Particle Swarm Method Research Articles

Energy harvesting from a rotational nonlinear energy sink in vortex-induced vibrations

The concept of nonlinear energy sinks (NES) has been studied recently for passive fluid-induced vibration mitigation. A NES presents a fast and irreversible capacity of efficiently dissipating energy for various vibration problems. Besides, energy harvesting (EH) applications are suitable for generating electricity in vibrating mechanical structures. This work investigates the combination of a rotational NES with EH for the vortex-induced vibrations (VIV) of a cylinder exposed to airflow. The study considers an energy harvesting device comprising an electric generator ideally attached to the rotational NES mass pendulum shaft, resulting in a cylinder-NES-EH assembly. The model consists of an elastically mounted cylinder subjected to transverse airflow. The NES-EH is attached to the cylinder as a rigid pendulum arm with a mass at its tip that can freely oscillate, simultaneously absorbing the cylinder vibration and generating electricity. The fluid modeling is based on a wake model represented by the Van der Pol oscillator. The study is carried out by computational simulations of the differential equations of motion, and the rotational NES parameters optimization is done with the particle swarm method. Results comprise the analyses of the cylinder-NES-EH nonlinear dynamics characterization, identification of response regimes of the NES-EH system through a parametric study, and comparison with results from the literature. An optimal configuration was presented to maximize the generation of electric energy. Combining an EH with a rotational NES has shown an adequate potential for the design of energy extraction devices.

Research on lightweight and fatigue life of engine hood based on multi-objective particle swarm optimization

A multi-objective optimization method is presented in this paper, aiming at improving the fatigue life of the engine hood while achieving light weight. By analyzing the factors affecting the fatigue life of the engine hood, a multi-objective optimization model was established that considered five design variables including the thickness of the inner plate, the thickness of the outer plate, the stiffness of the hook, the stiffness of the sealing strip, and the height of the buffer block. Then, the multi-objective particle swarm method was used for optimization, and the optimal solution was obtained in the form of a Pareto set. The ideal compromise solution was determined from the Pareto set by using fuzzy membership functions. On this basis, the optimal solution was determined from the Pareto set by comprehensively considering the steel plate material specification, mold and cost constraints. The torsional deformation test and switch fatigue test show that for the optimized engine hood, the fatigue life is increased by 117%, the mass is reduced by 0.51 kg, and the torsional deformation of the engine hood does not increase significantly. The proposed multi-objective optimization method is proved to be feasible and effective in improving engine hood fatigue life and lightweight design.

NUMERICAL OPTIMIZATION ALGORITHM AND PROGRAM IMPLEMENTING THE PARTICLE SWAR OPTIMIZATION

One of the numerical optimization methods is considered, which implements the so-called particle swarm method. A modification of the method based on the division of the iterative calculation process into two stages is proposed. To speed up calculations and reduce their complexity. At the first stage, the objective function is replaced by a simplified model, which allows you to quickly determine the approximate area of extremum localization. The final solution is sought in the found localization area, using the original objective function. A console application that implements the algorithm is described and the results of numerical experiments performed using this application are presented.

Devising a method for segmenting complex structured images acquired from space observation systems based on the particle swarm algorithm

This paper considers the improved method for segmenting complex structured images acquired from space observation systems based on the particle swarm algorithm. Unlike known ones, the method for segmenting complex structured images based on the particle swarm algorithm involves the following: – highlighting brightness channels in the Red-Green-Blue color space; – using a particle swarm method in the image in each channel of brightness of the RGB color space; – image segmentation is reduced to calculating the objective function, moving speed, and a new location for each swarm particle in the image in each RGB color space brightness channel. Experimental studies have been conducted on the segmentation of a complex structured image by a method based on the particle swarm algorithm. It was established that the improved segmentation method based on the particle swarm algorithm makes it possible to segment complex structured images acquired from space surveillance systems. A comparison of the quality of segmenting a complex structured image was carried out. The comparative visual analysis of well-known and improved segmentation methods indicates the following: – the improved segmentation method based on the particle swarm algorithm highlights more objects of interest (objects of military equipment); – the well-known k-means method assigns some objects of interest (especially those partially covered with snow) to the snow cover (marked in blue); – the improved segmentation method also associates some objects of interest that are almost completely covered with snow with the snow cover (marked in blue). It has been established that the improved segmentation method based on the particle swarm algorithm reduces segmentation errors of the first kind by an average of 12 % and reduces segmentation errors of the second kind by an average of 8 %

