Abstract
The quality of gearings is largely decided by their geometric design. If the geometric design is incorrect, the reliability of the transmission will not be ensured even by the use of the ...highest quality materials. Conversely, sometimes excellent geometric gear design can save expensive material costs. The work describes the procedure of optimizing the geometric model of a non-standard elliptical gear eccentrically mounted with a continuously changing gear number for specific parameters.
Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the ...applications of ML in ASO to date and provide a perspective on the state-of-the-art and future directions. We first introduce conventional ASO and current challenges. Next, we introduce ML fundamentals and detail ML algorithms that have been successful in ASO. Then, we review ML applications to ASO addressing three aspects: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands, such as interactive design optimization. Practical large-scale design optimizations remain a challenge because of the high cost of ML training. Further research on coupling ML model construction with prior experience and knowledge, such as physics-informed ML, is recommended to solve large-scale ASO problems.
In the present study, an effective optimization framework of aerodynamic shape design is established based on the multi-fidelity deep neural network (MFDNN) model. The objective of the current work ...is to construct a high-accuracy multi-fidelity surrogate model correlating the configuration parameters of an aircraft and its aerodynamic performance by blending different fidelity information and adaptively learning their linear or nonlinear correlation without any prior assumption. In the optimization framework, the high-fidelity model using a CFD evaluation with fine grid and the low-fidelity model using the same CFD model with coarse grid are applied. Moreover, in each optimization iteration, the high-fidelity infilling strategy by adding the current optimal solution of surrogate model into the high-fidelity database is applied to improve the surrogate accuracy. The low-fidelity infilling strategy which can generate the solutions distributed uniformly in the whole design space is used to update the low-fidelity database for avoiding local optimum. Then, the proposed multi-fidelity optimization framework is validated by two standard synthetic benchmarks. Finally, it is applied to the high-dimensional aerodynamic shape optimization of a RAE2822 airfoil parameterized by 10 design variables and a DLR-F4 wing-body configuration parameterized by 30 design variables. The optimization results demonstrate that the proposed multi-fidelity optimization framework can remarkably improve optimization efficiency and outperform the single-fidelity method.
•An aerodynamic shape optimization framework based on MFDNN is proposed.•The PSO algorithm is used for finding the optimal solution of surrogate model.•Various infilling strategies are used to improve the surrogate accuracy.•The present framework can remarkably improve optimization efficiency.
The adjoint method is used for high-fidelity aerodynamic shape optimization and is an efficient approach for computing the derivatives of a function of interest with respect to a large number of ...design variables. Over the past few decades, various approaches have been used to implement the adjoint method in computational fluid dynamics solvers. However, further advances in the field are hindered by the lack of performance assessments that compare the various adjoint implementations. Therefore, we propose open benchmarks and report a comprehensive evaluation of the various approaches to adjoint implementation. We also make recommendations on effective approaches, that is, approaches that are efficient, accurate, and have a low implementation cost. We focus on the discrete adjoint method and describe adjoint implementations for two computational fluid dynamics solvers by using various methods for computing the partial derivatives in the adjoint equations and for solving those equations. Both source code transformation and operator-overloading algorithmic differentiation tools are used to compute the partial derivatives, along with finite differencing. We also examine the use of explicit Jacobian and Jacobian-free solution methods. We quantitatively evaluate the speed, scalability, memory usage, and accuracy of the various implementations by running cases that cover a wide range of Mach numbers, Reynolds numbers, mesh topologies, mesh sizes, and number of CPU cores. We conclude that the Jacobian-free method using source code transformation algorithmic differentiation to compute the partial derivatives is the best option because it computes exact derivatives with the lowest CPU time and the lowest memory requirements, and it also scales well up to 10 million cells and over one thousand CPU cores. The superior performance of this approach is primarily due to its Jacobian-free adjoint strategy. The cases presented herein are publicly available and represent platform-independent benchmarks for comparing other current and future adjoint implementations. Our results and discussion provide a guide for discrete adjoint implementations, not only for computational fluid dynamics but also for a wide range of other partial differential equation solvers.
