Velocity Mode Research Articles

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Proper orthogonal decomposition of wall-bounded high-pressure transcritical fluids

This study explores the principal modes of high-pressure transcritical channel flow from direct numerical simulation data. The four cases investigated correspond to CO2 at high-pressure conditions (P/Pc=1.5) confined between a cold/bottom wall (T/Tc=0.8−0.95) and a hot/top wall (T/Tc=1.1−1.4); Pc and Tc correspond, respectively, to the pressure and temperature of the critical point. The bulk velocity ranges between Ub=0.5−1.0 m/s with corresponding bulk Reynolds numbers of Reb≈1000−2500. The four cases considered are first characterized into laminar and turbulent regimes, followed by an analysis of energy decay using singular value decomposition. This method allows us to identify the most energetic modes of velocity, temperature, and specific isobaric heat capacity for the laminar and turbulent cases considered. The results reveal that fewer modes are needed to represent the hydrodynamics compared to the thermodynamics of the system. The findings also highlight that the pseudo-boiling region, prevalent in high-pressure transcritical systems, disrupts the coherent structures formed (especially) in the hotter region of the flow. Finally, a correlation analysis between the most energetic modes shows an interdependence between velocity and specific isobaric heat capacity modes when conditioned to focus solely on the pseudo-boiling affected regions. This correlation underscores the complex interplay between hydrodynamic and thermodynamic variables in such high-pressure transcritical environments.

CONCEPTUAL ANALYSIS ON THE IMPACT OF ACOUSTIC LINERS IN FAN FLUTTER

Abstract This work investigates the impact of acoustically treated intakes on fan flutter. The propagation of the fan acoustic perturbations is studied using a simplified model, where the frequency of the waves in the intake is the natural frequency of the fan blade in the stationary frame of reference. The model consists of a constant cross-section annular duct, where the acoustic modes are computed for hard wall and lined wall regions, assuming a uniform axial flow. The interfaces between the lined and hard wall sections are solved by doing mode matching. The acoustic reflections in the zero-thickness intake are computed using the Wiener-Hopf technique following Rienstra's model. Analytical results show that the waves propagating from the fan are reflected and scattered radially at the interfaces between the hard wall and the liner. Furthermore, the liner damps and changes the phase velocity of acoustic modes. Due to the low frequency of the flutter waves, the radial scattering can activate different cut-off modes, which need to be retained in order to make accurate predictions. The likelihood of fan flutter is estimated using the phase of the reflected cut-on waves reaching the fan. This strategy is used to assess the impact of the acoustic liners on the stability of a realistic fan. It is concluded that the impact of the phasing and reflections induced by the acoustic liners is comparable to that of the intake and can alter the flutter characteristics of the fan significantly.

Relationship of proteins and subclinical cardiovascular traits in the population-based LIFE-Adult study

Background and aimsUnderstanding molecular processes of the early phase of atherosclerotic cardiovascular disease conditions is of utmost importance for early prediction and intervention measures. MethodsWe measured 92 cardiovascular-disease-related proteins (Olink, Cardiovascular III) in 2024 elderly participants of the population-based LIFE-Adult study. We analysed the impact of 27 covariables on these proteins including blood counts, cardiovascular risk factors and life-style-related parameters. We also analysed protein associations with 13 subclinical cardiovascular traits comprising carotid intima media thickness, plaque burden, three modes of Vicorder-based pulse-wave velocities, ankle-brachial index and ECLIA-based N-terminal prohormone of brain natriuretic peptide (NT-proBNP). ResultsEstimated glomerular filtration rate, triglycerides and sex where the most relevant covariables explaining more than 1 % variance of 49, 22 and 20 proteins, respectively. A total of 43 proteins were significantly associated with at least one of the analysed subclinical cardiovascular traits. NT-pro-BNP, brachial-ankle pulse-wave velocity (baPWV) and parameters of carotid plaque burden accounted for the largest number of associations. Association overlaps were relatively sparse. Only growth/differentiation factor 15, low density lipoprotein receptor and interleukin-1 receptor type 2 are associated with these three different cardiovascular traits. We confirmed several literature findings and found yet unreported associations for carotid plaque presence (von-Willebrand factor, galectin 4), carotid intima-media thickness (carboxypeptidase A1 andB1), baPWV (cathepsin D) and NT-proBNP (cathepsin Z, low density lipoprotein receptor, neurogenic locus homolog protein 3, trem-like transcript 2). Sex-interaction effects were observed, e.g. for spondin-1 and growth/differentiation factor 15 likely regulated by androgen response elements. ConclusionsWe extend the catalogue of proteome biomarkers possibly involved in early stages of cardiovascular disease pathologies providing targets for early risk prediction or intervention strategies.

