A novel method for mathematical modeling of a form-cutting-tool of the optimum design

A method that pertains to design of the optimal form-cutting-tool for machining of a given sculptured surface on a multi-axis NC   machine is discussed in the paper. The results reported in the paper are based in much on the author’s previous work in the field of R$\mathbb{R}$-mapping of a sculptured surface onto the machining surface of cutting tools. Mathematical foundations of a novel method of experimental modeling of the interaction of the form-cutting-tool and the work are disclosed. The last method is of critical importance for the experimental determination of the rate of conformity functions, those essential for consequent use of R$\mathbb{R}$-mapping of surfaces. The presented geometric criteria is helpful for designers since the maximal rate of conformity of the generating surface of the form-cutting-tool to the sculptured surface is a prerequisite for the development of extremely efficient machining operations, and in solving design problems. The results of the research reported in this paper can be considered as a portion of the DG/K-method of surface generation on a multi-axis NC machine earlier developed ¹ by the author. The method is based on the extensive use of reliable results worked out in classical differential geometry of surfaces. Topics covered in the paper enables one designing the form-cutting-tool for optimal machining of a given sculptured surface on a multi-axis NC machine. The usefulness of the approach is verified from two simple examples that are clear and easy for understanding.     

Recommendations for the optimum design of pultruded frameworks

Conclusions For the optimum choice of pultruded beam members in frameworks there is a need to have a greater understanding of framework behavior under load. Research on the lateral-torsional buckling of a symmetric I-section has shown how much the resistance may be affected by the loading position and the support boundary conditions. By changing the warping at the connections from free, as assumed in the USA design manual, to fixed, as may be achieved with practical connection designs it is shown that there is a potential doubling in the buckling resistance. In addition, practical connections have some initial stiffness and moment resistance, thus the connections behave in a semirigid manner. This connection behavior makes inappropriate the present procedure for choosing beam sections on the basis of limiting deflection for a simply supported member. It is proposed that research be conducted to establish the potential of semirigid design, as now being used with structural steelwork. Results from such research should provide the first stage in the process for the optimum design of frameworks.Published in Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 675–682, September–October, 1993.     

Bifurcation-free design method of pulse energy converter controllers

In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current–direct current (DC–DC) buck converter with an input electromagnetic interference filter.     

An analytical method for solving the problem of unshocked conical gas compression

The two-dimensional unsteady self-similar problem of unlimited unshocked conical compression of a gas is investigated. A solution is constructed in the form of a characteristic series in the domain bounded by a weak discontinuity and the sonic perturbation front. A recursion system of ordinary differential equations is obtained for the coefficients. A boundary-value problem corresponding to the next approximation is investigated in detail, a fundamental system of solutions is found by analytical methods and its asymptotic behaviour is investigated. Essentially independent solutions are determined and different methods are used to seek a solution of the inhomogeneous equation with the required asymptotic behaviour. An algorithm is constructed to compute gas flows induced by the motion of a piston taking the first terms of the series into consideration. The results are compared with those of computations carried out using the method of characteristics.     

Plastic limit analysis and optimum design of structures for uncertain conditions.

At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the plastic limit analysis provides no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore complementary strain energy of the residual forces could be considered an overall measure of the plastic performance of structures and the plastic deformations should be controlled by introducing a bound for magnitude of this energy. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended plastic limit design problem is formed. In this research, due to the uncertainties the bound for the complementary strain energy of the residual forces is given randomly and a general approach to evaluate the limit load capacity of structures for uncertain conditions is presented. The aim of this study is to evaluate limit load capacity of structures with limited residual strain energy on the probabilistically given conditions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical model and optimum design approach of sinusoidal pressure wave generator for downhole drilling tool

Mud pulse generators have been widely used for the real-time transmission of valuable directional and formation data from downholes with depths of thousands of meters. There have been numerous studies on the design of mud pulse generators in which the pressure waves were typically nonsinusoidal. Sinusoidal waves provide improved long-distance data transmission and signal noise suppression compared with nonsinusoidal waves. Although sinusoidal pressure wave generators have been studied in the published literature, the influence of the risks of clogging on the design of the generator for producing sinusoidal pressure waves has rarely been considered. To generate sinusoidal pressure waves and to reduce the risks of clogging, a mathematical model for the design of a sinusoidal pressure wave generator is developed in this paper. The effects of the axial and radial clearances between the rotor and stator on the design of the generator are considered in the model. An optimum design method for the generator is provided by combining the developed model and a computational fluid dynamics analysis. Finally, an experimental platform was built and experiments at frequencies 2 Hz and 10 Hz were conducted to validate the design result. The simulation and experimental results show that the optimized pressure waves closely approximate sine waves. Therefore, the developed mathematical model and optimization approach can be used to design a sinusoidal pressure wave generator.     

Application of the Arlequin method in the virtual engineering design process

The creation of a holistic model which is able to represent the global dynamic behavior as well as local effects in certain regions leads to finite element models consisting of domains with different local meshes and a combination of different model dimensions. The different model domains have to be coupled such causing in an additional coupling error. The Arlequin method seems to be a flexible tool which has some advantages in comparison to alternative methods. In this paper the application of the Arlequin method on the coupling of a 3D continua model and a beam model is studied. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Note on the non-stationary iterative method for the estimation of the optimum overrelaxation parameter

We study the cause for the overestimation of the optimum overrelaxation factor when a non-stationary iterative method of Carré's or Kulsud's type is used. In addition we show that when the overrelaxation factor is substantially changed the estimation process becomes more difficult. The overestimation phenomena are also shown numerically.     