Параметрическая оптимизация модального регулятора с ограничениями на основе метода роя частиц

The key to increasing the efficient functioning of automatic control systems for technical facilities and processes in various areas of industry is the optimal setting of the state feedback controller parameters, for instance, so as to minimize the duration of transient processes or achieve the minimum value of the integral control quality assessment. The optimization problem is solved for an integrand of a kind that ensures that the integral assessment better expresses the quality of control. At the same time, the control quality indicators are in a rather complex relation to the set parameters of the controller, which greatly complicates the analytical synthesis procedure. Numerical optimization algorithms differ in the way the adjustable parameters are changed, the most effective being those that achieve the result in a shorter computational time. Aim. The goal is to obtain the optimal parameter values for a state feedback controller with an integral component and limitations for continuous linear stationary systems based on the stochastic metaheuristic particle swarm method. Materials and methods. The modern theory of automatic control, swarm intelligence are used to solve the problem of optimizing the parameters of the state feedback controller and controlling technical systems. Results. The process of parametric optimization of a constrained state feedback controller using the particle swarm method for a one-dimensional controlled object is described. The results of simulation using the method of direct enumeration of the controller parameters and the particle swarm method are described and compared. Conclusion. The results of numerical studies allow us to conclude that the developed algorithm for particle swarm parametric optimization of a constrained state feedback controller is highly accurate and fast.

About Modeling Digital Twins of a Social Group

The object of the study is mathematical modeling methods. The subject of the study is the application of mathematical methods in modeling digital twins of a social group. The aim of the work is to model the digital counterparts of a social group. A digital double is a digital copy of a physical object or process, with the right approach, it helps to improve the main and auxiliary business processes. This concept is part of the fourth industrial revolution and is designed to help detect problems faster, find out what will happen to the original in different conditions and, as a result, produce better products. In this article, some applied aspects are considered, the main provisions of the mathematical theory of digital twins of social groups are presented. To solve the problem of creating a digital double of a social group (students) as one of the tools, the authors proposed to use the technologies of population algorithms. The novelty of the research consists in the application of the swarm part algorithm for modeling digital twins of a social group. The particle swarm method was chosen as a research tool. As the social group under study finds the optimal position in space, so the element of the digital twin of the particle swarm model based on them can search in space, in particular, the extremes of functions. Which, for example, is applicable to finding the minimum of the loss function in machine learning. A graphical simulation in the Java Script language was performed using the three library.js. Data processing was performed using the C# Job System, which provides parallelization of computing processes and is integrated into the Entity Component System. A program was implemented that simulates the activity of a student group as one of the constituent elements of a digital twin of a social group. Swarm algorithms are promising in the field of practical application. On their basis, it is possible not only to solve the problems of digital twins, but also to manage groups of robots, robotic systems and complexes.

Research on the Operational Strategy of the Hybrid Wind/PV/Small-Hydropower/Facility-Agriculture System Based on a Microgrid

The use of renewable energy sources, such as wind, photovoltaics (PV), and hydropower, to supply facility agriculture may effectively mitigate food and environmental pollution problems and ensure continuity of the energy supply. The operating conditions of a hybrid system are complex, so the operating strategy is very important for system configuration and scheduling purposes. In the current study, first, a hybrid wind/PV/small-hydropower/facility-agricultural system was constructed. Then, the chaotic particle swarm method was applied to optimize hybrid system operation, and a scheduling strategy of the hybrid system was proposed. Finally, combined with an example, according to wind and PV power output and load curves, supply-to-load curves for wind, PV, and small hydropower were obtained. The operational strategy proposed in this study maximizes the utilization of wind and solar resources and rationally allocates hydropower resources. The aforementioned operational strategy provides a basis for hybrid system capacity allocation and scheduling.

