First-Order Approximation Methods in Reliability-Based Design Optimization

2004 ◽  
Vol 127 (5) ◽  
pp. 851-857 ◽  
Author(s):  
Anukal Chiralaksanakul ◽  
Sankaran Mahadevan
Keyword(s):  
Design Optimization ◽  
Order Approximation ◽  
Mathematical Optimization ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Inverse Form ◽  
Numerical Studies ◽  
Reliability Method ◽  
First Order Approximation

Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.

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.

Reliability-Based Design Optimization Methods

2004 ◽  
Author(s):  
Anukal Chiralaksanakul ◽  
Sankaran Mahadevan
Keyword(s):  
Design Optimization ◽  
Common Ground ◽  
Optimization Algorithms ◽  
Probabilistic Constraints ◽  
Objective Functions ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Inverse Form ◽  
Reliability Method ◽  
Reliability Methods

Reliability-based design optimization (RBDO) methods are optimization algorithms that utilize reliability methods to evaluate probabilistic constraints and/or objective functions used to prescribe reliability. For practical applications, it is important that RBDO methods are efficient, i.e, they only require a manageable number of numerical evaluations of underlying functions since each one can be computationally expensive. The type of reliability methods and the manner in which they are used in conjunction with optimization algorithms strongly affect computational efficiency. The first order reliability method (FORM) and its inverse are proved to be efficient and widely accepted for reliability analysis. RBDO methods have therefore employed FORM or inverse FORM to numerically evaluate probabilistic constraints and objective functions. During the last decade, the efficiency of RBDO methods has been further improved through problem reformulation. Our goal is to present RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO formulations. This new perspective helps not only to clearly reveal their close relationships but also provides a common ground for understanding different types of RBDO methods. Using numerical studies reported in the literature, we indicate the numerical efficiency, convergence, and accuracy of existing RBDO methods.

Second-Order Reliability Method Based on Edgeworth Expansion With Application to Reliability-Based Design Optimization

2019 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Limit State ◽  
Probability Of Failure ◽  
Second Order ◽  
State Function ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Statistical Measures ◽  
Reliability Method

Abstract In the Second-Order Reliability Method, the limit-state function is approximated by a hyper-parabola in standard normal and uncorrelated space. However, there is no exact closed form expression for the probability of failure based on a hyper-parabolic limit-state function and the existing approximate formulas in the literature have been shown to have major drawbacks. Furthermore, in applications such as Reliability-based Design Optimization, analytical expressions, not only for the probability of failure but also for probabilistic sensitivities, are highly desirable for efficiency reasons. In this paper, a novel Second-Order Reliability Method is presented. The proposed expression is a function of three statistical measures: the Cornell Reliability Index, the skewness and the Kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the Most Probable Point. Furthermore, analytical sensitivities with respect to mean values of random variables and deterministic variables are presented. The sensitivities can be seen as the product of the sensitivities computed using the First-Order Reliability Method and a correction factor. The proposed expressions are studied and their applicability to Reliability-based Design Optimization is demonstrated.

Barrier Function Method in Reliability Based Design Optimization

2005 ◽  
Vol 297-300 ◽  
pp. 1882-1887
Author(s):  
Tae Hee Lee ◽  
Jung Hun Yoo
Keyword(s):  
Design Optimization ◽  
Barrier Function ◽  
Reliability Index ◽  
Feasible Solution ◽  
Reliability Based Design Optimization ◽  
User Requirement ◽  
Mean Values ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method

In practical design applications, most design variables such as thickness, diameter and material properties are not deterministic but stochastic numbers that can be represented by their mean values with variances because of various uncertainties. When the uncertainties related with design variables and manufacturing process are considered in engineering design, the specified reliability of the design can be achieved by using the so-called reliability based design optimization. Reliability based design optimization takes into account the uncertainties in the design in order to meet the user requirement of the specified reliability while seeking optimal solution. Reliability based design optimization of a real system becomes now an emerging technique to achieve reliability, robustness and safety of the design. It is, however, well known that reliability based design optimization can often have so multiple local optima that it cannot converge into the specified reliability. To overcome this difficulty, barrier function approach in reliability based design optimization is proposed in this research and feasible solution with specified reliability index is always provided if a feasible solution is available. To illustrate the proposed formulation, reliability based design optimization of a bracket design is performed. Advanced mean value method and first order reliability method are employed for reliability analysis and their optimization results are compared with reliability index approach based on the accuracy and efficiency.

Chaotic Amplitude Dynamics for Parametrically Excited Systems With Quadratic Nonlinearities

1995 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Order Approximation ◽  
Amplitude Equations ◽  
Analytical Technique ◽  
First Order ◽  
Numerical Studies ◽  
Quadratic Nonlinearities ◽  
First Order Approximation

Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.

Reliability Based Design Optimization of MEMS Considering Pull-In

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Michael Raulli ◽  
Kurt Maute
Keyword(s):  
Design Optimization ◽  
Reliability Based Design Optimization ◽  
Micro Electro Mechanical Systems ◽  
Operational Conditions ◽  
Electrostatically Actuated ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Optimization Methodology ◽  
Novel Devices ◽  
Fully Coupled

The increased use of micro-electro-mechanical systems (MEMS) as key components for actuation and sensing purposes in novel devices and systems emphasizes the need for optimal design methods. Stochastic variations in manufacturing and operational conditions must be considered in order to meet performance goals. This study proposes a reliability based design optimization methodology for the design of geometrically complex electrostatically actuated MEMS. The first order reliability method is used for reliability analysis of fully-coupled electrostatic-mechanical problems. A general methodology for predicting the instability phenomenon of pull-in and incorporating it into an automatic optimization process is proposed and verified with analytical and experimental results. The potential of this methodology is illustrated with the design of an analog micromirror.

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