Spatial Deformation Research Articles

Curvature programming of freestanding 3D mesostructures and flexible electronics based on bilayer ribbon networks

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

Detection and Mechanical Interpretation of Surface Displacement by Volcanic and Anthropogenic Interactions around Bandung Basin, through Multi Temporal Interferometric SAR (MT-InSAR) Technique

Abstract This study aims to evaluate capability of MT-InSAR (Multi Temporal interferometric synthetic aperture radar) technique for measuring the surface displacement caused by tectonic, volcanic, and anthropogenic activity around the Bandung Basin, West Java, Indonesia. For this, persistent scatterer (PS), small baseline subset (SBAS), and combined PS and SBAS techniques are adopted. The results reveal different displacement patterns within two areas anthropogenic-caused subsidence in the middle Bandung city and geothermal production field, and volcanic-caused uplift in the northern area around the Tangkuban Parahu volcano. In addition, each InSAR tehnique shows unique spatial deformation. A significant pattern is located around the Wayang Windu geothermal field that large displacements has been occurred around injection, production wells. Those detected displacements are crucial for mitigating geological hazards as well as geothermal production monitoring.

Graphene Sterically-Wrapped textile piezoresistive Sensors: A spray coating path for synergistically advancing sensitivity and response range

Trade-off between a high sensitivity and a broad sensing range remains a persistent challenge for flexible pressure sensors. Not to suffer from this dilemma, a flexible textile piezoresistive sensor sterically-wrapped with graphene by spray coating is reported, which constructs enriched three-dimensional conductive networks from leather fabric’s inherent fibers and pore structures, synergistically advancing the sensitivity and response range. Such a sensor renders bulky spatial deformation and augmented pressure-induced conducting paths, and hence affords an ultra-high sensitivity of 259.6 kPa−1(0–100 kPa) and an exceptional response range of up to 1 MPa. Besides, the graphene/textile sensor demonstrates outstanding durability (>12000 cycles). With these advantages, real-time monitoring of human physiological activities such as wrist pulses and throat swallowing is successfully achieved. Benefitting from the scalability of the spraying methodology, a large-size 45 × 45 cm2 sensing array with a 32 × 32 matrix is facilely fabricated to map the spatial pressure of human interactive behaviors for ergonomics. And smart insoles incorporating graphene/textile sensors can capture plantar pressure distribution and provide effective analysis for diverse static/dynamic movements of feet. Such spray-coated textile sensors could not only find potential applications in wearable electronics and intelligent robotics, but also open the possibility of monitoring complex heavy machinery and large-scale infrastructures.

Anatomical Features and Material Properties of Human Surrogate Head Models Affect Spatial and Temporal Brain Motion under Blunt Impact.

Traumatic brain injury (TBI) is a biomechanical problem where the initiating event is dynamic loading (blunt, inertial, blast) to the head. To understand the relationship between the mechanical parameters of the injury and the deformation patterns in the brain, we have previously developed a surrogate head (SH) model capable of measuring spatial and temporal deformation in a surrogate brain under blunt impact. The objective of this work was to examine how material properties and anatomical features affect the motion of the brain and the development of injurious deformations. The SH head model was modified to study six variables independently under blunt impact: surrogate brain stiffness, surrogate skull stiffness, inclusion of cerebrospinal fluid (CSF), head/skull size, inclusion of vasculature, and neck stiffness. Each experimental SH was either crown or frontally impacted at 1.3 m/s (3 mph) using a drop tower system. Surrogate brain material, the Hybrid III neck stiffness, and skull stiffness were measured and compared to published properties. Results show that the most significant variables affecting changes in brain deformation are skull stiffness, inclusion of CSF and surrogate brain stiffness. Interestingly, neck stiffness and SH size significantly affected the strain rate only suggesting these parameters are less important in blunt trauma. While the inclusion of vasculature locally created strain concentrations at the interface of the artery and brain, overall deformation was reduced.

