• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.7
• /
• pp.805-811
• /
• 2012

The reliability based design optimization (RBDO) approach requires high computing cost to consider uncertainties. In order to reduce the design cost, the single loop single vector (SLSV) approach has been developed for RBDO. This method can reduce the cost in calculating deign sensitivity by elimination of the nested optimization process. However, this process causes the increment of the instability or inaccuracy of the method according to the problem characteristics. Therefore, the method may not give accurate solution or the robustness of the solution is not guaranteed. Especially, when the function is concave, the process frequently diverges. In this research, the concept of the conjugate gradient method for unconstrained optimization is utilized to develop a new single loop single vector method. The conjugate gradient is calculated with gradient directions at the most probable points (MPP) of previous cycles. Mathematical examples are solved for the verification of the proposed method. The numeri cal performances of the obtained results are compared to those of other RBDO methods. The SLSV approach using conjugate gradient is not greatly influenced by the problem characteristics and improves its convergence capability.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.40 no.6
• /
• pp.587-593
• /
• 2016

Reliability-based design optimization (RBDO) requires a high computational cost owing to its reliability analysis. A surrogate model is introduced to reduce the computational cost in RBDO. The accuracy of the reliability depends on the accuracy of the surrogate model of constraint boundaries in the surrogated-model-based RBDO. In earlier researches, constraint boundary sampling (CBS) was proposed to approximate accurately the boundaries of constraints by locating sample points on the boundaries of constraints. However, because CBS uses sample points on all constraint boundaries, it creates superfluous sample points. In this paper, efficient constraint boundary sampling (ECBS) is proposed to enhance the efficiency of CBS. ECBS uses the statistical information of a kriging surrogate model to locate sample points on or near the RBDO solution. The efficiency of ECBS is verified by mathematical examples.

• Journal of Institute of Control, Robotics and Systems
• /
• v.17 no.11
• /
• pp.1082-1089
• /
• 2011

Most engineered systems are designed with high levels of system redundancies to satisfy required reliability requirements under adverse events, resulting in high systems' LCCs (Life-Cycle Costs). Recent years have seen a surge of interest and tremendous advance in PHM (Prognostics and Health Management) methods that detect, diagnose, and predict the effects of adverse events. The PHM methods enable proactive maintenance decisions, giving rise to adaptive reliability. In this paper, we present a RAP (Resilience Allocation Problem) whose goal is to allocate reliability and PHM efficiency to components in an engineering context. The optimally allocated reliability and PHM efficiency levels serve as the design specifications for the system RBDO (Reliability-Based Design Optimization) and the system PHM design, which can be used to derive the detailed design of components and PHM units. The RAP is demonstrated using a simplified aircraft control actuator design problem resulting in a highly resilient actuator with optimally allocated reliability, PHM efficiency and redundancy for the given parameter settings.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.2
• /
• pp.125-130
• /
• 2011

Since conventional optimization that is classified as a deterministic method does not consider the uncertainty involved in a modeling or manufacturing process, an optimum design is often determined to be on the boundaries of the feasible region of constraints. Reliability-based design optimization is a method for obtaining a solution by minimizing the objective function while satisfying the reliability constraints. This method includes an optimization process and a reliability analysis that facilitates the quantization of the uncertainties related to design variables. Moment-based reliability analysis is a method for calculating the reliability of a system on the basis of statistical moments. In general, on the basis of these statistical moments, the Pearson system estimates seven types of distributions and determines the reliability of the system. However, it is technically difficult to practically consider the Pearson Type IV distribution. In this study, we propose an enhanced Pearson Type IV distribution based on a kriging model and validate the accuracy of the enhanced Pearson Type IV distribution by comparing it with a Monte Carlo simulation. Finally, reliability-based design optimization is performed for a system with type IV distribution by using the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.30 no.1
• /
• pp.87-94
• /
• 2017

