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Abstract
In order to improve the safety of spacecraft, the research on artificial neural network and digital twin technology based on, to our best knowledge, a novel fiber Bragg grating (FBG) sensor array is proposed for intelligent sensing monitoring of spacecraft on-orbit collisions. Femtosecond FBG arrays were fabricated on the novel oxide-doped fiber by point-by-point writing technique. The femtosecond FBG is analyzed using the time-dependent perturbation theory of quantum mechanics. The FBG array can achieve high-temperature measurement of 1100 °C and large strain measurement of 15000 µε. The sensing arrays were deployed on the surface of the spacecraft. Constructed the multi-layer perceptron neural network structure and convolutional neural network structure. 1200 samples were trained. Conducted model accuracy testing. The accuracy rate is above 98%, and accuracy verification has been implemented. The digital twin model was designed based on various data such as strain and temperature of the spacecraft structure under impact monitored by FBG sensors. A precise mapping has been formed between the physical entities of spacecraft and digital twins. Empower spacecraft with functions such as self-monitoring, judgment, and response. To ensure the stable and safe operation of spacecraft.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the expansion of human space exploration activities, spacecraft are always facing the risk of encountering space junk, tiny space particles, space debris, and other impacts when they are in orbit. In space attack and defense, it faces the attack of various laser kinetic energy weapons. These factors can lead to fatigue, cracks, damage, and other catastrophic consequences for spacecraft structures [1–4]. If active real-time condition monitoring can be conducted during the service period, the early warnings can be given before the occurrence of major accidents [5,6].
In order to achieve real-time monitoring of spacecraft damage events and acquire impact damage signals, a variety of impact damage signal acquisition methods are studied [7,8]. Sensors such as resistance strain sensors, piezoelectric ceramic sensors and piezoelectric film sensors are widely used to obtain the impact strain signal. Ciambella et al. [9] used a resistance strain sensor to sense the strain signal. The modal curvature variation of the structure is obtained from the equation of motion of the beam. Due to the complex and ever-changing engineering application environment, strain gauges are prone to detachment, resulting in the failure of measurement points and reduced stability. Kim et al. [10] developed a piezoelectric film sensor capable of monitoring the fatigue damage, and evaluated the sensing performance. After long-term service, it is easy to fatigue and there may be problems such as data failure of measuring points. Liu et al. [11] used a piezoelectric ceramic sensor network to detect the manufacturing process of carbon fiber reinforced material plates and effectively monitor the life cycle of the material plates. Fu et al. [12] proposed an impact location method based on the intersection of hyperbolas.Other existing on-orbit sensing technologies mainly include acoustic emission, acceleration, thermal imaging, microwave emission, and surface optical photography according to different sensitive methods [13–17]. At present, the technology of structural health monitoring for spacecraft or aircraft cannot be applied to all monitoring objects [18–20]. Fiber Bragg grating (FBG) sensors are often used to monitor of the strain field and temperature field of the structure, and then monitor the operation state of the structure. Due to its small size, light weight and high sensitivity, FBG can be embedded in the spacecraft structure or pasted on the surface of the material for data acquisition [21–23]. By combining the feature changes of interferometric spectra with artificial neural network algorithm models, high-precision demodulation of Fabry-Perot interferometric sensors can be achieved. This system is expected to provide high-performance, cost-effective, and reliable solutions for practical engineering applications [24,25].
Most of this technology can only locate the impact source, making it is difficult to determine the degree of damage caused by the impact. There is still a lack of targeted research on the problem of optical fiber thermal strain monitoring of spacecraft structures, especially for the accuracy of strain and temperature decoupling under large strain and high temperature. Artificial neural network have shown some charm in damage identification, while the traditional artificial feature selection method will produce complexity and uncertainty [26,27]. Chen et al. introduced a high-performance and low-cost wavelength demodulation method for fiber optic grating sensors. Effectively expanding the wavelength demodulation range of the modulation system and greatly optimizing the wavelength demodulation error [28].
