Parametric Level-set Approach Research Articles

Stress-based shape and topology optimization with cellular level set in B-splines

A parametric level set approach based on B-splines is developed for the stress-based shape and topology optimization of cellular structures. In this method, the whole design domain is divided into a set of non-overlapping sub-domains, within each of which the structure is represented by an implicit B-spline level set function. This parameterization scheme ensures that the adjacent cells can be smoothly connected. The stress value of the structure is computed by using a p-norm function-based aggregation. The extended finite element method is implemented to calculate the structural stress. Moreover, a new optimization strategy based on a two-field formulation is proposed to eliminate numerical instability in the optimization process. A continuity scheme based on the least square method is proposed to guarantee the high-order connectivity at the adjacent cell boundary. In addition, optimized cellular structures with different cell partitions are obtained and discussed. Several numerical examples are presented to illustrate the applicability of the approach.

Pixel- and Model-Based Microwave Inversion With Supervised Descent Method for Dielectric Targets

We present a general framework of applying supervised descent method (SDM) to the pixel- and model-based full-wave inversion of microwave data for dielectric targets. SDM is a machine learning approach that utilizes the learned descent directions to reconstruct models. In this article, we study the pixel-based inversion with an online regularization scheme, and the model-based inversion with the parametric level set approach. Furthermore, an online restart scheme is studied to further reduce the data residual. In addition, we investigate the generalization ability of this machine-learning algorithm. In the numerical test, the pixel-based SDM inversion are used to process both single- or multi-frequency data, and the model-based inversion are performed on data with limited observations. Both synthetic and experimental results show good accuracy, speed, and generalization ability of this algorithm. SDM may provide us a potential way to improve reconstruction quality in nonlinear inversion through information fusion of measured data, microwave physics, and various prior information.

Weight Optimization of Thick Plate Structures Using Radial Basis Functions Parameterization

This study sought to optimize the weight of thick plate structures with topology optimization. Topology optimization is a numerical method for identification of voids in the design domain, to aid weight and material reduction. The level set approach is a new method in topology optimization. In this work, the radial basis functions level set approach is used to parameterize the continuum domain. The radial basis functions are used to parameterize the level set functions, which comprise axial symmetric, real value functions. These functions are suitable tools for function approximation. Thick plates are one of the most useful and familiar geometries in structural and mechanical engineering applications. Topology optimization of such structures would be very useful to identify efficient and lightweight plate structures. In this paper, the effectiveness of the parametric level set approach in topology optimization of clamped plate is demonstrated. The results show smooth boundaries and there are no intermediate densities, which constitutes a major advantage.

Concurrent optimization of structural topology and infill properties with a CBF-based level set method

In this paper, a parametric level-set-based topology optimization framework is proposed to concurrently optimize the structural topology at the macroscale and the effective infill properties at the micro/meso scale. The concurrent optimization is achieved by a computational framework combining a new parametric level set approach with mathematical programming. Within the proposed framework, both the structural boundary evolution and the effective infill property optimization can be driven by mathematical programming, which is more advantageous compared with the conventional partial differential equation-driven level set approach. Moreover, the proposed approach will be more efficient in handling nonlinear problems with multiple constraints. Instead of using radial basis functions (RBF), in this paper, we propose to construct a new type of cardinal basis functions (CBF) for the level set function parameterization. The proposed CBF parameterization ensures an explicit impose of the lower and upper bounds of the design variables. This overcomes the intrinsic disadvantage of the conventional RBF-based parametric level set method, where the lower and upper bounds of the design variables oftentimes have to be set by trial and error. A variational distance regularization method is utilized in this research to regularize the level set function to be a desired distanceregularized shape. With the distance information embedded in the level set model, the wrapping boundary layer and the interior infill region can be naturally defined. The isotropic infill achieved via the mesoscale topology optimization is conformally fit into the wrapping boundary layer using the shape-preserving conformal mapping method, which leads to a hierarchical physical structure with optimized overall topology and effective infill properties. The proposed method is expected to provide a timely solution to the increasing demand for multiscale and multifunctional structure design.

A Robust Scheme of Vertebrae Segmentation for Medical Diagnosis

Precise and reliable segmentation of vertebral column is crucial for accurate computer aided diagnostic system (CADx). It assists the radiologists and doctors in identifying various pathologies in the vertebrae with better visualizations. Accurate segmentation of vertebral disks and bones from the medical images is a tough job and becomes more challenging when dealing with various deformities and pathologies. While remarkable success was achieved by deep convolutional neural networks (DCNNs) in medical image segmentation, it is still a difficult task for DCNNs to handle the medical image segmentation problems with various deformities and anatomical complexities. In this paper, we propose a novel and efficient framework to address the subject problem by integrating a parametric level set approach in deep convolutional neural networks. The proposed scheme utilizes the probability map of pre-trained deep network to initialize the level set and it refines the output iteratively under the action of various forces to fine-tune the training of deep network. Thus the learning of the network is improved and the network is able to accommodate high topological shape variations in the vertebrae. This proposed method was evaluated on two different datasets. The first one is 20 publically available 3D spine MRI dataset to perform disc segmentation and the second one is 173 computed tomography scans for thoracolumbar (thoracic and lumbar) vertebrae segmentation. The dice score was found to be 90.37 ± 0.9 percent for disks segmentation and 94.7 ± 1.1 with ASSD of 0.1 ± 0.04 mm for thoracolumbar vertebrae segmentation. The results reveal that our proposed method is robust over multiple segmentations and outperformed the recently published state of art methods.

