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A GENERALIZED TRANSVERSALITY IN GLOBAL ANALYSIS 被引量:3
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作者 MaJipu 《Analysis in Theory and Applications》 2004年第4期391-394,共4页
关键词 TRANSVERSALITY generalized transversality perturbation analysis of generalized inverse Banach manifold global analysis
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gscaLCA in R: Fitting Fuzzy Clustering Analysis Incorporated with Generalized Structured Component Analysis
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作者 Ji Hoon Ryoo Seohee Park +1 位作者 Seongeun Kim Heungsun Hwang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第9期801-822,共22页
Clustering analysis identifying unknown heterogenous subgroups of a population(or a sample)has become increasingly popular along with the popularity of machine learning techniques.Although there are many software pack... Clustering analysis identifying unknown heterogenous subgroups of a population(or a sample)has become increasingly popular along with the popularity of machine learning techniques.Although there are many software packages running clustering analysis,there is a lack of packages conducting clustering analysis within a structural equation modeling framework.The package,gscaLCA which is implemented in the R statistical computing environment,was developed for conducting clustering analysis and has been extended to a latent variable modeling.More specifically,by applying both fuzzy clustering(FC)algorithm and generalized structured component analysis(GSCA),the package gscaLCA computes membership prevalence and item response probabilities as posterior probabilities,which is applicable in mixture modeling such as latent class analysis in statistics.As a hybrid model between data clustering in classifications and model-based mixture modeling approach,fuzzy clusterwise GSCA,denoted as gscaLCA,encompasses many advantages from both methods:(1)soft partitioning from FC and(2)efficiency in estimating model parameters with bootstrap method via resolution of global optimization problem from GSCA.The main function,gscaLCA,works for both binary and ordered categorical variables.In addition,gscaLCA can be used for latent class regression as well.Visualization of profiles of latent classes based on the posterior probabilities is also available in the package gscaLCA.This paper contributes to providing a methodological tool,gscaLCA that applied researchers such as social scientists and medical researchers can apply clustering analysis in their research. 展开更多
关键词 Fuzzy clustering generalized structured component analysis gscaLCA latent class analysis
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Generalized Method of Variational Analysis for 3-D Flow
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作者 兰伟仁 黄思训 项杰 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2004年第5期730-740,共11页
The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity... The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and ?ltered. The e?ciency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being ?ltered. 展开更多
关键词 regularization methods inverse problem generalized method of variational analysis ?lter- ing
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Analysis on the Problems in Start-up and Debugging of Two 600 MW Generating Units in Yangzhou No.2 Thermal Power Plant
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作者 蒯狄正 《Electricity》 2001年第2期11-15,共5页
The problems including excessive flow of attemperating water for boiler, failure of butterfly valve at the outlet of circulating water pump, burnt-out of thyristor for excitation regulator, load variation rate of CCS ... The problems including excessive flow of attemperating water for boiler, failure of butterfly valve at the outlet of circulating water pump, burnt-out of thyristor for excitation regulator, load variation rate of CCS not complying with the contract target, etc. occurred during start-up and debugging of two 600 MW generating units in Yangzhou No.2 Thermal Power Plant. Through analysis on these problems. the remedial measures were put forward, to which can be referred for similar units. 展开更多
关键词 start-up and debugging problems analysis remedial measures 600 MW generating unit
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Regularized canonical correlation analysis with unlabeled data 被引量:1
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作者 Xi-chuan ZHOU Hai-bin SHEN 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2009年第4期504-511,共8页
In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great po... In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great portion of data that we do not know which set it belongs to. This part of data is called unlabeled data, while the rest from definite datasets is called labeled data. We propose a novel method called regularized canonical correlation analysis (RCCA), which makes use of both labeled and unlabeled samples. Specifically, we learn to approximate canonical correlation as if all data were labeled. Then, we describe a generalization of RCCA for the multi-set situation. Experiments on four real world datasets, Yeast, Cloud, Iris, and Haberman, demonstrate that, by incorporating the unlabeled data points, the accuracy of correlation coefficients can be improved by over 30%. 展开更多
关键词 Canonical correlation analysis (CCA) REGULARIZATION Unlabeled data generalized canonical correlation analysis(GCCA)
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Methods for Force Analysis of Overconstrained Parallel Mechanisms: A Review 被引量:3
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作者 Wen-Lan Liu Yun-Dou Xu +1 位作者 Jian-Tao Yao Yong-Sheng Zhao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2017年第6期1460-1472,共13页
The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few liter- atures analyze the characteristics and application scopes o... The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few liter- atures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them prop- erly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the compre- hensiveness of considering limbs' deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engi- neers to quickly find a suitable method. The similarities and differences between the statically indeterminate prob- lem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview. 展开更多
