Application of the most popular traditional and mo

2022-08-24
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Analysis of the application of traditional and modern optimization methods in mechanical engineering

Abstract: This paper introduces the application of optimization methods in domestic mechanical engineering in recent years, including the application and improvement of traditional optimization methods, the application of modern optimization methods

, and analyzes the development trend of the application of optimization methods

optimization method developed rapidly with the application of computers in the 1960s, and was earlier applied to the design of mechanical engineering and other fields. Using the optimization method can not only make the scheme achieve some optimization results in the specified design requirements, but also do not need to consume too much calculation workload. Therefore, it has been widely valued and its application is becoming more and more extensive. This paper introduces the application of traditional and modern optimization methods in domestic mechanical engineering in recent years, and shows the direction of application and research of optimization methods

1. Application and improvement of traditional optimization methods

(1) application of traditional optimization methods

from Jung's engineering optimization design papers with 1-stream content table in recent years, it can be seen that traditional optimization methods are still widely used and have a role that cannot be ignored. In the field of mechanical engineering, traditional optimization methods are mainly used in the optimal design of mechanisms or mechanical parts, which optimize the structure, shape, performance and reliability, improve the quality of mechanical products, reduce the weight and improve the performance. In optimization design, random direction method, complex method, augmented Lagrange multiplication method and penalty function method are widely used

the literature adopts the constrained random direction method to optimize the design of the non circumferential oil return hydrostatic bearing. Under the same system stiffness, the total power consumption of the optimized hydrostatic bearing is reduced by 59% - 75%. Taking the bolted cross shaft universal coupling on the rolling mill as an example, the shape optimization design of the inner contour of the fork head is carried out by using the complex method in the literature. literature "The representative penalty function method and augmented Lagrange multiplication method in the indirect solution of constrained optimization problems are applied to the optimization design of the pentanomial cam profile of the valve mechanism. The literature uses the interior penalty function method to call Powell to carry out the reliability optimization design for the example of bolt group connection. On the premise of ensuring the reliability requirements, the reliability optimization design can significantly reduce the connection size and reduce the The production cost of the designed machine or parts has achieved better economic benefits

(2) improvement of traditional optimization methods

with the increasing expansion of engineering problems, the scale and complexity of the problems to be faced by optimization are gradually increasing. When traditional optimization methods solve these problems, their limitations and defects are exposed, so there are improvements based on the analysis of existing algorithms for the shortcomings of methods or application problems

in view of the defects of the widely used basic complex method, such as incomplete search, inflexible value of mapping coefficient, poor diversity of complex, the literature puts forward corresponding improvement measures, such as dynamic global mapping shrinkage calculation and maximum redundant point mapping criterion, forming a new type of complex method, which greatly improves the success rate of optimization. In the literature, the improved discrete variable penalty function method is used to solve the engineering problems of discrete variables. The whole optimization process is divided into two steps: the initial optimization of continuous variable penalty function method, the optimization of penalty function method with discrete variables, and the lattice test. The influence of the initial value of optimization variables on the optimization results is eliminated, and the optimization results are more accurate and reasonable. The literature puts forward the uniform discretization processing method of continuous variables and non-uniform discrete variables, and uses the search optimization method of discrete variables for reference. On the basis of the complex method of continuous variables, this paper discusses a method to solve the optimization design problem of constrained nonlinear mixed discrete variables - the mixed discrete complex method. This algorithm can be used in the optimization design of engineering structures, and its results do not need rounding, The reliability and efficiency of problem solving are greatly improved

(3) penalty function method

penalty function method is a commonly used indirect solution in constrained optimization problems

in the literature, the internal point penalty function method based on Powell is used to optimize the shear mechanism of the actual deflection pendulum flying shear, so that the mechanical parameters of the flying shear meet the requirements of the shear process, and improve the shear performance of the flying shear and the shear quality of rolled pieces. After using the interior penalty function method to transform the constrained optimization problem into an unconstrained problem, the conjugate gradient method is used to optimize the parameters of the parts in the main drive system of the machine tool, so that the scheme of the main drive system of the machine tool can be optimized, and at the same time, the design accuracy can be improved and the design cycle can be shortened. In the literature, the penalty function method is used to optimize the mathematical model of vehicle powertrain optimization, so that the overall performance of the vehicle is significantly improved. Aiming at the problems of initial point selection, possible local optimality and calculation time of hybrid penalty optimization method, a genetic penalty composite algorithm GPCM with low noise is proposed in the literature

2. Application of modern optimization methods

with the formation of computational complexity theory in the early 1970s, scientists found and made clear that a large number of longitudinal optimization problems derived from reality are very difficult to solve, many of which, such as knapsack problem, traveling salesman problem (TSP), packing problem, etc., have been proved to be NP complete problems, so the traditional optimization algorithm is powerless. In the early 1980s, a series of modern optimization calculation methods came into being, such as genetic algorithm, simulated annealing algorithm, ant colony algorithm, etc. their commonness is based on some natural phenomena in the objective world. By analogy with longitudinal optimization solution, we can find out some commonness of them and establish the corresponding algorithm

