The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To a...The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To address this problem, two dynamic Bayesian network(DBN) approaches are proposed. One approach prunes the DBN of system, and then uses particle filter(PF) for this pruned DBN(PDBN) to perform online diagnosis. The problem is that estimates from a PF tend to have high variance for small sample sets. Using large sample sets is computationally expensive. The other approach compiles the PDBN into a dynamic arithmetic circuit(DAC) using an offline procedure that is applied only once, and then uses this circuit to provide online diagnosis recursively. This approach leads to the most computational consumption in the offline procedure. The experimental results show that the DAC, compared with the PF for PDBN, not only provides more reliable online diagnosis, but also offers much faster inference.展开更多
We introduce an algebraicity criterion.It has the following form:Consider an analytic subvariety of some algebraic variety X over a global field K.Under certain conditions,if X contains many K-points,then X is algebra...We introduce an algebraicity criterion.It has the following form:Consider an analytic subvariety of some algebraic variety X over a global field K.Under certain conditions,if X contains many K-points,then X is algebraic over K.This gives a way to show the transcendence of points via the transcendence of analytic subvarieties.Such a situ-ation often appears when we have a dynamical system,because we can often produce infinitely many points from one point via iterates.Combining this criterion and the study of invariant subvarieties,we get some results on the transcendence in arithmetic dynamics.We get a characterization for products of Böttcher coordinates or products of multiplicative canonical heights for polynomial dynamical pairs to be algebraic.For this,we study the invariant subvarieties for products of endomorphisms.In particular,we partially generalize Medvedev-Scanlon’s classification of invariant subvarieties of split polynomial maps to separable endomorphisms on(P^(1))^(N) in any characteristic.We also get some high dimensional partial generalization via introducing a notion of independence.We then study dominant endomorphisms f on A^(N) over a number field of algebraic degree d≥2.We show that in most cases(e.g.when such an endomor-phism extends to an endomorphism on P^(N)),there are many analytic curves centered at infinity which are periodic.We show that for most of them,it is algebraic if and only if it contains at least one algebraic point.We also study the periodic curves.We show that for most f,all periodic curves have degree at most 2.When N=2,we get a more precise classification result.We show that under a condition which is satisfied for a general f,if f has infinitely many periodic curves,then f is homogenous up to change of origin.展开更多
基金Projects(2010ZD11007,20100751010)supported by Aeronautical Science Foundation of China
文摘The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To address this problem, two dynamic Bayesian network(DBN) approaches are proposed. One approach prunes the DBN of system, and then uses particle filter(PF) for this pruned DBN(PDBN) to perform online diagnosis. The problem is that estimates from a PF tend to have high variance for small sample sets. Using large sample sets is computationally expensive. The other approach compiles the PDBN into a dynamic arithmetic circuit(DAC) using an offline procedure that is applied only once, and then uses this circuit to provide online diagnosis recursively. This approach leads to the most computational consumption in the offline procedure. The experimental results show that the DAC, compared with the PF for PDBN, not only provides more reliable online diagnosis, but also offers much faster inference.
文摘We introduce an algebraicity criterion.It has the following form:Consider an analytic subvariety of some algebraic variety X over a global field K.Under certain conditions,if X contains many K-points,then X is algebraic over K.This gives a way to show the transcendence of points via the transcendence of analytic subvarieties.Such a situ-ation often appears when we have a dynamical system,because we can often produce infinitely many points from one point via iterates.Combining this criterion and the study of invariant subvarieties,we get some results on the transcendence in arithmetic dynamics.We get a characterization for products of Böttcher coordinates or products of multiplicative canonical heights for polynomial dynamical pairs to be algebraic.For this,we study the invariant subvarieties for products of endomorphisms.In particular,we partially generalize Medvedev-Scanlon’s classification of invariant subvarieties of split polynomial maps to separable endomorphisms on(P^(1))^(N) in any characteristic.We also get some high dimensional partial generalization via introducing a notion of independence.We then study dominant endomorphisms f on A^(N) over a number field of algebraic degree d≥2.We show that in most cases(e.g.when such an endomor-phism extends to an endomorphism on P^(N)),there are many analytic curves centered at infinity which are periodic.We show that for most of them,it is algebraic if and only if it contains at least one algebraic point.We also study the periodic curves.We show that for most f,all periodic curves have degree at most 2.When N=2,we get a more precise classification result.We show that under a condition which is satisfied for a general f,if f has infinitely many periodic curves,then f is homogenous up to change of origin.
