Topological Derivative Method Research Articles

Topological derivative-based topology optimization of structures subject to self-weight loading

Topology optimization of structures subject to self-weight loading has received considerable attention in the last decades. However, by using standard formulations based on compliance minimization under volume constraint, several difficulties arise once the self-weight of the structure becomes dominant, including non-monotonic behavior of the compliance, possible unconstrained character of the optimum, and parasitic effects for low densities when using density-based methods. In order to overcome such difficulties, a regularized formulation that allows for imposing any feasible volume constraint is proposed. The standard formulation based on compliance minimization under volume constraint is recovered when the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method leading to a 0-1 topology design algorithm, which seems to be crucial when the self-weight loading is dominant. Finally, several numerical experiments are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading.

Principle and Topology Derivation of Integrated Cascade Bidirectional Converters for Centralized Charge Equalization Systems

This article presents a systematic topology derivation method for developing integrated cascaded bidirectional (ICB) converters, and the centralized charge equalization system can be optimized with the proposed family of converters. On the basis of the traditional centralized system, the proposed ICB converters are generated by integrating the polarity switches and different bidirectional dc–dc converters. Compared with existing methods, the ICB converter-based centralized equalization system obtains the advantages of high voltage gain, high efficiency, high reliability, and low cost, which is more attractive in engineering applications. Since different topology structures have various performances, a half-bridge-based ICB converter with a bidirectional switch is analyzed in detail as an example to validate the feasibility and effectiveness of the proposed topology family. The operation principles, design guidelines, and soft-switching conditions are discussed in more depth. Finally, the experimental results and comparative analysis are conducted to verify the advantages of the proposed ICB converter and prove the evident performance improvement compared with conventional methods.

Pointwise antennas design in hyperthermia therapy

This work deals with pointwise antennas design in hyperthermia treatment. Hyperthermia is a non-invasive therapy usually combined with chemotherapy and/or radiotherapy, which consists in heating the diseased tissue in an attempt to kill the cancerous cells. In particular, we want to find the optimal values of current densities passing through each antenna to selectively heat a specified target. The forward problem is governed by the steady-state heat equation in living tissues which is coupled with the Helmholtz problem modeling the electromagnetism phenomenon. An objective functional measuring the difference between the target temperature and the solution to the model problem is minimized with respect to the current densities by using the topological derivative method. The resulting sensitivities are used to devise first and second order antenna design algorithms as well as a third one that combines both the previous algorithms. Numerical experiments are presented showing different features of the proposed methodology, including its capability in selectively heating the target up to the desired temperature. Finally, a selected result is used in a full transient analysis, where the hot spots are keeping over the diseased tissues during the whole heating process.

Topological asymptotic analysis of a diffusive–convective–reactive problem

PurposeThe purpose of this study is sensitivity analysis of the L2-norm and H1-seminorm of the solution of a diffusive–convective–reactive problem to topological changes of the underlying material.Design/methodology/approachThe topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method.FindingsRemarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization.Originality/valueThe topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.

On the Kohn–Vogelius formulation for solving an inverse source problem

An inverse source problem related to the Poisson equation is the main concern of this work. Specifically, we deal with the reconstruction of a mass distribution in a geometrical domain from a partial boundary measurement of the associated potential. The considered problem is motivated by various applications such as the identification of geological anomalies underneath the Earth's surface. The proposed approach is based on the Kohn–Vogelius formulation and the topological derivative method. An explicit second-order sensitivity related to circular shaped anomalies is calculated for different examples of the Kohn–Vogelius type functional. Then, the optimal location and size of the unknown support of the mass distribution are characterized as the solution to a minimization problem. The resulting reconstruction procedure is non-iterative and robust with respect to noisy data. Finally, we produce numerical results from four different examples of the Kohn–Vogelius type functional. The results first demonstrate the method and then compare the robustness of each functional in solving the inverse source problem.