Bioinspired Genetic and Chemical Engineering of Protein Hydrogels for Programable Multi-Responsive Actuation.

Protein hydrogels with tailored stimuli-responsive features and tunable stiffness have garnered considerable attention due to the growing demand for biomedical soft robotics. However, integrating multiple responsive features toward intelligent yet biocompatible actuators remains challenging. Here, a facile approach that synergistically combines genetic and chemical engineering for the design of protein hydrogel actuators with programmable complex spatial deformation is reported. Genetically engineered silk-elastin-like proteins (SELPs) are encoded with stimuli-responsive motifs and enzymatic crosslinking sites via simulation-guided genetic engineering strategies. Chemical modifications of the recombinant proteins are also used as secondary control points to tailor material properties, responsive features, and anisotropy in SELP hydrogels. As a proof-of-concept example, diazonium coupling chemistry is exploited to incorporate sulfanilic acid groups onto the tyrosine residues in the elastin domains of SELPs to achieve patterned SELP hydrogels. These hydrogels can be programmed to perform various actuations, including controllable bending, buckling, and complex deformation under external stimuli, such as temperature, ionic strength, or pH. With the inspiration of genetic and chemical engineering in natural organisms, this work offers a predictable, tunable, and environmentally sustainable approach for the fabrication of programmed intelligent soft actuators, with implications for a variety of biomedical materials and biorobotics needs.

The Mechanics of Building Functional Organs.

Organ morphogenesis is multifaceted, multiscale, and fundamentally a robust process. Despite the complex and dynamic nature of embryonic development, organs are built with reproducible size, shape, and function, allowing them to support organismal growth and life. This striking reproducibility of tissue form exists because morphogenesis is not entirely hardwired. Instead, it is an emergent product of mechanochemical information flow, operating across spatial and temporal scales-from local cellular deformations to organ-scale form and function, and back. In this review, we address the mechanical basis of organ morphogenesis, as understood by observations and experiments in living embryos. To this end, we discuss how mechanical information controls the emergence of a highly conserved set of structural motifs that shape organ architectures across the animal kingdom: folds and loops, tubes and lumens, buds, branches, and networks. Moving forward, we advocate for a holistic conceptual framework for the study of organ morphogenesis, which rests on an interdisciplinary toolkit and brings the embryo center stage.

Topographical Effects on Volcano Deformation Signal Intensity: Implications for GPS Network Configuration

AbstractVolcano GPS networks can capture vital information during volcanic unrest to aid with hazard assessment and eruption forecasting, but can be hindered by their discrete point locations and possibly miss key spatial information. We show how numerical models can reveal controls on spatial deformation signal intensity compared against GPS network design. Using the GPS network at Soufrière Hills Volcano (SHV), Montserrat, and a range of models, we explore expected surface deformation patterns. Peak horizontal deformation is located offshore, highlighting the difficulties with geodetic monitoring on small ocean‐island volcanoes. Onshore areas where the deformation signal is expected to be high are also identified. At SHV, topography plays a greater role in altering the relative distribution of surface displacement patterns than subsurface heterogeneity. Our method, which can be adapted for other volcanoes, highlights spatial areas that can be targeted for effective GPS station placement to help improve deformation monitoring efficiency.

Mechanical behaviour of weakly filled granite and a unified evaluation method for macro-fine-micro multi-scale fracture characteristics