Combined algorithm for training neural networks of direct propagation

The essence of learning neural networks of direct propagation is to minimize the function of the root mean square error of the output. This function is multimodal, ie it has several local minima. To find the minimum of such functions, gradient and stochastic methods are most often used, which do not guarantee finding the global minimum. The article analyzes the gradient algorithm of inverse error propagation and the stochastic method of particle swarm for training neural networks of direct propagation, their advantages and disadvantages are indicated. It is proposed to combine the advantages of both methods in a combined algorithm.The learning process using a combined algorithm is carried out in two stages. At the first stage, the stochastic method of particle swarm conducts a given number of learning epochs and determines the set of points in the vicinity of which there may be points of local minimum. In the second stage, the gradient backpropagation algorithm finds the local minimum for each point and selects the optimal one. If the set value of the standard error of the output is not reached, the learning steps are repeated.To evaluate the effectiveness of the proposed approach to the training of neural networks, a series of comparative experiments using the well-known database of computer attack recognition KDD Cup 1999 Data. The experiments compared the results of training the direct propagation neural network for the particle swarm method, the inverse error propagation algorithm, and the combined algorithm. The experimental results proved the superiority of the combined algorithm.

Optimizing Degree of Imbalance and Utilization Cost in Cloud Environment using Effective Particle Swarm Method

Optimizing Degree of Imbalance and Utilization Cost in Cloud Environment using Effective Particle Swarm Method

Motion analysis and modulation of steel particle swarm in high-pressure tank for particle impact drilling

Particle Impact Drilling (PID) is a new technology to effectively improve the rate of penetration (ROP) for oil and gas drilling in hard and strongly abrasive formations. In this paper, numerical simulation method is used to analyse the motion characteristics and the modulation method of particle swarm in high-pressure tank for the particle injection system based on differential pressure ejection in PID. The numerical simulation results show that: when there is no modulation elements, the motion of particle swarm in the high-pressure tank follows an asymmetric funnel flow with pulsating state, which could be divided into vertical flow domain, fast flow domain, slow flow domain and stagnation domain. The unstable dynamic arching effect of the funnel flow, the viscous effect of the liquid bridge force and the collapsing effect of the particle swarm could probably lead to the blockage of the discharge port of the high-pressure tank. When the semiapex angles of the high-pressure tank decreases, the volume flow rate of particles increases and the stagnation domain becomes smaller, but it becomes easier to form arching and blockage. The modelling results indicate that the pulsation of the funnel flow is minimum when the semiapex angle is 45° without the mutilation element, which means the funnel flow of the particle swarm is relatively stable. By introducing a conical modulating element above the discharge port, the unstable funnel flow of the particle swarm could be transformed to an overall uniform flow. The modelling results indicate that the installation height of the modulation element has the greatest influence on the pulsation degree. The optimized parameters for the conical modulation element based on numerical modelling tests are 70° for the vertex angle, 35 mm for the length of the flank and 70 mm for the installation heigh.

Research of the particle swarm method in the problem of optimizing the mode of motion of the manipulator along one of the generalized coordinates

The problems of optimizing the modes of movement of mechanical systems, in particular robots and manipulators, is relevant in the context of modern society. Algorithms for optimal movements of components of robots and manipulators allow to realize complex trajectories of movements of their working bodies with predicted energy consumption, positioning accuracy, speed. Finding optimal modes of motion is a complex task that requires accurate formulation of the optimization function, constraint equations and determination of optimal laws that would meet the criteria of the optimization problem. In this article, the classical particle swarm method for finding the optimal mode of motion of the manipulator boom at one of the generalized coordinates was analyzed. The target energy function is the "energy" of the accelerations of the mechanical system, and the search for the optimal law of displacement was carried out using a fourth-order polynomial.
 The theoretical study showed that the method of particle swarm can be used to find the optimal laws of motion, but when working with this method it is necessary to modernize the algorithm for determining its components, including particle velocity and their correction factors.
 In determining the optimal laws of motion of the manipulator by the swarm method, this study uses an approach where it is assumed that time is discrete, and the value of the objective function was determined only at the accepted sampling points of time.