In order to address the above problems, the high performance grating sensor network combined with artificial neural network analysis and spacecraft digital twin is proposed to monitor the on-orbit operation status of spacecraft. The femtosecond FBG sensor arrays for high temperature and large strain measurement are designed. The neural network algorithm model is built, and the classification and identification of damage characteristics are analyzed. The modeling process of the structural damage identification model is effectively improved. The digital twin model of spacecraft is studied, and the mapping model of digital twin is established. Through the femtosecond FBG sensing arrays, the virtual model and the real object are interconnected. It address the issue of intelligent identification of spacecraft damage in orbit, and has broad prospects in aerospace health monitoring.
It is mainly used to monitor the structural fatigue, crack, buckling, material property degradation and damage of spacecraft structural vibration, mission load and solar panels. The stress and deformation of the satellite's load-bearing components, carbon fiber skin, solar panel truss and other structures were monitored. Measured the ambient temperature of various complex instruments and equipment, mission payloads, optical structures, mechanical equipment and materials installed on the star to ensure that the equipment and instruments work within a reasonable temperature range. The analysis of the monitored sensor data provides the spacecraft on-orbit state diagnosis service for the spacecraft platform users.
2. Model establishment and theoretical analysis
2.1 Theoretical analysis of femtosecond FBG sensor
Designed oxide doped optical fibers. The doped materials are mainly Al2O3, Y2O3, and P2O5. Mainly doped in the fiber core. Enable optical fibers to have higher mechanical strength and stronger wear resistance. Simultaneously enhancing the temperature resistance of the fiber core. As shown in Fig. 1(a), the core diameter of the optical fiber is 10 µm. The diameter of the cladding is 125 µm. The numerical aperture is 0.21. The composition of doped optical fibers was analyzed using an electron probe microanalyzer. The results indicate that the core of oxide doped optical fibers contains a mass fraction of 4.9% Y2O3. The mass fraction of Al2O3 accounts for 3.2%. The mass fraction of P2O5 accounts for 2.3%. The effective refractive index of the optical fiber was measured, as shown in Fig. 1(b). The maximum refractive index of the optical fiber is located at the center of the core at 1.464. The refractive index of the cladding is lower than that of the fiber core. The refractive index distribution of the fiber cladding is relatively uniform, but the refractive index of the core shows almost a linear distribution from the center of the fiber to the junction between the core and cladding.
Fig. 1. Oxide doped optical fiber. (a) Cross section of the fiber; (b) Effective refractive index distribution of the fiber.
The theory of femtosecond FBG formation is analyzed by using the method of analogy in quantum theory. The refractive index of the core of the oxide-doped fiber is perturbed by the femtosecond laser direct writing. Time-dependent perturbation theory for writing technique of femtosecond FBG is established. The relationship between the variation of the optical wave field in the fiber core over time is ${e^{j\omega t}}$, and the equation can be expressed as:
When the fiber core is not engraved with femtosecond FBG, the state vector corresponding to the propagation constant ${\beta _k}$ of the light field analyzed is ${|\psi \rangle _k}\textrm{ = }{e^{j{\beta _k}z}}|{{\psi_k}(x,y)} \rangle$. $|{{\psi_k}(x,y)} \rangle$ is the transverse eigenfunction of the state vector, satisfying the eigenequation
When the core of oxide doped fiber is subjected to femtosecond laser engraving, the light field propagating in the femtosecond FBG is a superposition of multiple intrinsic modes of the fiber without refractive index modulation disturbance, which can be expressed as
According to the effect produced by the time-dependent perturbation of the quantum system, the superposition state $|\psi \rangle$ of the femtosecond FBG time-dependent perturbation theory can be evolved into the following equation
The coupled-mode equation for the mode amplitude of the femtosecond FBG can be obtained by the orthogonalization condition of the Hamiltonian as follows:
Time-dependent perturbation theory is relatively simple to calculate and is suitable for approximate solutions of many physical problems. It provides a correction to the energy level of the system, revealing small changes in the physical system. Accurate solutions can be obtained, especially for problems requiring high accuracy calculations. A method for solving the energy eigenstates of a system exactly for systems without a known energy spectrum.
Time-dependent perturbation theory may have convergence problems when dealing with strong perturbations or higher order corrections, and has a narrow range of applicability. What it provides is an approximate solution mainly at smaller perturbations. A huge amount of computation is required. The time-dependent perturbation theory has its validity and limitations. For strong field or long time perturbation, perturbation theory may no longer be applicable. In this case, more complex methods need to be considered.
