Inverse Parameter Research Articles

A rapid analysis framework for seismic response prediction and running safety assessment of train-bridge coupled systems

With high-speed railway lines increasing gradually, the running safety assessment (RSA) of train-bridge coupled (TBC) systems has become an indispensable part of railway seismic design. However, the modeling of TBC systems is difficult and computationally complex. Therefore, it is difficult to conduct real-time assessment and response analysis rapidly. With this in mind, this paper integrates a surrogate framework based on deep learning methods and can help rapid-diagnose the seismic response and RSA. Meanwhile, real-time information feedback is performed to determine the safe speed of the train. To this end, a convolutional neural network-long short-term memory (CNN-LSTM) model with excellent time-series data processing capability is newly used for the seismic response analysis of the TBC system. Furthermore, response data obtained are processed and input to an interpretable adaptive network-based fuzzy inference system (ANFIS). The ANFIS derives a series of fuzzy rules while conducting the RSA, and these rules can help non-specialists understand the assessment process. Finally, parameter inversion is performed by the ANFIS to determine a safe threshold of train speed. According to the tests, the proposed rapid analysis framework can be applied to seismic response analysis and RSA with high efficiency and accuracy in multiple engineering scenarios. The framework may be helpful for railway design and make it possible to realize real-time data analysis for TBC systems.

Research on Estimating and Evaluating Subtropical Forest Carbon Stocks by Combining Multi-Payload High-Resolution Satellite Data

Forest carbon stock is an important indicator reflecting the structure of forest ecosystems and forest quality, and an important parameter for evaluating the carbon sequestration capacity and carbon balance of forests. It is of great significance to study forest carbon stock in the context of current global climate change. To explore the application ability of multi-loaded, high-resolution satellite data in the estimation of subtropical forest carbon stock, this paper takes Huangfu Mountain National Forest Park in Chuzhou City as the study area, extracts remote sensing features such as spectral features, texture features, backscattering coefficient, and other remote sensing features based on multi-loaded, high-resolution satellite data, and carries out correlation analyses with the carbon stock of different species of trees and different age groups of forests. Regression models for different tree species were established for different data sources, and the optimal modeling factors for multi-species were determined. Then, three algorithms, namely, multiple stepwise regression, random forest, and gradient-enhanced decision tree, were used to estimate carbon stocks of multi-species, and the predictive ability of different estimation models on carbon stocks was analyzed using the coefficient of determination (R2) and the root mean square error (RMSE) as indexes. The following conclusions were drawn: for the feature factors, the texture features of the GF-2 image, the new red edge index of the GF-6 image, the radar intensity coefficient sigma, and radar brightness coefficient beta of the GF-3 image have the best correlation with the carbon stock; for the algorithms, the random forest and gradient-boosting decision tree have the better effect of fitting and predicting the carbon stock of multi-tree species, among which gradient-boosting decision tree has the best effect, with an R2 of 0.902 and an RMSE of 10.261 t/ha. In summary, the combination of GF-2, GF-3, and GF-6 satellite data and gradient-boosting decision tree obtains the most accurate estimation results when estimating forest carbon stocks of complex tree species; multi-load, high-resolution satellite data can be used in the inversion of subtropical forest parameters to estimate the carbon stocks of subtropical forests. The multi-loaded, high-resolution satellite data have great potential for application in the field of subtropical forest parameter inversion.

Enhancing Leaf Area Index Estimation with MODIS BRDF Data by Optimizing Directional Observations and Integrating PROSAIL and Ross–Li Models

