GAEを用いた自己組織化の概念に基づくアルゴリズムの実装と構造形態創生への適用

A new fuzzy strategy for size and topology optimization of truss structures

Y-stiffened panel multi-objective optimization using genetic algorithm

Traditionally, computational design optimization of commercial aircraft is performed by considering a small number of representative operating conditions. These conditions are based on the design Mach number, altitude, payload, and range for which the aircraft will be flown. However, the design also influences which routes and mission parameters are optimal, and so there is coupling that is ignored when using the traditional approach. Here, the aircraft design, mission profiles, and the allocation of aircraft to routes in an airline network are simultaneously optimized. This is a mixed-integer nonlinear programming problem that is reformulated as a nonlinear programming problem because of the large number of design variables. The reformulated problem is solved using a gradient-based optimization approach with a parallel computational framework that facilitates the multidisciplinary analysis and the derivative computation. A surrogate model is used for the computational fluid dynamics analysis that is retrained in each optimization iteration given the new set of shape design variables. The resulting optimization problem contains over 4,000 design variables and close to 14,000 constraints. The optimization results show a 2% increase in airline profit compared with the traditional multipoint optimization approach. The wing area increases to the upper bound, enabling a higher cruise altitude that improves propulsive efficiency. This study finds that simultaneously optimizing the allocation, mission, and design to maximize airline profit results in a different optimized wing design from that resulting from the multipoint optimization approach.

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.

Shear tests of rectangular sample are widely used by the scientific community for characterizing the material behavior due to large strains obtained. However, for some hard metals, such as the dual-phase steel DP 980, premature rupture occurs in the vicinity of the grips. Due to this fact, the shape of the shear specimen is optimized in this work with the aim of maximizing the deformation achieved in the central part of the specimen without the occurrence of rupture near the grips. As the rupture occurs at the corners of the shear specimen only the boundaries are subjected to shape optimization. A representation with cubic splines is adopted for the definition of the boundaries geometry. The material is defined by Hill’s 1948 yield criterion combined with an isotropic hardening law. Two macroscopic rupture criteria are considered and an objective function approach based on the maximization of the shear strain average value is defined. For this study, a direct search optimization method is used for minimizing the objective function. The optimized geometries obtained for the different rupture criteria and different set of design variables are compared. The use of a larger number of design variables allows to obtain optimized geometries with higher average shear strain. The best specimen geometry shape allows increasing the maximum deformation of DP 980 steel to 1.05 without occurrence of rupture. In addition, the final specimen geometries show a concave shape for the boundaries which means that this kind of shape is the best one to delay the rupture in shear specimens.

In this study, the binary bat algorithm (BBA) for structural topology optimization is implemented. The problem is to find the stiffest structure using a certain amount of material and some constraints using the bit-array representation method. A new filtering algorithm is proposed to make BBA find designs with no separated objects, no checkerboard patterns, less unusable material, and higher structural performance. A volition penalty function for topology optimization is also proposed to accelerate the convergence toward the optimal design. The main effect of using the BBA lies in the fact that the BBA is able to handle a large number of design variables in comparison with other well-known metaheuristic algorithms. Based on the numerical results of four benchmark problems in structural topology optimization for minimum compliance, the following conclusions are made: (1) The BBA with the proposed filtering algorithm and penalty function are effective in solving large-scale numerical topology optimization problems (fine finite elements mesh). (2) The proposed algorithm produces solid-void designs without gray areas, which makes them practical solutions that are applicable in manufacturing.

Designing a drive train for an industrial robot is a demanding task where a set of design variables need to be determined so that optimal performance is obtained for a wide range of different duty cycles. The paper presents a method where singular value decomposition (SVD) is used to reduce the design variable set. The application is a six degree of freedom serial manipulator, with nine drive train parameters for each axis and the objective is to minimize the cycle time on 122 representative design cycles without decreasing the expected lifetime of the robot. The optimization is based on a simulation model of the robot and conducted on a reduced set of the initial duty cycles and with the design variables suggested by the SVD analysis. The obtained design reduces the cycle time with 1.6% on the original design cycles without decreasing the life time of the robot.

as a comparatively new developed stochastic method particle swarm optimization (PSO), it is widely applied to various kinds of optimization problems especially of nonlinear, non-differentiable or non-convex types. In this paper, a modified guaranteed converged particle swarm algorithm (MGCPSO) is proposed in this paper, which is inspired by guaranteed converged particle swarm algorithm (GCPSO) proposed by von den Bergh. In this paper, the sizing and topological optimization problems of steel framed structures subjected to stress and displacement constraints are selected to illustrate the performance of the presented optimization algorithm. The obtained competitive results show that the MGCPSO exhibit good performance due to improved global searching ability.