Numerical modeling and suppression of combustion instabilities in a partially premixed combustor

To suppress the combustion instabilities faced in the lean premixed combustion, the impacts of swirler hub configurations on combustion instabilities under elevated pressure are investigated using large eddy simulation combined with a flamelet generation manifold model. Good agreement between the numerical predictions and experimental data is achieved. The flow fields of the combustors with three distinct swirler configurations are simulated: prototype, swirler with lobes on the hub of pilot stage, and with lobes on the hub of the first main stage. Furthermore, dynamic mode decomposition (DMD) is used to extract the dynamic characteristics, and a flame transfer function (FTF) is employed to characterize the fluctuation characteristics. The results show that the prototype combustor demonstrates a coupled fluctuation between flow and heat release. Influenced by the precessing vortex core (PVC), the flame angle varies between 70° and 90° and the first DMD modes of axial velocity, temperature, and heat release rate are all at a frequency of 470 Hz. The lobes on the hub of the pilot stage suppress the formation of PVC, making the combustion very stable. The flame angle remains constant at 80°, and the gain of FTF is lower than 1. However, adding lobes to the first main stage makes the combustion extremely unstable. The flow field structure undergoes drastic changes, mimicking a “breathe” process. The flame surface is highly distorted, and flashback phenomena occur.

Equivalent tensile elastic modulus measurement of cross-ply composite plates using S1 mode of Lamb wave

Abstract This paper proposes a simple and effective Lamb wave-based measurement method for the elastic moduli of cross-ply composite plates with large thickness, considered equivalent to a single-layer orthotropic plate with nine independent elastic constants. Due to the low-frequency signals required for measuring large thickness plates and the large wavelength of the low-frequency signals, the size of composite plates is highly required. Therefore, it is considered to use the first order symmetric (S1) mode wave to increase the signal frequency and reduce the wavelength. The effects of elastic constants on the phase velocities of the S1 mode are investigated. The phase velocity of the S1 mode depends only on the equivalent tensile elastic modulus and in-plane Poisson’s ratio in the low-dispersive frequency-thickness product regime. Moreover, the in-plane Poisson’s ratio of cross-ply laminates changes sufficiently small to neglect its effect on the phase velocities of the S1 mode. Therefore, the tensile elastic moduli of the cross-ply laminated plates can be estimated using the S1 mode, and the mapping relations between the phase velocities of S1 mode and the elastic moduli are established. The proposed approach has been numerically and experimentally tested on cross-ply glass fiber reinforced laminates with large thickness, and validated by theoretical values and conventional tensile tests.

