Journal of Aerospace Engineering

Hardware-in-the-loop simulation is an important way to test the complex contact process of two spacecraft docking in space. Hardware-in-the-loop simulations are known to be unstable and divergent because of various unexpected dynamics, including delays in the system. Existing force compensators for the force-sensing delay, dynamic response delay, and structural deformation of the upper and lower platforms require real-time identification of the contact parameters of the docking mechanisms (DMs), which is difficult because of the unknown contact model structure. However, the existing force- and position-based compensation methods do not consider the structural deformation of the upper platform. In this study, a force- and position-based compensation method is proposed to compensate for the force-sensing delay, actuation-response delay, and structural dynamic position error of the lower and upper platforms. It is not necessary to identify the contact parameters of the DMs. Many verifications by software and experiments show that by using the proposed method, a stable simulation with satisfactory accuracy can be achieved under different simulation conditions. Capture experiments on a space manipulator are provided to demonstrate the applications.

This study presents a design optimization of a circumferential feedback channel on the shroud casing between rotor trailing and leading edges to maximize the aerodynamic performance of a single-stage transonic axial compressor, NASA Stage 37, using three-dimensional Reynolds-averaged Navier–Stokes analysis (RANS) with the $\mathrm{k}\text{-}\epsilon$ turbulence model. The location of the injection and bleeding ports, angles of injection, and bleeding were the most influential factors on the aerodynamic performance and were selected as the design variables. A hybrid genetic algorithm and particle swarm optimization algorithm coupled with three different surrogate models were utilized to maximize the peak adiabatic efficiency and stall margin of the transonic axial compressor. The optimization results for the circumferential feedback channel indicated that an increase in stall margin was achievable with a slightly reduced peak efficiency in comparison with that of the smooth casing.

This study investigated the impact of wing design on the performance of the Cessna 172-R aircraft, focusing on modifications to its wing geometry. The study proposes two alternate configurations: one with increasing the span length and retaining the existing chord length, and the other with increasing the chord length retaining the existing span length. Experimental and analytical studies were conducted to evaluate the performance of these two configurations. The study found that the modified wingspan configuration significantly enhanced the aircraft’s performance, with an increase in lift coefficient, range, and endurance by 13.2%, 26.15%, and 29.26%, respectively. Additionally, the drag coefficient was decreased by 8.12%, indicating the potential for reduced fuel consumption and operational costs. In contrast, the modified wing chord configuration did not improve the performance output. These findings underscore the critical role of wing design in aircraft performance and highlight the potential for modifications to wing geometry to provide significant improvements in efficiency and operational cost. The results of this study indicate the scope for further research in this area, with efforts to optimize aircraft performance and reduce environmental impact.

This paper studies the issue of learning radial basis function neural network (RBFNN)-based robust reconfigurable fault-tolerant configuration control for spacecraft formation flying (SFF) systems subject to thruster faults and space perturbations. To robustly reconstruct thruster faults, a novel learning RBFNN estimator is innovatively explored, in which the P-type iterative learning algorithm is utilized to online update the weight matrix of the RBFNN model and the $H_{\infty }$ control technique is adopted to attenuate the effect of space perturbations. Further, a learning RBFNN output-feedback fault-tolerant control (FTC) method is developed for spacecraft formation configuration maintenance with high accuracy, and the learning RBFNN algorithm is used to update and compensate the synthesized perturbation. Finally, a numerical example is simulated to verify the presented learning RBFNN-based spacecraft formation FTC approach is feasible and superior.

This paper investigates the issue of integrated guidance and control (IGC) design for an unmanned aerial vehicle with an unknown control coefficient, approach angle constraint, and field-of-view limitations. Different from the existing methods, the proposed approach integrates the approach angle and field-of-view requirements into a single reference to satisfy the constraints simultaneously, and meanwhile guarantees the successful mission despite the unknown control coefficient. Based on the established IGC model, a novel sliding mode strategy is generated to ensure that the approach angle and field-of-view constraints can be obeyed once the designed reference is tracked precisely. Then, the IGC issue are transformed into a tracking problem under an unknown control direction, and the periodic sliding mode control technique is introduced to construct the IGC law. The stability of the closed-loop system is analyzed in detail. The effectiveness of the proposed method is verified by numerical simulations.

