Optimum topology design of various geometrically nonlinear latticed domes using improved harmony search method

Domes are elegant and economical structures used in covering large areas. They are built in various forms. According to their form, they are given special names such as lamella, network, and geodesic domes. In this paper, optimum topological design algorithm is presented that determines the optimum number of rings, the optimum height of crown and tubular section designations for the member groups of these domes. The design algorithm developed has a routine that generates the data required for the geometry of these domes automatically. The minimum weight of each dome is taken as the objective function. The design constraints are implemented according to the provision of LRFD-AISC (Load and Resistance Factor Design–American Institute of Steel Constitution). The optimum topological design problem that considers these constraints turns out to be discrete programming problem. Improved harmony search algorithm is suggested to determine its optimum solution. The design algorithm also considers the geometric nonlinearity of these dome structures. Design examples are presented to demonstrate the effectiveness and robustness of the design optimization algorithm developed.     

Automated optimal design of double-layer latticed domes using particle swarm optimization

Most of the conventional design methods of large-scale domes need deep engineering insight; furthermore, they hardly give the most economical solutions. Therefore, in this paper, a new practical design algorithm is presented to automate optimal geometry and sizing design of the latticed space domes through the idea of using parametric mathematical functions. Moreover, a simple approach is developed for the optimal sizing design of trusses with outsized number of elements. The robust technique of particle swarm optimization is employed to find the solution of the propounded optimization problem. Some numerical examples on the minimum weight design of several famous domes are provided to demonstrate the efficiency of the proposed design algorithm.     

Optimal topology selection of continuum structures with displacement constraints

This paper deals with the optimal topology selection of continuum structures subject to displacement constraints by using the performance-based design concept. The optimal topology of a continuum structure is generated by gradually eliminating underutilized elements from the discretized design domain. A performance index is developed for monitoring the optimization process and is used as a termination criterion in the optimization algorithm so that the global optimum can be selected from the optimization history. Maximizing the performance index in the design space is proposed as the performance-based optimization criterion. The performance index can be utilized to compare the efficiency of structural topologies produced by different continuum topology optimization methods. Several examples are provided to demonstrate the capabilities of the performance-based optimization approach in selecting the best configuration for the minimum-weight design of continuum structures with maximum stiffness.     

Optimum topological design of geometrically nonlinear single layer latticed domes using coupled genetic algorithm

Single layer latticed domes are lightweight and elegant structures that provide cost-effective solutions to cover the large areas without intermediate supports. The topological design of these structures present difficulty due to the fact that the number of joints and members as well as the height of the dome keeps on changing during the design process. This makes it necessary to automate the numbering of joints and members and the computation of the coordinates of joints in the dome. On the other hand the total number of joints and members in a dome is function of the total number of rings exist in the dome. Currently no study is available that covers the topological design of dome structures that give the optimum number of rings, the optimum height of crown and the tubular cross-sectional designations for the dome members under the given general external loading. The algorithm presented in this study carries out the optimum topological design of single layer lattice domes. The serviceability and strength requirements are considered in the design problem as specified in BS5950. The algorithm takes into account the nonlinear response of the dome due to effect of axial forces on the flexural stiffness of members. The optimum solution of the design problem is obtained using coupled genetic algorithm. Having the total number of rings and the height of crown as design variables provides the possibility of having a dome with different topology for each individual in the population. It is shown in the design example considered that the optimum number of joints, members and the optimum height of a geodesic dome under a given external loading can be determined without designer’s interference.     

