Multiscale Technique Research Articles

Bridging the Gap between Molecular Simulations and Surface Complexation Modeling for Heterogeneous Surfaces: A Case Study with Uranium and Arsenic Adsorption on Clay Minerals.

Among all natural submicrosized phases, clay minerals are ubiquitous in soils and sedimentary rocks in nature as well as in engineered environments, and while clay minerals' adsorption properties have been studied extensively, their unique level of surface reactivity heterogeneities necessitates further investigation at the molecular level to understand and predict the influence of these heterogeneities on their macroscopic properties. In this study, we investigated the surface structures and desorption-free energies of U(VI) species (UO22+) and As(V) species (H2AsO4- and HAsO42-) complexed at different edge surface reactive sites of a cis-vacant montmorillonite layer using first-principles molecular dynamics (FPMD). We show that U(VI) forms bidentate and tridentate complexes on montmorillonite edge surfaces, whereas As(V) monodentate complexes are the most stable. Then, we constrained a state-of-the-art surface complexation model (SCM) with surface acid-base chemistry and surface complexation properties obtained from the molecular-level simulation results. While our results highlighted the complexity of the interfacial chemistry controlling the complexation of inorganic contaminants on clay mineral surfaces, they also evidenced the reliability of an integrated workflow using modern multiscale simulation techniques to address the challenge of predicting heterogeneities in mineral surface reactivity.

Transport of a solute in primary and secondary flows through a rotating channel with an absorbing wall

This study uses a multi-scale homogenization technique to provide an analytical solution for solute transport in a viscous fluid flowing between rotating parallel plates. The analytical solutions for the mean and vertical concentration distributions of the solute are derived up to second-order approximations. The channel undergoes rotation around an axis perpendicular to its walls with uniform angular velocity, resulting in a secondary flow. Most previous literature focused on determining the dispersion coefficient for the primary flow. Apart from the dispersion coefficient, we also found the mean and vertical concentration distributions for both primary and secondary flows. The effects of a dimensionless rotation parameter (α) and boundary absorption parameters on solute mean and vertical concentration distributions in both flow directions are discussed. Results reveal that, for the primary flow, the peak of the mean concentration distribution of the solute increases until α=2.2, then becomes flat with higher α. This phenomenon is due to the emergence of the Coriolis force, which shifts the maximum velocity toward the walls, thereby increasing velocity variation across the channel, whereas for secondary flow, the mean concentration increases with increasing α. However, in the secondary flow direction, the vertical concentration distribution reaches uniformity over significantly longer timescales (e.g., dimensionless τ∼105, for α = 2) than the primary flow (dimensionless τ∼10).

Cell Nuclear Segmentation of B-ALL Images Based on MSFF-SegNeXt.

The diagnosis and treatment of B-Lineage Acute Lymphoblastic Leukemia (B-ALL) typically rely on cytomorphologic analysis of bone marrow smears. However, traditional morphological analysis methods require manual operation, leading to challenges such as high subjectivity and low efficiency. Accurate segmentation of individual cell nuclei is crucial for obtaining detailed morphological characterization data, thereby improving the objectivity and consistency of diagnoses. To enhance the accuracy of nucleus segmentation of lymphoblastoid cells in B-ALL bone marrow smear images, the Multi-scale Feature Fusion-SegNeXt (MSFF-SegNeXt) model is hereby proposed, building upon the SegNeXt framework. This model introduces a novel multi-scale feature fusion technique that effectively integrates edge feature maps with feature representations across different scales. Integrating the Edge-Guided Attention (EGA) module in the decoder further enhances the segmentation process by focusing on intricate edge details. Additionally, Hamburger structures are strategically incorporated at various stages of the network to enhance feature expression. These combined innovations enable MSFF-SegNeXt to achieve superior segmentation performance on the SN-AM dataset, as evidenced by an accuracy of 0.9659 and a Dice coefficient of 0.9422. The results show that MSFF-SegNeXt outperforms existing models in managing the complexities of cell nucleus segmentation, particularly in capturing detailed edge structures. This advancement offers a robust and reliable solution for subsequent morphological analysis of B-ALL single cells.

