1. Introduction
As performance requirements for aircraft continue to escalate, the structures of these aircraft are subjected to increasingly extreme mechanical environments [
1]. Consequently, the structural health monitoring and maintenance of aircraft are of critical importance. Currently, structural health monitoring mainly focuses on the wings and key areas associated with normal accelerations and loads based on the controlled maintenance costs [
2].
Methods for studying those accelerations or loads mainly include the theoretical, direct and indirect methods [
3]. In engineering, indirect methods are the most widely used and technically mature approach. The most common indirect method is based on strain gauge load measurements, which involve calculating key loads using measured strain data and stiffness matrices [
4]. Brown et al. [
5] were the first to propose the vision of applying this method to the structural health monitoring system of the F-35 aircraft. Davies et al. [
6] further emphasized the necessity of implementing this method for health monitoring of this aircraft model. Lei et al. [
7] provided a detailed description of the method, which includes the use of load equations and strain sensor measurements to determine external loads; strain measurements are primarily employed to establish, calibrate, and optimize these load equations. Research on the use of fiber Bragg grating (FBG) sensors for strain collection has become highly advanced. Hu et al. [
8] have conducted an in-depth study of these sensors, characterizing and quantifying the strain transfer mechanisms and measurement accuracy in composite structures.
However, traditional methods encounter issues with both efficiency and accuracy. First, in terms of accuracy, these conventional methods do not classify the maneuvers, and as a result, the accuracy of load analysis cannot be further improved [
9]. The recognition and classification of aircraft maneuvers, also known as FMR, facilitate the establishment of distinct calculation models for training and predicting flight parameter data with different characteristics, thereby significantly enhancing accuracy [
10]. Secondly, in terms of efficiency, both experimental measurements of strain and computational simulations involve high computational costs, resulting in low analytical efficiency. Currently, neural network models based on deep learning offer high research value by training on existing data to establish alternative models [
11,
12].
Although, one problem is that a high number of features in a dataset may lead to dimensional disaster for deep learning methods, increasing computational complexity, and leading to overfitting in some machine learning models [
13]. For example, Gandy et al. [
14] described the data recording system of the F-22, which captures a comprehensive set of 670 flight parameters. This dataset encompasses 219 state parameters, including normal overload, attitude angles, altitude, and velocity, alongside 451 switch parameters, such as fuel mass, landing gear status, and door positions, as depicted in
Figure 1.
The higher dimensionality of the flight parameter load strains makes it more difficult to build the prediction model, Silva et al. [
15] suggested that the dimensionality of the obtained flight parameters should be reduced while retaining some important dimensions. Common dimensionality reduction methods include Principal Component Analysis (PCA), AE, t-Distributed Stochastic Neighbor Embedding (t-SNE), and Locally Linear Embedding (LLE) [
16], where PCA belongs to linear dimensionality reduction methods [
17], while AE, t-SNE, and LLE belong to nonlinear dimensionality reduction methods [
18]. Linear dimensionality reduction methods assume that data can be represented by linear transformations during the dimensionality reduction process, where the reduced features are linear combinations of the original features. PCA achieves dimensionality reduction by finding the directions of maximum variance in the data and projecting the data onto these directions [
19]. Nonlinear dimensionality reduction methods, on the other hand, assume that data may contain nonlinear structures during the dimensionality reduction process, allowing for more accurate capture of complex relationships within the data structure. Among them, t-SNE is suitable for relatively small datasets, while the locality of LLE results in poor performance in preserving global structure [
20]. AE are unsupervised neural network models aimed at learning data compression and are used to reconstruct the original input data [
11,
21]. Flight parameters are extensive, and most parameters exhibit nonlinear relationships. AE models may be more suitable for reducing the dimensions of flight data in this case, which is an innovative approach. The neural network prediction models after AE dimensionality reduction should be selected for strain prediction of an aircraft. The recurrent neural network (RNN) [
22] and LSTM [
23] are the mostly used models for this purpose. However, there has been less previous research to determine which model is more suitable for predicting strain in aircraft structures.