2.2 Establishment of geometric impact model for spacecraft structures
Abaqus software was used to simulate the process of the ball impacting the satellite honeycomb plate. The aerospace standard test plate is used as the test sample. Simulate satellite fragments colliding with spacecraft in orbit using a small ball. The H62 copper material is selected as the material of the small ball. The diameter of the small ball is 30 mm. The materials of the pellet and spacecraft are shown given in Table 1.
Table 1. Material parameters
Two models set up in this simulation. The first model represents a square carbon fiber composite plate with dimensions of 40 cm in length, 40 cm in width, and 5 mm in thickness. Another model represents a small ball with a diameter of 30 mm, composed of high-carbon chromium-bearing steel. In ABAQUS, solid models of the plate and the steel ball are constructed, and meshing is performed for each model, As shown in Fig. 2.
These two models are assembled together, and constraint conditions are applied to the model. Constraints in the X and Y axes are applied to the steel ball. During the impact process, the plate model remains completely fixed, and the impact location on the plate is chosen freely. To avoid an excessively small impact force, considering the unknown magnitude of the impact force, the steel ball is dropped freely from a height of 30 cm above the plate, moving in the vertical downward direction of the Z-axis.
After completing the setting of the model, the finite element simulation analysis of the model is performed. Then submitting the analysis, the simulation result diagram of the impact of the flat plate as a simulated structural part of the aircraft can be obtained. It can be judged that the overall strain of the carbon fiber plate conforms to the impact loading form of the plate. In the strain near the impact point of the ball, the strain in the direction of the four right angles of the plate will change more than the other directions and can spread throughout the plate surface. Because the impact results are symmetrical and the propagation range is spread throughout the entire plate, the region with a length of 32 cm and a width of 32 cm in the middle of the plate is selected as the data extraction region.
Define the cell type as a hexahedral cell, and set the aluminum plate as a fixed constraint all around. The strain nephogram is shown in Fig. 3. When a ball with a diameter of 30 mm hits the aluminum plate at a speed of 300 m/s, the strain of the aluminum plate caused by the impact is elastic strain, and the strain value caused by the impact position is the largest. The overall strain variation law is to take the impact position as the origin and gradually attenuate to the periphery in an approximate circle. The strain range caused by the influence of the small ball on the sample is limited, and the impact position of the sample can be inferred through the data transmitted by the sensor network.
In order to study the effect of impact angle on the spacecraft surface, the angle between the spacecraft surface and the xoy plane is changed. The strain nephogram is shown in Fig. 4. Figure 4(a), (b), (c) and (d) correspond to collision angles of 5o, 10o, 15o and 20o, respectively. The strain produced by impacting the aluminum plate from different angles is elastic strain, and the strain value produced by the impact position is the largest. The range of the strain area generated after the impact can lay a foundation for the subsequent arrangement of the FBG sensing arrays.
Fig. 4. Cloud map of strain caused by spacecraft impact at different angles. (a) 5o; (b) 10o; (c) 15o; (d) 20o.
Because of the characteristic of the refractive index distribution in the core of oxide doped fiber, its writing technology is different from the conventional femtosecond FBG technology. In the experiment, the visible light of 520 nm is used as the laser source. The pulse width is 220 FS. Maximum single pulse energy 30 uJ. The maximum output power is 4 W. The output window of the femtosecond laser is provided with a shutter switch, and the frequency of the shutter is determined by the pulse repetition frequency set on the computer control software. The laser beam emitted by the femtosecond laser is transmitted through a series of mirrors in Fig. 5, and then irradiated on the oxide doped fiber after being limited and focused by the diaphragm. Immerse the laser machined area in oil. A motorized three-dimensional displacement stage capable of precise mechanical motion in three dimensions of space is utilized, and the minimum displacement of the displacement stage is 10 nm. The control software can design the grating structure to be inscribed. Adjust the distance between the focusing objective lens and the optical fiber so that the oxide doped fiber is clearly displayed in the viewing field. In the process of writing, the fiber connection demodulation system always pays attention to the FBG reflection spectrum.
