Topological optimization of ballistic protective structures through genetic algorithms in a vulnerability-driven environment

Reducing the vulnerability of a platform,i.e.,the risk of being affected by hostile objects,is of paramount importance in the design process of vehicles,especially aircraft.A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats.However,this type of solution can lead to a significant increase in weight,affecting the performance of the aircraft.For this reason,it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight.One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures.Among the many optimization techniques available in the literature for this purpose,multiobjective genetic algorithms stand out as promising tools.In this context,this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms,aiming to simultaneously minimize the weight of protective structures and vulnerability.In addition to the use of the in-house software,which itself represents a novelty in the field of topology optimization of structures,the method incorporates a custom mutation function within the genetic algorithm,specifically developed using a graph-based approach to ensure the continuity of the generated structures.The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects,namely bullets and fragments from detonating objects.The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.

APPROXIMATION TECHNIQUES FOR APPLICATION OF GENETIC ALGORITHMS TO STRUCTURAL OPTIMIZATION

Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.

Composite Structural Optimization by Genetic Algorithm and Neural Network Response Surface Modeling

Neural-Network Response Surfaces （NNRS） is applied to replace the actual expensive finite element analysis during the composite structural optimization process. The Orthotropic Experiment Method （OEM） is used to select the most appropriate design samples for network training. The trained response surfaces can either be objective function or constraint conditions. Together with other conven- tional constraints, an optimization model is then set up and can be solved by Genetic Algorithm （GA）. This allows the separation between design analysis modeling and optimization searching. Through an example of a hat-stiffened composite plate design, the weight response surface is constructed to be objective function, and strength and buckling response surfaces as constraints; and all of them are trained through NASTRAN finite element analysis. The results of optimization study illustrate that the cycles of structural analysis ean be remarkably reduced or even eliminated during the optimization, thus greatly raising the efficiency of optimization process. It also observed that NNRS approximation can achieve equal or even better accuracy than conventional functional response surfaces.

Structural-acoustic optimization of stiffened panels based on a genetic algorithm

For the structural-acoustic radiation optimization problem under external loading,acoustic radiation power was considered to be an objective function in the optimization method. The finite element method(FEM) and boundary element method(BEM) were adopted in numerical calculations,and structural response and the acoustic response were assumed to be de-coupled in the analysis. A genetic algorithm was used as the strategy in optimization. In order to build the relational expression of the pressure objective function and the power objective function,the enveloping surface model was used to evaluate pressure in the acoustic domain. By taking the stiffened panel structural-acoustic optimization problem as an example,the acoustic power and field pressure after optimized was compared. Optimization results prove that this method is reasonable and effective.

Multi-objective optimization of membrane structures based on Pareto Genetic Algorithm

A multi-objective optimization method based on Pareto Genetic Algorithm is presented for shape design of membrane structures from a structural view point.Several non-dimensional variables are defined as optimization variables,which are decision factors of shapes of membrane structures.Three objectives are proposed including maximization of stiffness,maximum uniformity of stress and minimum reaction under external loads.Pareto Multi-objective Genetic Algorithm is introduced to solve the Pareto solutions.Consequently,the dependence of the optimality upon the optimization variables is derived to provide guidelines on how to determine design parameters.Moreover,several examples illustrate the proposed methods and applications.The study shows that the multi-objective optimization method in this paper is feasible and efficient for membrane structures;the research on Pareto solutions can provide explicit and useful guidelines for shape design of membrane structures.

Hydraulic Self Servo Swing Cylinder Structure Optimization and Dynamic Characteristics Analysis Based on Genetic Algorithm

The dynamic characteristics of hydraulic self servo swing cylinder were analyzed according to the hydraulic system natural frequency formula. Based on that,a method of the hydraulic self servo swing cylinder structure optimization based on genetic algorithm was proposed in this paper. By analyzing the four parameters that affect the dynamic characteristics, we had to optimize the structure to obtain as larger the Dm( displacement) as possible under the condition with the purpose of improving the dynamic characteristics of hydraulic self servo swing cylinder. So three state equations were established in this paper. The paper analyzed the effect of the four parameters in hydraulic self servo swing cylinder natural frequency equation and used the genetic algorithm to obtain the optimal solution of structure parameters. The model was simulated by substituting the parameters and initial value to the simulink model. Simulation results show that: using self servo hydraulic swing cylinder natural frequency equation to study its dynamic response characteristics is very effective.Compared with no optimization,the overall system dynamic response speed is significantly improved.

Welding sequences optimization of box structure based on genetic algorithm method

In this article, The genetic algorithm method was proposed, that is, to establish the box structure＇s nonlinear three-dimension optimization numerical model based on thermo-mechanical coupling algorithm, and the objective function of welding distortion has been utilized to determine an optimum welding sequence by optimization simulation. The validity of genetic algorithm method combining with the thermo-mechanical nonlinear finite element model is verified by comparison with the experimental data where available. By choosing the appropriate objective function for the considered case, an optimum weldiing.sequence is determined by a genetic algorithm. All done in this study indicates that the new method presented in this article will have important practical application for designing the welding technical parameters in the future.

