Small Time Delay Research Articles

Iterative learning robust security predictive tracking control for small delay batch processes: Deception attacks on unreliable network channel

During the batch process, the need for security control is becoming increasingly urgent with the gradual penetration of network control technology. For small time delay batch processes subject to deception attacks, an iterative learning robust security predictive tracking control approach is developed. Reviewing previous studies for iterative learning control, the issue that the repetitive character of the batch process would mask the characteristics of deception attacks was not considered. Moreover, the gains of iterative learning control law are utilized offline, which makes large deviations for the system state as the operating time increases. This will lead to “excessive-input” conditions for control inputs, which means more consumption of energy and production resources. To address these challenges, we introduce robust security invariant sets to improve the robustness of the system by constraining the system state to be in a safe range. Also, the design of the iterative learning controller incorporates deception attack data for historical batches, which is continuously improved and optimized to withstand deception attacks. Meanwhile, by calculating stability conditions online, the real-time control law gain is obtained, which could make the control inputs adjusted online based on the real-time system’s dynamic characteristics, avoiding excessive inputs and improving the efficiency of energy and resource utilization. Additionally, the stability analysis proves that the system is input to state stability. Ultimately, simulation verifies the effectiveness and feasibility of the developed method.

Synchronization and limit cycles in a simple contagion model with time delays

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N−asset models with appropriate parameterization.

A Space–Time Coding Array Sidelobe Optimization Method Combining Array Element Spatial Coding and Mismatched Filtering

Digital array radar (DAR) can fully realize digitalization at both the transmitting and receiving ends. However, the development of freedom at the transmitting end is far from mature. So, the new concept of multi-dimensional waveform coding array has appeared, which can optimize the transmitting resources in space–time/frequency waveform or another dimension. Space–time coding array (STCA) is a typical kind of multi-dimensional waveform coding array, which can make full use of the high degree of freedom at the transmitting end. It realizes emission diversity by introducing a small time delay between different transmission array elements. In this paper, an optimization method for STCA, which combines the array spatial coding at the transmitting end and mismatched filter design at the receiving end, is proposed. This method aims to solve the sidelobe problems of STCA: the inherent resonance phenomenon and the resolution loss problem. The experimental verification and quantitative comparative analysis prove the effectiveness of the proposed method. The resolution is restored to the ideal level under the premise of maintaining the beam-scanning ability and ultra-low sidelobe, and the resonance phenomenon caused by spectrum discontinuity is eliminated simultaneously.

Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises

In this study, a delayed generalist prey–predator model incorporating the logistic-like growth and Holling type-III functional response for predator subjected to two Lévy noises is established. Such environmental fluctuations can describe abrupt change in population density. First, we conduct stability analysis and determine the critical value of time delay when Hopf bifurcation takes place. Then, the existence of the global positive solution and stability in distribution of stochastic model are studied. Numerical results are given to illustrate the analytical findings, and mainly dedicated to the consequences of time delay and Lévy noises on the stationary distribution, mean extinction time and reproduction rate of prey–predator populations, via stationary probability distribution function (PDF), mean first passage time (MFPT) and relaxation time, respectively. Our findings indicate that the decreases in time delay, noise intensities (Di,i=1,2), and stability indexes within the range of αi∈[1,2] are more likely to maintain the population in a high density state. Phase transition occurs when the system is in the suitable parameter regime. Additionally, there exist optimal noise intensities that slow down switching of prey species from a stable state to an extinction state. Smaller time delay τ and stability indexes αi inhibit population extinction, whereas smaller skewness parameter β speed up prey extinction. More importantly, two noises can tune the enhanced stability characteristic of the system.

A novel method to select time-varying multivariate time series models for the surveillance of infectious diseases

