Development of a multi-objective optimization algorithm based on lichtenberg figures

This doctoral dissertation presents the most important concepts of multi-objective optimization and a systematic review of the most cited articles in the last years of this subject in mechanical engineering. The State of the Art shows a trend towards the use of metaheuristics and the use of a posteriori decision-making techniques to solve engineering problems. This fact increases the demand for algorithms, which compete to deliver the most accurate answers at the lowest possible computational cost. In this context, a new hybrid multi-objective metaheuristic inspired by lightning and Linchtenberg Figures is proposed. The Multi-objective Lichtenberg Algorithm (MOLA) is tested using complex test functions and explicit contrainted engineering problems and compared with other metaheuristics. MOLA outperformed the most used algorithms in the literature: NSGA-II, MOPSO, MOEA/D, MOGWO, and MOGOA. After initial validation, it was applied to two complex and impossible to be analytically evaluated problems. The first was a design case: the multi-objective optimization of CFRP isogrid tubes using the finite element method. The optimizations were made considering two methodologies: i) using a metamodel, and ii) the finite element updating. The last proved to be the best methodology, finding solutions that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the Tsai-Wu failure index and increased by at least 52.57% the natural frequency. In the second application, MOLA was internally modified and associated with feature selection techniques to become the Multi-objective Sensor Selection and Placement Optimization based on the Lichtenberg Algorithm (MOSSPOLA), an unprecedented Sensor Placement Optimization (SPO) algorithm that maximizes the acquired modal response and minimizes the number of sensors for any structure. Although this is a structural health monitoring principle, it has never been done before. MOSSPOLA was applied to a real helicopter’s main rotor blade using the 7 best-known metrics in SPO. Pareto fronts and sensor configurations were unprecedentedly generated and compared. Better sensor distributions were associated with higher hypervolume and the algorithm found a sensor configuration for each sensor number and metric, including one with 100% accuracy in identifying delamination considering triaxial modal displacements, minimum number of sensors, and noise for all blade sections.Esta tese de doutorado traz os conceitos mais importantes de otimização multi-objetivo e uma revisão sistemática dos artigos mais citados nos últimos anos deste tema em engenharia mecânica. O estado da arte mostra uma tendência no uso de meta-heurísticas e de técnicas de tomada de decisão a posteriori para resolver problemas de engenharia. Este fato aumenta a demanda sobre os algoritmos, que competem para entregar respostas mais precisas com o menor custo computacional possível. Nesse contexto, é proposta uma nova meta-heurística híbrida multi-objetivo inspirada em raios e Figuras de Lichtenberg. O Algoritmo de Lichtenberg Multi-objetivo (MOLA) é testado e comparado com outras metaheurísticas usando funções de teste complexas e problemas restritos e explícitos de engenharia. Ele superou os algoritmos mais utilizados na literatura: NSGA-II, MOPSO, MOEA/D, MOGWO e MOGOA. Após validação, foi aplicado em dois problemas complexos e impossíveis de serem analiticamente otimizados. O primeiro foi um caso de projeto: otimização multi-objetivo de tubos isogrid CFRP usando o método dos elementos finitos. As otimizações foram feitas considerando duas metodologias: i) usando um meta-modelo, e ii) atualização por elementos finitos. A última provou ser a melhor metodologia, encontrando soluções que reduziram pelo menos 45,69% da massa, 18,4% do coeficiente de instabilidade, 61,76% do TW e aumentaram em pelo menos 52,57% a frequência natural. Na segunda aplicação, MOLA foi modificado internamente e associado a técnicas de feature selection para se tornar o Seleção e Alocação ótima de Sensores Multi-objetivo baseado no Algoritmo de Lichtenberg (MOSSPOLA), um algoritmo inédito de Otimização de Posicionamento de Sensores (SPO) que maximiza a resposta modal adquirida e minimiza o número de sensores para qualquer estrutura. Embora isto seja um princípio de Monitoramento da Saúde Estrutural, nunca foi feito antes. O MOSSPOLA foi aplicado na pá do rotor principal de um helicóptero real usando as 7 métricas mais conhecidas em SPO. Frentes de Pareto e configurações de sensores foram ineditamente geradas e comparadas. Melhores distribuições de sensores foram associadas a um alto hipervolume e o algoritmo encontrou uma configuração de sensor para cada número de sensores e métrica, incluindo uma com 100% de precisão na identificação de delaminação considerando deslocamentos modais triaxiais, número mínimo de sensores e ruído para todas as seções da lâmina