Application of evolutionary optimization techniques for finding the optimal set of concentric circular antenna array

In this paper the maximum sidelobe level (SLL) reductions, optimal beam patterns and optimal beam widths of various designs of three-ring planar concentric circular antenna arrays (PCCAA) are examined using three different classes of evolutionary optimization techniques to finally determine the global optimal three-ring PCCAA design and then establish some sort of ranking among the techniques. Apart from physical construction of a PCCAA, one may broadly classify its design into two major categories: uniformly excited arrays and non-uniformly excited arrays. The present paper assumes non-uniform excitations and uniform spacing of excitation elements in each three-ring PCCAA design and a design goal of maximizing SLL reduction associated with optimal beam patterns and beam widths. The design problem is modeled as an optimization problem for each PCCAA design and solved using different evolutionary optimization techniques to determine an optimum set of normalized excitation weights for PCCAA elements, which, when incorporated, results in a radiation pattern with optimal (maximum) SLL reduction. Among the various PCCAA designs, one which yields the global minimum SLL with global minimum first null beamwidth is the global optimal design. In this work the three-ring PCCAA containing (N₁ = 4, N₂ = 6, N₃ = 8) elements proves to be such global optimal design. The optimization techniques employed are real coded GA (RGA), canonical PSO (CPSO), craziness based PSO (CRPSO), evolutionary programming (BEP), hybrid evolutionary programming (HEP). While ranking the techniques after 30 total runs for each design, HEP, CRPSO, RGA, CPSO, BGA hold the first five ranks in order of optimization capability. HEP yields global minimum SLL (?32.86 dB) and global minimum BWFN (77.0°) for the optimal design. BEP often changes the rank from second to fifth depending on the design set. Further, when compared to a uniformly excited PCCAA having equal number of elements and same radii a reduction of major lobe beamwidth is also observed in the optimal non-uniformly excited case.     

Shape optimization of shallow domes subjected to external pressure

Shallow domes subjected to external pressure are extensively used in missile structures. The critical failure mode for these domes is buckling due to external pressure. Different closed form solutions are available to evaluate buckling pressure of dome shapes like ellipsoid and torisphere. The torisiphere dome is the optimum dome shape among conventional domes. Shape optimization is carried out to find the optimal dome shape among shallow domes subjected to external pressure. Dome geometry is generalized by cubic bezier polynomials. For carrying out shape optimization, a low fidelity model is preferred which can predict the critical buckling pressure of a general dome shape. Towards this a unified model is proposed which meets the above requirement. Using this unified model, shape optimization of dome for minimization of mass is carried out subjected to buckling constraint. The study yielded a dome shape different from conventional dome shapes with a mass saving of 6% over torispherical dome while meeting the buckling constraint. The results of unified model are also validated with high fidelity Finite Element Analysis.

     

On optimal topology of grillage structures

Two problems of optimum topological design of grillages are discussed: (1) the Equilibrium Linear Programming (ELP), where the analysis model is based only on equilibrium conditions and (2) the Nonlinear Program (NLP), where the ELP formulation is extended to include compatibility conditions. The structural topology is optimized by allowing elimination of elements. Three different force method formulations are presented for each of the problems. It is shown that the optimal topology for the NLP problem might correspond to a singular point in the design space. The optimal topology for the ELP problem is obtained by solving a linear program (LP).

Conditions for selecting a geometry of Multiple Optimal Topologies (MOT) are derived. The objective function for the MOT geometry is shown to be independent of the redundant forces, and some of the optimal topologies are usually statically determinate structures. In such cases the lower bound on the optimal value obtained by the ELP solution is equal to the final global optimum. Examples are given to illustrate how the optimal topology and its corresponding load path change with the geometric parameters. Design procedures that combine automated optimization and CAD techniques are most suitable for solving the presented problems.

     

3D and multiple load case bi-directional evolutionary structural optimization (BESO)

Evolutionary Structural Optimization (ESO), is a numerical method of structural optimization that is integrated with finite element analysis (FEA). Bi-directional ESO (BESO) is an extension to this method and can begin with minimal amount of material (only that necessary to support the load and support cases) in contrast to ESO which uses an initially oversized structure. Using BESO the structure is then allowed to grow into the optimum design or shape by both adding elements where the stresses are the highest and taking elements away where stresses are the lowest. In conducting this research, a methodology was developed (and integrated into the ESO program EVOLVE) which produced the optimal 3D finite element models of a structure in a more reliable way than the traditional ESO method. Additionally, the BESO method was successfully extended to multiple load cases for both 2D and 3D. Two different algorithms were used to find the best structure experiencing more than one load case and the results of each are included.     

