Метод определения параметров утечек в трубопроводах на основе гидродинамических моделей

It is known that on the basis of the pipeline non-stationary hydrodynamic model after identification of parameters included in it, it is possible to adequately reproduce the full-scale hydraulic characteristics of transported medium flow by resolving the primal problem of hydraulics, in particular, the primal problem of identifying leakage parameters. The numerical solution of the inverse problem, in contrast to the analytical solution, is usually reduced to a multiple solution of the primal problem. In the present work, the hydrodynamic mathematical model of a pipeline with two parameters that have been identified and fluid withdrawal in the set section is confined to differential equations of evolutionary type for medium cross-section pressure and mass flow. Based on the built partial analytical solutions of these equations, dependences have been obtained for calculation of pressure values in the oil pipeline operated in stationary mode with existing liquid withdrawal (leakage). Results of application of analytical solutions to the method of sensitivity functions in the inverse problem of identifying leakage parameters have been reviewed. Exact analytical solution (in implicit form) of the inverse problem has been obtained to make it possible to relate the location of the leak to readings of pressure sensors, to the pipeline and the transported fluid parameters. Известно, что на основе нестационарной гидродинамической модели трубопровода после идентификации входящих в нее параметров можно адекватно воспроизводить натурные гидравлические характеристики потока транспортируемой среды путем решения прямой задачи гидравлики, в частности, прямой задачи об утечке, когда местоположение и расход отбора заданы. Численное решение обратной задачи, в отличие от аналитического обычно сводится к многократному решению прямой задачи. В предлагаемой работе гидродинамическая математическая модель трубопровода с двумя параметрами, прошедшими идентификацию, и отбором жидкости в заданном сечении сведена к дифференциальным уравнениям эволюционного типа для среднего по сечению давления и массового расхода. На основе частных аналитических решений данных уравнений получены зависимости для определения давления в работающем в стационарном режиме нефтепроводе при наличии отбора (утечки). Рассмотрены результаты применения аналитических решений к методу функций чувствительности в обратной задаче утечки. Получено точное аналитическое решение (в неявной форме) обратной задачи, позволяющее связать местоположение утечки с показаниями датчиков давления, характеристиками трубопровода и транспортируемой среды.

Diversifikasi dan Optimasi Usahatani Terintegrasi pada Lahan Kering di Desa Musi Kecamatan Gerokgak Kabupaten Buleleng

Tujuan penelitian adalah (1) menganalisis besarnya pendapatan aktual (gross margin) usahatani terintegrasi (2) menganalisis apakah diversifikasi usahatani pada usahatani terintegrasi lahan kering sudah optimal. Metode yang digunakan dalam menentukan sampel pada penilitian ini adalah teknik sensus sample. Teknik sampel ini menggunakan semua anggota SIMANTRI 001 sebagai sampel dengan anggota kelompok sebanyak 20 orang. Analisis pendapatan aktual yang dipergunakan adalah analisis usahatani melalui perhitungan gross margin. Analisis optimasi dan pendapatan maksimun dianalisis menggunakan metode linear programming (LP) yang diselesaikan dengan bantuan software BPLX88. Hasil penelitian menunjukkan bahwa berdasarkan hasil analisis gross margin, dengan rata-rata luas lahan kering sebesar 0,497 ha, diperoleh pendapatan aktual usahatani jagung MT-1, jagung MT-2, kacang tanah dan ternak sapi sebesar Rp. 696.326.650 per tahun. Berdasarkan hasil analisis linear programming yang dilihat dari primal problem solution menunjukkan jagung (PJG1), jagung (PJG2), kacang tanah (PKT) dan sapi (PSAPI) yang diusahakan bersatus basic atau profitable. Hal ini menunjukkan bahwa lahan seluas 0,497 ha telah berkontribusi dalam memperoleh pendapatan maksimum sebesar Rp. 697.333.800 per tahun. Selanjutnya pada dual problem solution, semua kendala lahan per cabang usahatani dengan luas lahan masing-masing tanaman sebesar 9,95 ha telah habis terpakai, Hal ini menunjukkan bahwa kendala lahan jagung MT-1, jagung MT-2, dan kacang tanah berstatus binding atau habis terpakai tanpa ada sisa (slack). Namun sebagian kendala tidak bersifat binding hal ini terlihat pada stok tenaga kerja bulan Januari-Desember yang belum habis digunakan. Berdasarkan analisis optimasi melalui metode linear programming dengan bantuan BLPXX8 terselenggara dengan optimal, hal ini terbukti dengan pendapatan maksimum sebesar Rp. 697.334.000 artinya mengalami peningakatan pendapatan sebesar Rp.1.007.350 (0,14%), dari pendapataan aktual saat penelitiaan sebesar Rp.696.326.650.