Interlaminar fracture toughness and impact resistance of carbon fiber reinforced composite with magnetic aligned CNTs

This study draws inspiration from Z-pins employed in fiber composites. Carbon fiber reinforced polymer (CFRP) laminates modified with Z-oriented carbon nanotubes (Z-CNTs) were fabricated utilizing a magnetic field orientation technique. The interlaminar fracture toughness, impact resistance and damage tolerance of CFRP modified with Z-CNTs were evaluated through end-notched flexure (ENF), low-velocity impact (LVI) tests, and compression after impact (CAI) testing. The enhancement mechanisms were investigated using multiscale techniques, including digital image correlation (DIC), scanning electron microscopy (SEM), molecular dynamics (MD), and finite element (FE) simulations. CFRP modified with 0.3 wt% CNTs showed optimum interlaminar fracture toughness, which improved by 62.9 % in CNT-random samples compared to non-modified samples and further enhanced by 95.2 % in CNT-oriented samples. The DIC and SEM analysis revealed the enhancement mechanism of Z-CNTs in fracture toughness, including (1) enlarging the toughness deformation of resin; (2) broadening the fracture process zone to dissipate the energy; and (3) shifting the failure mode of CNTs from pull-out dominance to fracture dominance. Furthermore, MD simulations showed that the crack propagation location significantly influences the different enhancement mechanisms exhibited by CNTs, which was accord with SEM observations. LVI and CAI tests indicated that specimens modified with Z-CNTs exhibit greater impact resistance and damage tolerance. FE simulation revealed that the mode II interlaminar fracture toughness plays a dominant role in the impact resistance of the laminate. These findings provide an effective strategy and theoretical supports for the design of impact resistance of composite laminates.

Challenges in Mathematics Arising from Theoretical and Computational Chemistry

The combination of theoretical chemistry and mathematics represents a significant advancement in science since it has yielded insights into the enigmas surrounding atoms and molecules. The advancement of technology has greatly benefited drug development, leading to significant advancements in both medicine and materials research. This summary discusses innovative methodologies and computational challenges in the expansive domain of theoretical and computational chemistry. Despite the computational challenges associated with the Schrodinger equation and Density Functional Theory (DFT), quantum mechanics offers a basic understanding of the behaviour of molecules and atoms. While MD simulations may not handle long-range interactions and complex configuration spaces, they nonetheless excel at capturing various time scales of molecular behaviour. Nevertheless, the process of transforming abstract notions into computer models for the purpose of solving MD simulations continues to be difficult; statistical mechanics offers a theoretical framework for understanding MD simulations. Data-driven methodologies and machine learning have significantly transformed the perspective of computational chemistry by enabling the observation and comprehension of very complex chemical interactions. We must also address concerns about interpretability, reliability in limited data streams, and system transferability. These challenges expedite the advancement of novel materials, product designs, and pharmaceuticals by leveraging machine learning and integrating it with specialised domain expertise. We used available data from many reputable databases, spanning the time period from 2010 to 2024. It is imperative to prioritise the advancement of multiscale modelling techniques and hybrid quantum-classical tools in order to achieve sufficient mastery over chemical phenomena. Another potential benefit is the use of novel mathematical models to uncover previously unknown patterns and connections in genetic data. The most effective way to tackle mathematical problems is by employing a straightforward approach and engaging in collaboration with experts from other fields. By adopting this approach, we can effectively address significant societal issues and propel advancements in chemistry. Keywords: mathematics, computational, chemistry, theoretical, challenges, quantum mechanics

A multi-scale modeling approach for predicting and mitigating thermal runaway in electric vehicle batteries

This study presents a unique multi-scale modelling technique for electric vehicle (EV) battery thermal runaway prediction models using electrochemical, thermal, and machine learning approaches. This modelling framework has illuminated the thermal runaway’s physical process and the race between heat production and dissipation at the cell, module, and pack levels.Experimental evaluation has demonstrated solid predictive performance for each component. The modified pseudo-two-dimensional (P2D) electrochemical model has achieved high voltage prediction accuracy (mean absolute error: 8.5 mV), and the 3D thermal model has captured battery module temperatures with an average error of ± 1.5 °C.The machine learning model has exhibited 96.8% accuracy, excellent classification precision, and an 18.3-minute early warning time. It was also demonstrated that the integrated multi-scale model outperformed standalone single-scale models with 15% higher prediction accuracy and 32% higher average early warning time.Based on these findings, adaptive cooling techniques, unique charge/discharge procedures, and early isolation methods were created. Simulations showed that these mitigation techniques decreased thermal runaway occurrence by 78% and severity by 93%. Despite its high computing cost, this technique might improve EV battery safety, guide battery pack design, and accelerate EV adoption, which would cut carbon emissions.

