Topological Derivative Method Research Articles

A Novel Topology Derivation Method Revealed From Classical Cuk, Sepic, and Zeta Converters

A Novel Topology Derivation Method Revealed From Classical Cuk, Sepic, and Zeta Converters

Topology derivation and control method of high‐reliability buck‐boost double‐grounded transformerless three‐phase inverters

SummaryAs the traditional transformerless three‐phase (TTP) inverters have the shoot‐through and common mode leakage current (CMLC) problems, as well as not being able to realize the buck‐boost conversion, topology derivation and control method of high‐reliability buck‐boost double‐grounded TTP inverters are proposed. These topologies consist of two‐port or three‐port converters with boost capability and three dual‐buck inverters. The two‐port or three‐port converters with boost capability provide the positive and negative bus voltages for the three dual‐buck inverters, realizing the boost conversion. The dual‐buck inverters address the shoot‐through problem. The double‐grounded structure is used to solve the CMLC problem. Dead time between switches is not needed, which reduces the complexity of the control system. Detailed topology derivation of the dual‐buck double grounded TTP inverters with boost capability is given. The operating principle, parameters design of the filters, and stability analysis of this inverter are analyzed in detail. Loss analysis of the inverter is given. The simulation and experimental results of a 750‐W TTP inverter are used to verify the theoretical analysis.

Topology optimization of three-dimensional structures subject to self-weight loading

PurposeTopology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.Design/methodology/approachIn order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.FindingsA novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.Originality/valueAn alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

A Novel Systematic Topology Derivation Method for Single-Inductor Three-Port DC-DC Converters from Separate Components

A Novel Systematic Topology Derivation Method for Single-Inductor Three-Port DC-DC Converters from Separate Components

From Components to Converters: A Fundamental Topology Derivation Method for Nonresonant DC–DC Converters Based on Graph Theory

From Components to Converters: A Fundamental Topology Derivation Method for Nonresonant DC–DC Converters Based on Graph Theory

A noniterative reconstruction method for the inverse potential problem for a time-fractional diffusion equation

This paper is concerned with the reconstruction of the support of the potential term for a time-fractional diffusion equation from the final measured data. The aim of this paper is to propose an accurate approach based on the topological derivative method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing a given cost function. We derive a topological asymptotic expansion for the fractional model. The unknown support is reconstructed using the level-set curve of the topological gradient. We finally make some numerical examples proving the efficiency and accuracy of the proposed algorithm.

Directed Graph-Based Topology Derivation Method for Single-Stage Multiport Inverters

Directed Graph-Based Topology Derivation Method for Single-Stage Multiport Inverters

Reconstruction and stability analysis of potential appearing in time‐fractional subdiffusion

In this work, we establish a local stability estimate for a problem involving the reconstruction of a domain in the time‐fractional diffusion equation with an order of : from the knowledge of a Neumann additional data on a part of the boundary. This problem is motivated by several applications in anomalous diffusion phenomena. The stability estimate is obtained through a straightforward approach utilizing shape optimization techniques. To reconstruct the domain , we formulate the inverse problem as a shape optimization one by minimizing a least‐squares cost function. Using the topological derivative method, we perform a noniterative algorithm for numerically recovering the location and shape of the unknown domain. Finally, we demonstrate the effectiveness of our approach in reconstructing multiple subdomains of varying shapes and sizes, considering noisy data, through numerical experiments.

Topology Derivation of Multiport DC–DC Converters Based on Reinforcement Learning

Multiport dc–dc convertersare attracting wide attention in various applications. However, conventional topology derivation methods for multiport dc–dc converters are usually intricate and time-consuming. In this article, a reinforcement learning (RL)-based topology derivation method is proposed, which can derive topologies of complex converters quickly. To apply the RL framework, the topology derivation process is regarded as a Markov decision process. In each step, the agent selects and connects two components until a complete topology is made. To ensure that the derived topologies are feasible and match given voltage specifications, basic circuit constraints and duty cycle constraints are added as hard constraints. Soft constraints are also added to obtain optimal circuits with low voltage stresses or low current stresses. The testing on topology derivation of multiport dc–dc converters shows the great speed of the proposed method. Simulation and experimental results verify that the derived topologies cannot only satisfy given voltage specifications, but also achieve optimization targets of low voltage stresses or current stresses.