Simulation and experimental analysis for hysteresis behavior of a piezoelectric actuated micro stage using modified charge system search

The main goal of this study is to investigate the hysteresis behavior of a piezoelectric actuated micro stage. The hysteresis of piezoelectric actuators (PA) is formulated using the generalized Duhem model (GDM) and a modified charge system search (CSS) is proposed to identify the hysteresis model. Different from the present CSS method, the proposed method applies a construction factor to prevent converging to a local optimum. The modified CSS is used to evaluate the parameters of the GDM to compare with the particle swarm optimization (PSO). The use of MCSS-based optimization is superior to the CSS and the PSO for identification of the GDM. The experimental result also validated the modeling correctness using the proposed method.     

An enhanced charged system search for configuration optimization using the concept of fields of forces

The concept of the “fields of forces” is utilized as a general model of meta-heuristic algorithms from physics. This model is capable of representing the properties of different meta-heuristics and in this paper, it is used to enhance the recently developed meta-heuristic, the Charged System Search (CSS). The enhanced CSS is then applied to determine the configuration optimum design of structures. Comparison of the results for some examples, illustrates the efficiency of the enhanced CSS algorithm.     

Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm

In this paper, the seismic design of reinforced concrete (RC) frames subjected to time-history loadings was formulated as an optimization problem. Because finding the optimum design is relatively difficult and time-consuming for structural dynamics problems, an innovative algorithm combining multi-criterion decision-making (DM) and Particle Swarm Optimization (PSO), called DMPSO, was presented for accelerating convergence toward the optimum solution. The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete optimization problems. The main goal was to minimize the cost or weight of structures subjected to time-history loadings while satisfying all design requirements imposed by building design codes. The results confirmed the ability of the proposed algorithm to find the optimal solutions for structural optimization problems subjected to time-history loadings.     

Data-driven,using design of dynamic experiments,versus model-driven optimization of batch crystallization processes

A new data-driven experimental design methodology, design of dynamic experiments (DoDE), is proposed as a means of developing a response surface model that can be used to effectively optimize batch crystallization processes. This data-driven approach is especially useful for complex processes for which it is difficult or impossible to develop a knowledge-driven model in a timely fashion for the optimization of an industrial process. Design of dynamic experiments [1] generalizes the formulation of time-invariant design variables from design of experiments, allowing for consideration of time-variant design variables in the experimental design. When combined with response surface modeling and an appropriate optimization algorithm, a data-driven optimization methodology is produced, which we call DoDE optimization. The method is used here to determine the optimal cooling rate profile, which integrates to give the optimum temperature profile, for a batch crystallization process. To examine the effectiveness of the DoDE optimization method, the data-driven optimum temperature profile is compared to the optimum temperature profile obtained using a model-based optimization technique for the potassium nitrate–water batch crystallization model developed by Miller and Rawlings [2]. The temperature profiles calculated using DoDE optimization yield response values within a few percent of the true model-based optimum values. A sensitivity analysis is performed on one case study to evaluate the distribution of the response variable from each method in the presence of parameter and initial seed distribution variability. It is demonstrated that there is partial overlap in the distributions when only variability in the model parameters is evaluated and there is substantial overlap when variability is included in both the model and initial seed distribution parameters. From this evidence, it can be concluded that the DoDE optimization method has the potential to be a useful data-driven optimization tool for batch crystallization processes where a first-principles model is not available or cannot be developed due to time and/or cost constraints.     