Mixed-flow pump performance improvement based on circulation method

Mixed-flow pumps have been extensively employed in daily life, improving their energy characteristics contribute to the reduction of energy consumption worldwide. In this study, to overcome the decrease of optimization upper limit caused by using a single type of parameter as the design parameter, a typical mixed-flow pump was chosen for study, and its impeller was parameterized by five geometric and eight hydrodynamic parameters. With head and efficiency as the constraint and optimization objective respectively, 27 schemes were constructed by the Taguchi method. The influence of design factors to the objective and constraint was analyzed based on range and regression analysis. The optimization mechanism was elucidated using the entropy production method. The result reveals that the geometric and hydrodynamic parameters have a significantly impact on the mixed-flow pump’s energy characteristics. The optimized model head is 12.43m, which meets the constraints, while the efficiency increases by 3.2%–88.51%. Therefore, considering both geometric and hydrodynamic parameters in the mixed-flow pump optimization is workable and necessary. This paper can provide practical instructions on the optimal design of different turbomachines

Generalized Lorenz-Mie theory : application to scattering and resonances of photonic complexes

Les structures photoniques complexes permettent de façonner la propagation lumineuse à l’échelle de la longueur d’onde au moyen de processus de diffusion et d’interférence. Cette fonctionnalité à l’échelle nanoscopique ouvre la voie à de multiples applications, allant des communications optiques aux biosenseurs. Cette thèse porte principalement sur la modélisation numérique de structures photoniques complexes constituées d’arrangements bidimensionnels de cylindres diélectriques. Deux applications sont privilégiées, soit la conception de dispositifs basés sur des cristaux photoniques pour la manipulation de faisceaux, de même que la réalisation de sources lasers compactes basées sur des molécules photoniques. Ces structures optiques peuvent être analysées au moyen de la théorie de Lorenz-Mie généralisée, une méthode numérique permettant d’exploiter la symétrie cylindrique des diffuseurs sous-jacents. Cette dissertation débute par une description de la théorie de Lorenz-Mie généralisée, obtenue des équations de Maxwell de l’électromagnétisme. D’autres outils théoriques utiles sont également présentés, soit une nouvelle formulation des équations de Maxwell-Bloch pour la modélisation de milieux actifs appelée SALT (steady state ab initio laser theory). Une description sommaire des algorithmes d’optimisation dits métaheuristiques conclut le matériel introductif de la thèse. Nous présentons ensuite la conception et l’optimisation de dispositifs intégrés permettant la génération de faisceaux d’amplitude, de phase et de degré de polarisation contrôlés. Le problème d’optimisation combinatoire associé est solutionné numériquement au moyen de deux métaheuristiques, l’algorithme génétique et la recherche tabou. Une étude théorique des propriétés de micro-lasers basés sur des molécules photoniques – constituées d’un arrangement simple de cylindres actifs – est finalement présentée. En combinant la théorie de Lorenz-Mie et SALT, nous démontrons que les propriétés physiques de ces lasers, plus spécifiquement leur seuil, leur spectre et leur profil d’émission, peuvent être affectés de façon nontriviale par les paramètres du milieu actif sous-jacent. Cette conclusion est hors d’atteinte de l’approche établie qui consiste à calculer les étatsméta-stables de l’équation de Helmholtz et leur facteur de qualité. Une perspective sur la modélisation de milieux photoniques désordonnés conclut cette dissertation.Complex photonic media mold the flow of light at the wavelength scale using multiple scattering and interference effects. This functionality at the nano-scale level paves the way for various applications, ranging from optical communications to biosensing. This thesis is mainly concerned with the numerical modeling of photonic complexes based on twodimensional arrays of cylindrical scatterers. Two applications are considered, namely the use of photonic-crystal-like devices for the design of integrated beam shaping elements, as well as active photonic molecules for the realization of compact laser sources. These photonic structures can be readily analyzed using the 2D Generalized Lorenz-Mie theory (2D-GLMT), a numerical scheme which exploits the symmetry of the underlying cylindrical structures. We begin this thesis by presenting the electromagnetic theory behind 2D-GLMT.Other useful frameworks are also presented, including a recently formulated stationary version of theMaxwell-Bloch equations called steady-state ab initio laser theory (SALT).Metaheuristics, optimization algorithms based on empirical rules for exploring large solution spaces, are also discussed. After laying down the theoretical content, we proceed to the design and optimization of beam shaping devices based on engineered photonic-crystal-like structures. The combinatorial optimization problem associated to beam shaping is tackled using the genetic algorithm (GA) as well as tabu search (TS). Our results show the possibility to design integrated beam shapers tailored for the control of the amplitude, phase and polarization profile of the output beam. A theoretical and numerical study of the lasing characteristics of photonic molecules – composed of a few coupled optically active cylinders – is also presented. Using a combination of 2D-GLMT and SALT, it is shown that the physical properties of photonic molecule lasers, specifically their threshold, spectrum and emission profile, can be significantly affected by the underlying gain medium parameters. These findings are out of reach of the established approach of computing the meta-stable states of the Helmholtz equation and their quality factor. This dissertation is concluded with a research outlook concerning themodeling of disordered photonicmedia

Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine

Optimal performance of the electric machine/drive system is mandatory to improve the energy consumption and reliability. To achieve this goal, mathematical models of the electric machine/drive system are necessary. Hence, this motivated the editors to instigate the Special Issue “Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine”, aiming to collect novel publications that push the state-of-the art towards optimal performance for the electric machine/drive system. Seventeen papers have been published in this Special Issue. The published papers focus on several aspects of the electric machine/drive system with respect to the mathematical modelling. Novel optimization methods, control approaches, and comparative analysis for electric drive system based on various electric machines were discussed in the published papers

Multi-objective Optimization of Industrial Ammonia Synthesis

The thesis describes modelling and optimization work of an industrial ammonia synthesis. Author developed first-principle mathematical model of the commercial converter based on gas-solid reaction and heat transfer within the system. The model is validated with industrial data and showed satisfactory accuracy. Further, optimization study is performed in multi-objective manner to intensify ammonia production and decrease heat duty of the process. Result have revealed a potential to improve current operating condition int terms of both objectives

Application of Surrogate Based Optimisation in the Design of Automotive Body Structures

The rapid development of automotive industry requires manufacturers to continuously reduce the development cost and time and to enhance the product quality. Thus, modern automotive design pays more attention to using CAE analysis based optimisation techniques to drive the entire design flow. This thesis focuses on the optimisation design to improve the automotive crashworthiness and fatigue performances, aiming to enhance the optimisation efficiency, accuracy, reliability, and robustness etc. The detailed contents are as follows: (1) To excavate the potential of crash energy absorbers, the concept of functionally graded structure was introduced and multiobjective designs were implemented to this novel type of structures. First, note that the severe deformation takes place in the tubal corners, multi-cell tubes with a lateral thickness gradient were proposed to better enhance the crashworthiness. The results of crashworthiness analyses and optimisation showed that these functionally graded multi-cell tubes are preferable to a uniform multi-cell tube. Then, functionally graded foam filled tubes with different gradient patterns were analyzed and optimized subject to lateral impact and the results demonstrated that these structures can still behave better than uniform foam filled structures under lateral loading, which will broaden the application scope of functionally graded structures. Finally, dual functionally graded structures, i.e. functionally graded foam filled tubes with functionally graded thickness walls, were proposed and different combinations of gradients were compared. The results indicated that placing more material to tubal corners and the maximum density to the outmost layer are beneficial to achieve the best performance. (2) To make full use of training data, multiple ensembles of surrogate models were proposed to maximize the fatigue life of a truck cab, while the panel thicknesses were taken as design variables and the structural mass the constraint. Meanwhile, particle swarm optimisation was integrated with sequential quadratic programming to avoid the premature convergence. The results illustrated that the hybrid particle swarm optimisation and ensembles of surrogates enable to attain a more competent solution for fatigue optimisation. (3) As the conventional surrogate based optimisation