关键词 Redundantly actuated PM ~ Passiveoverconstrained PM ~ Statically indeterminate problemForce analysis ~ Weighted generalized inverse
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Analysis of normal human retinal vascular network architecture using multifractal geometry 被引量:1
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作者 Stefan Talu Sebastian Stach +2 位作者 Dan Mihai Calugaru Carmen Alina Lupascu Simona Delia Nicoara 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2017年第3期434-438,共5页
AIM:To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS:Fifty volunteers were enrolled in ... AIM:To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS:Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS:The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα=α_(max)-α_(min))and the spectrum arms' heights difference(│Δf│)of the normal images were expressed as mean±standard deviation(SD):for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα)and the spectrum arms' heights difference(│Δf│)of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION:The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases. 展开更多
关键词 generalized dimensions multifractal retinal vessel segmentation retinal image analysis retinal microvasculature standard box-counting method
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Robust GEFA Assessment of Climate Feedback to SST EOF Modes 被引量:3
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作者 范磊 刘征宇 刘秦玉 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2011年第4期907-912,共6页
Atmospheric response to SST variability was estimated using generalized equilibrium feedback analysis (GEFA) in the SST EOF space with synthesis data from an idealized climate model. Results show that the GEFA atmos... Atmospheric response to SST variability was estimated using generalized equilibrium feedback analysis (GEFA) in the SST EOF space with synthesis data from an idealized climate model. Results show that the GEFA atmospheric response to the leading SST EOF modes is much more accurate and robust than the GEFA feedback matrix in physical space. Therefore, GEFA provides a practical method for assessing atmospheric response to large-scale SST anomalies in terms of the leading EOFs. 展开更多
关键词 generalized equilibrium feedback analysis (GEFA) ASSESSMENT CLIMATE feedback SST EOF
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Simple waves for two-dimensional compressible pseudo-steady Euler system 被引量:2
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作者 赖耕 盛万成 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期827-838,共12页
A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that "the theory of simple waves is fundamental in building up the solutions of flow problems out of elementa... A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that "the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns" see Courant and Friedrichs's chassical book "Supersonic Flow and Shock Waves". This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems. 展开更多
关键词 self-similar Euler system simple wave generalized characteristic analysis pseudo-stream line sonic circle sonic edge
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Guckenheimer structure of solution of Riemann problem with four pieces of constants in two space dimensions for scalar conservation laws 被引量:2
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作者 张华 盛万成 《Journal of Shanghai University(English Edition)》 CAS 2006年第4期305-307,共3页
By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which invo... By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which involve the Guckenheimer structure, were constructed. 展开更多
关键词 two-dimensional Riemann problem scalar conservation laws generalized characteristic analysis method Guckenheimer structure.
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Fractal-based weak target detection within sea clutter 被引量:2
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作者 LI Yang LV Xiaowen +1 位作者 LIU Kuisheng ZHAO Shangzhuo 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2014年第9期68-72,共5页
The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis (DFA) has been us... The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis (DFA) has been used successfully to extract the time-domain Hurst exponent of sea-clutter series. Since the frequency of the sea clutter mainly concentrates around Doppler center so that we consider to extract frequency-do- main fractal characterization and then detect a weak target within sea clutter by using the difference of frequency-domain fractal characterization. The generalized detrended fluctuation analysis (GDFA) is more flexible than traditional DFA owing to its smoothing action for the clutters. In this paper, we apply the GDFA to evaluate the generalized Hurst exponent of sea-clutter series in the frequency domain. The difference of generalized Hurst exponents between different sea-clutter range bins would be used to determine whether the target exists. Moreover, some simulations with the real IPIX radar data have also been demonstrated in order to suooort this conclusion. 展开更多
关键词 sea clutter weak target detection generalized detrended fluctuation analysis
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A Closed Form Solution to Segment 3D Motion Using Straight-line Optical Flow 被引量:2
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作者 张婧 石繁槐 +1 位作者 马文娟 刘允才 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第1期76-80,共5页
A closed form solution to the problem of segmenting multiple 3D motion models was proposed from straight-line optical flow. It introduced the multibody line optical flow constraint (MLOFC), a polynomial equation relat... A closed form solution to the problem of segmenting multiple 3D motion models was proposed from straight-line optical flow. It introduced the multibody line optical flow constraint (MLOFC), a polynomial equation relating motion models and line parameters. The motion models can be obtained analytically as the derivative of the MLOFC at the corresponding line measurement, without knowing the motion model associated with that line. Experiments on real and synthetic sequences were also presented. 展开更多