General Topology Derivation Methods and Control Strategies of Field Winding-Based Flux Adjustable PM Machines for Generator System in More Electric Aircraft

The field winding-based flux adjustable permanent magnet (FWFAPM) machines, including the hybrid excitation (HE) topology and the memory topology, can offer excellent capabilities in terms of flux regulation, wide constant power operation as well as de-excitation (flux-weakening) under fault; thus, they are capable for use in More Electric Aircraft (MEA) generator systems. First, this article probes four basic HE modes, and based on that, a general method deriving permanent magnet (PM) machines to HE machines is established. The basic characteristics of each HE mode considering the relationship between S-pole and N-pole are obtained for the first time. The performance differences of each HE mode combined with different PM machines are summarized. Then, this general topology derivation method is extended for the memory topology. The unified derivation method of the single-PM topologies, the double-PM topologies, and the triple-PM topologies for memory machines is systematically established. The general laws of the electromagnetic performance of each double-PM mode and triple-PM mode considering different relationships between NdFeB and AlNiCo are summarized for the first time. Finally, the control strategies for voltage regulation of aircraft generator systems are discussed based on the different critical control variables and controller types; a torque impulse balance control method which shows excellent dynamic performance for both target control variable and critical control variable has been achieved experimentally.

Pollution Sources Reconstruction Based on the Topological Derivative Method

The topological derivative method is used to solve a pollution sources reconstruction problem governed by a steady-state convection-diffusion equation. To be more precise, we are dealing with a shape optimization problem which consists of reconstruction of a set of pollution sources in a fluid medium by measuring the concentration of the pollutants within some subregion of the reference domain. The shape functional measuring the misfit between the known data and solution of the state equation is minimized with respect to a set of ball-shaped geometrical subdomains representing the pollution sources. The necessary conditions for optimality are derived with the help of the topological derivative method which consists in expanding the shape functional asymptotically and then truncate it up to the second order term. The resulting expression is trivially minimized with respect to the parameters under consideration which leads to a noniterative second-order reconstruction algorithm. Two different cases are considered. Firstly, when the velocity of the leakages is given and we reconstruct the support of the unknown sources, including their locations and sizes. In the second case, we consider the size of the pollution sources to be known and find out the mean velocity of the leakages and their locations. Numerical examples are presented showing the capability of the proposed algorithm in reconstructing multiple pollution sources in both cases.

Optimization of the electromagnetic scattering problem based on the topological derivative method.

A new optimization method based on the topological derivative concept is developed for the electromagnetic design problem. Essentially, the purpose of the topological derivative method is to measure the sensitivity of a given shape functional with respect to a singular domain perturbation, so that it has applications in many relevant fields such as shape and topology optimization for imaging processing, inverse problems, and design of metamaterials. The topological derivative is rigorously derived for the electromagnetic scattering problem and used as gradient descent direction to find local optima for the design of electromagnetic devices. We demonstrate that the resulting topology design algorithm is remarkably simple and efficient and naturally leads to binary designs, while depending only on the solution of the conventional finite element formulation for electrodynamics. Finally, several numerical experiments in two and three spatial dimensions are presented to illustrate the performance of the proposed formulation.

An Overview of Capacitive DC-Links-Topology Derivation and Scalability Analysis

Capacitive dc-links are widely used in voltage source converters for power balance, voltage ripple limitation, and short-term energy storage. A typical solution, which uses aluminum electrolytic capacitors for such applications, is assumed to be one of the weakest links in power electronic systems, therefore, also becoming one of the lifetime bottlenecks of power electronic systems. Various passive and active capacitive dc-link solutions have been proposed intending to improve the reliability of the dc-links qualitatively, making great effort to diverting the instantaneous pulsating power into extra reliable storage components. In this paper, a generic topology derivation method for single-phase power converters with active capacitive dc-link integrated has been proposed, which can derive all existing topologies, and identify a few new topologies. According to the synthesis results, the main achievements in research on capacitive dc-link solutions are reviewed and presented chronologically as well as thematically ordered. Furthermore, the reliability-oriented design procedure is applied to size the chip area of active switching devices and the passive components to fulfill a specific lifetime target and system specification, as well as compare the overall capacitive energy storage, energy buffer ratio, and the cost of different solutions. The cost comparisons are performed with a scalable lifetime target and power rating. It reveals that different conclusions can be drawn with different lifetime targets in terms of cost-effectiveness.

