Reliability-based Multidisciplinary Design Optimization Research Articles

A reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model for nuclear fuel assembly bottom nozzle

The design of intricate systems such as the nuclear fuel assembly necessitates elevated levels of multi-disciplinary performance and reliability. In current reliability-based multidisciplinary design optimization methods, the decoupling strategy between optimization and reliability assessment involves sequential optimization and reliability assessment, with reliability serving as a constraint for optimization. This approach often suffers failure in locating the global optimal solution. In light of this issue, a reliability-based multidisciplinary design parallel optimization method based on double-layer approximation model is hereby proposed, achieving parallel separation and global efficient optimization of deterministic disciplinary performances and reliability, while performing efficient and accurate calculation on the multi-disciplinary reliability numerical solution. This method has been implemented for the multi-disciplinary uncertain optimization of the nuclear fuel assembly bottom nozzle. In comparison to conventional optimization methods, this approach demonstrates enhanced global optimization effectiveness.

Reliability-based multidisciplinary design optimization of an aeroelastic unpowered guided aerial vehicle

Most Aeronautical and Astronautical Systems (AAS) are inherently complex, multidisciplinary, nonlinear, and computationally intensive for design and analysis. Utilizing the Reliability-Based Multidisciplinary Design Optimization framework can address the multidisciplinary nature of these systems while accounting for inherent uncertainties. In this paper, an efficient methodology for Reliability-Based Multidisciplinary Design optimization of an aerial vehicle is developed. The computational burden of reliability assessment could make its integration within a Multidisciplinary Design Optimization cycle a formidable task. In this respect, a multilevel Multidisciplinary Design Optimization architecture is proposed in which the computational cost is reduced by considering the reliability analysis, as needed only for critical subsystems. To this end, a single-level Reliability-Based Multidisciplinary Design Optimization is derived using the Performance Measure Analysis and the Karush-Kuhn-Tucker condition. The work demonstrates the integration of this formulation into the proposed multilevel Reliability-Based Multidisciplinary Design Optimization architecture. The proposed design architecture is implemented for an aeroelastic Unpowered Guided Aerial Vehicle whose outcomes are compared with previous results obtained via a mono-level Uncertainty-Based Multidisciplinary Design Optimization architecture.

A Crossrate-Based Approach for Reliability-Based Multidisciplinary Dynamic System Design Optimization

In practical applications, the multidisciplinary dynamic system design optimization (MDSDO)-based solution is limited by uncertainty, which causes random variation in the physical design variable in the static discipline and the equation of state in the dynamic discipline. To address the lack of reliability of the MDSDO solution, a crossrate-based MDSDO approach (C-MDSDO), consisting of the MDSDO stage and a reliability assessment stage, is proposed in this paper. In the reliability assessment stage, a sub-optimization problem based on the crossrate of the objective reliability index sample trajectory is designed to obtain the shifting vector, which is employed to obtain a sufficiently reliable solution. In addition, the proposed approach adopts a sequential problem-solving framework that avoids nested optimization and a reliability assessment. One numerical case and two engineering cases were employed to validate the effectiveness of the proposed method. The results show that the reliability of the proposed solutions significantly improved.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization (RBMDO) of engineering structures, the saddlepoint approximation (SA) method can be utilized to enhance the accuracy and efficiency of reliability evaluation. However, the random variables involved in SA should be easy to handle. Additionally, the corresponding saddlepoint equation should not be complicated. Both of them limit the application of SA for engineering problems. The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments. However, the traditional moment matching method is not very accurate generally. In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization, a fourth-moment saddlepoint approximation (FMSA) method is introduced into RBMDO. In FMSA, the approximate cumulative generating functions are constructed based on the first four moments of the limit state function. The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function. Furthermore, the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment, which is based on the performance measure approach strategy. Two engineering examples are introduced to verify the effectiveness of proposed method.

A novel Kriging-model-assisted reliability-based multidisciplinary design optimization strategy and its application in the offshore wind turbine tower

In Reliability-based Multidisciplinary Design Optimization (RBMDO), the key performance functions of wind turbine are usually implicit, which means the performance response can only be obtained through time-consuming Physics Experiment (PE) or Finite Element Analysis (FEA). However, for practical engineering, the computational cost of repeatedly using PE or FEA is prohibitive. To tackle this challenge, in this study, an adaptive Kriging-model-assisted RBMDO strategy is proposed. The novel updated-strategy for performance function in RBMDO is discussed to find effective training samples of active learning for Kriging model. Also, a powerful decoupling strategy of RBMDO is introduced and combined with the proposed method to enhance computational efficiency further. Two case studies, including a mathematic example and a hydraulic turbine rotor bracket design example, are utilized to illustrate the advantage of the given strategy. Finally, the proposed method is applicated into an engineering design of 5 MW offshore wind turbine tower to ensure its reliability and safety.