关键词 SEGMENTATION optical flow LINE generalized principal component analysis (GPCA)
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Key Social Determinants to Narrow the Gap between Health-adjusted Life Expectancy and Life Expectancy in Megacities 被引量:1
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作者 XI Jun Yan CHEN Yuan Yuan +7 位作者 ZHANG Yu Qin LUO Ao DU Zhi Cheng LIANG Bo Heng DONG Hang LIN Xiao QIN Peng Zhe HAO Yuan Tao 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 2022年第9期773-781,共9页
Objective Improvement in the quality of life is reflected in the narrowing of the gap between healthadjusted life expectancy(HALE)and life expectancy(LE).The effect of megacity expansion on narrowing the gap is rarely... Objective Improvement in the quality of life is reflected in the narrowing of the gap between healthadjusted life expectancy(HALE)and life expectancy(LE).The effect of megacity expansion on narrowing the gap is rarely reported.This study aimed to disclose this potential relationship.Methods Annual life tables were constructed from identified death records and population counts from multiple administrative sources in Guangzhou,China,from 2010 to 2020.Joinpoint regression was used to evaluate the temporal trend.Generalized principal component analysis and multilevel models were applied to examine the county-level association between the gap and social determinants.Results Although LE and HALE in megacities are increasing steadily,their gap is widening.Socioeconomic and health services are guaranteed to narrow this gap.Increasing personal wealth,a growing number of newborns and healthy immigrants,high urbanization,and healthy aging have helped in narrowing this gap.Conclusion In megacities,parallel LE and HALE growth should be highly considered to narrow their gap.Multiple social determinants need to be integrated as a whole to formulate public health plans. 展开更多
关键词 generalized principal component analysis Health-adjusted life expectancy MEGACITIES Quality of life Social determinants Temporal trend Urban expansion
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Response of the North Pacific Storm Track Activity in the Cold Season to Multi-scale Oceanic Variations of Kuroshio Extension System: A Statistical Assessment 被引量:1
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作者 Peilong YU Minghao YANG +3 位作者 Chao ZHANG Yi LI Lifeng ZHANG Shiyao CHEN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2023年第3期514-530,共17页
In this paper,a statistical method called Generalized Equilibrium Feedback Analysis(GEFA)is used to investigate the responses of the North Pacific Storm Track(NPST)in the cold season to the multi-scale oceanic variati... In this paper,a statistical method called Generalized Equilibrium Feedback Analysis(GEFA)is used to investigate the responses of the North Pacific Storm Track(NPST)in the cold season to the multi-scale oceanic variations of the Kuroshio Extension(KE)system,including its large-scale variation,oceanic front meridional shift,and mesoscale eddy activity.Results show that in the cold season from the lower to the upper troposphere,the KE large-scale variation significantly weakens the storm track activity over the central North Pacific south of 30°N.The northward shift of the KE front significantly strengthens the storm track activity over the western and central North Pacific south of 40°N,resulting in a southward shift of the NPST.In contrast,the NPST response to KE mesoscale eddy activity is not so significant and relatively shallow,which only shows some significant positive signals near the dateline in the lower and middle troposphere.Furthermore,it is found that baroclinicity and baroclinic energy conversion play an important role in the formation of the NPST response to the KE multi-scale oceanic variations. 展开更多
关键词 generalized equilibrium feedback analysis Kuroshio Extension multi-scale oceanic variations North Pacific storm track
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GENERALIZED VARIATIONAL OPTI MAZATION ANALYSIS FOR2-D FLOW FIELD 被引量:1
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作者 HUANG Si-xun XU Ding-hua +1 位作者 LAN Wei-ren TENG Jia-jun 《Journal of Hydrodynamics》 SCIE EI CSCD 2005年第4期459-465,共7页
The Variational Optimization Analysis Method (VOAM) for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are h... The Variational Optimization Analysis Method (VOAM) for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are high frequency noises in 2-D flow field, it appears to be inefficient. In the present paper, based on Sasaki's VOAM, a Generalized Variational Optimization Analysis Method (GVOAM) was proposed with regularization ideas, which could deal well with flow fields containing high frequency noises. A numerical test shows that observational data can be both variationally optimized and filtered, and therefore the GVOAM is an efficient method. 展开更多
关键词 variational optimization analysis regularization methods generalized variational optimization analysis
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A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty 被引量:27
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作者 Cao Yalu Peng Li +2 位作者 Li Jinzhou Yang Le Guo Fucheng 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2015年第5期1510-1518,共9页