BackgroundDescribing the transmission dynamics of infectious diseases across different regions is crucial for effective disease surveillance. The multivariate time series (MTS) model has been widely adopted for constructing cross-regional infectious disease transmission networks due to its strengths in interpretability and predictive performance. Nevertheless, the assumption of constant parameters frequently disregards the dynamic shifts in disease transmission rates, thereby compromising the accuracy of early warnings. This study investigated the applicability of time-varying MTS models in multi-regional infectious disease monitoring and explored strategies for model selection.MethodsThis study focused on two prominent time-varying MTS models: the time-varying parameter-stochastic volatility-vector autoregression (TVP-SV-VAR) model and the time-varying VAR model using the generalized additive framework (tvvarGAM), and intended to explore and verify their applicable conditions for the surveillance of infectious diseases. For the first time, this study proposed the time delay coefficient and spatial sparsity indicators for model selection. These indicators quantify the temporal lags and spatial distribution of infectious disease data, respectively. Simulation study adopted from real-world infectious disease surveillance was carried out to compare model performances under various scenarios of spatio-temporal variation as well as random volatility. Meanwhile, we illustrated how the modelling process could help the surveillance of infectious diseases with an application to the influenza-like case in Sichuan Province, China.ResultsWhen the spatio-temporal variation was small (time delay coefficient: 0.1–0.2, spatial sparsity:0.1–0.3), the TVP-SV-VAR model was superior with smaller fitting residuals and standard errors of parameter estimation than those of the tvvarGAM model. In contrast, the tvvarGAM model was preferable when the spatio-temporal variation increased (time delay coefficient: 0.2–0.3, spatial sparsity: 0.6–0.9).ConclusionThis study emphasized the importance of considering spatio-temporal variations when selecting appropriate models for infectious disease surveillance. By incorporating our novel indicators—the time delay coefficient and spatial sparsity—into the model selection process, the study could enhance the accuracy and effectiveness of infectious disease monitoring efforts. This approach was not only valuable in the context of this study, but also has broader implications for improving time-varying MTS analyses in various applications.

Complex dynamics in nonlinear small time-delayed optoelectronic oscillator and application in fast reservoir computing and pulse generation

We investigated a time-delayed optoelectronic oscillator (OEO) that displays a wide range of complex dynamic behavior under small time delay. The phase-space trajectory distributions in different dynamic regimes were compared which brings a new perspective on the underlying mechanism of the transition process. It was found that bifurcation is always possible no matter how small the time delay is even if the universal adiabatic approximation model is invalid. Hereby we proposed a versatile simple oscillator which has a potential capacity as memory carrier and high-dimensional state spatial mapping ability that brings 1000 times computing-efficiency improvements of reservoir computing over the large time delay one. Furthermore, we demonstrated a new approach for a tunable optoelectronic pulse generator (repetition rate at 0.2 MHz and 0.25 GHz) which depends critically on time-delayed input electrical pulse. The proposed oscillator is also a promising system for the applications of fast chaos-based communication.

[formula omitted]adaptive resonance ratio control for series elastic actuator with guaranteed transient performance

Series elastic actuator (SEA) technology is promising for the development of compliant robotic joints. Despite advancements in the realization of precise tracking, challenges persist in controlling the vibration and transient performance. This study enhanced the resonance ratio control (RRC) algorithm by integrating it with the L1 adaptive control (L1AC) method to address overshoot, static error, and vibration in SEA position control. Initially, the resonance between the motor and link sides caused by the elastic transmission structure was analyzed, which can result in overshoots and vibrations that affect the transient performance of the SEA control. Subsequently, a control scheme based on L1AC was introduced to enhance the performance. The stability of the proposed algorithm was demonstrated through a comprehensive exploration of key control parameters. Furthermore, the algorithm was augmented with gravity compensation, effectively reducing the predicted and reference errors. Consequently, the transient performance was improved. The efficacy of this enhanced algorithm was validated through simulations and experimental platforms, and comparisons with the RRC and model reference adaptive control algorithms. In all the experiments, the overshoot did not exceed 1.1%, the maximum jitter amplitude on the link side was within 0.2° , and a larger time constant in the controller could effectively eliminate the overshoot and vibration with a small response time delay. Furthermore, the algorithm exhibited a protective response during link side collisions by moderating link velocity and limiting motor current, to safeguard the contact environment, humans, and the SEA itself, which take advantage of the L1AC’s low-pass filter (LPF) properties in disturbance handling.

A mechanism for slow rhythms in coordinated pancreatic islet activity

Insulin levels in the blood oscillate with a variety of periods, including rapid (5–10 min), ultradian (50–120 min), and circadian (24 h). Oscillations of insulin are beneficial for lowering blood glucose and disrupted rhythms are found in people with type 2 diabetes and their close relatives. These in vivo secretion dynamics imply that the oscillatory activity of individual islets of Langerhans are synchronized, although the mechanism for this is not known. One mechanism by which islets may synchronize is negative feedback of insulin on whole-body glucose levels. In previous work, we demonstrated that a negative feedback loop with a small time delay, to account for the time required for islets to be exposed to a new glucose concentration in vivo, results in small 3–6 islet populations synchronizing to produce fast closed-loop oscillations. However, these same islet populations could also produce slow closed-loop oscillations with periods longer than the natural islet oscillation periods. Here, we investigate the origin of the slow oscillations and the bistability with the fast oscillations using larger islet populations (20–50 islets). In contrast to what was observed earlier, larger islet populations mainly synchronize to longer-period oscillations that are approximately twice the delay time used in the feedback loop. A mean-field model was also used as a proxy for a large islet population to uncover the underlying mechanism for the slow rhythm. The heterogeneous intrinsic oscillation periods of the islets interferes with this rhythm mechanism when islet populations are small, and is similar to adding noise to the mean-field model. Thus, the effect of a time delay in the glucose feedback mechanism is similar to other examples of time-delayed systems in biology and may be a viable mechanism for ultradian oscillations.

