THE INFLUENCE OF FLEXIBILITY OF THE SUPPORT ON DYNAMIC BEHAVIOR OF A CRANE

2011 ◽  
Vol 21 (10) ◽  
pp. 2963-2974 ◽  
Author(s):  
ANDRZEJ URBAŚ ◽  
MAREK SZCZOTKA ◽  
STANISŁAW WOJCIECH
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Dynamic Behavior ◽  
Dynamic Optimization ◽  
Optimization Method ◽  
Numerical Calculations ◽  
Final Position ◽  
Joint Coordinates ◽  
The Mathematical Model

The problem of control of the motion of a crane is considered in the paper. The mathematical model of the system is formulated using joint coordinates and homogenous transformations. The dynamic optimization method is applied in order to find drive functions realizing the desired trajectory and stabilizing the final position of the load at the end of motion in spite of the flexibility of the support. The results of numerical calculations and possible applications of models developed using artificial neural networks are also presented.

scholarly journals Mathematical model for the evaluation of risk of emergency situations at a dangerous technical object based on artificial neural networks

2018 ◽  
Vol 44 ◽  
pp. 00069
Author(s):  
Nikolay Peganov ◽  
Aleksandr Tumanov ◽  
Vladimir Tumanov
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Risk Assessment ◽  
Artificial Neural Networks ◽  
Fire Risk ◽  
Management Decision ◽  
Technical Object ◽  
Emergency Situations ◽  
Artificial Neural ◽  
The Mathematical Model

In the work performed adaptation of artificial neural networks in modern security systems potentially dangerous technical objects — high-rise buildings as tools for assessing and forecasting in management decision. The study obtained the main scientific results: the mathematical model of risk assessment of man-made emergencies based on artificial neural networks; the mathematical model, adapted to the cumulative model of development technogene emergency-fire; provided risk assessment technique manmade emergencies based on artificial neural networks; represented private man-made fire risk assessment methodology using artificial neural networks.

scholarly journals An Optimistic Solver for the Mathematical Model of the Flow of Johnson Segalman Fluid on the Surface of an Infinitely Long Vertical Cylinder

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7798
Author(s):  
Naveed Ahmad Khan ◽  
Fahad Sameer Alshammari ◽  
Carlos Andrés Tavera Romero ◽  
Muhammad Sulaiman ◽  
Seyedali Mirjalili
Keyword(s):  
Thin Film ◽  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Velocity Profile ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Thin Film Flow ◽  
Sqp Algorithm ◽  
The Mathematical Model

In this paper, a novel soft computing technique is designed to analyze the mathematical model of the steady thin film flow of Johnson–Segalman fluid on the surface of an infinitely long vertical cylinder used in the drainage system by using artificial neural networks (ANNs). The approximate series solutions are constructed by Legendre polynomials and a Legendre polynomial-based artificial neural networks architecture (LNN) to approximate solutions for drainage problems. The training of designed neurons in an LNN structure is carried out by a hybridizing generalized normal distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP). To investigate the capabilities of the proposed LNN-GNDO-SQP algorithm, the effect of variations in various non-Newtonian parameters like Stokes number (St), Weissenberg number (We), slip parameters (a), and the ratio of viscosities (ϕ) on velocity profiles of the of steady thin film flow of non-Newtonian Johnson–Segalman fluid are investigated. The results establish that the velocity profile is directly affected by increasing Stokes and Weissenberg numbers while the ratio of viscosities and slip parameter inversely affects the fluid’s velocity profile. To validate the proposed technique’s efficiency, solutions and absolute errors are compared with reference solutions calculated by RK-4 (ode45) and the Genetic algorithm-Active set algorithm (GA-ASA). To study the stability, efficiency and accuracy of the LNN-GNDO-SQP algorithm, extensive graphical and statistical analyses are conducted based on absolute errors, mean, median, standard deviation, mean absolute deviation, Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE). Statistics of the performance indicators are approaching zero, which dictates the proposed algorithm’s worth and reliability.

scholarly journals Integration of Classical Mathematical Modeling with an Artificial Neural Network for the Problems with Limited Dataset

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5127
Author(s):  
Szymon Buchaniec ◽  
Marek Gnatowski ◽  
Grzegorz Brus
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Network ◽  
Artificial Neural Networks ◽  
Mathematical Models ◽  
Box Model ◽  
Advantages And Disadvantages ◽  
Artificial Neural ◽  
The Mathematical Model

One of the most common problems in science is to investigate a function describing a system. When the estimate is made based on a classical mathematical model (white-box), the function is obtained throughout solving a differential equation. Alternatively, the prediction can be made by an artificial neural network (black-box) based on trends found in past data. Both approaches have their advantages and disadvantages. Mathematical models were seen as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. Simultaneously, the approximation of neural networks can reproduce the solution exceptionally well if fed sufficient data. The difference is that an artificial neural network requires big data to build its accurate approximation, whereas a typical mathematical model needs several data points to estimate an empirical constant. Therefore, the common problem that developers meet is the inaccuracy of mathematical models and artificial neural networks. Another common challenge is the mathematical models’ computational complexity or lack of data for a sufficient precision of the artificial neural networks. Here we analyze a grey-box solution in which an artificial neural network predicts just a part of the mathematical model, and its weights are adjusted based on the mathematical model’s output using the evolutionary approach to avoid overfitting. The performance of the grey-box model is statistically compared to a Dense Neural Network on benchmarking functions. With the use of Shaffer procedure, it was shown that the grey-box approach performs exceptionally well when the overall complexity of a problem is properly distributed with the mathematical model and the Artificial Neural Network. The obtained calculation results indicate that such an approach could increase precision and limit the dataset required for learning. To show the applicability of the presented approach, it was employed in modeling of the electrochemical reaction in the Solid Oxide Fuel Cell’s anode. Implementation of a grey-box model improved the prediction in comparison to the typically used methodology.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Development of turning process digital twin based on machine learning