Parametric shape and topology optimization: A new level set approach based on cardinal basis functions

SummaryThe parametric level set approach is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, level set methods can be directly coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Moreover, the parametric level set scheme can not only inherit the primary advantages of the conventional level set methods, such as clear boundary representation and the flexibility in handling topological changes, but also alleviate some undesired features from the conventional level set methods, such as the need for reinitialization. However, in the existing radial basis function–based parametric level set method, it is difficult to identify the range of the design variables. Besides, the parametric level set evolution often struggles with large fluctuations during the optimization process. Those issues cause difficulties both in numerical stability and in material property mapping. In this paper, a cardinal basis function is constructed based on the radial basis function partition of unity collocation method to parameterize the level set function. The benefit of using cardinal basis function is that the range of the design variables can now be clearly specified as the value of the level set function. A distance regularization energy functional is also introduced, aiming to maintain the desired signed distance property during the level set evolution. With this desired feature, the level set evolution is stabilized against large fluctuations. In addition, the material properties mapped from the level set function to the finite element model can be more accurate.

3D parametric hybrid inversion of time-domain airborne electromagnetic data

We have developed a method to invert time-domain airborne electromagnetic (AEM) data using a parametric level-set approach combined with a conventional voxel-based technique to form a parametric hybrid inversion. The approach was designed for situations in which a voxel-based inversion alone may struggle. Such an example is where a distinct anomaly is present with sharp boundaries, and there is a large contrast between a low-resistivity target and a high-resistivity background. The first step of the proposed hybrid method used our novel parametric inversion to recover a best-fitting skewed Gaussian ellipsoid that represented the target of interest. Subsequently, the parametric result was set as an initial and reference model for the second stage, where smooth features with smaller resistivity contrasts were introduced into the model through a conventional voxel-based approach. The approach was tested with synthetic and field data. In the synthetic case, we recovered the size and dip of a conductive, thin, dipping plate with better accuracy compared with a voxel-based inversion. In the field example, we inverted AEM data over the Caber volcanogenic massive sulfide deposit. Based on information from past drilling, our results improve upon previous parametric plate inversions of the deposit itself, while additionally imaging the conductive cover over the deposit. These findings showcased how our parametric hybrid method can improve the accuracy of time-domain AEM inversions for thin dipping targets with large resistivity contrasts compared with the background.

A Parametric Level-Set Approach to Simultaneous Object Identification and Background Reconstruction for Dual-Energy Computed Tomography

Dual-energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual-energy processing algorithm, with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown cluttered background. Physical properties of the objects, particularly the Compton scattering and photoelectric absorption coefficients, are assumed to be known with some level of uncertainty. Our approach is based on a level-set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object and the fundamental physics-based limitations associated with our ability to jointly recover the Compton scattering and photoelectric absorption properties of the scene. In the absence of an object with appropriate physical properties, our approach returns a null characteristic function and, thus, can be viewed as simultaneously solving the detection and characterization problems. Unlike the vast majority of methods that define the level-set function nonparametrically, i.e., as a dense set of pixel values, we define our level set parametrically via radial basis functions and employ a Gauss-Newton-type algorithm for cost minimization. Numerical results show that the algorithm successfully detects objects of interest, finds their shape and location, and gives an adequate reconstruction of the background.

A parametric level-set approach for topology optimization of flow domains

Traditional methods based on an element-wise parameterization of the material distribution applied to the topology optimization of fluidic systems often suffer from slow convergence of the optimization process, as well as robustness issues at increased Reynolds numbers. The local influence of the design variables in the traditional approaches is seen as a possible cause for the slow convergence. Non-smooth material distributions are suspected to trigger premature onset of instationary flows which cannot be treated by steady-state flow models. In the present work, we study whether the convergence and the versatility of topology optimization methods for fluidic systems can be improved by employing a parametric level-set description. In general, level-set methods allow controlling the smoothness of boundaries, yield a non-local influence of design variables, and decouple the material description from the flow field discretization. The parametric level-set method used in this study utilizes a material distribution approach to represent flow boundaries, resulting in a non-trivial mapping between design variables and local material properties. Using a hydrodynamic lattice Boltzmann method, we study the performance of our level-set approach in comparison to a traditional material distribution approach. By numerical examples, the parametric level-set approach is validated through comparison with traditional material distribution based methods. While the parametric level-set approach leads to similar optimal designs, the present study reveals no general improvements of the convergence of the optimization process and of the robustness of the nonlinear flow analyses when compared to the traditional material distribution approach. Instead, our numerical experiment suggests that a continuation method operating on the volume constraint is needed to achieve optimal designs at higher Reynolds numbers.