Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem

The increasing demands for travelling comfort and reduction of carbon dioxide emissions have been considered substantially in the stage of conceptual aircraft design. However, the design of a modern aircraft is a multidisciplinary process, which requires the coordination of information from several specific disciplines, such as structures, aerodynamics, control, etc. To address this problem with adequate accuracy, the multidisciplinary analysis and optimization (MAO) method is usually applied as a systematic and robust approach to solve such complex design issues arising from industries. Since MAO method is tedious and computationally expensive, genetic programming (GP)-based metamodeling techniques incorporating MAO are proposed as an effective approach to minimize the wing stiffness of a large aircraft subject to aerodynamic, aeroelastic and stability constraints in the conceptual design phase. Based on the linear small-disturbance theory, the state-space equation is employed for stability analysis. In the process of multidisciplinary analysis, aeroelastic response simulations are performed using Nastran. To construct metamodels representing the responses of the interests with high accuracy as well as less computational burden, optimal Latin hypercube design of experiments (DoE) is applied to determine the optimized distribution of sampling points. Following that, parametric optimization is carried out on metamodels to obtain the optimal wing geometry shape, elastic axis positions and stiffness distribution, and then the solution is verified by finite element simulations. Finally, the superiority of the GP-based metamodel technique over genetic algorithm is demonstrated by multidisciplinary design optimization of a representative beam-frame wing structure in terms of accuracy and efficiency. The results also show that GP metamodel-based strategy for solving MAO problems can provide valuable insights to tailoring parameters for the effective design of a large aircraft in the conceptual phase

Metamodel-assisted design optimization of piezoelectric flex transducer for maximal bio-kinetic energy conversion

Energy Harvesting Devices (EHD) have been widely used to generate electrical power from the bio-kinetic energy of human body movement. A novel Piezoelectric Flex Transducer (PFT) based on the Cymbal device has been proposed by Daniels et al. (2013) for the purpose of energy harvesting. To further improve the efficiency of the device, optimal design of the PFT for maximum output power subject to stress and displacement constraints is carried out in this paper. Sequential Quadratic Programming (SQP) on metamodels generated with Genetic Programming from a 140-point optimal Latin hypercube design of experiments is used in the optimization. Finally, the optimal design is validated by finite element simulations. The simulations show that the magnitude of the electrical power generated from this optimal PFT harvesting device can be up to 6.5 mw when a safety design factor of 2.0 is applied

Extremal measures maximizing functionals based on simplicial volumes

We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension k ≤ d formed by k + 1 independent copies and raised to some power δ. We study properties of extremal measures that maximize these functionals. In particular, for positive δ we characterize their support and for negative δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented

Maximum energy conversion from human motion using piezoelectric flex transducer: A multi-level surrogate modeling strategy

Conventional engineering design optimization requires a large amount of expensive experimental tests from prototypes or computer simulations, which may result in an inefficient and unaffordable design process. In order to overcome these disadvantages, a surrogate model may be used to replace the prototype tests. To construct a surrogate model of sufficient accuracy from limited number of tests/simulations, a multi-level surrogate modeling strategy is introduced in this article. First, a chosen number of points determined by optimal Latin Hypercube Design of Experiments are used to generate global-level surrogate models with genetic programming and the fitness landscape can be explored by genetic algorithms for near-optimal solutions. Local-level surrogate models are constructed then from the extended-optimal Latin Hypercube samples in the vicinity of global optimum on the basis of a much smaller number of chosen points. As a result, an improved optimal design is achieved. The efficiency of this strategy is demonstrated by the parametric optimization design of a piezoelectric flex transducer energy harvester. The optimal design is verified by finite element simulations and the results show that the proposed multi-level surrogate modeling strategy has the advantages of faster convergence and more efficiency in comparison with the conventional single-single level surrogate modeling technique

Application of Permutation Genetic Algorithm for Sequential Model Building–Model Validation Design of Experiments

YesThe work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient Design of Experiment (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to support an exploration-based sequential DoE strategy for complex real-life engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of Model Building–Model Validation (MB-MV) sequences, by generating optimal infill sets of test points as OLH DoEs, that preserve good space filling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB-MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back (SHCB) function, as well as the Gasoline Direct Injection (GDI) engine steady state engine mapping problem that motivated this research. The case studies show that the algorithm is effective at delivering quasi-orthogonal space-filling DoEs with good properties even after several MB-MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The practical importance of this work, demonstrated through the engine case study, also is that significant reduction in the effort and cost of testing can be achieved.The research work presented in this paper was funded by the UK Technology Strategy Board (TSB) through the Carbon Reduction through Engine Optimization (CREO) project

A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels

The frictional performance of a bearing is of significant interest in any mechanical system where there are lubricated surfaces under load and in relative motion. Surface topography plays a major role in determining the coefficient of friction for the bearing because the size of the fluid film and topography are of a comparable order. The problem of optimising topography for such a system is complicated by the separation in scales between the size of the lubricated domain and that of the topography, which is of at least one order of magnitude or more smaller. This paper introduces a multiscale method for optimising the small scale topography for improved frictional performance of the large scale bearing. The approach fully couples the elastohydrodynamic lubrication at both scales between pressure generated in the lubricant and deformation of the bounding surfaces. Homogenised small scale data is used to inform the large scale model and is represented using Moving Least Squares metamodels calibrated by cross validation. An optimal topography for a minimum coefficient of friction for the bearing is identified and comparisons made of local minima in the response, where very different topographies with similar frictional performance are observed. Comparisons of the optimal topography with the smooth surface model demonstrated the complexity of capturing the non-linear effect of topography and the necessity of the multiscale method in capturing this. Deviations from the smooth surface model were quantified by the metamodel coefficients and showed how topographies with a similar frictional performance have very different characteristics