This paper considers the problem of geolocating a target on the Earth surface whose altitude is known previously using the target signal time difference of arrival (TDOA) and frequency difference of arrival (FDOA)... This paper considers the problem of geolocating a target on the Earth surface whose altitude is known previously using the target signal time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements obtained at satellites. The number of satellites available for the geolocation task is more than sufficient and their locations are subject to random errors. This paper derives the constrained Cramor-Rao lower bound (CCRLB) of the target position, and on the basis of the CCRLB analysis, an approximately efficient constrained maximum likelihood estimator (CMLE) for geolocating the target is established. A new iterative algorithm for solving the CMLE is then proposed, where the updated target position estimate is shown to be the globally optimal solution to a generalized trust region sub-problem (GTRS) which can be found via a simple bisection search. First-order mean square error (MSE) analysis is conducted to quantify the performance degradation when the known target altitude is assumed to be precise but indeed has an unknown but deterministic error. Computer simulations are used to compare the performance of the proposed iterative geolocation technique with those of two benchmark algorithms. They verify the approximate efficiency of the proposed algorithm and the validity of the MSE analysis. 展开更多
关键词 Constrained Cram6r-Raolower bound (CCRLB):Frequency difference ofarrival (FDOA) generalized trust regionsub-problem (GTRS):Performance analysis:Time difference of arrival(TDOA)
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Effect of Breed and Sex on Pork Meat Sensory Evaluation 被引量:1
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作者 Sandra Rodrigues Alfredo Teixeira 《Food and Nutrition Sciences》 2014年第7期599-605,共7页
This work had an objective to evaluate the sensory quality of two categories of pork meat from a commercial pork meat and a selected meat from the Portuguese black pork (Preto Alentejano breed). Sixteen animals were u... This work had an objective to evaluate the sensory quality of two categories of pork meat from a commercial pork meat and a selected meat from the Portuguese black pork (Preto Alentejano breed). Sixteen animals were used, 8 females and 8 males from each breed. Animals had 80 - 100 kg of live weight. The longissimus muscle between the 5th thoracic vertebra and the 10th lumbar vertebra was used in the analysis. Sensory analysis was performed by a trained taste panel of 10 elements, in 5 sessions. All evaluation conditions were standardized, and the attributes studied were odor intensity, toughness, juiciness and flavor intensity. The taste panel found differences mainly between breeds. The panellists scored Preto Alentejano meat as being juicier, tenderer, and with richer taste than Commercial meat. The higher juiciness score of Preto Alentejano meat was probably attributable to the higher intramuscular fat content compared with Commercial meat. The Commercial pork was characterized mainly by high toughness. 展开更多
关键词 Pork Meat Sensory Evaluation generalized Procrustes analysis
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A symmetric substructuring method for analyzing the natural frequencies of conical origami structures
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作者 Chenhao Lu Yao Chen +2 位作者 Weiying Fan Jian Feng Pooya Sareh 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2024年第3期203-210,共8页
Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight s... Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness. 展开更多
关键词 Natural structural vibration Origami design Group theory Symmetric substructuring method(SSM) generalized eigenvalue analysis
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Application of Kernel GDA to Performance Monitoring and Fault Diagnosis for Rotating Machinery
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作者 马思乐 张曦 邵惠鹤 《Journal of Donghua University(English Edition)》 EI CAS 2010年第5期709-714,共6页
Faults in rotating machine are difficult to detect and identify,especially when the system is complex and nonlinear.In order to solve this problem,a novel performance monitoring and fault diagnosis method based on ker... Faults in rotating machine are difficult to detect and identify,especially when the system is complex and nonlinear.In order to solve this problem,a novel performance monitoring and fault diagnosis method based on kernel generalized discriminant analysis(kernel GDA,KGDA)was proposed.Through KGDA,the data were mapped from the original space to the high-dimensional feature space.Then the statistic distance between normal data and test data was constructed to detect whether a fault was occurring.If a fault had occurred,similar analysis was used to identify the type of faults.The effectiveness of the proposed method was evaluated by simulation results of vibration signal fault dataset in the rotating machinery,which was scalable to different rotating machinery. 展开更多
关键词 kernel generalized discriminant analysis(KGDA) performance monitoring fault diagnosis rotating machinery
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SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD Σ_r OF B(E,F) AND A DIMENSION FORMULA IN B(R^n,R^m)
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作者 Jipu Ma 《Analysis in Theory and Applications》 2008年第4期395-400,共6页
Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear operators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑r^# the number of path connected components of ∑... Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear operators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑r^# the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submanifold in B(E,F) with given expression of its tangent space at each A ∈ ∑r. In this paper, the equality ∑r^# = 1 is proved. Consequently, the following theorem is obtained: for any nonnegative integer r,∑r is a smooth and path connected Banach submanifold in B(E, F) with the tangent space TA∑r = {B E B(E,F) : BN(A) belong to R(A)} at each A ∈ ∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = R^n and F = R^m, then ∑r is a smooth and path connected submanifold of B(R^n,R^m) and its dimension is dim ∑r = (m + n)r- r^2 for each r, 0≤r 〈 min{n,m}. 展开更多
关键词 operator of finite rank smooth Banach submanifolcl path connectivity perturbation analysis of generalized inverse
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