How do time delays influence dynamics and controls of a generalized SEAIR model?

Given the critical role of time delays in epidemic modeling, this paper delves into the dynamics and finite-time optimal stabilization of a novel epidemic system characterized by such delays. Our findings reveal that time delays significantly influence both the system’s dynamics and the formulation of an optimal control strategy. Specifically, the system’s endemic equilibrium point remains locally asymptotically stable under mild conditions for small time delays. However, exceeding critical delay thresholds induces Hopf bifurcation. To closely regulate the system’s state towards the equilibrium point and minimize control costs, we propose an optimal control problem. We derive the explicit form of the optimal control strategy employing Pontryagin’s Maximum Principle. Finally, numerical simulations further confirm the theoretical results obtained in this paper.

High-Performance Sub-10 nm Two-Dimensional SbSeBr Transistors through Transport Orientation.

Exploring two-dimensional (2D) materials with a small carrier effective mass and suitable band gap is crucial for the design of metal oxide semiconductor field effect transistors (MOSFETs). Here, the quantum transport properties of stable 2D SbSeBr are simulated on the basis of first-principles calculations. Monolayer SbSeBr proves to be a competitive channel material, offering a suitable band gap of 1.18 eV and a small electron effective mass (me*) of 0.22m0. The 2D SbSeBr field effect transistor (FET) with 8 nm channel length exhibits a high on-state current of 1869 μA/μm, low power consumption of 0.080 fJ/μm, and small delay time of 0.062 ps, which can satisfy the requirements of the International Technology Roadmap for Semiconductors for high-performance devices. Moreover, despite the monolayer SbSeBr having an isotropic me*, the asymmetrical band trends enable SbSeBr FETs to display transport orientation, which emphasizes the importance of band trends and provides valuable insights for selecting channel materials.

Emergent behaviours of a non-abelian quantum synchronisation model over the unitary group

Abstract We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.

Boosted Incremental Nonlinear Dynamic Inversion for Flexible Airplane Gust Load Alleviation

Active gust load alleviation is an important technology for reducing loads on future commercial airplanes so that the structure can be designed to be lighter in order to save fuel. For the intense reduction of gust loads, a highly reactive control system of sensors, control algorithms, and actuators is required, which is not yet available. In this paper, a control algorithm based on incremental nonlinear dynamic inversion is extended so that actuators respond faster. The control algorithm is applied to a future medium-range aircraft with distributed trailing-edge flaps. It is assumed that the vertical acceleration of the center of gravity and the displacement, velocity, and acceleration of the first wing bending mode are available as feedback variables. To allow comparability with other actuator and sensor setups, the authors abstract the actuator dynamics and sensor filter as control system time delay. The feedback gains are adjusted automatically to the control system time delay. In simulation, the authors investigate the influence of the control system time delay on the peak gust loads. They show that gust loads can indeed be intensely reduced with sufficiently small control system time delay in simulation.

Predictive fault-tolerant control for nonlinear batch processes with small time delays via iterative learning control: A Lyapunov–Razumikhin approach

For batch processes with small time delays and actuator partial fault, the existing methods based on iterative learning control still have some limitations, including the conservative and computationally burdensome of stability conditions and the limited fault-tolerant control capabilities. For this background, an iterative learning robust predictive fault-tolerant control method is developed, which integrates the Lyapunov–Razumikhin function method and derives stability conditions based on robust positive definite invariant set and terminal constraint set. With small time delays, the stability conditions of the system deduced using the Lyapunov–Razumikhin function are solved at a lower computational cost, which is due to the fact that the dimensionality of the stabilization condition is directly related to the size of the time delay, and thus the small time delay implies a lower dimensionality. Especially, the computational effort for solving the stability conditions online is reduced, allowing real-time control law gains to be obtained and combined with historical batches of control inputs, reducing the learning cycles of the system, and realizing stable tracking of the setpoints within shorter operating batches. Moreover, the robust positive invariant set and the set of terminal constraints are able to constrain the state of the system within a safe range for all possible uncertainties, bounded disturbances, and faults. This makes the proposed methods based on them more robust and fault tolerant. Finally, a nonlinear batch reactor is used as an example to demonstrate the effectiveness and feasibility of the developed method.

