Hybrid Intelligent Optimization Methods for Engineering Problems

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles

STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations

The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magnetic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. To apply these techniques to spectral lines that sample the chromosphere, NLTE effects must be included in the calculations. We developed a new inversion code STiC to study spectral lines that sample the upper chromosphere. The code is based the RH synthetis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.Comment: Accepted for publication in Astronomy & Astrophysic

Deep Reinforcement Learning for the Design of Structural Topologies

Advances in machine learning algorithms and increased computational efficiencies have given engineers new capabilities and tools for engineering design. The presented work investigates using deep reinforcement learning (DRL), a subset of deep machine learning that teaches an agent to complete a task through accumulating experiences in an interactive environment, to design 2D structural topologies. Three unique structural topology design problems are investigated to validate DRL as a practical design automation tool to produce high-performing designs in structural topology domains. The first design problem attempts to find a gradient-free alternative to solving the compliance minimization topology optimization problem. In the proposed DRL environment, a DRL agent can sequentially remove elements from a starting solid material domain to form a topology that minimizes compliance. After each action, the agent receives feedback on its performance by evaluating how well the current topology satisfies the design objectives. The agent learned a generalized design strategy that produced topology designs with similar or better compliance minimization performance than traditional gradient-based topology optimization methods given various boundary conditions. The second design problem reformulates mechanical metamaterial unit cell design as a DRL task. The local unit cells of mechanical metamaterials are built by sequentially adding material elements according to a cubic Bezier curve methodology. The unit cells are built such that, when tessellated, they exhibit a targeted nonlinear deformation response under uniaxial compressive or tensile loading. Using a variational autoencoder for domain dimension reduction and a surrogate model for rapid deformation response prediction, the DRL environment was built to allow the agent to rapidly build mechanical metamaterials that exhibit a diverse array of deformation responses with variable degrees of nonlinearity. Finally, the third design problem expands on the second to train a DRL agent to design mechanical metamaterials with tailorable deformation and energy manipulation characteristics. The agent’s design performance was validated by creating metamaterials with a thermoplastic polyurethane (TPU) constitutive material that increased or decreased hysteresis while exhibiting the compressive deformation response of expanded thermoplastic polyurethane (E-TPU). These optimized designs were additively manufactured and underwent experimental cyclic compressive testing. The results showed the E-TPU and metamaterial with E-TPU target properties were well aligned, underscoring the feasibility of designing mechanical metamaterials with customizable deformation and energy manipulation responses. Finally, the agent\u27s generalized design capabilities were tested by designing multiple metamaterials with diverse desired loading deformation responses and specific hysteresis objectives. The combined success of these three design problems is critical in proving that a DRL agent can serve as a co-designer working with a human designer to achieve high-performing solutions in the domain of 2D structural topologies and is worthy of incorporation into a wide array of engineering design domains

CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics 1999

These proceedings represent a collection of the latest advances in aeroelasticity and structural dynamics from the world community. Research in the areas of unsteady aerodynamics and aeroelasticity, structural modeling and optimization, active control and adaptive structures, landing dynamics, certification and qualification, and validation testing are highlighted in the collection of papers. The wide range of results will lead to advances in the prediction and control of the structural response of aircraft and spacecraft

Inverse design of transonic/supersonic aerofoils based on deep neural networks

Transonic and supersonic aerofoil inverse design for different flight conditions is carried out using Deep Neural Networks (DNN). DNN are combined with a comprehensive and complete database of aerodynamic data and aerofoil geometry parameters to form the pillars of a surrogate inverse aerodynamic design tool. The framework of this research starts with the aerofoil parameterisation. The Class/Shape Transformation functions (CST) was selected for the parameterisation process due to its high accuracy and flexibility when describing complex shapes. An automated mesh technique is created and implemented to discretise the flow domain. The aerodynamic computations are performed for 395 aerofoils. Spatial discretisation is accomplished with the Jameson-Schmidt-Turkel (JST) scheme and convergence is reached by the backward Euler implicit numerical scheme. Data are collected and managed with the CST parameters for all aerofoils and their respective aerodynamic characteristics from the CFD solver. The Deep Neural Network is then trained, validated using cross-validation and evaluated against CFD data. An extensive investigation of the effect from different DNN configurations takes place in this research. Within this thesis, different case studies are presented for different numbers of design objectives. For the inverse design process the NACA 66-206 aerofoil was selected as the baseline aerofoil, to reduce the aerodynamic drag coefficient while maintaining or improving the lift coefficient, to obtain a superior lift/drag ratio compared with the baseline aerofoil. The framework of this thesis have proved to output aerofoil designs with an improved lift/drag ratio in comparison with the baseline aerofoil.Aerospac

Natural Parameterization

The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of “natural parameters” can be extracted by a new subdivision algorithm so they reflect what is called the object’s “geometric DNA”. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of “new” stochastic phantoms which possessthe same stochastic behavior as the “original” cross-sections