Application of the conjugate system method for optimal parametric design of stochastic dynamic systems for final position control

Efficient numerical algorithms are proposed for computer design of linear stochastic dynamic systems for final position control. The algorithms use the method of inverse-conjugate systems with dimension reduction of the space of optimized parameters.Sevastopol' Instrument-Building Institute. Translated from Dinamicheskie Sistemy, No. 10, pp. 51–57, 1992.     

Minimax estimation method for the optimum decomposition of a sample space based on prior information

Summary Existences and expressions of minimax estimators based on prior information for the optimum decomposition of a given sample space are studied in a unifying way such that answers can be easily obtained by applying the theorems given in this paper to various statistical problems—optimum selection regions, tolerance regions, prediction regions, optimum stratifications and so on. Further, ε-approximations to those estimators are given by choosing a finite family of probability measures from the infinite family of them under consideration in such a way that the former may be considered to be a sufficiently good approximation to the latter in the sense of risk function. Besides, those estimators are proved to be consistent in the sense that the risk decreases to zero as the amount of prior information increases infinitely. The Institute of Statistical mathematics     

Application of the string method to compute minimum energy paths for a chain of bi-stable elements using the finite element method and molecular dynamics

Activated processes are frequently found in solid state mechanics. The energy landscape of such processes show a non-convex behaviour, and therefore the computation of energy barriers between two stable minima is of importance. Such barriers are revealed by computing minimum energy paths. The string method is a simple and efficient algorithm to move curves over an energy landscape and to identify minimum energy paths. A hierarchical two-scale model recently introduced to the literature (molecular dynamics coupled with the finite element method) is used in this paper to investigate the string method in a model phase transition in a copper single crystal. To do so, bi-stable elements are constructed and the energetic behaviour of a two-elements chain is investigated. We identify successfully the minimum energy path between two local stable minima of the chain and demonstrate thereby the performance of the string method applied to a complex multiscale model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

战略采购中供应商选择的AHP—PROMETHEE方法研究

在供应链环境下,战略采购的出现给供应商群体的优化设计提出了一些新问题,并且多准则决策理论(MCDM)在供应商选择中并没有得到充分运用;本文结合战略采购的特点,选择指标着重体现供应商的合作性和长期性,选择方法上结合了层次分析法(AHP)和偏好顺序结构评估法(PROMETHEE),并进行了算例分析;旨在对战略采购中的供应商选择进行合理、客观的判断.     

Application of the sequential parametric convex approximation method to the design of robust trusses

We study an algorithm recently proposed, which is called sequential parametric approximation method, that finds the solution of a differentiable nonconvex optimization problem by solving a sequence of differentiable convex approximations from the original one. We show as well the global convergence of this method under weaker assumptions than those made in the literature. The optimization method is applied to the design of robust truss structures. The optimal structure of the model considered minimizes the total amount of material under mechanical equilibrium, displacements and stress constraints. Finally, Robust designs are found by considering load perturbations.     

A global optimization method for the design of space trajectories

The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization (GTOP database). We show that many trajectory optimization problems can be quite efficiently solved by means of relatively simple global optimization techniques relying on standard methods for local optimization. We show in this paper that our approach has been able to find trajectories which in many cases outperform those already known. We also conjecture that this problem displays a “funnel structure” similar, in some sense, to that of molecular optimization problems.     

Direct method for the design of optimal three-dimensional aerodynamic shapes

A direct optimization method for a broad class of three-dimensional aerodynamic shapes based on the approximation of the desired geometry by Bernstein-Bézier surfaces is developed. The high efficiency of the method is demonstrated by applying it to the design of an optimal supersonic section of an axisymmetric maximum-thrust de Laval nozzle. The method is also tested as applied to the design of a three-dimensional supersonic nozzle section in a dense multi-nozzle setup. In addition to three-dimensional supersonic nozzle sections with a circular throat, nozzles with a varying throat shape are considered. The results suggest that the method can be applied to various problems of 3D shape optimization.     

Protocol-based control for nonlinear systems with environment-dependent energy harvesting sensors: An average dwell-time method

In this paper, a protocol-based controller is designed for nonlinear systems with multiple sensors, which are powered by environment-dependent energy harvesting (EDEH) devices. The Round–Robin (RR) protocol is adopted to coordinate the data transmission of sensors. The protocol-based transmission can be realized only when the energy harvested by EDEH devices is sufficient. The aim of this paper is to design the protocol-based controller to ensure the stochastic finite-time boundedness with EDEH and RR protocol. Firstly, modeling the EDEH by a switching sequence with varying sojourn probabilities, assuming a finite battery capacity constraint, and associating protocol-based transmission with a given energy cost, we propose a new recursive model to depict the dynamic of energy levels for each sensor. Then, combining with the stochastic analysis method and the dynamic of energy levels, the explicit expressions of the controller for each environment with average dwell time (ADT) are obtained. Finally, an example is provided to demonstrate the effectiveness of the designed controllers.     

人才评价与选拔的一种模型及应用

为了客观公正地评价与选拔人才，本在实践经验总结的基础上，采用定量的数学计算和定性的评价分析相结合的方式，对人才评价与选拔给出了一种数学模型，并用实例说明了模型的应用。