下分层不同层位千米钻孔稳定性研究

抽采钻孔的稳定性影响到抽采工程效果的好坏.采动作用下,位于底板下方不同层位千米钻孔的加卸载路径不同.为得到采动作用对不同层位钻孔稳定性的影响,分析了底板不同层位钻孔加卸载路径,依据该路径,设计十种数值模拟计算方案,对底板钻孔在不同速率加卸载、变速加卸载两种方式下的破坏范围、孔壁位移进行了分析,得到了加卸载结束后各方案对应的塑性区分布范围及加卸载过程中孔壁位移曲线.依据数值计算得到的卸载速率与形变恢复滞后性的关系,建立了考虑卸载速率变化的钻孔周边切应力计算模型.研究结果表明:加载速率对钻孔周边的破坏范围几乎不产生影响;卸载过程中,钻孔周边破坏范围与初始卸载应力及卸载速率相关,在进行底板顺层抽采钻孔布置时需综合考虑布孔位置处的应力值及卸载速率.     

Direct and inverse problems of gas emission and the sorptive deformation of coal beds

Using the equations of state for fractured-porous media that describe the sorptioninduced deformation of coal, we develop a geomechanical model for radial gas influx to a borehole drilled in a coal bed with the concurrent evolution of stress field in the borehole environment. A numerical-and-analytical method is proposed for solving the corresponding system of equations for poroelastic media. A relation is found between the volume of slack withdrawn in the borehole (when opening up the gas-bearing seams), the sorption-and-storage capacities of coal, the permeability k, and the horizontal component σ _h of the natural stress field. We demonstrate the solvability of the inverse boundary-coefficient problem of determining k and σ _h on the basis of pressure in the closed borehole. We substantiate an express-method for estimating the permeability by the measurements of pressure in the borehole operating in the “pressure drop” mode.     

Objective Functions for the Shape Optimization of Temperature Control Channels in High-Pressure Die Casting

In high-pressure die casting, the quality of the produced cast parts highly depends on the die quality. One die component are temperature control channels. The state-of-the art approach for the temperature control channels are boreholes drilled from the sides into the die that are afterwards formed into a closed flow channel by inserting plugs. Since additive manufacturing methods are available to manufacture the dies, an obvious step is to construct more advanced temperature control channels. The shape of these free-form channels can be obtained by numerical optimization. To find the optimal shape of the channels, appropriate objective functions are required. This contribution is focused on such objective functions. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Location of paths on trees with minimal eccentricity and superior section

Network location theory has traditionally been concerned with the optimal location of a single-point facility at either a vertex or along an arc in the network. Recently, some authors have departed from this traditional problem and have considered the location of extensive facilities, such as paths, trees or cycles. In this paper, we consider the optimal location of paths on trees with regard to two objective functions: the eccentricity and the superior section. We first present methods to find paths with minimal eccentricity and minimal superior section on trees with arbitrary positive lengths. Then, we analyse the biobjective optimization problem and propose an algorithm, based on a progressive reduction of the initial tree, to obtain all efficient paths. Modifications of the proposed algorithm to solve the problem when a general objective function is used instead of the eccentricity function are also given. This work has been supported by Fundación Séneca under grant PB/11/FS/97     

Determination of common due window location in a single machine scheduling problem

We consider the static deterministic single machine scheduling problem in which all jobs have a common due window. Jobs that are completed within the window incur no penalty. The objective is to find the optimal sequence and the optimal common due window location given that the due window size is a problem parameter such that the weighted sum of earliness, tardiness, and due window location penalties is minimized. We propose an O(n log n) algorithm to solve the problem. We also consider two special cases for which simple solutions can be obtained.     

A Lattice-Based Smoother for Regions With Irregular Boundaries and Holes

We consider the problem of estimating a smooth function over a spatial region that is delineated by an irregular boundary and potentially contains holes within the boundary. Methods commonly used for spatial function estimation are well-known to suffer from bias along such boundaries. The estimator we propose is a kernel regression estimator, where the kernel is an approximation to a two-dimensional diffusion process contained within the region of interest. The diffusion process is approximated by the distribution of length-k random walks originating from each observation location and constrained to stay within the domain boundaries. We propose using a cross-validation criterion to find the optimal walk length k, which controls the smoothness of the resulting estimate. Simulations show that the method outperforms the soap film smoother of Wood, Bravington, and Hedley in many realistic scenarios, when data are noisy and borders are highly irregular. We illustrate the practical use of the estimator using measurements of soil manganese concentration around Port Moller, Alaska. Supplementary materials for this article are available online.     

