weights. The weights of ELM are updated according to the prey rounded up by gray wolves, followed by retraining of the ELM network.

(4) Iterative update. The new network is rounded up as the new prey object, and the calculated fitness value is returning to step (2). If the updated fitness value is below the previous generation, step (3) is performed. The update is stopped, when the fitness value is below the set value or the number of iterations reaches the maximum.

(5) Finally, test the trained ELM model to identify the location and degree of impact on the aluminum alloy stiffened plate.

After the intelligent damage identification model was established, the damage identification of the model became more accurate after optimizing such parameters as the activation function, the hidden layer and the model parameters (weight matrix, bias matrix, etc.). First, the experiment estimated the activation function and hidden layer, taking three damage degrees of aluminum alloy stiffened plates and the amplitude and frequency characteristics of 68 impact areas as the input. The experimental procedure and results are shown in

Activation function | Hidden layer | |||||
---|---|---|---|---|---|---|

Sigmoid | 25 | 50 | 75 | 100 | 150 | 200 |

Sine | ||||||

Hard limit |

According to

Further, the Gray Wolf algorithm is adopted to optimize the model parameters, with the Wolf size of the GWO algorithm set to 30.

In terms of impact location,

Model | Impact location | Degree of damage | ||||
---|---|---|---|---|---|---|

Precision | Recall | F1-score | Precision | Recall | F1-score | |

ELM | 93.37% | 93.37% | 93.34% | 99.12% | 99.12% | 99.11% |

BP | 95.28% | 95.28% | 95.27% | 99.55% | 99.55% | 99.55% |

GWO-ELM | 98.90% | 98.90% | 98.88% | 99.55% | 99.55% | 99.55% |

As

To effectively monitor the engineering requirements of spacecraft structure, reverse the inaccurate traditional damage identification methods with the complex impact stress waves of aluminum alloy reinforced structures, and optimize ELM algorithm-generated random weights and its instability and poor classification effect, an impact damage identification method based on GWO-ELM for aluminum alloy stiffened plate is proposed. This method works in the impact location and damage degree identification of the ELM model, where the impact damage characteristics are extracted from the model, and its weight parameters are optimized by the GWO algorithm. The experimental results show the GWO-ELM model’s advantages to ELM and BP neural network in identification accuracy, with a higher accuracy of 5.53% and 3.62%, respectively. For damage degree identification, GWO-ELM and BP achieve the similar accuracy, but the GWO-ELM model overran ELM by 0.43%. The comparison shows that the GWO-ELM model is a practical with considerable generalization capability, which makes impact damage identification stable.

None.

This work was supported by National Key Research and Development Project (2020YFE0204900), National Natural Science Foundation of China (Grant Nos. 61903224, 62073193, 61873333), and Key Research and Development Plan of Shandong Province (Grant Nos. 2019TSLH0301, 2021CXGC010204).

The authors confirm contribution to the paper as follows: study conception and design: Wei Li, Benjian Zou, Faye Zhang; data collection: Benjian Zou; analysis and interpretation of results: Wei Li, Yuxiang Luo, Mingshun Jiang, Lei Jia; draft manuscript preparation: Wei Li, Ning Yang. All authors reviewed the results and approved the final version of the manuscript.

The authors confirm that the data supporting the findings of this study are available within the article.

The authors declare that they have no conflicts of interest to report regarding the present study.