In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermit...In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for ...The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.展开更多
A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general para...A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
Thermal image, or thermogram, becomes a new type of signal for machine condition monitoring and fault diagnosis due to the capability to display real-time temperature distribution and possibility to indicate the mach...Thermal image, or thermogram, becomes a new type of signal for machine condition monitoring and fault diagnosis due to the capability to display real-time temperature distribution and possibility to indicate the machine’s operating condition through its temperature. In this paper, an investigation of using the second-order statistical features of thermogram in association with minimum redundancy maximum relevance (mRMR) feature selection and simplified fuzzy ARTMAP (SFAM) classification is conducted for rotating machinery fault diagnosis. The thermograms of different machine conditions are firstly preprocessed for improving the image contrast, removing noise, and cropping to obtain the regions of interest (ROIs). Then, an enhanced algorithm based on bi-dimensional empirical mode decomposition is implemented to further increase the quality of ROIs before the second-order statistical features are extracted from their gray-level co-occurrence matrix (GLCM). The highly relevant features to the machine condition are selected from the total feature set by mRMR and are fed into SFAM to accomplish the fault diagnosis. In order to verify this investigation, the thermograms acquired from different conditions of a fault simulator including normal, misalignment, faulty bearing, and mass unbalance are used. This investigation also provides a comparative study of SFAM and other traditional methods such as back-propagation and probabilistic neural networks. The results show that the second-order statistical features used in this framework can provide a plausible accuracy in fault diagnosis of rotating machinery.展开更多
By using the Riccati technique and the technique, new oscillation criteriaare obtained for the second order matrix differential system (P(t)Y'(t))' + r(t)P(t)Y(t) + Q(t)Y (t)= 0, t ≥ t_0. These results in the...By using the Riccati technique and the technique, new oscillation criteriaare obtained for the second order matrix differential system (P(t)Y'(t))' + r(t)P(t)Y(t) + Q(t)Y (t)= 0, t ≥ t_0. These results in the present paper generalize and improve many known conclusions.Furthermore, some results are different from the most known ones in the sense that they are based onthe information only on a sequence of subintervals of [t 0,), rather than on the whole half–line.In particular, our results complement a number of existing results and handle the case that is notcovered by the known criteria.展开更多
文摘In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
文摘The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.
基金This work was supported by the Chinese National Natural Science Foundation ( No. 69925308).
文摘A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
文摘Thermal image, or thermogram, becomes a new type of signal for machine condition monitoring and fault diagnosis due to the capability to display real-time temperature distribution and possibility to indicate the machine’s operating condition through its temperature. In this paper, an investigation of using the second-order statistical features of thermogram in association with minimum redundancy maximum relevance (mRMR) feature selection and simplified fuzzy ARTMAP (SFAM) classification is conducted for rotating machinery fault diagnosis. The thermograms of different machine conditions are firstly preprocessed for improving the image contrast, removing noise, and cropping to obtain the regions of interest (ROIs). Then, an enhanced algorithm based on bi-dimensional empirical mode decomposition is implemented to further increase the quality of ROIs before the second-order statistical features are extracted from their gray-level co-occurrence matrix (GLCM). The highly relevant features to the machine condition are selected from the total feature set by mRMR and are fed into SFAM to accomplish the fault diagnosis. In order to verify this investigation, the thermograms acquired from different conditions of a fault simulator including normal, misalignment, faulty bearing, and mass unbalance are used. This investigation also provides a comparative study of SFAM and other traditional methods such as back-propagation and probabilistic neural networks. The results show that the second-order statistical features used in this framework can provide a plausible accuracy in fault diagnosis of rotating machinery.
基金This work is supported by National Key Basic Research Special Fundation of China(No.G1998020309)National Natural Science Foundation of China(No.10461002)Science Foundation of Guangxi Province of China (No.0236012) 34A30,34C10
文摘By using the Riccati technique and the technique, new oscillation criteriaare obtained for the second order matrix differential system (P(t)Y'(t))' + r(t)P(t)Y(t) + Q(t)Y (t)= 0, t ≥ t_0. These results in the present paper generalize and improve many known conclusions.Furthermore, some results are different from the most known ones in the sense that they are based onthe information only on a sequence of subintervals of [t 0,), rather than on the whole half–line.In particular, our results complement a number of existing results and handle the case that is notcovered by the known criteria.