Femtosecond FBG arrays were fabricated on oxide-doped fibers by point-by-point writing. Figure 6(a) is the trace of the FBG inscribed in an oxide-doped fiber seen under a microscope. With the distinct refractive index modulation amplitude. Figure 6(b) shows the spectrum of an array of 10 femtosecond FBG inscribed on a single oxide-doped fiber. The extinction ratio of ten FBGs can reach 30 dB. The writing technique eliminates the side lobe of the FBG perfectly. The reflection spectrum of the FBG array can be accurately controlled. The length of the unique FBG regions is 2 mm. The reflection bandwidth is 0.2 nm.
Fig. 6. Oxide doped fiber FBG. (a) Write grating micrographs point by point; (b) FBGs array spectrum.
3. Experimental testing and algorithm research
3.1 Temperature and strain sensing characteristics test of high performance FBG
The grating demodulator model is BJU-32 independently developed by the author's laboratory. The demodulator has 32 channels. The wavelength range of the demodulator is 40 nm. The signal acquisition frequency is 1000 Hz. The wavelength resolution is 1 pm. The temperature difference between day and night can reach nearly 400 °C during the spacecraft's orbit. The attack of kinetic energy weapons such as lasers is one of the reasons why spacecraft will encounter damage. When the laser hits the surface of the spacecraft, the temperature of the spacecraft will rise. For this reason, the temperature experiment of the sensor is carried out. Place the femtosecond FBG in the incubator, as shown in Fig. 7. The maximum temperature of the incubator can be measured to 1500 °C.
The temperature was raised from 20 °C to 1100 °C, during which the signal of the femtosecond FBG reflection spectrum was measured dynamically in real time by demodulator. The temperature maintained at each recording point for a period of time, as shown in Fig. 8(a). The reflection spectrum of the femtosecond FBG moves to the long wavelength direction with the change of temperature, and the energy of the spectrum does not decrease. A linear fit of wavelength and temperature was performed on the temperature spectrum, and the results are shown in Fig. 8(b). Temperature sensitivity is 14.5 pm/°C. The high sensitivity is attributed to the high thermal optical coefficient and thermal expansion coefficient of oxide doped optical fibers. The temperature resolution can be calculated to be 0.07 °C.
Fig. 8. High-temperature sensing characteristics (a) High-temperature sensing spectrum; (b) Linear fit.
The strain of the designed femtosecond FBG was tested, and the results are shown in Fig. 9. The sensor is designed to measure strain at least in the range from 0 µε to 15000 µε. femtosecond FBG linearity up to 0.992. This shows that the measurement error caused by the linear demodulation is very small. The strain sensitivity is 1.2 pm/µε. The strain resolution of the sensor can be calculated to be 0.8 µε.
3.2 Damage location analysis of spacecraft based on artificial neural network
The high-performance femtosecond FBG sensor array is pasted on the surface of the spacecraft according to a certain arrangement mode to form a sensing network. The length, width and thickness of the surface plate of the small spacecraft are 40 cm, 40 cm and 5 mm, respectively. The material of the spacecraft surface plate is a mixture of carbon fiber and titanium alloy. In this experiment, five oxide doped fibers are pasted on the surface of the spacecraft, and each oxide doped fiber has five femtosecond FBG sensors. The specific arrangement is shown in the Fig. 10(a), in which the five-pointed star represents the FBG sensor. After determining the fixing position of the sensor, fix the five oxide doped fibers with curing glue. Then a rectangular area with a length of 24 mm, a width of 6 mm and a thickness of three layers of adhesive tape are fixed around each FBG sensor by using curing glue. This not only leaves room for the glue to be applied later, but also controls the amount of glue above each sensor to reduce the impact of the fixed fiber glue on the experimental data. The curing glue can resist high temperature. FBG in the process of pasting need is require a certain amount of prestress. Figure 10(b) shows the spacecraft used in the experiment and the femtosecond FBG fixed on the surface.
Fig. 10. Layout of sensor array.(a) Distribution of sensors; (b) Adhesion of sensor arrays on spacecraft surfaces.
