A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Enhancing the Interaction of Carbon Nanotubes by Metal-Organic Decomposition with Improved Mechanical Strength and Ultra-Broadband EMI Shielding Performance

The remarkable properties of carbon nanotubes(CNTs)have led to promising applications in the field of electromagnetic inter-ference(EMI)shielding.However,for macroscopic CNT assemblies,such as CNT film,achieving high electrical and mechanical properties remains challenging,which heavily depends on the tube-tube interac-tions of CNTs.Herein,we develop a novel strategy based on metal-organic decomposition(MOD)to fabricate a flexible silver-carbon nanotube(Ag-CNT)film.The Ag particles are introduced in situ into the CNT film through annealing of MOD,leading to enhanced tube-tube interactions.As a result,the electrical conductivity of Ag-CNT film is up to 6.82×10^(5) S m^(-1),and the EMI shielding effectiveness of Ag-CNT film with a thickness of~7.8μm exceeds 66 dB in the ultra-broad frequency range(3-40 GHz).The tensile strength and Young’s modulus of Ag-CNT film increase from 30.09±3.14 to 76.06±6.20 MPa(~253%)and from 1.12±0.33 to 8.90±0.97 GPa(~795%),respectively.Moreover,the Ag-CNT film exhibits excellent near-field shield-ing performance,which can effectively block wireless transmission.This innovative approach provides an effective route to further apply macroscopic CNT assemblies to future portable and wearable electronic devices.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Modified multiple-component scattering power decomposition for PolSAR data based on eigenspace of coherency matrix

A modified multiple-component scattering power decomposition for analyzing polarimetric synthetic aperture radar(PolSAR)data is proposed.The modified decomposition involves two distinct steps.Firstly,ei⁃genvectors of the coherency matrix are used to modify the scattering models.Secondly,the entropy and anisotro⁃py of targets are used to improve the volume scattering power.With the guarantee of high double-bounce scatter⁃ing power in the urban areas,the proposed algorithm effectively improves the volume scattering power of vegeta⁃tion areas.The efficacy of the modified multiple-component scattering power decomposition is validated using ac⁃tual AIRSAR PolSAR data.The scattering power obtained through decomposing the original coherency matrix and the coherency matrix after orientation angle compensation is compared with three algorithms.Results from the experiment demonstrate that the proposed decomposition yields more effective scattering power for different PolSAR data sets.

MSD-Net: Pneumonia Classification Model Based on Multi-Scale Directional Feature Enhancement

Computer-aided diagnosis of pneumonia based on deep learning is a research hotspot.However,there are some problems that the features of different sizes and different directions are not sufficient when extracting the features in lung X-ray images.A pneumonia classification model based on multi-scale directional feature enhancement MSD-Net is proposed in this paper.The main innovations are as follows:Firstly,the Multi-scale Residual Feature Extraction Module(MRFEM)is designed to effectively extract multi-scale features.The MRFEM uses dilated convolutions with different expansion rates to increase the receptive field and extract multi-scale features effectively.Secondly,the Multi-scale Directional Feature Perception Module(MDFPM)is designed,which uses a three-branch structure of different sizes convolution to transmit direction feature layer by layer,and focuses on the target region to enhance the feature information.Thirdly,the Axial Compression Former Module(ACFM)is designed to perform global calculations to enhance the perception ability of global features in different directions.To verify the effectiveness of the MSD-Net,comparative experiments and ablation experiments are carried out.In the COVID-19 RADIOGRAPHY DATABASE,the Accuracy,Recall,Precision,F1 Score,and Specificity of MSD-Net are 97.76%,95.57%,95.52%,95.52%,and 98.51%,respectively.In the chest X-ray dataset,the Accuracy,Recall,Precision,F1 Score and Specificity of MSD-Net are 97.78%,95.22%,96.49%,95.58%,and 98.11%,respectively.This model improves the accuracy of lung image recognition effectively and provides an important clinical reference to pneumonia Computer-Aided Diagnosis.