Particle Swarm Optimization Algorithm vs Genetic Algorithm to Develop Integrated Scheme for Obtaining Optimal Mechanical Structure and Adaptive Controller of a Robot

The performances of Particle Swarm Optimization and Genetic Algorithm have been compared to develop a methodology for concurrent and integrated design of mechanical structure and controller of a 2-dof robotic manipulator solving tracking problems. The proposed design scheme optimizes various parameters belonging to different domains (that is, link geometry, mass distribution, moment of inertia, control gains) concurrently to design manipulator, which can track some given paths accurately with a minimum power consumption. The main strength of this study lies with the design of an integrated scheme to solve the above problem. Both real-coded Genetic Algorithm and Particle Swarm Optimization are used to solve this complex optimization problem. Four approaches have been developed and their performances are compared. Particle Swarm Optimization is found to perform better than the Genetic Algorithm, as the former carries out both global and local searches simultaneously, whereas the latter concentrates mainly on the global search. Controllers with adaptive gain values have shown better performance compared to the conventional ones, as expected.

Research on Optimizing Computer Network Structure based on Genetic Algorithm and Modified Convex Optimization Theory

In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in the background and one of its core problems is to solve the optimization problem. Unlike traditional batch algorithm, stochastic gradient descent algorithm in each iteration calculation, the optimization of a single sample point only losses could greatly reduce the memory overhead. The experiment illustrates the feasibility of our proposed approach.

An adaptive reanalysis method for genetic algorithm with application to fast truss optimization

Although the genetic algorithm （GA） for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the design process, the authors present an adaptive reanalysis method for GA and its applications in the optimal design of trusses. This reanalysis technique is primarily derived from the Kirsch＇s combined approximations method. An iteration scheme is adopted to adaptively determine the number of basis vectors at every generation. In order to illustrate this method, three classical examples of optimal truss design are used to validate the proposed reanalysis-based design procedure. The presented numerical results demonstrate that the adaptive reanalysis technique affects very slightly the accuracy of the optimal solutions and does accelerate the design process, especially for large-scale structures.

Elitism-based immune genetic algorithm and its application to optimization of complex multi-modal functions

A novel immune genetic algorithm with the elitist selection and elitist crossover was proposed, which is called the immune genetic algorithm with the elitism （IGAE）. In IGAE, the new methods for computing antibody similarity, expected reproduction probability, and clonal selection probability were given. IGAE has three features. The first is that the similarities of two antibodies in structure and quality are all defined in the form of percentage, which helps to describe the similarity of two antibodies more accurately and to reduce the computational burden effectively. The second is that with the elitist selection and elitist crossover strategy IGAE is able to find the globally optimal solution of a given problem. The third is that the formula of expected reproduction probability of antibody can be adjusted through a parameter r, which helps to balance the population diversity and the convergence speed of IGAE so that IGAE can find the globally optimal solution of a given problem more rapidly. Two different complex multi-modal functions were selected to test the validity of IGAE. The experimental results show that IGAE can find the globally maximum/minimum values of the two functions rapidly. The experimental results also confirm that IGAE is of better performance in convergence speed, solution variation behavior, and computational efficiency compared with the canonical genetic algorithm with the elitism and the immune genetic algorithm with the information entropy and elitism.

Application of a Machine Learning Algorithm for the Structural Optimization of Circular Arches with Different Cross-Sections

Arches are employed for bridges. This particular type of structures, characterized by a very old use tradition, is nowadays, widely exploited because of its strength, resilience, cost-effectiveness and charm. In recent years, a more conscious design approach that focuses on a more proper use of the building materials combined with the increasing of the computational capability of the modern computers, has led the research in the civil engineering field to the study of optimization algorithms applications aimed at the definition of the best design parameters. In this paper, a differential formulation and a MATLAB code for the calculation of the internal stresses in the arch structure are proposed. Then, the application of a machine learning algorithm, the genetic algorithm, for the calculation of the geometrical parameters, that allows to minimize the quantity of material that constitute the arch structures, is implemented. In this phase, the method used to calculate the stresses has been considered as a constraint function to reduce the range of the solutions to the only ones able to bear the design loads with the smallest volume. In particular, some case studies with different cross-sections are reported to prove the validity of the method and to compare the obtained results in terms of optimization effectiveness.

Application of Modified Genetic Algorithm to Optimal Design of Supporting Structure

The modified genetic algorithm was used for the optimal design of supporting structure in deep pits.Based on the common genetic algorithm, using niche technique and reserving the optimum individual the modified genetic algorithm was presented. By means of the practical engineering, the modified genetic algorithm not only has more expedient convergence, but also can enhance security and operation efficiency.

Immune Genetic Algorithm for Optimal Design

A computing model employing the immune and genetic algorithm (IGA) for the optimization of part design is presented. This model operates on a population of points in search space simultaneously, not on just one point. It uses the objective function itself, not derivative or any other additional information and guarantees the fast convergence toward the global optimum. This method avoids some weak points in genetic algorithm, such as inefficient to some local searching problems and its convergence is too early. Based on this model, an optimal design support system (IGBODS) is developed.IGBODS has been used in practice and the result shows that this model has great advantage than traditional one and promises good application in optimal design.

