Reliability-based Design Optimization Methodology Research Articles

Multi-Task Learning for Design Under Uncertainty With Multi-Fidelity Partially Observed Information

Abstract The assessment of system performance and identification of failure mechanisms in complex engineering systems often requires the use of computation-intensive finite element software or physical experiments, which are both costly and time-consuming. Moreover, when accounting for uncertainties in the manufacturing process, material properties, and loading conditions, the process of reliability-based design optimization (RBDO) for complex engineering systems necessitates the repeated execution of expensive tasks throughout the optimization process. To address this problem, this paper proposes a novel methodology for RBDO. First, a multi-fidelity surrogate modeling strategy is presented, leveraging partially observed information (POI) from diverse sources with varying fidelity and dimensionality to reduce computational cost associated with evaluating expensive high-dimensional complex systems. Second, a multi-task surrogate modeling framework is proposed to address the concurrent evaluation of multiple constraints for each design point. The multi-task framework aids in the development of surrogate models and enhances the effectiveness of reliability analysis and design optimization. The proposed multi-fidelity multi-task machine learning model utilizes a Bayesian framework, which significantly improves the performance of the predictive model and provides uncertainty quantification of the prediction. Additionally, the model provides a highly accurate and efficient framework for reliability-based design optimization through knowledge sharing. The proposed method was applied to two design case studies. By incorporating POI from various sources, the proposed approach improves the accuracy and efficiency of system performance prediction, while simultaneously addressing the cost and complexity associated with the design of complex systems.

Reliability based design optimization of wire bonding in power microelectronic devices

This paper presents a numerical investigation of the probabilistic approach in estimating the reliability of wire bonding, and develops a reliability-based design optimization Methodology (RBDO) for microelectronic device structures. The objective of the RBDO method is to design structures which should be both economical and reliable where the solution reduces the structural weight in uncritical regions. It does not only provide an improved design, but also a higher level of confidence in the design. The Finite element simulation model intends to analyze the sequence of the failure events in power microelectronic devices. This numerical model is used to estimate the probability of failure of power module regarding the wire bonding connection. However, due to time-consuming of the multiphysics finite element simulation, a response surface method is used to approximate the response output of the limit state, in this way the reliability analysis is performed directly to the response surface by using the First and the Second Order Reliability Methods FORM/SORM. Subsequently the reliability analysis is integrated in the optimization process to improve the performance and reliability of structural design of wire bonding. The sequential RBDO algorithm is used to solve this problem and to find the best structural designs which realize the best compromise between cost and safety.

Sequential optimization and reliability assessment based on dimension reduction method for accurate and efficient reliability-based design optimization

This study develops an efficient and accurate methodology for reliability-based design optimization (RBDO) by combining the most probable point (MPP)-based dimension reduction method (DRM) to enhance accuracy and the sequential optimization and reliability assessment (SORA) to enhance efficiency. In many researches, first-order reliability method (FORM) has been utilized for RBDO methods due to its efficiency and simplicity. However, it might not be accurate enough for highly nonlinear performance functions. Therefore, the MPP-based DRM is introduced for the accurate reliability assessment in this study. Even though the MPP-based DRM significantly improves the accuracy, additional computations for the moment-based integration are required. It is desirable to reduce the number of reliability analyses in the RBDO process. Since decoupled approaches such as SORA reduce necessary reliability analyses considerably, DRM-based SORA is proposed in this study for accurate and efficient RBDO. Furthermore, convex linearization is introduced to approximate inactive probabilistic constraints to additionally improve the efficiency. The efficiency and accuracy of the proposed method are verified through numerical examples.

목표 성능치 기반의 확률구속조건 평가 기법을 이용한 전자기 장치의 신뢰도 기반 최적설계

본 논문에서는 전자기 관련 제품의 효율적인 신뢰도 기반 최적설계를 위해 확률구속조건을 평가하는 기법으로 해의 안정성과 효율성이 우수한 목표 성능치법을 제시 하였다. 목표 성능치법을 적용한 신뢰도 기반 최적설계의 효율성 검증을 위하여 스피커 모델과 초전도 자기에너지 저장장치 모델에 대한 최적설계를 수행하였고, 이를 기존 신뢰도 지수법을 적용한 최적설계 결과와 비교하였다. 또한 몬테카를로 수치모사기법을 이용하여 도출된 최적해의 신뢰도를 재 계산 후 비교함으로써 제안된 기법의 신뢰도 평가 결과의 정밀도를 검증하였다. This paper introduces an effective methodology for reliability-based design optimization of electromagnetic products, where a performance measure approach is adopted to accurately assess probabilistic constrains. Two design problems consisting of a loudspeaker and a superconducting magnetic energy storage system are considered. The efficiency of the proposed method in evaluating the failure probability of performances during the optimization process are compared with the existing method based on the reliability index approach. Moreover, in term of the accuracy of probability failure values, optimized design results are examined with reference values obtained from the Monte Carlo simulation.

Efficient Reliability-Based Design Optimization for Microelectromechanical Systems

The miniaturization of microelectromechanical systems (MEMS) makes cheaper products (due to less chip size consumption) and new applications, e.g., in chip cards, possible. With further miniaturization, however, the influence of manufacturing variances increases: hence it is more and more important to consider them already in the design optimization phase. The widely used Monte Carlo (MC) simulation is not suitable for the implementation in optimization algorithms, as a large number of required samples result in long simulation times. Instead we apply the Sigma-Point approach which enables the accurate calculation of the output variances, even for nonlinear functions with only few sample calculations. In conjunction with a MEMS resonator model the Sigma-Point approach turns out to be four orders of magnitude faster than an equivalent MC calculation. Therefore, it is optimally suited for an efficient reliability-based design optimization (RBDO). Furthermore, the Sigma-Point approach is simple to implement and matrix notation enables fast calculation, even for large models. A versatile analysis of the interaction between optimized sensor design, yield requirements, and manufacturing tolerances is feasible with the suggested RBDO methodology.