Metamorphic development: a new topology optimization method for continuum structures

An effective optimization procedure for finding structural shapes and topologies that minimize structural compliance and weight subject to stress and deflection constraints is presented. This new approach, called “Metamorphic Development” (MD), can allow a structure to grow and degenerate towards an optimum topological layout. In this method, the optimization can start from the simplest possible geometry (layout) or any degree of development of the structure rather than from a complex ground mesh. The structure is then developed metamorphically using rectangular and triangular elements that can be of any specified sizes. Examples demonstrate the potential of the MD optimization procedure to generate innovative solutions to structural design problems. Results are given and the growth and degeneration histories during optimization are illustrated. Received August 20, 1999     

Numerical method for shape optimization using T-spline based isogeometric method

Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. However, the finite-element-based shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. In this paper, as a remedy for these problems, an isogeometric-based shape design sensitivity analysis and optimization methods are developed incorporating with T-spline basis. In the shape design sensitivity analysis and optimization procedure using a standard finite element approach, the design boundary should be parameterized for the smooth variation of the boundary using a separate geometric modeler, such as a CAD system. Otherwise, the optimal design usually tends to fall into an undesirable irregular shape. In an isogeometric approach, the NURBS basis function that is used in representing the geometric model in the CAD system is directly used in the response analysis, and the design boundary is expressed by the same NURBS function as used in the analysis. Moreover, the smoothness of the NURBS can allow the large perturbation of the design boundary without a severe mesh distortion. Thus, the isogeometric shape design sensitivity analysis is free from remeshing during the optimization process. In addition, the use of T-spline basis instead of NURBS can reduce the number of degrees of freedom, so that the optimal solution can be obtained more efficiently while yielding the same optimum design shape.     

Minimum cost design of a welded orthogonally stiffened cylindrical shell

In this study the optimal design of a cylindrical orthogonally stiffened shell member of an offshore fixed platform truss, loaded by axial compression and external pressure, is investigated. Ring stiffeners of welded box section and stringers of halved rolled I-section are used. The design variables considered in the optimization are the shell thickness as well as the dimensions and numbers of stiffeners. The design constraints relate to the shell, panel ring and panel stringer buckling, as well as manufacturing limitations. The cost function includes the cost of material, forming of plate elements into cylindrical shape, welding and painting. In the optimization a number of relatively new mathematical optimization methods (leap-frog - LFOPC, Dynamic-Q, ETOPC, and particle swarm - PSO) are used, in order to ensure confidence that the finally computed optimum design is accurately determined, and indeed corresponds to a global minimum. The continuous optimization procedures are adapted to allow for discrete values of the design variables to be used in the final manufacturing of the truss member. A comparison of the computed optimum costs of the stiffened and un-stiffened assemblies, shows that significant cost savings can be achieved by orthogonal stiffening, since the latter allows for considerable reduction of the shell thickness, which results in large material and manufacturing cost savings.     

The effects of rehabilitation objectives on near optimal trade-off relation between minimum weight and maximum drift of 2D steel X-braced frames considering soil-structure interaction using a cluster-based NSGA II

A cluster-based non-dominated sorting genetic algorithm (NSGA) II has been considered to investigate the effects of rehabilitation objectives on multi-objective design optimization of two-dimensional (2D) steel X-braced frames in the presence of soil-structure interaction. The substructure elasto-perfect plastic model has been adopted for modeling of the soil-structure interaction and the nonlinear pushover analysis is used to evaluate the performance level of the frames for a specified hazard level. Cross-sections of grouped elements of the frames are considered to be discontinuous design variables of the problem. Via implementing some of the constraints, which are independent of doing the time-consuming nonlinear analysis, input population of the optimization technique has been clustered. By using the nonlinear analysis technique in conjunction with the cluster-based NSGA II, near optimal trade-off relation between minimum weight and maximum story drifts of the frames are obtained. The allowable rotations, geometry, and resistance constraints of the structural elements are considered in the optimization design of the frames. The effects of the enhanced basic safety and limited selective rehabilitation objectives on optimum design of the frame are studied. The results show differences between the optimum results of the three mentioned rehabilitation objectives and effects of soil types.