The Leaf Area Index (LAI) is a crucial vegetation parameter for climate and ecological models. Reflectance anisotropy contains valuable supplementary information for the retrieval of properties of an observed target surface. Previous studies have utilized multi-angular reflectance data and physically based Bidirectional Reflectance Distribution Function (BRDF) models with detailed vegetation structure descriptions for LAI estimation. However, the optimal selection of viewing angles for improved inversion results has received limited attention. By optimizing directional observations and integrating the PROSAIL and Ross–Li models, this study aims to enhance LAI estimation from MODIS BRDF data. A dataset of 20,000 vegetation parameter combinations was utilized to identify the directions in which the PROSAIL model exhibits higher sensitivity to LAI changes and better consistency with the Ross–Li BRDF models. The results reveal significant variations in the sensitivity of the PROSAIL model to LAI changes and its consistency with the Ross–Li model over the viewing hemisphere. In the red band, directions with high sensitivity to LAI changes and strong model consistency are mainly found at smaller solar and viewing zenith angles. In the near-infrared band, these directions are distributed at positions with larger solar and viewing zenith angles. Validation using field measurements and LAI maps demonstrates that the proposed method achieves comparable accuracy to an algorithm utilizing 397 viewing angles by utilizing reflectance data from only 30 directions. Moreover, there is a significant improvement in computational efficiency. The accuracy of LAI estimation obtained from simulated multi-angle data is relatively high for LAI values below 3.5 when compared with the MODIS LAI product from two tiles. Additionally, there is also a slight improvement in the results when the LAI exceeds 4.5. Overall, our results highlight the potential of utilizing multi-angular reflectance in specific directions for vegetation parameter inversion, showcasing the promise of this method for large-scale LAI estimation.

Bayesian Inversion of Lithology and Liquid Phase Parameters From Seismic Velocity and Electrical Conductivity in the Crust and Uppermost Mantle

AbstractTo deeply understand various geodynamic processes, including volcanic activities and earthquakes, it is essential to extract detailed information about Earth materials, such as lithology and geofluid, from geophysical, petrological, and geochemical observations of Earth's interior. We developed a Bayesian probabilistic framework that can estimate the lithology and geofluid type (aqueous fluid or melt), geofluid amount (porosity), and parameters related to the fluid geometry (aspect ratio and critical fluid fraction related to connectivity) from P‐wave and S‐wave seismic velocities and electrical conductivity data obtained from geophysical tomography. By conducting synthetic inversion tests, we showed that methods based on a joint probability distribution, which simultaneously determines all parameters, sometimes fail to narrow the number of possible answers from 78 lithologies (e.g., basalt, granite, and eclogite) × two geofluid type (melt or aqueous fluid) candidate sets. This failure is derived directly from the difficult nature of inversion problems with relatively large data uncertainties. The proposed method uses a marginalization technique that first estimates lithology and geofluid type and then quantifies geofluid parameter values, which can narrow the probable lithology, geofluid type, and geofluid parameter sets in many cases. In addition, the computational cost of the proposed marginalization method is comparative to a former joint‐estimation method, which is theoretically identical to a previous heuristic method based on the least squares method. Therefore, the marginalization method is useful for geophysical data analyses that involve large amounts of observational data with relatively large uncertainties.

Experimental and numerical studies on low-velocity impact of laminated C/SiC structures

Laminated C/SiC(carbon fiber reinforced silicon carbide composites) has the complicated nature of composite failure which include cracks for void defects at the meso and micro scales, complex cracks propagation of tunnel cracks, matrix cracks, delaminations and fiber cracks, orthotropic, and pseudoplastic behavior. It has technical challenge to solve all of them for complicated-mechanics problems by using multi-scale methodology. This paper focused tackling it by a model that lies between macro and meso scales, and proposed a new conceptual 3D FE-PDM(Finite Element - Progressive Damage Method). 3D FE-PDM was validated by the experiments of low-velocity impact of 2D C/SiC and 3D needled C/SiC. Damage initiation and evolution were controlled by strain in order to preventing stress chaos which could occur as cracks leading local stress relief. The multi-linear constitutive relations were adopted in orthotropic directions. The coupled effects of stresses between in-plane and out-of-plane were computed by adding damage coefficients into stiffness matrix. Cohesive Zone Method was used for delamination. The PDM approach was introduced for the 3D elements for intralaminar and cohesive elements for the interfaces. A parametric inversion methodology was put forward to determine the model parameters iteratively by comparing simulation results with the load-time curves, damage CT details of the experiments. Validation implies that, with small number of parameters, 3D FE-PDM is able to predict damage initiation of each phase knee, damage evolution, and load–displacement curve with good convergence for the low-velocity impact case. 2D woven and 3D needled non-woven C/SiC both have impact energy threshold and different damage evolution types.

