As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of im...As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.展开更多
A new authentication algorithm for grid identity trusted computing unlimited by hardware is presented;the trusted root is made as an image data.The grid entity is trusted in the soft platform when its feature of image...A new authentication algorithm for grid identity trusted computing unlimited by hardware is presented;the trusted root is made as an image data.The grid entity is trusted in the soft platform when its feature of image root is entirely matched with that from the other entities＇ feature database in a scale space process.To recognize and detect the stable image root feature,the non-homogeneous linear expandable scale space is proposed.Focusing on relations between the scale parameter of the inhomogeneous Gaussian function terms and the space evolution of thermal diffusion homogeneous equations,three space evolution operators are constructed to exact and mark the feature from image root.Analysis and verification are carried on the new scale space,operators and the core of making decisions for grid entities certifications.展开更多
Partial similarity of shapes is a challenging problem arising in many important applications in computer vision,shape analysis,and graphics,e.g.when one has to deal with partial information and acquisition artifacts.T...Partial similarity of shapes is a challenging problem arising in many important applications in computer vision,shape analysis,and graphics,e.g.when one has to deal with partial information and acquisition artifacts.The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation.Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two,taking into account possibly different parts.In this paper,we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation.We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match.The problem is regularized using the Mumford-Shah functional.We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes,and present experiments demonstrating the success of the proposed method.展开更多
In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s wo...In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.展开更多
In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusio...In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusion among others.Via the standard resolvent approach,the associated generalized diffusion processes are constructed.展开更多
We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-si...We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-sided estimates for the transition density functions(or heat kernels) of the processes,a priori Hlder estimate and parabolic Harnack inequalities for their parabolic functions.In contrast to the second order elliptic differential operator case,the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.展开更多
Social media have dramatically changed the mode of information dissemination.Various models and algorithms have been developed to model information diffusion and address the influence maximization problem in complex s...Social media have dramatically changed the mode of information dissemination.Various models and algorithms have been developed to model information diffusion and address the influence maximization problem in complex social networks.However,it appears difficult for state-of-the-art models to interpret complex and reversible real interactive networks.In this paper,we propose a novel influence diffusion model,i.e.,the Operator-Based Model(OBM),by leveraging the advantages offered from the heat diffusion based model and the agent-based model.The OBM improves the performance of simulated dissemination by considering the complex user context in the operator of the heat diffusion based model.The experiment obtains a high similarity of the OBM simulated trend to the real-world diffusion process by use of the dynamic time warping method.Furthermore,a novel influence maximization algorithm,i.e.,the Global Topical Support Greedy algorithm(GTS-Greedy algorithm),is proposed corresponding to the OBM.The experimental results demonstrate its promising performance by comparing it against other classic algorithms.展开更多
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One ... This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.展开更多
Yau made the following conjecture:For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional.we extend the result o...Yau made the following conjecture:For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional.we extend the result on the Laplace operator to that on the symmetric diffusion operator,and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finitedimensional,when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.展开更多
基金co-supported by the National Science Foundation of China(NSFC)(Nos.61573365,61603398,61374126,61473094,and 61773386)the Young Talent Fund of University Association for Science and Technology in Shaanxi,Chinathe Young Elite Scientists Sponsorship Program(YESS)by China Association for Science and Technology(CAST)
文摘As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.
基金Foundation item: Supported by the National Natural Science Foundation (61070151,60903203,61103246)the Natural Science Foundation of Fujian Province (2010J01353)+1 种基金the Xiamen University of Technology Scientific Research Foundation (YKJ11024R)Xiamen Scientific Research Foundation (3502Z20123037)
文摘A new authentication algorithm for grid identity trusted computing unlimited by hardware is presented;the trusted root is made as an image data.The grid entity is trusted in the soft platform when its feature of image root is entirely matched with that from the other entities＇ feature database in a scale space process.To recognize and detect the stable image root feature,the non-homogeneous linear expandable scale space is proposed.Focusing on relations between the scale parameter of the inhomogeneous Gaussian function terms and the space evolution of thermal diffusion homogeneous equations,three space evolution operators are constructed to exact and mark the feature from image root.Analysis and verification are carried on the new scale space,operators and the core of making decisions for grid entities certifications.
基金The author would like to thank the referees for the helpful suggestionsThis work has been supported in part by the Israeli Science Foundation grant 615/11+1 种基金the German-Israeli Foundation grant 2269/2010and the Swiss High Performance and High Productivity Computing(HP2C)grant.
文摘Partial similarity of shapes is a challenging problem arising in many important applications in computer vision,shape analysis,and graphics,e.g.when one has to deal with partial information and acquisition artifacts.The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation.Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two,taking into account possibly different parts.In this paper,we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation.We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match.The problem is regularized using the Mumford-Shah functional.We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes,and present experiments demonstrating the success of the proposed method.
基金China Scholarship Council for financial support(2007U13020)
文摘In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.
基金Supported in part by NSFC(Grant No.11771047)Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai(Grant No.2019RS1057)。
文摘In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusion among others.Via the standard resolvent approach,the associated generalized diffusion processes are constructed.
基金supported by National Science Foundation of USA(Grant No.DMS-0600206)
文摘We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-sided estimates for the transition density functions(or heat kernels) of the processes,a priori Hlder estimate and parabolic Harnack inequalities for their parabolic functions.In contrast to the second order elliptic differential operator case,the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.
文摘Social media have dramatically changed the mode of information dissemination.Various models and algorithms have been developed to model information diffusion and address the influence maximization problem in complex social networks.However,it appears difficult for state-of-the-art models to interpret complex and reversible real interactive networks.In this paper,we propose a novel influence diffusion model,i.e.,the Operator-Based Model(OBM),by leveraging the advantages offered from the heat diffusion based model and the agent-based model.The OBM improves the performance of simulated dissemination by considering the complex user context in the operator of the heat diffusion based model.The experiment obtains a high similarity of the OBM simulated trend to the real-world diffusion process by use of the dynamic time warping method.Furthermore,a novel influence maximization algorithm,i.e.,the Global Topical Support Greedy algorithm(GTS-Greedy algorithm),is proposed corresponding to the OBM.The experimental results demonstrate its promising performance by comparing it against other classic algorithms.
基金in part by the National Science Foundation under grant DMS-9971608in part by the Office of Naval Research under grant N00014-95-1-0793+1 种基金in part by the National Science Foundation under grant DMS-9971608in part by the National Science Foundation
文摘 This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
基金supported by National Natural Science Foundation of China(Grant No.10571135)
文摘Yau made the following conjecture:For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional.we extend the result on the Laplace operator to that on the symmetric diffusion operator,and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finitedimensional,when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.