Spatial Aligned Mean: A Method to Improve Consensus Forecasts of Precipitation from Convection-Allowing Model Ensembles

Abstract Ensembles of convection-allowing model (CAM) forecasts are increasingly being used in operational numerical weather forecasting. Several approaches have been devised to find consensus among ensemble forecast fields, including the arithmetic ensemble mean and, more recently, the patchwise localized probability-matched (LPM) mean. However, differences in spatial distribution and intensity of precipitation features among ensemble members make it difficult to construct an ensemble mean product that characterizes the consensus while preserving precipitation structures forecasted by the individual ensemble members. To overcome this problem, this study aims to develop and test a method for improving ensemble consensus precipitation forecasts by directly considering the spatial offsets among ensemble members. This study uses a multiscale spatial alignment technique to align the precipitation features of each ensemble member to a common location, and the spatial aligned mean (SAM) is obtained by averaging the realigned members. It is shown that implementing SAM and subsequently applying the LPM technique to the average of all aligned members (SAM–LPM) can significantly improve the warm season precipitation forecast scores using common metrics such as equitable threat score (ETS). Also, improvement in the structure of features of heavy rainfall is shown from summer 2023 flash-flooding cases. Thus, SAM and SAM–LPM can be excellent candidate methods for calculating an ensemble consensus and providing ensemble consensus guidance to forecasters. Significance Statement High-impact rainfall events, such as flash floods, result in many billion-dollar loss events in the United States each year. This study seeks to improve the prediction of such events when using guidance from convection-allowing model (CAM) ensemble forecasts, such as the U.S. operational High-Resolution Ensemble Forecast (HREF) and the nascent Rapid Refresh Forecast System (RRFS). The proposed method, the spatial aligned mean (SAM), directly addresses the common issue of disparity in the predicted location of convective systems among ensemble members that confounds traditional ensemble consensus methods. In this study, it is found that SAM improves ensemble consensus guidance for high-impact rainfall events in both the HREF and the Center for Analysis and Prediction of Storms (CAPS) Finite-Volume Cubed-Sphere (FV3)-limited area model (LAM) CAM ensemble forecast system, a proxy for the future RRFS.

African sovereign risk premia and international market assets: A relook under the COVID-19 outbreak

Using the wavelet multiscale coherence technique, the paper examines the interdependences between global market assets, sovereign credit default swap (CDS) and yield-to-maturity on bond spread for African economies from January 2019 to March 2023. The empirical results primarily reveal a high level of coherence between global market assets and Africa's sovereign CDS and yield-to-maturity, although varying across countries and time-frequency domain. Notably, the high degree of coherence and the positive co-movement between sovereign CDS and global market assets are more concentrated at the medium and upper frequency bands. The observed intensity of co-movements between global market assets and sovereign CDS/yield-to-maturity (YTM) of bond spread, with global market assets broadly serving as leading variables, suggests that an increased global investor's risk aversion positively affects the yields on Africa market bonds. Among the global market assets, we identified that VIX (which is implied volatility of S&P500) has the dominant influence on Africa sovereign CDS/YTM compared to that emanating from Bitcoin and Godman Sachs Commodity Index. This is highly conceivable as VIX gauges bubbling global risks and uncertainties which considerably influences investor's risk aversion. The heterogeneous lead/lag dynamics also provide useful information to global investors, including by utilizing African markets to rebalance their portfolios for risk management purposes. The empirical findings thus provide further critical information to investors for hedging purposes, and to policymakers in formulating sovereign risk management policies oriented towards minimizing sovereign default risks.

