Multilevel Optimization Approach Research Articles

Structural design optimization of a tiltrotor aircraft composite wing to enhance whirl flutter stability

In order to enhance the aeroelastic stability of a tiltrotor aircraft, a structural optimization framework is developed by applying a multi-level optimization approach. Each optimization level is designed to achieve a different purpose; therefore, relevant optimization schemes are selected for each level. Enhancement of the aeroelastic stability is selected as an objective in the upper-level optimization. This is achieved by seeking the optimal structural properties of a composite wing, including its mass, vertical, chordwise, and torsional stiffness. In the upper-level optimization, the response surface method (RSM), is selected. On the other hand, lower-level optimization seeks to determine the local detailed cross-sectional parameters, such as the ply orientation angles and ply thickness, which are relevant to the wing structural properties obtained at the upper-level. To avoid manufacturing difficulties, only a few discrete ply orientation angles and an integral number of plies are considered as constraints. A genetic algorithm is selected as the optimizer at the lower-level. Use of the upper-level optimization causes a 13–18% increase in the flutter speed when compared to the baseline configuration. In the lower-level optimization, the optimization results were obtained considering the resulting failure margin and the location of the shear center.

Existence Conditions for an Optimal Affine Leader Function in the Reverse Stackelberg Game

We investigate the solvability of the reverse Stackelberg game. Here, a leader player acts first by presenting a leader function that maps the follower decision space into the leader decision space. Subsequently, the follower acts by determining his optimal decision variable. Such a game setting can be adopted within a multi-level optimization approach for large-scale control problems like road tolling. However, due to the complexity of the general game, results often rely on specific examples. As a starting point towards developing a systematic approach for the use of reverse Stackelberg games in control, a characterization of cases is given in which the desired leader equilibrium can be achieved by an affine leader function. Here, we focus on the single-leader single-follower deterministic, static (one-shot) case. This characterization follows a geometric approach and extends the special cases considered in the existing literature to also incorporate the more general case in which nonconvex and nonsmooth sublevel sets apply.

System design of a wind turbine using a multi-level optimization approach

In this paper a multi-level system design (MLS) algorithm is presented and utilized for a wind turbine system analysis. The MLS guides the decision making process for designing a complex system where many alternatives and many mutually competing objectives and disciplines need to be considered and evaluated. Mathematical relationships between the design variables and the multiple discipline performance objectives are developed adaptively as the various design considerations are evaluated and as the design is being evolved. These relationships are employed for rewarding performance improvement during the decision making process by allocating more resources and influence to the disciplines which exhibit the improvement. Simulation tools developed by the National Renewable Energy Laboratory (NREL) are employed in the wind turbine design analysis. The Cost Of Energy (COE) comprises the overall system level objective, while performance improvements at two technical design disciplines are pursued at the same time. The optimal design of the blade geometry for maximum Annual Energy Production (AEP), and the structural design of the blade for minimum bending moment at the root of the blade comprise the two technical design disciplines. Scalar metamodels are developed for linking the design variables with the performance metrics associated with the design of the blade geometry. Main characteristics of the wind turbine, namely, the rotor diameter, the rotational speed, the maximum rated power, the hub height, the structural characteristics of the blade, and the geometric characteristics of the blade (distribution of thickness, twist angle, and chord) are employed as design variables for the overall design analysis. The optimization results and the physical insight which can be gained through a sensitivity analysis for the optimal configuration are presented and discussed.

Morphing Aircraft Sizing Using Design Optimization

This paper summarizes design optimization approaches for sizing a morphing aircraft for which the wing can make significant shape changes in flight. The approaches include single-level problems solved by gradient-free and gradient-based optimizers and a multilevel problem solved by gradient-based optimizers; of these, the multilevel approach proved most efficient. In the multilevel approach, a top-level problem minimizes the aircraft gross weight using reference design variables (T=W, S, AR, t=c, � , and � ), along with morphing limit variables describing the maximumshapechangeasafunctionofthereferencegeometry (e.g., � b, � c,and �� ).Asublevelproblemforeach mission segment determines an optimal wing-shape scheduling that minimizes fuel consumption, satisfies performance constraints, and operates within the geometric domain prescribed by the top-level problem. While the empty-weight buildup uses traditional predictors for fixed-geometry components, the wing weight prediction uses a parametric equation derived from structural optimization studies of morphing wings. The multilevel optimization approach then sizes an aircraft for which the wing can change sweep and root chord length, demonstrating: 1) the optimal wing-shape scheduling and maximum shape change for the morphing strategy, 2) the approach’s ability to facilitate continuousmorphingduringmissionsegmentanalysis,and3)improvedeffectiveness overprevioussinglelevel morphing aircraft sizing approaches.

