Discrete Variable Structural Optimization of Systems under Stochastic Earthquake Excitation

2012 ◽  
pp. 51-75 ◽  
Author(s):  
Héctor Jensen ◽  
Marcos Valdebenito ◽  
Juan Sepúlveda ◽  
Luis Becerra
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimization Strategy ◽  
Earthquake Excitation ◽  
Hybrid Form ◽  
Reliability Based Design ◽  
Passive Energy Dissipation ◽  
Design Variables ◽  
Stochastic Sensitivity Analysis

The reliability-based design optimization of structural systems under stochastic excitation involving discrete sizing type of design variables is considered. The design problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The excitation is modeled as a non-stationary stochastic process with uncertain model parameters. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal, and quadratic approximations. The approximations are combined with an effective stochastic sensitivity analysis in order to generate explicit expressions of the reliability constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. Two example problems that consider structures with passive energy dissipation systems under earthquake excitation are presented to illustrate the effectiveness of the approach reported herein.

Improvement of the Static and Dynamic Characteristics of Magnetic Head Sliders by Optimum Design

1999 ◽  
Vol 122 (1) ◽  
pp. 280-287 ◽  
Author(s):  
Hiromu Hashimoto ◽  
Yasuhisa Hattori
Keyword(s):  
Objective Function ◽  
Optimum Design ◽  
Amplitude Ratio ◽  
Optimization Technique ◽  
Hard Disk Drives ◽  
Maximum Amplitude ◽  
Disk Surface ◽  
Operating Conditions ◽  
Magnetic Head ◽  
Design Variables

The aim of this paper is to develop a general methodology for the optimum design of magnetic head sliders in improving the spacing characteristics between a slider and disk surface under static and dynamic operating conditions of hard disk drives and to present an application of the methodology to the IBM 3380-type slider design. To generate the optimal design variables, the objective function is defined as the weighted sum of the minimum spacing, the maximum difference in the spacing due to variation of the radial location of the head, and the maximum amplitude ratio of the slider motion. Slider rail width, taper length, taper angle, suspension position, and preload are selected as the design variables. Before the optimization of the head, the effects of these five design variables on the objective function are examined by a parametric study, and then the optimum design variables are determined by applying the hybrid optimization technique, combining the direct search method and successive quadratic programming. From the obtained results, the effectiveness of optimum design on the spacing characteristics of magnetic heads is clarified. [S0742-4787(00)03701-2]

Reliability-Based Design Optimization on Qualitative Objective With Limited Information

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Khaldon T. Meselhy ◽  
G. Gary Wang
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Probability Distributions ◽  
Random Variables ◽  
Limited Information ◽  
Reliability Based Design Optimization ◽  
Mathematical Formula ◽  
Reliability Based Design ◽  
Design Structure ◽  
Design Variables

Reliability-based design optimization (RBDO) algorithms typically assume a designer's prior knowledge of the objective function along with its explicit mathematical formula and the probability distributions of random design variables. These assumptions may not be valid in many industrial cases where there is limited information on variable variability and the objective function is subjective without mathematical formula. A new methodology is developed in this research to model and solve problems with qualitative objective functions and limited information about random variables. Causal graphs and design structure matrix are used to capture designer's qualitative knowledge of the effects of design variables on the objective. Maximum entropy theory and Monte Carlo simulation are used to model random variables' variability and derive reliability constraint functions. A new optimization problem based on a meta-objective function and transformed deterministic constraints is formulated, which leads close to the optimum of the original mathematical RBDO problem. The developed algorithm is tested and validated with the Golinski speed reducer design case. The results show that the algorithm finds a near-optimal reliable design with less initial information and less computation effort as compared to other RBDO algorithms that assume full knowledge of the problem.

Reliability Based Design Optimization for Selective Excitation of the Vibration Modes of a Cantilever Spring

2012 ◽  
Vol 498 ◽  
pp. 102-114
Author(s):  
Khalil El-Hami ◽  
Abdelkhalak El Hami
Keyword(s):  
Cantilever Beam ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Design Parameters ◽  
Optimization Strategy ◽  
High Dimensions ◽  
Engineering Structures ◽  
Reliability Based Design ◽  
Piezoelectric Polymer ◽  
Reliability Based Optimization

This paper is devoted to procedures for the reliability-based optimization methods of engineering structures combining measurement and sensitivity technique, for the purpose of the better sensitivity in force-gradient detection. In the experiment part of this study, the mica muscovite cantilever beam clamped-free is used. The excitation of a cantilever beam with several small sheets of piezoelectric polymer adequately glued to it selects one high-frequency vibration mode of the cantilever. The proposed strategy is design into a framework that allows the solution of optimization problems involving a several number of design parameters that characterizes the systems, including dimensional tolerance, material properties, boundary conditions, loads, and model predictions, considered to be uncertainties or variables. The proposed methodology directly supports quality engineering aspects enabling to specify the manufacturing tolerances normally required to achieve desired product reliability. Within this context, the robust design obtained is optimal over the range of variable conditions because it considers uncertainties during the optimization process. The large number of exact evaluations of problem, combined with the typically high dimensions of FE models of industrial structures, makes reliability-based optimization procedures very costly, sometimes unfeasible. Those difficulties motivate the study reported in this paper, in which a strategy is proposed consisting in the use of reliability-based optimization strategy combined with measurement and sensitivity technique specially adapted to the structures of industrial interested.

