Earticle

The design variables and material properties as well as the external loads concerned with structural engineering are used to be deterministic in optimization process. These values, however, have variability from expected performance. Therefore, deterministic optimum designs that are obtained without taking these uncertainty into account could lead to unreliable designs, which necessitates the Reliability-Based Design Optimization(RBDO). RBDO involves an evaluation of probabilistic constraints which constitutes another optimization procedure. So, an expensive computational cost is required. Therefore, how to decrease the computational cost has been an important challenge in the RBDO research field. Approximation models, response surface model and Kriging model, are employed to improve an efficiency of the RBDO.

A reliability-based optimization method for electromagnetic design is presented to take uncertainties of design parameters into account. The method can provide an optimal design satisfying a specified confidence level in the presence of uncertain parameters. To achieve the goal, the reliability index approach based on the firstorder reliability method is adopted to deal with probabilistic constraint functions and a double-loop optimization algorithm is implemented to obtain an optimum. The proposed method is applied to the TEAM Workshop Problem 22 and its accuracy and efficiency is verified with reference of Monte Carlo simulation results.

A moment method known as the fourth moment method can perform reliability analysis without optimization using the first four statistical moments. Numerical integration is used to calculate the statistical moments, where a moment-based quadrature rule can be used for integration nodes and weights. However, the moment-based quadrature rule has to solve a system of linear equations that can be numerically unstable. Considering this point, an improved moment-based quadrature rule is proposed and is applied to reliability-based design optimization. Finally, the moment-based RBDO is applied to numerical examples with a variety of random variables and target reliability indexes. From the numerical results, the performance of the improved moment-based quadrature rule can be confirmed and several guidelines are given for the moment-based RBDO.

When Deterministic Design Optimization (DDO) methods are used, deterministic optimum designs are frequently pushed to the design constraint boundary, leaving little or no room for tolerances (or uncertainties) in design, manufacture, and operating processes. In the Reliability-Based Design Optimization (RBDO) model for robust system design, the mean values of uncertain system variables are usually used as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide an improved design but also a higher level of confidence in the design. In this work, we seek to improve the quality of RBDO processes using efficient optimization techniques with object of improving the resulting objective function and satisfying the required constraints. Our recent RBDO developments show its efficiency and applicability in this context. So we present some recent structural engineering applications demonstrate the efficiency of these developed RBDO methods.

Design variables for suspension systems cannot always be realized in the actual suspension systems due to tolerances in manufacturing and assembly processes. In order to deal with these tolerances, design variables associated with kinematic configuration and compliance characteristics of suspensions are treated as random variables. The reliability of a design target with respect to a design variable is defined as the probability that the design target is in the acceptable design range for all possible values of the design variable. To compute reliability, the limit state, which is the boundary between the acceptable and unacceptable design, is expressed mathematically by a limit state function with value greater than 0 for acceptable design, and less than 0 for unacceptable design. Through reliability analysis, the acceptable range of design variables that satisfy a reliability target is specified. Furthermore, through sensitivity analysis, a general procedure for optimization of the design target with respect to the design variables has been established.

This study introduces the Reliability-Based Design Optimization (RBDO) to enhance the kinematic and compliance (K & C) characteristics of automotive suspension system. In previous studies, the deterministic optimization has been performed to enhance the K & C characteristics. Unfortunately, uncertainties in the real world have not been considered in the deterministic optimization. In the design of suspension system, design variables with the uncertainties, such as the bushing stiffness, have a great influence on the variation of the suspension performances. There is a need to quantify these uncertainties and to apply the RBDO to obtain the design, satisfying the target reliability level. In this research, design variables including uncertainties are dealt as random variables and reliability of the suspension performances, which are related the K & C characteristics, are quantified and the RBDO is performed. The RBD-optimum is compared with the deterministic optimum to verify the enhancement in reliability. Thus, the reliability of the suspension performances is estimated and the RBD-optimum, satisfying the target reliability level, is determined.

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis 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. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability 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 RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO's results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.