Seismic fluid identification method based on the joint PP‐ and SH–SH‐wave stochastic inversion

AbstractPre‐stack seismic inversion is an effective method for elastic parameter inversion using seismic data, which facilitates seismic fluid identification. However, pure PP‐wave inversion has issues of strong multi‐solution and limited prediction accuracy. Therefore, we propose a seismic fluid identification approach based on the joint PP‐ and SH–SH‐wave stochastic inversion. First, the linearized SH–SH‐wave amplitude variation with offset approximation parameterized by shear modulus and density is derived. Numerical simulations demonstrate that the SH–SH‐wave amplitude variation with offset approximation has a good accuracy. Reflection coefficient contribution analysis indicates that the new formulation has better parameter sensitivity to shear modulus and density than the PP wave amplitude variation with offset approximation derived by Russell, which helps one to improve the inversion of shear modulus and density. On this basis, we construct a joint inversion equation of PP and SH–SH waves for a Russell fluid indicator, a shear modulus and density and present a novel joint stochastic inversion method based on the ensemble smoother with multiple data assimilation. Stanford VI‐E model tests reveal that the Russell fluid indicator factor, shear modulus and density obtained from the joint PP‐ and SH–SH‐wave inversion have higher identification accuracy and smaller relative errors than those from pure PP‐wave inversion. Furthermore, field data tests indicate that this method has practical applicability in seismic fluid identification.

Gradient optimization method for tunnel resistivity and chargeability joint inversion based on deep learning

The water inrush hazards have become one of the bottleneck problems that constrain tunnel construction. Ahead geological prospecting is the major tool to avoid geo-hazards and ensure safe, economical and efficient tunnelling. This work proposes a novel deep learning-based electrical method, which jointly inverses resistivity and chargeability to estimate water-bearing structures and water volume. Specifically, we design an encoder–decoder network, with one shared encoder to extract features from input data, two encoders to output resistivity and chargeability models, respectively, and an elaborate collinear regularization on the two outputs to reduce solution multiplicity. Moreover, our input is first transformed to the gradient domain to address the spatial incorrespondence issue between observation data and the electrical model. Compared with traditional linear inversion methods, our proposed method demonstrates superiority in locating and delineating anomalous bodies. The ablation study also shows that joint inversion of two parameters could benefit and outperform independent parameter inversion.

Prediction of surface settlement caused by synchronous grouting during shield tunneling in coarse-grained soils: A combined FEM and machine learning approach

This paper presents a surrogate modeling approach for predicting ground surface settlement caused by synchronous grouting during shield tunneling process. The proposed method combines finite element simulations with machine learning algorithms and introduces an intelligent optimization algorithm to invert geological parameters and synchronous grouting variables, thereby predicting ground surface settlement without conducting numerous finite element analyses. Two surrogate models based on the random forest algorithm are established. The first is a parameter inversion surrogate model that combines an artificial fish swarm algorithm with random forest, taking into account the actual number and distribution of complex soil layers. The second model predicts surface settlement during synchronous grouting by employing actual cover-diameter ratio, inverted soil parameters, and grouting variables. To avoid changes to input parameters caused by the number of overlying soil layers, the dataset of this model is generated by the finite element model of the homogeneous soil layer. The surrogate modeling approach is validated by the case history of a large-diameter shield tunnel in Beijing, providing an alternative to numerical computation that can efficiently predict surface settlement with acceptable accuracy.

Potentiality of ultraspectral sensor in biophysical and biochemical vegetation parameter inversion