Dispersion of thermoelastic guided waves in multi-layered porous media

The mechanical properties of the graphite electrode will dynamically change during the charge-discharge cycle, which will affect the propagation characteristics of guided waves in lithium-ion batteries. Meanwhile, lithium-ion batteries experience fluctuations in operating temperature during cycling, which will also influence the propagation of guided waves. This research aims to investigate the guided wave propagation problem of porous electrode material with electrolyte versus temperature. The problem is under the framework of Green-Naghdi theory and Biot theory, and a numerical approach is presented to solve the thermoelastic wave propagation characteristics in such a multi-layered porous electrode. A frequency domain simulation for a multi-layered porous anode will be established. The simulation results confirm the feasibility and accuracy of the proposed approach. The porosity of the anode material shows obvious dynamic variation during cycling, which illustrates a strong correlation with the elastic modulus of the solid skeleton. Then, the effects of porosity and temperature variations on the propagation characteristics of thermoelastic guided waves in multi-layered porous graphite electrodes will be analyzed in detail. The phase velocity of fundamental modes appears regularly shift in the low frequency range. This may provide theoretical support for the acoustic nondestructive characterization of the operating states of the lithium-ion batteries.

Controller design and remote piloting training module development for unmanned cropped delta reflex wing configuration

In this study, a cost-effective high-fidelity six-degree of freedom module augmented with an onboard controller is developed. The unmanned aerial vehicle (UAV) under consideration is a wing-alone configuration with a cropped delta planform and reflex airfoil cross-section designed to perform manoeuvres at high angles of attack. The six-degree of freedom dynamics for the aforementioned configuration is developed based on Newtonian mechanics incorporating linear and nonlinear aerodynamic models to expand flight simulations in corresponding regimes. Aerodynamic stability and control parameters for the simulations are obtained from full-scale wind tunnel measurements and flight tests. It is observed that the linear aerodynamic model is valid in angle of attack (α) domain −5°≤α≤10°, followed by nonlinearity up to α≈21°, post which lift coefficient remains almost constant with angle of attack till 45°. The simulation model is validated with the corresponding flight data obtained from flight tests. A user-friendly graphical interface with real-time animation of UAV has been developed for the aforementioned configuration by integrating MATLAB and Flightgear environment with real-time control input from the hardware to enable the pilot for visual and tactile feedback, respectively. A controller based on total energy control is designed for velocity and altitude hold modes, while an attitude hold controller is designed for pitch and roll angle tracking to enable controller-in-the-loop remote piloting simulations. In order to enhance practical applicability, the designed module has been tested under various simulated wind conditions. It is noticed from the results that the steady-state error in attitude remains below 2% with a maximum overshoot of 5° from reference. The total energy controller achieves a zero steady-state error with a maximum overshoot of 2 m/s for velocity and 6 m for altitude, respectively. The developed module enhances remote piloting training, flight response assessment, and control algorithm testing for cropped delta planform UAVs.

Self-consistent effects in the ponderomotive acceleration of electron beams

In the present work, we extend the results of a previous investigation on the dynamics of electrons under the action of an inverse free-electron-laser scheme (Almansa et al., Phys. Plasmas, vol. 26, 2019, 033105). While the former work examined electrons as single test particles subject to the combined action of a modulated wiggler plus a laser field, we now look at electrons as composing a particle beam, where collective space-charge effects are relevant and included in the analysis. Our previous work showed that effective acceleration is achieved when the initial velocities of the particles are close enough to the phase velocity of the beat-wave mode formed by the laser and the wiggler fields. Electrons are then initially accelerated by a ponderomotive uphill effect generated by the beat mode and, once reaching the phase velocity of the beat, undergo a final strong resonant acceleration step resembling a catapult effect. The present work shows that, under proper conditions, space-charge effects play a similar role as the initial (or injected) velocity of the beam. Even if acceleration is absent when space charge is neglected, it may be present and effective when charge effects are taken into account. We also discuss how far the space charge can grow without affecting the sustainability of the acceleration process.