In this paper, a fast online guidance law generation method is proposed to resolve the flight time control guidance design problem for time adjustable flight consensus via an analytical polynomial shaping approach. The obtained guidance command is explicit such that fast online trajectory generation is applicable without blind parameters to be designed or tuned. Specifically, the polynomial shaping approach is employed to construct a reference relative range profile by a cubic polynomial in terms of a look angle-based auxiliary. The reference profile is solved by initial and terminal flight conditions. Meanwhile, the field-of-view limit is also achieved by explicitly deriving the conditions to be met for the reference profile’s coefficients. Notably, the proposed technique does not rely on the error-prone time-to-go approximation. The trajectory generation command is derived using the guidance model under the expected relative range profile, and is finally presented as a proportional navigation guidance-like law which has simple structure and guaranteed effectiveness. Extensive numerical simulations under various flight consensus scenarios, comparison study, as well as Monte Carlo test under measurement errors and uncertainties are conducted to validate the proposed method.

It is easy for rotating machinery to produce looseness at the pedestal after long-term operation. The looseness of the pedestal causes the sudden increase of the vibration for the rotor, which leads to the rub-impact between the rotor and the stator. Compared with the middle disc rotor, the offset disc rotor in actual engineering is more universal; the gyro effect of the rotor is often neglected in the study of complicated systems, but the effect generates deflecting torque and affects the vibration characteristics, stability, maneuverability, and life of the system. Considering the disc offset and gyro effects of the rotor, the rub-impact dynamic characteristics of an unbalanced rotor system with pedestal looseness are investigated in this paper. This work is novel and more general in comparison with the traditional research on the imbalance-looseness-rubbing rotor system. The piecewise linear stiffness and damping of the support are used to describe the pedestal looseness, and Coulomb friction is applied to simulate the friction of the rub-impact. Based on the Lagrange equation, the equation of motion for the system is developed, and the Runge-Kutta method of the fourth-fifth order variable step is employed to solve the equation. The influence mechanism of the key parameters on the dynamics of the system is studied. The results show that the rotating speed, disc offset, loosening mass, and the rub-impact stiffness have vital effects on the dynamic responses of the system; the dynamic characteristics of only loosening fault and the coupling faults of the looseness and the rub-impact are obtained; there exists an optimal the rub-impact clearance value between the rotor and the stator for the efficiency and the stability of the machinery.

Large hoop truss antennas are locked into a stable structure during deployment in space. The key to characterizing the performance of each mechanism, and discovering problems in the deployment process, is the three-dimensional motion of the antenna. Therefore, it is important to measure antenna motion with high precision for antenna design. Contact measurement requires sensors to be attached to the object, affecting the motion of the antenna; thus, noncontact measurement is the preferred measurement method. For a large antenna, a large field of view and observation angle are required to measure the deployment process. Traditional binocular stereo vision measurement is not sufficiently accurate. In this paper, 36 cameras were combined into an array to measure antenna deployment. A high-precision triggering system was designed, a calibration method suitable for large-scale, multiangle measurement was developed, and a reconstruction method based on the geometric constraints was proposed, greatly improving measurement resolution. The camera array was used to measure the motion of a large hoop truss antenna with a diameter of 4 m during deployment. Based on the measured parameters, the angular velocity of each antenna mechanism was calculated, and the synchronization of the antenna structure was analyzed.