ABSTRACT Biophysical and biochemical vegetation parameters are important indicators for quantitatively monitoring vegetation growth status and ecosystem. Compared to hyperspectral data, the emergence of ultraspectral remote sensing technology supports the acquisition of thousands of more narrow bands in near-infrared spectrum. It is helpful to capture more detailed vegetation spectral features, thereby providing more accurate quantitative inversion. However, there are still many unknowns in utilizing ultraspectral sensors for vegetation biochemical and biophysical parameters inversion, particularly in extracting meaningful inversion information from thousands of spectral bands. Here, we discuss the potentiality, efficiency and accuracy of the ultraspectral sensor AisaIBIS in this field. Firstly, we conducted sensitivity analysis based on simulated sensor dataset and the PROSAIL model to determine the vegetation parameters suitable for inversion. Secondly, in order to enhance the inversion efficiency and reduce the effects of multicollinearity in ultraspectral data, we proposed the stepped asymptotic optimization strategy that combined random forest (RF) and Gaussian process regression (GPR-BAT) methods for dimensionality reduction. Lastly, using experimental data, we compared the inversion accuracy between traditional band selection methods and our proposed method, thereby validating the application potential of ultraspectral sensors. The experimental results indicate that leaf area index (LAI), chlorophyll content, and brown pigment are the most sensitive parameters to the spectral information and are suitable for inversion. Based on the stepped asymptotic optimization strategy, we effectively avoid incomplete information extraction caused by high correlation and spectral redundancy, achieving optimal bands covering the entire spectrum of the sensor. The LAI inversion shows a correlation of 0.691 and an RMSE of 1.955 with the original data, outperforming the accuracy of the traditional band selection methods RF and principal component analysis (PCA). Moreover, the inversion time has decreased by approximately 66% after the dimensionality reduction. This study illustrates the application value of monitoring vegetation parameters by ultraspectral sensor.

Response and inversion of skewness parameters to meteorological factors based on RGB model of leaf color digital image.

In the natural environment, complex and changeable meteorological factors can influence changes in the internal physiology and phenotype of crops. It is important to learn how to convert complex meteorological factor stimuli into plant perception phenotypes when analyzing the biological data obtained under the natural field condition. We restored the true gradation distribution of leaf color, which is also known as the skewed distribution of color scale, and obtained 20 multi-dimensional color gradation skewness-distribution (CGSD) parameters based on the leaf color skewness parameter system. Furthermore, we analyzed the correlation between the five corresponding meteorological factors and canopy CGSD parameters of peppers growing in a greenhouse and cabbages growing in an open air environment, built response model and inversion mode of leaf color to meteorological factors. Based on the analysis, we find a new method for correlating complex environmental problems with multi-dimensional parameters. This study provides a new idea for building a correlation model that uses leaf color as a bridge between meteorological factors and plants internal physiological state.

The Effect of Different Polyol Precursors on Disordered Spinel ZnAl2O4 Structure Prepared by the Polymeric Citrate Complex Method and the Corresponding Catalytic Behavior in the Glycerolysis of Urea

ZnAl2O4 is a cubic close‐packed oxide with tetrahedral and octahedral sites in the lattice structure. The catalytic activity of ZnAl2O4 is strongly connected with the surface properties caused by the partially inverse spinel ZnAl2O4 structure. In this research, ZnAl2O4 catalysts are prepared for the glycerolysis of urea via the polymeric citrate complex method using polymeric templates made of citric acid with a different polyol precursor. Depending on the polyol precursor, the partial inversion parameters representing the disordered bulk ZnAl2O4 structure are controlled, which results in different surface AlO4/AlO6 ratios and surface acidity. The specific surface areas of the prepared ZnAl2O4 catalysts are proportional to the molecular weight of the polyol precursor. The s–ZnAl2O4 (polyol precursor = sorbitol) prepared via two pathways from citrate complex and polymeric citrate complex shows the highest inversion parameter and surface acidity, leading to the highest glycerol carbonate (GC) yield and glycerol conversion in the glycerolysis of urea. A relationship between the GC yield and the surface properties, such as the acidity and inversion parameters, is established.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain’s white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.

Creep Properties and Creep Modelling of Guilin Red Clay

In order to explore the creep characteristics of red clay under different pressures, the stress–strain curve and stress–strain–time curve of red clay under different pressures were obtained, and the triaxial shear and creep characteristics of red clay under different pressures were analysed. A triaxial shear test and creep test were carried out on red clay from Guilin as the research object under different pressures. The results show that: ➀ the cohesion and the angle of internal friction of red clay from Guilin, obtained from a triaxial shear test, are 57.20 kPa and 22.47°, respectively; ➁ according to the physical meaning of the parameters of the Burgers creep model, a simple and practical parameter inversion method is proposed, which can be used to obtain the parameters of the Burgers model for red clay under different perimeter pressures and differing deviatoric stress; and ➂ when comparing the calculation results with the test results, the correlation coefficients R2 of the two are above 0.9, with a good fitting effect, so the model can accurately describe the creep characteristics of red clay from Guilin. This study can provide a theoretical basis and technical support for engineering construction in the red clay area of Guilin.