This study presents the effectiveness of a composite structure at improving blast resistance. The proposed composite structure consists of carbon fiber reinforced polymer (CFRP) and steel layers. While CFRP layer is used for blast energy reflection due to its high strength, steel layer is used for blast energy absorption due to its high ductility. A dynamic model is used to simulate the elastoplastic behavior of the proposed composite structure subject to blast load. Considering the magnitude variations of a blast event, the probability of failure of each layer is evaluated using reliability analysis. By assigning design probability of failure of each layer in the composite structure, the thickness of layers is optimized. A case study for the design of CFRP-steel composite structure subjected to an uncertain blast event is also presented.

In this paper, for constrained optimization problem, one multi-objective optimization algorithm that ensures both performance robustness and constraint feasibility is proposed when uncertainties are involved in design variables. In the proposed algorithm, the gradient index of objective function assisted by design sensitivity with the help of finite element method is applied to evaluate robustness; the reliability calculated by the sensitivity-assisted Monte Carlo simulation method is used to assess the feasibility of constraint function. As a demonstration, the performance and numerical efficiency of the proposed method is investigated through application to the optimal design of TEAM problem 22--a superconducting magnetic energy storage system.

Autonomous Underwater Vehicle (AUV), which are becoming more and more important in ocean exploitation tasks, needs energy conservation urgently when sailing the complex mission path in long time cruise. As hull lines optimization design becomes the key factor, which closely related with resistance, in AUV preliminary design stage, uncertainty parameters need to be considered seriously. In this research, Myring axial symmetry revolution body with parameterized expression is assumed as AUV hull lines, and its travelling resistance is obtained via modified DATCOM formula. The problems of AUV hull lines design for the minimum travelling resistance with uncertain parameters are studied. Based on reliability-based optimization design technology, Design For Six Sigma (DFSS) for high quality level is conducted, and is proved more reliability for the actual environment disturbance.

In order to help decision-makers in the early design phase to improve and make more cost-efficient system safety and reliability baselines of aircraft design concepts, a method (Multi-objective Optimization for Safety and Reliability Trade-off) that is able to handle trade-offs such as system safety, system reliability, and other characteristics, for instance weight and cost, is used. Multi-objective Optimization for Safety and Reliability Trade-off has been developed and implemented at SAAB Aeronautics. The aim of this paper is to demonstrate how the implemented method might work to aid the selection of optimal design alternatives. The method is a three-step method: step 1 involves the modelling of each considered target, step 2 is optimization, and step 3 is the visualization and selection of results (results processing). The analysis is performed within Architecture Design and Preliminary Design steps, according to the company's Product Development Process. The lessons learned regarding the use of the implemented trade-off method in the three cases are presented. The results are a handful of solutions, a basis to aid in the selection of a design alternative. While the implementation of the trade-off method is performed for companies, there is nothing to prevent adapting this method, with minimal modifications, for use in other industrial applications.

The military communication equipment is required the high reliability for operating adequate functions under severe conditions. This reliability is the essential element for the quality of the product, for the uncontrolled factors, such as the clearance, damage of the material, the reduction of stiffness, which are the designer is unable to handle. In this paper, the uncertainty for the design was supposed to the probability model for the military communication equipment, and the average of the objective function was minimized for reducing design uncertainty. The reliability-based design optimization which was implemented the limit state function was formulated into the mathematical model, so the reliable optimized structure was implemented than the base-line design.

본 연구에서는 NREL 5MW 풍력발전기 타워 설계 모델을 다물체 동역학과 신뢰성 기반 최적 설계를 이용하여 최적화하는 연구를 수행하였다. 타워 모델은 티모센코 빔 이론을 이용하여 얻은 동특성을 내포한 링크와 조인트로 이루어진 수학적 모델로 표현하였다. 최적화 문제에서는 높이가 일정한 타워에서 두께, 내 외곽 지름이 변할 때 나타나는 민감도 변화를 비교하여 결과를 도출하였으며, 비교 기준으로 굽힘 응력과 좌굴 안정성을 사용하였다. 일계 이차 모멘트법을 이용한 최적화 알고리즘에서 얻은 최종 모델은 유한요소법을 이용한 정하중 해석에서 최대 응력 분포를 이용한 안전성을 고려를 통해 유효성을 검증하였다. 본 연구 방법을 통해 동역학적 모델과 유한요소 모델간의 연계성을 확인하고, 낮은 타워 설치 비용으로 더 강건한 시스템을 구축할 수 있는 설계 방향을 제시하였다.