Comparative analysis of numerical methods for determining parameters of chemical reactions from experimental data

The aim of this paper is to select an optimal numerical method for determining the parameters of chemical reactions. The importance of the topic is due to the modern needs of industry, such as the improvement of chemical reactors and oil or gas processing. The paper deals with the problem of determining reaction rate constants using gradient methods and stochastic optimization algorithms. To solve an forward problem, implicit methods for solving stiff ODE systems are used. A correlation method of practical identifiability of the required parameters is used. The genetic algorithm, particle swarm method, and fast annealing method are implemented to solve an inverse problem. The gradient method for the solution of the inverse problem is implemented, and a formula for gradient of the functional is given with the corresponding adjoint problem. We apply an identifiability analysis of the unknown coefficients and arrange the coefficients in the order of their identifiability. We show that the best approach is to apply global optimization methods to find the interval of global solution and after that we refine inverse problem solution using gradient approach.

A Boosted Particle Swarm Method for Energy Efficiency Optimization of PRO Systems

The analytical solutions of complex dynamic PRO systems pose challenges to ensuring that maximum power can be harvested in stable, rapid, and efficient ways in response to varying operational environments. In this paper, a boosted particle swarm optimization (BPSO) method with enhanced essential coefficients is proposed to enhance the exploration and exploitation stages in the optimization process. Moreover, several state-of-the-art techniques are utilized to evaluate the proposed BPSO of scaled-up PRO systems. The competitive results revealed that the proposed method improves power density by up to 88.9% in comparison with other algorithms, proving its ability to provide superior performance with complex and computationally intensive derivative problems. The analysis and comparison of the popular and recent metaheuristic methods in this study could provide a reference for the targeted selection method for different applications.

Development, research and optimization of weight measuring system

The main task of the research is to improve technical and economic indicators of weight measuring system and to increase the efficiency of its research on the basis of cost-optimal planning of experiments.
 A system with a measuring tray has been developed, and it is different from existing systems with a possibility to control inclination angle of a tray, moisture content and temperature of a bulk substance, what provides better accuracy of mass measurement.
 The researches of weight measuring system were performed using the following methods of cost-optimal experiment planning: taboo search, particle swarm method, exhaustive search, Gray code based method. It gave possibility to reduce cost of implementing the experiment.
 To perform the research of weight measuring system, a plan of a full-factor experiment was selected, which was optimized for the cost of its implementation by using a method based on the Gray code.
 In the result of research, mathematical models in coded and natural values of factors were obtained. They characterize the dependence of the measurement acceptable error on such indicators as the angle of the measuring tray, the humidity of the bulk material, the coefficient of friction of the bulk material in motion. Using a mathematical model, rational values of the design parameters of the weight measuring system were obtained, which provide high accuracy (measurement acceptable error does not exceed 0.20%): the angle of the weight measuring tray α = 41.9°; humidity of loose material W = 14%; the coefficient of friction of the bulk material in motion fd = 0.70.
 The developed weight measuring system can be widely used for dosing of bulk materials in various technological productions.

Роевой интеллект в задачах обнаружения аномалий и состояний природно-технических систем и объектов

An approach to solving the problem of detecting and classifying anomalies and states of natural-technical systems and objects using swarm intelligence methods is considered. The main directions of development of the proposed approach include ant algorithms, bee swarm algorithms, and the particle swarm method. The structure of the swarm intelligence system of decision support based on collective preference rules is proposed. The application of the proposed approach makes it possible to optimize the processes of processing, analysis, integration of heterogeneous data, to increase the sensitivity, reliability and efficiency of decisions made.