A hybrid multi-level optimization approach for the dynamic synthesis/design and operation/control under uncertainty of a fuel cell system

During system development, large-scale, complex energy systems require multi-disciplinary efforts to achieve system quality, cost, and performance goals. As systems become larger and more complex, the number of possible system configurations and technologies, which meet the designer’s objectives optimally, increases greatly. In addition, both transient and environmental effects may need to be taken into account. Thus, the difficulty of developing the system via the formulation of a single optimization problem in which the optimal synthesis/design and operation/control of the system are achieved simultaneously is great and rather problematic. This difficulty is further heightened with the introduction of uncertainty analysis, which transforms the problem from a purely deterministic one into a probabilistic one. Uncertainties, system complexity and nonlinearity, and large numbers of decision variables quickly render the single optimization problem unsolvable by conventional, single-level, optimization strategies. To address these difficulties, the strategy adopted here combines a dynamic physical decomposition technique for large-scale optimization with a response sensitivity analysis method for quantifying system response uncertainties to given uncertainty sources. The feasibility of such a hybrid approach is established by applying it to the synthesis/design and operation/control of a 5 kW proton exchange membrane (PEM) fuel cell system.

Optimal laminate sequence of thin-walled composite beams of generic section using evolution strategies

A problem formulation and solution methodology for design optimization of laminated thin-walled composite beams of generic section is presented. Objective functions and constraint equations are given in the form of beam stiffness. For two different problems one for open section and the other for closed section, the objective function considered is bending stiffness about x-axis. Depending upon the case, one can consider bending, torsional and axial stiffnesses. The different search and optimization algorithm, known as Strategies (ES) has been applied to find the optimal fibre orientation of composite laminates. A multi-level optimization approach is also implemented by narrowing down the size of search space for individual design variables in each successive level of optimization process. The numerical results presented demonstrate the computational advantage of the proposed method Evolution strategies which become pronounced to solve optimization of thin-walled composite beams of generic section.

Sustainability-Based Optimization of Bioprocesses Design and Retrofit

AbstractThe bioprocesses, meaning the transformation of raw materials by either free or attached enzymes produced by living matter or by microorganisms themselves, were a technological constant presence in human history. Up to the present days, the bioprocesses were designed and operated with the aim of achieving some economic, environmental, and social criteria, while sustainability was only another assessment of the aforementioned criteria. In the context of the present knowledge in the domain, sustainability-based optimization would be the next ideal step towards the improvement of the economical, environmental and social parameters of bioprocesses. In the frame of this work, sustainability will be treated as an optimization task where the objective function(s) is/are either a performance index or a set of performance indices, subject to economic, environmental and social restrictions. The aforementioned original multi-level optimization approach refers to two aspects: first, the hierarchic top-down procedure, from plant to process unit scales; second, a combined interaction of manpower and plant networks. For each level and/or network, several objective functions will be derived from sustainability concepts, together with the subjacent penalties. The optimization process will use either an averaged objective function (the sum of the weighted objective functions on to the same level), or a vector objective function aiming to emphasize the Pareto front in the space of feasible solutions. The models of bioprocesses used in the optimization belong to one of these two categories: a) the first principle models encoded into the SuperPro Designer™ simulator; b) original models, of theoretical nature and/or based on artificial neural networks (ANN). An attempt to quantify some qualitative ecological and social sustainability indicators (in connection with the specificity of the test cases) will be made. Due to the incertitude that is present in both bioprocesses modeling, and evaluation of sustainability indicators, some studies involving informational entropy, sensitivity analysis and Monte Carlo simulations must be done.

Optimal laminate sequence of non-prismatic thin-walled composite spatial members of generic section

A problem formulation and a solution methodology for minimum weight design of laminated non-prismatic thin-walled composite spatial members of generic section is presented. Optimal design is carried out subjected to deflection, buckling and frequency constraints. The values of the constraints are determined using the finite element method developed in another paper [Rajasekaran, Equations for tapered thin-walled hybrid composite spatial members of generic section. Solids and Structures, submitted for publication]. The different search and optimization algorithm, known as evolution strategies (ES) has been applied to find the optimal fibre orientation of composite laminates. A multi-level optimization approach is also implemented by narrowing down the size of search space for individual design variables in each successive level of optimization process. The numerical results presented demonstrate the computational advantage of the proposed method “ evolution strategies” which become pronounced to solve optimization of non-prismatic thin-walled spatial members of generic section.

