In order to recognize the different operating conditions of a distributed and complex electromechanical system in the process industry,this work proposed a novel method of condition recognition by combining complex ne...In order to recognize the different operating conditions of a distributed and complex electromechanical system in the process industry,this work proposed a novel method of condition recognition by combining complex network theory with phase space reconstruction.First,a condition-space with complete information was reconstructed based on phase space reconstruction,and each condition in the space was transformed into a node of a complex network.Second,the limited penetrable visibility graph method was applied to establish an undirected and un-weighted complex network for the reconstructed condition-space.Finally,the statistical properties of this network were calculated to recognize the different operating conditions.A case study of a real chemical plant was conducted to illustrate the analysis and application processes of the proposed method.The results showed that the method could effectively recognize the different conditions of electromechanical systems.A complex electromechanical system can be studied from the systematic and cyber perspectives,and the relationship between the network structure property and the system condition can also be analyzed by utilizing the proposed method.展开更多
Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition,...Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and e展开更多
Space systems have become a key enabler for a wide variety of applications that are vital to the functioning of advanced societies. The trend is one of quantitative and qualitative increase of this dependence, so much...Space systems have become a key enabler for a wide variety of applications that are vital to the functioning of advanced societies. The trend is one of quantitative and qualitative increase of this dependence, so much so that space systems have been described as a new example of critical infrastructure. This article argues that the existence of critical space infrastructures implies the emergence of a new category of disasters related to disruption risks. We inventory those risks and make policy recommendations for what is, ultimately, a resilience governance issue.展开更多
Mobius transforms,Blaschke products and starlike functions as typical conformal mappings of one complex variable give rise to nonlinear phases with non-negative phase derivatives with the latter being de ned by instan...Mobius transforms,Blaschke products and starlike functions as typical conformal mappings of one complex variable give rise to nonlinear phases with non-negative phase derivatives with the latter being de ned by instantaneous frequencies of signals they represent.The positive analytic phase derivative has been a widely interested subject among signal analysts(see Gabor(1946)).Research results of the positive analytic frequency and applications appears in the literature since the middle of the 20th century.Of the positive frequency study a directly related topic is positive frequency decomposition of signals.The mainly focused methods of such decompositions include the maximal selection method and the Blaschke product unwinding method,and joint use of the mentioned methods.In this paper,we propose a class of iterative greedy algorithms based on the Blaschke product and adaptive Fourier decomposition.It generalizes the Blaschke product unwinding method by subtracting constants other than the averages of the remaining functions,aiming at larger winding numbers,and subtracting n-Blaschke forms of the remaining functions,aiming at generating larger numbers of zero-crossings,to fast reduce energy of the remaining terms.Furthermore,we give a comprehensive and rigorous proof of the converging rate in terms of the zeros of the remainders.Finite Blaschke product methods are proposed to avoid the in nite phase derivative dilemma,and to avoid the computational diculties.展开更多
基金supported by the National Natural Science Foundation of China (Grant by No. 51175402)
文摘In order to recognize the different operating conditions of a distributed and complex electromechanical system in the process industry,this work proposed a novel method of condition recognition by combining complex network theory with phase space reconstruction.First,a condition-space with complete information was reconstructed based on phase space reconstruction,and each condition in the space was transformed into a node of a complex network.Second,the limited penetrable visibility graph method was applied to establish an undirected and un-weighted complex network for the reconstructed condition-space.Finally,the statistical properties of this network were calculated to recognize the different operating conditions.A case study of a real chemical plant was conducted to illustrate the analysis and application processes of the proposed method.The results showed that the method could effectively recognize the different conditions of electromechanical systems.A complex electromechanical system can be studied from the systematic and cyber perspectives,and the relationship between the network structure property and the system condition can also be analyzed by utilizing the proposed method.
基金supported by Cultivation Program for Oustanding Young Teachers of Guangdong Province (Grant No. Yq2014060)Macao Science Technology Fund (Grant No. FDCT/099/ 2014/A2)
文摘Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and e
基金supported by a grant of the Program for Research,Development and Innovation for Space Technology and Advanced Research(STAR)administered by the Romanian Space Agency,project number 191/2017
文摘Space systems have become a key enabler for a wide variety of applications that are vital to the functioning of advanced societies. The trend is one of quantitative and qualitative increase of this dependence, so much so that space systems have been described as a new example of critical infrastructure. This article argues that the existence of critical space infrastructures implies the emergence of a new category of disasters related to disruption risks. We inventory those risks and make policy recommendations for what is, ultimately, a resilience governance issue.
基金supported by National Natural Science Foundation of China(Grant Nos.61471132 and 11671363)the Science and Technology Development Fund,Macao Special Administration Region(Grant No.0123/2018/A3).
文摘Mobius transforms,Blaschke products and starlike functions as typical conformal mappings of one complex variable give rise to nonlinear phases with non-negative phase derivatives with the latter being de ned by instantaneous frequencies of signals they represent.The positive analytic phase derivative has been a widely interested subject among signal analysts(see Gabor(1946)).Research results of the positive analytic frequency and applications appears in the literature since the middle of the 20th century.Of the positive frequency study a directly related topic is positive frequency decomposition of signals.The mainly focused methods of such decompositions include the maximal selection method and the Blaschke product unwinding method,and joint use of the mentioned methods.In this paper,we propose a class of iterative greedy algorithms based on the Blaschke product and adaptive Fourier decomposition.It generalizes the Blaschke product unwinding method by subtracting constants other than the averages of the remaining functions,aiming at larger winding numbers,and subtracting n-Blaschke forms of the remaining functions,aiming at generating larger numbers of zero-crossings,to fast reduce energy of the remaining terms.Furthermore,we give a comprehensive and rigorous proof of the converging rate in terms of the zeros of the remainders.Finite Blaschke product methods are proposed to avoid the in nite phase derivative dilemma,and to avoid the computational diculties.