The mechanical properties of weakly filled rock are critical for engineering rock stability control. With the help of 3D DIC (Digital Image Correlation) and AE (Acoustic Emission) monitoring system, and the industrial CT (Computed Tomography), 3D laser scanning and SEM (Scanning Electron Microscope) technology, the mechanical behaviour and fracture characteristics of granite with different inclination angles of planar weak filling were analyzed comprehensively. Firstly, the influence law of the inclination angle of planar weak filling on the basic mechanical properties of the specimens was investigated, and it was confirmed that the specific angle had an obvious weakening effect on the specimen’s ability to resist deformation. Then, the spatial deformation field evolution and failure mode of the specimen were analysed, and it was found that when the inclination angle increased from 0° to 90°, the failure mode of the specimen will gradually change from “Y”-shaped shearing and splitting mixed failure to “chain” splitting failure, and then to overall splitting failure. Then, the spatial distribution of the micro-fracture event was analysed, and the results show that the spatio-temporal evolution and distribution characteristics of the micro-fracture events, the distribution characteristics of the spatio-temporal evolutionary local enlargement zone of the deformation field and the spatial distribution of the main fracture surface at the time of final failure are highly consistent and correlated. The spatio-temporal evolution and distribution characteristics of micro-fracture events provide important references for predicting the location, time and degree of spatial failure in weakly filled rock mass. Finally, based on the fractal theory, the fracture characteristics within the multiscale of the specimen were analysed, and the method of evaluating the unity of the multiscale fracture characteristics of the rock mass was summarised and given.

A temporal graph neural network for cross-scale modelling of polycrystals considering microstructure interaction

Machine learning (ML) based methods have achieved preliminary success in the constitutive modeling for single crystals or homogenized polycrystals with remarkable computational efficiency. However, existing ML-based constitutive models neglect grain-level anisotropy, which limits the accurate analysis of local effects. In the current work, a temporal graph neural network (TGNN) model is proposed to simulate cross-scale deformation behaviors of polycrystals under complex loading conditions, with straightforward consideration of microstructure variation and local interaction. The TGNN-based model, a variant of Linearized Minimal State Cells (LMSCs), extends its scope from macroscopic stress response to the mechanical response and orientation evolution of all grains within the aggregate. Specifically, the polycrystalline microstructure is represented with a graph to incorporate essential features of grains, including the spatial connectivity, crystallographic orientation and deformation state. Graph neural network (GNN) is used to capture the spatial correlation of grains, and the features extracted by the GNN are further processed with LMSCs to account for the history-dependent deformation and microstructure evolution. Moreover, the representative volume element (RVE) simulation with crystal plasticity is performed to provide reliable datasets for model establishment. The proposed model demonstrates high efficiency, accuracy and self-consistency in predicting the strain-stress response and orientation evolution at the scale of both individual grain and the overall aggregate under complex loading cases, such as cyclic loading and arbitrary loading.

A method for predicting deformation field of deep foundation pit considering spatial effect

Urban underground spaces have experienced significant development and utilization due to the rapid progress of urban construction and continuous advancements in construction technology. The number of foundation-pit projects immediately adjacent to buildings, structures, and pipelines has been increasing. Ensuring the safety of construction and surrounding facilities, it is essential to predict deformation caused by foundation pit excavations. In this study, a simple calculation method was proposed for predicting deformation of an envelope structure and surface settlement caused by deep foundation excavation with spatial effects. Firstly, the principle of minimum potential energy was applied and the lateral displacement equation of the envelope structure was derived, considering spatial deformation effects. Secondly, based on linear elasticity theory, a surface settlement expression was formulated utilizing the plane strain boundary. Finally, the stratigraphic loss method was used to establish a connection between horizontal envelope deformation and surface settlement, allowing for calculations of surface settlement at any position behind the envelope structure. The effectiveness and practicability of the proposed method were demonstrated by comparison of two existing foundation-pit engineering examples.

