Overall Parameters Design of Air-Launched Rockets Using Surrogate Based Optimization Method

In this paper, the design and optimization method of rocket parameters based on the surrogate model and the trajectory simulation system of the 3-DOF air-launched rockets were established. The Gaussian kernel width determination method based on the relationship between local density and width is used to ensure the efficiency and reliability of the optimization method, and at the same time greatly reduces the amount of calculation. An adaptive sampling point updating method was established, which includes three stages: location sampling, exploration sampling, and potential optimal sampling of the potential feasible region. The adaptive sampling is realized by the distance constraint. Based on the precision of the surrogate model, the convergence end criterion was established, which can achieve efficient and reliable probabilistic global optimization. The objective function of the optimization problem was deduced to determine the maximum load mass and reasonable constraints were set to ensure that the rocket could successfully enter orbit. For solid engine rockets with the same take-off mass as Launcherone, the launch altitude and target orbit were optimized and analyzed, and verified by 3-DOF trajectory simulation. The surrogate-based optimization algorithm solved the problem of the overall parameter design optimization of the air-launched rocket and it provides support for the design of air-launched solid rockets.

A Fusion-Based Method of State-of-Charge Online Estimation for Lithium-Ion Batteries Under Low Capacity Conditions

The accurate estimation of the battery state of charge (SOC) is crucial for providing information on the performance and remaining range of electric vehicles. Based on the analysis of battery charge and discharge data under actual vehicle driving cycles, this paper presents an online estimation method of battery SOC based on the extended Kalman filter (EKF) and neural network (NN). A battery model is established to identify and calibrate battery parameters. SOC estimation is conducted in the low-SOC area by exploring the relationship between battery parameters and SOC through many experimental results. In the fusion online estimation method, the NN is carried out to propose the estimation as the global mainstream trend providing a high precision feasible region; the EKF algorithm is used to provide the initial assessment and the local fluctuation boundary revision. Verified results show that it can improve the SOC estimation in low-battery capacity accuracy. It has achieved good adaptability to the estimation accuracy of low battery capacity SOC in different cycle conditions.

The Dynamics of H2O Suspended by Multiple Shaped Cu Nanoadditives in Rotating System

Heat transfer investigation in the nanofluids is significant for real world applications. The investigation of heat transfer over a stretchable magnetized surface has broad applications in various industries. Therefore, heat transfer featuring in the nanofluid synthesized by various shaped Cu and H2O is organized over a shrinking surface. The problem is organized properly via similarity equations by inducing the influences of magnetic field. Then, OVIM is adopted and performed the solutions for the particular model. The results are furnished for the governing quantities over the feasible region and deeply discussed in the view of their physical significance. It is examined that the nanoliquids angular motion and shear stresses drops by strengthen magnetic field effects. Moreover, nanoliquid containing brick Cu-particles is better heat conductor and could be used broadly for industrial applications as for as heat transport concerned. In end, authentication of the study is provided by comparing the results with previous science literature and an excellent agreement is seems between them.

Research on machining parameter optimization in finishing milling with multiple constraints

High efficiency and high precision milling, as the eternal goal of CNC machining, needs to balance many constraints for selecting the most reasonable processing parameters. This paper presents an efficient machining parameter optimization method for finishing milling operation with multiple constraints. Firstly, under the multiple constraints of parameter feasible region, milling force, milling stability, roughness, and machining contour accuracy, a multi-variable parameter optimization model with machining efficiency as the objective is established. A four level cycle optimization strategy has been detailly described for solving the optimization problem, in which the feed per tooth is optimized by using the golden section method, and with the aid of the random vector search method, the spindle speed, radial, and axial depth cuts are both numerically iterated. The optimal machining parameter combination of the tooth number, feed per tooth, spindle speed, radial, and axial depth of cuts are achieved at last. Finally, the experimental verification results show that the proposed method can greatly improve the machining efficiency under chatter free condition and achieve an efficient finishing milling with consideration of the multiple constraints.