In this paper, based on the recording data with a small fixed-wing unmanned aerial vehicle (UAV) sourced from the xx Institute of China, we identify the states of typical flight parameters, establish stiffness matrices between loads and strains through virtual ground calibration experiments, and develop a physical model to establish the mapping relationship between measured strain areas and critical strains. This provides necessary inputs and outputs to solve the mapping relationship between flight parameters and critical loads (and strains). The obtained data will serve as raw data for training AE model dimensionality reduction and deep learning neural network models, which will then be used to predict structural strains of new aircraft models and compare their accuracy. This study will proceed through five steps of strain prediction research, including dimensionality reduction of flight parameters, maneuver recognition based on flight parameters using MRF, wing virtual ground calibration testing, dimensionality reduction using AE neural networks, and strain prediction using LSTM. The research process is illustrated in
Figure 2.
3. Flight Maneuver Recognition
In order to improve the identification accuracy of the load and strain models, it is necessary to identify the states of the flight parameters and build the models in the identified states, respectively. This chapter focuses on typical load state delineation and typical maneuver action delineation. The flight parameters used to delineate the states in this chapter are the flight parameters reflecting the flight attitude in the flight parameters after the removal and supplemental processing of the distorted data and the filtering process.
3.1. Typical Load State Recognition
During aircraft operation, it is almost impossible to compile load spectra for all possible states due to the rapid changes in load status [
25]. Therefore, this paper adopts a multi-parameter statistical combination and induction method to identify transient load states with significant impacts. After selecting 1 h takeoff and landing data, based on the classification results of typical load states, six typical load states are identified: symmetric subsonic low altitude small angle of attack (M1), symmetric subsonic low altitude large angle of attack (M2), symmetric subsonic medium altitude small angle of attack (M3), symmetric subsonic medium altitude large angle of attack (M4), symmetric subsonic high altitude small angle of attack (M5), and symmetric subsonic high altitude large angle of attack (M6). Identification is based on thresholds of several typical flight parameters, and these datasets will serve as inputs for the flight parameter neural network model in our work. Additionally, strain data measured at different positions during virtual ground calibration testing are also included as inputs. The following are the characteristic values of the selected identification results for these six load states, as shown in
Table 4.
3.2. Flight Maneuver Recognition
Despite the preceding preprocessing, the regularity of the flight parameter data persists poorly, posing challenges in distinguishing between different maneuvers. Identifying maneuver segments is imperative, relying on the characteristics exhibited by flight parameter data of various maneuver types and comparing these traits to ascertain the corresponding maneuver segments for the current data segment. An illustration of the general maneuver recognition process is depicted in
Figure 3.
Generally, aircraft maneuvers are classified into three categories: vertical plane, horizontal plane, and spatial maneuvers. The maneuver recognition algorithm based on the time series of significant points, utilizing the trend states of trajectories projected onto the horizontal and vertical planes, which can be referred to our previous proposed Sequence Important Point-Based Method. The specific steps are as follows:
Step 1: Divide the flight parameters into multiple segment sequences with fixed lengths, and then project the trajectory of each sequence onto the horizontal plane.
Step 2: Apply certain merging rules, utilizing the piecewise linear representation and perceptually important point algorithm (PLR-PIP) to segment the trajectory projection, identify the sequence trend, and merge adjacent trend sequences with the same state.
Step 3: Project the merged trend sequences onto the vertical plane; then, the PLR–PIP algorithm is used to segment the trajectory projection, identify the sequence trend, and subdivide the trend sequences by subdivision rules.
Step 4: Superimpose the trend states of the two plane projections to obtain the basic aircraft maneuvers, as illustrated in
Figure 4.
Details can be found in our previous work [
26].
4. Strain Measurement and Calculation of Wings
Finite element modeling (FEM) and virtual strain gauges for ground calibration testing were utilized. This process allowed us to establish stiffness matrices and correlation matrices between load input and strain gauge output paths, enabling us to obtain strain data for the aircraft wing.
4.1. Finite Element Modelling
The 3D shell cells of the wing model were discretized using Finite Element Analysis (FEA) software HyperMesh (Ansys 19.0) [
7]. Unnecessary edges and lines were removed, and the model was geometrically processed into a common nodal model. The mesh used in this study consisted of S4R elements, which are four-node surface thin shell elements aimed at reducing integration and eliminating circular controls. The mesh size was 10, resulting in a total of 83,990 elements. The wing material chosen was LY12, and based on ground calibration tests, the wing components were firmly connected to the fuselage structure. The boundary conditions for virtual ground calibration testing were applied at the nodes where the wing connects to the fuselage in the finite element model. These boundary conditions were restricted to six degrees of freedom. The boundary conditions for virtual ground calibration testing were applied to all nodes connected to the wing and fuselage junction, and constrained to have six degrees of freedom, representing a fully fixed support.
