Total variation regularization of multi-material topology optimization

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.

A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images

Preliminary design and optimization of toroidally-wound limited angle servo motor based on a generalized magnetic circuit model

This paper proposes a new generalized equivalent magnetic circuit model for the preliminary design of a toroidally-wound limited angle servo motor (LASM). In the model, the magnetic networks are formulated as a function of the pole number and geometric dimensions. Nonlinear saturation effect of the ferromagnetic material is also taken into consideration. A multi-objective optimization function involving the torque requirement, the mass, the time constant, and magnetic saturations of ferromagnetic material is introduced. Based on the proposed model, six design cases with different objectives have been carried by the particle swarm optimization (PSO) method. The comparisons of different optimization cases demonstrate the effectiveness and computation efficiency of the proposed method, and hence its suitability in preliminary design. Moreover, the generalized model can be readily applied in the other electromagnetic modelling

A case study of process facility optimization using discrete event simulation and genetic algorithm

Optimization problems such as resource allocation, job-shop scheduling, equipment utilization and process scheduling occur in a broad range of processing industries. This paper presents modeling, simulation and optimization of a port facility such that effective operational management is obtained. A GA base approach has been integrated with the port system model to optimize its operation. A case study of bulk material port handling systems is considered

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models

Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: \removed{downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization} \added{particle swarm optimization, differential evolution, and Bayesian optimization as well as multi-start versions of downhill simplex optimization and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm}. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.Comment: 11 pages, 4 figure

Computer program for transient response of structural rings subjected to fragment impact

Mathematical optimization of containment/deflection system would save time, effort, and material as well as afford designer greater opportunity to investigate new ideas and variety of materials