Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design

1995 ◽  
Vol 117 (3) ◽  
pp. 425-432 ◽  
Author(s):  
L. P. Pomrehn ◽  
P. Y. Papalambros
Keyword(s):  
Mathematical Model ◽  
Solution Space ◽  
Global Optimum ◽  
Gear Train ◽  
Discrete Variables ◽  
Multistage Process ◽  
Model Formulation ◽  
Space Reduction ◽  
Nonlinear Design ◽  
The Mathematical Model

Techniques employed for nonlinear design optimization with discrete variables are studied in the context of a particular problem arising from the design of a gear train. The mathematical model formulation was presented in an earlier article. In this sequel, a solution derivation is described, patterned as a multistage process. After certain reformulation and relaxation, a variety of infeasibility and non-optimality tests are performed, greatly reducing the size of the space containing the global optimum. Methods used to investigate the remaining space do not guarantee a global optimum, but could be replaced by more costly methods that do provide such guarantees. A global infimum is generated, bounding any improvements on the best known solution.

Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design

1992 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Mathematical Model ◽  
Solution Space ◽  
Global Optimum ◽  
Gear Train ◽  
Discrete Variables ◽  
Multistage Process ◽  
Model Formulation ◽  
Space Reduction ◽  
Nonlinear Design ◽  
The Mathematical Model

Abstract Techniques to be employed for nonlinear design optimization with discrete variables are studied in the context of a particular problem arising from the design of a gear train. The mathematical model formulation was presented in an earlier article. In this sequel, a solution derivation is described, patterned as a multistage process. After certain reformulation and relaxation, a variety of infeasibility and non-optimality tests are performed, greatly reducing the size of the space containing the global optimum. Methods used to investigate the remaining space do not guarantee a global optimum, but could be replaced by more costly methods that do provide such guarantees. A global infimum is generated, bounding any improvements on the best known solution.

Optimization of Structures Using Improved Genetic Algorithms for Discrete Variables

2010 ◽  
Vol 163-167 ◽  
pp. 2437-2440
Author(s):  
Yuan Tian ◽  
Qing Xuan Shi ◽  
Chao Yan Zhu
Keyword(s):  
Mathematical Model ◽  
Genetic Algorithms ◽  
Efficient Method ◽  
Solution Space ◽  
Structure Optimization ◽  
Search Algorithms ◽  
Darwinian Evolution ◽  
Discrete Variables ◽  
Engineering Problems ◽  
The Mathematical Model

Genetic algorithms (GA) have been shown to be very effective optimization tools for a number of engineering problems. Genetic algorithms which are based upon the principles of Darwinian evolution explores the region of the whole solution space and can obtain the golbal optimum. This paper introduces the standard GA and the forward-and-back search algorithms (FBSA) and demonstrates the use of improved genetic algorithms (IGA) for structure optimization of discrete variables. The mathematical model of structural optimization is derived. A 10-bar benchmark example is studied, the result shows that IGA, as an efficient method,can be applied to structure optimization of discrete variables.

Discrete Optimal Design Formulations: Application to Gear Train Design

1992 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Spur Gear ◽  
Gear Train ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Interesting Aspect ◽  
Model Formulation ◽  
Design Models ◽  
Different Types

Abstract The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intellegence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

Study on Spatial Nonlinear Vibration Characteristics of Cables with a Particular Constraint

2015 ◽  
Vol 724 ◽  
pp. 222-229
Author(s):  
Jian Mei Liu ◽  
Bin Di You
Keyword(s):  
Mathematical Model ◽  
Nonlinear Vibration ◽  
Simulation Analysis ◽  
Solution Space ◽  
Dimensional Solution ◽  
Resonance Modes ◽  
Safety And Reliability ◽  
Object Of Study ◽  
The Galerkin Method ◽  
The Mathematical Model

In order to study the nonlinear vibration problems of cable with a particular constraint, the mathematical model for the object of study should be established firstly with the elastic mechanics method. In order to obtain the mathematical model of differential form, the Galerkin method is used to make the mathematical model discrete and modal truncation, so the infinite dimensional solution space of the mathematical model can be transformed into the finite dimensional one. Main factors influencing the vibration of the cable system are analyzed, and the simulation analysis about the effects of various parameters on frequency is carried out. The analysis results show that the internal resonance modes may exist, and provide a theoretical basis for improving the safety and reliability of laying cables in actual conditions.