     

On optimal fuzzy c-means clustering for energy efficient cooperative spectrum sensing in cognitive radio networks

This work explores the scope of Fuzzy C-Means (FCM) clustering on energy detection based cooperative spectrum sensing (CSS) in single primary user (PU) cognitive radio network (CRN). PU signal energy sensed at secondary users (SUs) is forwarded to the fusion center (FC). Two different combining schemes, namely selection combining (SC) and optimal gain combining are performed at FC to address the sensing reliability problem on two different optimization frameworks. In the first work, optimal cluster center points are searched for using differential evolution (DE) algorithm to maximize the probability of detection under the constraint of meeting the probability of false alarm below a predefined threshold. Simulation results highlight the improved sensing reliability compared to the existing works. In the second one, the problem is extended to the energy efficient design of CRN. The SUs act here as amplify-and-forward (AF) relays and PU energy content is measured at the FC over the combined signal from all the SUs. The objective is to minimize the average energy consumption of all SUs while maintaining the predefined sensing constraints. Optimal FCM clustering using DE determines the optimal SU amplifying gain and the optimal number of PU samples. Simulation results shed a light on the performance gain of the proposed approach compared to the existing energy efficient CSS schemes.     

Design optimization with back-propagation neural networks

A methodology with back-propagation neural network models is developed to explore the artificial neural nets (ANN) technology in the new application territory of design optimization. This design methodology could go beyond the Hopfield network model, Hopfield and Tank (1985), for combinatorial optimization problems In this approach, pattern classification with back-propagation network, the most demonstrated power of neural networks applications, is utilized to identify the boundaries of the feasible and the infeasible design regions. These boundaries enclose the multi-dimensional space within which designs satisfy all design criteria. A feedforward network is then incorporated to perform function approximation of the design objective function. This approximation is performed by training the feedforward network with objective functions evaluated at selected design sets in the feasible design regions. Additional optimum design sets in the classified feasible regions are calculated and included in the successive training sets to improve the function mapping. Iteration is continued until convergent criteria are satisfied. This paper demonstrates that the artificial neural nets technology provides a global perspective of the entire design space with good and near optimal solutions. ANN can indeed be a potential technology for design optimization.     

Collaborative service system design for music content creation

This article presents a novel collaborative service system (CSS) design methodology supporting the work of multiple participating users and collaborative services processes. The CSS application of music content creation paradigm called DesignStorming as it pertains to CSS modeling and developing. CSS is an interactive service system that can be systematic service innovation and automatic semi-automated value co-creation between service providers and customers to enhance service productivity. The objectives of this research are threefold─to propose a novel design methodology for CSS, to incorporate simple service machine (SSM) and intelligent service machine (ISM) for CSS, and to demonstrate a CSS application of music content creation. SSM is a road map that can be used to define the salient attribute elements for CSS design. According to the predefined SSM, ISM conducts modeling the cognitive process of service exchanges and service provision, their knowledge representations, and value co-production process for a computerized CSS. DesignStorming demonstrates how a CSS can be automated the interactive communications and problem solving processes during the music content creation work. The CSS application involves the three system components: 1) Ontology Developer, 2) SFGA Partnership Matcher, and 3) Co-created Value Appraiser. In addition, a service evaluation model is described and evaluated, so that some of their important characteristics can be identified. Such a comprehensive design methodology can provide the foundation for building future more diversified and innovative collaborative service system.     

An optimal circular antenna array design considering mutual coupling using heuristic approaches

This article shows the design of a non‐uniformly excited single ring circular antenna array (CAA) for the synthesis of optimal far‐field radiation characteristics. A recently proposed meta‐heuristic based optimization algorithm called gray wolf optimization (GWO) and state‐of‐the‐art swarm intelligence based evolutionary optimization technique known as particle swarm optimization with a distribution based update mechanism (PSOd) are individually applied to determine the optimum set of current excitation amplitude weights and the inter‐element spacing among the array elements to reduce the side lobe level and 3‐dB beamwidth considering the mutual coupling. The results obtained by employing PSOd and GWO are compared to those of the uniform radiation pattern and the recently published results of state‐of‐the‐art literature having equal sets of elements to show the superiority of employed approaches. Three different design examples of 8, 10, and 12 elements CAA are reported in this article to study the performances of PSOd and GWO algorithm‐based results over the results of other recently reported literature.