Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.

Stability analysis of combined project of fish, broiler and ducks： Dynamical system in imprecise environment

In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parame- ters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present dif- ferent characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.

Analysis of the current situation of environmental policy of China and establishment of distributed environmental policy framework

In this study, China＇s current macro-environ- mental policies as well as their implementation and management tools are analyzed. By using the basic economic methodology, detailed studies are conducted focusing on the implementation effect of contemporary China＇s typical environmental policy of the total pollutant discharge quantity control type, and also the two types of environmental management tools are compared from the perspective of implementation costs and policy uncertainty. By introduction of distributed management tools into the implementation of environmental policies, marketoriented means and the methods of economic analysis are introduced into environmental policy decision-making mechanisms, which could afford a new method for changing the current relatively low efficiency of environ- mental policy, solving the problem of＂government failure＂ in environmental policy implementation, and providing a new way to make environmental policy system more flexible and more efficient. It is of great practical significance to solve China＇s current structural, complex and accumulative environmental problems.