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This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method.

Continuous adjoint method is combined with the S2 surface code.

The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection.

The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method.

The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

The presented study aims to minimize the energy consumed by a Hall effect thruster (HET) under a constraint which makes it possible to generate a specified magnetic field in a target region of the thruster.

Herein topology optimization (TO) is used to reduce the energy consumption of an HET while keeping its performance unchanged. The design variables are the current densities in the coils and the distribution of materials in the polar pieces of the thruster. Intermediate values of material distribution are penalized using the solid isotropic material with penalization method to favor binary solutions. By means of the adjoint method, this paper provides the derivatives of the objective and constraint functions with respect to material distribution and current density variables.

The TO-based design methodology is developed and validated on a design example involving 2,051 variables. The approach shows its interest and its effectiveness of on a large scale two-criteria problem.

In this paper, TO is presented as a tool that has allowed to explore new and innovative designs. However, although the design presented is original, its fabrication is not feasible. Despite this, the designs found give a good idea of the starting points for shape and parametric optimization tools.

Through the HET design problem, TO shows the ability to explore more original design possibilities of a complex magnetostatic design problem and to discover designs that make a HET more efficient with respect to several criteria at the same time.

A new way to reduce the energy consumption of a HET is presented. To achieve this, an adjoint-based TO method is developed and then implemented in a simple way. This approach shows that, for efficiency purposes, TO is a key tool for extending the state of the art of HET designs.

Design sensitivities of plates and shells under transient dynamic loads with constraints on displacements and stresses are likely to be highly erroneous if proper care is not taken in selecting appropriate finite element mesh and time step size to be used in the analysis. An accurate value of design derivative is assured if an optimal mesh coupled with a reasonably fine time step size is used. The optimal mesh can be obtained iteratively and a number of examples are solved to demonstrate the importance of controlling discretization errors in space and time.

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.

First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.

The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.

Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

A novel 3D shape optimization algorithm is presented for electromagnetic devices carrying eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity for the surface nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of transformer and the effectiveness is proved.

In the reliability assessment of composite laminate structures with multiple components, the uncertainty space defined around design solutions easily becomes over-dimensioned, and not all of the random variables are relevant. The purpose of this study is to implement the importance analysis theory of Sobol’ to reduce the dimension of the uncertainty space, improving the efficiency toward global convergence of evolutionary-based reliability assessment.

Sobol’ indices are formulated analytically for implicit structural response functions, following the theory of propagation of moments and without violating the fundamental principles presented by Sobol’. An evolutionary algorithm capable of global convergence in reliability assessment is instrumented with the Sobol’ indices. A threshold parameter is introduced to identify the important variables. A set of optimal designs of a multi-laminate composite structure is evaluated.

Importance analysis shows that uncertainty is concentrated in the laminate where the critical stress state is found. Still, it may also be reasonable in other points of the structure. An accurate and controlled reduction of the uncertainty space significantly improves the convergence rate, while maintaining the quality of the reliability assessment.

The theoretical developments assume independent random variables.

Applying Sobol’ indices as an analytical dimension reduction technique is a novelty. The proposed formulation only requires one adjoint system of equilibrium equations to be solved once. Although a local estimate of a global measure, this analytical formulation still holds because, in structural design, uncertainty is concentrated around the mean-values.

The design of multi‐domain that considers all components of electromagnetic systems such as air, iron, magnet, and coil is investigated using topology optimization, interpolation method, and FEM. The design sensitivity equation for topology optimization is derived using the adjoint variable method and the continuum approach. The proposed method is applied to topology optimization of C‐core actuator and shows significant improvement.

The purpose of this paper is to present a new method to obtain robust solutions to electromagnetic optimization problems, solved with evolutional algorithms, which are insensitive to changes in design parameters such as spatial size, positioning and material constant.

Adjoint variable method is employed to evaluate the sensitivity of individuals in evolutional processes.

It is shown in the numerical examples, where the present method is applied to optimization of a superconducting energy storage system and C‐shape magnet, that robust solutions are actually obtained which are insensitive to deviations in spatial sizes.

Unlike usual optimization methods, the present method takes into account deviation in the design parameters due to production errors and long‐term changes. Moreover, the present method is limited to about twice the computational cost of non‐robust optimization methods.

Two new benchmark inverse problems for eddy currents are proposed. The first originates in the optimal design of the tubular inductive heater. The authors’ goal is to offer a simple problem which will check whether new software is able to minimize a multimodal objective function. The second benchmark is a simplified model of a hardening device. The purpose of this problem is to test the ability of the software to deal with different design parameters. This benchmark can be easily extended for more complicated, coupled fields problems. For both benchmarks reference standard solutions are presented. They were obtained using a finite element package for electromagnetics, developed by the authors.

The purpose of this paper is to demonstrate an inverse problem approach for the determination of stress zones in steel plates of electrical machines. Steel plates of electrical machines suffer large mechanical stress by processes like cutting or punching during the fabrication. The mechanical stress has effects on the electrical properties of the steel, and thus on the losses of the machine.

In this paper, the authors present a sensor arrangement and an appropriate algorithm for determining the spatial permeability distribution in steel plates. The forward problem for stress zone imaging is explained and an appropriate numerical solution technique is proposed. Then an inverse problem formulation is introduced and the nature of the problem is analyzed.

Based on sensitivity analysis, different measurement procedures are compared and a measurement setup is suggested. Further the ill‐posed nature of the inverse problem is analyzed by the Picard condition.

Because of the increased losses due to stress zones, the quantification of stress effects is of interest to adjust the production process. Stress zone imaging is a first approach for the application of an imaging system to quantify these material defects.

This paper presents a simulation study about the applicability of an inverse problem for stress zone imaging and presents first reconstruction results. Further, the paper discusses several issues about stress zone imaging for the ongoing research.