Abstract

The study proposes a method for the trajectory tracking control of a fixed-wing unmanned aerial vehicle (UAV) based on the deep deterministic policy gradient (DDPG). First, the problem of controlling the trajectory of a fixed-wing UAV is combined with the reinforcement learning framework and transformed into a Markov decision process, and a DDPG agent is established in the framework of TensorFlow. Second, we conducted simulations to train and optimize the model in a 3D environment of trajectory tracking control and obtained an integrated DDPG-based trajectory tracking controller that can regulate functions ranging from the state of flight of the UAV to rudder control. Third, we constructed a digital simulation system to verify the proposed method while considering the influence of parametric uncertainties, measurement-induced noise, and delays in the response of the control system. The effectiveness and robustness of the proposed DDPG controller were verified by comparing its performance with that of traditional proportional-integral-derivative (PID) control.

Practical Applications

Unmanned aerial vehicles have gained widespread use across numerous sectors of society. However, the control process for fixed-wing UAVs is more intricate and challenging than that for rotor type UAVs due to the coupled and nonlinear nature of their dynamic models. To address this issue, decoupling and splitting hierarchical control methods are commonly employed. However, these methods can introduce errors and affect flight performance. In contrast, artificial intelligence, particularly deep learning and reinforcement learning, has made significant advancements and found successful applications in areas such as robot control and gaming. To address the challenges posed by complex forms, excessive measurement information, and manual parameter tuning associated with traditional control approaches for fixed-wing UAVs, this paper introduces a deep reinforcement learning algorithm, i.e., the deep deterministic policy gradient, into the control process of fixed-wing UAVs. The paper presents a trajectory tracking control policy for UAVs, which efficiently achieves the task of tracking a desired trajectory without the need for selecting multiple working state nodes or designing linear control laws. Further, through simulation verification, the proposed policy demonstrates adaptability to interference caused by parameter bias, measurement noise, and control system response delays while achieving control accuracy comparable with classical control methods.

The use of flared folding wingtip (FFWT) for load alleviation has been considered in recent studies. Most studies analyzed FFWT based on the linear assumption and ignored the nonlinearity of large wingtip folding angle. In this paper, for FFWT, a nonlinear aeroelastic modeling method based on multibody dynamics and unsteady vortex lattice method (UVLM) is developed. For wing with free-float FFWT, equilibrium and gust responses are simulated, and the gust responses were compared to the results of wind tunnel test to verify the validity of this method. The simulation results show that the geometric nonlinearity of the wingtip has little effect on the main wing but obvious effect on the wingtip. For a wing with active wingtip, the responses excited by wingtip active folding are simulated and compared to the linear modal method, which shows that the nonlinearity has large effects on the wing, especially at low excitation frequencies, and may lead to occurrence of response frequencies different from excitation.

With a focus on crewed spaceflight and space station construction, this research developed a high-accuracy inertia simulation system for the drive joints of the space station transfer arm. To achieve this objective, both mechanical inertia and electric inertia simulation methods were utilized. To enhance the dynamic characteristics of the electric inertia simulation system, a rigorous electric inertia simulation model was developed, and a comprehensive controller, along with a feedforward controller based on the structure invariance principle, was designed. The simulation results demonstrated that the controller significantly enhances the control performance of the system, with extraneous torque being suppressed by more than 95%. The mechanical inertia simulation method accurately models the invariant inertia, whereas the electric inertia simulation method can precisely simulate the time-varying inertia. To validate the effectiveness of the simulation system, experiments were conducted. The results confirm that the electric inertia simulation method is comparable to the mechanical inertia simulation method in aerospace engineering applications. The simulation performance of the electric inertia simulation system for both constant and time-varying inertia is excellent.