Use of FreeStyle Libre for continuous glucose monitoring in adult horses.

To evaluate the feasibility of using the FreeStyle Libre (a continuous glucose monitoring system [CGMS]) for instantaneous continuous monitoring of interstitial glucose in adult horses and examine the applicability and accuracy of this system in horses submitted to combined glucose-insulin test (CGIT). Laboratory measurements and continuous glucose monitoring system (CGMS) readings were analyzed using a 2 × 2 factorial statistical model with repeated measures over time. This analysis assessed the effects of the test (factor 1), group (factor 2), and their interactions (test × group, test × time, and group × time). Pearson's correlation analysis was applied to blood glucose values. Mean comparisons were conducted using the t-test, and agreement between techniques was assessed via the Bland-Altman method, with a 95% confidence interval. Field study on private horse farms in association with a veterinary school. Ten healthy stallions were assigned to one of two groups based on their body condition scores (BCS). Group 1 (G1, n= 5) consisted of nonobese horses with a BCS of 5 or 6, while Group 2 (G2, n= 5) consisted of obese horses with a BCS of 7 or higher. A CGMS sensor was attached to the dorsolateral aspect of the proximal one third of each horse's neck. Laboratory blood glucose measurements and CGMS interstitial glucose readings were compared at different time points for up to 7days after sensor fixation. Obese horses were also submitted to CGIT on Day 4. A comparative analysis of glucose measurements obtained in G1 and G2 horses using the CGMS and enzymatic methods revealed significant group×time interactions (P<0.001) and time effects (P<0.001). No interactions were detected between group (P=0.45), test (P=0.62), group and test (P=0.28), or time and test (P=0.92). In G1 and G2, tests were significantly correlated (r=0.84 and P=0.00) at all time points (T0-T5). Agreement between the glucose values obtained using different methods was excellent despite a small time delay in CGMS detection of rapid changes in blood glucose. It was concluded that the CGMS can be used for indirect assessment of glycemic status (ie, based on interstitial glucose measurements) in nonobese and obese adult horses submitted to CGIT.

Toroidal mantle flow beneath the NE termination of the Kuril–Kamchatka subduction zone from seismic anisotropy

SUMMARY This study presents the findings of a splitting analysis conducted on core-refracted teleseismic shear waves (SKS, SKKS and PKS, called together as XKS) and local shear waves, obtained from a dense seismological network spanning the Kamchatka Peninsula. The objective of the study is to examine the pattern of mantle flow beneath the study area through the investigation of seismic anisotropy. The peninsula is situated at the northeastern end of the Kuril–Kamchatka subduction zone, where the Kuril trench intersects with the western boundary of the Aleutian trench. The data set utilized in this study comprises waveform data from a dense network of seismic stations (99 broad-band and short-period stations for the local shear wave splitting analysis and 69 broad-band stations for the SKS splitting analysis). The seismograms were downloaded from publicly available data repositories including the IRIS Data Management Center and the GFZ Data Services (GEOFON program). The dense station coverage allows us to investigate the lateral variations in anisotropy, providing insights into the flow patterns within the mantle. The processing of the combined data sets of local shear wave and teleseismic XKS waves allowed us to partially decipher the source of anisotropy in the mantle. Small delay (splitting) times (∼0.35 s) observed from the local-S data suggest that anisotropy in the mantle wedge is relatively weak with lateral variations. Larger splitting times (∼1.1 s) observed for the XKS waves relative to local S suggest that the main part of splitting on the XKS waves occurs in the subslab mantle. On the other hand, the rotational pattern of seismic anisotropy observed by both the local S and XKS waves suggests the presence of a toroidal flow at the NE edge of the subducting slab, which affects both the mantle wedge and subslab mantle. For the regions away from the edge of the slab, the mantle flow seems to be governed mainly by the drag of the lithospheric plate over the underlying asthenosphere.

Satellite-derived bathymetry from correlation of Sentinel-2 spectral bands to derive wave kinematics: Qualification of Sentinel-2 S2Shores estimates with hydrographic standards

There is a pressing need for a fast and efficient satellite remote sensing tool to estimate coastal bathymetry for any coastline in the world. To date, satellite methods for deriving bathymetry have mainly focused on linking the radiometric response to a known water depth, as with SPOT, Landsat and Sentinel. Here, wave properties (static and dynamic) are approximated using the small time delay between the different color bands of Sentinel-2 to then calculate a depth using wave linear dispersion theory. In this paper, we present a spatial correlation method within the S2Shores (Satellites to Shores) Python toolbox: a processing chain/toolbox of coastal observations using methods applied to optical satellites. The resulting individual bathymetries are finally qualified according to the standards of the International Hydrographic Organization, anticipating their operational use.