Motion Analysis and Modulation of Steel Particle Swarm in High-Pressure Tank for Particle Impact Drilling

Particle Impact Drilling (PID) is a new technology to effectively improve the rate of penetration (ROP) for oil and gas drilling in hard and strongly abrasive formations. In this paper, numerical simulation method is used to analyze the motion characteristics and the modulation method of particle swarm in high-pressure tank for the particle injection system based on differential pressure ejection in PID. The numerical simulation results show that: when there is no modulation elements, the motion of particle swarm in the high-pressure tank follows an asymmetric funnel flow with pulsating state, which could be divided into vertical flow domain, fast flow domain, slow flow domain and stagnation domain. The unstable dynamic arching effect of the funnel flow, the viscous effect of the liquid bridge force and the collapsing effect of the particle swarm could probably lead to the blockage of the discharge port of the high-pressure tank. When the semiapex angles of the high-pressure tank decreases, the volume flow rate of particles increases and the stagnation domain becomes smaller, but it becomes easier to form arching and blockage. The modelling results indicate that the pulsation of the funnel flow is minimum when the semiapex angle is 45° without the mutilation element, which means the funnel flow of the particle swarm is relatively stable. By introducing a conical modulating element above the discharge port, the unstable funnel flow of the particle swarm could be transformed to an overall uniform flow. The modelling results indicate that the installation height of the modulation element has the greatest influence on the pulsation degree. The optimized parameters for the conical modulation element based on numerical modelling tests are 70° for the vertex angle, 35mm for the length of the flank and 70mm for the installation height.

Parameter estimation of Nash IUH for multiple storm events using particle swarm optimization method

In present study, we proposed to optimize the parameters of Nash Instantaneous Unit Hydrograph using particle swarm optimization method. The application of particle swarm optimization method made the optimal parameter estimation for multiple storm events possible. The effectiveness of the proposed method was tested by published data sets. Compared with the reported results, the simulation accuracy in terms of peak magnitude and peak time is all improved, and the convergence rate is significantly improved, which demonstrates that the superiority of particle swarm method in parameter optimization of Nash IUH model.

CALCULATING THE BOUNDARIES OF THE AIRCRAFT EXIT ZONE TO A SET POINT

The article considers the method of calculating the boundaries of the exit zone of the aircraft to a given point based on the optimal control method. To find the optimal control, it is proposed to use a direct method based on parameterization of the desired control signals using third-order Hermitian splines. The choice of Hermitian cubic splines was motivated by the fact that these splines and their first order derivatives are smooth and continuous functions, on the one hand, and, on the other, do not require the additional solution of algebraic equations to meet the specific conditions in spline nodes which is obligatory for classic cubic splines. Spline parameters estimation is achieved through solution of the unconditional multiparametric optimization problem. The target functional includes the squares of mismatches between the desired output signals and the object model output signals. In this paper the parameter estimates are obtained using the widely known numerical optimization algorithm – the particle swarm method. The paper considers the aircraft motion in the vertical plane, for which a mathematical model of the control object is formed and the target functional is formulated. The proposed solution is advisable to apply when calculating the optimal trajectories and flight profiles of aircraft when planning their functioning for the designed purpose. The developed method allows solving a number of tasks in the process of modern aircraft design and flight tests. The application of the proposed method, the required structure of the mathematical model of the object and the features of the formation of the minimized functional are shown in a specific example.

Симметричные системы управления

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

Parameter identification of Hammerstein–Wiener nonlinear systems with unknown time delay based on the linear variable weight particle swarm optimization

This paper deals with the parameter estimation of Hammerstein–Wiener (H–W) nonlinear systems which have unknown time delay. The linear variable weight particle swarm method is formulated for such time delay systems. This algorithm transforms the nonlinear system identification issue into a function optimization issue in the parameter space, then utilizes the parallel searching ability of the particle swarm optimization and the iterative identification technique to realize the simultaneous estimation of all parameters and the unknown time delay. Finally, parameters in the linear submodule, nonlinear submodule and the time delay are separated from the optimum parameter. Moreover, two illustrative examples are exhibited to evaluate the effectiveness of the proposed method. The simulation results demonstrate that the derived method has fast convergence speed and high estimation accuracy for estimating H–W systems with unknown time delay, and it is applied to the identification of the bed temperature systems.