Inversion of the Seepage Parameters of Earth/Rockfill Dams Considering the Coupling Effect of Seepage and Thermal Transfer

The estimation of inversion parameters for seepage models is very important for ensuring the safety of earth/rockfill dams. In most existing studies, only hydraulic characteristics have been determined based on seepage pressure or discharge observation information, which may result in inversion results that do not accurately characterize the true properties of dam materials. In this paper, an advanced parameter inversion method considering the coupling effect of seepage and thermal transfer is proposed. A seepage–thermal transfer coupled finite element model is established, and hydraulic head and temperature data of monitoring points are obtained through the forward simulation method. The entropy weight (EW) method is used to preprocess the hydraulic head and temperature data, and a universal kriging (UK) surrogate model is established to replace the time-consuming finite element simulations. The multi-island genetic algorithm (MIGA) is applied to find the optimal solution, thereby obtaining the inversion results. The effectiveness and accuracy of the proposed method are verified through laboratory tests involving seepage and thermal transfer monitoring of a core rockfill dam. Joint inversion based on temperature and hydraulic head observation information can result in improvement in the accuracy of the inversion results.

Parameter inversion analysis of rubber-mortar cohesive zone model in rubberized concrete

The rapid development of urban rail transit has brought convenience to travel, but also causes serious environmental vibration problems. Some scholars have proposed rubberized concrete invert-filling as a damping measure. The addition of rubber particles creates the rubber-mortar interface, which is an important factor that affects the damping performance of rubberized concrete. In this study, we propose an interface modification method of coating rubber with zinc stearate powder to improve the damping performance of rubberized concrete. The stiffness, strength, and fracture energy of the rubber-mortar interface were obtained by an inversion analysis technique based on numerical simulation and experimental results. The results show that: (1) The uniaxial tensile test determined the bonding strength of the rubber-mortar interface treated with water, sodium hydroxide, and zinc stearate as 0.144 MPa, 0.160 MPa, and 0.074 MPa, respectively. (2) Based on numerical simulations and experimental results, the bonding strength of the rubber-mortar interface treated by three methods was 0.142 MPa, 0.146 MPa, and 0.080 MPa, respectively, with relative errors of less than 10 %. (3) Compared with the interface obtained by water treatment, the interface modified by zinc stearate showed a 43.7 % reduction in bonding strength and a 46.0 % reduction in fracture energy.

Inverse parameter identifications and forward strip temperature simulations of the continuous annealing line with physics-informed neural network and operation big data

The continuous annealing line is a key equipment in industrial metal heat treatment. It is a large-thermal-inertia cascade thermal system, and has minute-level time hysteresis between adjustable control parameters and outlet strip temperature, which is challenging for real operation. Large strip temperature deviation from targets will greatly damage the mechanical properties and the surface coating quality of the strip. Traditional methods such as energy balance method, computational fluid dynamics and end-to-end data-driven model are hard to solve the problem due to complex parameter settings, large computing costs and low interpretability, respectively. Here, a novel way seamlessly coupling physical model and data based on physics-informed neural network is used to solve the problem. The mathematical-physical model of the continuous annealing line is developed and a physics-informed neural network model is built to solve inverse problem to identify the heat transfer coefficient of the continuous annealing line. The strip temperature is numerically simulated both with physics-informed neural network model and computational fluid dynamics model. The simulated results are compared with the measured data. The simulated outlet strip temperatures of the two models agree well with the measured data and the accuracy of the identified heat transfer coefficient is verified, where the computational fluid dynamics model has higher accuracy. The physics-informed neural network models developed here will benefit intelligent feedforward cascade control of the continuous annealing line and improve the strip quality in real productions.