Model predictive control is performed by solving a constrained optimization problem at every time step. Since, this optimization problem is a function of the control signal in the prediction horizon, long prediction horizon for large-scale plant model is not practical for model predictive control applications. However, it can be shown that when the control signal sampled by a coarse time step is represented with linear or cubic splines, these splines can be used to interpolate control signal series to calculate the missing data values. Hence, it can be shown that control signal is a function of the coefficients of splines. Using this fact, it is shown that the quadratic optimization defined in terms of control signal can be replaced by a new optimization problem defined in terms of the coefficients of splines. Thereby, it is shown that the size optimization problem can be reduced and model predictive control can be accelerated in order of magnitudes.

With the rapid advancement of computing technology, mathematical modeling and computer simulations have become common and standard methods for design of complex systems. To exercise these models intelligently and eliminate the burden of manual iteration, manipulating inputs and reviewing outputs, optimization strategies are applied in a simulation-based design environment. In reality, the knowledge that engineers have about the design problem is imperfect and incomplete, uncertainty always exists in simulation-based design. The conventional deterministic optimization techniques do not consider the impact of such uncertainties. If the system responses driving the design decisions are very sensitive to these uncertainties, serious problems might confront the designer. Performance of the actual system may differ greatly from expected optimum performance. Again, if the design solution is near one or more constraint boundaries, then even slight uncertainties or changes in the operating environment could produce failed, unsafe designs, and/or result in substantial performance degradation. In recent years, the concept of reliability and robust design has become very popular. Probabilistic design analysis and statistical modeling allow the identification of designs that qualify as not only feasible, but as consistently feasible in the face of uncertainty. Reliability based topology optimization (RBTO) extends the reliability notion to the area of structural topology optimization. Although reliability based design optimization (RBDO) is a well established research area, very few work has been presented in the area of RBTO. In this study, we give an overview of the various works done in the field of RBTO. Ever since Bendsoe and Kikuchi introduced the topology optimization using a homogenization method, many topology optimization methods have been developed for the both linear and nonlinear structures. Traditional topology optimization methods drive the topology of a structure to an optimum design based on the constraint on mass. Kharmanda et al. introduced reliability constraints in deterministic topology optimization problem. They proposed a heuristic strategy that aims to reduce mass while improving the reliability level of the structure without greatly increasing its weight. But the limit state function used by them was not based on failure criteria for the structure. Their formulation considered uncertainty with respect to ∗Design Automation Laboratory †Advisor geometrical dimension and applied load only. Also their reliability analysis seems to be independent of the boundary and loading condition, so their results showed similar values for the uncertain variables for different structures. Tovar et al. have developed the Hybrid Cellular Automaton (HCA) method for structural synthesis of continuum material where the state of each cell is defined by both density and strain energy. In Agarwal, a decoupled RBDO approach is employed such that the topology optimization is separate from the reliability analysis. Patel et al. showed the use of RBTO using the gradient free Hybrid Cellular Automata (HCA) method. Their formulation incorporates uncertainty with respect to material property also. They considered limit state function based on failure modes on the output displacements. This study aims at giving a comparative study on these methods. It points out the advantages and disadvantages of the methods, and their significance in the field of RBTO. As large numbers of design variables are associated with continuum topology optimization problems, RBTO methods are inherently computationally expensive because of additional required system analysis associate with RBDO. Based on the observations, this study presents an efficient method for incorporating reliability analysis in topology optimization.