Reliability analysis(RA) and Reliability-based design optimization(RBDO) require statistical modeling of input random variables, which is parametrically or nonparametrically determined based on experimental data. For the parametric method, goodness-of-fit (GOF) test and model selection method are widely used, and a sequential statistical modeling method combining the merits of the two methods has been recently proposed. Kernel density estimation(KDE) is often used as a nonparametric method, and it well describes a distribution function when the number of data is small or a density function has multimodal distribution. Although accurate statistical models are needed to obtain accurate RA and RBDO results, accurate statistical modeling is difficult when the number of data is small. In this study, the accuracy of two statistical modeling methods, SSM and KDE, were compared according to the number of data. Through numerical examples, the RA results using the input models modeled by two methods were compared, and appropriate modeling method was proposed according to the number of data.

• International Journal of Precision Engineering and Manufacturing
• /
• v.5 no.4
• /
• pp.61-68
• /
• 2004

Necessity to address engineering system uncertainties in design processes has long been acknowledged. To obtain quality of product, a safety factor is traditionally used by many design engineers due to its easy of use and comprehension. However, the safety factor approach often yields either conservative or unreliable designs, since it ignores the type of probability distribution and the mechanism of uncertainty propagation from the input to the output. For a consistent reliability-based design, two fundamental issues must be investigated thoroughly. First, the design-decision process that clearly identifies a mechanism of uncertainty propagation under system uncertainties needs to be developed, which must be an efficient and accurate process. To identify the mechanism more effectively, an adaptive probability analysis is proposed by adaptively setting probability levels through a posteriori error estimation. The second is to develop the design process that not only yields a high quality design but also a cost-effective optimum design from manufacturing point of view. As a result, a response surface methodology is specially developed for RBDO, thus enhancing numerical challenges of efficiency and complicatedness. Side crashworthiness application is used to demonstrate the integrated design process for product and manufacturing process design.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2009.04a
• /
• pp.101-104
• /
• 2009

최적설계는 설계자가 요구하는 제한조건을 만족시키는 범위에서 목적함수가 최소가 되는 설계점을 찾는 방법이다. 그러나 기존의 최적설계는 불확실성의 영향을 고려하지 않아 최적해가 제한조건의 경계에 위치하고 이것은 모델링과정이나 가공 등으로 인한 오차에 대한 영향을 고려하지 않는 문제점이 있다. 신뢰성 기반 최적설계는 불확실성을 정량화하면서 신뢰도를 계산하는 신뢰도 해석과정과 최적설계과정을 포함한다. 일반적으로 신뢰성 해석은 크게 추출법, 급속 확률 적분법, 모멘트 기반 신뢰성해석이 있다. 가장 널리 사용되는 급속 확률 적분법 중 최대 손상 가능점(MPP) 방법은 많은 MPP점이 존재하는 경우 수치적 비용이 증가하는 문제점과 표준 정규분포 공간으로 변환하는 과정에서 제한조건의 비선형성을 증가시켜 큰 오차를 발생시키는 문제점이 있다. 본 논문에서는 RBDO를 수행하기에 앞서 선행되어야 할 신뢰성해석 방법으로 곱분해기법을 사용하였고 이로부터 민감도 정보를 유도하여 기울기 기반 최적화 알고리즘을 적용하였다.

• Journal of the Korea Convergence Society
• /
• v.13 no.4
• /
• pp.287-292
• /
• 2022

In this paper, the stochastic distribution of the springback amount is investigated for the stamping process of a U-channel shaped-product with ultra-high strength steel. Using the reliability-based design optimization technique (RBDO), stochastic distribution of process parameters is considered in the analysis including material properties and process variation. Quantification of the springback scatters is carried out with the statistical analysis method according to the material strength. It is found that the scattering amount of springback decreases while the amount of springback increases as the tensile strength of the blank material increases, which is investigated by analyzing the strain and stress distribution of the punch and die shoulder. It is noted that the proposed scheme is capable of predicting and responding to the unavoidable scattering of springback in the sheet metal forming process.