A structural displacement field reconstruction method is proposed to aim at the problems of deformation monitoring and displacement field reconstruction of flexible plate-like structures in the aerospace field. This method combines the deep neural network model of the cross-layer connection structure with the fiber grating sensor network. This paper first introduces the principle of strain detection of fiber grating sensor, studies the mapping relationship between strain and displacement, and proposes a strain-displacement conversion model based on an improved neural network. Then the intelligent structure deformation monitoring system is built. By controlling the stepping distance of the motor to produce different deformations of the plate structure, the strain information and real displacement information are obtained based on the high-density fiber grating sensor network and the dial indicator array. Finally, based on the deformation prediction model obtained by training, the displacement field reconstruction of the structure under different deformation states is realized. Experimental results show that the mean absolute error of the deformation of the measuring points obtained by this method is less than 0.032 mm. This method is feasible in theory and practice and can be applied to the deformation monitoring of aerospace vehicle structures.

The flexible plate structure is widely used in the aerospace field. This structure has the characteristics of large span, lightweight, and low rigidity [

At present, scholars have carried out certain researches on morphological reconstruction methods of large-scale flexible structures. Foss et al. [

Deep learning originates from the research of artificial neural networks. The concept of deep learning was first proposed by Professor Hinton in 2006 [

The aim of the study reported in this paper was to demonstrate the feasibility of the proposed flexible structure reconstruction algorithm based on an improved neural network. The rest of this paper is organized as follows. The next section describes the strain detection principle of the fiber grating sensor, the improved neural network model, and how to establish the mapping relationship between sensor strain and displacement. The following section of the paper then describes a series of structural deformation tests and structural reconstruction model comparison tests employed to demonstrate the feasibility of the reconstruction algorithm proposed in this paper. The last section opens a brief discussion of possible further improvements of the reconstruction model in this paper and concludes some of the advantages of the model.

The grating in the fiber grating sensor can be regarded as a narrow-band filter. When light beams with different wavelengths pass through the fiber grating, they will be reflected if their center wavelength meets the grating conditions; otherwise, they will generally pass through the fiber grating. The peak of the reflected light spectrum appears in the center wavelength region of the grating, which is called the Bragg wavelength [_{eff} represents the effective refractive index of fiber grating; Λ represents refractive index change period; _{B} represents the central wavelength of reflected light.

To avoid the influence of temperature on the experimental results, a temperature sensor was arranged at the edge of the sensor network for temperature compensation when building the sensor network. The experimental data shows that the temperature is constant during the experiment, so the influence of temperature on the central wavelength of the fiber grating can be ignored, and the relationship between the change of the central wavelength and the strain can be obtained as

where _{e} and _{B} are constants. The center wavelength change of the fiber grating has a linear relationship with the axial strain. Therefore, after studying the mapping relationship between strain and displacement, the structural displacement can be calculated by the change in the center wavelength of the sensor.

A depth neural network is a non-linear mapping. The neurons in the same layer are not connected, and the neurons in adjacent network layers are fully connected. Suppose the input data is _{1}, _{2} ⋅ ⋅ ⋅ _{n}}, the output data is _{1}, _{2}, _{3}, ⋅ ⋅ ⋅ , _{m}}. The network structure model is shown in

A neural network needs an activation function to be able to fit any nonlinear function [

The specific structure of the cross-layer connection is shown in

In _{i}(_{i}(_{i}(_{l−2} is the input of the layer _{i}} and {_{i}} are the weight set and bias set when

As can be seen from

Combining

Assuming that the network structure has

After adding the cross-layer structure to the single hidden layer neural network structure, the cross-layer structure part only needs to learn the difference between the hidden layer output of the single hidden layer neural network structure and the cross-layer structure output.

The output value of the last layer is

Based on the above formula, the relationship between the input and output of the improved neural network model can be expressed as

Suppose the cost function of the network model is_{L} is the number of neurons in the last layer.

The essence of the neural network learning process is to find the appropriate parameters to minimize the cost function. The Adam algorithm uses the first-order momentum to adjust the update direction of the parameters and also uses the second-order momentum to adjust the learning rate of different parameters [

According to the chain derivation rule, the partial derivative of the total error to the weight of the cross-layer structure can be obtained_{l}_{+2} represents the error generated by the output of the

In the backpropagation, the gradient descent method is used to update the weight and bias of each layer, so that the error between the output of the network model and the true value is as small as possible.

