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.

Individual consistency in spatiotemporal characteristics of migratory Whimbrels in the East Asian-Australasian Flyway

Many migratory birds exhibit interannual consistency in migration schedules,routes and stopover sites.Detecting the interannual consistency in spatiotemporal characteristics helps understand the maintenance of migration and enables the implementation of targeted conservation measures.We tracked the migration of Whimbrel(Numenius phaeopus)in the East Asian-Australasian Flyway and collected spatiotemporal data from individuals that were tracked for at least two years.Wilcoxon non-parametric tests were used to compare the interannual variations in the dates of departure from and arrival at breeding/nonbreeding sites,and the inter-annual variation in the longitudes when the same individual across the same latitudes.Whimbrels exhibited a high degree of consistency in the use of breeding,nonbreeding,and stopover sites between years.The variation of arrival dates at nonbreeding sites was significantly larger than that of the departure dates from nonbreeding and breeding sites.Repeatedly used stopover sites by the same individuals in multiple years were concentrated in the Yellow Sea coast during northward migration,but were more widespread during southward migration.The stopover duration at repeatedly used sites was significantly longer than that at sites used only once.When flying across the Yellow Sea,Whimbrels breeding in Sakha(Yakutia)exhibited the highest consistency in migration routes in both autumn and spring.Moreover,the consistency in migration routes of Yakutia breeding birds was generally higher than that of birds breeding in Chukotka.Our results suggest that the northward migration schedule of the Whimbrels is mainly controlled by endogenous factors,while the southward migration schedule is less affected by endogenous factors.The repeated use of stopover sites in the Yellow Sea coast suggests this region is important for the migration of Whimbrel,and thus has high conservation value.

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.

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.

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.

Differentiating consistency of meningioma based on grey-level histogram analysis of T2WI

Objective To observe the value of grey-level histogram analysis based on T2WI for differentiating consistency of meningioma.Methods Data of 109 patients with meningioma were retrospectively analyzed.The patients were divided into hard group(n=71)and soft group(n=38)according to the consistency of tumors.Tumor ROI was outlined on axial T2WI showing the largest tumor section,gray levels were extracted and histogram analysis was performed.The value of each histogram parameter were compared between groups.Then receiver operating characteristic curve was drawn,and the area under the curve(AUC)was calculated to evaluate the efficiency for differentiating soft and hard meningioma.Results P 1,P 10,P 50,P 90,P 99 and the mean grey levels on T2WI in soft group were all higher than those in hard group(all P<0.05),while the variance,the kurtosis and the skewness were not significantly different between groups(all P>0.05).The differentiating efficiency of P 1,P 10,P 50,P 90,P 99 and the mean grey levels on T2WI were all fine,with AUC of 0.774 to 0.833,and no significant difference was found(all P>0.05).Conclusion Parameters of grey-level histogram analysis such as P 1,P 10,P 50,P 90,P 99 and the mean values based on T2WI were all valuable for differentiating soft and hard meningioma.

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.

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.

Cross-Modal Consistency with Aesthetic Similarity for Multimodal False Information Detection

With the explosive growth of false information on social media platforms, the automatic detection of multimodalfalse information has received increasing attention. Recent research has significantly contributed to multimodalinformation exchange and fusion, with many methods attempting to integrate unimodal features to generatemultimodal news representations. However, they still need to fully explore the hierarchical and complex semanticcorrelations between different modal contents, severely limiting their performance detecting multimodal falseinformation. This work proposes a two-stage detection framework for multimodal false information detection,called ASMFD, which is based on image aesthetic similarity to segment and explores the consistency andinconsistency features of images and texts. Specifically, we first use the Contrastive Language-Image Pre-training(CLIP) model to learn the relationship between text and images through label awareness and train an imageaesthetic attribute scorer using an aesthetic attribute dataset. Then, we calculate the aesthetic similarity betweenthe image and related images and use this similarity as a threshold to divide the multimodal correlation matrixinto consistency and inconsistencymatrices. Finally, the fusionmodule is designed to identify essential features fordetectingmultimodal false information. In extensive experiments on four datasets, the performance of the ASMFDis superior to state-of-the-art baseline methods.

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.

