Partial Differential Equation Filter Research Articles

An improved partial differential equation filter scheme for topology optimization of additively manufactured coated structure

In this paper, an improved partial differential equation (PDE) filter is presented for density-based topology optimization of coated structures with both regular and irregular design domains. The proposed filter efficiently addresses the boundary effect problems that causes identification failure of the material interface for modeling coating layer during topology optimization by replacing the original Dirichlet boundary conditions with non-homogeneous Neumann boundary conditions. One attractive feature of the proposed approach is that it can serve as an ideal alternative to the common domain extension approach, particularly for designing geometrically complex engineering structures with irregular design domain meshed by unstructured mesh. Based on the improved PDE filter, a new topology optimization design framework for coated structures with complete coating layer and controllable coating thickness is achieved. Examples of designing regular and irregular two-dimensional and three-dimensional coated structures are provided to demonstrate the effectiveness of the proposed approach.

Stress-based evolutionary topology optimization via XIGA with explicit geometric boundaries

This paper presents a novel approach to stress-based topology optimization that employs NURBS representations of explicit geometric boundaries to address stress minimization and stress-constrained problems. The proposed methodology is compatible with CAD systems and utilizes Extended IsoGeometric Analysis (XIGA) to ensure an accurate representation of stress field in the evolving structure. A p-norm aggregation scheme is used to measure global stress levels, and the aggregated stress constraint is augmented to the objective (compliance) via a Lagrange multiplier in stress-constrained problems. The proposed approach introduces a novel and efficient Lagrange multiplier trail strategy aimed at reducing computational costs. Additionally, a normalization scheme and a partial differential equation filter are presented to stabilize the highly nonlinear stress-based optimization. Validation studies demonstrate the effectiveness and characteristics of the proposed approach. Moreover, control points of the structural design can be directly edited to further improve strength performance. Comparative studies show clear advantages of the proposed methodology in terms of computational efficiency compared to other Finite element analysis (FEA)-based optimization methods. Overall, this paper presents a practical and novel approach that addresses the limitations of existing FEA-based optimization methods in terms of accuracy, flexibility, and degree of freedom (DOF) cost, and makes a significant contribution to the field of stress-based topology optimization.

Multi‐material topology optimization method for transient thermal structure with constraint on permissible temperatures

AbstractExcessive temperature may lead material to performance degradation, ablation, and phase change. Thus, controlling the maximum temperature of used material within a safe range is of great significance to the safe operation of thermal structures. In this article, a density‐based multi‐material topology optimization method for transient thermal structures is proposed, in which the maximal temperature for each material is controlled not greater than its permissible temperature. In this method, a projection algorithm based on the PDE (partial differential equation) filter and Heaviside projection is set up and used to identify the domains occupied by each material. The maximal temperature of each specific material occupying domain is approximately expressed by the condensed integrals in the time and space domains. The permissible temperature constraint is satisfied by controlling the condensed integrals not great than a specific threshold value (depending on the corresponding material's permissible temperature). Several examples illustrate that the permissible temperature plays an important role in the selection and the distribution scheme of the candidate materials for the design of multi‐material thermal structures. The proposed method can effectively control the maximal temperature of each material within its constraint range, and achieve the rational design for multi‐material thermal structures. In addition, different thermal loading time may also lead to different material selection of structure. This work has potential applications in the lightweight design of thermal insulation structures.

A Novel Speckle Suppression Method with Quantitative Combination of Total Variation and Anisotropic Diffusion PDE Model

Speckle noise seriously affects synthetic aperture radar (SAR) image application. Speckle suppression aims to smooth the homogenous region while preserving edge and texture in the image. A novel speckle suppression method based on the combination of total variation and partial differential equation denoising models is proposed in this paper. Taking full account of the local statistics in the image, a quantization technique—which is different from the normal edge detection method—is supported by the variation coefficient of the image. Accordingly, a quantizer is designed to respond to both noise level and edge strength. This quantizer automatically determines the threshold of diffusion coefficient and controls the weight between total variation filter and anisotropic diffusion partial differential equation filter. A series of experiments are conducted to test the performance of the quantizer and proposed filter. Extensive experimental results have demonstrated the superiority of the proposed method with both synthetic images and natural SAR images.