Multi-scale context-aware network for continuous sign language recognition

The hands and face are the most important parts for expressing sign language morphemes in sign language videos.However,we find that existing Continuous Sign Language Recognition(CSLR)methods lack the mining of hand and face information in visual backbones or use expensive and time-consuming external extractors to explore this information.In addition,the signs have different lengths,whereas previous CSLR methods typically use a fixed-length window to segment the video to capture sequential features and then perform global temporal modeling,which disturbs the perception of complete signs.In this study,we propose a Multi-Scale Context-Aware network(MSCA-Net)to solve the aforementioned problems.Our MSCA-Net contains two main modules:(1)Multi-Scale Motion Attention(MSMA),which uses the differences among frames to perceive information of the hands and face in multiple spatial scales,replacing the heavy feature extractors;and(2)Multi-Scale Temporal Modeling(MSTM),which explores crucial temporal information in the sign language video from different temporal scales.We conduct extensive experiments using three widely used sign language datasets,i.e.,RWTH-PHOENIX-Weather-2014,RWTH-PHOENIX-Weather-2014T,and CSL-Daily.The proposed MSCA-Net achieve state-of-the-art performance,demonstrating the effectiveness of our approach.

YOLO-MFD:Remote Sensing Image Object Detection with Multi-Scale Fusion Dynamic Head

Remote sensing imagery,due to its high altitude,presents inherent challenges characterized by multiple scales,limited target areas,and intricate backgrounds.These inherent traits often lead to increased miss and false detection rates when applying object recognition algorithms tailored for remote sensing imagery.Additionally,these complexities contribute to inaccuracies in target localization and hinder precise target categorization.This paper addresses these challenges by proposing a solution:The YOLO-MFD model(YOLO-MFD:Remote Sensing Image Object Detection withMulti-scale Fusion Dynamic Head).Before presenting our method,we delve into the prevalent issues faced in remote sensing imagery analysis.Specifically,we emphasize the struggles of existing object recognition algorithms in comprehensively capturing critical image features amidst varying scales and complex backgrounds.To resolve these issues,we introduce a novel approach.First,we propose the implementation of a lightweight multi-scale module called CEF.This module significantly improves the model’s ability to comprehensively capture important image features by merging multi-scale feature information.It effectively addresses the issues of missed detection and mistaken alarms that are common in remote sensing imagery.Second,an additional layer of small target detection heads is added,and a residual link is established with the higher-level feature extraction module in the backbone section.This allows the model to incorporate shallower information,significantly improving the accuracy of target localization in remotely sensed images.Finally,a dynamic head attentionmechanism is introduced.This allows themodel to exhibit greater flexibility and accuracy in recognizing shapes and targets of different sizes.Consequently,the precision of object detection is significantly improved.The trial results show that the YOLO-MFD model shows improvements of 6.3%,3.5%,and 2.5%over the original YOLOv8 model in Precision,map@0.5 and map@0.5:0.95,separately.These results illustrate the clear advantages of the method.

Transfer learning framework for multi-scale crack type classification with sparse microseismic networks

Rock fracture mechanisms can be inferred from moment tensors(MT)inverted from microseismic events.However,MT can only be inverted for events whose waveforms are acquired across a network of sensors.This is limiting for underground mines where the microseismic stations often lack azimuthal coverage.Thus,there is a need for a method to invert fracture mechanisms using waveforms acquired by a sparse microseismic network.Here,we present a novel,multi-scale framework to classify whether a rock crack contracts or dilates based on a single waveform.The framework consists of a deep learning model that is initially trained on 2400000+manually labelled field-scale seismic and microseismic waveforms acquired across 692 stations.Transfer learning is then applied to fine-tune the model on 300000+MT-labelled labscale acoustic emission waveforms from 39 individual experiments instrumented with different sensor layouts,loading,and rock types in training.The optimal model achieves over 86%F-score on unseen waveforms at both the lab-and field-scale.This model outperforms existing empirical methods in classification of rock fracture mechanisms monitored by a sparse microseismic network.This facilitates rapid assessment of,and early warning against,various rock engineering hazard such as induced earthquakes and rock bursts.