Research on the algorithm for optimal selection of detection modes for rail crack detection

In the application of ultrasonic guided wave testing for rail crack detection, it is necessary to select a guided wave mode that is more sensitive to cracks as the detection mode. However, ultrasonic guided waves have multi-mode and dispersive characteristics. In order to extract mode information from complex signals, this paper proposes an optimal detection mode selection method based on the sensitivity of guided wave modes to cracks. This method is different from the traditional method of determining mode types by calculating the mode velocity through the arrival time of wave packets in the time domain signal. Based on the dispersion characteristics and mode features of guided wave modes, this paper establishes a crack sensitivity evaluation index. In a wide frequency band and among numerous modes, the guided wave modes suitable for detecting cracks in different regions of the full cross-section of rails are accurately selected. Experimental results show that the guided wave modes selected by the mode selection method proposed in this paper, based on the crack area energy and crack reflection intensity evaluation indexes, can accurately identify rail cracks, laying a foundation for the research on rail crack detection and localization methods.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Dynamic look-ahead feedrate scheduling method based on sliding mode velocity control

In the feedrate scheduling of complex curve direct interpolation, dynamic constraints such as axis acceleration and jerk are related to the actual state of the tool. Most existing methods convert dynamic constraints to velocity constraints at sampling points. However, it cannot guarantee the dynamic constraints are satisfied between sampling points. Addressing the issue, this paper proposes a dynamic look-ahead feedrate scheduling method based on sliding mode velocity control, which generates the motion command considering dynamic constraints in every interpolation cycle. To dynamically generate commands based on the current tool state, the acceleration and deceleration method based on sliding mode velocity control has been proposed, which can control tool state to transition to the command state with any initial state. To ensure sufficient distance for acceleration and deceleration, this paper uses braking distance to dynamically estimate the look-ahead distance. Then the minimum value within the look-ahead interval is selected as the command velocity for this scheduling cycle and the actual motion command is determined based on the dynamic constraints of each axis. Simulation and experiment results prove that compared with the existing method, this method effectively reduces the overshoot of dynamic constraints without significantly increasing the machining time. The analysis of real-time computation time has demonstrated the potential of the method proposed in this paper for real-time applications.

Flexures for Kibble balances: minimizing the effects of anelastic relaxation

We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e. bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields 1.2×10−4 . This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure’s internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.

Impact of the Metal Volume Fraction on the Propagation of Guided Ultrasonic Waves in Fiber Metal Laminates

This study investigates the impact of metal volume fraction (MVF) on the propagation of guided ultrasonic waves (GUW) in fiber metal laminates (FML). GUW interactions with various metal and prepreg layers are influenced by changes in the FML composition. A crucial parameter for FML characterization is the metal volume fraction (MVF), representing the volume of metal to prepreg. This research assumes that variations in MVF affect GUW propagation in FMLs. The study analyzes the influence of MVF on GUW propagation in FML, specifically comparing GUW propagation in GLARE plates with nearly identical geometry but different MVF and layer structures. Initially, simulations were conducted to predict expected changes in dispersion properties. To validate these predictions, pitch-catch measurements were performed on the panels, measuring three transducer paths for each panel to enhance measurement significance. An intensive study of wave modes was undertaken to investigate the influence of MVF on mode velocities. The simulation results were validated through experiments, highlighting the significant impact of MVF on GUW propagation in FML. Interestingly, in FMLs with varying MVFs and layer structures, the structural conditions of the layers (such as fiber orientation) demonstrated a non-negligible influence on GUW propagation, surpassing the influence of MVF alone.

Large eddy simulation of a supersonic lifted hydrogen flame: Impacts of Lewis, turbulent Schmidt and Prandtl numbers