The FEM of the wing is depicted in
Figure 5.
(a) Schematic diagram of the wing finite element method (FEM): This diagram illustrates the structural analysis of the wing using the finite element method, which is a computational tool for predicting the behavior of the wing under various loading conditions. The engine loads were not directly simulated, because the engine layout of this type of Unmanned Aerial Vehicle (UAV) is within the fuselage. However, the loads were correlated with strains by extracting corresponding loads from the FE model provided by the research institute.
(b) Arrangement of the Bending Moment Bridge: Based on the structural characteristics of the wing, the upper and lower flanges of the wing beam primarily bore the bending moments generated by the wing. Consequently, the bending moment strain gauge bridges were positioned on the upper and lower flanges of the wing beam at the section where measurements are taken. Strain gauge bridges numbered 1 and 4 were placed along the lengthwise direction of the flanges, while strain gauge bridges numbered 2 and 3 were oriented perpendicular to bridges 1 and 4, respectively.
(c) Arrangement of the Shear Bridge: The webs and skins of the wing beam and rib primarily withstand the shear forces produced by the wing. Therefore, the shear strain gauge bridges were positioned on the neutral axis or a location close to the neutral axis of the webs and skins of the wing beam and rib. A shear full bridge, composed of four strain gauges arranged at 90-degree intervals to each other, was used to measure the shear forces. This arrangement ensures that the relative bending moment load was minimized, and it was the direction where the maximum shear stress could be most accurately measured by the strain gauges.
(d) Arrangement of the torque bridge: The wing box of the aircraft wing is mainly subjected to the torque generated by the wing. Hence, the torque strain gauge bridges were positioned at the center of the skin of the wing box section where measurements were conducted. A torque full bridge, consisting of four strain gauges arranged at 90-degree intervals, was utilized to measure the torque. This configuration allowed for the accurate detection of the torque effects on the wing structure.
4.2. Virtual Strain Bridge
Owing to the complexity of the wing structure and loading conditions, strain often arises from the combination of multiple loads. To decouple this strain data, the design of the placement and paths of strain gauge components must allow for the separation of multiple loads. The Virtual Strain Bridge technique is an advanced method employed for measuring material strain, renowned for its non-contact nature, high accuracy, and flexible arrangement. This paper employed this method for strain measurement.
4.2.1. Arrangements of Virtual Strain Bridges
The arrangement of strain bridges should ensure accurate and reliable measurement of the structure’s strain. This requires selecting appropriate placement positions and orientations.
The upper and lower spar caps of the wing beam primarily withstand the bending moment generated by the characteristics of wing’s structural force. Bending moment strain gauges No. 1 and No. 4 were positioned along the length of the spar caps, while strain gauges No. 2 and No. 3 were oriented perpendicular to strain gauges No. 1 and No. 4. The ribs and web of the wing beam, along with the wing skin, primarily experienced shear forces generated by the wing. Each shear strain gauge comprised four interconnected 90° strain gauges. The arrangement of shear strain gauges is illustrated in
Figure 5c. The wing box primarily experienced torsional forces generated by the wing. Each torsion strain gauge comprised four interconnected 90° strain gauges. The arrangement of torsion strain gauges is illustrated in
Figure 5d.
4.2.2. The formation of Virtual Strain Bridge
The ground calibration test strain group bridge method utilized a Wheatstone full bridge, comprising four strain gauges employing the group bridge method depicted in
Figure 6. Each strain bridge represented a bridge arm, providing strain data based on the layout position and direction.
4.2.3. Strain Measurement by Virtual Strain Bridge
The strain response of the four virtual strain bridges arranged at the top and bottom rim strips of the wing girder was denoted as
ε1,
ε2,
ε3,
ε4, while the response of the bending moment virtual bridge was represented as
where
ε1 and
ε4 could be directly extracted from the nodal strains of the finite element results,
ε1 and
ε2 were obtained from the equations of mechanics of materials:
where
represents the Poisson’s ratio of the material at the location where the strain bridge is affixed. Then, the strain response of the bending moment bridge is
The calculation of shear force and torque can be referred by the virtual strain bridge, which is in
Appendix A.1 Note 1.