Spatiotemporal Mechanism-Based Spacetimeformer Network for InSAR Deformation Prediction and Identification of Retrogressive Thaw Slumps in the Chumar River Basin

The increasing incidence of retrogressive thaw slumps (RTSs) in permafrost regions underscores the need for detailed spatial and temporal analysis using InSAR technology to monitor and predict dynamic changes in the process of RTSs. Nevertheless, current InSAR deformation forecasting methods employing deep learning strategies such as the traditional long short-term memory (LSTM) and recent transformer models encounter difficulties in effectively capturing temporal features. Moreover, they are limited in their ability to directly integrate spatial information. In this paper, an innovative deep learning approach named Spacetimeformer is proposed for predicting medium- and short-term InSAR deformation of RTSs in the Chumar River area. This method employs a transformer architecture with a spatiotemporal attention mechanism, which enhances the long-term prediction capabilities of time series models and dynamic spatial modeling. It is applicable to multivariate InSAR spatiotemporal deformation prediction problems. The findings include a list of 72 RTSs compiled based on derived InSAR deformation maps and Sentinel-2 optical images, of which 64 have an average deformation rate exceeding 10 mm/year, indicating signs of permafrost degradation. The density distribution of the displacement maps predicted by the Spacetimeformer model aligned well with the InSAR deformation maps obtained from the small baseline subset (SBAS) method, with the overall prediction deviation controlled within 20 mm. In addition, the point-scale prediction results were compared with LSTM and transformer models. This study indicates that the Spacetimeformer network achieved good results in predicting the deformation of RTSs, with a root mean square error of 1.249 mm. The Spacetimeformer method for deformation prediction with the spacetime mechanism presented in this study can serve as a general framework for multivariate deformation prediction based on InSAR results. It can also quantitatively assess the spatial deformation characteristics and deformation trends of RTSs.

Field research on supersized rectangle pipe-jacked tunnels beneath a navigable river in the urban area

With technological progress in recent years, supersized rectangular jacked pipe tunnels have been increasingly used for developing urban road-crossing nodes, owing to their convenient construction and economic benefits. However, owing to the weak waterproofing performance of the joint, jacked supersized rectangular pipes have been employed beneath a navigable river. This study used on-site monitoring data of an underground expressway with supersized rectangular jacked pipe tunnels in Shanghai. Additionally, we analyzed the deformation of the ground surface and embankment and the mutual influence of jacked adjacent pipes. The results revealed the following. 1) the over-excavation of the jacked pipe causes partial surface subsidence. The jacking parameters were adjusted through feedback to control the surface deformation. 2) The spatial deformation of the old embankment were stabilized, suggesting the successful realization of micro-disturbance jacking construction. 3) The secondary disturbance of the soil due to post-construction causes a slight sinking and tilting trend of the former jacked tunnel.

A 4D spontaneous micro‐expression database: Establishment and evaluation

AbstractMicro‐expressions are spontaneous and unconscious facial movements that reveal individuals’ genuine inner emotions. They hold significant potential in various psychological testing fields. As the face is a 3D deformation object, the emergence of facial expression leads to spatial deformation of the face. However, existing databases primarily offer 2D video sequences, limiting descriptions of 3D spatial information related to micro‐expressions. Here, a new micro‐expression database is proposed, which contains 2D image sequences and corresponding 3D point cloud sequences. These samples were classified using both an objective method based on the facial action coding system and a non‐objective emotion classification method that considers video contents and participants’ self‐reports. A variety of feature extraction techniques are applied to 2D data, including traditional algorithms and deep learning methods. Additionally, a novel local curvature‐based algorithm is developed to extract 3D spatio‐temporal deformation features from the 3D data. The authors evaluated the classification accuracies of these two features individually and their fusion results under leave‐one‐subject‐out (LOSO) and tenfold cross‐validation. The results demonstrate that fusing 3D features with 2D features results in improved recognition performance compared to using 2D features alone.