Metal ball impact experiments are carried out on the surface of a square spacecraft satellite. In each measurement process, the small ball moves freely from a fixed height with an initial velocity of 0. The height of the small ball falling and the impact of the satellite on the plate remain constant, and the initial velocity of each drop of the small ball is 0. This can ensure the stability and repeatability of the ball's fall. Each measuring point has 75 impacts. The diameter of the small ball is 30 mm. The ball is made of stainless steel 304 metal material. The mass is 110 g. In the middle of every sensors, a steel ball was used to carry out multiple impact experiments and collect the wavelength signal data of the sensors. There are four rows, each with four impact points, for a total of 16 impact points. In this experiment, the wavelength data collected at the time of impact is measured. In order to include the complete wavelength variation curve in the truncated segment of each sensor impact data, the wavelength drift data generated by the impact was truncated at an interval of 0.05 seconds in this experiment. The experimental setup is shown in Fig. 11.
The data collected by the demodulator contains a lot of null values and useless annotation data. In addition, data preprocessing is needed before data analysis and modeling. For those outliers, the operation of this experiment is to replace the data by the moving average window method. The data at that moment is replaced according to the average of the points around the outlier. And further carry out noise reduction processing on that wavelength data. The wavelet transform is used to remove the fundamental frequency noise to obtain the data that can better reflect the wavelength characteristics. The formula for decomposing the original signal by using the wavelet packet transform is:
Two different network structures are used to construct the damage location model. One is the multilayer perceptron neural network, and the other is the convolutional neural network. The multilayer perceptron is based on Python's keras library. The convolutional neural network is built based on Pytorch. The data set of the neural network for training the lesion localization is a plurality of groups of data measured by taking 30 cm as the falling height of the small ball. Finally, after data processing, there are 1200 training samples in total.
The evaluation of model performance is essential for establishing its efficacy. The coefficient of determination, commonly known as R2, is employed as a quantitative metric to gauge the goodness of fit between the predicted values and the actual observations. R2 serves as an indicator of the proportion of the variance in the dependent variable that is captured by the model. The R2 value is calculated using the following formula:
The numerator represents the sum of squared differences between the actual and predicted values, while the denominator captures the total variance in the actual values. A value closer to 1 indicates a higher degree of explained variability, signifying a better-fitting model.
The dataset for training the neural network for damage localization is multiple sets of data measured at a drop height of 30 cm for the ball. The channel of the optical fiber demodulation instrument is set as: channel 1: FBG1-FBG5, channel 2: FBG6-FBG10, channel 3: FBG11-FBG15, channel 4: FBG16-FBG20, channel 5: FBG21-FBG25. In the loading impact experiment, the ball, assisted by a cylinder, falls from a height of 30 cm each time with an initial velocity of 0 to do free fall and hit the plate. The experiments are carried out successively in the middle of the four sensors (a total of four rows, each row has 4 impact points, a total of 16 impact points), that is, coordinates (8 cm, 8 cm), (16, 8), (24,8), (32,8), (8, 16) … (32,32) and repeat 10 times for each coordinate. During each measurement process, the optical fiber demodulator should be on and use the corresponding computer software to record the wavelength signal data.
Extract wavelength data from each collected data file and save it in a fixed format as a document for easy data reading. The specific format of the data in the document is that one row represents a sample data, where the first 25 data in each row represent the data of the first to 25th sensors, and the last two data bits represent the horizontal and vertical coordinates of the ball hitting the metal composite plate when measuring this set of data. The Fig. 12 shows a comparison of the surface of the spacecraft before and after collision.
Fig. 12. Spacecraft collision simulation interface. (a) Surface of spacecraft before collision; (b) Surface of spacecraft after collision.
The method of clipping data adopted is to take a total of 50 frames, equivalent to a time interval of 0.05 seconds, starting from 10 frames before each time frame when the wavelength data changes. This effectively removes unwanted data, allowing subsequent analysis to focus more on the central wavelength shift data of interest. Some abnormal data will be generated during the data collection process of the optical fiber demodulation instrument.
