Although industrial processes often perform perfectly under design conditions, they may deviate from the optimal operating point owing to parameters drift, environmental disturbances, etc. Thus, it is necessary to dev...Although industrial processes often perform perfectly under design conditions, they may deviate from the optimal operating point owing to parameters drift, environmental disturbances, etc. Thus, it is necessary to develop efficacious strategies or procedure to assess the process performance online. In this paper, we explore the issue of operating optimality assessment for complex industrial processes based on performance-similarity considering nonlinearities and outliers simultaneously, and a general enforced online performance assessment framework is proposed. In the offline part, a new and modified total robust kernel projection to latent structures algorithm,T-KPRM, is proposed and used to evaluate the complex nonlinear industrial process, which can effectively extract the optimal-index-related process variation information from process data and establish assessment models for each performance grades overcoming the effects of outlier. In the online part, the online assessment results can be obtained by calculating the similarity between the online data from a sliding window and each of the performance grades. Furthermore, in order to improve the accuracy of online assessment, we propose an online assessment strategy taking account of the effects of noise and process uncertainties. The Euclidean distance between the sliding data window and the optimal evaluation level is employed to measure the contribution rates of variables, which indicate the possible reason for the non-optimal operating performance. The proposed framework is tested on a real industrial case: dense medium coal preparation process, and the results shows the efficiency of the proposed method comparing to the existing method.展开更多
The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of...The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed by G. Liu in [23]. In the first part, we will give a survey on the progress.In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number C_1~n is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that,under bounded curvature conditions, C_1~n is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on K¨ahler manifolds with minimal volume growth.展开更多
In this paper, a corrector-predictor interior-point algorithm is proposed for symmetric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-pat...In this paper, a corrector-predictor interior-point algorithm is proposed for symmetric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iterates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algorithm is shown and it is proved that the algorithm has the complexity bound O(r^(1/2) L) for the well-known Nesterov-Todd search direction and O(r L) for the xs and sx search directions.展开更多
The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-mom...The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the RiemannCartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system, the differential equations of motion in its Riemann-Cartan configuration space may be simpler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained problems, which are difficult to be solved by the traditional analytical mechanics method.Three examples are given to illustrate the effectiveness of the method.展开更多
基金Supported by the National Natural Science Foundation of China(61503384,61603393)Natural Science Foundation of Jiangsu(BK20150199,BK20160275)+1 种基金the Foundation Research Funds for the Central Universities(2015QNA65)the Postdoctoral Foundation of Jiangsu Province(1501081B)
文摘Although industrial processes often perform perfectly under design conditions, they may deviate from the optimal operating point owing to parameters drift, environmental disturbances, etc. Thus, it is necessary to develop efficacious strategies or procedure to assess the process performance online. In this paper, we explore the issue of operating optimality assessment for complex industrial processes based on performance-similarity considering nonlinearities and outliers simultaneously, and a general enforced online performance assessment framework is proposed. In the offline part, a new and modified total robust kernel projection to latent structures algorithm,T-KPRM, is proposed and used to evaluate the complex nonlinear industrial process, which can effectively extract the optimal-index-related process variation information from process data and establish assessment models for each performance grades overcoming the effects of outlier. In the online part, the online assessment results can be obtained by calculating the similarity between the online data from a sliding window and each of the performance grades. Furthermore, in order to improve the accuracy of online assessment, we propose an online assessment strategy taking account of the effects of noise and process uncertainties. The Euclidean distance between the sliding data window and the optimal evaluation level is employed to measure the contribution rates of variables, which indicate the possible reason for the non-optimal operating performance. The proposed framework is tested on a real industrial case: dense medium coal preparation process, and the results shows the efficiency of the proposed method comparing to the existing method.
文摘The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed by G. Liu in [23]. In the first part, we will give a survey on the progress.In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number C_1~n is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that,under bounded curvature conditions, C_1~n is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on K¨ahler manifolds with minimal volume growth.
基金Shahrekord University for financial supportpartially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran
文摘In this paper, a corrector-predictor interior-point algorithm is proposed for symmetric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iterates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algorithm is shown and it is proved that the algorithm has the complexity bound O(r^(1/2) L) for the well-known Nesterov-Todd search direction and O(r L) for the xs and sx search directions.
基金Project supported by the National Natural Science Foundation of China(Nos.11772144,11572145,11472124,11572034,and 11202090)the Science and Technology Research Project of Liaoning Province(No.L2013005)+1 种基金the China Postdoctoral Science Foundation(No.2014M560203)the Natural Science Foundation of Guangdong Provience(No.2015A030310127)
文摘The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the RiemannCartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system, the differential equations of motion in its Riemann-Cartan configuration space may be simpler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained problems, which are difficult to be solved by the traditional analytical mechanics method.Three examples are given to illustrate the effectiveness of the method.