IBOA-Based Optimization of Cross-Sectional Dimension of Rods for a 3-RRR PPM to Minimize Energy Consumption

For obtaining optimal cross-sectional dimensions of rods for a 3-RRR planar parallel manipulator (PPM) to minimize energy consumption, the inverse dynamics of the manipulator is modeled based on the Newton–Euler method, after which the coefficient matrix of the inverse dynamics equation is decomposed based on matrix theory. Hence, the objective function, that is, the logical relationship between the energy consumption of the manipulator and the cross-sectional dimension of each rod, is established. However, in solving the multidimensional constrained single-object optimization problem, there are difficulties such as the penalty function’s sensitivity to the penalty factors if the problem is transformed into the one of unconstrained multiobjective optimization. Therefore, to properly handle the constraints, an improved butterfly optimization algorithm (IBOA) is presented to ensure that the new iterated point always falls into the feasible region according to the butterfly optimization algorithm (BOA). Finally, the comparisons among the IBOA, particle swarm optimization (PSO), and BOA and further experiments of the physical prototype are implemented to validate the effectiveness of the proposed theoretical model and numerical algorithm. Results indicate that the proposed IBOA is more suitable for solving the constrained single-object optimization problem with better convergence speed and accuracy.

STATIONARY DISTRIBUTION AND EXTINCTION OF STOCHASTIC CORONAVIRUS (COVID-19) EPIDEMIC MODEL

The aim of this paper is to model corona-virus (COVID-19) taking into account random perturbations. The suggested model is composed of four different classes i.e. the susceptible population, the smart lockdown class, the infectious population, and the recovered population. We investigate the proposed problem for the derivation of at least one unique solution in the positive feasible region of nonlocal solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function and the condition for the extinction of the disease is also established. The obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been simulated numerically.

On validation of solutions to linear programming problems on cluster computing systems

В статье представлен параллельный алгоритм валидации решений задач линейного программирования. Идея метода состоит в том, чтобы генерировать регулярный набор точек на гиперсфере малого радиуса, центрированной в точке тестируемого решения. Целевая функция вычисляется для каждой точки валидационного множества, принадлежащей допустимой области. Если все полученные значения меньше или равны значению целевой функции в точке, проверяемой как решение, то эта точка считается корректным решением. Параллельная реализация алгоритма VaLiPro выполнена на языке C++ с использованием параллельного BSF-каркаса, инкапсулирующего в проблемно-независимой части своего кода все аспекты, связанные с распараллеливанием программы на базе библиотеки MPI. Приводятся результаты масштабных вычислительных экспериментов на кластерной вычислительной системе, подтверждающие эффективность предложенного подхода. The paper presents and evaluates a scalable algorithm for validating solutions to linear programming (LP) problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a small-radius hypersphere centered at the solution point submitted to validation. The objective function is computed at each point of the validation that belongs to the feasible region. If all the values are less than or equal to the value of the objective function at the point that is to be validated, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is written in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the VaLiPro algorithm.

Synchronization and Global Dynamics of a Cournot Model with Nonlinear Demand and R&D Spillovers

In this paper, a dynamical Cournot model with nonlinear demand and R&D spillovers is established. The system is symmetric when the duopoly firms have same economic environments, and it is proved that both the diagonal and the coordinate axes are the one-dimensional invariant manifolds of system. The results show that Milnor attractor of system can be found through calculating the transverse Lyapunov exponents. The synchronization phenomenon is verified through basins of attraction. The effects of adjusting speed and R&D spillovers on the dynamical behaviors of the system are discussed. The topological structures of basins of attraction are analyzed through critical curves, and the evolution process of “holes” in the feasible region is numerically simulated. In addition, various global bifurcation behaviors, such as two kinds of contact bifurcation and the blowout bifurcation, are shown.

Branch-and-Bound for Biobjective Mixed-Integer Linear Programming

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space. The various algorithms are implemented using a data structure for storing Pareto sets. Computational experiments are carried out on literature instances and on a new set of instances that we generate using a benchmark library (MIPLIB2017) for single objective problems. We also perform comparisons against the triangle splitting method from literature, which is an objective space search algorithm. Summary of Contribution: Biobjective mixed-integer optimization problems have two linear objectives and a mixed-integer feasible region. Such problems have many applications in operations research, because many real-world optimization problems naturally comprise two conflicting objectives to optimize or can be approximated in such a manner and are even harder than single objective mixed-integer programs. Solving them exactly requires the computation of all the nondominated solutions in the objective space, whereas some applications may also require finding at least one solution in the decision space corresponding to each nondominated solution. This paper provides an exact algorithm for solving these problems using the branch-and-bound method, which works predominantly in the decision space. Of the many ingredients of this algorithm, some parts are direct extensions of the single-objective version, but the main parts are newly designed algorithms to handle the distinct challenges of optimizing over two objectives. The goal of this study is to improve solution quality and speed and show that decision-space algorithms perform comparably to, and sometimes better than, algorithms that work mainly in the objective-space.