MSC-YOLO:Improved YOLOv7 Based on Multi-Scale Spatial Context for Small Object Detection in UAV-View

Accurately identifying small objects in high-resolution aerial images presents a complex and crucial task in thefield of small object detection on unmanned aerial vehicles(UAVs).This task is challenging due to variations inUAV flight altitude,differences in object scales,as well as factors like flight speed and motion blur.To enhancethe detection efficacy of small targets in drone aerial imagery,we propose an enhanced You Only Look Onceversion 7(YOLOv7)algorithm based on multi-scale spatial context.We build the MSC-YOLO model,whichincorporates an additional prediction head,denoted as P2,to improve adaptability for small objects.We replaceconventional downsampling with a Spatial-to-Depth Convolutional Combination(CSPDC)module to mitigatethe loss of intricate feature details related to small objects.Furthermore,we propose a Spatial Context Pyramidwith Multi-Scale Attention(SCPMA)module,which captures spatial and channel-dependent features of smalltargets acrossmultiple scales.This module enhances the perception of spatial contextual features and the utilizationof multiscale feature information.On the Visdrone2023 and UAVDT datasets,MSC-YOLO achieves remarkableresults,outperforming the baseline method YOLOv7 by 3.0%in terms ofmean average precision(mAP).The MSCYOLOalgorithm proposed in this paper has demonstrated satisfactory performance in detecting small targets inUAV aerial photography,providing strong support for practical applications.

Rate-limiting factors in hydrate decomposition through depressurization across various scales:A mini-review

Natural gas hydrate is an energy resource for methane that has a carbon quantity twice more than all traditional fossil fuels combined.However,their practical application in the field has been limited due to the challenges of long-term preparation,high costs and associated risks.Experimental studies,on the other hand,offer a safe and cost-effective means of exploring the mechanisms of hydrate dissociation and optimizing exploitation conditions.Gas hydrate decomposition is a complicated process along with intrinsic kinetics,mass transfer and heat transfer,which are the influencing factors for hydrate decomposition rate.The identification of the rate-limiting factor for hydrate dissociation during depressurization varies with the scale of the reservoir,making it challenging to extrapolate findings from laboratory experiments to the actual exploitation.This review aims to summarize current knowledge of investigations on hydrate decomposition on the subject of the research scale(core scale,middle scale,large scale and field tests)and to analyze determining factors for decomposition rate,considering the various research scales and their associated influencing factors.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites(3D C/SiC).Represent volume element(RVE)models of microscale,void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites.An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture.The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions.Three RVE models of cuboid,hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale.Besides,the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models.The prediction results at the mesoscale correspond closely to the experimental values.The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration.The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Evolutionary Multi/Many-Objective Optimisation via Bilevel Decomposition

Decomposition of a complex multi-objective optimisation problem(MOP)to multiple simple subMOPs,known as M2M for short,is an effective approach to multi-objective optimisation.However,M2M facilitates little communication/collaboration between subMOPs,which limits its use in complex optimisation scenarios.This paper extends the M2M framework to develop a unified algorithm for both multi-objective and manyobjective optimisation.Through bilevel decomposition,an MOP is divided into multiple subMOPs at upper level,each of which is further divided into a number of single-objective subproblems at lower level.Neighbouring subMOPs are allowed to share some subproblems so that the knowledge gained from solving one subMOP can be transferred to another,and eventually to all the subMOPs.The bilevel decomposition is readily combined with some new mating selection and population update strategies,leading to a high-performance algorithm that competes effectively against a number of state-of-the-arts studied in this paper for both multiand many-objective optimisation.Parameter analysis and component analysis have been also carried out to further justify the proposed algorithm.

