The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
The mechanical properties of granitic residual soils vary with depth due to changes in soil type and heterogeneity caused by weathering.The purpose of this study was to relate the spatial variation of particle-size di...The mechanical properties of granitic residual soils vary with depth due to changes in soil type and heterogeneity caused by weathering.The purpose of this study was to relate the spatial variation of particle-size distribution(PSD)of granitic soils with soil shrinkage parameters using multifractal theory.The heterogeneity of PSD and pedogenic processes were depicted in detail by multifractal dimensions.The PSD generally increased with the increase of profile depth in accordance with the variation of single fractal dimension(D)ranging from 2.45 to 2.65.The shrinkage limit was greatly influenced by the multifractal dimension parameters,including information dimension(D1)and capacity dimension(D0)(Adjusted R2=0.998,P<0.01),and the maximum linear extensibility(κv)was determined by spectral width(?α)and bulk density,with the latter explaining 89%of the total variance ofκv(P<0.01).Soil shrinkage characteristic curve was fitted by the modified logistic model(R2>0.97,root sum of squares<0.1),and the water variation corresponding to the maximum change rate of linear extensibility was determined by the silt content(R2=0.81,P<0.01).Overall,the shrinkage of granitic soils was primarily influenced by PSD and soil compactness.展开更多
The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface tex...The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.展开更多
提出了一种数学形态学与GG(Gath-Geva)模糊聚类相结合的旋转机械故障诊断方法,通过对滚动轴承信号的多尺度形态运算得到信号的形态谱,定量反映了信号在不同尺度下的形态变化特征。为进一步对滚动轴承信号进行故障识别,提取出基于形态学...提出了一种数学形态学与GG(Gath-Geva)模糊聚类相结合的旋转机械故障诊断方法,通过对滚动轴承信号的多尺度形态运算得到信号的形态谱,定量反映了信号在不同尺度下的形态变化特征。为进一步对滚动轴承信号进行故障识别,提取出基于形态学操作的分形维数和描述不同信号形态特征的指标即形态谱熵,并把这2个参数作为GG聚类的故障特征向量,进行聚类分析,同时对GG聚类与FCM(fuzzy center means)聚类和GK(Gustafaon-Kessel)聚类进行了比较。实验证明了基于数学形态学与GG聚类相结合的机械故障诊断方法的有效性,且证明了GG聚类更适合对不同形状、大小和密度的空间故障数据模糊聚类,聚类效果更好。展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10171028)the Special for Major State Basic Research Projects of China.
文摘The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
基金supported by the National Natural Science Foundation of China(Nos.41807065 and 41630858)
文摘The mechanical properties of granitic residual soils vary with depth due to changes in soil type and heterogeneity caused by weathering.The purpose of this study was to relate the spatial variation of particle-size distribution(PSD)of granitic soils with soil shrinkage parameters using multifractal theory.The heterogeneity of PSD and pedogenic processes were depicted in detail by multifractal dimensions.The PSD generally increased with the increase of profile depth in accordance with the variation of single fractal dimension(D)ranging from 2.45 to 2.65.The shrinkage limit was greatly influenced by the multifractal dimension parameters,including information dimension(D1)and capacity dimension(D0)(Adjusted R2=0.998,P<0.01),and the maximum linear extensibility(κv)was determined by spectral width(?α)and bulk density,with the latter explaining 89%of the total variance ofκv(P<0.01).Soil shrinkage characteristic curve was fitted by the modified logistic model(R2>0.97,root sum of squares<0.1),and the water variation corresponding to the maximum change rate of linear extensibility was determined by the silt content(R2=0.81,P<0.01).Overall,the shrinkage of granitic soils was primarily influenced by PSD and soil compactness.
基金This work was supported by the Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University,the Youth Science Foundation of Lanzhou Jiaotong University(No.2019029)the University Innovation Fund Project of Gansu Provincial Department of Education(No.2020A-036)the Young Doctor Foundation of JYT.GANSU.GOV.CN(No.2021QB-060).
文摘The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.
文摘提出了一种数学形态学与GG(Gath-Geva)模糊聚类相结合的旋转机械故障诊断方法,通过对滚动轴承信号的多尺度形态运算得到信号的形态谱,定量反映了信号在不同尺度下的形态变化特征。为进一步对滚动轴承信号进行故障识别,提取出基于形态学操作的分形维数和描述不同信号形态特征的指标即形态谱熵,并把这2个参数作为GG聚类的故障特征向量,进行聚类分析,同时对GG聚类与FCM(fuzzy center means)聚类和GK(Gustafaon-Kessel)聚类进行了比较。实验证明了基于数学形态学与GG聚类相结合的机械故障诊断方法的有效性,且证明了GG聚类更适合对不同形状、大小和密度的空间故障数据模糊聚类,聚类效果更好。
