Woochul Lim

Reliability-Based Design Optimization Using Akaike Information Criterion for Discrete Information

최적설계는 제한조건을 만족하면서 목적함수를 최소화하는 설계변수의 값을 찾는 설계 기법이다. 확정론적 접근 방법의 최적설계에서는 설계변수가 평균과 같은 대표 값을 갖는다는 가정하에 최적설계를 수행하고 변수들의 변동에 의한 시스템의 불확실성을 고려하기 위해 안전계수와 같은 경험적인 방법을 이용하여 신뢰성을 확보한다. 반면에 확률론적 접근 방법의 최적설계는 시스템의 신뢰성을 확보하기 위해 설계변수와 환경변수의 통계적 특성을 고려한다. 신뢰성 기반 최적설계를 수행하기 위해서는 시스템의 신뢰도를 판단하는 신뢰성해석을 수행해야 한다. 실제 공학문제에서는 신뢰성해석에 사용되는 비용의 문제로 신뢰성 기반 최적설계를 적용하는데 어려움이 있으며 이를 해결하기 위해 많은 연구들이 수행되고 있다. 신뢰성해석을 수행하는 방법으로 추출법, 급속확률적분법, 모멘트법 등이 제안되었다. 추출법을 제외한 기존의 연구들은 변수들의 통계적 특성을 고려하기 위해 변수의 분포를 연속함수로 정의되Key Words : Akaike Information Criterion(AIC: Akaike정보척도), Maximum Likelihood Estimation(MLE: 최우량추정법), Reliability Analysis(신뢰성해석), Reliability-based Design Optimization(신뢰성 기반 최적설계), Monte Carlo Simulation(몬테카를로 시뮬레이션), Bogie Frame(대차 틀) 초록: 신뢰성 기반 최적설계는 설계변수들의 변동을 평균이나 분산 등의 통계적 특성으로 고려하여 설계자가 원하는 신뢰도를 만족하는 해를 구한다. 신뢰도를 구하기 위한 기존의 신뢰성해석 기법들은 변수들이 연속함수로 정의되는 특정 확률분포를 따른다는 가정을 하지만 실제 문제에서 변수들은 한정적인 이산정보의 형태인 경우가 많기 때문에 변수들에 대한 가정을 하지 않고 이산정보로부터 신뢰성해석을 수행하는 것은 매우 중요하다. 본 연구에서는 후보 분포들 중에서 이산정보를 가장 잘 추정하는 분포를 결정하는 기법인 Akaike정보척도를 이용하여 신뢰성해석 및 신뢰성 기반 최적설계를 수행하는 기법을 제안한다. 수학예제를 통해 정확성을 검증하고 철도차량 용접대차의 신뢰성 기반 최적설계에 적용하여 제안한 기법의 유용성을 확인한다. Abstract: Reliability-based design optimization (RBDO) can be used to determine the reliability of a system by means of probabilistic design criteria, i.e., the possibility of failure considering stochastic features of design variables and input parameters. To assure these criteria, various reliability analysis methods have been developed. Most of these methods assume that distribution functions are continuous. However, in real problems, because real data is often discrete in form, it is important to estimate the distributions for discrete information during reliability analysis. In this study, we employ the Akaike information criterion (AIC) method for reliability analysis to determine the best estimated distribution for discrete information and we suggest an RBDO method using AIC. Mathematical and engineering examples are illustrated to verify the proposed method.

Design Optimization of PZT-Based Piezoelectric Cantilever Beam by Using Computational Experiments

Piezoelectric energy harvesting is gaining huge research interest since it provides high power density and has real-life applicability. However, investigative research for the mechanical–electrical coupling phenomenon remains challenging. Many researchers depend on physical experiments to choose devices with the best performance which meet design objectives through case analysis; this involves high design costs. This study aims to develop a practical model using computer simulations and to propose an optimized design for a lead zirconate titanate (PZT)-based piezoelectric cantilever beam which is widely used in energy harvesting. In this study, the commercial finite element (FE) software is used to predict the voltage generated from vibrations of the PZT-based piezoelectric cantilever beam. Because the initial FE model differs from physical experiments, the model is calibrated by multi-objective optimization to increase the accuracy of the predictions. We collect data from physical experiments using the cantilever beam and use these experimental results in the calibration process. Since dynamic analysis in the FE analysis of the piezoelectric cantilever beam with a dense step size is considerably time-consuming, a surrogate model is employed for efficient optimization. Through the design optimization of the PZT-based piezoelectric cantilever beam, a high-performance piezoelectric device was developed. The sensitivity of the variables at the optimum design is analyzed to suggest a further improved device.