The nonlinear stability characteristics of doubly curved panels made of three-phase composites with randomly dispersed carbon nanotubes [randomly dispersed carbon nanotube reinforced fiber composites (RD-CNTRFC)] subjected to practically relevant nonuniform in-plane loads are investigated in this study. Carbon nanotubes (CNTs), when mixed with resin polymer, may give rise to bundles, termed as agglomerations, which can have a profound impact on the effective material properties. There exists a strong rationale to investigate the influence of such agglomeration on the nonlinear equilibrium path of panels, which can subsequently be included in the structural stability design process to enhance operational safety. A multistage, bottom-up numerical framework is developed here to probe the nonlinear stability characteristics. The effective material properties of RD-CNTRFC panels are determined using the Eshelby–Mori–Tanaka approach and the Chamis method of homogenization. By considering von Kármán nonlinearity and Reddy’s higher-order shear deformation theory, strain–displacement relations are established for the nonlinear stability analysis. The governing partial differential equations are simplified into nonlinear algebraic relations using Galerkin’s method. Subsequently, by reducing the stiffness matrix neglecting the nonlinear terms and solving the Eigenvalue problem, we obtain critical load and nonlinear stability path of shell panels based on the arc-length approach. In the present study, various shell geometries such as cylindrical, elliptical, spherical, and hyperbolic shapes are modeled along with the flat plate-like geometry to investigate the nonlinear equilibrium paths, wherein a geometry-dependent programmable softening and hardening behavior emerges.

Accurate prediction of Mach numbers is of paramount importance in wind tunnel experiments. While ensemble prediction models have shown promising performance compared with single-model approaches, existing ensemble methods often prioritize ensemble generation while neglecting the critical aspect of ensemble fusion. This oversight has led to suboptimal precision in Mach number prediction. In this paper, we address this issue by proposing a novel approach that leverages metalearning for ensemble fusion. By incorporating metalearning techniques, our framework effectively combines the strengths of multiple base learners to enhance predictive accuracy. Extensive experiments conducted on a comprehensive data set demonstrate the superiority of our proposed approach over traditional ensemble methods. The results highlight the significance of ensemble fusion in achieving high-precision Mach number prediction in wind tunnel experiments. This research contributes to the advancement of ensemble modeling by emphasizing the importance of fusion techniques and provides valuable insights for improving ensemble prediction models in various domains.

This paper proposed an axial multistage compressor aerodynamic design methodology based on dimensional zooming. Two-dimensional design parameters are acquired through the dimensionality reduction of three-dimensional data to avoid dependence on the empirical loss models. The research on the zooming design method is conducted on a self-designed five-stage compressor. The method has considered the three-dimensional end wall viscosity loss and modified the blade profiles and blade stacking. It provided a path on how to improve the blade design based on computational fluid dynamics analysis. The aerodynamic performance, compressor characteristics of the prototype, and the zooming design are investigated and compared. The results show that the zooming design compressor performances are improved than those of the prototype one.

Fault detection is an important part of aeroengine health management. Intelligent fault detection methods represented by machine learning have been widely studied. However, most studies assume that training and test data follow the same distribution, which is unrealistic. Due to the degradation of engine performance or change of engine operating environment, the historical operation data of aeroengines are different from the current operation data of the engine. If the engine history operation data are directly used to train a fault detection model, the fault detection of the current engine may lead to low efficiency and affect the reliability of fault detection. In order to overcome this problem, transfer learning is introduced into aircraft engine fault detection in this paper. This paper combines transfer learning with support vector data description (SVDD), a common fault detection algorithm, and proposes SVDD-based transfer learning (SVDD-TL). This algorithm takes the spherical center of the SVDD as the knowledge structure to transfer from the source domain to the target domain, which can improve the detection accuracy of the model in the target domain. A fault detection experiment for an aeroengine was designed. Single and mixed fault data were used in the experiment, and the variation of fault data quantity was considered. Experimental results showed that the proposed method can improve the fault detection accuracy of the model in the target domain and still have good detection performance when the amount of fault data changes.