Dynamic Properties for Time-Delayed Grazing Ecosystem Driven by Lévy Noise and Gaussian Noise

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.

Fitted Numerical Scheme for Singularly Perturbed Convection‐Diffusion Equation with Small Time Delay

In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection‐diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples.

Comparison of PI/PID/PIDD2 Controllers for Higher Order Processes

PI, PID and PIDD2 controllers are compared for higher order processes. Tuning rules with robustness constraints are first proposed in this paper for PI, PID and PIDD2 controllers. Then the tuned rules are applied to the benchmark higher order processes and a three-tank system. It is shown that higher order derivatives can improve the control performance for processes with small time delays, while it is of no significant performance improvement for processes with large delays.

Comparative study on generation of attosecond pulse train and phase information reconstruction

&lt;sec&gt;Attosecond pulses provide higher measurement precision for analyzing ultrafast dynamics in atoms, molecules, and electrons, laying the foundation for studying electronic motion in atomic and molecular systems. The most important method currently is to generate attosecond pulse trains and isolated attosecond pulses through the interaction of femtosecond lasers with gases. The temporal information of attosecond pulses and the dynamic information of electrons can be extracted from spectrograms by using attosecond streak camera or the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method based on two-photon transition interference. Although the differences in phase among different high-order harmonics can be directly extracted from the oscillation frequencies of sidebands, the iterative algorithm of attosecond streak camera can provide complete phase information of attosecond pulse trains to better support the study of electron dynamics in atoms.&lt;/sec&gt; &lt;sec&gt; &lt;b&gt;Research purpose&lt;/b&gt; This work is dedicated to the investigation of the generation, measurement, and characterization of attosecond pulse train (APT), which are essential for probing ultrafast dynamics in atomic, molecular, and electronic systems. The focus is on the generation of APTs through interactions between femtosecond lasers and gases, as well as the extraction of temporal and dynamic information from these pulses by using advanced spectroscopic techniques such as the RABITT method.&lt;/sec&gt; &lt;sec&gt; &lt;b&gt;Methods&lt;/b&gt; The experimental approach involves the use of a homebuilt femtosecond titanium sapphire regenerative amplifier to produce high-order harmonics, leading to the generation of APTs. The setup includes the homebuilt titanium sapphire chirped pulse amplifier and a collinear attosecond pulse generation and measurement beamline, which are used to conduct RABITT experiments. The process requires the interaction of femtosecond lasers with gas targets to generate high-energy photons in the extreme ultraviolet and soft X-ray spectral ranges. By optimizing the phase-matching conditions within the gas target, strong high-order harmonic signals are observed on an XUV spectrometer. The temporal information of the attosecond pulses is indirectly measured through the photoelectron spectrum produced by the interaction of attosecond pulses with femtosecond lasers. The research also employs the FROG-CRAB algorithm and the extended phase retrieval and iterative engine (ePIE) algorithm for temporally reconstructing APTs and attempts to use a genetic algorithm to extract phase information.&lt;/sec&gt; &lt;sec&gt; &lt;b&gt;Results&lt;/b&gt; The study yields three sets of RABITT spectrograms, which are analyzed by using the RABITT sideband phase method to directly reconstruct APTs. Fourier transform analysis is used to extract phase differences between sidebands, offering insights into the phase differences between corresponding high-order harmonics. This method, however, provides an estimation of the phase in the center of each harmonic order, which does not fully represent the actual pulse shape. The FROG-CRAB algorithm and ePIE algorithm successfully reconstructs the attosecond pulse trains from the RABITT spectrograms, revealing similar temporal pulse train morphologies. In contrast, the genetic algorithm, despite its potential for high constraint optimization, does not yield satisfactory results, possibly due to the sensitivity of the algorithm to discrepancies between theoretical simulations and experimental data.&lt;/sec&gt; &lt;sec&gt; &lt;b&gt;Conclusions&lt;/b&gt; The research concludes that achieving ideal inversion results for APTs necessitates small time delay steps and a wide scanning range in the experimental data collection process to ensure a rich dataset for inversion. The FROG-CRAB algorithm and ePIE algorithm demonstrate their effective performance in reconstructing APTs, with ePIE showing higher computational efficiency. The genetic algorithm, while offering a high degree of constraint, faces challenges and requires to be further refined. The study underscores the importance of the signal-to-noise ratio in experimental data for the accuracy of inversion results. This work provides significant guidance for future measuring electron dynamics and explaining their evolution patterns, contributing valuable experimental methods and data analysis techniques to the field of attosecond science.&lt;/sec&gt;