Practical Optimization Algorithm for Discrete Variables

2010 ◽  
Vol 42 ◽  
pp. 39-42
Author(s):  
De Sheng Wang ◽  
Ai Ping Zhou
Keyword(s):  
Objective Function ◽  
High Speed ◽  
Optimization Problems ◽  
Discrete Variables ◽  
Design Variables ◽  
Low Dimension ◽  
The Difference ◽  
Calculation Ability ◽  
Minimum Objective Function ◽  
Upper Boundary

In order to solve the optimization problems of discrete variable in mechanism design, beginning vertexes to meet all of performance restriction conditions can be given by the technician from upper boundary of design variables by means of man-machine interactive method. Objective function of each beginning vertex is calculated and arranged from small to large, the vertex of maximum and minimum of objective function are found. The difference between the vertex of minimum and maximum of objective function are calculated and new point is made up from the minimum point and the difference. The new point is used in stead of the vertex of the maximum objective function if the objective function of the new point is less than the maximum of beginning vertexes. The new composite figure is made up again and the new point is calculated until all design variables reach to under boundary. Then the vertex of minimum objective function is regarded to as the optimization point. This method is very fit for the optimization of discrete variables of low dimension and is higher calculation efficiency because the hominine brightness is combined with the high speed calculation ability.

Inverse modelling of constitutive parameters for elastoplastic problems

2000 ◽  
Vol 35 (6) ◽  
pp. 471-478 ◽  
Author(s):  
T. G Faurholdt
Keyword(s):  
Finite Element ◽  
Objective Function ◽  
Inverse Method ◽  
Optimization Technique ◽  
Global Optimum ◽  
Constitutive Parameter ◽  
Explicit Finite Element ◽  
Hardening Model ◽  
Design Variables ◽  
Constitutive Parameters

To obtain an improved identification of constitutive parameters to be used in finite element method simulations of elastoplastic deep-drawing processes an inverse method was applied using an explicit finite element code to simulate material tests. This problem was addressed by formulating the constitutive parameter identification as an optimization problem. The method was to minimize the objective function defined as the error between the result from the material test and the result from the finite element simulation. The optimization technique is based on the Levenberg-Marquardt method. The objective function was established in a least-squares sense where the design variables were the constitutive parameters of the material. The inverse method was started and, when a global optimum was reached, a set of constitutive parameters were identified. This was performed for both a linear hardening model and a power-law hardening model. It is shown that the inverse method predicts two models which qualitatively show the same overall characteristics for the investigated material.

An inner-point modification of PSO for constrained optimization

2015 ◽  
Vol 32 (7) ◽  
pp. 2005-2019 ◽  
Author(s):  
Daniele Peri
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Real Life ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Parallel Structure ◽  
Feasible Region ◽  
Content Type ◽  
Design Variables ◽  
Particle Level

Purpose – The purpose of this paper is to propose a modification of the original PSO algorithm in order to avoid the evaluation of the objective function outside the feasible set, improving the parallel performances of the algorithm in the view of its application on parallel architectures. Design/methodology/approach – Classical PSO iteration is repeated for each particle until a feasible point is found: the global search is performed by a set of independent sub-iteration, at the particle level, and the evaluation of the objective function is performed only once the full swarm is feasible. After that, the main attractors are updated and a new sub-iteration is initiated. Findings – While the main qualities of PSO are preserved, a great advantage in terms of identification of the feasible region and detection of the best feasible solution is obtained. Furthermore, the parallel structure of the algorithm is preserved, and the load balance improved. The results of the application to real-life optimization problems, where constraint satisfaction sometime represents a problem itself, gives the measure of this advantage: an improvement of about 10 percent of the optimal solution is obtained by using the modified version of the algorithm, with a more precise identification of the optimal design variables. Originality/value – Differently from the standard approach, utilizing a penalty function in order to discharge unfeasible points, here only feasible points are produced, improving the exploration of the feasible region and preserving the parallel structure of the algorithm.

