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Machine-Level Case Study: Fingerprint of Industrial Motors
Published in Pedro Larrañaga, David Atienza, Javier Diaz-Rozo, Alberto Ogbechie, Carlos Puerto-Santana, Concha Bielza, Industrial Applications of Machine Learning, 2019
Pedro Larrañaga, David Atienza, Javier Diaz-Rozo, Alberto Ogbechie, Carlos Puerto-Santana, Concha Bielza
The parameters used in each algorithm are described below:Hierarchical agglomerative clustering: Ward’s was the selected linkage criterion and the Euclidean distance was selected as the distance metric.K-means: we employed the scikit-learn default parameters using K-means++ for cluster initialization and the Euclidean distance.Spectral clustering: we also calculated the affinity matrix using the kneighbors_graph function. We used the arpack eigenvalue decomposition strategy, designed to solve large-scale eigenvalue problems more efficiently.Affinity propagation: the damping value (λ $ \lambda $ ) was set to 0.75. The preference value for this case study was set to five times the minimum input similarity to find an appropriate number of clusters. Input similarities were precalculated using the euclidean_distances function.Gaussian mixture model: the covariance type was set to full, and for the initialization we use K-means.In order to check the behavior of the algorithms when the number of clusters changes, the algorithms were executed with the value K set as 3, 5, and 7. This selection of K values is not applicable for the affinity propagation algorithm as explained in Section 1.3.4.
Unsymmetric Matrix Eigenvalue Techniques
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
The most widely used method for the sparse unsymmetric eigenvalue problem is the implicitly restarted Arnoldi method, as implemented in ARPACK [LSY98], which is discussed in Chapter 76. A promising variant is the Krylov–Schur algorithm of Stewart [Ste01]. Matlab’s sparse eigenvalue command “eigs” calls ARPACK.
Global linear stability analysis of flow inside an axial swirl generator with a rotating vortex rope
Published in Journal of Hydraulic Research, 2023
Zeinab Seifi, Mehrdad Raisee, Michel J Cervantes
Equations (10–13) are solved using the finite element method implemented in the software Freefem++ (Hecht, 2012) to obtain the direct and adjoint eigenvectors, and in addition to the eigenfrequency, ω. The resulting eigenvalue equation is solved by ARPACK library and UMFPACK package for matrix inversion. Finite element space P2–P1 is applied for velocity and pressure, respectively. Because the linear stability analysis is conducted with an axisymmetric assumption, the three-dimensional unsteady base flow results in CFX are averaged in time and azimuthal direction and interpolated on an axisymmetric triangular mesh using MATLAB software. The axisymmetric mesh consists of about triangular elements generated by Gmsh (Geuzaine & Remacle, 2009). The interpolated mean flow is then imported to Freefem++ (Hecht, 2012) to conduct stability analysis. Dirichlet homogeneous boundary conditions are specified at the inlet and walls. In addition, the Neumann boundary condition is imposed as the domain outlet.
Development of an analytical model for the flexural vibration of fish bone active camber structures with truncated, variable thickness partitions
Published in Mechanics Based Design of Structures and Machines, 2022
Mahdi Nejati, Saeed Shokrollahi, Masoud Cheraghi
The effect of taper factors and truncation constants requires a series of comparisons with FEM. Accordingly, a two-section plate with the notation shown in Fig. 7 is designed in the 3 D Solid Mechanics environment of COMSOL Multiphysics as its most accurate technique of eigenfrequency analysis. Proper boundary conditions are also defined in the software, and a mesh with “Finer” resolution is adopted, followed by the implementation of ARPACK eigenfrequency solver. Furthermore, the properties of this configuration are implemented in the developed code in Mathematica, and the results are obtained using the “Eigensystem” function and the method of “Arnoldi” which is generally used for machine- and arbitrary-precision matrices and is also based on the ARPACK library (Wolfram Research 2020). Further description of the modeling procedure in COMSOL is provided in the following sections (Table 2).
Enhancing parallelism of distributed algorithms with the actor model and a smart data movement technique
Published in International Journal of Parallel, Emergent and Distributed Systems, 2021
Anatoliy Doroshenko, Eugene Tulika, Olena Yatsenko
A similar approach focused on tasks is used in Spark, particularly the mathematic package Spark ML. Spark ML implements distributed algorithms using representation in the form of an acyclic graph to depict data dependencies. Central orchestrator Spark Master monitors the course of process execution and restarts tasks in case of exceptional states. Similar to Hadoop, a task is divided into subtasks arranged into a sequence. Some tasks can be executed in parallel with data deployed across the cluster. Along with all these tasks, Spark creates tasks flow represented as a directed acyclic graph in which nodes are data blocks and edges are operations over data blocks. Cholesky decomposition is implemented in Spark ML package for single-processor systems with shared memory and uses Breeze library, a wrapper over Netlib for Scala language. Netlib-java, in turn, is a wrapper over low-level libraries BLAS, LAPACK, and ARPACK and provides a Java interface for C/Fortran code. However, Spark does not provide a distributed implementation of factorisation. Instead, there is research [16,17] on the possibility of using Spark for scalability and fault tolerance. Spark manages the system of control points and rollbacks to the previous state in case of exceptional states.