Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively....Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a(r+s) ×(r+s) dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr+s/Zr+s areΓΩ={[γT h,ζ T q] T:γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton's condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2(Rr+s).Properties,including Lawton's condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2(Rr+1) are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].展开更多
An accurate estimation of the remaining useful life(RUL) not only contributes to an effective application of an aviation piston pump, but also meets the necessity of condition based maintenance(CBM). For the curre...An accurate estimation of the remaining useful life(RUL) not only contributes to an effective application of an aviation piston pump, but also meets the necessity of condition based maintenance(CBM). For the current RUL evaluation methods, a model-based method is inappropriate for the degradation process of an aviation piston pump due to difficulties of modeling, while a data-based method rarely presents high-accuracy prediction in a long period of time. In this work,an adaptive-order particle filter(AOPF) prognostic process is proposed aiming at improving long-term prediction accuracy of RUL by combining both kinds of methods. A dynamic model is initialized by a data-driven or empirical method. When a new observation comes, the prior state distribution is approximated by a current model. The order of the current model is updated adaptively by fusing the information of the observation. Monte Carlo simulation is employed for estimating the posterior probability density function of future states of the pump's degradation.With updating the order number adaptively, the method presents a higher precision in contrast with those of traditional methods. In a case study, the proposed AOPF method is adopted to forecast the degradation status of an aviation piston pump with experimental return oil flow data, and the analytical results show the effectiveness of the proposed AOPF method.展开更多
We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple con...We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results.展开更多
基金Supported by the National Natural Science Foundation of China(11071152)the Natural Science Foundation of Guangdong Province(10151503101000025)
文摘Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a(r+s) ×(r+s) dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr+s/Zr+s areΓΩ={[γT h,ζ T q] T:γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton's condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2(Rr+s).Properties,including Lawton's condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2(Rr+1) are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].
基金co-supported by the National Natural Science Foundation of China(Nos.51620105010,51575019)National Basic Research Program of China(No.2014CB046400)Program 111 of China
文摘An accurate estimation of the remaining useful life(RUL) not only contributes to an effective application of an aviation piston pump, but also meets the necessity of condition based maintenance(CBM). For the current RUL evaluation methods, a model-based method is inappropriate for the degradation process of an aviation piston pump due to difficulties of modeling, while a data-based method rarely presents high-accuracy prediction in a long period of time. In this work,an adaptive-order particle filter(AOPF) prognostic process is proposed aiming at improving long-term prediction accuracy of RUL by combining both kinds of methods. A dynamic model is initialized by a data-driven or empirical method. When a new observation comes, the prior state distribution is approximated by a current model. The order of the current model is updated adaptively by fusing the information of the observation. Monte Carlo simulation is employed for estimating the posterior probability density function of future states of the pump's degradation.With updating the order number adaptively, the method presents a higher precision in contrast with those of traditional methods. In a case study, the proposed AOPF method is adopted to forecast the degradation status of an aviation piston pump with experimental return oil flow data, and the analytical results show the effectiveness of the proposed AOPF method.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 11071152), the Natural Science Foundation of Guangdong Province (Grant No. $2011010004511) Education Department of Henan Province and the Science and Technology Research of (Grant No. 14B520045).
文摘We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results.