Programmable Topology Derivation and Analysis of Integrated Three-Port DC-DC Converters with Reduced Switches for Low-Cost Applications

Thanks to the favorable advantage of low cost, integrated three-port dc–dc converters with reduced switches have attracted extensive attention. In order to provide more new topologies, this paper aims to propose a programmable topology derivation method, which effectively simplifies the cumbersome process of the conventional combination method. Instead of the manual connection and examination, the proposed alternative can quickly and rigorously derive multiple viable integrated three-port dc–dc topologies from a great number of possible connections with the aid of computer program. Besides, generalized analysis is also accomplished, with which performance characteristics of all derived converters are simultaneously obtained and then a comprehensive comparison can be easily conducted to select a preferred one for the practical application. Finally, an example-specific application with one input and two outputs is given, with topology selection, design, and experimental results demonstrated in detail.

A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

Dual-DC-Port Asymmetrical Multilevel Inverters With Reduced Conversion Stages and Enhanced Conversion Efficiency

A new concept of dual-dc-port asymmetrical multilevel inverter (DP-AMI), which is able to interface a low-voltage dc port, a high-voltage dc port, and an ac port simultaneously using only one topology, is presented in this paper. A systematic method to derive the DP-AMI is proposed. With the proposed DP-AMI, a low-voltage dc source, e.g., photovoltaic (PV) modules or battery, can directly supply power to the ac load within single-stage power conversion. Therefore, in comparison with a traditional two-stage dc/ac power conversion system, the power conversion stages are reduced and the voltage/current stress of the front-end dc/dc converter can be significantly alleviated, which can improve the overall conversion efficiency dramatically. Furthermore, by using the low-voltage dc source as a new voltage level, asymmetrical multiple voltage levels are generated by the proposed DP-AMI, which is beneficial for the reducing switching losses and the size/volume of the output filter. The topology derivation method of the DP-AMIs is presented. The operation principles, modulation schemes, and characteristics of one of the proposed DP-AMIs are analyzed in detail. A 1-kW prototype is built and tested to verify the effectiveness and advantages of the proposed method.

Secondary-Side-Regulated Soft-Switching Full-Bridge Three-Port Converter Based on Bridgeless Boost Rectifier and Bidirectional Converter For Multiple Energy Interface

A systematic method for deriving soft-switching three-port converters (TPCs), which can interface multiple energy, is proposed in this paper. Novel full-bridge (FB) TPCs featuring single-stage power conversion, reduced conduction loss, and low-voltage stress are derived. Two nonisolated bidirectional power ports and one isolated unidirectional load port are provided by integrating an interleaved bidirectional Buck/Boost converter and a bridgeless Boost rectifier via a high-frequency transformer. The switching bridges on the primary side are shared; hence, the number of active switches is reduced. Primary-side pulse width modulation and secondary-side phase shift control strategy are employed to provide two control freedoms. Voltage and power regulations over two of the three power ports are achieved. Furthermore, the current/voltage ripples on the primary-side power ports are reduced due to the interleaving operation. Zero-voltage switching and zero-current switching are realized for the active switches and diodes, respectively. A typical FB-TPC with voltage-doubler rectifier developed by the proposed method is analyzed in detail. Operation principles, control strategy, and characteristics of the FB-TPC are presented. Experiments have been carried out to demonstrate the feasibility and effectiveness of the proposed topology derivation method.

Multiport Converters Based on Integration of Full-Bridge and Bidirectional DC–DC Topologies for Renewable Generation Systems

A systematic method for deriving multiport converters (MPCs) from the full bridge (FB) converter (FBC) and bidirectional dc-dc converters (BDCs) is proposed in this paper through sharing the parasitized switching legs by the BDCs and the FBC. By employing the proposed method, families of FB and BDC-based MPCs (FB-BDC-MPCs), including some existing ones, are developed for renewable generation systems with the merits of simple topology, reduced devices, and single-stage power conversion. Voltage regulations between any two ports can be achieved by employing pulsewidth modulation and phase-angle-shift control scheme. Furthermore, zero-voltage switching for all the switches can be realized in the proposed FB-BDC-MPCs. A typical four-port converter developed by the proposed method, named buck/boost four-port converter (BB-FPC), is analyzed in detail as an example in terms of operation principles, design considerations, and control strategy. Experiments have been carried out on a 500-W prototype of BB-FPC, which demonstrate the feasibility and effectiveness of the proposed topology derivation method.