Optimization of Multibody Dynamics Using Pointwise Constraints and Arbitrary Functions

1996 ◽  
Author(s):  
Javier Urruzola ◽  
Alejo Avello ◽  
Juan T. Celigüeta
Keyword(s):  
Objective Function ◽  
Multibody Dynamics ◽  
Symbolic Computation ◽  
Optimization Problems ◽  
Variable Method ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Design Variables ◽  
Complex Optimization ◽  
Pointwise Constraints

Abstract Multibody dynamics optimization requires the computation of sensitivities of the objective function and the constraints. This calculation can be done by two methods, direct differentiation and adjoint variable method, that are reviewed in this paper. In either cases, the complexity of the terms that appear in the formulation makes almost a need the use of symbolic computation for the derivation of sensitivities. An existing symbolic manipulator designed for multibody optimization has been enhanced with new and more powerful capabilities. The use of arbitrary functions as design variables and pointwise constraints permits the solution of more complex optimization problems. Some illustrative examples prove the capacity of the method to handle complex optimization problems.

scholarly journals Least-Cost Structural Optimization Oriented Preliminary Design

2001 ◽  
Vol 17 (04) ◽  
pp. 202-215 ◽  
Author(s):  
Philippe Rigo
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Plate Thickness ◽  
Construction Cost ◽  
Global Structure ◽  
Design Stage ◽  
Preliminary Design ◽  
Labor Costs ◽  
Rational Analysis ◽  
Design Variables

A computer design package is presented that provides optimum midship scantlings(plating, longitudinal members and frames). Basic characteristics such as L,B,T,Cb, the global structure layout, and applied loads are the requested data. It is not necessary to provide a feasible initial scantling. Within about one hour of computation time with a usual PC or laptop the LBR-5software automatically provides a rational optimum design. This software is an optimization tool dedicated to preliminary design. Its main advantages, in the early stage of design, are ease of structural modeling, rapid 3-D rational analysis of a ship's hold, and scantling optimization. Preliminary design is the most relevant and the least expensive time to modify design scantling and to compare different alternatives. Unfortunately, it is often too early for efficient use of many commercial software systems, such as FEM. This paper explains how it is now possible to perform optimization at the early design stage, including a 3-D numerical structural analysis. LBR-5 is based on the Module Oriented Approach. Design variables are the dimensions of the longitudinal and transversal members, plate thickness and spacing between members. The software contains three major modules. First, the Cost Module to assess the construction cost which is the objective function (least construction cost). So, unit material costs (Euro/kg or $/kg), welding, cutting, fairing, productivity (man-hours/m) and basic labor costs(Euro/man-hour) have to be specified by the user to define an explicit objective function. Then, there is the Constraint Module to perform a rational analysis of the global structure. This structure is modeled using stiffened plate and stiffened cylindrical shell elements. Finally, the Opti Module which contains a mathematical programming code (CONLIN) to solve constrained nonlinear optimization problems with a reduced number of re-analyses. Usually less than 15 analyses are required even with hundreds of design variables and hundreds of constraints. Optimum analysis of a FSO unit (Floating Storage Offloading) is presented as an example of the performance of the LBR-5 tool.

Optimization of a Dimpled Channel Using a Surrogate Model

2007 ◽  
Author(s):  
Kwang-Yong Kim ◽  
Dong-Yoon Shin
Keyword(s):  
Heat Transfer ◽  
Objective Function ◽  
Rectangular Channel ◽  
Optimization Technique ◽  
Numerical Procedure ◽  
Weighting Factor ◽  
Diameter Ratio ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Design Variables

A numerical procedure to optimize the shape of a staggered dimpled surface to enhance the turbulent heat transfer in a rectangular channel is presented in this work. A Kriging model-based optimization technique is used with Reynolds-averaged Navier-Stokes analysis of the fluid flow and heat transfer with Shear Stress Transport turbulence model. The dimple depth-to-dimple print diameter ratio, channel height-to-dimple print diameter ratio, and dimple print diameter-to-pitch ratio are chosen as design variables. The objective function is defined as a linear combination of terms related to heat transfer and friction loss with a weighting factor. Latin Hypercube Sampling is used to determine the training points as a mean of the Design of Experiment. Through a sensitivity analysis, it was found that the objective function is most sensitive to the ratio of the dimple depth to dimple print diameter. Optimal values of the design variables were obtained in a range of the weighting factor.

Feature Based Problems in Inverse Airfoil Design

1996 ◽  
Author(s):  
P. Venkataraman
Keyword(s):  
Optimization Problems ◽  
Optimization Technique ◽  
Inverse Design ◽  
Integral Boundary ◽  
New Approach ◽  
Design Variables ◽  
Boundary Layer Development ◽  
Feature Based ◽  
Inverse Design Problem ◽  
Layer Development

Abstract A new approach to the design of optimal airfoil shapes is presented in the paper. This requires redefinition of airfoil geometry through Bezier parametric curves whose vertices are the design variables of the problem. A basic panel method incorporating an integral boundary layer development model provides the aerodynamic analysis necessary to solve the optimization problems in airfoil shapes. The optimization technique can be easily adapted to solve the inverse design problem of determining the airfoil geometry for a specified pressure distribution. In this paper it is shown how the inverse problem can be further extended to incorporate additional aerodynamic and geometric features that are important in determining useful airfoil shapes.

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