As an important part of rotating machinery,gearboxes often fail due to their complex working conditions and harsh working environment.Therefore,it is very necessary to effectively extract the fault features of the gea...As an important part of rotating machinery,gearboxes often fail due to their complex working conditions and harsh working environment.Therefore,it is very necessary to effectively extract the fault features of the gearboxes.Gearbox fault signals usually contain multiple characteristic components and are accompanied by strong noise interference.Traditional sparse modeling methods are based on synthesis models,and there are few studies on analysis and balance models.In this paper,a balance nonconvex regularized sparse decomposition method is proposed,which based on a balance model and an arctangent nonconvex penalty function.The sparse dictionary is constructed by using Tunable Q-Factor Wavelet Transform(TQWT)that satisfies the tight frame condition,which can achieve efficient and fast solution.It is optimized and solved by alternating direction method of multipliers(ADMM)algorithm,and the non-convex regularized sparse decomposition algorithm of synthetic and analytical models are given.Through simulation experiments,the determination methods of regularization parameters and balance parameters are given,and compared with the L1 norm regularization sparse decomposition method under the three models.Simulation analysis and engineering experimental signal analysis verify the effectiveness and superiority of the proposed method.展开更多
Hyperbolic conservation laws arise in the context of continuum physics,and are mathematically presented in differential form and understood in the distributional(weak)sense.The formal application of the Gauss-Green th...Hyperbolic conservation laws arise in the context of continuum physics,and are mathematically presented in differential form and understood in the distributional(weak)sense.The formal application of the Gauss-Green theorem results in integral balance laws,in which the concept of flux plays a central role.This paper addresses the spacetime viewpoint of the flux regularity,providing a rigorous treatment of integral balance laws.The established Lipschitz regularity of fluxes(over time intervals)leads to a consistent flux approximation.Thus,fully discrete finite volume schemes of high order may be consistently justified with reference to the spacetime integral balance laws.展开更多
A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and genera...A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.展开更多
Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps,and utilize convolutional neural networks(CNNs)to learn data-driven priors.However,their performance is limited for two mai...Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps,and utilize convolutional neural networks(CNNs)to learn data-driven priors.However,their performance is limited for two main reasons.Firstly,priors learned in deep feature space need to be converted to the image space at each iteration step,which limits the depth of CNNs and prevents CNNs from exploiting contextual information.Secondly,existing methods only learn deep priors at the single full-resolution scale,so ignore the benefits of multi-scale context in dealing with high level noise.To address these issues,we explicitly consider the image denoising process in the deep feature space and propose the deep unfolding multi-scale regularizer network(DUMRN)for image denoising.The core of DUMRN is the feature-based denoising module(FDM)that directly removes noise in the deep feature space.In each FDM,we construct a multi-scale regularizer block to learn deep prior information from multi-resolution features.We build the DUMRN by stacking a sequence of FDMs and train it in an end-to-end manner.Experimental results on synthetic and real-world benchmarks demonstrate that DUMRN performs favorably compared to state-of-theart methods.展开更多
This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT prob...This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.52075353,52007128).
文摘As an important part of rotating machinery,gearboxes often fail due to their complex working conditions and harsh working environment.Therefore,it is very necessary to effectively extract the fault features of the gearboxes.Gearbox fault signals usually contain multiple characteristic components and are accompanied by strong noise interference.Traditional sparse modeling methods are based on synthesis models,and there are few studies on analysis and balance models.In this paper,a balance nonconvex regularized sparse decomposition method is proposed,which based on a balance model and an arctangent nonconvex penalty function.The sparse dictionary is constructed by using Tunable Q-Factor Wavelet Transform(TQWT)that satisfies the tight frame condition,which can achieve efficient and fast solution.It is optimized and solved by alternating direction method of multipliers(ADMM)algorithm,and the non-convex regularized sparse decomposition algorithm of synthetic and analytical models are given.Through simulation experiments,the determination methods of regularization parameters and balance parameters are given,and compared with the L1 norm regularization sparse decomposition method under the three models.Simulation analysis and engineering experimental signal analysis verify the effectiveness and superiority of the proposed method.
基金supported by the NSFC(Nos.11771054,12072042,91852207)the Sino-German Research Group Project(No.GZ1465)the National Key Project GJXM92579.
文摘Hyperbolic conservation laws arise in the context of continuum physics,and are mathematically presented in differential form and understood in the distributional(weak)sense.The formal application of the Gauss-Green theorem results in integral balance laws,in which the concept of flux plays a central role.This paper addresses the spacetime viewpoint of the flux regularity,providing a rigorous treatment of integral balance laws.The established Lipschitz regularity of fluxes(over time intervals)leads to a consistent flux approximation.Thus,fully discrete finite volume schemes of high order may be consistently justified with reference to the spacetime integral balance laws.
基金Supported by NSF of China(No.10001005) and Com~2MaC-KOSEF
文摘A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.
基金partially supported by the National Key R&D Program of China(No.2020YFA0714101)the National Nature Science Foundation of China(Nos.61872162,62102414,62172415,and 52175493).
文摘Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps,and utilize convolutional neural networks(CNNs)to learn data-driven priors.However,their performance is limited for two main reasons.Firstly,priors learned in deep feature space need to be converted to the image space at each iteration step,which limits the depth of CNNs and prevents CNNs from exploiting contextual information.Secondly,existing methods only learn deep priors at the single full-resolution scale,so ignore the benefits of multi-scale context in dealing with high level noise.To address these issues,we explicitly consider the image denoising process in the deep feature space and propose the deep unfolding multi-scale regularizer network(DUMRN)for image denoising.The core of DUMRN is the feature-based denoising module(FDM)that directly removes noise in the deep feature space.In each FDM,we construct a multi-scale regularizer block to learn deep prior information from multi-resolution features.We build the DUMRN by stacking a sequence of FDMs and train it in an end-to-end manner.Experimental results on synthetic and real-world benchmarks demonstrate that DUMRN performs favorably compared to state-of-theart methods.
基金Scientific Research Project for Introduced Talents of Guizhou University of Finance and Economics(No.2021YJ007)National Natural Science Foundation of China(Grant Nos.61862051,61762019,62241206)+2 种基金Top-notch Talent Program of Guizhou Province(No.KY[2018]080)Science and Technology Foundation of Guizhou Province(No.20191299)foundation of Qiannan Normal University for Nationalities(Nos.QNSYRC201715,QNSY2018JS013).
文摘This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.
