Application of the Ritz Method to the Optimization of Vibrating Structures

2012 ◽  
Author(s):  
J. Gregory McDaniel ◽  
Andrew S. Wixom
Keyword(s):  
Optimization Problems ◽  
Ritz Method ◽  
Global Optimum ◽  
Vibration Characteristics ◽  
Exhaustive Search ◽  
Computationally Efficient ◽  
Convergence Properties ◽  
Vibrating Structures ◽  
Computationally Intensive ◽  
Made In

This work presents an application of the Ritz Method to the optimization of vibrating structures. The optimization problems considered here involve local design choices made in various regions of the structure in hopes of improving the vibration characteristics of the structure. In order to find the global optimum, one must perform an exhaustive search over all combinations of such choices. Even a modest number of design choices may give rise to a large number of combinations, so that an exhaustive search becomes computationally intensive. In the present work, the Ritz Method is employed to efficiently compute cost functions related to the vibration characteristics of the structure. Since the Ritz Method is based on integral expressions of the potential and kinetic energies of the structure, one may naturally divide these integrals over regions of the structure. In doing so, the concept of substructuring appears naturally in the formulation without explicitly considering boundary conditions between regions. This advantage, combined with the well-known convergence properties of the Ritz Method, provide for a computationally efficient approach for optimization problems. Numerical examples related to the optimization of a vibrating plate illustrate the approach.

Parameterized Design Optimization of a Magnetohydrodynamic Liquid Metal Active Cooling Concept

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Darren J. Hartl ◽  
Edgar Galvan ◽  
Richard J. Malak ◽  
Jeffrey W. Baur
Keyword(s):  
Liquid Metal ◽  
Design Optimization ◽  
Optimization Problems ◽  
Material Design ◽  
Element Model ◽  
Algebraic Model ◽  
Engineering Problem ◽  
Computationally Efficient ◽  
Design Selection ◽  
Computationally Intensive

The success of model-based multifunctional material design efforts relies on the proper development of multiphysical models and advanced optimization algorithms. This paper addresses both in the context of a structure that includes a liquid metal (LM) circuit for integrated cooling. We demonstrate for the first time on a complex engineering problem the use of a parameterized approach to design optimization that solves a family of optimization problems as a function of parameters exogenous to the subsystem of interest. This results in general knowledge about the capabilities of the subsystem rather than a restrictive point solution. We solve this specialized problem using the predictive parameterized Pareto genetic algorithm (P3GA) and show that it efficiently produces results that are accurate and useful for design exploration and reasoning. A “population seeding” approach allows an efficient multifidelity approach that combines a computationally efficient reduced-fidelity algebraic model with a computationally intensive finite-element model. Using data output from P3GA, we explore different design scenarios for the LM thermal management concept and demonstrate how engineers can make a final design selection once the exogenous parameters are resolved.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design

1999 ◽  
Vol 122 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Problems ◽  
Practical Significance ◽  
Engineering Practice ◽  
Probabilistic Optimization ◽  
Importance Sampling Method ◽  
Feasibility Evaluation ◽  
Feasibility Robustness ◽  
Computationally Intensive ◽  
Six Sigma Approach

In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses and methods that do not. Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques under different circumstances. Under the framework of probabilistic optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry. [S1050-0472(00)00904-1]

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

Real-Time Robot Capability Analysis

2005 ◽  
Author(s):  
Chalongrath Pholsiri ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Decision Making ◽  
Path Planning ◽  
Real Time ◽  
Computationally Efficient ◽  
New Approach ◽  
Ellipsoid Method ◽  
Capability Analysis ◽  
Computationally Intensive ◽  
Planar Robots

Robot Capability Analysis (RCA) is a process in which force/motion capabilities of a manipulator are evaluated. It is very useful in both the design and operational phases of robotics. Traditionally, ellipsoids and polytopes are used to both graphically and numerically represent these capabilities. Ellipsoids are computationally efficient but tend to underestimate while polytopes are accurate but computationally intensive. This article proposes a new approach to RCA called the Vector Expansion (VE) method. The VE method offers accurate estimates of robot capabilities in real time and therefore is very suitable in applications like task-based decision making or online path planning. In addition, this method can provide information about the joint that is limiting a robot capability at a given time, thus giving an insight as to how to improve the performance of the robot. This method is then used to estimate capabilities of 4-DOF planar robots and the results discussed and compared with the conventional ellipsoid method. The proposed method is also successfully applied to the 7-DOF Mitsubishi PA10-7C robot.

scholarly journals A Modified Fourier–Ritz Formulation for Vibration Analysis of Arbitrarily Restrained Rectangular Plate with Cutouts

2018 ◽  
Vol 2018 ◽  
pp. 1-22
Author(s):  
Yiming Liu ◽  
Zhuang Lin ◽  
Hu Ding ◽  
Guoyong Jin ◽  
Sensen Yan
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Vibration Characteristics ◽  
Geometric Parameters ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Stiffness Constant ◽  
Proper Values

