A signed graph G˙=(G,σ)is a graph G=(V(G),E(G))with vertex set V(G)and edge set E(G),together with a functionσ:E→{+1,−1}assigning a positive or negative sign to each edge.In this paper,we present a more elementary...A signed graph G˙=(G,σ)is a graph G=(V(G),E(G))with vertex set V(G)and edge set E(G),together with a functionσ:E→{+1,−1}assigning a positive or negative sign to each edge.In this paper,we present a more elementary proof for the matrix-tree theorem of signed graphs,which is based on the relations between the incidence matrices and the Laplcians of signed graphs.As an application,we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.展开更多
A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Lapl...A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.展开更多
Let G=Cay^(+)(Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk),Φ)be a simple graph having vertex set V(G)=Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk)and edge set E(G)={{x,y}:x+y∈Φ},where all p_(1),p_(2),…,p_(...Let G=Cay^(+)(Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk),Φ)be a simple graph having vertex set V(G)=Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk)and edge set E(G)={{x,y}:x+y∈Φ},where all p_(1),p_(2),…,p_(k)are distinct prime factors andΦis the set of all units of the ring Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk).LetΣ=(G,σ)be a signed graph whose underlying graph is G and signature function isσ:E(G)→{+1,-1}defined asσ({x,y})={+1,ifx∈φ(p_(1))or y∈φ(p_(1)^(α1)p_(2)^(α2)…p_(k)^(αk));-1,otherwise.In this paper,we characterize the balance ofΣand some graphs derived from it such asη(Σ),L(Σ)and C_(E)(Σ).Moreover,we investigate the clusterability and sign-compativility ofΣ.展开更多
Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a majo...Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph (SDG) method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure (BCP) sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.展开更多
This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite stead...This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.展开更多
In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic ...In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.展开更多
It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ flow will admit a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. Zyka improved the result...It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ flow will admit a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. Zyka improved the result with 6 replaced by 30. Xu and Zhang showed that the conjecture is true for 6-edge-connected graphs. And for 4-edge-connected graphs, Raspaud and Zhu proved it is true with 6 replaced by 4. In this paper, we show that Bouchet's conjecture is true with 6 replaced by 15 for 3-edge-connected graphs.展开更多
This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge dynamics.Two types of network-underlying graphs are studied,the positively weighted and signed gr...This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge dynamics.Two types of network-underlying graphs are studied,the positively weighted and signed graphs,respectively.We apply an edge Laplacian matrix for a positively weighted network to represent the edge connections.The properties of the edge Laplacian matrix are analyzed and incorporated into the proposed conditions.These conditions take account of the dynamics of edge-connected oscillators instead of all oscillator pairs in conventional studies.For a network with positive and negative weights,we represent the network by its spanning tree dynamics,and derive conditions to evaluate the synchronization state of this network.These conditions show that if all edge weights in the spanning tree are positive,and the tree-induced dynamics are in a dominant position over the negative edge dynamics,then this network achieves synchronization.The theoretical findings are validated by numerical examples.展开更多
This paper presents some practical applications of signed directed graphs (SDGs) to computeraided hazard and operability study (HAZOP) and fault diagnosis, based on an analysis of the SDG theory. The SDG is modele...This paper presents some practical applications of signed directed graphs (SDGs) to computeraided hazard and operability study (HAZOP) and fault diagnosis, based on an analysis of the SDG theory. The SDG is modeled for the inversion of synthetic ammonia, which is highly dangerous in process industry, and HAZOP and fault diagnosis based on the SDG model are presented. A new reasoning method, whereby inverse inference is combined with forward inference, is presented to implement SDG fault diagnosis based on a breadth-first algorithm with consistency rules. Compared with conventional inference engines, this new method can better avoid qualitative spuriousness and combination explosion, and can deal with unobservable nodes in SDGs more effectively. Experimental results show the validity and advantages of the new SDG method.展开更多
文摘A signed graph G˙=(G,σ)is a graph G=(V(G),E(G))with vertex set V(G)and edge set E(G),together with a functionσ:E→{+1,−1}assigning a positive or negative sign to each edge.In this paper,we present a more elementary proof for the matrix-tree theorem of signed graphs,which is based on the relations between the incidence matrices and the Laplcians of signed graphs.As an application,we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.
