Facing sampling techniques as an optimal design problem

Summary The aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure.

An optimal design problem with non-standard growth and no concentration effects

We obtain an integral representation for certain functionals arising in the context of optimal design and damage evolution problems under non-standard growth conditions and perimeter penalisation. Under our hypotheses, the integral representation includes a term which is absolutely continuous with respect to the Lebesgue measure and a perimeter term, but no additional singular term. We also study some dimension reduction problems providing results for the optimal design of thin films.

R-optimal designs for second-order Scheffé model with qualitative factors

<abstract><p>Considering a mixture model with qualitative factors, the $ R $-optimal design problem is investigated when the levels of the qualitative factor interact with the mixture factors. In this paper, the conditions for $ R $-optimality of designs with mixture and qualitative factors are presented. General analytical expressions are also derived for the decision function under the $ R $-optimal designs, in order to verify that the resulting designs satisfy the general equivalence theorem. In addition, the relative efficiency of the $ R $-optimal design is discussed.</p></abstract>

Optimum design of friction pair with uniform pressure for a brake mechanism

В работе теоретически найдена микрогеометрия поверхности трения фрикционной пары тормозного механизма, соответствующая равномерному распределению контактного давления на поверхности. Построена замкнутая система алгебраических уравнений, позволяющая получить решение задачи оптимального проектирования пары трения «барабаннакладка» тормозного механизма грузового автомобиля в зависимости от геометрических и механических характеристик его элементов. In the present work a microgeometry of friction surface for friction pair of a brake mechanism is theoretically found. The obtained microgeometry corresponds to uniform distribution of contact pressure on the surface. A closed system of algebraic equations is constructed. It allows one to obtain the solution of the optimal design problem for a “drum-lining” friction pair of the truck’s brake mechanism depending on geometric and mechanical characteristics of brake mechanism elements.

Minimization of heat state for friction lining of truck brake mechanism

A theoretical analysis to determine a microgeometry of friction surface for the drum—lining pair is carried out. The sought-for microgeometry provides a uniform temperature distribution on the contact surface. The model of a rough friction surface is used. A closed system of algebraic equations is constructed. This system allows the solution of the optimal design problem for the drum- lining friction pair of the truck brake mechanism depending on geometric and mechanical characteristics of the pair elements. Keywords friction pair, drum, lining, wear, optimal microgeometry, uniform temperature distribution

The Optimal Design Problem of a Flat Steel Frame Structure with Soft Connection to the P - Delta Effect

In the report, the optimal design problem of flat steel frame structure in the deformed state is considered, considering the softness of “the beam-column connection pinned” with “the moments-rotation angle relationship of the connection” is nonlinear, linearized by three straight lines, the material of the structure is elastic – plastic material in ideal state and considering the P-Delta effect. Establish and solve the problem of flat steel frame structure in the form of nonlinear planning and solve the problem thanks to MATLAB 6.0 programming language. Create a specialized program to optimize the steel frame structure, the results illustrate the effect of bonding softness and P-Delta effect on the weight of steel frame structure