largely depends on the number of initial sample data, sequential surrogate modeling was proposed to practical applications in automotive industry. (a) To maximize the fatigue life of spot-welded joints, an expected improvement based sequential surrogate modeling method was utilized. The results showed that by using this method the performance can be significantly improved with only a relatively small number of finite element analyses. (c) A multiojective sequential surrogate modeling method was proposed to address a multiobjective optimisation of a foam-filled double cylindrical structure. By adding the sequential points and updating the Kriging model adaptively, more accurate Pareto solutions are generated. (4) While various uncertainties are inevitably present in real-life optimisations, conventional deterministic optimisations could probably lead to the violation of constraints and the instability of performances. Therefore, nondeterministic optimisation methods were introduced to solve the automotive design problems. (a) A multiobjective reliability-based optimisation for design of a door was investigated. Based on analysis and design responses surface models, the structural mass was minimized and the vertical sag stiffness was maximized subjected to the probabilistic constraint. The results revealed that the Pareto frontier is divided into the sensitive region and insensitive region with respect to uncertainties, and the decision maker is recommended to select a solution from the insensitive region. Furthermore, the reduction of uncertainties can help improve the reliability but will increase the manufacturing cost, and the tradeoff between the reliability target and performance should be made. (b) A multiobjective uncertain optimisation of the foam-filled double cylindrical structure was conducted by considering randomness in the foam density and wall thicknesses. Multiobjective particle swarm optimisation and Monte Carlo simulation were integrated into the optimisation. The results proved that while the performances of the objectives are sacrificed slightly, the nondeterministic optimisation can enhance the robustness of the objectives and maintain the reliability of the constraint. (c) A multiobjective robust optimisation of the truck cab was performed by considering the uncertainty in material properties. The general version of dual response surface model, namely dual surrogate model, was proposed to approximate the means and standard deviations of the performances. Then, the multiobjective particle optimisation was used to generate the well-distributed Pareto frontier. Finally, a hybrid multi-criteria decision making model was proposed to select the best compromise solution considering both the fatigue performance and its robustness. During this PhD study, the following ideas are considered innovative: (1) Surrogate modeling and multiobjective optimisation were integrated to address the design problems of novel functionally graded structures, aiming to develop more advanced automotive energy absorbers. (2) The ensembles of surrogates and hybrid particle swarm optimisation were proposed for the design of a truck cab, which could make full use of training points and has a strong searching capacity. (3) Sequential surrogate modeling methods were introduced to several optimisation problems in the automotive industry so that the optimisations are less dependent on the number of initial training points and both the efficiency and accuracy are improved. (4) The surrogate based optimisation method was implemented to address various uncertainties in real life applications. Furthermore, a hybrid multi-criteria decision making model was proposed to make the best compromise between the performance and robustness

Plant Modeling, Model Reduction and Power Optimization for an Organic Rankine Cycle Waste Heat Recovery System in Heavy Duty Diesel Engine Applications