A Reliability-Based Multidisciplinary Design Optimization Strategy considering Interval Uncertainty Based on the Point-Infilled Kriging Model

Generally, traditional uncertainty design optimization (UDO) methods are based on probability density distribution function or fuzzy membership function. In this situation, a large amount of uncertain information is necessary to construct the UDO model accurately. While, the interval UDO methods require less design information. Only the upper and lower bounds of interval uncertainty are utilized to construct the optimization model. In this study, to enhance the efficiency and accuracy of UBDO considering interval uncertainty, a reliability-based multidisciplinary design optimization (RBMDO) strategy using the point-infilled Kriging model is proposed. In the given method, a double-nested RBMDO model considering interval uncertainty is established. The collaborative optimization is utilized to deal with coupling relationships among complex systems. Then, the point-infilled Kriging response surface strategy is introduced to approximate the RBMDO model. The procedure of the interval multidisciplinary collaborative optimization method based on the Kriging model is discussed. Two examples are given to illustrate the application of the proposed method.

Multidisciplinary design optimization of engineering systems under uncertainty: a review

PurposeAs an advanced calculation methodology, reliability-based multidisciplinary design optimization (RBMDO) has been widely acknowledged for the design problems of modern complex engineering systems, not only because of the accurate evaluation of the impact of uncertain factors but also the relatively good balance between economy and safety of performance. However, with the increasing complexity of engineering technology, the proposed RBMDO method gradually cannot effectively solve the higher nonlinear coupled multidisciplinary uncertainty design optimization problems, which limits the engineering application of RBMDO. Many valuable works have been done in the RBMDO field in recent decades to tackle the above challenges. This study is to review these studies systematically, highlight the research opportunities and challenges, and attempt to guide future research efforts.Design/methodology/approachThis study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.FindingsFirst, the multidisciplinary design optimization (MDO) preliminaries are given. The basic MDO concepts and the corresponding mathematical formulas are illustrated. Then, the procedures of three RBMDO methods with different reliability analysis strategies are introduced in detail. These RBMDO methods were proposed for the design optimization problems under different uncertainty types. Furtherly, an optimization problem for a certain operating condition of a turbine runner blade is introduced to illustrate the engineering application of the above method. Finally, three aspects of future challenges for RBMDO, namely, time-varying uncertainty analysis; high-precision surrogate models, and verification, validation and accreditation (VVA) for the model, are discussed followed by the conclusion.Originality/valueThe scope of this study is to introduce the RBMDO theory systematically. Three commonly used RBMDO-SORA methods are reviewed comprehensively, including the methods' general procedures and mathematical models.

An Efficient Sequential Reliability Analysis Method for Multidisciplinary System

Multidisciplinary reliability analysis (MRA) is an important part of reliability-based multidisciplinary design optimization (RBMDO). In order to solve the problem of low computational efficiency caused by nested loops in multidisciplinary reliability analysis, an efficient multidisciplinary reliability analysis method based on decoupling idea is proposed. The method decouples system analysis, system sensitivity analysis and reliability analysis of Single discipline to form a recursive cycle, which eliminates the complete optimization calculation of reliability analysis model by system-level optimizer in each iteration. In the process of system sensitivity analysis, the global sensitivity equation is used to perform the concurrent subspace sensitivity analysis, which improves the efficiency of MRA. The decoupled multidisciplinary reliability analysis can get rid of the restriction that the traditional reliability analysis can only be carried out by using nonlinear optimization method, and the modified advanced mean value (MAMV) and other most probable point (MPP) search algorithms can be used to solve the reliability problem. Finally, three examples are used to verify the effectiveness of the method.