Multi-material topology optimization for additive manufacturing considering dimensional constraints

Recent advances in additive manufacturing have enabled the fabrication of structures in which members made of multiple materials are placed in appropriate positions. However, dimensional constraints must be considered in such a process because of the size limitations of the 3D printer. This paper proposes a topology optimization method that considers the dimensional constraints of each material component. An extended level-set method is used to represent multiple material phases in the structural design. Constraint functions are formulated to control the size of each component. The weighted covariance matrix is used for the bounding box constraint. The sensitivity is based on the topological derivative and adjoint variable method. The proposed method was applied to solving the minimum compliance problem for two- and three-dimensional numerical examples to demonstrate its effectiveness and its potential contribution to enriching designs in additive manufacturing.

Imaging of mass distributions from partial domain measurement

Abstract This paper deals with an inverse source problem governed by the Poisson equation. The aim is to reconstruct multiple anomalies from internal observation data within an arbitrary sub-region. The considered model problem is motivated by various applications such as the identification of geological anomalies underneath the Earth’s surface. To overcome the ill-posedness, the inverse problem is formulated as a self-regularized topology optimization one. A least-square functional measuring the misfit between the observed quantities and the values provided by the model problem is introduced. The misfit function involves a regularization term penalizing the relative perimeter of the unknown domain. Finally, it is minimized with respect to a finite number of circular-shaped anomalies. The existence and stability of the solution to the inverse problem are demonstrated. The reconstruction process is based on the topological derivative method. The variation of the shape functional with respect to a small geometric perturbation is studied, and the leading terms of a second-order topological asymptotic expansion are derived. A non-iterative reconstruction algorithm is developed via the minimization of the obtained asymptotic formula with respect to the location and size parameters of the unknown set of anomalies. The efficiency and accuracy of the proposed approach are justified by some numerical experiments.

Damage identification in plate structures based on the topological derivative method

Damage identification in plate structures based on the topological derivative method

Topology design optimization of nanophotonic devices for energy concentration

In this work, a novel topology optimization method for the synthesis of nanophotonic energy concentrators is proposed. The forward problem is governed by the Maxwell equations in the frequency domain. The basic idea consists in finding the best two phase material distribution that concentrates the energy in a given target domain. More precisely, a shape functional measuring the electrical energy of the system within a small region of the nanodevice is maximized with respect to silicon and glass spatial distribution by using the topological derivative method. Therefore, since the resulting optimization method is based on a scattering problem formulation, any issues that would come from eigenmode calculations are here avoided. In addition, the proposed shape functional can be properly defined both outside or overlapping the design (moving) domain itself, increasing the range of applications of the proposed approach. The associated topological gradient is rigorously derived and used to devise a simple and efficient black/white binary topology design algorithm, which naturally conforms to practical fabrication constraints for nanodevices. Finally, a set of numerical experiments are presented showing different features of the proposed approach, including its capability in selectively producing the required hot-spots within the nanodevices.

A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements

In this paper, a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation is proposed. The basic idea consists in reconstructing the geometrical support of the unknown source from partial boundary measurements of the associated potential. A Kohn–Vogelius type shape functional is considered together with a regularization term penalizing the relative perimeter of the unknown set of anomalies. Identifiability result is derived and uniqueness of a minimizer is ensured. The shape functional measuring the misfit between the solutions of two auxiliary problems containing information about the boundary measurements is minimized with respect to a finite number of ball-shaped trial anomalies by using the topological derivative method. In particular, the second-order topological gradient is exploited to devise an efficient and fast noniterative reconstruction algorithm. Finally, some numerical experiments are presented, showing different features of the proposed approach in reconstructing multiple anomalies of varying shapes and sizes by taking noisy data into account.