Numerical simulation of an underexpanded rectangular sonic jet controlled with a pair of normally injected supersonic minijets on mixing promotion was carried out using a commercial computational fluid dynamics (CFD) solver. Results from three-dimensional (3D) Reynold’s-averaged Navier Stokes simulations exhibited very good agreement with experimental results for all the cases studied. Detailed analysis was carried out to quantify the influence of mass flow rate ratio and orientation of the air-tab injected along minor axis and diagonal axis, and pressure gradient at nozzle exit on the jet mixing. Centerline Mach number decay, density gradient contours, generation and propagation of streamwise vortices, axis switching, average shear layer thickness, and mass entrainment are used to quantify the jet mixing. It was found that fluidic injection along diagonal axis generates asymmetrical counter-rotating streamwise vortices causing rapid jet spread along the minor axis, resulting in axis switching and enhanced mass entrainment, leading to a shorter core and rapid characteristic decay. Although injection along the minor axis is capable of reducing shock strength, the decay caused by it is only marginal. Effectiveness of the fluidic injection diminishes with increases in the favorable pressure gradient. A maximum of about 53% reduction in jet core length was caused by injection along diagonal (IAD), corresponding to a mass flow rate ratio of 4%.

This paper proposes a time-varying unmanned aerial vehicle (UAV) formation control method based on trajectory prediction and nonlinear model predictive control (NMPC). First, in formation control, the nominal controller is constructed using a linear model and consensus for theoretical stability assurance. The time-varying formation control of nonholonomic UAVs subsequently is achieved by integrating the nonholonomic model with the NMPC, using the desired state derived from the nominal controller. Furthermore, considering the optimal obstacle avoidance problem of moving obstacles, the transformer is used to predict the trajectory in the predictive horizon, the safety constraints are established in combination with the discrete control barrier function (DCBF), and the optimal obstacle avoidance is realized by reducing the additional motion generated during obstacle avoidance. Subsequently, the NMPC-DCBF-transformer is integrated to realize the optimal obstacle avoidance control of nonholonomic UAV time-varying formation. Finally, the algorithm’s effectiveness was verified by numerical simulation, and the advantages of the algorithm were verified by comparison.

Abstract

In this paper, results of a flow visualization study on the flow around a square cylinder with corner chamfering are presented. The corners of the test cylinders were chamfered with each corner forming a triangle with chamfer dimension $b$. Experiments were conducted for $b/Bo$ ratios of 0.05, 0.1, 0.2, and 0.3 where $Bo$ is the side dimension of the uncut square cylinder. The flow structures, particularly the vortex shedding mode and mechanism around the uncut as well as chamfered square cylinders, were investigated in order to deduce the effect of corner modification. All the studies were conducted at a Reynolds number value of 2,100 (based on $Bo$) on both stationary and oscillating cylinders. For oscillating cases, a special mechanism was built to oscillate the cylinders (forced oscillation) at desired amplitudes and frequencies. Results indicates that corner chamfering brings notable changes in the near-wake flow structures of a square section cylinder both in stationary and oscillating conditions. In view of aerospace structures with similar geometries, the present results carry considerable practical significance.

Practical Applications

Many engineering structures carry square section geometry, such as buildings, bridge pylons, and so on, and are subjected to fluid flows. Flow around them can induce certain static and dynamic loads on these structures due to which eventually, they can fail if not designed properly. Flow-induced loads majorly depend on the body geometry. For square section cylinders (structures), corner shape is found to be a crucial factor that decides the nature of the flow field developed over them. This is because a properly designed corner shape can significantly bring down hydrodynamic/aerodynamic loads imposed on structures, ensuring structural safety. In this study, the corners of a square section cylinder are chamfered, and influence of this corner shape is studied through flow visualization. Flow visualization enables qualitative (mainly) as well as quantitative analysis of the flow field developed on the cylinder with different degrees of corner chamfering. This study brings out the effectiveness of corner chamfering in influencing the flow around a square cylinder, which represents an engineering structure in real world scenarios.