Plastic work constrained elastoplastic topology optimization

AbstractAn elastoplastic topology optimization framework for limiting plastic work generation while maximizing stiffness is presented. The kinematics and constitutive model are based on finite strain linear isotropic hardening plasticity, and the balance laws are solved using a total Lagrangian finite element formulation. Aggregation of the specific plastic work combined with an adaptive normalization scheme efficiently constrains the maximum specific plastic work. The optimization problem is regularized using an augmented partial differential equation filter, and is solved by the method of moving asymptotes where path‐dependent sensitivities are derived using the adjoint method. The numerical examples show a clear dependence on the optimized maximum stiffness structures for different levels of constrained specific plastic work. It is also shown that due to the history dependency of the plasticity, the load path significantly influences the structural performance and optimized topology.

Topology optimization for designing periodic microstructures based on finite strain viscoplasticity

This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.

Vibration signal denoising using partial differential equations of arbitrary order

In this paper, partial differential equations (PDE) denoising characteristics are investigated and a unified vibration denoising model is proposed based on arbitrary order PDE. The numerical solution for PDE filters with arbitrary order is demonstrated. The noise reduction features of the proposed model are analysed on Gaussian white noise, Pearson noise and Weibull noise. The realization of the PDE filter generally include the following steps: (1) Obtain the discretization equation according to the given order using the backward Euler scheme; (2) Compute the grid ratio according to the given order, the cut-off frequency and the sample frequency; (3) acquire the filter matrix. Numerical simulations are conducted and the results indicate that the proposed method exceeds relevant works in noise reduction and time-consuming performances. A shaft centreline orbit experiment has also been conducted to verify the efficacy of the proposed method in field application.

Topology optimization of finite strain viscoplastic systems under transient loads

SummaryA transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.

General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition.

Filtering off speckle noise from a fringe image is one of the key tasks in electronic speckle pattern interferometry (ESPI). In general, ESPI fringe images can be divided into three categories: low-density fringe images, high-density fringe images, and variable-density fringe images. In this paper, we first present a general filtering method based on variational image decomposition that can filter speckle noise for ESPI fringe images with various densities. In our method, a variable-density ESPI fringe image is decomposed into low-density fringes, high-density fringes, and noise. A low-density fringe image is decomposed into low-density fringes and noise. A high-density fringe image is decomposed into high-density fringes and noise. We give some suitable function spaces to describe low-density fringes, high-density fringes, and noise, respectively. Then we construct several models and numerical algorithms for ESPI fringe images with various densities. And we investigate the performance of these models via our extensive experiments. Finally, we compare our proposed models with the windowed Fourier transform method and coherence enhancing diffusion partial differential equation filter. These two methods may be the most effective filtering methods at present. Furthermore, we use the proposed method to filter a collection of the experimentally obtained ESPI fringe images with poor quality. The experimental results demonstrate the performance of our proposed method.

Towards a partial differential equation remote sensing image method based on adaptive degradation diffusion parameter

For the anisotropy diffusion feature, Partial Differential Equation (PDE) methods keep edge detail characters well in case of denoising, thus being widely applied in remote sense image denoising, smoothing, filtering and reconstruction. A PDE remote sensing image denoising method based on Adaptive Degradation Diffusion Parameter (ADDP) was proposed in the paper to deal with fuzzy detail problem caused by increasing iteration number. The PDE denoising method with ADDP enlarged diffusion size in the plat region of remote sensing image without affecting the remote sensing image edge, thus avoiding loss of remote sensing image detail and intersections caused by Gaussian convolution smoothing in the PDE filtering model based on curvature-based movement (CM) and image denoising model based on total variation (TV). In the region where gradation value changes little, the method executed isotropic diffusion to remove isolated noise. The upwind scheme was applied for model numerical realization. Experimental in remote sensing image denoising results proved its feasibility and effectiveness.

A Vision System Based on TOF 3d Imaging Technology Applied to Robotic Citrus Harvesting

This study was conducted to develop a fast machine vision system based on TOF (time of flight) three-dimensional (3D) imaging technology for automatic citrus recognition and location. Supported algorithms were specifically developed and programmed for image acquisition and processing. An adaptive filter coupled between partial differential equations filter and shock filter was presented to remove noise and sharpen edges efficiently. Image analysis algorithms integrated both range and amplitude information to generate regions of interest and parameters that are characteristic or very likely to belong to spherical objects. The three-dimensional position of the fruit and radius are obtained after the recognition stages. The total classification results showed that approximately 81.8% were detected and false detection occurred only once. On the whole, the process of imaging, recognition and location consumes less than 50 ms/fruit.

