Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the con...Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the consistency of solution sets, the original interval equations are equivalently transformed into some deterministic inequations. On this basis, calculating the structural displacement response with interval parameters is predigested to a number of deterministic linear optimization problems. The results are proved to be accurate to the interval governing equations. Finally, a numerical example is given to demonstrate the feasibility and efficiency of the proposed method.展开更多
In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current ...In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.展开更多
The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robus...The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities(LMI) toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained results.展开更多
To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns...To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeofffactor (α) into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty- based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of a was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demon- strate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.展开更多
基金supported by the National Natural Science Foundation of China(Nos.90816024,10872017,and 10876100)the Defense Industrial Technology Development Program(Nos.A2120110001 and 2120110011)the 111 Project(No.B07009)
文摘Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the consistency of solution sets, the original interval equations are equivalently transformed into some deterministic inequations. On this basis, calculating the structural displacement response with interval parameters is predigested to a number of deterministic linear optimization problems. The results are proved to be accurate to the interval governing equations. Finally, a numerical example is given to demonstrate the feasibility and efficiency of the proposed method.
基金Supported by the National Natural Science Foundation of China(11971433)First Class Discipline of Zhe-jiang-A(Zhejiang Gongshang University-Statistics,1020JYN4120004G-091),Graduate Scientic Research and Innovation Foundation of Zhejiang Gongshang University.
文摘In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.
基金Supported by the Natural Science Foundation of Shandong Province (ZR2010FM038,ZR2010FL017)
文摘The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities(LMI) toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained results.
基金This paper was supported by the National Natural Science Foundation of China (Grant No. 41222002), Research Fund for the Doctoral Program of Higher Education of China (20100001120020) and "China National Water Pollution Control Program" (2013ZX07102-006). Special thanks to Dr. Daniel Obenour in University of Michigan.
文摘To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeofffactor (α) into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty- based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of a was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demon- strate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.