Algorithms for Design and Interrogation of Functionally Gradient Material Objects

Chapter 8 Design (with analysis) of efficient algorithms

Comprehensive studies of SS316L/IN718 functionally gradient material fabricated with directed energy deposition: Multi-physics & multi-materials modelling and experimental validation

In this paper, we present two new, very efficient and accurate algorithms for computing optical flow. The first is a modified gradient-based regularization method, and the other is an SSD-based regularization method. To amend the errors in the image flow constraint caused by the discontinuities in the brightness function, we propose to selectively combine the image flow constraint and the contour-based flow constraint into the data constraint in a regularization framework. The image flow constraint is disabled in the neighborhood of discontinuities, while the contour-based flow constraint is active at discontinuity locations. To solve the linear system resulting from the regularization formulation, the incomplete Cholesky preconditioned conjugate gradient algorithm is employed, leading to an efficient algorithm. Our SSD-based regularization method uses the SSD measure as the data constraint in a regularization framework. The preconditioned nonlinear conjugate gradient with a modified search direction scheme is developed to minimize the resulting energy function. Experimental results for these two algorithms are given to demonstrate their performance.

We propose an efficient and generic algorithm for rigorous integration forward in time of partial differential equations written in the Fourier basis. By rigorous integration we mean a procedure which operates on sets and return sets which are guaranteed to contain the exact solution. The presented algorithm generates, in an efficient way, normalized derivatives which are used by the Lohner algorithm to produce a rigorous bound. The algorithm has been successfully tested on several partial differential equations (PDEs) including the Burgers equation, the Kuramoto-Sivashinsky equation, and the Swift-Hohenberg equation. The problem of rigorous integration in time of partial differential equations is a problem of large computational complexity and efficient algorithms are required to deal with PDEs on higher dimensional domains, like the Navier-Stokes equation. Technicalities regarding the various optimization techniques implemented in the software used in this paper will be reported elsewhere.

With the advancement of modern industries and processes, numerous structures are now required to function in thermal environments, leading to a new class of composite materials known as functional gradient materials (FGMs). Initially developed as thermal barrier materials for structural applications in aerospace and fusion reactors, FGMs have gained global recognition as vital composite materials. The overall properties of FMG are unique and different from any of the individual material that forms it. There is a wide range of applications for FGM and it is expected to increase as the cost of material processing and fabrication processes are reduced by improving these processes. Their application is increasingly recognized as a highly effective method for achieving sustainable development across various industries. In this study, an an overview of resents a detailed examination of the development, features, and essential manufacturing processes of FGMs is presented, based on a review of existing literature.

Arterial stiffness is a well-known biomarker of early cardiovascular disease. Shear wave dispersion ultrasound vibrometry (SDUV) has emerged as a promising technique to estimate local arterial stiffness from the observed dispersion of guided waves. With the ultimate goal of developing real-time inversion for arterial stiffness from SDUV measurements, we develop and validate highly efficient and accurate computational algorithms that compute the wave dispersion in multi-layered immersed tubes. The proposed approach carefully combines Fourier transformation and one-dimensional finite-element discretization to accurately capture fully three-dimensional wave propagation. The method is several orders of magnitude more efficient than three-dimensional finite element simulation, and eliminates other complexities such as the need for absorbing boundary conditions. The method is validated using SDUV experiments on tissue-mimicking phantoms. The validation exercise uncovered an important detail that is often overlooked—the dispersion curve captured through SDUV experiments does not correspond to a single dispersion curve, but a combination of multiple dispersion curves. This implies that proper identification of the dispersion curves could be critical to estimating the arterial stiffness. In this talk, we present the details of the proposed method including formulation, computational complexity, verification and validation.Arterial stiffness is a well-known biomarker of early cardiovascular disease. Shear wave dispersion ultrasound vibrometry (SDUV) has emerged as a promising technique to estimate local arterial stiffness from the observed dispersion of guided waves. With the ultimate goal of developing real-time inversion for arterial stiffness from SDUV measurements, we develop and validate highly efficient and accurate computational algorithms that compute the wave dispersion in multi-layered immersed tubes. The proposed approach carefully combines Fourier transformation and one-dimensional finite-element discretization to accurately capture fully three-dimensional wave propagation. The method is several orders of magnitude more efficient than three-dimensional finite element simulation, and eliminates other complexities such as the need for absorbing boundary conditions. The method is validated using SDUV experiments on tissue-mimicking phantoms. The validation exercise uncovered an important detail that is often overlo...