Modeling the Swelling Behavior of Clayey Geomaterials Across Scales: Advances and Challenges

ABSTRACTMost soils and rocks contain varying fractions of clay minerals within their solid matrix. These geomaterials can exhibit a significant swelling potential toward chemo‐thermo‐hydromechanical loadings. Several multiscale modeling techniques have been developed to ascertain their swelling behavior across various scales, with molecular dynamics (MD), micromechanics‐based approaches, and double‐porosity models being the most common. MD simulation is a computational technique that applies Newton's second law of motion to depict the movement of particles within a granular system. Micromechanics‐based approaches upscale the poro‐elasticity law from the clay layer level to the sample scale through homogenization. Dual‐porosity models are generally based on elasto‐plasticity, incorporating different hydro‐mechanical laws at two distinct scales. These models have been extensively used, particularly for clayey soils and bentonites, though their application to clayey rocks has not been reported in the literature. Although their significant contribution to the understanding of clay swelling behavior, these techniques have been insufficiently reviewed, compared, and discussed mutually in the literature. This paper aims to provide a cross‐look on these multiscale approaches by presenting the theoretical background of existing formulations, highlighting breakthrough results, discussing major differences and current challenges, and proposing future perspectives.

LES and RANS Modeling of an 84-Pin Hexagonal Rod Bundle with Spacer Grid and Experimental Validation

As part of an ongoing integrated research project (IRP), detailed investigations of the flow characteristics of an 84-pin hexagonal rod bundle representing a potential modular gas-cooled fast reactor design have been performed. The rod bundle features a pitch-to-diameter ratio of 1.5 and a large central guide tube, along with simple spacer grids and an outer enclosure. The primary focus of the current work is modeling and simulation of this geometry using multiple computational techniques. These include high-fidelity large eddy simulation (LES) and advanced Reynolds-averaged Navier-Stokes (RANS) approaches. The flow predictions are validated at a Reynolds number of 12 000 using matched index of refraction particle image velocimetry experimental data that were also generated by Texas A&M University as part of the IRP. The comparison data include velocity magnitude and turbulent kinetic energy (TKE) at different lateral locations and at multiple distances downstream of the spacer grid. Many characteristics of the experimental flow are replicated in the LES and RANS runs, and a general agreement between simulation and experiment is shown. Except for the immediate vicinity of the grid, LES is able to capture the velocity magnitude within a 10% error and the TKE to within the experimental uncertainty. The LES shows notably better agreement with the experimental data than RANS, particularly regarding the TKE decay behavior downstream of the grid. Both methods show significant departures from the experiment in their predictions close to the central guide tube. The experimental and high-fidelity data will be used to inform closures for novel multiscale methodologies. The long-term goal of the work is to use the high-fidelity data to yield improved multiscale thermal analysis techniques for solving fuel performance problems of direct relevance to industry.

PMformer: A novel informer-based model for accurate long-term time series prediction

When applied to long-term time series forecasting, Informer struggles to capture temporal dependencies effectively, leading to suboptimal forecasting accuracy. To address this issue, we propose PMformer, a novel model based on Informer for long-term time series prediction. First, we introduce a probabilistic patch sampling attention mechanism that utilizes a patch-based strategy to compute attention scores within randomly selected sequence patches. This localized approach enhances the model's capability to capture local temporal dependencies, allowing it to better understand and process critical local features in time series while reducing computational complexity. Additionally, we propose a multi-scale scaling sparse attention technique that balances attention distribution by combining coarse- and fine-grained attention scores, thereby improving the model's ability to capture global sequence information. Finally, we design a dilated causal pooling layer and a multilayer perceptual cross self-attention decoder to further enhance the model's prediction accuracy by capturing key information in long-term correlations and precisely focusing on sequences. We conducted experiments on both multivariate and univariate time series forecasting tasks. The results show that PMformer outperforms six baseline models, including PatchTST and FEDformer, in terms of MAE and MSE metrics. This demonstrates its superior ability to capture temporal dependencies, achieving more accurate predictions.

Curved-pipe flow with boundary conditions involving Bernoulli pressure

In this article, we study the steady-state flow of the incompressible viscous fluid through a thin distorted pipe with an arbitrary central curve. We prescribe the inflow and outflow boundary conditions involving the Bernoulli pressure with a given pressure drop. Using the multiscale expansion technique with respect to the pipe's thickness, we construct the higher-order asymptotic approximation of the flow given by the explicit formulae for the velocity and pressure. We also perform a detailed error analysis justifying the usage of the proposed solution and indicating its order of accuracy. For more information see https://ejde.math.txstate.edu/Volumes/2024/63/abstr.html

Multi-scale asynchronous correlation and 2D convolutional autoencoder for adolescent health risk prediction with limited fMRI data.