On the sensitivity of sea ice deformation statistics to plastic damage

Abstract. We implement a plastic damage parametrization, distinct from the elastic damage in the elasto-brittle framework, in the standard viscous–plastic (VP) sea ice model to disentangle its effect from resolved model physics (visco-plastic with and without damage) on its ability to reproduce observed scaling laws of deformation. To this end, we compare scaling properties and multifractality of simulated divergence and shear strain rate, as proposed in the Sea Ice Rheology Experiment (SIREx) studies, with those derived from the RADARSAT Geophysical Processor System (RGPS). Results show that including a plastic damage parametrization in the standard viscous–plastic model increases the spatial but decreases the temporal localization of simulated linear kinematic features (LKFs) and brings all spatial deformation rate statistics in line with observations from RGPS without the need to increase the mechanical shear strength of sea ice as recently proposed for lower-resolution viscous–plastic sea ice models. In fact, including damage with a healing timescale of th=30 d and an increased mechanical strength unveils multifractal behavior that does not fit the theory. Therefore, a plastic damage parametrization is a powerful tuning knob affecting the deformation statistics of viscous–plastic sea ice.

Detection and monitoring of mining-induced subsidence with Gaofen-3 and Sentinel-1A SAR datasets

ABSTRACT The mining-induced subsidence has caused severe casualties and poses a threat to the safe operation of coal extraction, especially under the roads, buildings and rivers. This alarming situation demands the large-area subsidence detection and the large-gradient deformation monitoring to ensure safety. Although the traditional Interferometric Synthetic Aperture Radar (InSAR) technology can monitor surface deformation in high accuracy, unfortunately, it often fails to recover the sufficient deformation when facing the effects of decorrelation and large gradient displacement. Therefore, this study firstly proposes a Stacking-InSAR and coherence gradient fusion method to detect the mining-induced subsidence over large area. Secondly, the robust offset tracking method is applied to retrieve the large-gradient deformation in Buertai mining site. Both Gaofen-3 and Sentinel-1A Synthetic Aperture Radar (SAR) datasets are acquired over the border of Shaanxi and Inner Mongolia, China, for experimental test. The results show that 179 mining-induced subsidence sites are detected with the proposed method, and the complete spatial temporal deformation fields are obtained by both Gaofen-3 and Sentinel-1A offset tracking method with maximum deformation of 3 m in range direction. This study provides a valuable tool for detecting the fine boundary of mining subsidence and recovering the accurate deformation time series.

GNSS Ground deformation observation network optimization assisted using prior InSAR-derived ground surface deformation and multiscale iteration estimation

ABSTRACT Ground surface deformation must be monitored to understand and prevent geological hazards. Global navigation satellite system (GNSS) technology has been widely used in deformation monitoring; however, current GNSS station layout strategies are often subjective and lack theoretical guidance. Therefore, in this study, a GNSS deformation observation network optimization method was developed based on interferometric synthetic aperture radar (InSAR) prior to deformation assistance. This method considers the deformation distribution, cost, accuracy, topography, and actual monitoring requirements and uses kriging interpolation and multiscale iterative optimization to obtain the reference number, spatial distribution, and deformation capture accuracy of GNSS stations in areas experiencing deformation. Simulation experiments showed that the proposed method strengthened the spatial deformation monitoring ability of GNSS by 46%–68% compared with the traditional station layout methods, which ignore the distribution of the deformation. Then, based on the small baseline subset (SBAS) InSAR technology and applying the new method, we evaluated the number and location of the most suitable GNSS stations for a mining area and found that 89.6% of the error was less than 1.5 cm, which further illustrates the practicability and reliability of the proposed method. This method provides an effective supplement to station layouts for monitoring GNSS deformation.

Preparation of 3D flexible SERS substrates by mixing gold nanorods in hydrogels for the detection of malachite green and crystal violet.