Functionally gradient materials (FGM) are innovative materials in which final properties varies gradually with dimensions. It is the recent development in traditional composite materials which retains their strengths and eliminates their weaknesses. It can be formed by varying chemical composition, microstructure or design attributes from one end to other as per requirement. This feature allows FGM to have best material properties in required quantities only where it is needed. In this study, an overview of fabrication processes, area of application, some recent research studies and the need to focus more research effort on improving the most promising FGM fabrication method (solid freeform SFF and Friction Stir Welding) is presented. Improving the performance of SFF and Friction Stir Processing processes and extensive studies on material characterization on components produced will go a long way in bringing down the manufacturing cost of FGM and increase productivity in this regard. Applications of FGM, Functionally graded material, Material characterization of FGM, Processing technique of FGM

Additive manufacturing of three-dimensional metal-glass functionally gradient material components by laser powder bed fusion with in situ powder mixing

Excessive time complexity has severely restricted the application of support vector machine (SVM) in large-scale multi-label classification. Thus, this paper proposes an efficient multi-label SVM classification algorithm by combining approximate extreme points method and divide-and-conquer strategy (AEDC-MLSVM). The AEDC-MLSVM classification algorithm firstly uses the approximate extreme points method to obtain the representative set from the multi-label training data set. While persisting almost all the useful information of multi-label training set, representative set can effectively reduce the scale of multi-label training set. Secondly, to acquire an efficient multi-label SVM classification model, the SVM based on the improved divide-and-conquer strategy is trained on the representative set, which will further improve the training speed and classification performance. The improvement is reflected in two aspects. (1) The improved divide-and-conquer strategy is applied to divide the representative set into subsets and this can ensure that each representative subset contains a certain number of positive and negative instances. This will avoid singular problems and overcome computation load imbalance problem. (2) The different error cost (DEC) method is applied to overcome the label imbalance problem. Effective experiments have proved that the training and testing speed of AEDC-MLSVM classification algorithm can be accelerated substantially while ensuring the classification performance.

In this paper, we describe two algorithmic techniques for the design of efficient algorithms in dual-cube. The first uses cluster structure of dual-cube, and the second uses recursive structure of the dual-cube. We propose efficient algorithms for parallel prefix computation and sorting in dual-cube based on the two techniques, respectively. For a dual-cube D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> with 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2n-1</sup> nodes and n links per node, the communication and computation times of the algorithm for parallel prefix computation are at most 2n+1 and 4n-2, respectively; and those of the algorithm for sorting are at most 6n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 2n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively.

Topological domains have been proposed as the backbone of interphase chromosome structure. They are regions of high local contact frequency separated by sharp boundaries. Genes within a domain often have correlated transcription. In this paper, we present a computational efficient spectral algorithm to identify topological domains from chromosome conformation data (Hi-C data). We consider the genome as a weighted graph with vertices defined by loci on a chromosome and the edge weights given by interaction frequency between two loci. Laplacian-based graph segmentation is then applied iteratively to obtain the domains at the given compactness level. Comparison with algorithms in the literature shows the advantage of the proposed strategy. An efficient algorithm is presented to identify topological domains from the Hi-C matrix. The Matlab source code and illustrative examples are available at http://bionetworks.ccmb.med.umich.edu/ : indikar@med.umich.edu Supplementary data are available at Bioinformatics online.