Isodistant points in competitive network facility location

An isodistant point is any point on a network which is located at a predetermined distance from some node. For some competitive facility location problems on a network, it is verified that optimal (or near-optimal) locations are found in the set of nodes and isodistant points (or points in the vicinity of isodistant points). While the nodes are known, the isodistant points have to be determined for each problem. Surprisingly, no algorithm has been proposed to generate the isodistant points on a network. In this paper, we present a variety of such problems and propose an algorithm to find all isodistant points for given threshold distances associated with the nodes. The number of isodistant points is upper bounded by nm, where n and m are the number of nodes and the number of edges, respectively. Computational experiments are presented which show that isodistant points can be generated in short run time and the number of such points is much smaller than nm. Thus, for networks of moderate size, it is possible to find optimal (or near-optimal) solutions through the Integer Linear Programming formulations corresponding to the discrete version of such problems, in which a finite set of points are taken as location candidates.     

GASUB: finding global optima to discrete location problems by a genetic-like algorithm

In many discrete location problems, a given number s of facility locations must be selected from a set of m potential locations, so as to optimize a predetermined fitness function. Most of such problems can be formulated as integer linear optimization problems, but the standard optimizers only are able to find one global optimum. We propose a new genetic-like algorithm, GASUB, which is able to find a predetermined number of global optima, if they exist, for a variety of discrete location problems. In this paper, a performance evaluation of GASUB in terms of its effectiveness (for finding optimal solutions) and efficiency (computational cost) is carried out. GASUB is also compared to MSH, a multi-start substitution method widely used for location problems. Computational experiments with three types of discrete location problems show that GASUB obtains better solutions than MSH. Furthermore, the proposed algorithm finds global optima in all tested problems, which is shown by solving those problems by Xpress-MP, an integer linear programing optimizer (21). Results from testing GASUB with a set of known test problems are also provided.     

Dynamics of the pressure relaxation in a “depressurized” borehole

A problem of the pressure relaxation in a borehole after its “depressurization” is considered. An integral equation describing the evolution of the pressure in the borehole is obtained. It is shown that, by a choice of the initial bulk gas content and the height of the Impermeable part of the borehole, it is possible to obtain that the half-period of the pressure relaxation in the borehole lies within limits which are convenient for the technical realization of “depressurization”. Nomograms are constructed which enable one, when the values of the borehole parameters are known, to estimate the permeability of the surrounding porous medium using the half-period of the pressure relaxation.     

Effect of the structure of a fibrous layer on its permeability for a nonlinearly viscous fluid

The solution of the problem of the percolation of a nonlinearly viscous (with a power flow law) fluid through unit cells is used to find the dependence of the permeability coefficient of a unidirectional layer of fibers on fiber concentration, parameters characterizing the location of the fibers, and the parameters of the fluid (the exponent in the flow law) for random and regular fiber configurations in the transverse plane. It is established that the degree of nonuniformity of the pore space of the layer has a significant effect on its permeability and that this effect increases with an increase in the nonlinearity of the fluid. Data from a model experiment and computer simulation are used to describe the mechanism of transformation of the pore space by the fluid front. It is shown that consolidation of the layer also affects its permeability.Belarus State Technological University (Minsk, Belarus). Translated from Mekhanik Kompozitnykh Materialov, Vol. 33, No. 4, pp. 554–563, July–August, 1997.     

Applications of Variational Analysis to a Generalized Fermat-Torricelli Problem

In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of its distances to these sets is minimal. This problem can be viewed as an extension of the celebrated Fermat-Torricelli problem: given three points on the plane, find another point that minimizes the sum of its distances to the designated points. The generalized Fermat-Torricelli problem formulated and studied in this paper is of undoubted mathematical interest and is promising for various applications including those frequently arising in location science, optimal networks, etc. Based on advanced tools and recent results of variational analysis and generalized differentiation, we derive necessary as well as necessary and sufficient optimality conditions for the extended version of the Fermat-Torricelli problem under consideration, which allow us to completely solve it in some important settings. Furthermore, we develop and justify a numerical algorithm of the subgradient type to find optimal solutions in convex settings and provide its numerical implementations.     