Reliability-based design optimization of an automotive structure using a variable uncertainty

Reliability-based design optimization is an optimization technique based on the stochastic approach. Many studies using this approach assume the uncertainty in the design variable to be constant. However, when the uncertainty depends on the values of the design variable, this assumption results in the wrong conclusions. Therefore, the uncertainty should be considered as a variable in reliability-based design optimization. The uncertainty in the thickness during optimization, such as the tolerance, had been assumed to be a constant in automotive structures. However, in practice, the tolerance of the thickness depends on the nominal thickness. Hence, in this paper, reliability-based design optimization of an automotive structure such as an engine cradle and a body-in-white with a variable uncertainty is carried out. General Motors Korea provides the tolerance guide which defines the dependence between the nominal thickness and the tolerance. The information is adopted to define the variable uncertainty. Thus, the variable uncertainty can modify the uncertainty with respect to the design point, resulting in an accurate reliability estimation. Finally, reliability-based design optimization with a variable uncertainty is performed using the Akaike information criterion method which determines the fittest distribution of the performance based on the maximum likelihood estimation of the candidate distributions. Consequently, the automotive structures are optimized to reduce the mass while still satisfying the target reliabilities of the performances when considering a variable uncertainty.

Reliability-based Design Optimization for Lower Control Arm using Limited Discrete Information

Lower control arm (LCA) is a part of chassis in automotive. Performances of LCA such as stiffness, durability and permanent displacement must be considered in design optimization. However it is hard to consider different performances at once in optimization because these are measured by different commercial tools like Radioss, Abaqus, etc. In this paper, firstly, we construct the integrated design automation system for LCA based on Matlab including Hypermesh, Radioss and Abaqus. Secondly, Akaike information criterion (AIC) is used for assessment of reliability of LCA. It can find the best estimated distribution of performance from limited and discrete stochastic information and then obtains the reliability from the distribution. Finally, we consider tolerances of design variables and variation of elastic modulus and achieve the target reliability by carrying out reliability-based design optimization (RBDO) with the integrated system.

Model-Driven Design Framework for Future Combat Vehicle Development based on Firepower and Mobility: (1) Integrated Performance Modeling

Received 15 September 2014; received in revised form 22 October 2014; accepted 24 October 2014ABSTRACTThis paper proposes the 3D modeling and simulation technique for predicting the integrated per-formance of combat vehicle. To consider the practical driving and firing condition of a combatvehicle, the full vehicle model, which can define the six degrees-of-freedom of vehicle motionand various firing angles, is developed. The critical design parameters such as the stiffness anddamping coefficient of suspension system are applied to construct the analysis model of vehi-cle. A simple ballistic model, which incorporates the empirical interior ballistic model and thepoint mass trajectory model, is built to estimate the firing range and the firing recoil force. Topredict the integrated performance and analyze the effect of system parameters, MATLAB/SIM-ULINK model of a combat vehicle for performing the real time simulation is also developed.Several simulation tests incorporating the road bump and the firing recoil force are presented toconfirm the effectiveness of the proposed vehicle model.Key Words: Combat vehicle, Firepower, Integrated performance, Mobility, Modeling andsimulation, 3D vehicle model

Efficient Robust Design Optimization Using Statistical Moment Based on Multiplicative Decomposition Considering Non-normal Noise Factors

The performance of a system can be affected by the variance of noise factors, which arise owing to uncertainties of the material properties and environmental factors acting on the system. For robust design optimization of the system performance, it is necessary to minimize the effect of the variance of the noise factors that are impossible to control. However, present robust design techniques consider the variation of design factors, and not the noise factors, as being important. Furthermore, it is necessary to assume a normal distribution; however, a normal distribution is often not suitable to estimate the variations. In this study, a robust design technique is proposed to consider the variation of noise factors that are estimated as non-normal distributions in a real experiment. As an example of an engineering problem, a deep-sea manganese nodule miner tracked vehicle is used to demonstrate the feasibility of the proposed method.

