Search results for "Modeling and Simulation"
showing 10 items of 1561 documents
Black box scatter search for general classes of binary optimization problems
2010
The purpose of this paper is to apply the scatter search methodology to general classes of binary problems. We focus on optimization problems for which the solutions are represented as binary vectors and that may or may not include constraints. Binary problems arise in a variety of settings, including engineering design and statistical mechanics (e.g., the spin glass problem). A distinction is made between two sets of general constraint types that are handled directly by the solver and other constraints that are addressed via penalty functions. In both cases, however, the heuristic treats the objective function evaluation as a black box. We perform computational experiments with four well-k…
A symmetric nonlocal damage theory
2003
The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present app…
Thermodynamically consistent residual-based gradient plasticity theory and comparison
2006
A gradient plasticity theory for small deformations is presented within the framework of nonlocal continuum thermodynamics. The second principle (Clausius–Duhem inequality), enriched by an additional term named energy residual, is employed in conjunction with the concepts of insulation condition and locality recovery condition, in order to derive all the pertinent restrictions upon the constitutive equations. These include the expressions of the energy residual and of the plastic dissipation density, as well as the PDEs governing the gradient kinematic and isotropic hardening of the material, together with the related higher-order boundary conditions for both the fixed and the moving bounda…
Discrete Learning Control with Application to Hydraulic Actuators
2015
In this paper the robustness of a class of learning control algorithms to state disturbances, output noise, and errors in initial conditions is studied. We present a simple learning algorithm and exhibit, via a concise proof, bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories. Furthermore, these bounds are continuous functions of the bounds on the initial condition errors, state disturbance, and output noise, and the bounds are zero in the absence of these disturbances.
Optimal damping coefficient for a class of continuous contact models
2020
AbstractIn this study, we develop an analytical formula to approximate the damping coefficient as a function of the coefficient of restitution for a class of continuous contact models. The contact force is generated by a logical point-to-point force element consisting of a linear damper connected in parallel to a spring with Hertz force–penetration characteristic, while the exponent of deformation of the Hertz spring can vary between one and two. In this nonlinear model, it is assumed that the bodies start to separate when the contact force becomes zero. After separation, either the restitution continues or a permanent penetration is achieved. Therefore, this model is capable of addressing …
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
Probabilistic interpretation of the Calderón problem
2017
In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.
On utilizing an enhanced object partitioning scheme to optimize self-organizing lists-on-lists
2020
With the advent of “Big Data” as a field, in and of itself, there are at least three fundamentally new questions that have emerged, namely the Artificially Intelligence (AI)-based algorithms required, the hardware to process the data, and the methods to store and access the data efficiently. This paper (The work of the second author was partially supported by NSERC, the Natural Sciences and Engineering Council of Canada. We are very grateful for the feedback from the anonymous Referees of the original submission. Their input significantly improved the quality of this final version.) presents some novel schemes for the last of the three areas. There have been thousands of papers written rega…
RMS Based Health Indicators for Remaining Useful Lifetime Estimation of Bearings
2022
Estimating the remaining useful life (RUL) of bearings from healthy to faulty is important for predictive maintenance. The bearing fault severity can be estimated based on the energy or root mean square (RMS) of vibration signals, and a stopping criterion can be set based on a threshold given by an ISO standard. However, the vibration RMS is often not monotonically increasing with damage, which renders a challenge for predicting the RUL. This study proposes a novel method for splitting the vibration signal into multiple frequency bands before RMS calculations to generate multiple health indicators. Monotonic health indicators are identified using the Spearman coefficient, and the RUL is aft…