Adolescence is a fundamental period of transformation, encompassing extensive physical, psychological, and behavioral changes. Effective health risk assessment during this stage is crucial for timely intervention, yet traditional methodologies often fail to accurately predict mental and behavioral health risks due to the intricacy of neural dynamics and the scarcity of quality-annotated fMRI datasets. This study introduces an innovative deep learning-based framework for health risk assessment in adolescents by employing a combination of a two-dimensional convolutional autoencoder (2DCNN-AE) with multi-sequence learning and multi-scale asynchronous correlation information extraction techniques. This approach facilitates the intricate analysis of spatial and temporal features within fMRI data, aiming to enhance the accuracy of the risk assessment process. Upon examination using the Adolescent Risk Behavior (AHRB) dataset, which includes fMRI scans from 174 individuals aged 17-22, the proposed methodology exhibited a significant improvement over conventional models. It attained a precision of 83.116%, a recall of 84.784%, and an F1-score of 83.942%, surpassing standard benchmarks in most pertinent evaluative measures. The results underscore the superior performance of the deep learning-based approach in understanding and predicting health-related risks in adolescents. It underscores the value of this methodology in advancing the precision of health risk assessments, offering an enhanced tool for early detection and potential intervention strategies in this sensitive developmental stage.

Structural topology optimization based on deep learning

In the mechanical design of structures, traditional topology optimization methods involve numerous finite element iterative analyses, leading to a significant expenditure of computational resources. Therefore, the improved multi-scale gradient generative adversarial networks topology optimization technique is proposed. The topology optimization condition parameters are compressed into a low-dimensional latent space feature representation using the encoder, allowing the model to better extract features from these parameters. To speed up model training, the generator and discriminator networks use lightweight residual convolutional blocks. The hybrid attention mechanism extracts prominent region features from the topology optimization structure map. The model training process is guided by a multi-dimensional fusion loss function to enhance the quality of generated model samples. Finally, transferring the parameters of the low-resolution topology optimization model to the high-resolution model enables complete training on a limited amount of high-resolution topology optimization datasets. The experimental data on the low- and high-resolution topology optimization datasets demonstrate that, when compared to alternative methods, this method produces better-quality topology optimization structure maps. Additionally, it can generate high-resolution topology optimization structure maps in minimal time, enabling real-time topology optimization.

A Low-Cost and Lightweight Real-Time Object-Detection Method Based on UAV Remote Sensing in Transportation Systems

Accurate detection of transportation objects is pivotal for enhancing driving safety and operational efficiency. In the rapidly evolving domain of transportation systems, the utilization of unmanned aerial vehicles (UAVs) for low-altitude detection, leveraging remotely-sensed images and videos, has become increasingly vital. Addressing the growing demands for robust, real-time object-detection capabilities, this study introduces a lightweight, memory-efficient model specifically engineered for the constrained computational and power resources of UAV-embedded platforms. Incorporating the FasterNet-16 backbone, the model significantly enhances feature-processing efficiency, which is essential for real-time applications across diverse UAV operations. A novel multi-scale feature-fusion technique is employed to improve feature utilization while maintaining a compact architecture through passive integration methods. Extensive performance evaluations across various embedded platforms have demonstrated the model’s superior capabilities and robustness in real-time operations, thereby markedly advancing UAV deployment in crucial remote-sensing tasks and improving productivity and safety across multiple domains.

Strategically Modulating Proton Activity and Electric Double Layer Adsorption for Innovative All-Vanadium Aqueous Mn2+/Proton Hybrid Batteries.

Aqueous Mn-ion batteries (MIBs) exhibit a promising development potential due to their cost-effectiveness, high safety, and potential for high energy density. However, the development of MIBs is hindered by the lack of electrode materials capable of storing Mn2+ ions due to acidic manganese salt electrolytes and large ion radius. Herein, the tunnel-type structure of monoclinic VO2 nanorods to effectively store Mn2+ ions via a reversible (de)insertion chemistry for the first time is reported. Utilizing exhaustive in situ/ex situ multi-scale characterization techniques and theoretical calculations, the co-insertion process of Mn2+/proton is revealed, elucidating the capacity decay mechanism wherein high proton activity leads to irreversible dissolution loss of vanadium species. Further, the Grotthuss transfer mechanism of protons is broken via a hydrogen bond reconstruction strategy while achieving the modulation of the electric double-layer structure, which effectively suppresses the electrode interface proton activity. Consequently, the VO2 demonstrates excellent electrochemical performance at both ambient temperatures and -20°C, especially maintaining a high capacity of 162mAhg-1 at 5Ag-1 after a record-breaking 20000 cycles. Notably, the all-vanadium symmetric pouch cells are successfully assembled for the first time based on the "rocking-chair" Mn2+/proton hybrid mechanism, demonstrating the practical application potential.