With pressure from strict emission and fuel consumption regulations, researchers are searching for improved internal combustion engine performance. Especially for the heavy-duty vehicles, which takes up 7% of the total vehicle volume while consume around 30% of transportation energy in US. Around 40-60% of energy is wasted as heat in heavy-duty diesel (HDD) vehicles in different engine operating conditions, which mainly includes the waste heat in exhaust gas, exhaust gas recirculation (EGR) circuit, and engine coolant. Waste heat recovery (WHR) techniques are potential to achieve the fuel economy and emission reduction goals. Among the available WHR techniques, organic Rankine cycle (ORC) is preferred by many researchers for its mature technologies and high efficiency. The aim of this dissertation is to analyze the power of HDD vehicle by: (i) building a high fidelity, physics-based ORC-WHR dynamic system plant model, (ii) building a reduced order model framework, and (iii) conducting the power analysis based on the developed plant and reduced models. The dynamic system plant model is built, which includes heat exchangers, a turbine expander, pumps, control valves, compressible volumes, junctions and a reservoir. Components are modelled and calibrated individually. Subsequently, the component models are integrated into an entire ORC-WHR system model. The entire ORC-WHR system model is validated over transient engine conditions. Actuator sensitivity study is conducted for the ORC-WHR power generation analysis using the ORC-WHR plant model. Besides the ORC-WHR plant model, a reduced order model framework is developed utilizing Proper Orthogonal Decomposition (POD) and Galerkin projection approaches. The POD-Galerkin reduced order model framework inherits the system physics from the high fidelity, physics-based ORC-WHR plant model. POD Galerkin reduced order models are compared with three existing models (finite volume model, moving boundary model and 0D lumped model) and show their advantages over the existing models in terms of accuracy or computation cost. In addition, identification method is applied to the low order POD Galerkin reduced order model to increase the accuracy. Given the validated ORC-WHR plant model and POD Galerkin reduced order model framework, the ORC-WHR system power analysis is conducted. Steady state power analysis is conducted over two quasi-steady driving cycles using the ORC-WHR plant model. An engine model is developed to predict the exhaust conditions in transient engine operating conditions. Transient power analysis is conducted with ORC-WHR plant model and engine model co-simulation by optimizing three vapor temperature reference trajectories. Finally, dynamic programming (DP) is implemented with the POD-Galerkin reduced order model to generate ORC-WHR power benchmark in a driving cycle, which can give the guidance on the ORC power optimization and evaluate the controller performance

Development of a novel gerotor pump for lubrication systems of aeronautic engines

The technology of lubrication systems for aircrafts engines has seen significant development during the history of aeronautics and has progressed in parallel with the evolution of the engines themselves. Starting from the first, wetsump schemes derived from automotive applications, more complex systems and components have been introduced. The progressive increase of aeronautic engines’ power and speed, as well as that of the maximum operative altitude of the aircraft, have increased the lubricant flow rate required to avoid severe mechanical issues that can cause dangerous conditions for the vehicle and its users. Currently, the main focus on the development of novel lubrication pumps is aimed at reducing the pumps’ weight and envelope while maintaining, or possibly increasing, their reliability. The first two objective could be pursued by searching for novel pump types and/or increasing the pump speed in order to downsize its required capacity, but the low-pressure environment, typical of the lubrication circuits, over imposes a few, severe, limitations to avoid cavitation occurrence that decrease the effectiveness of this approach. The central aim of the presented research, performed within the program “Greening the Propulsion”, is to provide a theoretical framework to help in the development of a novel gerotor pump for the lubrication of aeronautic engines.The first step of the research involves the study of the state of the art of aeronautic engines’ lubrication systems, providing particular care to the effect that any design choice and possible operational condition may have on the lubrication pump design. Hence, the state of the art for gerotor pumps is investigated; results of this study are used, along with catalogue comparisons, to build simplified sizing tools to perform a benchmarking activity involving gerotors and other low pressure pumps type. This activity, performed to position gerotor pumps in the aeronautic engine lubrication market, is then used as a starting point to highlight the weak points of gerotors traditional design and to propose some possible solutions to enhance the pumps performances. To study the outcomes of these modifications, a rigorous theoretical framework is required; sizing and modeling criteria, based on the theory of gearing and compressible fluids, are hence detailed and used to build an Automatic Design and Simulation Framework, able to automatically design, validate and simulate a novel gerotor pump given a minimum number of geometrical and physical input parameters. This design and simulation tool is then used to evaluate the performance boost provided by the proposed variations and to optimize the gears profiles by pairing it with a multiobjective algorithm based on evolutionary strategies. Another critical component of any lubrication system is the pressure relief valve used to avoid the occurrence of dangerous conditions for the pipes integrity. A side activity involving the study of a preliminary sizing tool for pressure relief valve is hence performed. A preliminary design framework is presented and discussed, highlighting the importance of the valve discharge coefficient. To study its dependence on the valve’s geometry, a lengthy CFD simulation campaign is performed varying the poppet shape and the fluid Reynolds’ number. Results are hence discussed and used inside the design framework