Topology optimization of structures subject to self-weight loading under stress constraints

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

Brittle fracture on plates governed by topological derivatives

PurposeIn the paper an approach for crack nucleation and propagation phenomena in brittle plate structures is presented.Design/methodology/approachThe Francfort–Marigo damage theory is adapted to the Kirchhoff and Reissner–Mindlin plate bending models. Then, the topological derivative method is used to minimize the associated Francfort–Marigo shape functional. In particular, the whole damaging process is governed by a threshold approach based on the topological derivative field, leading to a notable simple algorithm.FindingsNumerical simulations are driven in order to verify the applicability of the proposed method in the context of brittle fracture modeling on plates. The obtained results reveal the capability of the method to determine nucleation and propagation including bifurcation of multiple cracks with a minimal number of user-defined algorithmic parameters.Originality/valueThis is the first work concerning brittle fracture modeling of plate structures based on the topological derivative method.

Experimental validation of a topological derivative-based crack growth control method using digital image correlation

PurposeThe purpose of this paper is to experimentally validate the crack growth control based on the topological derivative of the famous Rice's integral.Design/methodology/approachSingle edge notch tensile specimens with two configurations were tested. Displacement fields near notch were experimentally obtained using the digital image correlation method. These displacements were used to verify the minimization of the associated shape functional, which is defined in terms of the Rice's integral, when a set of controls (holes) positioned according to the topological derivative information, is inserted. Based on the Griffth's energy criterion, this minimization represents an improvement in the fracture toughness of cracked bodies.FindingsThe experimental tests confirmed that a decrease around 27% in the value of the associated shape functional can be obtained following this approach. Therefore, the results allow us to conclude that the predictive methodology for crack growth control based on the topological derivative is feasible.Originality/valueThis is the first work concerning experimental validation of crack growth control based on the topological derivative method.

Imaging of small penetrable obstacles based on the topological derivative method

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Topology Derivation of Multiple-Port DC–DC Converters Based on Voltage-Type Ports

Multiple-port dc–dc converters are characterized by a variety of kinds and a large number of circuit topologies. In this article, we aim to reveal the intrinsic relationship among the topologies of multiple-port dc–dc converters and propose the topology derivation method. First, the voltage- and current-type ports are summarized from basic dc–dc converters, and the approach of converting current-type ports into voltage-type ports is discussed. Then, according to Kirchhoff's law, four types of multiple-input multiple-output converters named input-port-series output-port-series, input-port-series output-port-parallel, input-port-parallel output-port-series, and input-port-parallel output-port-parallel are presented. Second, the topology derivation method of multiple-port bidirectional dc–dc converters based on the voltage-type ports is studied in terms of power flow paths in various operation modes, and then the topology optimization method is proposed. Particularly, a flow diagram for the optimal design procedure is given to guide the topology derivation for some specific requirements. Based on the proposed approach, a family of multiple-port dc–dc converters can be derived, which provides lots of viable candidates for practical engineering. Furthermore, one derived converter named the parallel-type three-port bidirectional buck converter is analyzed in three operation modes to demonstrate the topology derivation. Finally, the effectiveness of the above theoretical analysis is verified by those experimental results.

A Shape Optimization Technique for Medical Images

Segmentation and restoration are among the primary objectives in the field of medical image processing. Among many methods available today, derivative method specifically domain based derivative method helps immensely in this field of medical imaging. There was a time-based improvement in the aspects of establishing results in a medical image with the aid of topological derivative. Advantage of this method lies in establishing a link between that of the perturbed domain and that of the original domain and solving for the required metrics in the problem. Treating the original domain as the original image and the diseased image to be the perturbed domain, topological derivative helps to solve the problem. Asymptotic analysis also helps in handling both large and small amount of data based on the big-O notation and small-o notation. It also establishes the supremacy of topological derived image metrics to that of other metrics. Here attempts are made for solving problems in medical images with the help of topological derivative method by adapting minimization procedure. Also, the end results are arrived in an outstanding way with help of the receiver operating characteristic curve.