A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning

The graph-partitioning problem is to divide a graph into several pieces so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges is minimised. Important applications of the problem arise, for example, in parallel processing where data sets need to be distributed across the memory of a parallel machine. Very effective heuristic algorithms have been developed for this problem which run in real-time, but it is not known how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. A distinctive feature is the use of a multilevel heuristic algorithm to provide an effective crossover. The technique is tested on several example graphs and it is demonstrated that our method can achieve extremely high quality partitions significantly better than those found by the state-of-the-art graph-partitioning packages.

The optimisation of space structures using evolution strategies with functional networks

In this work, the input for large space structures is created using the Formex algebra of the Formian software. The different search and optimisation algorithm known as evolution strategies (ESs) has been applied to find the optimal design of the space trusses considering the areas of the members of the space structures as discrete variables. The objective function is obtained for first few generations by using a structural analysis package such as Feast and for other generations by functional networks (FNs). Initially, to obtain the data for a functional network, a structural package such as Feast is used. The use of a functional network is motivated by time consuming repeated analyses required by evolution strategies during the optimisation process. In addition, a multilevel optimisation approach is implemented by reducing the size of the search space for individual design variables in each successive level of the optimisation process for the first example; for the remaining three examples, a functional network has been combined with evolution strategies to get away with the use of a structural analysis package and a multilevel optimisation technique. The numerical tests presented demonstrate the computational advantage of the proposed approach of ESs combined with functional networks (FNs) which become pronounced for fairly large scale optimisation problems involving about 700 degrees of freedom.

Optimization of Large Scale Three Dimensional Reticulated Structures Using Cellular Genetics and Neural Networks

In this work, the input for large space structures is created using Formian [1]. In this paper, a new optimization technique called Cellular Automata (CA) has been combined with Genetic algorithm (GA) to develop a different search and optimization algorithm known as Cellular Genetic Algorithm (CGA), which considers the areas of the members of the space structures as discrete variables. The objective function for each cell in Cellular automata is obtained either by using structural analysis package like FEAST (ISRO 1995), ANSYS or SAP or by using neural networks. Initially to obtain the data for training the neural network structural analysis package is used. The use of Neural Network is motivated by time consuming repeated analysis required by Cellular Genetics during Optimization process. In addition, a multilevel optimization approach is implemented by reducing the size of the search space for individual design variables in each successive level of optimization process. The non- linear load deflection behavior of the optimized structure is also studied. The numerical tests presented demonstrate the computational advantages of the proposed approach “Cellular Genetic Algorithm” combined with Neural Networks (NN) become pronounced for large scale Optimization problems.

Novel Development and Applications in Finite Element Technologies. Optimum Design of Vehicle Frontal Structure and Occupant Restraint System for Crashworthiness. A Multilevel Approach Using SDSS.

CAE tools have been applied for the crash safety design of vehicles, though they haven’t satisfied the optimum design of vehicles. The authors have proposed a Statistical Design Support System (SDSS), and have found that the SDSS is one of available optimization approaches for the nonlinear and dynamic phenomena. This system is a synthetic design method which is based on the response surface methodology and the design of experiments. In this study, a multilevel optimization approach using the SDSS is presented. This approach is well-suited to large-scale multilevel and multidisciplinary optimization problems, and optimum design of vehicle frontal structure and occupant restraint system for crashworthiness is solved. It is shown that successfully and effectively collaborative optimization for frontal structure and occupant restraint system can be conducted by this new approach.

Collaborative optimization with disciplinary conceptual design

For the first time, a multilevel optimization approach with disciplinary conceptual design is demonstrated. Collaborative optimization is used to decompose an example bridge design problem among two groups of designers --- a superstructure design group and a deck design group. The disciplinary groups are allowed to search over different design concepts and formulate the design variables and constraints for each. The autonomy of the two groups is managed by a system-level group which insures that overall system objectives are met and coupling is properly accounted for. Even though discrete conceptual design occurs within the disciplinary groups, a continuous gradient-based optimization algorithm is used at the system level. The procedure was started from a nonoptimal concept, and converged to the optimal concept.