We give new and efficient black-box reconstruction algorithms for some classes of depth-3 arithmetic circuits. As a consequence, we obtain the first efficient algorithm for computing the tensor rank and for finding the optimal tensor decomposition as a sum of rank-one tensors when then input is a constant-rank tensor. More specifically, we provide efficient learning algorithms that run in randomized polynomial time over general fields and in deterministic polynomial time over and for the following classes: 1) Set-multilinear depth-3 circuits of constant top fan-in ((k) circuits). As a consequence of our algorithm, we obtain the first polynomial time algorithm for tensor rank computation and optimal tensor decomposition of constant-rank tensors. This result holds for d dimensional tensors for any d, but is interesting even for d=3. 2) Sums of powers of constantly many linear forms ((k) circuits). As a consequence we obtain the first polynomial-time algorithm for tensor rank computation and optimal tensor decomposition of constant-rank symmetric tensors. 3) Multilinear depth-3 circuits of constant top fan-in (multilinear (k) circuits). Our algorithm works over all fields of characteristic 0 or large enough characteristic. Prior to our work the only efficient algorithms known were over polynomially-sized finite fields (see. Karnin-Shpilka 09’). Prior to our work, the only polynomial-time or even subexponential-time algorithms known (deterministic or randomized) for subclasses of (k) circuits that also work over large/infinite fields were for the setting when the top fan-in k is at most 2 (see Sinha 16’ and Sinha 20’).

This paper presents the challenges and solutions encountered while designing and then printing functionally gradient material (FGM) objects using an off the shelf fused deposition modeling (FDM) 3D printer. The printer, Big Builder Dual-Feed Extruder from 3dprinter4u, Noordwijkerhout, The Netherlands, has the unique design of extruding two different filaments out of one nozzle. By controlling the rate at which the two filaments are pulled into the melt chamber, FGM objects can be printed. Software challenges associated with process planning required to print an FGM object are solved by showing a method for printing a discretized gradient and by designing an open-loop control mechanism for the extruder motors. A design method is proposed that models an object using a level-set function (LSF) with a material gradient. Instead of merely identifying the boundaries of the object, the level set also models the material gradient within the object. This representation method along with a genetic algorithm finds an optimal design for an FGM cantilever beam that is then printed on the FDM printer. The model and genetic algorithm are also used to solve a standard topology optimization problem. The results are compared to a similar FGM topology optimization method in the literature. All the codes for this paper are made open source to facilitate future research.

The idea of functionally gradient material (FGM) theory was used to design ceramic nozzle based on the erosion wear behaviors of the ceramic nozzles and the outstanding properties of FGM. The purpose is to reduce the tensile stress at the entry region of the nozzle during sand blasting processes. The design theory and methods of gradient ceramic nozzle were proposed. The physical, micromechanical, and composition distribution models of gradient ceramic nozzle were established. The optimum composition distribution of the gradient ceramic nozzle material was determined from the solution of the multi-objective optimization calculation by constructing the models of the composition distribution versus the structural integrity of the compact in fabricating process. Results showed that compressive residual stresses appeared at the entry area of the gradient ceramic nozzle. The optimized component distribution exponent p is 0.5. An SiC/(W,Ti)C gradient ceramic nozzle material was synthesized by hot-pressing according to the design result. Results showed that the surface Vickers hardness of the FGM-1 gradient ceramic nozzle materials was greatly improved in comparison with that of the other layers.

In this paper we present an efficient hybrid classification algorithm based on combining case-based reasoning and random decision trees, which is based on a general approach for combining lazy and eager learning methods. We use this hybrid classification algorithm to predict the pain classification for palliative care patients, and compare the resulting classification accuracy to other similar algorithms. The hybrid algorithm consistently produces a lower average error than the base algorithms it combines, but at a higher computational cost.