Probabilistic Designs of Air-Bearing Surface on Manufacturing Tolerances

2005 ◽  
Vol 127 (1) ◽  
pp. 149-154 ◽  
Author(s):  
Sang-Joon Yoon ◽  
Dong-Hoon Choi
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Computation Time ◽  
Probabilistic Constraints ◽  
Air Bearing ◽  
Probabilistic Design ◽  
Bearing Surface ◽  
Deterministic Optimization ◽  
Design Variables ◽  
Conventional Optimization

The focus in this paper is to automatically design the air-bearing surface (ABS) considering the randomness of its geometry as an uncertainty of design variables. Designs determined by the conventional optimization could only provide a low level of confidence in practical products due to the existence of uncertainties in either engineering simulations or manufacturing processes. This calls for a reliability-based approach to the design optimization, which increases product or process quality by addressing randomness or stochastic properties of design problems. In this study, a probabilistic design problem is formulated considering the reliability analysis which is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Beginning with this solution, the reliability-based design optimization (RBDO) is continued with the probabilistic constraints affected by the random variables. Probabilistic constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with a minimum increase in the objective. The simulation results of the probabilistic design are directly compared with the values of the initial design and the results of the deterministic optimum design, respectively. In order to show the effectiveness of the proposed approach, the reliability analyses by the Monte Carlo simulation are carried out. And the results demonstrate how efficient the proposed approach is, considering the enormous computation time of the reliability analysis.

Probabilistic Designs of Air-Bearing Surface on Manufacturing Tolerances

2004 ◽  
Author(s):  
Sang-Joon Yoon ◽  
Dong-Hoon Choi
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Computation Time ◽  
Probabilistic Constraints ◽  
Air Bearing ◽  
Probabilistic Design ◽  
Bearing Surface ◽  
Deterministic Optimization ◽  
Design Variables ◽  
Conventional Optimization

The focus in this paper is to automatically design the air-bearing surface (ABS) considering the randomness of its geometry as an uncertainty of design variables. Designs determined by the conventional optimization could only provide a low level of confidence in practical products due to the existence of uncertainties in either engineering simulations or manufacturing processes. This calls for a reliability-based approach to the design optimization, which increases product or process quality by addressing randomness or stochastic properties of design problems. In this study, a probabilistic design problem is formulated considering the reliability analysis which is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Beginning with this solution, the reliability-based design optimization (RBDO) is continued with the probabilistic constraints affected by the random variables. Probabilistic constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the probabilistic design are directly compared with the values of the initial design and the results of the deterministic optimum design, respectively. In order to show the effectiveness of the proposed approach, the reliability analyses by the Monte Carlo simulation are carried out. And the results demonstrate how efficient the proposed approach is, considering the enormous computation time of the reliability analysis.

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on Reliability-Based Design Optimization (RBDO), i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with a numerical example.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

An Optimization Method for Design of Subambient Pressure Shaped Rail Sliders

1999 ◽  
Vol 121 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Dong-Hoon Choi ◽  
Tae-Sik Kang
Keyword(s):  
Design Methodology ◽  
Optimization Method ◽  
Flying Height ◽  
Air Bearing ◽  
Bearing Surface ◽  
Programming Technique ◽  
Design Synthesis ◽  
Method Of Feasible Directions ◽  
Design Variables ◽  
Simulation Results

This study proposes a design methodology for determining configurations of subamient pressure shaped rail sliders by using a nonlinear programming technique in order to meet the desired flying characteristics over the entire recording band. The desired flying characteristics considered in this study are to minimize the variation in flying height from a target value, to keep the pitch angle within a suitable range, and to ensure that the outside rail flies lower than the inside rail even with the roll distribution due to manufacturing process. The design variables selected are recess depth, geometry of the air bearing surface, and pivot location in the transverse direction of the slider. The method of feasible directions in Automated Design Synthesis (ADS) is utilized to automatically find the optimum design variables which simultaneously meet all the desired flying characteristics. To validate the suggested design methodology, a computer program is developed and applied to a 30 percent/15 nm twin rail slider and a 30 percent/15 nm tri-rail slider. Simulation results for both sliders demonstrated the effectiveness of the proposed design methodology by showing that the flying characteristics of the optimally designed sliders are enhanced in comparison with those of the initial ones.

Structural Topology Design Considering Reliability

2005 ◽  
Vol 297-300 ◽  
pp. 1901-1906 ◽  
Author(s):  
Seung Jae Min ◽  
Seung Hyun Bang
Keyword(s):  
Topology Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Performance Measure ◽  
Topology Design ◽  
Optimization Process ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Most Probable Point ◽  
Design Variables

In the design optimization process design variables are selected in the deterministic way though those have uncertainties in nature. To consider variances in design variables reliability-based design optimization problem is formulated by introducing the probability distribution function. The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop singlevariable approach, requires the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop singlevariable approach, which approximates searching the most probable point analytically, to reduce the time cost and dealing with several constraints to handle practical design requirements. The density method in topology optimization including SLP (Sequential Linear Programming) algorithm is implemented with object-oriented programming. To examine uncertainties in the topology design of a structure, the modulus of elasticity of the material and applied loadings are considered as probabilistic design variables. The results of a design example show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Po Ting Lin ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Design Space ◽  
Optimization Problems ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Original Design ◽  
Design Point ◽  
Standard Normal

Reliability-based design optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the modified reliability index approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the performance measure approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. To this end, a new algorithm, ensemble of Gaussian reliability analyses (EoGRA), was developed to estimate the failure probability using Gaussian-based kernel density estimation (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations (FEs). Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The results showed that EoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods. Furthermore, experiments of image processing with arbitrarily distributed photo pixels are performed. The lighting of image pixels is maximized subject to the acceptable limit. Our implementation showed that the accuracy of the estimation of normal distribution is poor while the proposed method is capable of finding the optimal solution with acceptable accuracy.

A Reliability-Based Formulation for Simulation-Based Control Co-design Using Generalized Polynomial Chaos Expansion

2021 ◽  
pp. 1-15
Author(s):  
Mohammad Behtash ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Polynomial Chaos ◽  
Probabilistic Constraints ◽  
Stochastic Dynamic ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
And Control ◽  
Stochastic Dynamic Systems

Abstract Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Probabilistic Design Optimization of Frequency Dispersion for Rotating Blades

2010 ◽  
Author(s):  
Liqiang An ◽  
G. Gary Wang ◽  
Zhangqi Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Design Optimization ◽  
Optimization Problem ◽  
Frequency Dispersion ◽  
Probabilistic Constraints ◽  
Design Parameters ◽  
Probabilistic Design ◽  
Rotating Blades ◽  
Element Method

In this paper, a probabilistic design optimization method based on finite element method is proposed to calculate the variability of design parameters subject to a specified dispersion of natural frequencies of rotating blades. The element stiffness and mass matrices are derived using a two-stage finite element method and numerical integration. Based on the perturbation technology, the sensitivity of the frequencies, as well as relationship between the frequency dispersion and the coefficient of variability (CV) of the design parameters can be obtained. Such sensitivity information is then used to convert the probabilistic design optimization problem into a deterministic optimization problem. Two case studies are given to illustrate the proposed method. From the results, it is concluded that rotation of blade changes the sensitivity of CV to the design parameters considered, and using the proposed method can transform the probabilistic constraints to deterministic constraints.

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