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Industrial simulations of turbulent flows often rely on Reynolds-averaged Navier-Stokes (RANS) turbulence models, which contain numerous closure coefficients that need to be calibrated. This paper aims to address this issue by proposing a semi-automated calibration of these coefficients using a new framework (referred to as turbo-RANS) based on Bayesian optimization.

The authors introduce the generalized error and default coefficient preference (GEDCP) objective function, which can be used with integral, sparse or dense reference data for the purpose of calibrating RANS turbulence closure model coefficients. Then, the authors describe a Bayesian optimization-based algorithm for conducting the calibration of these model coefficients. An in-depth hyperparameter tuning study is conducted to recommend efficient settings for the turbo-RANS optimization procedure.

The authors demonstrate that the performance of the k-ω shear stress transport (SST) and generalized k-ω (GEKO) turbulence models can be efficiently improved via turbo-RANS, for three example cases: predicting the lift coefficient of an airfoil; predicting the velocity and turbulent kinetic energy fields for a separated flow; and, predicting the wall pressure coefficient distribution for flow through a converging-diverging channel.

To the best of the authors’ knowledge, this work is the first to propose and provide an open-source black-box calibration procedure for turbulence model coefficients based on Bayesian optimization. The authors propose a data-flexible objective function for the calibration target. The open-source implementation of the turbo-RANS framework includes OpenFOAM, Ansys Fluent, STAR-CCM+ and solver-agnostic templates for user application.

This paper delves into the aerodynamic optimization of a single-stage axial turbine employed in aero-engines.

An efficient integrated design optimization approach tailored for turbine blade profiles is proposed. The approach combines a novel hierarchical dynamic switching PSO (HDSPSO) algorithm with a parametric modeling technique of turbine blades and high-fidelity Computational Fluid Dynamics (CFD) simulation analysis. The proposed HDSPSO algorithm introduces significant enhancements to the original PSO in three pivotal aspects: adaptive acceleration coefficients, distance-based dynamic neighborhood, and a switchable learning mechanism. The core idea behind these improvements is to incorporate the evolutionary state, strengthen interactions within the swarm, enrich update strategies for particles, and effectively prevent premature convergence while enhancing global search capability.

Mathematical experiments are conducted to compare the performance of HDSPSO with three other representative PSO variants. The results demonstrate that HDSPSO is a competitive intelligent algorithm with significant global search capabilities and rapid convergence speed. Subsequently, the HDSPSO-based integrated design optimization approach is applied to optimize the turbine blade profiles. The optimized turbine blades have a more uniform thickness distribution, an enhanced loading distribution, and a better flow condition. Importantly, these optimizations lead to a remarkable improvement in aerodynamic performance under both design and non-design working conditions.

These findings highlight the effectiveness and advancement of the HDSPSO-based integrated design optimization approach for turbine blade profiles in enhancing the overall aerodynamic performance. Furthermore, it confirms the great prospects of the innovative HDSPSO algorithm in tackling challenging tasks in practical engineering applications.

The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

This paper aims to use the crankshaft-bearing system of a four-cylinder internal combustion engine as the studying object, and develop a multi-objective optimization design of the crankshaft-bearing. In the current optimization design of engine crankshaft-bearing, only the crankshaft-bearing was considered as the studying object. However, the corresponding relations of major structure dimensions exist between the crankshaft and the crankshaft-bearing in internal combustion engine, and there are the interaction effects between the crankshaft and the crankshaft-bearing during the operation of internal combustion engine.

The crankshaft mass and the total frictional power loss of crankshaft-bearing s are selected as the objective functions in the optimization design of crankshaft-bearing. The Particle Swarm Optimization algorithm based on the idea of decreasing strategy of inertia weight with the exponential type is used in the optimization calculation.

The total frictional power loss of crankshaft-bearing and the crankshaft mass are decreased, respectively, by 26.2 and 5.3 per cent by the multi-objective optimization design of crankshaft-bearing, which are more reasonable than the ones of single-objective optimization design in which only the crankshaft-bearing is considered as the studying object.

The crankshaft-bearing system of a four-cylinder internal combustion engine is taken as the studying object, and the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system is developed. The results of this paper are helpful to the design of the crankshaft-bearing for engine. There is universal significance to research the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system. The research method of the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system can be used to the optimization design of the bearing in the shaft-bearing system of ordinary machinery.

The purpose of this paper is to develop a multi-material topology optimization method for permanent magnet-assisted synchronous reluctance motors.

In the proposed method, the optimization procedure consists of two steps. In the first step, the entire rotor area was selected for the design region and the distribution of the core and air materials was optimized. In the second step, the design region was limited to the air region of the former solution and the distribution of magnets and cores or magnets and air was optimized.

Because of the two-step process of the proposed method, the design parameters can be reduced compared to the conventional method. As a result, this study can prevent the solution space from becoming more complex and superior solutions can be founded effectively.

Since limited case study is denoted in this paper, much more case studies, for example, three-dimensional optimization problems, are needed to be discussed.

The optimal solutions obtained by the proposed method have a smaller magnet volume and higher average torque than that of the conventional method.

In the proposed methods, optimization methodology, which consists of two-steps process, is differed from the conventional method.

This paper aims to present a deep learning–based surrogate model for fast multi-material topology optimization of an interior permanent magnet (IPM) motor. The multi-material topology optimization based on genetic algorithm needs large computational burden because of execution of finite element (FE) analysis for many times. To overcome this difficulty, a convolutional neural network (CNN) is adopted to predict the motor performance from the cross-sectional motor image and reduce the number of FE analysis.

To predict the average torque of an IPM motor, CNN is used as a surrogate model. From the input cross-sectional motor image, CNN infers dq-inductance and magnet flux to compute the average torque. It is shown that the average torque for any current phase angle can be predicted by this approach, which allows the maximization of the average torque by changing the current phase angle. The individuals in the multi-material topology optimization are evaluated by the trained CNN, and the limited individuals with higher potentials are evaluated by finite element method.

It is shown that the proposed method doubles the computing speed of the multi-material topology optimization without loss of search ability. In addition, the optimized motor obtained by the proposed method followed by simplification for manufacturing is shown to have higher average torque than a reference model.

This paper proposes a novel method based on deep learning for fast multi-material topology optimization considering the current phase angle.

Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.

The paper aims to apply numerical optimization to the aircraft design procedures applied in the airspace industry.

It is harder than ever to achieve competitive construction. This is why numerical optimization is becoming a standard tool during the design process. Although optimization procedures are becoming more mature, yet in the industry practice, fairly simple examples of optimization are present. The more complicated is the task to solve, the harder it is to implement automated optimization procedures. This paper presents practical examples of optimization in aerospace sciences. The methodology is discussed in the article in great detail.

Encountered problems related to the numerical optimization are presented. Different approaches to the solutions of the problems are shown, which have impact on the time of optimization computations and quality of the obtained optimum. Achieved results are discussed in detail with relation to the used settings.

Investigated different aspects of handling optimization problems, improving quality of the obtained optimum or speeding-up optimization by parallel computations can be directly applied in the industry optimization practice. Lessons learned from multidisciplinary optimization can bring industry products to higher level of performance and quality, i.e. more advanced, competitive and efficient aircraft design procedures, which could be applied in the industry practice. This can lead to the new approach of aircraft design process.

Introduction of numerical optimization methods in aircraft design process. Showing how to solve numerical optimization problems related to advanced cases of conceptual and preliminary aircraft design.