Formation and transformation of metastable LPSO building blocks clusters in Mg-Gd-Y-Zn-Zr alloys by spinodal decomposition and heterogeneous nucleation

To study the formation and transformation mechanism of long-period stacked ordered(LPSO)structures,a systematic atomic scale analysis was conducted for the structural evolution of long-period stacked ordered(LPSO)structures in the Mg-Gd-Y-Zn-Zr alloy annealed at 300℃~500℃.Various types of metastable LPSO building block clusters were found to exist in alloy structures at different temperatures,which precipitate during the solidification and homogenization process.The stability of Zn/Y clusters is explained by the first principles of density functional theory.The LPSO structure is distinguished by the arrangement of its different Zn/Y enriched LPSO structural units,which comprises local fcc stacking sequences upon a tightly packed plane.The presence of solute atoms causes local lattice distortion,thereby enabling the rearrangement of Mg atoms in the different configurations in the local lattice,and local HCP-FCC transitions occur between Mg and Zn atoms occupying the nearest neighbor positions.This finding indicates that LPSO structures can generate necessary Schockley partial dislocations on specific slip surfaces,providing direct evidence of the transition from 18R to 14H.Growth of the LPSO,devoid of any defects and non-coherent interfaces,was observed separately from other precipitated phases.As a result,the precipitation sequence of LPSO in the solidification stage was as follows:Zn/Ycluster+Mg layers→various metastable LPSO building block clusters→18R/24R LPSO;whereas the precipitation sequence of LPSO during homogenization treatment was observed to be as follows:18R LPSO→various metastable LPSO building block clusters→14H LPSO.Of these,14H LPSO was found to be the most thermodynamically stable structure.

Improved multi-scale inverse bottleneck residual network based on triplet parallel attention for apple leaf disease identification

Accurate diagnosis of apple leaf diseases is crucial for improving the quality of apple production and promoting the development of the apple industry. However, apple leaf diseases do not differ significantly from image texture and structural information. The difficulties in disease feature extraction in complex backgrounds slow the related research progress. To address the problems, this paper proposes an improved multi-scale inverse bottleneck residual network model based on a triplet parallel attention mechanism, which is built upon ResNet-50, while improving and combining the inception module and ResNext inverse bottleneck blocks, to recognize seven types of apple leaf(including six diseases of alternaria leaf spot, brown spot, grey spot, mosaic, rust, scab, and one healthy). First, the 3×3 convolutions in some of the residual modules are replaced by multi-scale residual convolutions, the convolution kernels of different sizes contained in each branch of the multi-scale convolution are applied to extract feature maps of different sizes, and the outputs of these branches are multi-scale fused by summing to enrich the output features of the images. Second, the global layer-wise dynamic coordinated inverse bottleneck structure is used to reduce the network feature loss. The inverse bottleneck structure makes the image information less lossy when transforming from different dimensional feature spaces. The fusion of multi-scale and layer-wise dynamic coordinated inverse bottlenecks makes the model effectively balances computational efficiency and feature representation capability, and more robust with a combination of horizontal and vertical features in the fine identification of apple leaf diseases. Finally, after each improved module, a triplet parallel attention module is integrated with cross-dimensional interactions among channels through rotations and residual transformations, which improves the parallel search efficiency of important features and the recognition rate of the network with relatively small computational costs while the dimensional dependencies are improved. To verify the validity of the model in this paper, we uniformly enhance apple leaf disease images screened from the public data sets of Plant Village, Baidu Flying Paddle, and the Internet. The final processed image count is 14,000. The ablation study, pre-processing comparison, and method comparison are conducted on the processed datasets. The experimental results demonstrate that the proposed method reaches 98.73% accuracy on the adopted datasets, which is 1.82% higher than the classical ResNet-50 model, and 0.29% better than the apple leaf disease datasets before preprocessing. It also achieves competitive results in apple leaf disease identification compared to some state-ofthe-art methods.