In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More speciflcally, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is separate from the reliability analysis. In this paper, a maximum allowable displacement failure mode is considered. In this methodology, starting from a continuum design space of uniform material distribution and initial uncertain variable values, a deterministic topology optimization is followed by a reliability assessment of the resulting structure to determine the most probable point of failure (MPP) for the current structure. The MPP is determined with respect to the maximum allowable de∞ection of the structure when loaded. This is generally a computationally expensive process using traditional techniques due to the large number of design variables associated with topology optimization problem. However, combining the e‐cient methods of the non-gradient HCA algorithm with the decoupled approach for RBDO aims to reduce this burden. The topology optimization was without constraint in previous applications of the HCA method. To accommodate RTBO, a mechanism for a global constraint for maximum allowable displacement is developed. This paper details the methodology for the six-sigma design of structures using topology optimization.

This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design.

The Method of Imprecision (MOI) is a multi-objective design method that maximizes the overall degree of both design and performance preferences. Sets of design variables are iteratively selected, and the corresponding performances are approximately computed. The designer’s judgment (expressed as preferences) are combined (aggregated) with the customer’s preferences, to determine the overall preference for sets of points in the design space. In addition to degrees of preference for values of the design and performance variables, engineering design problems also typically include uncertainties caused by uncontrolled variations, for example, measuring and fabrication limitations. This paper illustrates the computation of expected preference for cases where the uncertainties are uncorrelated, and also where the uncertainties are correlated. The result is a “best” set of design variable values for engineering problems, where the overall aggregated preference is maximized. As is illustrated by the examples shown here, where both preferences and uncontrolled variations are present, the presence of uncertainties can have an important effect on the choice of the overall best set of design variable values.

In this paper we develop an as-yet-missing theoretical framework as well as a general methodology for model-based robust design. At the outset, a distinction is made between three sets: the set of design variables, grouped in the n-dimensional vector x, which are to be assigned values as an outcome of the design job; the set of design-environment parameters (DEP), grouped in the v-dimensional vector p, over which the designer has no control; and the set of performance functions, arrayed in the m-dimensional vector f, representing the functional relations among performance, design variables and DEP. Resorting to the mathematical model available for the object under design, an m × v design performance matrix F, mapping the space of relative variations of p into that of relative variations of f, is derived. Moreover, two pertinent concepts are introduced: the design sensitivity matrix, which plays a major role in the transmission of the variations of p into variations off, and its associated bandwidth, defined as the logarithm of the square root of the ratio between the maximum to the minimum singular values of the design performance matrix, measured in decades. A result stating the relation between the bandwidth of a matrix and its inverse is shown. Consequently, the aforementioned bandwidth represents an index for evaluating the robustness of a design. To demonstrate our approach, case studies are included

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper explains how 9 5/8" turbine diamond bit designs for the North Sea were optimized through the combined results of practical field developments and analytical practical field developments and analytical design studies. Various mechanical characteristics such as bit face contour, diamond size, and diamond pattern were analyzed with the aid of the diamond drilling theory, taking into account the particular conditions encountered in North Sea drilling. The mathematical model for rotary and turbine diamond drilling as used in this study was developed during recent years, and is now considered an effective aid to design optimization. The drilling theory is based on previously reported studies on the cutting actions of single diamonds in rocks, now expanded to encompass the total effect of all diamonds on the cutting surfaces of the bit. Using specific drilling conditions and rock properties, expressions for bit torque, properties, expressions for bit torque, penetration rate, rotary power and other penetration rate, rotary power and other performance characteristics are obtained in performance characteristics are obtained in terms of bit weight, rotary speed and the design parameters, like diamond size, fluid handling characteristics and geometric factors. The evolution of the bit designs leads to a bit style which, within the known limitations on diamonds, has best theoretical performance and best field performance. Introduction In view of the expanding use and importance of turbo diamond drilling techniques, particularly in modern offshore development, particularly in modern offshore development, it is important to study the way in which diamond bits work under the specific conditions imposed by turbines, and to use this knowledge to improve the performance of the diamond tools. In this study, several practical turbo diamond bit design approaches are practical turbo diamond bit design approaches are studied analytically in an effort to isolate the best performing or "optimum" combination of bit design variables. The goal of optimization is to find the particular set of design variables which yields the highest penetration rate under the selected operating conditions, without violating any of the assumed practical limitations on loading and application of the diamonds, the diamond bits and the turbines.