A modified Fourier–Ritz method is developed for the flexural and in-plane vibration analysis of plates with two rectangular cutouts with arbitrary boundary conditions, aiming to provide a unified solving process for cases that the plate has various locations or sizes of cutout, and different kinds of boundary conditions. Under the current framework, modifying the position of the cutout or the boundary conditions of the plate is just as changing the geometric parameters of the plate, and there is no need to change the solution procedures. The arbitrary boundary conditions can be obtained by setting the stiffness constant of the boundary springs which are fixed uniformly along the edges of the plate at proper values. The strain and kinetic energy functions of a plate with rectangular cutout are derived in detail. The convergence and accuracy of the present method are demonstrated by comparing the present results with those obtained from the FEM software. In this paper, free in-plane and flexural vibration characteristics of the plate with rectangular cutout under general boundary conditions are studied. From the results, it can be found that the geometric parameters and positions of the cutout and the boundary conditions of the plate will obviously influence the natural vibration characteristics of the structures.

scholarly journals A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1283-1296
Author(s):  
Keyvan Amini ◽  
Somayeh Bahrami ◽  
Shadi Amiri
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Convergence Properties ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Secant Condition ◽  
Approximate Hessian ◽  
Modified Secant Condition

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

scholarly journals REINFORCED CONCRETE COATING PLATES OF HIGHWAYS ON AN ELASTIC HALF-SPACE

2018 ◽  
Vol 14 (2) ◽  
pp. 149-157
Author(s):  
Slav D. Semeniuk ◽  
Roman V. Kumashov
Keyword(s):  
Reinforced Concrete ◽  
Static Analysis ◽  
Elastic Foundation ◽  
Strain State ◽  
Ritz Method ◽  
Elastic Half Space ◽  
Numerical Studies ◽  
Concrete Coating ◽  
Plate On Elastic Foundation ◽  
Made In

Static analysis of the stress-strain state of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. These plates are considered as a planar structure on an elastic foundation. The plates are calculated by the method of B.N. Zhemochkin using the Ritz method to determine plate deflections in the main system using the mathematical package «MathCad». Also the plates are calculated on the PC «LIRA». There are given the results of experimental and numerical studies in this article

Self-adaptively Commensal Learning-based Jaya Algorithm with Multi-populations and its Application

2021 ◽  
Author(s):  
Zuanjia Xie ◽  
Chunliang Zhang ◽  
Haibin Ouyang ◽  
Steven Li ◽  
Liqun Gao
Keyword(s):  
Learning Strategy ◽  
Optimization Problems ◽  
State Of The Art ◽  
Global Optimum ◽  
Benchmark Problems ◽  
Series System ◽  
Jaya Algorithm ◽  
Roulette Wheel Selection ◽  
Roulette Wheel ◽  
Distribution Scheme

Abstract Jaya algorithm is an advanced optimization algorithm, which has been applied to many real-world optimization problems. Jaya algorithm has better performance in some optimization field. However, Jaya algorithm exploration capability is not better. In order to enhance exploration capability of the Jaya algorithm, a self-adaptively commensal learning-based Jaya algorithm with multi-populations (Jaya-SCLMP) is presented in this paper. In Jaya-SCLMP, a commensal learning strategy is used to increase the probability of finding the global optimum, in which the person history best and worst information is used to explore new solution area. Moreover, a multi-populations strategy based on Gaussian distribution scheme and learning dictionary is utilized to enhance the exploration capability, meanwhile every sub-population employed three Gaussian distributions at each generation, roulette wheel selection is employed to choose a scheme based on learning dictionary. The performance of Jaya-SCLMP is evaluated based on 28 CEC 2013 unconstrained benchmark problems. In addition, three reliability problems, i.e. complex (bridge) system, series system and series-parallel system are selected. Compared with several Jaya variants and several state-of-the-art other algorithms, the experimental results reveal that Jaya-SCLMP is effective.

Multimodal Biometric Hand-Off for Robust Unobtrusive Continuous Biometric Authentication

2013 ◽  
pp. 389-409
Author(s):  
P. Daphne Tsatsoulis ◽  
Aaron Jaech ◽  
Robert Batie ◽  
Marios Savvides
Keyword(s):  
Tracking System ◽  
Operation Time ◽  
Face Verification ◽  
Computationally Efficient ◽  
Authorized User ◽  
Continuous Authentication ◽  
Training Stage ◽  
Hand Off ◽  
Authentication System ◽  
Computationally Intensive

Conventional access control solutions rely on a single authentication to verify a user’s identity but do nothing to ensure the authenticated user is indeed the same person using the system afterwards. Without continuous monitoring, unauthorized individuals have an opportunity to “hijack” or “tailgate” the original user’s session. Continuous authentication attempts to remedy this security loophole. Biometrics is an attractive solution for continuous authentication as it is unobtrusive yet still highly accurate. This allows the authorized user to continue about his routine but quickly detects and blocks intruders. This chapter outlines the components of a multi-biometric based continuous authentication system. Our application employs a biometric hand-off strategy where in the first authentication step a strong biometric robustly identifies the user and then hands control to a less computationally intensive face recognition and tracking system that continuously monitors the presence of the user. Using multiple biometrics allows the system to benefit from the strengths of each modality. Since face verification accuracy degrades as more time elapses between the training stage and operation time, our proposed hand-off strategy permits continuous robust face verification with relatively simple and computationally efficient classifiers. We provide a detailed evaluation of verification performance using different pattern classification algorithms and show that the final multi-modal biometric hand-off scheme yields high verification performance.

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