Based-restraining interval extension improved truncation algorithm for response analysis of uncertain mechanical systems

Purpose This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function. Design/methodology/approach To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed. Findings The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results. Originality/value Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

Topological entropy of Markov set-valued functions

We investigate the entropy for a class of upper semi-continuous set-valued functions, called Markov set-valued functions, that are a generalization of single-valued Markov interval functions. It is known that the entropy of a Markov interval function can be found by calculating the entropy of an associated shift of finite type. In this paper, we construct a similar shift of finite type for Markov set-valued functions and use this shift space to find upper and lower bounds on the entropy of the set-valued function.

INTERVAL EXTENSION STRUCTURE BASIC TYPES OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER

. In this article, the interval expansion of the structure of solving basic types of boundary value problems for partial differential equations of the second order of making the basic operations that compose interval arithmetic is developed. For the differential equation (1) of the type, when constructing the interval expansion of the structure of the formula, structural formulas were used to construct with the Rfunction method and 4 problems were studied — the Dirichlet problem, the Neumann problem, the third type problem, the mixed boundary conditions problem. For the Dirichlet problem, the solution is an interval expansion of the structure in the form (5), where 𝑃 = {𝜔𝛷 , 𝜔𝛷̅, 𝜔̅𝛷, 𝜔̅𝛷̅} и [ 𝛷, 𝛷̅]is an indefinite interval function. For the Neumann problem, a solution is solved in the interval extension of the structure, [ 𝛷1, 𝛷1̅̅̅̅], [ 𝛷2, 𝛷2̅̅̅̅] is an indefinite interval function and 𝐷1 is a differential operator of the form. For the problem of the third type, the solution is solved in the interval extension of the structure, [ 𝛷1, 𝛷1̅̅̅̅], [𝛷2, 𝛷2̅̅̅̅] -indefinite, interval function, 𝐷1 - differential operator of the form (9). For the problem, mixed boundary conditions are treated. The solution In the interval extension of the structure,[ 𝛷1, 𝛷1], [ 𝛷2, 𝛷2̅̅̅̅] is an indefinite interval function and 𝐷1 is a differential operator of the form.

INTERVAL EXTENSION STRUCTURE BASIC TYPES OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF FORTH ORDER

In this article, the interval expansion of the structure of solving basic types of boundary value problems for partial differential equations of the fourth order has been developed. Used Method of R-functions for constructed coordinate sequences. Constructing interval extensions of structural formulas, we consider problems (1) on the transverse bending of thin plates and 5 problems on a plate - rigidly clamped plate, loosely supported plate, elastically fixed plates, partially rigidly clamped and partially elastically fixed plates, plates, partially rigidly clamped and partially free . For the problem, the rigidly clamped plate Formula (7) is an interval structure for solving the boundary value problem (4). Here L={▁ω ▁ψ,ω ̅▁ψ,▁ω ψ ̅,ω ̅ψ ̅ },L_1={▁ω D_1 ▁φ,ω ̅D_1 ▁φ,▁ω D_1 φ ̅,ω ̅D_1 φ ̅ } L_2={▁ω^2 ▁Φ,ω ̅^2 ▁Φ,▁ω^2 Φ ̅,ω ̅^2 Φ ̅ }, [ ▁Φ,Φ ̅ ] is an indefinite interval function. For the free-supported plate problem, a solution is obtained for the interval expansion of the structure in the form (15), (17), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval function, D_2, T_2 - differential operators of the form (11) and (12). For the problem of elastically fixed plates, a solution was obtained in the interval expansion of the structure in the form (21) - (24), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval functions, D_2,T_2,D_1- differential operators of the form (11) and (12), (3). For the problem of partially rigidly clamped and partially elastically fixed plates, a solution was obtained in the interval expansion of the structure in the form of (28), (30), (32), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ]- indefinite interval functions, D_2,T_2,D_1- differential operators of the form (11) and (12), (6). For the plate problem, partially rigidly pinched and partially free, a solution is obtained in the interval extension of the structure (40), (41), (42), [ ▁(Φ_1 ),(Φ_1 ) ̅ ], [ ▁(Φ_2 ),(Φ_2 ) ̅ ] - indefinite interval functions, D_2,T_2,D_1,D_3- differential operators of the form (11), (12), (6) and (38).