Parametric large eddy simulations (LES) of a supersonic lifted hydrogen flame are reported. The emphases are on two aspects: impacts of (1) Lewis number (Lei of the ith species) and (2) turbulent Schmidt and Prandtl numbers (Sct and Prt) on supersonic turbulent flame and flow structures. Five cases are considered: species-specific Lei, Sct=Prt=1.0 (C0); unity Lei, Sct=Prt=1.0 (C1); species-specific Lei, Sct=0.5, Prt=1.0 (C2); species-specific Lei, Sct=1.0, Prt=0.5 (C3); and species-specific Lei, Sct=Prt=0.5 (C4). Numerical results of instantaneous and/or time-averaged species mole fractions, mixture fraction, heat release rate, flame base location, and mixed modes of premixed and diffusion combustion are compared between cases C0 and C1. Differences in auto-ignition locations and strengths and flame structures and stabilization specify the impacts of Lewis number. They are triggered by different predictions of species mass and thermal diffusions at fuel-coflow and/or coflow-ambient air mixing layers. These differences are rationalized by a scale analysis of mass/thermal diffusion and convection for case C0, which suggests the relatively low but non-negligible former against the latter. Cases C0 and C2–C4 barely see differences in terms of instantaneous and/or time-averaged temperature, velocity, and mixed combustion modes except for further downstream areas where combustion occurs. Both Sct and Prt impose less significant influences than Lewis number, as sub-grid scale mass/thermal diffusion is subordinate to its resolved counterpart according to their scale analysis for case C4.

Guided Wave Phased Array Ultrasonic Imaging for Thin Plate Inspection

This study focuses on the application of phased array ultrasonic testing with guided waves for Structural Health Monitoring (SHM) in thin plates. Addressing the limitations of conventional ultrasonic testing efficiently by inspecting thin, long structures. This study employs phased array technology to thin isotropic plates at high frequency(2MHz), thereby elevating imaging and defect detection in structural components. Through the utilization of the full matrix capture (FMC) scanning approach in 3-D finite element (FE) simulations, A0 and S0 modes were generated on steel plates with through-hole geometries. The process involved capturing reflected signals to form an FMC matrix that includes all A-scan signals. Subsequently, the total focusing method (TFM) algorithm was applied to FMC data for the reconstruction of focused images of A0 and S0 modes separately. A key improvement in our approach is integrating a time-domain filtering method into the FMC data. This enhancement addresses the dispersive nature of guided waves, thus improving the accuracy in identifying defect locations and sizes within the images. Our finite element simulations on steel specimens, with varied through-hole locations, revealed the method's potential in accurately imaging defects located deeper within the structure. Additionally, the study expanded to evaluate the efficacy of phased array ultrasonic testing (PAUT) in SHM, particularly in conjunction with guided waves to study the flaw detection sensitivity of the defect through the TFM algorithm on isotropic steel plates up to wavelength(λ)/16. This whole analysis considered crucial factors such as ultrasonic wave mode, frequency, and group velocity for the structure under inspection. This study represents a significant contribution to the field of SHM, introducing a sophisticated, real-time monitoring methodology that promises to enhance structural integrity assessment. Keywords: SHM, PAUT, GW, FMC, TFM FE Simulations, Time Domain Filtering, Ultrasonic Testing.

A guided wave propagation method for delamination detection in fiber-metal laminates

This study aimed to assess the delamination detection in FMLs via the finite element (FE) simulations of Lamb wave propagation. An FE model of an FML specimen with [Al/902/Al/902/Al] layup was developed. Delamination damage of 10 and 25 mm diameters was induced between different layers of the FML specimen. The fundamental antisymmetric Lamb wave mode (A0) at 60 kHz and the fundamental symmetric Lamb wave mode (S0) at the frequency of 206 kHz were propagated on the developed FE models. The Lamb wave phase velocity was obtained from the FE models and compared with those obtained from the Lamb wave propagation tests. The sensitivity of the A0 and S0 Lamb wave modes to the delamination and its diameter were examined. The inverse Lamb wave propagation problem was then solved, and the elastic modulus of the FML specimen was estimated in the intact and delamination regions. It was observed that the phase velocity of the S0 Lamb wave mode had a higher sensitivity to the delamination damage compared to that of the A0 Lamb wave mode. The phase velocity of the A0 Lamb wave mode was more sensitive to the delamination diameter. The capability of the proposed simulated Lamb wave propagation method as a virtual lab for detecting delamination in the FMLs was confirmed.