Reliability Based Design Optimization of MEMS Considering Pull-In

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.

Reliability Simulation and Design Optimization for Mechanical Maintenance

Reliability model of a mechanical product system will be newly reconstructed and maintenance cost will increase because failed parts can be replaced with new components during service,which should be accounted for in system design. In this paper,a reliability model and reliability-based design optimization methodology for maintenance are presented. First,based on the time-to-failure density function of the part of the system,the age distributions of all parts of the system during service are investigated,a reliability model of the mechanical system for maintenance is developed. Then,reliability simulations of the systems with Weibull probability density functions are performed,the system minimum reliability and steady reliability for maintenance are defined based on reliability simulation during the life cycle of the system. Thirdly,a maintenance cost model is developed based on replacement rates of the parts,a reliability-based design optimization model for maintenance is presented,in which total life cycle cost is considered as design objective and system reliability as design constrain. Finally,the reliability-based design optimization methodology for maintenance is used to design of a link ring for the chain conveyor,which shows that optimal design with the lowest maintenance cost can be obtained,and minimum reliability and steady reliability of the system can satisfy requirement of system reliability during service of the chain conveyor.

Improving the fatigue life of a vehicle knuckle with a reliability-based design optimization approach

A major issue in vehicle industry is the presence of variability in the physical properties and manufacturing processes. Deterministic approaches are unable to take into account these variabilities without leading to oversized structures. The necessity of assessing the robustness of a particular design requires a new methodology based on reliability analysis and design optimization through probabilistic models of design variables. The vehicle lifetime is highly determined by the fatigue life of its components. Variability in the material parameters (such as Young's modulus and tensile strength) may have a strong effect on the fatigue life. This is demonstrated in this paper for a vehicle knuckle structure. As a first step, a probabilistic approach to fatigue life prediction is worked out to assess the reliability of vehicle fatigue predictions in the presence of material variability. In a second step, a reliability based design optimization methodology is applied to improve the design reliability for the given material variability. These two steps not only provide better insight in the effect of variability on the fatigue life prediction, but also guidelines to improve the material definition and manufacturing tolerances. One thus obtains a powerful tool to reduce design conservatism while maintaining and even improving the structural safety. This paper intends to demonstrate the effectiveness of this innovative approach by integrating probabilistic design methods into the traditional design process, stressing the advantages that such methodologies bring to the improvement of product fatigue life prediction and structural reliability.

Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method

In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty-based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However, Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver, the eigenvector dimension reduction (EDR) method, for Bayesian reliability analysis. The EDR method takes a sensitivity-free approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration.

Reliability-based design using variable-fidelity optimization

Competitive marketplaces have driven the need for simulation-based design optimization to produce efficient and cost-effective designs. However, such design practices typically do not take into account model uncertainties or manufacturing tolerances. Such designs may lie on failure-driven constraints and are characterized by a high probability of failure. Reliability-based design optimization (RBDO) methods have been developed to obtain designs that optimize a merit function while ensuring a target reliability level is satisfied. Unfortunately, these methods are notorious for the high computational expense they require to converge. In this research variable-fidelity methods are used to reduce the cost of RBDO. Variable-fidelity methods use a set of models with varying degrees of fidelity and computational expense to aid in reducing the cost of optimization. The variable-fidelity RBDO methodology developed in this investigation is demonstrated on two test cases: a nonlinear analytic problem and a high-lift airfoil design problem. For each of these problems the proposed method shows considerable savings for performing RBDO as compared with standard approaches.

Structural optimization considering the probabilistic system response

In engineering problems, the randomness and uncertainties are inherent and the scatter of structural parameters from their nominal ideal values is unavoidable. In Reliability Based Design Optimization (RBDO) and Robust Design Optimization (RDO) the uncertainties play a dominant role in the formulation of the structural optimization problem. In an RBDO problem additional non deterministic constraint functions are considered while an RDO formulation leads to designs with a state of robustness, so that their performance is the least sensitive to the variability of the uncertain variables. In the first part of this study a metamodel assisted RBDO methodology is examined for large scale structural systems. In the second part an RDO structural problem is considered. The task of robust design optimization of structures is formulated as a multi-criteria optimization problem, in which the design variables of the optimization problem, together with other design parameters such as the modulus of elasticity and the yield stress are considered as random variables with a mean value equal to their nominal value. .

A new response surface methodology for reliability-based design optimization

Deterministic optimum designs that are obtained without consideration of uncertainties could lead to unreliable designs, therefore calling for reliability-based design optimization (RBDO). However, it has been reported in literatures that when RBDO involves evaluation of probabilistic constraints it is prohibitively expensive or even diverges for many large-scale applications. Therefore, the hybrid mean value (HMV) method had been proposed by authors for highly efficient and stable RBDO by evaluating the probabilistic constraint effectively. However, even with the HMV method, the RBDO process could be still expensive for large-scale applications or applications where efficient design sensitivity analysis method is unavailable. To alleviate this difficulty, a new RBDO methodology developed integrating the HMV method with a proposed response surface method, which is specifically developed for reliability analysis and optimization. A large-scale example problem is employed to demonstrate the proposed RBDO method.