4.3. Definition of Load Condition
The load of the ground calibration test includes three factors: loading point, loading direction and load value. Usually, in the FEM, the intersection point of the wing beam and the wing rib is selected as the loading point, including single point and multi-point; the loading direction is generally perpendicular to the wing surface, upwards or downwards; the load is loaded step by step under different working conditions, and the load condition of each working condition is satisfied by transforming the position of the loading point. The magnitude of the load (5 kN) primarily originates from the surface pressure of the wings and the equivalent engine load on the fuselage, which are obtained through strain gauges and sensors attached to critical components. In this article, the magnitude of loads was directly extracted from the FE model provided by the research institute. The boundary conditions were defined as shown in
Figure 7a, and the calibration load was applied vertically upwards at the intersection of the wing rib and the wing beam; the loading point is shown in
Figure 7b.
4.4. Virtual Calibration Sample Data
4.4.1. Load Strain Sample Data
After completing the virtual ground calibration experiment, it is imperative to analyze the response of the strain gauges to ascertain their suitability for integration into the load equation. Details can be found in
Appendix A.2 Note 2. After considering the repeatability of strain gauge responses and loading conditions, the loads were applied at the intersection points near the wingtip of the wing beams and ribs. Subsequently, calibration equations for the load-strain data at six single-point loads, namely RP1, RP3, RP5, RP7, RP9, and RP11, were derived. The data for each loading point included the shear force, bending moment, torsional moment, the response values of bending moment, torsional moment and shear strain gauges measuring the load profiles. The original data of the loading model are presented in
Table 5, which will serve as the training sample library for subsequent deep learning models.
As shown in
Table 5, there was a significant disparity between the values of loads and strain data. In order to improve the identification accuracy of the load model, the data were normalized prior to modeling [
27]. Additionally, the actual load data can be obtained through inverse normalization [
28]. The normalized load and strain data are presented in
Table 6.
4.4.2. Strain Sample Data at Critical Locations
Since the processing method is unchanged, the strain data for the critical parts are given here, the raw strain data are shown in
Table 7 and the normalized strain data are shown in
Table 8.
6. Conclusions
This study focuses on the flight parameters obtained from a certain type of aircraft, combined with data processing methods (pre-processing interpolation, flight maneuver recognition), and wing virtual ground calibration experiments. The study obtained complete flight data including strain based on this, and established a high-precision flight parameter-strain prediction model. Considering the large volume and high dimensionality of the flight data, the study (1) adopted flight maneuver recognition (FMR) to segment aircraft maneuver actions, segmenting different maneuver actions for targeted deep learning training, thus improving prediction accuracy; (2) Autoencoder (AE) neural network models were used for data dimensionality reduction, reducing the dimensions of subsequent learning models to improve accuracy while increasing efficiency. The study draws several conclusions as follows:
- (1)
Compared to methods such as locally linear embedding (LLE), principal component analysis (PCA), etc., the AE model has the smallest maximum MSE (the maximum MSE does not exceed 0.068, meeting the requirements), and the clustering effect is also obvious. Under equal conditions, the priority should be given to the AE model for flight data dimensionality reduction.
- (2)
The long short-term memory (LSTM) model has temporal characteristics. Combined with the AE model and FMR, this model can accurately estimate the load or strain of key parts. Particularly, the accuracy of predicting strain amplitudes is higher than that of RNN and other neural network models.
- (3)
Compared to recurrent neural network (RNN) model, the LSTM model has a smaller area of uncertainty within the 95% confidence interval, indicating better stability. Therefore, the LSTM model is more suitable for learning and training the flight data model, and can be also used for subsequent preparation of the aircraft load and stress spectrum.
In conclusion, future research can utilize specific flight data for a particular aircraft type as the main dataset. Based on the methods proposed in this paper, including flight data preprocessing, FMR, and data obtained from virtual ground calibration tests, combined with the AE dimensionality reduction and LSTM method, a flight parameter-strain prediction model can be established to analyze aircraft loading and damage conditions.