钻井布局的数学模型

本文对钻井布局问题的研究 ,是从全局搜索入手 ,逐步深入讨论了各种算法的有效性、适用性和复杂性 ,得到不同条件下求最多可利用旧井数的较好算法 .对问题 1 ,我们给出了全局搜索模型、局部精化模型与图论模型 ,讨论了各种算法的可行性和复杂度 .得到的答案为 :最多可使用 4口旧井 ,井号为 2 ,4 ,5,1 0 .对问题 2 ,我们给出了全局搜索、局部精化和旋转矢量等模型 ,并对局部精化模型给出了理论证明 ,答案为 :最多可使用 6口旧井 ,井号为 1 ,6,7,8,9,1 1 ,此时的网格逆时针旋转 4 4.37度 ,网格原点坐标为 (0 .4 7,0 .62 ) .对问题 3,给出判断 n口井是否均可利用的几个充分条件、必要条件和充要条件及其有效算法     

A BSSS algorithm for the single facility location problem in two regions with different norms

Suppose the plane is divided by a straight line into two regions with different norms. We want to find the location of a single new facility such that the sum of the distances from the existing facilities to this point is minimized. This is in fact a non-convex optimization problem. The main difficulty is caused by finding the distances between points on different sides of the boundary line. In this paper we present a closed form solution for finding these distances. We also show that the optimal solution lies in the rectangular hull of the existing points. Based on these findings then, an efficient big square small square (BSSS) procedure is proposed.     

Single-machine scheduling problems with both start-time dependent learning and position dependent aging effects under deteriorating maintenance consideration

In this paper we introduce a new model of joint start-time dependent learning and position dependent aging effects into single-machine scheduling problems. The machine may need maintenance to improve its production efficiency. The objectives are to find jointly the optimal maintenance position and the optimal sequence such that the makespan, the total completion time, and the total absolute deviation of completion times (TADC) are minimized. We also aim to determine jointly the optimal maintenance position, the optimal due-window size and location, and the optimal sequence to minimize the sum of earliness, tardiness and due-window related costs function. We show that all the studied problems can be optimally solved by polynomial time algorithms.     

Common due window size and location determination in a single machine scheduling problem

We consider a single machine static and deterministic scheduling problem in which jobs have a common due window. Jobs completed within the window incur no penalties, other jobs incur either earliness or tardiness penalties. The objective is to find the optimal size and location of the window as well as an optimal sequence to minimise a cost function based on earliness, tardiness, window size, and window location. We propose an O(n log n) algorithm to solve the problem.     

A graph theoretical bound for the p-median problem

The p-median problem is a minisium network location problem that seeks to find the optimal location of p centres in a network. In the present paper a graph-theoretical bound is developed for the problem. This bound is based on shortest spanning trees and arborescences and other graphical properties of the problem. It is shown that the graph-theoretical bound dominates a bound based on shortest distances.     

Location-allocation on congested networks

This paper deals with location-allocation decisions in networks under conditions of congestion, i.e. taking into consideration the possible arrival of calls for service while no server is available. The problem is to find simultaneously the optimal districting policy which determines how a region should be partitioned into separate service areas, and the optimal locations of facilities to house the service units. An alternate location and allocation solution improvement procedure is developed to combine an existing location algorithm of a single mobile service unit [3] with an existing districting heuristic for two servers [5]. The 2-server districting heuristic is further extended to treat the general case of m servers, and combined with the location algorithm for a single server it forms a general location-allocation heuristic for n nodes and m servers.     

A Parametric 1-Maximin Location Problem

We introduce a version of the weighted 1-maximin problem in a convex polygon, where the weights are functions of a parameter. The 1-maximin problem is applicable in the location of undesirable facilities. Its objective is to find an optimal location such that the minimum weighted distance to a given set of points is maximized. We show that the parametric 1-maximin problem is equivalent to a 1-minimax problem, where the costs are non-linearly decreasing functions of distance. Using different values of the parameter in the 1-maximin problem, one can model different disutility functions for the users of the facility. Furthermore, the parameterization provides for a systematic way of reducing the effects of the weights, resulting in the unweighted 1-maximin problem in the limit. For two example problems we construct the optimal trajectory as a function of the parameter, and demonstrate that the trajectory may be discontinuous.     

Comparison of Two Suboptimal Sensor Placement Strategies in Thermo-Elastic Models

We are interested in thermo-elastic deformations of solid bodies, in particular of machine tools. The goal is to estimate the displacement at a certain point of interest from a few temperature measurements. We present a method to find nearly optimal sensor positions, which allow an accurate and robust estimation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Facility location models for planning a transatlantic communications network

This paper presents two facility location models for the problem of determining how to optimally serve the requirements for communication circuits between the United States and various European and Middle Eastern countries. Given a projection of future requirements, the problem is to plan for the economic growth of a communications network to satisfy these requirements. Both satellite and submarine cable facilities may be used. The objective is to find an optimal placement of cables (type, location, and timing) and the routing of individual circuits between demand points (over both satellites and cables) such that the total discounted cost over a T-period horizon is minimized. This problem is cast as a multiperiod, capacitated facility location problem. Two mathematical models differing in their provisions for network reliability are presented. Solution approaches are outlined and compared by means of computational experience. Use of the models both in planning the growth of the network and in the economic evaluation of different cable technologies is also discussed.