Generalized load graphical forecasting method based on modal decomposition

In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized loads.From the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal decomposition.First,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest algorithms.Subsequently,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B channels.The generated images are diversified,and an optimized DenseNet neural network was used for training and prediction.Finally,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise algorithm.Based on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.

Few-shot image recognition based on multi-scale features prototypical network

In order to improve the models capability in expressing features during few-shot learning,a multi-scale features prototypical network(MS-PN)algorithm is proposed.The metric learning algo-rithm is employed to extract image features and project them into a feature space,thus evaluating the similarity between samples based on their relative distances within the metric space.To sufficiently extract feature information from limited sample data and mitigate the impact of constrained data vol-ume,a multi-scale feature extraction network is presented to capture data features at various scales during the process of image feature extraction.Additionally,the position of the prototype is fine-tuned by assigning weights to data points to mitigate the influence of outliers on the experiment.The loss function integrates contrastive loss and label-smoothing to bring similar data points closer and separate dissimilar data points within the metric space.Experimental evaluations are conducted on small-sample datasets mini-ImageNet and CUB200-2011.The method in this paper can achieve higher classification accuracy.Specifically,in the 5-way 1-shot experiment,classification accuracy reaches 50.13%and 66.79%respectively on these two datasets.Moreover,in the 5-way 5-shot ex-periment,accuracy of 66.79%and 85.91%are observed,respectively.

Multi-Scale Mixed Attention Tea Shoot Instance Segmentation Model

Tea leaf picking is a crucial stage in tea production that directly influences the quality and value of the tea.Traditional tea-picking machines may compromise the quality of the tea leaves.High-quality teas are often handpicked and need more delicate operations in intelligent picking machines.Compared with traditional image processing techniques,deep learning models have stronger feature extraction capabilities,and better generalization and are more suitable for practical tea shoot harvesting.However,current research mostly focuses on shoot detection and cannot directly accomplish end-to-end shoot segmentation tasks.We propose a tea shoot instance segmentation model based on multi-scale mixed attention(Mask2FusionNet)using a dataset from the tea garden in Hangzhou.We further analyzed the characteristics of the tea shoot dataset,where the proportion of small to medium-sized targets is 89.9%.Our algorithm is compared with several mainstream object segmentation algorithms,and the results demonstrate that our model achieves an accuracy of 82%in recognizing the tea shoots,showing a better performance compared to other models.Through ablation experiments,we found that ResNet50,PointRend strategy,and the Feature Pyramid Network(FPN)architecture can improve performance by 1.6%,1.4%,and 2.4%,respectively.These experiments demonstrated that our proposed multi-scale and point selection strategy optimizes the feature extraction capability for overlapping small targets.The results indicate that the proposed Mask2FusionNet model can perform the shoot segmentation in unstructured environments,realizing the individual distinction of tea shoots,and complete extraction of the shoot edge contours with a segmentation accuracy of 82.0%.The research results can provide algorithmic support for the segmentation and intelligent harvesting of premium tea shoots at different scales.

Progress in the research on organic piezoelectric catalysts for dye decomposition

Organic contaminants have posed a direct and substantial risk to human wellness and the environment.In recent years,piezo-electric catalysis has evolved as a novel and effective method for decomposing these contaminants.Although piezoelectric materials offer a wide range of options,most related studies thus far have focused on inorganic materials and have paid little attention to organic materi-als.Organic materials have advantages,such as being lightweight,inexpensive,and easy to process,over inorganic materials.Therefore,this paper provides a comprehensive review of the progress made in the research on piezoelectric catalysis using organic materials,high-lighting their catalytic efficiency in addressing various pollutants.In addition,the applications of organic materials in piezoelectric cata-lysis for water decomposition to produce hydrogen,disinfect bacteria,treat tumors,and reduce carbon dioxide are presented.Finally,fu-ture developmental trends regarding the piezoelectric catalytic potential of organic materials are explored.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.