Composite interpretability optimization ensemble learning inversion surrounding rock mechanical parameters and support optimization in soft rock tunnels

The mechanical parameters of the surrounding rock of a tunnel are the premise and foundation of the supporting design in soft rock tunnel engineering. To obtain the mechanical parameters of the surrounding rock accurately and quickly, a composite inversion model is proposed, and different models are used to invert different mechanical parameters. In this paper, first, the Latin hypercube and Monte Carlo sampling methods are used to construct the mechanical parameter samples from the surrounding rocks. The numerical simulation of the water diversion project in central Yunnan is carried out by using FLAC3D, and the corresponding displacement data are obtained, three sets of effective inversion datasets are formed along with the mechanical parameter samples. Second, the adjusted coefficient of determination and the symmetrical mean absolute percentage error are used as the performance evaluation indices. The Bayesian 10-fold cross-validation iteration is used to optimize the five regression model hyperparameters for the three sets of inversion parameters. The base model of the best performance is selected for inverting the friction angle (φ) and cohesion (c). For the deformation modulus (Em) inversion parameters, LIME interpretability is used to optimize the weights and integrate the five models. Finally, by developing a calculation tool for the elastic modulus of tunnel support, an orthogonal experimental design is applied based on the verified engineering numerical model. The results show that the average error of the inversion results of the mechanical parameters of the surrounding rock by the proposed composite model is 9.32%, the minimum error is only 0.81%, and the error is within 15%. The inversion trend is similar to the actual displacement height, and the optimized support scheme provides a reference for the engineering site.

Seepage Model and Pressure Response Characteristics of Non-Orthogonal Multi-Fracture Vertical Wells with Superimposed Sand Body in Tight Gas Reservoirs

Faced with difficulties stemming from the complex interactions between tight gas sand bodies and fractures, when describing and identifying reservoirs, a composite reservoir model was established. By setting the supply boundary to characterize the superposition characteristics of sand bodies, a mathematical model of unstable seepage in fractured vertical wells in tight sandstone gas reservoirs was developed, considering factors such as stress sensitivity, fracture density and fracture symmetry. The seepage law and pressure response characteristics of gas wells in tight sandstone discontinuous reservoirs with stress sensitivity, semi-permeable supply boundary and complex fracture topology were determined, and the reliability of the model was verified. The research results more accurately display the pressure characteristic of a vertical well in the superimposed sand body with complex fractures and provide a more comprehensive model for tight gas production dynamic analysis and well test data analysis, which can more accurately guide the dynamic inversion of reservoir and fracture parameters.

Analysis of civil and commercial law protection based on decentralized Internet

Abstract To promote fairness and justice in law, it is important to explore the protective role of civil and commercial law. The relationship between civil and commercial law and public opinion supervision is examined through Internet public opinion. A decentralized Internet public opinion index system has been established, and a better random network public opinion dissemination model is proposed through parameter inversion of the SIR model and network simulation. The protection of transaction security and information rights by civil and commercial law is the focus of the evolution of Internet public opinion cases. The promotion of industry self-regulation is enhanced by 14.63% when civil and commercial law intervenes. On the flip side, it aids in protecting personal information, and the likelihood of personal information leakage is reduced by 25.48%. This study can effectively reference the implementation of civil and commercial law in the Internet era.

Terahertz bandwidth absorption metamaterial based on composite structure of single layer graphene

With the development of science and technology, people have realized the value of studying the terahertz band, in this paper, a terahertz bandwidth tunable metamaterial based on composite structure of single layer graphene is proposed, which can have an absorption higher than 0.9 at 3–6.7 THz and exhibit polarization insensitivity. By employing parameter inversion to calculate the relative impedance, the metamaterial adheres to the principles of impedance matching theory. The metamaterial exhibits considerable chemical and physical tuning capabilities, and it can be substantiated that the enhanced absorption rate of the metamaterial stems from a multitude of graphical configurations. Simultaneously, the metamaterial demonstrates a notable level of stability towards the incidence angle of electromagnetic waves and can function reliably at an incidence angle of 30°. In conclusion, the metamaterial holds promising potential for applications in radar stealth, communication, and other related domains.