高速铁路轮轨滚动噪声的分形描述及分形维估计  

Fractal description and fractal dimension estimation of the wheel-rail rolling noise in high-speed railway

作　　者：郝秋实 沈毅[1] 王艳[1] 章欣[1] 刘俭[2] HAO Qiushi;SHEN Yi;WANG Yan;ZHANG Xin;LIU Jian(Department of Control Science and Engineering,Harbin Institute,of Technology Harbin 150001;Department of Instrumentation Science and Technology,Harbin Institute of Technology Harbin 150001)

机构地区：[1]哈尔滨工业大学控制科学与工程系,哈尔滨150001 [2]哈尔滨工业大学仪器科学与技术系,哈尔滨150001

出　　处：《声学学报》2020年第2期196-204,共9页Acta Acustica

基　　金：国家自然科学基金项目(61771161,61601139);中国博士后科学基金项目(2017M610209)资助。

摘　　要：提出基于分形分析的轮轨滚动噪声研究方法,研究了不同尺度下轮轨滚动噪声增量的统计特性,证明轮轨滚动噪声具有分形特性,可由分形布朗运动描述。在此基础上,利用分形布朗运动的小波系数方差与分形维的幂律关系估计了轮轨滚动噪声的分形维,并估计了以裂纹扩展为代表的钢轨伤损声发射信号的分形维,对比研究发现:轮轨滚动噪声分形维本身具有随机性,不同车速下的轮轨滚动噪声分形维估计以1.5666为均值随机分布在小于2的小区间内;分形维是轮轨滚动噪声的固有特征,与车速无关,不同车速的轮轨滚动噪声可由统一的分形布朗运动模型描述;裂纹扩展信号与轮轨滚动噪声不同,其分形维估计大于2,不满足分形布朗运动模型的要求,但分形维可作为二者的区别特征。研究提取了轮轨滚动噪声的分形维作为固有特征,为高速轮轨滚动噪声描述及轮轨伤损检测提供了有效的分析方法。A fractal analysis method is proposed to investigate the wheel-rail rolling noise,in which statistics of the noise’s increments with different scales are studied.It is proven that the noise has fractality and can be described by the Fractional Brownian Motion(FBM).On this basis,the power-law relation of the FBM regarding the variance of its wavelet coefficients and the fractal dimension is utilized to estimate the fractal dimension.Comparisons of fractal dimensions are made among noises at different speeds and the rail defect AE signals of crack propagations.It is revealed that the fractal dimension of the noise is stochastic and its estimations at different speeds distribute in a small margin below 2 with mean 1.5666.Moreover,the fractal dimension is irrelevant to the speed and is an intrinsic feature of the noise.Thus,the noises with different speeds can be modeled by an identical FBM.On the contrary,fractal dimensions of AE signals of crack propagations are all above 2 and don’t meet the modeling requirement of the FBM.Therefore,the fractal dimension can be taken advantage of as a distinct feature,too.The work extracts the fractal dimension of the wheel-rail rolling noise as the intrinsic feature and offers an effective analysis approach for the description of wheel-rail rolling noise and defect detection in high-speed railway.

关 键 词：滚动噪声 分形特性 分形布朗运动模型 分形维 高速铁路 

分 类 号：U211.5[交通运输工程—道路与铁道工程] U238