Principal component analysis (PCA) is applied as a denoising technique, specifically emphasizing the use of a singular principal component during the data dimensionality reduction process. This deliberate choice aims to accentuate the dominant features within the data, namely, those aligned with the maximum variance direction. By focusing on the wavelength data region with the most significant variation, a clearer capture of primary information is achieved, rendering the dimensionally reduced data more representative by effectively filtering out noise. Figure 13 depicting a comparison between the original and PCA-denoised wavelength data illustrate a conspicuous reduction in noise following PCA processing.
The data collected by the optical fiber demodulator is continuous, and there are some unwanted data. For example, the data in the blue rectangular range in Fig. 14 represents the center wavelength shift caused by the impact of the ball, while the rest of the approximately straight-line data is the initial data of the sensor in the state of no external forces.
3.2.1 Structure design and model accuracy test of multi-layer perceptron neural network
Two multilayer perceptron neural networks with different widths and depths were built to find a more suitable artificial neural network design for this experimental data set. The input layer of the multilayer perceptron network model with three hidden layers and five hidden layers is 25 sensor data. The differences between the two networks are the number of hidden layers, the number of neurons in each hidden layer and whether there is a dropout layer.
In the multi-layer perceptron model, there are five hidden layers, and each hidden layer is followed by a hidden layer to reduce the complexity of the model and the probability of over-fitting. The number of neurons in the five hidden layers is distributed symmetrically and Relu is used as the activation function. Since the final prediction is the coordinate position of the impact point, the output of the model is the coordinate value of x and y, and the dimensions of the input layer are divided into two types. One is the data denoised by PCA, the input dimension is 1*25, and each input sample contains the data of 25 sensors at the same time. The other is the data after feature extraction, the input dimension is 1*125, and the five feature vectors are concatenated horizontally. For two different inputs after PCA denoising and feature extraction, using a similar model structure, the model parameters need to be adjusted to achieve the best prediction accuracy.
Input the dataset that has not been deployed into the model for training. After model training and testing, the prediction accuracy of the three hidden layers is significantly lower than that of the five hidden layers MLP. If the model prediction error is calculated based on the sum of two coordinate errors within 4 centimeters. At present, the accuracy of the model trained with five hidden layers MLP on the test set is around 60%. R-Square is 0.48. However, under the same error calculation method, the accuracy of the training set has approached 100%. The loss function variation curve of model training is shown in Fig. 15(a). Train five hidden layers of MLP using PCA denoised data. The variation of its loss function is shown in Fig. 15(b). The best testing accuracy of the model trained on the PCA dimensionality reduction dataset reached 0.98. The R-square value also reached 0.96. And the accuracy of testing with other untrained data reached 0.9.
Fig. 15. Multi-layer perceptual neural network results. (a) Loss function images for MLP training and validation sets; (b) Changes in training loss function of PCA denoising dataset.
3.2.2 Convolutional neural network architecture design and model accuracy testing
Since convolutional neural network has the function of feature extraction, the original data set is used as the input sample in this study. Three identical convolutional layers are used in the network, each convolution layer has three convolution kernels, the convolution kernel size is 3, the Relu activation function is used, the weights are initialized by Lecun normal, and the L2 regularization term is added. In order to preserve the typical characteristics of metadata, Max pooling is selected for the pooling layer. In the connection layer, the outputs of the three convolutional layers are concatenated together. Finally, a fully connected layer with output dimension 2 is used, and Relu is the activation function.
The input of a one-dimensional convolutional network is the same as that of a multi-layer perceptron. The input samples of a two-dimensional convolutional network are composed of 50 rows and 25 columns of matrices. Train these two convolutional neural networks using the dataset trained on MLP, and the corresponding MAE loss function image of the model is shown in Fig. 16(a). The convergence effect of the loss function in two-dimensional convolution is better than that in one-dimensional convolution. In terms of R-square metric, one-dimensional convolution is 0.6102 and two-dimensional convolution is 0.8841. And in terms of accuracy, two-dimensional convolution is also relatively high. Due to the fact that the training set of two-dimensional convolutional neural networks is transformed from one-dimensional to two-dimensional data, the training set has been reduced from 1200 training samples to 48. Therefore, multiple sets of data were measured at a height of 30 cm to expand the dataset. Then load the convolutional neural network model that has been trained on 1200 datasets. Perform a second training on the newly measured dataset. The MAE loss function images of the model training set and test set vary with epoch as shown in Fig. 16(b). After training on two different datasets, the two-dimensional convolutional neural network tested with an R-square of 0.9329 and an accuracy of 0.93.