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on ...the Hessian of the considered shape function, so that critical stable domains (i.e. such that the first order derivative vanishes and the second order one is positive) are local minima for smooth perturbations; as we are in an infinite dimensional framework, and that in most applications there is a norm-discrepancy phenomenon, this type of result require a lot of work. We show that these hypotheses are satisfied by classical functionals, involving the perimeter, the Dirichlet energy or the first Laplace-Dirichlet eigenvalue. We also explain how we can easily deal with constraints and/or invariance of the functionals. As an application, we retrieve or improve previous results from the existing literature, and provide new local stability results. We finally test the sharpness of our results by showing that the local minimality is in general not valid for non-smooth perturbations.
In the case of mega-structures such as tall buildings and long-span bridges, the mitigation of the intensity of the wind excitation through aerodynamic tailoring of the external shape can be ...fundamental for meeting the performance goals. The search for the best performing shape through an automatic CFD-enabled optimization methodology is potentially less expensive, less time-consuming and more thorough than the common trial-and-error approach based on wind tunnel test results, therefore very attractive. This paper investigates the possibility of carrying out the multi-objective aerodynamic shape optimization of civil structures through an approach in which evolutionary algorithms are used in synergy with ordinary Kriging surrogates. A specifically developed strategy is adopted to update the Kriging models making efficient use of additional CFD runs. Shell scripting, parallelized computations and mesh morphing algorithms are exploited for enhancing the framework's efficiency and consistency. As a case study, the optimization of the shape of a tall building cross-section in terms of both the lift and the drag coefficient is considered.
•Multi-objective aerodynamic shape optimization of civil structures is considered.•Kriging surrogates are investigated for reducing the computational effort of CFD.•Evolutionary strategies are used for finding Pareto sets of optimal configurations.•A novel validation and updating strategy is defined based on the Kriging surrogate.•The potential of the proposed optimization approach is illustrated on a case study.
Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often ...employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from
N
v
to
8N
v
(
N
v
here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.
Antony Jameson pioneered CFD-based aerodynamic design optimization in the late 1980s. In addition to developing the fundamental theory, Jameson implemented that theory in codes that were practical ...enough to be used in industry. As a result of Jameson’s seminal efforts, a research community has been established in aerodynamic design optimization. This research area has experienced sustained improvements in CFD solvers, mesh deformation, sensitivity computation, and optimization tools. We review recent developments for each of these components and present open-source tools available for aerodynamic shape optimization. A variety of applications is presented, including the optimization of a supercritical airfoil starting from a circle, a web application that optimizes airfoils within a few seconds, aircraft aerodynamic and aerostructural optimization, and aeropropulsive optimization. We also review the Aerodynamic Design Optimization Discussion Group (ADODG) benchmarks and other aerodynamic shape optimization problems. Among the ADODG benchmarks, we focus on the RANS-based problems and discuss some of the issues encountered, including comparing Euler and RANS results and design-space multimodality. The availability of these benchmarks and the open-source tools is expected to enable further studies and benchmarks in CFD-based aerodynamic design optimization and MDO.
•Jameson made aerodynamic design optimization possible through the adjoint method.•Many design optimization challenges identified in a 2014 study have been addressed.•Aerodynamic optimization benchmarks made it easier to compare different approaches.•Open-source aerodynamic optimization software opens the door to widespread use.
We present isogeometric shape optimization for shell structures applying sensitivity weighting and semi-analytical analysis. We use a rotation-free shell formulation and all involved geometry models, ...i.e., initial design, analysis model, optimization model, and final design use the same geometric basis, in particular NURBS. A sensitivity weighting scheme is presented which eliminates certain effects of the chosen discretization on the design update. A multilevel design approach is applied such that the design space can be chosen independently from the analysis space. The use of semi-analytical sensitivities allows having different polynomial degrees for design and analysis model. Different numerical examples are performed which confirm the applicability of the proposed method. Furthermore, a shape optimization example with an exact solution is presented which can serve as general benchmark for shape optimization methods.
We propose an effective shape optimization method to generate mechanically robust, lightweight porous structures. Central to our algorithm is a non-uniform thermal conduction process, which diffuses ...from the given heat source to minimize structure compliance under the volume-bounded constraint. The diffusivity at each voxel forms the design variable set, and the structure compliance is differentiable concerning the diffusivities; thus, we can easily reformulate the traditional topology optimization to update diffusivities for compliance minimization. Our method is able to receive various heat sources as inputs. To make the optimized structures porous, the input heat sources are constrained to be porous, e.g., wireframe models, stress lines inputs. This framework is available for 2D and 3D porous structure generation. We demonstrate the robustness and practicability of our method over various models.
PDF