High-speed flows over a 34° compression corner subjected to several types of applied electromagnetic fields are numerically investigated. A coupled model for the turbulent flow field and the externally applied electromagnetic field is established based on the low magnetic Reynolds number assumption. The advection upstream splitting method with pressure-based weight function (AUSMPW) scheme and the lower upper symmetric Gauss Seidel (LUSGS) method are implemented to solve turbulent magnetohydrodynamic (MHD) flow equations. Numerical results demonstrate that the performance of MHD separation flow control is determined mainly by the Lorentz force in the turbulent boundary layer. For the counter-flow Lorentz force, the velocity fluid in the boundary layer can be retarded, and a significant temperature increase was observed. The decelerating Lorentz force significantly brings negative effects on the turbulent skin friction coefficients and increases the static pressure locally. Furthermore, the position of the MHD zone has a significant impact on the control efficiency of the ramp-induced separation. With an external electric and magnetic field applied, the low-velocity fluid in the boundary layer can be accelerated, and the Lorentz force directed along the stream can reduce the size of the separation bubble.

The current work evaluates the effectiveness of the pressure-corrected osculating axisymmetric flows method in the design of hypersonic wavecatcher intakes with shape transition. The original osculating axisymmetric flows method, which is essentially used in waverider design, has drawbacks in accurately demonstrating the three-dimensional flowfield due to ignoring the cross-flow effects between the osculating planes. This negatively impacts the intake performance due to the presence of lateral pressure gradients. The pressure-corrected method takes into account these effects by incorporating lateral pressure gradient corrections into the original design methodology using cross-flow velocity information. This results in the generation of three-dimensional streamlines rather than the two-dimensional streamlines of the original method. The semirectangular-to-ellipse wavecatcher intake is selected as the subject of investigation, and the design procedure is reviewed. The characteristics of the wavecatcher intakes with a design point of Mach 6.0 are studied. Computational fluid dynamics analysis of pressure-corrected wavecatcher intakes is presented to assess the design technique. It is found that the initial conical shock impinges at the intake’s entrance and the streamtube is completely captured. Furthermore, the comparison with the original wavecatcher intake indicates that the pressure-corrected wavecatcher intake demonstrated better performance in terms of total pressure recovery and flow uniformity. The wavecatcher intake with entrance-to-exit shapes transition showed higher performance than those with the same entrance and exit shapes.

A new beam element only having the translational displacement degrees of freedom is developed to analyze fracture and buckling behaviors of bilayer beams or columns with delamination using the multilayer modeling method. By comparing their degrees of freedom, it is found that the present beam element is equivalent to the conventional Timoshenko beam element. The upper and lower layers are both divided into one or several sublayers, which are modeled by the developed beam elements. The element stiffness matrix, load vector, and geometric stiffness matrix using the linear interpolation polynomial are derived by the principle of minimum potential energy. To illustrate the effectiveness, accuracy, and efficiency, both the fracture and buckling analyses are conducted. Four typical fracture specimens (i.e., homogeneous and asymmetric double cantilever beams, single leg bending, and asymmetric end-notched flexure specimens) are analyzed using the developed beam element, and the obtained energy release rate and its components using the virtual crack closure technique are compared with those of analytical and conventional two-dimensional (2D) finite element solutions. Further, buckling analysis of bilayer beam-columns with delamination is conducted, focusing on the effect of the number of sublayers. The results show that the developed beam element is capable of effectively and efficiently calculating the convergent stress intensity factor ratio, total energy release rate and its components, and critical buckling load of delaminated bilayer beams or columns with relatively few elements, but without introducing the interface continuity condition in comparison to the conventional modeling method.