scholarly journals Operations Research Model Formulation for Road Maintenance Case

2019 ◽  
Vol 22 ◽  
pp. 32-36
Author(s):  
Jānis Pekša ◽  
Kristaps-Pēteris Rubulis
Keyword(s):  
Mathematical Model ◽  
Literature Review ◽  
Operations Research ◽  
Analytical Methods ◽  
Road Maintenance ◽  
Research Model ◽  
Model Formulation ◽  
Basic Principles ◽  
The Mathematical Model

Operations research can be used to apply analytical methods that help make precise and reasonable decisions. In road maintenance, basic principles of operations research are used to create model formulation that could help lower costs in case of an inaccurately made decision. First, the paper provides a literature review on different model formulations. Afterward, hypotheses are proposed regarding the model formulation, and then the model that minimises total generalised costs from wrong duty orders for road maintenance is offered. In conclusion, the paper evaluates the hypotheses and the process of improving the mathematical model.

Discrete Optimal Design Formulations With Application to Gear Train Design

1995 ◽  
Vol 117 (3) ◽  
pp. 419-424 ◽  
Author(s):  
L. P. Pomrehn ◽  
P. Y. Papalambros
Keyword(s):  
Artificial Intelligence ◽  
Optimal Design ◽  
Spur Gear ◽  
Gear Train ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Interesting Aspect ◽  
Model Formulation ◽  
Design Models ◽  
Different Types

The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intelligence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

Mathematical Modeling and Dynamic Analysis of a Compact Vectored Thruster

2021 ◽  
Vol 55 (6) ◽  
pp. 139-155
Author(s):  
Hongyi Du ◽  
Tianhong Yan ◽  
Bo He ◽  
Yujie Zhang ◽  
Yingbo Gong
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Gear Train ◽  
Coordinate Systems ◽  
Scaling Factors ◽  
Space Transformation ◽  
Motion Modes ◽  
Change Trend ◽  
Relationship Of ◽  
The Mathematical Model

Abstract In this paper, a compact vectored thruster based on a composite gear train is proposed. First, the space transformation between different coordinate systems is carried out, and the mathematical model of the vectored thruster is established, according to classical navigation mechanics theory. Then, the swing and roll motion analysis of the composite gear train is implemented, and the motion relationship of the whole thruster structure is analyzed systematically. Moreover, SolidWorks and MATLAB software are used for simulation to verify the accuracy of the mathematical model. In addition, the trajectories of the propeller shaft under different motion modes are analyzed and compared. Finally, the dynamic analysis of the vectored thruster is carried out, and the change trend of the scaling factors of the vector thrust components with the swing angle δ and the roll angle χ is studied, and comparison with the scaling factors of the vectored water jet propeller presented in other literature is taken into account. To endow the thruster with superior maneuverability, the fairwater structure of the vectored thruster is optimized, and the lateral vector component of the optimized vectored thruster is greatly increased.

scholarly journals THE SELECTION OF OPTIMAL REVERSIBLE TWO-SPEED PLANETARY GEAR TRAINS FOR MACHINE TOOL GEARBOXES

2020 ◽  
Vol 18 (1) ◽  
pp. 121
Author(s):  
Sanjin Troha ◽  
Željko Vrcan ◽  
Dimitar Karaivanov ◽  
Madina Isametova
Keyword(s):  
Mathematical Model ◽  
Optimal Solution ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Parameters ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
The Mathematical Model ◽  
Selection Of

The application of multi-criteria optimization to two-carrier two-speed planetary gear trains is outlined in this paper. In order to determine the mathematical model of multi-criteria optimization variables, the objective functions and conditions must be determined first. Two-carrier two-speed planetary gear trains with brakes on coupled shafts are analyzed in this paper. The mathematical model covers the determination of the set of the Pareto optimal solutions as well as the method for selecting an optimal solution from this set. A numerical example is provided to illustrate the procedure in which the optimal two-speed planetary gear train is selected and defined by design parameters.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

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