Decoding the inconsistency of six cropland maps in China

Accurate cropland information is critical for agricultural planning and production,especially in foodstressed countries like China.Although widely used medium-to-high-resolution satellite-based cropland maps have been developed from various remotely sensed data sources over the past few decades,considerable discrepancies exist among these products both in total area and in spatial distribution of croplands,impeding further applications of these datasets.The factors influencing their inconsistency are also unknown.In this study,we evaluated the consistency and accuracy of six cropland maps widely used in China in circa 2020,including three state-of-the-art 10-m products(i.e.,Google Dynamic World,ESRI Land Cover,and ESA WorldCover)and three 30-m ones(i.e.,GLC_FCS30,GlobeLand 30,and CLCD).We also investigated the effects of landscape fragmentation,climate,and agricultural management.Validation using a ground-truth sample revealed that the 10-m-resolution WorldCover provided the highest accuracy(92.3%).These maps collectively overestimated Chinese cropland area by up to 56%.Up to 37%of the land showed spatial inconsistency among the maps,concentrated mainly in mountainous regions and attributed to the varying accuracy of cropland maps,cropland fragmentation and management practices such as irrigation.Our work shed light on the promotion of future cropland mapping efforts,especially in highly inconsistent regions.

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.

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.

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.

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.

Multi-Scale Design and Optimization of Composite Material Structure for Heavy-Duty Truck Protection Device

In this paper,to present a lightweight-developed front underrun protection device(FUPD)for heavy-duty trucks,plain weave carbon fiber reinforced plastic(CFRP)is used instead of the original high-strength steel.First,the mechanical and structural properties of plain carbon fiber composite anti-collision beams are comparatively analyzed from a multi-scale perspective.For studying the design capability of carbon fiber composite materials,we investigate the effects of TC-33 carbon fiber diameter(D),fiber yarn width(W)and height(H),and fiber yarn density(N)on the front underrun protective beam of carbon fiber compositematerials.Based on the investigation,a material-structure matching strategy suitable for the front underrun protective beam of heavy-duty trucks is proposed.Next,the composite material structure is optimized by applying size optimization and stack sequence optimization methods to obtain the higher performance carbon fiber composite front underrun protection beam of commercial vehicles.The results show that the fiber yarn height(H)has the greatest influence on the protective beam,and theH1matching scheme for the front underrun protective beamwith a carbon fiber composite structure exhibits superior performance.The proposed method achieves a weight reduction of 55.21% while still meeting regulatory requirements,which demonstrates its remarkable weight reduction effect.

Disparity estimation for multi-scale multi-sensor fusion

The perception module of advanced driver assistance systems plays a vital role.Perception schemes often use a single sensor for data processing and environmental perception or adopt the information processing results of various sensors for the fusion of the detection layer.This paper proposes a multi-scale and multi-sensor data fusion strategy in the front end of perception and accomplishes a multi-sensor function disparity map generation scheme.A binocular stereo vision sensor composed of two cameras and a light deterction and ranging(LiDAR)sensor is used to jointly perceive the environment,and a multi-scale fusion scheme is employed to improve the accuracy of the disparity map.This solution not only has the advantages of dense perception of binocular stereo vision sensors but also considers the perception accuracy of LiDAR sensors.Experiments demonstrate that the multi-scale multi-sensor scheme proposed in this paper significantly improves disparity map estimation.

Identifying Brand Consistency by Product Differentiation Using CNN

This paper presents a new method of using a convolutional neural network(CNN)in machine learning to identify brand consistency by product appearance variation.In Experiment 1,we collected fifty mouse devices from the past thirty-five years from a renowned company to build a dataset consisting of product pictures with pre-defined design features of their appearance and functions.Results show that it is a challenge to distinguish periods for the subtle evolution of themouse devices with such traditionalmethods as time series analysis and principal component analysis(PCA).In Experiment 2,we applied deep learning to predict the extent to which the product appearance variation ofmouse devices of various brands.The investigation collected 6,042 images ofmouse devices and divided theminto the Early Stage and the Late Stage.Results show the highest accuracy of 81.4%with the CNNmodel,and the evaluation score of brand style consistency is 0.36,implying that the brand consistency score converted by the CNN accuracy rate is not always perfect in the real world.The relationship between product appearance variation,brand style consistency,and evaluation score is beneficial for predicting new product styles and future product style roadmaps.In addition,the CNN heat maps highlight the critical areas of design features of different styles,providing alternative clues related to the blurred boundary.The study provides insights into practical problems for designers,manufacturers,and marketers in product design.It not only contributes to the scientific understanding of design development,but also provides industry professionals with practical tools and methods to improve the design process and maintain brand consistency.Designers can use these techniques to find features that influence brand style.Then,capture these features as innovative design elements and maintain core brand values.

Nonlinear Flap-Wise Vibration Characteristics ofWind Turbine Blades Based onMulti-Scale AnalysisMethod

This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.