Structural Parameter Optimization of Multilayer Conductors in HTS Cable

In this paper, the design optimization of the structural parameters of multilayer conductors in high temperature superconducting （HTS） cable is reviewed. Various optimization methods, such as the particle swarm optimization （PSO）, the genetic algorithm （GA）, and a robust optimization method based on design for six sigma （DFSS）, have been applied to realize uniform current distribution among the multilayer HTS conductors. The continuous and discrete variables, such as the winding angle, radius, and winding direction of each layer, are chosen as the design parameters. Under the constraints of the mechanical properties and critical current, PSO is proven to be a more powerful tool than GA for structural parameter optimization, and DFSS can not only achieve a uniform current distribution, but also improve significantly the reliability and robustness of the HTS cable quality.

Optimal Building Frame Column Design Based on the Genetic Algorithm

Building structure is like the skeleton of the building,it bears the effects of various forces and forms a supporting system,which is the material basis on which the building depends.Hence building structure design is a vital part in architecture design,architects often explore novel applications of their technologies for building structure innovation.However,such searches relied on experiences,expertise or gut feeling.In this paper,a new design method for the optimal building frame column design based on the genetic algorithm is proposed.First of all,in order to construct the optimal model of the building frame column,building units are divided into three categories in general:building bottom,main building and building roof.Secondly,the genetic algorithm is introduced to optimize the building frame column.In the meantime,a PGA-Skeleton based concurrent genetic algorithm design plan is proposed to improve the optimization efficiency of the genetic algorithm.Finally,effectiveness of the mentioned algorithm is verified through the simulation experiment.

Structural Optimization of Concrete Slab Frame Bridges Considering Investment Cost

The present study investigates computer-antomated design and structural optimization of concrete slab frame bridges considering investment cost based on a complete 3D model. Thus, a computer code with several modules has been developed to produce parametric models of slab frame bridges. Design loads and load combinations are based on the Eurocode design standard and the Swedish design standard for bridges. The necessary reinforcement diagrams to satisfy the ultimate and serviceability limit states, including fatigue checks for the whole bridge, are calculated according to the aforementioned standards. Optimization techniques based on the genetic algorithm and the pattern search method are applied. A case study is presented to highlight the efficiency of the applied optimization algorithms. This methodology has been applied in the design process for the time-effective, material-efficient, and optimal design of concrete slab frame bridges.

Structural Design Optimization of a Vertical Axis Wind Turbine for Seismic Qualification and Lightweight

Recently, there is a growing interest in seismic qualification of ridges, buildings and mechanical equipment worldwide due to increase of accidents caused by earthquake. Severe earthquake can bring serious problems in the wind turbines and eventually lead to an interruption to their electric power supply. To overcome and prevent these undesirable problems, structural design optimization of a small vertical axis wind turbine has performed, in this study, for seismic qualification and lightweight by using a Genetic Algorithm (GA) subject to some design constraints such as the maximum stress limit, maximum deformation limit, and seismic acceleration gain limit. Also, the structural design optimizations were conducted for the four different initial design variable sets to confirm robustness of the optimization algorithm used. As a result, all the optimization results for the 4 different initial designs showed good agreement with each other properly. Thus the structural design optimization of a small vertical-axis wind turbine could be successfully accomplished.

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURE WITH FUNDAMENTAL FREQUENCY AND FREQUENCY DOMAIN DYNAMIC RESPONSE CONSTRAINTS

In this paper, adaptive genetic algorithm （AGA） is applied to topology optimization of truss structure with frequency domain excitations. The optimization constraints include fundamental frequency, displacement responses under force excitations and acceleration responses under foundation acceleration excitations. The roulette wheel selection operator, adaptive crossover and mutation operators are used as genetic operators. Some heuristic strategies are put forward to direct the deletion of the extra bars and nodes on truss structures. Three examples demonstrate that the proposed method can yield the optimum structure form and the lightest weight of the given ground structure while satisfying dynamic response constraints.

Optimal Structural Design of the Midship of a VLCC Based on the Strategy Integrating SVM and GA

In this paper a hybrid process of modeling and optimization, which integrates a support vector machine （SVM） and genetic algorithm （GA）, was introduced to reduce the high time cost in structural optimization of ships. SVM, which is rooted in statistical learning theory and an approximate implementation of the method of structural risk minimization, can provide a good generalization performance in metamodeling the input-output relationship of real problems and consequently cuts down on high time cost in the analysis of real problems, such as FEM analysis. The GA, as a powerful optimization technique, possesses remarkable advantages for the problems that can hardly be optimized with common gradient-based optimization methods, which makes it suitable for optimizing models built by SVM. Based on the SVM-GA strategy, optimization of structural scantlings in the midship of a very large crude carrier （VLCC） ship was carried out according to the direct strength assessment method in common structural rules （CSR）, which eventually demonstrates the high efficiency of SVM-GA in optimizing the ship structural scantlings under heavy computational complexity. The time cost of this optimization with SVM-GA has been sharply reduced, many more loops have been processed within a small amount of time and the design has been improved remarkably.