Accurate nuclear quantum statistics on machine-learned classical effective potentials.

The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead of incorporating NQEs in complex systems is sizable, particularly at low temperatures. In this work, we leverage deep learning and multiscale coarse-graining techniques to mitigate the computational burden of path integral molecular dynamics (PIMD). In particular, we employ a machine-learned potential to accurately represent corrections to classical potentials, thereby significantly reducing the computational cost of simulating NQEs. We validate our approach using four distinct systems: Morse potential, Zundel cation, single water molecule, and bulk water. Our framework allows us to accurately compute position-dependent static properties, as demonstrated by the excellent agreement obtained between the machine-learned potential and computationally intensive PIMD calculations, even in the presence of strong NQEs. This approach opens the way to the development of transferable machine-learned potentials capable of accurately reproducing NQEs in a wide range of molecular systems.

Modelling across Multiple Scales to Design Biopolymer Membranes for Sustainable Gas Separations: 2-Multiscale Approach

The majority of materials used for membrane-based separation of gas mixtures are non-renewable and non-biodegradable, and the assessment of alternative bio-based polymers requires expensive and time-consuming experimental campaigns. This effort can be reduced by adopting suitable modelling approaches. In this series of works, we propose various modelling approaches to assess the CO2/CH4 separation performance of eight different copolymers of 3-hydroxybutyrate and 3-hydroxyvalerate (PHBV) using a limited amount of experimental data for model calibration. In part 1, we adopted a fully atomistic approach based on Molecular Dynamics (MD), while, in this work, we propose a multiscale methodology where a molecular description of the polymers is bridged to a macroscopic prediction of its gas sorption behaviour. PHBV structures were simulated using MD to obtain pressure–volume–temperature data, which were used to parametrise the Sanchez–Lacombe Equation of State. This, in turn, allows for the evaluation of the CO2 and CH4 solubility in the copolymers at various pressures and compositions with little computational effort, enabling the estimate of the sorption-based selectivity. The gas separation performance obtained with this multiscale technique was compared to results obtained with a fully atomistic model and experimental data. The solubility–selectivity for the CO2/CH4 mixture is in reasonable agreement between the two models and the experimental data. The multiscale method presented is a time-efficient alternative to fully atomistic methods and detailed experimental campaigns and can accelerate the introduction of renewable materials in different applications.

The dual role of dissolution at a crack tip

The scientific literature is rife with conflicting reports regarding the effect of dissolution on fracture. The complexity arises, in part, due to dissolution often being intertwined with various other mechanisms such as hydrogen embrittlement and the formation of debris behind an advancing crack, which can obfuscate the sole contribution of dissolution. Here, we report on the effect of dissolution when acting in isolation via the utilization of an efficient atomistic-based multiscale modeling technique and a specialized interatomic potential. Our results reveal a dual role of dissolution on crack behavior, introducing an additional layer of complexity to the mechanistic basis of environmental effects. This finding, while challenging for engineering prognosis, provides a route for engineering improved materials. Recognizing and navigating this duality could be pivotal to precluding potentially disastrous consequences in a broad array of engineering applications, from harnessing earth’s energy resources to aerospace technologies.

Advanced Copula-based Methods for Nonparametric Detection and Characterization of Wideband Radar Signals

This paper introduces advanced copula-based methods for the nonparametric detection and characterization of wideband radar signals. The research focuses on developing signal detection algorithms that are invariant to changes in the probability density function of the sounding or reflected signals, employing multiscale analysis techniques and copula-based statistics. Two primary approaches are explored: multiscale analysis using wavelet transforms and rank-based signal detection with copula-based ambiguity functions. Simulation results confirm the effectiveness of the proposed approaches. The research demonstrates that integrating rank-based methods with copula-based statistics significantly improves the detection and analysis of wideband radar signals, particularly in complex scenarios where signals exhibit intricate dependency structures. This comprehensive detection framework is well-suited for handling high-dimensional radar signal data, enhancing accuracy and reliability under varied conditions. Future work will focus on optimizing copula selection and permutation strategies to further improve performance.