Akaike Information Criterion-Based Reliability Analysis for Discrete Bimodal Information

The distribution of a response usually depends on the distribution of the variables. When a variable shows a distribution with two different modes, the response also shows a distribution with two different modes. In this case, recently developed methods for reliability analysis assume that the distribution functions are continuous with a mode. In actual problems, however, because information is often provided in a discrete form with two or more modes, it is important to estimate the distributions for such information. In this study, we employ the finite mixture model to estimate the response distribution with two different modes, and we select the best candidate distribution through AIC. Mathematical examples are illustrated to verify the proposed method.

Taguchi Robust Design of Tracked Vehicle for Manganese Nodule Test Miner in Collecting Operation Considering Deep-sea Noise Factors

A deep-sea manganese nodule miner consists of 4 parts: the pickup device, crusher, disposal device, and tracked vehicle. The tracked vehicle is an essential component to keep the self-propelled miner moving across deep-sea soil. The performances of the tracked vehicle are influenced by noise factors: the shear strength of the seafloor, bottom current, seafloor slope, track speed, reaction forces of flexible hose, etc. It is necessary to adopt a robust design method that improves the performances and minimizes the variation caused by noise factors. Taguchi`s method, the most widely known robust design method, searches for the robust optimum using an orthogonal array composed of the product of the inner array and outer array. In this paper, we propose a new screening technique to reduce the number of input factors and apply the MRSN (Multi-Response Signal to Noise) ratio to convert multiple performances into single one in order to overcome the difficulties and limitations of using Taguchi`s method in a case with many input factors and multiple performances. A test miner was already designed and tested. It has about 1/10 the capacity of a commercial one and was successfully operated at an in-shore area. Taguchi`s robust design was applied to the tracked vehicle of the test miner, and design improvements were implemented for the vehicle.

Bootstrap Guided Information Criterion for Reliability Analysis Using Small Sample Size Information

Several methods for reliability analysis have been established and applied to engineering fields bearing in mind uncertainties as a major contributing factor. Small sample size based reliability analysis can be very beneficial when rising uncertainty from statistics of interest such as mean and standard deviation are considered. Model selection and evaluation methods like Akaike Information Criteria (AIC) have demonstrated efficient output for reliability analysis. However, information criterion based on maximum likelihood can provide better model selection and evaluation in small sample size scenario by considering the well-known measure of bootstrapping for curtailing uncertainty with resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion based reliability analysis to check for uncertainty arising from statistics of interest for small sample size problems. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection frequency devised from information criterion to be combined with reliability analysis. It is also beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest under replication based approach. The proposed simulation scheme is verified using a number of small and moderate sample size focused mathematical example with AIC based reliability analysis for comparison and Monte Carlo simulation (MCS) for accuracy. The results show that the proposed simulation scheme favors the statistics of interest by reducing the spread and hence the uncertainty in small sample size based reliability analysis when compared with conventional methods whereas moderate sample size based reliability analysis did not show any considerable favor.

정확한 신뢰성 해석을 위한 아카이케 정보척도 기반 일반화파레토 분포의 임계점 추정

공학분야의 신뢰성 해석은 점점 더 높은 신뢰도 영역에 대한 확률밀도함수의 예측을 요구한다. 따라서 높은 신뢰도를 정확하게 해석하기 위해 분포의 꼬리부분을 정확하게 표현해야 한다. 최근 들어 꼬리부분에 대한 표본만을 이용해 꼬리 모형을 생성하여 신뢰도를 추정할 수 있는 방법인 일반화파레토 분포에 대한 연구가 활발히 진행되고 있다. 하지만 기존의 연구에서는 부정확한 임계점 추정으로 꼬리 부분에서 신뢰도의 정확도가 떨어진다. 따라서 본 논문에서는 아카이케 정보척도를 이용하여 임계점을 정확하고 강건하게 추정하고 이를 통해 꼬리 모형의 정확도를 향상시키는 아카이케 정보척도 기반 일반화파레토 분포 기법을 제안한다. 또한 제안하는 기법을 이용한 신뢰성 해석을 수행하여 정확도가 향상된 신뢰성 해석 결과를 도출하였다.