In

Taking the plate structure as the experimental object, the displacement field of this structure subjected to external load is reconstructed. The experimental flowchart is shown in

The model diagram of the intelligent structural deformation monitoring system built in this experiment is shown in

Carry out a loading test on the plate structure, as shown in

Serial number | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Coordinates for step loading (mm) | (330, 330) | Null | (440, 440) | (330, 330) |

Coordinates for maximum loading (mm) | Null | (440, 440) | (330, 330) | (440, 440) |

Three sets of experiments were carried out for each loading method, and a total of 120 sample data were collected. The input of the reconstruction model is the structural strain information, and the output is the deformation of the displacement measurement point of the structure. The strain information of the structure can be directly calculated from the center wavelength offset of the sensor network. Some experimental data of the center wavelength offset are shown in

The network model structure in this paper is composed of a single hidden layer neural network and residual structures. The residual structure is located between the hidden layer and the output layer of the single hidden layer neural network. The network structure is shown in

In order to evaluate the practical effect of the proposed reconstruction model, the mean absolute error (

_{ij} is the predicted value output by the model and

In this paper, the initial value of the number of hidden layer nodes is set to 10, and the number of hidden layer nodes is increased by 10 before the next experiment. To prevent the contingency of the experimental results, each experiment was performed 10 times, and the average of the 10 results was taken as the final result of the experiment. The experimental results are shown in

Number of hidden layer nodes | ||
---|---|---|

10 | 0.0383 | 0.0037 |

20 | 0.0285 | 0.0027 |

30 | 0.0273 | 0.0029 |

40 | 0.0252 | 0.0026 |

50 | 0.0226 | 0.0025 |

60 | 0.0236 | 0.0026 |

70 | 0.0242 | 0.0026 |

80 | 0.0229 | 0.0026 |

90 | 0.0231 | 0.0026 |

100 | 0.0228 | 0.0026 |

Each group of experimental data is randomly divided into training data and test data at a ratio of 4:1, and there is no duplicate data. In order to observe the reconstruction effect of the improved neural network model proposed in this paper, compare it with decision tree regression and conventional neural network. Classification And Regression Tree (CART) is a kind of decision tree, which can be used to create a classification tree, a regression tree, and a model tree. In this paper, we use CART to build a regression tree with structural strain as input and displacement as output. The variation of the average error value obtained by CART with the depth of the tree is shown in

In order to verify the effectiveness and stability of the improved neural network proposed in this paper, the three structural reconstruction methods were trained 50 times, respectively. The network structure is shown in

Algorithm model | ||
---|---|---|

CART | 0.0256 | 0.0061 |

Normal neural network | 0.0255 | 0.0028 |

Cross-layer neural network | 0.0223 | 0.0025 |

Define the floating ratio _{max} is the maximum error of the sample and

It can be seen from

The test data is reconstructed based on three different reconstruction models, and the inversion effect of the displacement field of the structure is experimentally verified.

Different loading modes of loads | Algorithm model | |||
---|---|---|---|---|

1 | CART | 0.0355 | 0.0198 | 3.31 |

Normal network | 0.0369 | 0.0076 | 4.26 | |

Cross-layer network | 0.0312 | 0.0077 | 3.65 | |

2 | CART | 0.0202 | 0.0016 | 12.19 |

Normal network | 0.0192 | 0.001 | 13.40 | |

Cross-layer network | 0.0179 | 0.001 | 10.08 | |

3 | CART | 0.0287 | 0.0016 | 2.47 |

Normal network | 0.0196 | 0.0006 | 1.61 | |

Cross-layer network | 0.0151 | 0.0003 | 1.20 | |

4 | CART | 0.0217 | 0.0009 | 1.51 |

Normal network | 0.0292 | 0.0016 | 1.92 | |

Cross-layer network | 0.0229 | 0.0012 | 1.46 |

As shown in

In this paper, an intelligent structural deformation monitoring platform based on the fiber Bragg grating sensor array is built for the flat structure on the aerospace vehicle, and a cross-layer connection deep neural network reconstruction model is proposed. The structure deformation experiments under different stresses are carried out on the platform, and the structure displacement field is reconstructed using the proposed reconstruction model. The novelty of this paper is that the idea of residual learning is applied to the conventional fully connected neural network to obtain an improved neural network structure, and this model is applied to the reconstruction of flexible structures.

Compared with the other traditional structural reconstruction models introduced in the introduction, the reconstruction model proposed in this paper establishes the mapping relationship between structural strain and displacement, and obtains displacement information directly from the collected strain information, without the need to establish complex conversion equations. The experimental results show that the reconstruction algorithm obtained by improving the conventional fully connected neural network based on the idea of residual learning is better than the conventional neural network and decision tree regression algorithm. As shown in the experimental results in

Based on the conventional neural network, this paper proposes a cross-layer connection neural network reconstruction model based on the idea of residual learning. The reconstruction effect of the cross-layer network model is better than that of CART and conventional neural network, and we can conclude that it has the following advantages:

(1) Higher accuracy and better stability. Compared with the conventional neural network, due to the addition of a cross-layer structure, the learning of the entire network structure is more accessible, and the reconstruction accuracy is improved. In addition, the stability of the learning ability is also improved.

(2) Wider scope of application. The improved deep neural network effectively solves network degradation caused by the superposition of network layers after adding a cross-layer structure. When the measured structure is broad and many fiber Bragg grating sensors are needed for measurement, a more complex network structure is needed to learn the correspondence between strain and displacement. Compared with the conventional neural network structure, the cross-layer connection network structure proposed in this paper is more applicable.

The authors are grateful for the financial support provided by National Natural Science Foundation of China, National Key Research and Development Project and Key Research and Development Plan of Shandong Province.