Fig. 16. Convolutional Neural Network Results. (a) One-dimensional convolutional training loss function image; (b) 2D convolutional loss function image.
In order to further verify the accuracy of neural networks in predicting and analyzing spacecraft damage locations, validation experiments were conducted. Impact the spacecraft at different positions on the surface, and predict the positions through neural network analysis. The experiment actually measures the position of the small ball hitting the surface of the spacecraft. Comparing the two, the results are shown in Fig. 17. The combination of FBG sensing array and neural network algorithm can effectively locate, analyze, and predict the damage status of spacecraft. The prediction accuracy reaches over 93%, and the maximum error is equal to 2 cm.
3.3 Digital twin structure of spacecraft satellite based on FBG sensing arrays
Digital twin at the heart of the intelligent control of spacecraft. It uses physical models and sensor perception to achieve precise mapping of virtual and real space. To ensure that the digital twin accurately reflects the real state of the spacecraft in orbit, so that the digital twin with high fidelity can be used to improve the level of spacecraft design, manufacture and maintenance [29]. Introduce the five dimensional structural model of digital twins. Build a sensor network scene model for digital twins. The MDT is used to represent the conceptual model of sensor network scenes, and the formula for the composition of the conceptual model of sensor network scenes is expressed as follows:
where EI represents the in orbit entity information of the spacecraft. It mainly contains entity information of spacecraft sensor network entity scenes. VE represents the virtual scene. The information parameters involved in the model can be divided into geometric information, physical information and behavioral information. The information of the virtual scene is expressed by the following equation:By providing a detailed description and expression of the conceptual model for sensor network scenarios, the overall framework diagram of the conceptual model can be constructed, as shown in Fig. 18.
The physical model of the spacecraft satellite is combined with the layout of the femtosecond FBG sensor array, and the digital twin model is realized through digital twin driving engine, as shown in Fig. 19. There are multiple sensors on the surface of the satellite in the interface. Each line on a spacecraft satellite represents an optical fiber. Each fiber from top to bottom corresponds to each fiber channel to which the demodulator is connected.
A data display area will pop up on the right side of the twin interface, which can display the historical data monitored by each femtosecond FBG in the spacecraft entity. The real-time strain and temperature status of each sensing point can be displayed in real time, as shown in Fig. 20. The data communication of the digital twin model is achieved through the wdog program and learn_d program. The twin is connected to the actual spacecraft satellite structure through communication. The strain and temperature characteristics of the satellite monitored by femtosecond FBG can be reflected in real-time in the twin body.
Compared with the traditional electrical sensors, from the perspective of economic benefits, save a lot of money for the country, and have good social value. From the technical research level, the establishment of space all-fiber sensing and monitoring system has become the frontier of the development of aerospace science and technology in the world. It has practical significance for national information security and anti-military attack.
4. Conclusion
In this paper, based on the novel oxide-doped fiber, the high-performance femtosecond FBG array is written by point-by-point writing technology. The femtosecond FBG is analyzed from the time dependent perturbation theory of quantum mechanics. The femtosecond FBG can realize high temperature measurement at 1100 °C and large strain range measurement at 15000 µε. The mechanical distribution characteristics of spacecraft impact damage are studied, and the FBG array is laid on the surface of spacecraft satellite. The multilayer perception neural network structure and two-dimensional convolutional neural network structure are designed. The accuracy of the model is tested. 1200 experiments were carried out. The accuracy of the training is 98%. The experimental verification is carried out. Automatic and comprehensive feature extraction of different collision positions is realized. And carry out damage positioning analysis and degree prediction on that degree and the position of the collision damage of the spacecraft. The digital twin model of is developed using digital twin driving engine. Achieve accurate mapping of the physical state and digital twins of the spacecraft. This provides reliable data support for the accurate monitoring of the in orbit operation status of aerospace.
Funding
Foundation of Equipment Pre-research Area (20204511032); National Natural Science Foundation of China (62275008).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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