Asymptotic analysis of fluid thermodynamic behaviors in the near-critical region under highly variable physical properties

Asymptotic analysis based on the fluids governing equations with the exponential model of thermophysical properties is introduced to quantify the influence of each property on the heat and mass transfer behavior of the near-critical fluid. The one-dimensional asymptotic model finds the different behavior in boundary layers and bulk regions controlled by the diffusion and wave mode, respectively. From the asymptotic model, three characteristic parameters are found: nondimensional wave velocity for wave mode, nondimensional diffusion coefficient for diffusion mode, and nondimensional mass transport coefficient for the coupling in between. Larger thermal conductivity, fluid compressibility, and lower specific heat are found to enhance the thermal wave. However, the efficiency of heat transfer by thermal waves is irrelevant to the thermal diffusivity but related to the fluid compressibility. From the calculation of the asymptotic model for supercritical carbon dioxide (sCO2), such efficiency is 0.150, which indicates that most of the thermal energy is accumulated in the boundary layers.

Non-destructive evaluation of a composite honeycomb sandwich panel with in-plane waviness damage using ultrasonic guided waves

ABSTRACT Composite honeycomb sandwich structures (CHSS) are often manufactured using an autoclave co-cure process, which can introduce in-plane waviness (IW) damage due to fibre misalignment. Such fibre waviness, whether in-plane or out-of-plane, significantly weakens the strength of these structures. Therefore, developing reliable non-destructive evaluation (NDE) techniques is essential for detecting IW. This study presents an NDE technique utilising ultrasonic guided waves (GW) to identify IW damage in CHSS panels. A numerical model was created using COMSOL Multiphysics, where IW damage is simulated through curvilinear coordinate physics, followed by a time-dependent study of GW propagation. This model simulates local fibre orientation changes due to IW damage, enhancing our understanding of GW interaction with IW. Experimental investigations are performed using contact-type transducers to corroborate the numerical observations. The presence of in-plane waviness causes a reduction in the group velocity of the A0 mode, a characteristic that can be exploited for detecting in-plane fibre waviness in CHSS. Also, parametric studies were performed to examine the effects of IW severity (aspect ratio) and increased IW area on GW characteristics. Finally, a technique for IW damage localisation is demonstrated using a convex hull algorithm based on changes in correlation coefficient values of the A0 mode.

Global sensitivity analysis of stochastic re-entry trajectory using explainable surrogate models

The assessment of casualty risks associated with re-entry necessitates a comprehensive analysis of trajectories and the examination of pertinent safety-related quantities such as the ground impact area and ground reaching velocity. In practical scenarios, the presence of uncertainty in input conditions introduces variability in safety-related quantities. Consequently, employing stochastic re-entry trajectory analysis becomes crucial in overcoming the limitations of conventional deterministic analyses. Conducting sensitivity assessments during the break-up phase is imperative to gain more insights into how to manage the variability of safety-related measures. Therefore, this paper conducted a surrogate-based global sensitivity analysis and employed explainability machine learning techniques to unveil the complexities of the relationship between input uncertainty conditions and three key measures: ground-reaching velocity, falling range, and falling time, with the object of interest being the Apollo-type capsule. A three-step polynomial chaos expansion-based strategy was devised to efficiently approximate the discontinuous relationships. The results show that the relationship is characterized by severe discontinuity that separates two modes: low- and high-ground reaching velocity caused by the presence of two distinct trim points, with precautionary measures that should be taken to prevent the occurrence of the latter. From this set of procedures, three key input conditions that significantly affect the safety-related measures were identified, namely, the altitude, pitch rate, and path angle of the capsule during the breakup. Subsequently, explainability techniques were utilized to give suggestions on how to control the input variability and avoid the high ground reaching velocity mode, aiming to achieve more dependable predictions for the three safety parameters mentioned earlier.