Importance measure analysis of design variables and uncertain parameters in multidisciplinary systems

The traditional reliability-based multidisciplinary design optimization consumes large computation resources due to a large number of design variables and uncertain parameters in multidisciplinary systems. Therefore, the screening of important design variables and uncertain parameters contributes to reducing the difficulty of optimization. However, the current methods ignore the interaction between design variables and uncertain parameters. Via a probabilistic and nonprobabilistic reliability model, the work in this paper establishes the concept of a comprehensive reliability-based importance measure that considers both design variables and uncertain parameters. An efficient method based on the Bayesian theorem is applied to calculate the above-mentioned indices of the proposed importance measure, which can estimate importance measure accurately adopting the same samples with reliability analysis. Therefore, the probabilistic method has faster convergence speed than traditional methods. The nonprobabilitic analysis method can promote the computation efficiency but ensure accuracy when the system performance functions are monotonic. Furthermore, the developed approach contributes to decreasing the time cost of reliability-based optimization in multidisciplinary systems. Additionally, the developed approach can also be applicable to single-disciplinary systems. Moreover, two practical engineering examples and the multidisciplinary design of a hypersonic wing are employed to demonstrate the validity and applicability of the proposed method.

RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

Actual engineering systems will be inevitably affected by uncertain factors. Thus, the Reliability-Based Multidisciplinary Design Optimization (RBMDO) has become a hotspot for recent research and application in complex engineering system design. The Second-Order/First-Order Mean-Value Saddlepoint Approximate (SOMVSA/FOMVSA) are two popular reliability analysis strategies that are widely used in RBMDO. However, the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution, which significantly limits its application. In this study, the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation (GMM-SOMVSA) is introduced to tackle above problem. It is integrated with the Collaborative Optimization (CO) method to solve RBMDO problems. Furthermore, the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO) are proposed. Finally, an engineering example is given to show the application of the GMM-SOMVSA-CO method.

A Decoupling Strategy for Reliability Analysis of Multidisciplinary System with Aleatory and Epistemic Uncertainties

In reliability-based multidisciplinary design optimization, both aleatory and epistemic uncertainties may exist in multidisciplinary systems simultaneously. The uncertainty propagation through coupled subsystems makes multidisciplinary reliability analysis computationally expensive. In order to improve the efficiency of multidisciplinary reliability analysis under aleatory and epistemic uncertainties, a comprehensive reliability index that has clear geometric meaning under multisource uncertainties is proposed. Based on the comprehensive reliability index, a sequential multidisciplinary reliability analysis method is presented. The method provides a decoupling strategy based on performance measure approach (PMA), probability theory and convex model. In this strategy, the probabilistic analysis and convex analysis are decoupled from each other and performed sequentially. The probabilistic reliability analysis is implemented sequentially based on the concurrent subspace optimization (CSSO) and PMA, and the non-probabilistic reliability analysis is replaced by convex model extreme value analysis, which improves the efficiency of multidisciplinary reliability analysis with aleatory and epistemic uncertainties. A mathematical example and an engineering application are demonstrated to verify the effectiveness of the proposed method.

Reliability-based multidisciplinary design optimization of an underwater vehicle including cost analysis

Reliability-based multidisciplinary design optimization of an underwater vehicle including cost analysis

Reliability-based multidisciplinary concurrent design optimization method for complex engineering systems

Reliability-based multidisciplinary design optimization (RBMDO) has been considered as an efficient technology for addressing complex engineering design optimization problems under uncertainties. Current RBMDO methods, however, perform design optimization either in a sequential manner or in an all-at-once manner, which does not support design autonomy in various disciplines and has low computational efficiency. In this article, a reliability-based multidisciplinary concurrent design optimization (RBMCDO) method is proposed to solve the problems of lack of design autonomy and low computational efficiency in current RBMDO methods. In RBMCDO, the multidisciplinary reliability constraints are first transformed into deterministic constraints using the multidisciplinary probabilistic constraint transformation method, developed in this work based on the performance measure approach and Karush–Kuhn–Tucker conditions. The RBMDO problem is then decomposed into several optimization problems of a single discipline, which are solved in parallel based on the collaborative optimization strategy. Two examples are used to verify the proposed method.