High‐order partial differential equation de‐noising method for vibration signal

A novel approach for 1D vibration signal de‐noising filter using partial differential equation (PDE) is presented. In particular, the numerical solution of higher‐order PDE is generated, and we show that it enables the amplitude‐frequency characteristic in filter to be estimated more accurately, which results in better de‐noising performance in comparison with the low‐order PDE. The de‐noising tests on different degree of artificial noise are conducted. Experimental tests have been rigorously compared with different de‐noising methods to verify the efficacy of the proposed high‐order PDE filter method. Copyright © 2014 John Wiley & Sons, Ltd.

Switching degenerate diffusion PDE filter based on impulselike probability for universal impulse noise removal

In this paper, a switching degenerate diffusion partial differential equation filter (SDDPDE) is developed by introducing the switching operators for reducing all kinds of impulse noise, and especially for images having a mixture of salt-and-pepper impulse noise and random-valued impulse noise which is a shortage for most of the existing filtering models. Our SDDPDE consists of the coarse and fine filtering stages. In the coarse filtering stages, the switching operator depends on a simple noise detector. In the fine filtering stages, we introduce the notion of impulselike probability, and the switching operator depends on both a simple noise detector and impulselike probability. Our SDDPDE will denoise noise pixels detected by the coarse detector while further modify the so-called noise-free pixels according to impulselike probability. The main advantages of our SDDPDE over published approaches are its simplicity and universality. In addition, we demonstrate the performance of our SDDPDE via application to three standard test images, corrupted by salt-and-pepper impulse noise, random-valued impulse noise and mixed impulse noise with high-noise levels, and the comparison with the other well-known filters. Experimental results show that our SDDPDE achieves high peak signal-to-noise ratio and better visual effect.

Application of two oriented partial differential equation filtering models on speckle fringes with poor quality and their numerically fast algorithms

In this paper, we are concerned with denoising in experimentally obtained electronic speckle pattern interferometry (ESPI) speckle fringe patterns with poor quality. We extend the application of two existing oriented partial differential equation (PDE) filters, including the second-order single oriented PDE filter and the double oriented PDE filter, to two experimentally obtained ESPI speckle fringe patterns with very poor quality, and compare them with other efficient filtering methods, including the adaptive weighted filter, the improved nonlinear complex diffusion PDE, and the windowed Fourier transform method. All of the five filters have been illustrated to be efficient denoising methods through previous comparative analyses in published papers. The experimental results have demonstrated that the two oriented PDE models are applicable to low-quality ESPI speckle fringe patterns. Then for solving the main shortcoming of the two oriented PDE models, we develop the numerically fast algorithms based on Gauss-Seidel strategy for the two oriented PDE models. The proposed numerical algorithms are capable of accelerating the convergence greatly, and perform significantly better in terms of computational efficiency. Our numerically fast algorithms are extended automatically to some other PDE filtering models.

Adaptive fourth-order partial differential equation filter for image denoising

To overcome the staircasing effects and simultaneously avoid edge blurring, this paper describes a fourth-order partial differential equation based edge-preserving regularization filter for noise removal. This technique is closely related to the nonlinear anisotropic diffusion. Compared results distinctly demonstrate the superiority of our proposed scheme over the LLT model, in terms of removing noise while sharply maintaining the edge features.

Shock filter coupled to curvature diffusion for image denoising and sharpening

The frequent problem in low-level vision arises from the goal to eliminate noise and uninteresting details from an image, without blurring semantically important structures such as edges. Partial differential equations (PDEs) have recently dominated image processing research, as a very good tool for noise elimination, image enhancement and edge detection. In this paper, we present a biased PDE filter based on a coupling between shock filter and curvature diffusion. This model removes noise and sharpens edges efficiently. It preserves well the location of the shocks by synchronising both effects of smoothing and deblurring. Empirical results on different kinds of images confirm these advantages.

Image restoration combining a total variational filter and a fourth-order filter

In this paper, a noise removal algorithm based on variational method and partial differential equations (PDEs) is proposed. It combines a total variational filter (ROF filter) with a fourth-order PDE filter (LLT filter). The combined algorithm takes the advantage of both filters since it is able to preserve edges while avoiding the staircase effect in smooth regions. The existence and uniqueness of a solution to the minimization problem is established. Experimental results illustrate the effectiveness of the model in image restoration.

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

A noise removal technique using partial differential equations (PDEs) is proposed here. It combines the Total Variational (TV) filter with a fourth-order PDE filter. The combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions. A weighting function is used in an iterative way to combine the solutions of the TV-filter and the fourth-order filter. Numerical experiments confirm that the new method is able to use less restrictive time step than the fourth-order filter. Numerical examples using images with objects consisting of edge, flat and intermediate regions illustrate advantages of the proposed model.