2021 ◽  
pp. 32-41
Author(s):  
D. A. Rastorguev ◽  
◽  
A. A. Sevastyanov ◽  
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Information Technologies ◽  
Cutting Process ◽  
Turning Process ◽  
Force Load ◽  
Cnc Machine ◽  
Digital Twin ◽  
Artificial Neural

Today, manufacturing technologies are developing within the Industry 4.0 concept, which is the information technologies introduction in manufacturing. One of the most promising digital technologies finding more and more application in manufacturing is a digital twin. A digital twin is an ensemble of mathematical models of technological process, which exchanges information with its physical prototype in real-time. The paper considers an example of the formation of several interconnected predictive modules, which are a part of the structure of the turning process digital twin and designed to predict the quality of processing, the chip formation nature, and the cutting force. The authors carried out a three-factor experiment on the hard turning of 105WCr6 steel hardened to 55 HRC. Used an example of the conducted experiment, the authors described the process of development of the digital twin diagnostic module based on artificial neural networks. When developing a mathematical model for predicting and diagnosing the cutting process, the authors revealed higher accuracy, adaptability, and versatility of artificial neural networks. The developed mathematical model of online diagnostics of the cutting process for determining the surface quality and chip type during processing uses the actual value of the cutting depth determined indirectly by the force load on the drive. In this case, the model uses only the signals of the sensors included in the diagnostic subsystem on the CNC machine. As an informative feature reflecting the force load on the machine’s main motion drive, the authors selected the value of the energy of the current signal of the spindle drive motor. The study identified that the development of a digital twin is possible due to the development of additional modules predicting the accuracy of dimensions, geometric profile, tool wear.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

scholarly journals Modified grey wolf method for optimization of PM motors

2019 ◽  
Vol 28 ◽  
pp. 01020
Author(s):  
Łukasz Knypiński
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
Permanent Magnet Synchronous Motor ◽  
Computer Software ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Grey Wolf ◽  
Electromagnetic Devices ◽  
The Mathematical Model ◽  
Grey Wolf Algorithm

The paper presents an algorithm and computer software for the optimization of electromagnetic devices. The mathematical model of the optimization method was presented. The modification of the classical grey wolf algorithm was developed. The modification consists in decreasing the coefficient responsible for the possibility of migration individuals in the permissible area of solved task. The optimization procedure was elaborated in the Borland Delphi environment. The optimization of the rotor of the line-start permanent magnet synchronous motor has been carried out. It has been pointed out that the grey wolf algorithm is effective method for optimization of electromagnetic devices.

Research on Mathematical Model and Calibration of Weighing System by Digital Addition

2012 ◽  
Vol 151 ◽  
pp. 101-104
Author(s):  
Chao Fu Zhu ◽  
Shu Jian Ji ◽  
Jin Long Zhao
Keyword(s):  
Mathematical Model ◽  
Calibration Method ◽  
Optimization Method ◽  
Load Cells ◽  
On Line ◽  
The Mathematical Model ◽  
Multiple Load

In practice the method is widely used, by which a gravity is measured using multiple load cells. A weighing system is introduced in this paper, in which a gravity is measured by multiple load cells with digital addition. The mathematical model of weighing system with digital addition is established. Normal calibration method is not suitable for the on-line calibration of weighing system with digital addition. When the mathematical model is given, the accurate on-line calibration of weighing system with digital addition is achieved by using optimization method.

Genetic Algorithm Optimization of a Double Four-Bar Manipulator

2013 ◽  
Vol 834-836 ◽  
pp. 1323-1326
Author(s):  
Qi Jing Tang ◽  
Tie Shi Zhao
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Structural Strength ◽  
Optimization Method ◽  
Installation Space ◽  
Algorithm Optimization ◽  
Genetic Algorithm Optimization ◽  
Transmission Angle ◽  
The Mathematical Model

In order to optimize the dimension of a manipulator, the optimization requirements are analyzed. Then the mathematical model and optimization objectives are established. Next, the lengths of the manipulator are optimized by Matlab genetic algorithm optimization toolbox. The structural strength and bearing installation space are considered at the same time. The trajectory and transmission angle are compared. Finally, the lengths which meet the use requirements are obtained. This optimization method provides a reference for similar mechanism.

A High-Fidelity Real-Time Simulation Code of Gas Turbine Dynamics for Control Applications

2002 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Computational Time ◽  
High Fidelity ◽  
Simulation Code ◽  
Real Time Simulation ◽  
Time Simulation ◽  
The Mathematical Model

A novel high-fidelity real-time simulation code based on a lumped, non-linear representation of gas turbine components is presented. The aim of the work is to develop a general-purpose simulation code useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of the gas turbine engine. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

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