基金supported by the NSF of China(No.19971056)SRP(No.03B019) from the Education Committee of Hunan Province
文摘A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.
基金Supported by the National Natural Science Foundation of China(11561042,11961040)the Natural Science Foundation of Gansu Province(20JR5RA 418)
文摘Let G=Cay^(+)(Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk),Φ)be a simple graph having vertex set V(G)=Z_(p1)×Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk)and edge set E(G)={{x,y}:x+y∈Φ},where all p_(1),p_(2),…,p_(k)are distinct prime factors andΦis the set of all units of the ring Z_(p1)^(α1)_(p2)^(α2)…_(pk)^(αk).LetΣ=(G,σ)be a signed graph whose underlying graph is G and signature function isσ:E(G)→{+1,-1}defined asσ({x,y})={+1,ifx∈φ(p_(1))or y∈φ(p_(1)^(α1)p_(2)^(α2)…p_(k)^(αk));-1,otherwise.In this paper,we characterize the balance ofΣand some graphs derived from it such asη(Σ),L(Σ)and C_(E)(Σ).Moreover,we investigate the clusterability and sign-compativility ofΣ.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA110503-3)Fundamental Research Funds for the Central Universities of China(Grant No.2860219030)Foundation of Traction Power State Key Laboratory of Southwest Jiaotong University,China(Grant No.TPL1308)
文摘Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph (SDG) method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure (BCP) sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.
文摘This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.
基金Supported by the Basic Research Foundation of Beijing Institute of Technology(20130342035)
文摘In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.
基金Supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China Project(Grant No.10XNB054)
文摘It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ flow will admit a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. Zyka improved the result with 6 replaced by 30. Xu and Zhang showed that the conjecture is true for 6-edge-connected graphs. And for 4-edge-connected graphs, Raspaud and Zhu proved it is true with 6 replaced by 4. In this paper, we show that Bouchet's conjecture is true with 6 replaced by 15 for 3-edge-connected graphs.
基金supported by the Hainan Provincial Natural Science Foundation of China(422RC667).
文摘This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge dynamics.Two types of network-underlying graphs are studied,the positively weighted and signed graphs,respectively.We apply an edge Laplacian matrix for a positively weighted network to represent the edge connections.The properties of the edge Laplacian matrix are analyzed and incorporated into the proposed conditions.These conditions take account of the dynamics of edge-connected oscillators instead of all oscillator pairs in conventional studies.For a network with positive and negative weights,we represent the network by its spanning tree dynamics,and derive conditions to evaluate the synchronization state of this network.These conditions show that if all edge weights in the spanning tree are positive,and the tree-induced dynamics are in a dominant position over the negative edge dynamics,then this network achieves synchronization.The theoretical findings are validated by numerical examples.
基金the National High-Tech Research and Development (863) Program of China (No. 2003AA412310)
文摘This paper presents some practical applications of signed directed graphs (SDGs) to computeraided hazard and operability study (HAZOP) and fault diagnosis, based on an analysis of the SDG theory. The SDG is modeled for the inversion of synthetic ammonia, which is highly dangerous in process industry, and HAZOP and fault diagnosis based on the SDG model are presented. A new reasoning method, whereby inverse inference is combined with forward inference, is presented to implement SDG fault diagnosis based on a breadth-first algorithm with consistency rules. Compared with conventional inference engines, this new method can better avoid qualitative spuriousness and combination explosion, and can deal with unobservable nodes in SDGs more effectively. Experimental results show the validity and advantages of the new SDG method.