Multi-level optimisation approach to switched capacitor filter synthesis

A multi-level optimisation approach to switched capacitor filter synthesis in which the top-down synthesis flow consists of high level and circuit level optimisers is presented. At high level, generalised macromodels of switched capacitor filter circuits are optimised to meet the given filter specifications. Parameters optimised at high level are treated as specifications for a circuit level optimiser, which is based on a novel algorithm that combines evolution strategies (ES) with simulated annealing. The optimisation strategy combines the advantages of SPICE-type simulations, neural performance models and knowledge-based approach in satisfying the constraints and specifications. The algorithmic details of the synthesis system are discussed in detail, and illustrative examples that demonstrate the validity of the approach are presented.

Structural-acoustic control system design by multi-level optimization

A multi-level optimization approach for the design of feedforward active structural acoustic control (ASAC) systems is presented. The formulation takes advantage that both the structural response and the acoustic radiation from a controlled structure can be completely defined in the modal domain. All the physical parameters that define the control inputs and the error sensors are defined in the modal domain in terms of the unit modal control forces and the modal error sensor components, respectively. The upper level of the optimization solves for the optimum modal parameters that minimize the total radiated acoustic power. Then, these optimum modal parameters are used in a set of lower level or physical domain optimization problems to determine the physical characteristics of the actuators and sensors to be implemented. Since the response of the system is evaluated in the upper level using a modal approach, the formulation permits the implementation of numerical techniques and/or experimental data during the design process. Therefore, the proposed methodology can be used for the design of control systems for realistic structures with complex disturbances in an efficient manner. The design formulation is illustrated for the case of a simply supported plate excited by an off-resonance disturbance.

A multilevel optimization approach considering product realization process alternatives and parameters for improving manufacturability

Abstract A multilevel global optimization approach considering product realization process alternatives and parameters of these alternatives is proposed to improve manufacturability measures, including feasibility, cost, and time of production. Development of product realization processes is described by an AND/OR graph. A feasible product realization process alternative can be identified from this graph and is described by a number of parameters. The optimal parameters regarding a product realization process alternative are achieved at the parameter optimization level, while the optimal alternative is obtained from all the feasible alternatives. Two global optimization methods, genetic algorithm and simulated annealing, are employed for identifying the optimal product realization process alternative and its parameters. The introduced approach serves as a key component in an integrated concurrent design system. A case study example is given to show how the proposed method is used for solving engineering problems.

A multilevel optimization approach considering product realization process alternatives and parameters for improving manufacturability

A multilevel optimization approach considering product realization process alternatives and parameters for improving manufacturability

A Multilevel Approach for the Station-Keeping of a Phased Satellite Constellation

This paper considers the station-keeping of a phased satellite constellation. We have to control a perturbed constellation with the aim to warrant a multiple visibility and to maintain a continuous earth coverage. Based on a simplified linear model of the constellation behavior, two problem formulations with a multilevel optimization approach of the orbital maneuvers are considered. Experimental results applied to a class of IGO constellations (Iridium, Globalstar, Odyssey) are given.

Optimum Management of a Hierarchically Exploited Open Access Resource: A Multilevel Optimization Approach

AbstractA multilevel optimization approach is presented for determining the optimum management of the Texas brown shrimp fishery. Independent fisher groups harvest this open access resource in a hierarchical order without cooperation among themselves or with the management authority. The special structure of the problem is exploited to derive the fishers' optimum responses to any arbitrary specification of the policy variables (season and area closures). Empirical results indicate that significant losses of income and harvest value would occur if the fishery were unmanaged. The results also indicate that optimum closure policies vary significantly depending on the policy objective specification.

An algorithm for solving the system-level problem in multilevel optimization

A multilevel optimization approach applicable to nonhierarchic coupled systems is presented. The approach includes a general treatment of design (or behaviour) constraints and coupling constraints at the discipline level through the use of norms. Three different types of norms are examined - the max norm, the Kreisselmeier-Steinhauser (KS) norm, and theℓ p norm. The max norm is recommended. The approach is demonstrated on a class of hub frame structures that simulate multidisciplinary systems. The max norm is shown to produce system-level constraint functions which are nonsmooth. A cutting-plane algorithm is presented, which adequately deals with the resulting corners in the constraint functions. The algorithm is tested on hub frames with an increasing number of members (which simulate disciplines), and the results are summarized.