(1) genetic algorithm

genetic algorithm (GA) is a new probability optimization method proposed by Professor Holland of Michigan University in the early 1970s. GA is a non deterministic quasi natural algorithm, which imitates the law of biological evolution in nature, reproduces and evolves a randomly generated group and makes natural selection, so that the survival of the pass and elimination of the unfit can be achieved. In this way, the quality of the group and the quality of individuals in the group can evolve continuously, and finally converge to the global optimal solution

genetic algorithm has robustness, adaptability, global optimization and implicit parallelism. The main application fields are: function optimization direction, longitudinal optimization, machine learning, control direction, image processing, fault diagnosis, artificial life, neural network, etc. In recent years, genetic algorithm has also carried out multi-directional applications in the field of mechanical engineering, mainly in:

(1.) Optimization design of mechanical structure: Aiming at the fact that the linear fitness, constant crossover and mutation probability of simple genetic algorithm can not dynamically adapt to the whole optimization process, the literature proposes an improved genetic algorithm using nonlinear fitness, adaptive crossover and mutation probability. This algorithm provides a reference for solving the optimization design of engineering structure and the extreme value of multi peak function

(2.) Reliability analysis: literature and THF can be further used to process spandex. Based on the reliability analysis of frame structure system, a genetic algorithm for reliability optimization of frame structure system is proposed

(3.) Fault diagnosis: the literature takes the complex weight and biased real number form as the genes to form the chromosome vector, and uses the gene multi-point crossover and dynamic mutation to carry out the optimal selection of the population. A new genetic algorithm is proposed, and on this basis, a transformer fault diagnosis system based on genetic algorithm and dissolved gas analysis is designed

(4.) Parameter identification: Based on the existing parameter identification methods of T-S fuzzy model, the literature puts forward a parameter identification method that applies the least square method to roughly identify the conclusion parameters to determine the approximate range of parameters, and then applies genetic algorithm to optimize the premise parameters and conclusion parameters at the same time

(5.) Mechanical scheme design: the literature regards the mechanical scheme design process as a problem of solving the state space, controls its search process with genetic algorithm, and constructs and improves a new genetic coding system. In order to adapt to the new coding system, genetic operations such as crossover and mutation are rebuilt, and operations such as replication, exchange and mutation are used to iterate again and again, and finally an optimal design scheme is automatically generated

in addition, GA is also used in fuzzy logic controller (FLC), robot kinematics, reverse engineering, energy-saving design, composite material optimization, metal forming optimization, NC machining error adaptive prediction control and other directions

Although genetic algorithm has solved many problems, there are still many problems, such as the parameter optimization of the algorithm itself, how to avoid premature convergence, how to improve the operation means or introduce new operations to improve the efficiency of the algorithm, the combination of genetic algorithm and other optimization algorithms, etc

when using genetic algorithm to solve constrained optimization problems, the penalty function method is generally used. How to reasonably select the penalty factor is the difficulty of the algorithm. If the penalty factor is too small, the minimum solution of the whole penalty function may not be the minimum solution of the original objective function; When the penalty factor is too large, it may cause multiple local extreme points outside the feasible region, which makes the search process more difficult. However, from the perspective of retrieval, few people have been involved in the research on general, efficient and robust methods of dealing with constraints in common use of genetic algorithm. Therefore, in order to ensure that GA can give full play to its advantages in solving constrained optimization problems, the method of solving constrained optimization problems by genetic algorithm still needs further research

(2) simulated annealing algorithm

simulated annealing algorithm (SA for short), the earliest idea was proposed by metropolis in 1953, and Kirkpatrick was successfully applied to longitudinal optimization problems in 1983. SA is a global optimization algorithm. Based on the similarity between the solution of the optimization problem and the annealing process of the physical system, the simulated annealing is realized by using the Metropolis algorithm and appropriately controlling the temperature drop process, so as to achieve the purpose of solving the global optimization problem

simulated annealing algorithm is a general optimization algorithm to solve different nonlinear problems; For the optimization of non differentiable or even discontinuous functions, the global optimization solution can be obtained with a high probability; It has strong robustness, global convergence, implicit parallelism and wide adaptability; And it can deal with different types of optimization design variables (discrete, continuous and mixed); No auxiliary information is required, and there are no requirements for the objective function and constraint function. At present, it has been widely used in engineering, such as VLSI production scheduling, control engineering, Journal of machine science, neural network, image processing, numerical analysis and other fields

although simulated annealing algorithm can find the global best advantage of the objective function in the sense of probability with random search technology, its calculation time is long and the effect is low. In view of the "congenital deficiency" of the algorithm, on the basis of ensuring the required optimization quality, the algorithm can be improved and upgraded. It can also be combined with other algorithms to mix and optimize SA algorithm. In the literature, a hybrid optimization algorithm is proposed, which combines the descent simplex algorithm with the simulated annealing algorithm, which implicitly uses the gradient information of the objective function and converges rapidly, and can effectively carry out global optimization

(3) ant colony algorithm

ant colony algorithm (ACA) is inspired by the collective behavior of real ant colonies in nature

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