Topology Derivation of Nonisolated Three-Port DC–DC Converters From DIC and DOC

A systematic approach is proposed for the derivation of nonisolated three-port converter (TPC) topologies based on dual-input converters (DIC) and dual-output converters (DOC), which serves as an interface for a renewable source, a storage battery, and a load simultaneously. The power flow in a TPC is analyzed and compared with that in a DIC or a DOC, respectively. Beginning with building the power flow paths of a TPC from a DIC or a DOC, the general principles and detailed procedures for the generation and optimization of TPC topologies are presented. Based on these works, a family of nonisolated TPC topologies is developed. The derived TPCs feature single-stage power conversion between any two of the three ports, and result in high integration and high efficiency. One of the proposed TPCs, named Boost-TPC, is taken as an example for verifying the performance of its circuit topology with related operational methods. Pulsewidth modulation and power management methods, used in this circuit, are analyzed in detail. Experiments have been carried out on a 1-kW prototype of the Boost-TPC, which demonstrate the feasibility and effectiveness of the proposed topology derivation method.

Multi-object segmentation approach based on topological derivative and level set method

In this paper we propose a segmentation approach that applies the topological derivative as a pre-processing step. The obtained result is used for initializing a Level Set model in order to get the final result. First, the method uses a low-pass filt

Level set method for optimization of contact problems

This paper deals with the numerical solution of topology and shape optimization problems of an elastic body in unilateral contact with a rigid foundation. The contact problem with the prescribed friction is described by an elliptic variational inequality of the second order governing a displacement field. The structural optimization problem consists in finding such shape of the boundary of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The shape of this boundary and its evolution is described using the level set approach. Level set methods are numerically efficient and robust procedures for the tracking of interfaces. They allow domain boundary shape changes in the course of iteration. The evolution of the domain boundary and the corresponding level set function is governed by the Hamilton–Jacobi equation. The speed vector field driving the propagation of the level set function is given by the Eulerian derivative of an appropriately defined functional with respect to the free boundary. In this paper the necessary optimality condition is formulated. The level set method, based on the classical shape gradient, is coupled with the bubble or topological derivative method, which is precisely designed for introducing new holes in the optimization process. The holes are supposed to be filled by weak phase mimicking voids. Since both methods capture a shape on a fixed Eulerian mesh and rely on a notion of gradient computed through an adjoint analysis, the coupling of these two method yields an efficient algorithm. Moreover the finite element method is used as the discretization method. Numerical examples are provided and discussed.

A topological derivative method for topology optimization

We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.

Energy change due to the appearance of cavities in elastic solids

The paper presents an overview of the problem of assessing an increment of strain energy due to the appearance of small cavities in elastic solids. The following approaches are discussed: the compound asymptotic method by Mazja et al., the Eshelby-like method used in the classical works on the mechanics of composites, the homogenization method, and the topological derivative method proposed by Sokołowski and Żochowski. The increment of energy is expressed by a quadratic form with respect to strains referring to the virgin solid. All the methods lead to the same formula for the increment of energy. It is expressed by a quadratic form with respect to strains referring to the virgin solid. This quadratic form turns out to be unconditionally positive definite. Explicit formulae are derived for an elliptical hole and for a spherical cavity. The results derived determine the characteristic function of the bubble method of the optimal shape design of elastic 2D and 3D structures.

Optimality Conditions for Simultaneous Topology and Shape Optimization

New optimality conditions are derived for a class of shape optimization problems. The conditions are established on the boundary by an application of the boundary variations technique and in the interior of an optimal domain by exploiting the topological derivative method. An example is provided for which the classical second order sufficient optimality conditions are verified for an optimal simply connected domain. However, the value of the cost can be improved by the topology variations, and therefore, the optimal solution can be substantially changed by applying the topology optimization.