Numerical modelling of bidirectional dry gas face seals

The optimization of the geometrical parameters of the aerodynamic lift features and the analysis of the fluid flow in the seal interface are inter-twined. Any small changes in the geometrical parameters of the aerodynamic lift features significantly affect the performance of a non-contacting gas face seal. For a gas face seal to function with optimum performance requires that the optimum geometrical parameters be identified. This can be achieved through a lengthy trial and error process, often heavily dependent on the designer’s depth of insight, itself dependent on experience, or can be achieved through automated numerical methods. The purpose of this research was to develop a reliable numerical model that can serve as a design tool for simulating the performance of both unidirectional and bidirectional dry gas face seals. This was achieved in three steps. The first approach consisted in developing a 2D numerical model that employed the Reynolds equation for seals operating at very low rotating speeds and low pressure differentials. In the second step a 3D-CFD model was assembled and the practicability of using CFD, in a seal design loop, for seals operating in wide range of operating conditions, was investigated. This model employed a commercial CFD package (ANSYS CFX version 11). For last approach both models were incorporated into an automatic optimization tool that can generate optimal seal geometries with a minimum of human intervention. An extensive set of results from the analysis of dry gas face seals spanning across different operating conditions and geometrical seal face profiles, with the inclusion of convergent radial taper, are presented and discussed in this thesis. The results obtained from the Reynolds equation and 3D CFD models are compared and critically analysed. Results obtained with both models are validated against test data obtained from AESSEAL plc, the sponsor of this research. The 3D CFD model predictions showed a better agreement with the test data on the seal leakage than the Reynolds equation model. The leakage rates and fluid film thickness predictions illustrate how the 3D CFD model can be used for seal design while overcoming some of the shortcomings of the Reynolds equation based models. The major limitation of the 3D CFD model is that it is computationally expensive. An automatic optimization tool which can be used for the design of dry gas face seals has been presented. The improvements achieved from the optimization of a spiral groove face seal utilising the automatic optimization tool are: 4.8% increase of opening force, 13.2% reduction of seal leakage, 20.7% increase of design efficiency parameter, 28.3% increase of axial film stiffness and 15.9% reduction of power consumption. A proposed new design of dry gas face seal capable of bidirectional operation has been presented. This type of seal outperformed the spiral groove face seal, in reverse rotation of the sealing shaft, in terms of opening force and positive axial film stiffness

Metamodel-based design optimization in industrial turbomachinery

Fans and Blowers community is experiencing, during those years, an incredible push in rethinking design approaches and strategies. The change in regulations on minimum efficiency grades and market requirements on even more customized products demand a changing in the way design in fan technology is perceived. In this context, even if synthetic approaches for fan design and analysis are still valuable tools, they need to be flanked by metamodels in order to overcome the limitations and criticism introduced by empirical relationships developed in the past for specific applications. In addition, by replacing computation-intensive functions with approximate surrogate models, it is possible to adopt advanced and nested optimization methods, such as those based on Evolutionary Algorithms, drastically improving the overall optimization computational time. Surrogate-based Optimizations based on Evolutionary Algorithm should become common practice in design optimization because of their capability of find optima in the design space, thanks to their intrinsic balance between exploitation and exploration. This work proposes methods for interweave elements of metamodeling techniques and multi-objective optimization problems with the synthetic approaches classically developed by the turbomachinery community. The entire Thesis can be ideally divided into two parts; the first gives a brief survey on the classical fan design and analysis approaches and reports two synthetic in-house codes for axial fan performance prediction. The second part present the state-of-the-art in metamodeling and optimization techniques, underlining the role of metamodeling in supporting design optimization and focusing in the more reliable and accurate framework for multi-objective optimization in fans engineering design