In this study, the NREL 5 MW wind turbine tower model was optimized according to the multi-body dynamics and reliability-based design. The mathematical model was defined as a link-joint system including dynamic characteristics derived from Timoshenko's beam theory. For the optimization problem, the sensitivities to variations in the tower thicknesses and inner and outer diameters were acquired and arranged in terms of safety and efficiency according to bending stress and buckling standards. An optimal design was calculated with the advanced first-order second moment method and used to define a finite element model for validation. The finite element model was simulated by static analysis. The relationship between the multi-body dynamic and finite element method throughout the process was investigated, and the optimal model, which had high endurance despite its low mass, was determined.

본 연구에서는 환경, 재료 물성 및 제작 등에서의 불확실성을 고려하여 130m급 고정식 해양구조물의 신뢰성 기반 최적설계를 수행하였다. 구조물의 구조건전성을 엄밀하게 반영하기 위해 작용 및 허용 응력의 비인 UC 값을 신뢰성 해석 및 신뢰성 기반 최적설계의 제약조건으로 고려하였다. 해양구조물의 제작비용을 저감하기 위해 자켓형 지지구조물의 중량을 최소화하였다. 불확실성의 통계적 특성은 문헌 등을 참고하여 관측되거나 측정된 데이터를 기반으로 정의하였다. 자켓형 해양구조물의 신뢰성 해석과 신뢰 기반 최적설계는 부재 수가 많아 계산 부담이 큼으로 문제의 차원을 축소하기 위해 응답의 중요성을 기준으로 설계변수를 선별할 수 있는 방법을 제안한다. 또한 효율적인 계산을 위해 신뢰성 기반 최적설계를 수행하기 전 결정론적 최적설계를 먼저 수행하였다. 마지막으로, 도출된 최적설계(안)을 기존 각 급 규정 기반 설계와 안전성 및 경제성 측면에서 비교 분석하였다.

In this study, a reliability-based design optimization of a 130-m class fixed-type offshore platform, to be installed in the North Sea, was carried out, while considering environmental, material, and manufacturing uncertainties to enhance its structural safety and economic aspects. For the reliability analysis, and reliability-based design optimization of the structural integrity, unity check values (defined as the ratio between working and allowable stress, for axial, bending, and shear stresses), of the members of the offshore platform were considered as constraints. Weight of the supporting jacket structure was minimized to reduce the manufacturing cost of the offshore platform. Statistical characteristics of uncertainties were defined based on observed and measured data references. Reliability analysis and reliability-based design optimization of a jacket-type offshore structure were computationally burdensome due to the large number of members; therefore, we suggested a method for variable screening, based on the importance of their output responses, to reduce the dimension of the problem. Furthermore, a deterministic design optimization was carried out prior to the reliability-based design optimization, to improve overall computational efficiency. Finally, the optimal design obtained was compared with the conventional rule-based offshore platform design in terms of safety and cost.

Deep-seabed test miner operated by a self-propelled mining system moving on soft soil is an essential device to secure floating and towing performances. The performances of the tracked vehicle are seriously influenced by noise factors such as the shear strength of the seafloor, bottom current, seafloor slope, speed of tracked vehicle, reaction forces of flexible hose, steering ratio, etc. Due to uncertainties related to noise factors, the design of a deep-sea manganese nodules test miner that satisfies target reliabilities is difficult. Therefore, reliability-based design optimization (RBDO) is required to guarantee system reliability under circumstances where uncertainties related to noise factors prevail. Among noise factors, the bottom current, a bimodal distribution, is censored due to the observation limit of measurement devices. Therefore, estimated distribution of the bottom current is inaccurate without considering these characteristics and the result of RBDO cannot be guaranteed. In this paper, we define censored data as unknown values over the limit of observation. If this data is estimated by using Akaike information criterion (AIC) that cannot consider the characteristics of censored data, the distribution of estimated data cannot guarantee accurate reliability. Therefore, censored AIC that can consider the characteristics of data is used to estimate accurate distribution of the bottom current. Finally, RBDO, under circumstances where uncertainties related to noise factors combined censored data are present, is performed on the mobility of a deep-sea manganese nodules test miner.

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.

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.