Reliability Assessment and Reliability-Based Design Optimization of Large Scale Box-Girder Structural System

2014 ◽  
Vol 1065-1069 ◽  
pp. 1087-1091
Author(s):  
Chang Li Yu ◽  
Joo Sung Lee
Keyword(s):  
Design Optimization ◽  
Large Scale ◽  
Optimization Problem ◽  
Reliability Assessment ◽  
Safety Margin ◽  
Structural System ◽  
Reliability Based Design Optimization ◽  
Box Girder ◽  
Reliability Based Design ◽  
Structural Resistance

Reliability analysis and reliability-based design optimization of large scale box-girder structural system is an interesting topic in the field of structural design. Structural resistance, loading, plating thickness and cross-sectional area of beam are considered as stochastic variables. Safety margin equations of both beam and plate element are constructed. Since the safety margin equations are implicit function of random variables, the stochastic finite element method (SFEM) is adequate for sensitivity analysis. The advanced first order second moment (AFOSM) method is used to calculate the safety indices of structural components. In addition to this, branch and bound method is used to identify the dominant failure paths. Probabilistic Network Evaluation Technique (PNET) method is used to assess failure probability of structural system. The optimization problem of structure is formulated as a nonlinear programming problem that aims at minimizing structural weight with constraints on reliability and range constraints of design variables. An optimum vector algorithm is applied to solve the optimization problem. One illustrative example is carried out to elucidate present process of reliability assessment and reliability-based design optimization.

scholarly journals Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

2021 ◽  
Author(s):  
Yoshihiro Kanno
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Structural Reliability ◽  
Reliability Based Design Optimization ◽  
Input Distribution ◽  
Reliability Based Design ◽  
Optimal Value ◽  
Reliability Constraint ◽  
Distributionally Robust ◽  
Robust Reliability

AbstractThis study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.

An Efficient Approach for Reliability-Based Design Optimization Combined Sequential Optimization with Approximate Models

2018 ◽  
Vol 15 (04) ◽  
pp. 1850018 ◽  
Author(s):  
Bao Quoc Doan ◽  
Guiping Liu ◽  
Can Xu ◽  
Minh Quang Chau
Keyword(s):  
Design Optimization ◽  
Reliability Assessment ◽  
Latin Hypercube Sampling ◽  
Assessment Method ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Efficient Approach ◽  
Reliability Based Design ◽  
Approximate Models

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints which can be time-consuming in engineering structural design problems. In this paper, an efficient approach combined sequential optimization with approximate models is suggested for RBDO. The radial basis functions and Latin hypercube sampling are used to construct approximate models of the probabilistic constraints. Then, a sequential optimization with approximate models is carried out by the sequential optimization and reliability assessment method which includes a serial of cycles of deterministic optimization and reliability assessment. Three numerical examples are presented to demonstrate the efficiency of the proposed approach.

The Response Surface Single Loop Reliability-Based Design Optimization Method With Reliability Requirement on System Failure

2016 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Optimization Problem ◽  
Optimization Method ◽  
Reliability Based Design Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method ◽  
Deterministic Solution

In reliability-based design optimization (RBDO), an optimal design which minimizes an objective function while satisfying a number of probabilistic constraints is found. As opposed to deterministic optimization, statistical uncertainties in design variables and design parameters have to be taken into account in the design process in order to achieve a reliable design. In the most widely used RBDO approaches, the First-Order Reliability Method (FORM) is used in the probability assessment. This involves locating the Most Probable Point (MPP) of failure, or the inverse MPP, either exactly or approximately. If exact methods are used, an optimization problem has to be solved, typically resulting in computationally expensive double loop or decoupled loop RBDO methods. On the other hand, locating the MPP approximately typically results in highly efficient single loop RBDO methods since the optimization problem is not necessary in the probability assessment. However, since all these methods are based on FORM, which in turn is based on a linearization of the deterministic constraints at the MPP, they may suffer inaccuracies associated with neglecting the nonlinearity of deterministic constraints. In a previous paper presented by the authors, the Response Surface Single Loop (RSSL) Reliability-based design optimization method was proposed. The RSSL-method takes into account the non-linearity of the deterministic constraints in the computation of the probability of failure and was therefore shown to have higher accuracy than existing RBDO methods. The RSSL-method was also shown to have high efficiency since it bypasses the concept of an MPP. In RSSL, the deterministic solution is first found by neglecting uncertainties in design variables and parameters. Thereafter quadratic response surface models are fitted to the deterministic constraints around the deterministic solution using a single set of design of experiments. The RBDO problem is thereafter solved in a single loop using a closed-form second order reliability method (SORM) which takes into account all elements of the Hessian of the quadratic constraints. In this paper, the RSSL method is used to solve the more challenging system RBDO problems where all constraints are replaced by one constraint on the system probability of failure. The probabilities of failure for the constraints are assumed independent of each other. In general, system reliability problems may be more challenging to solve since replacing all constraints by one constraint may strongly increase the non-linearity in the optimization problem. The extensively studied reliability-based design for vehicle crash-worthiness, where the provided deterministic constraints are general quadratic models describing the system in the whole region of interest, is used to demonstrate the capabilities of the RSSL method for problems with system reliability constraints.

Reliability-Based Design Optimization of Microstructures With Analytical Formulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Pinar Acar
Keyword(s):  
Design Optimization ◽  
Material Properties ◽  
Optimization Problem ◽  
Optimization Under Uncertainty ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Analytical Formulation ◽  
Reliability Based Design ◽  
Safe Approach

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

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