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves kℓ(s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves fℓ(s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

Joint Congestion Control and Resource Allocation for Delay-Aware Tasks in Mobile Edge Computing

Recently, in order to extend the computation capability of smart mobile devices (SMDs) and reduce the task execution delay, mobile edge computing (MEC) has attracted considerable attention. In this paper, a stochastic optimization problem is formulated to maximize the system utility and ensure the queue stability, which subjects to the power, subcarrier, SMDs, and MEC server computation resource constraints by jointly optimizing congestion control and resource allocation. With the help of the Lyapunov optimization method, the primal problem is transformed into five subproblems including the system utility maximization subproblem, SMD congestion control subproblem, SMD computation resource allocation subproblem, joint power and subcarrier allocation subproblem, and MEC server scheduling subproblem. Since the first three subproblems are all single variable problems, the solutions can be obtained directly. The joint power and subcarrier allocation subproblem can be efficiently solved by utilizing alternating and time-sharing methods. For the MEC server scheduling subproblem, an efficient algorithm is proposed to solve it. By solving the five subproblems at each slot, we propose a delay-aware task congestion control and resource allocation (DTCCRA) algorithm to solve the primal problem. Theoretical analysis shows that the proposed DTCCRA algorithm can achieve the system utility and execution delay trade-off. Compared with the intelligent heuristic (IH) algorithm, when the control parameter V increases from 10 6 to 10 7 , the total backlogs are decreased by 5.03% and the system utility is increased by 3.9% on average for the extensive performance by using the proposed DTCCRA algorithm.

The back-and-forth method for Wasserstein gradient flows

We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced in Jacobs and Léger [Numer. Math. 146 (2020) 513–544.]. to solve optimal transport problems. We evolve the gradient flow by solving the dual problem to the JKO scheme. In general, the dual problem is much better behaved than the primal problem. This allows us to efficiently run large scale gradient flows simulations for a large class of internal energies including singular and non-convex energies.

Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative

In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

Duality for multiobjective variational problems under second-order (Ф,ρ)-invexity

The purpose of this article is to introduce the concept of second order (?,?)-invex function for continuous case and apply it to discuss the duality relations for a class of multiobjective variational problem. Weak, strong and strict duality theorems are obtained in order to relate efficient solutions of the primal problem and its second order Mond-Weir type multiobjective variational dual problem using aforesaid assumption. A non-trivial example is also exemplified to show the presence of the proposed class of a function.

Optimality conditions for set-valued optimization problems via scalarization function

One of the most important and popular topics in optimization problems is to find its optimal solutions, especially Pareto optimal points, a well-known solution introduced in multi-objective optimization. This topic is one of the oldest challenges in many issues related to science, engineering and other fields. Many important practical-problems in science and engineering can be expressed in terms of multi-objective/ set-valued optimization problems in order to achieve the proper results/ properties. To find the Pareto solutions, a corresponding scalarization problem has been established and studied. The relationships between the primal problem and its scalarization one should be investigated for finding optimal solutions. It can be shown that, under some suitable conditions, the solutions of the corresponding scalarization problem have uniform spread and have a close relationship to Pareto optimal solutions for the primal one. Scalarization has played an essential role in studying not only numerical methods but also duality theory. It can be usefully applied to get relationships/ important results between other fields, for example optimization, convex analysis and functional analysis. In scalarization, we ussually use a kind of scalarized-functions. One of the first and the most popular scalarized-functions used in scalarization method is the Gerstewitz function. In the paper, we mention some problems in set-valued optimization. Then, we propose an application of the Gerstewitz function to these problems. In detail, we establish some optimality conditions for Pareto/ weak solutions of unconstrained/ constrained set-valued optimization problems by using the Gerstewitz function. The study includes the consideration of problems in theoretical approach. Some examples are given to illustrate the obtained results.

A Novel Lagrangian Multiplier Update Algorithm for Short-Term Hydro-Thermal Coordination

The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem.

Dinkelbach-Type Algorithm for Computing Quantal Stackelberg Equilibrium

Stackelberg security games (SSGs) have been deployed in many real-world situations to optimally allocate scarce resource to protect targets against attackers. However, actual human attackers are not perfectly rational and there are several behavior models that attempt to predict subrational behavior. Quantal response is among the most commonly used such models and Quantal Stackelberg Equilibrium (QSE) describes the optimal strategy to commit to when facing a subrational opponent. Non-concavity makes computing QSE computationally challenging and while there exist algorithms for computing QSE for SSGs, they cannot be directly used for solving an arbitrary game in the normal form. We (1) present a transformation of the primal problem for computing QSE using a Dinkelbach's method for any general-sum normal-form game, (2) provide a gradient-based and a MILP-based algorithm, give the convergence criteria, and bound their error, and finally (3) we experimentally demonstrate that using our novel transformation, a QSE can be closely approximated several orders of magnitude faster.