Asimple and cost-effective fabrication method of gold nanorods (AuNRs) nanoparticles hybridized with polyvinyl alcohol hydrogel(AuNR/PVA) for SERS substrateis described. The AuNR/PVAachieves the control of inter-particle nanogap by modulating the density of gold nanorods, and inter-particle nanogap by the spatial deformation of the hydrogel, and the reduction of the gap between the AuNRs deposited on hydrogel makes the SERS enhancement. In addition, the AuNR/PVA substrate maintains high SERS activity after more than 100 cycles of bending and storage in air for 30 days, and the substrate possesses high sensitivity and high reproducibility. Combining a flexible and transparent surface-enhanced Raman spectroscopy (SERS) substrate for in situ detection with a small portable Raman can be applied to scenarios such as environmental detection and hazardous materials detection. The substrate showed excellent SERS activity against malachite green (MG) and crystal violet (CV) with limits of detection of 1.18 × 10-13 M and 7.17 × 10-12 M, respectively. The usability of the proposed SERS substrate was demonstrated by detecting the above contaminants in aquatic water. This work not only utilizes a cost-effective method for mass production but also provides a reliable and convenient platform for the preparation of other noble metal flexible substrates.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

Exploring the possibility of undesirable manufacturing heritage reduction in parts made of composites and their joints

The object of the research is the possibility of improving the quality of parts made of composites (CM) by means of pre-polymerization treatment of the wet package with intensive pulse loading. The existing technologies for forming parts from CM involve the compaction of the collected impregnated package of reinforcement layers and their subsequent polymerization under the influence of pressure and temperature. As a result of this technology, residual thermal and shrinkage stresses occur in the composite package, which lead to undesirable spatial deformations of profile parts, a violation of monolithicity in the areas of the connection of the composite and metal ends. Using the example of an angular composite profile with a profile with doubler on one of the caps, the residual stress calculation is given and the method of choosing rational angles for stacking the reinforcing material is demonstrated in order to reduce the amount of residual thermal stresses that arise in the composite during its polymerization. The dependence of the twisting parameter of a long-dimensional composite profile of constant cross-section along its axis on the modulus of elasticity and the coefficient of linear temperature expansion is plotted. The work explains the mechanism of the emergence of such harmful technological heredity. The value of the residual deformations was estimated. Based on the analysis of the impregnation process of dry reinforcing material with a binder, the task of increasing the maximum contact area of the binder with fibers is formulated and a possible method of its increase is analyzed. Thus, using the model of capillaries between the fibers of the composite, it is concluded that it is necessary to apply additional pressure to the binder for its deeper advancement between the fibers. Using a synergistic method of combining knowledge from various branches of industry and based on experimental data, a process of pre-polymerization loading of the impregnated package with intense impulse loading (shock waves) is proposed. This process greatly improves the quality of parts of the units produced.

Automatic detection method for tobacco beetles combining multi-scale global residual feature pyramid network and dual-path deformable attention

Aiming at the problems of identifying storage pest tobacco pest beetles from images that have few object pixels and considerable image noise, and therefore suffer from lack of information and identifiable features, this paper proposes an automatic monitoring method of tobacco beetle based on Multi-scale Global residual Feature Pyramid Network and Dual-path Deformable Attention (MGrFPN-DDrGAM). Firstly, a Multi-scale Global residual Feature Pyramid Network (MGrFPN) is constructed to obtain rich high-level semantic features and more complete information on low-level features to reduce missed detection; Then, a Dual-path Deformable receptive field Guided Attention Module (DDrGAM) is designed to establish long-range channel dependence, guide the effective fusion of features and improve the localization accuracy of tobacco beetles by fitting the spatial geometric deformation features of and capturing the spatial information of feature maps with different scales to enrich the feature information in the channel and spatial. Finally, to simulate a real scene, a multi-scene tobacco beetle dataset is created. The dataset includes 28,080 images and manually labeled tobacco beetle objects. The experimental results show that under the framework of the Faster R-CNN algorithm, the detection precision and recall rate of this method can reach 91.4% and 98.4% when the intersection ratio (IoU) is 0.5. Compared with Faster R-CNN and FPN, when the intersection ratio (IoU) is 0.7, the detection precision is improved by 32.9% and 6.9%, respectively. The proposed method is superior to the current mainstream methods.