This study focuses on the implementation of the spectral difference (SD) method on hexahedral elements to NVIDIA graphics processing units (GPUs) using the Compute Unified Device Architecture (CUDA) for aeroacoustic problems. Three problems were addressed in the implementation of this study: thread parallelism strategy optimization within the GPU, data access patterns management, and multi-GPU parallelization implementation. Computational speed testing showed that the three factors significantly affect the efficiency of the code on the GPU. The implemented GPU solver was validated using an inviscid problem and a viscous problem. The numerical results show that the GPU solver achieves the same level of accuracy as the CPU program, with remarkable speed improvements. Specifically, compared with a single CPU core with a turbo boost frequency of 3.2 GHz (Intel Xeon Silver 4210), the inviscid case tested on an RTX 2070 Super GPU achieved acceleration of $122.4\times$, and the viscous case conducted on an RTX 3090 GPU achieved acceleration of $229.7\times$. Additionally, the GPU solver exhibits a parallel efficiency exceeding 93% when performing parallel computing on a platform with multiple RTX 3090 GPU cards. Furthermore, the GPU-accelerated computational aeroacoustics solver was applied to compute the noise from a low-speed propeller. The computed results were compared with experimental data, and the excellent agreement demonstrated the effectiveness and feasibility of the GPU implementation of the SD solver.

The buzz evolution process of an axisymmetric supersonic inlet was investigated numerically and analyzed using the high-order dynamic mode decomposition (HODMD) method. Driven by an increasing back-pressure, the flow field evolves from a steady state to little buzz and then to big buzz. The computational dominant frequencies in the stages of little buzz and big buzz were basically consistent with those in the experiment. To analyze the buzz evolution of the global flow field quantitatively, the HODMD method was adopted to provide some dynamics information of modal amplitude and growth rate. During the buzz onset period, the disturbance from the oscillating shock gradually induces pressure fluctuation of the entire inlet. During the buzz transition, the shockwave dynamics at the entrance section of the inlet change first. When the amplitude of the big buzz mode exceeds that of the little buzz mode, the inlet is in the big buzz state, in which the pressure oscillation intensity in the downstream channel is significantly greater than that in the region swept by the shock at the entrance. During the buzz triggering and transition, the growth and attenuation rates of the little buzz mode are higher than those of the big buzz mode, suggesting that the little buzz is less stable than the big buzz. The appearance of high growth rates could be regarded as the precursor of the buzz triggering and the buzz transition.

This paper studies the distributed attitude tracking control problem for rigid spacecraft under a directed graph with external disturbances and full-state constraints. First, because only a subset of the follower spacecraft can acquire the states of the leader spacecraft, a distributed finite-time observer was used to estimate the leader spacecraft’s attitude and angular velocity accurately. Then a nonhomogeneous disturbances observer (NDO) was employed to estimate and compensate for external disturbances. Next, based on the barrier Lyapunov functions (BLFs), a distributed finite-time command-filtered backstepping controller was designed to make the tracking error converge to a small neighborhood of the origin in finite time. The BLFs were used to ensure the full-state constraints and the compensating signals were designed to eliminate the influence of the command filter errors. Furthermore, stability of the closed-loop system was analyzed based on the finite-time Lyapunov stability theory. Numerical simulations were conducted to validate the effectiveness of the proposed control law.

Accurate real-time displacement field reconstruction based on limited measurement points is crucial for spacecraft on-orbit monitoring. This study proposes a data-driven displacement field reconstruction method called stacked convolutional autoencoder with denoising autoencoder and filter. Precise reconstruction of the structural displacement from a small number of local strains was made possible by the two primary components of the method: low-resolution displacement field reconstruction and result optimization. Given the significant imbalance between the limited strain information input and the structural displacement field output, a deep learning model with multiple deconvolution layers was built in the low-resolution displacement field reconstruction part using the layer-wise training property of a stacked autoencoder and the sparse mapping property of a convolutional neural network. The result optimization part utilized a denoising autoencoder and a linear density filter to effectively alleviate the checkerboard phenomenon and displacement field discontinuity caused by the deconvolution operation. The results of the case study indicate that the proposed method can accurately reconstruct the structural displacement field of both simple regular geometric structures and irregular geometric structures with complex boundaries without prior information. Additionally, the method exhibits excellent robustness to unavoidable measurement noise, providing a new implementation approach for real-time monitoring of spacecraft.