This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or ...This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.展开更多
For the characteristics of the continuous stirred-tank reactor(CSTR) with coil and jacket cooling system,a CSTR temperature dual control solution based on the analysis of the CSTR exothermic reaction control character...For the characteristics of the continuous stirred-tank reactor(CSTR) with coil and jacket cooling system,a CSTR temperature dual control solution based on the analysis of the CSTR exothermic reaction control characteristic was proposed for an organic material polymerization production.The control solution has passive fault-tolerant ability for the jacket cooling water cutting off fault and active fault-tolerant potential for the coil cooling water cutting off fault,and it has good control ability,high saving energy and reducing consumption performance.Fault detection and diagnosis and fault-tolerant control strategy are designed for the coil cooling fault to achieve the active fault-tolerant control function.The CSTR temperature dual control,process fault detection and diagnosis and active fault-tolerant control were full integrated into the CSTR temperature fault-tolerant control system,which achieve fault tolerance control of CSTR temperature for any severe malfunction of jacket cooling or coil cooling cutting off,and the security for CSTR exothermic reaction is improved.Finally,the effectiveness of this system was validated by semi-physical simulation experiment.展开更多
For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-m...For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.展开更多
文摘This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.
基金Project(2013JM8024)Supported by Natural Science Basic Research Plan in Shaanxi Province of China
文摘For the characteristics of the continuous stirred-tank reactor(CSTR) with coil and jacket cooling system,a CSTR temperature dual control solution based on the analysis of the CSTR exothermic reaction control characteristic was proposed for an organic material polymerization production.The control solution has passive fault-tolerant ability for the jacket cooling water cutting off fault and active fault-tolerant potential for the coil cooling water cutting off fault,and it has good control ability,high saving energy and reducing consumption performance.Fault detection and diagnosis and fault-tolerant control strategy are designed for the coil cooling fault to achieve the active fault-tolerant control function.The CSTR temperature dual control,process fault detection and diagnosis and active fault-tolerant control were full integrated into the CSTR temperature fault-tolerant control system,which achieve fault tolerance control of CSTR temperature for any severe malfunction of jacket cooling or coil cooling cutting off,and the security for CSTR exothermic reaction is improved.Finally,the effectiveness of this system was validated by semi-physical simulation experiment.
基金Supported by NSFC(Grant Nos.11626245 and 11571043)
文摘For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.