An efficient strategy for reliability-based multidisciplinary design optimization of twin-web disk with non-probabilistic model

The twin-web disk holds big promise for increasing efficiency of the aircraft engine. Its reliability-based multidisciplinary design optimization involves several disciplines including fluid mechanics, heat transfer, structural strength, and vibration. The solution to this optimization problem requires three-loop calculations including loops for optimization, reliability, and interdisciplinary consistence often making its computational cost unacceptably high. The lack of sufficient amount of probabilistic data, especially for this brand-new turbine disk, makes matters worse. In this paper, the non-probabilistic uncertain variables are described by an evidence theory-based fuzzy set method, which we extend to general structure of uncertain data. We also propose two modifications of the active learning kriging model: one of them for the purpose of optimization with respect to the distance from the optimum point and another one for the purpose of assessing reliability by introducing the importance concept. Applications of these two modifications are demonstrated in this paper. Finally, a multi-adaptive learning kriging strategy for non-probabilistic reliability-based multidisciplinary design optimization of twin-web disk is proposed to improve its power efficiency and reliability in a computationally effective way.

Sequential optimization and fuzzy reliability analysis for multidisciplinary systems

To meet the rising demand for high reliability in complex multidisciplinary engineering systems, more attention has been paid to reliability-based multidisciplinary design optimization (RBMDO). In this paper, a sequential optimization and fuzzy reliability analysis (SOFRA) method for multidisciplinary systems is developed to decouple the fuzzy reliability analysis from the optimization. In SOFRA, the multidisciplinary design optimization (MDO) and fuzzy reliability analysis are conducted in a sequential manner. Furthermore, a novel adaptive collocation method (ACM) is proposed to conduct the fuzzy reliability analysis for multidisciplinary systems. The ACM arranges points adaptively at the axis of the membership to obtain more accurate results. The shifting distance of the constraint is calculated by the bi-section method. Both numerical and engineering examples are used to demonstrate the validity of the proposed method.

Sequential multidisciplinary design optimization and reliability analysis under interval uncertainty

With the rapid development of modern technology and the rising demand for high reliability in complex multidisciplinary engineering systems, more and more attention has been paid to reliability based multidisciplinary design optimization (RBMDO). The regular RBMDO is a triple-level nested optimization loop which is computationally expensive. In this paper, a sequential multidisciplinary design optimization and reliability analysis method under non-probabilistic theory is developed to decouple the reliability analysis from the optimization. The multidisciplinary design optimization (MDO), interval uncertainty analysis and the reliability analysis are conducted in a sequential manner. Furthermore, a dimension-by-dimension method (DDM) is proposed to conduct the interval uncertainty analysis. The calculation of the reliability under interval uncertainty is deduced based on the volume ratio theory. The shifting distance of the limit state function is also deduced. Both numerical and engineering examples are employed to demonstrate the validity of the proposed method.

A novel methodology of reliability-based multidisciplinary design optimization under hybrid interval and fuzzy uncertainties

Various uncertainties exist in engineering practice, which brings adverse effects to the reliability of complicated engineering systems. Considering the case that interval and fuzzy uncertainties exist simultaneously, a new reliability estimation model is proposed based on the level cut strategy and volume ratio theory. The new reliability model is better than the traditional one which is very conservative. Moreover, a sequential optimization and reliability assessment (SORA) approach for multidisciplinary systems under hybrid interval and fuzzy uncertainties is developed to decouple the reliability analysis from the deterministic multidisciplinary design optimization (MDO). In the framework of SORA, the deterministic MDO and reliability analysis are executed sequentially, thus the efficiency can be improved. For the multidisciplinary uncertainty analysis, the first order Taylor expansion method and the interval vertex method are formulated. The calculation of the safety possibility under the volume ratio theory and the calculation of the shifting distance are deduced. Both numerical and engineering examples are employed to demonstrate the validity of the proposed method.

A Reliability-Based Multidisciplinary Design Optimization Method with Evidence Theory and Probability Theory

Uncertainties, including aleatory and epistemic uncertainties, always exist in multidisciplinary system. Due to the discontinuous nature of epistemic uncertainty and the complex coupled relation among subsystems, the computational efficiency of reliability-based multidisciplinary design optimization (RBMDO) with mixed aleatory and epistemic uncertainties is extremely low. A novel RBMDO procedure is presented in this paper based on combined probability theory and evidence theory (ET) to deal with hybrid-uncertainties and improve the computational efficiency. Firstly, based on Bayes method, a novel method to define the probability density function of the aleatory variables is proposed. Secondly, the conventional equivalent normal method (J-C method) is modified to reliability analysis with hybrid-uncertainties. Finally, a novel RBMDO procedure is suggested by integrating the modified J-C method into the frame of sequence optimization and reliability analysis (SORA). Numerical examples and engineering example are applied to demonstrate the performance of the proposed method. The examples show the excellence of the RBMDO method both in computational efficiency and accuracy. The proposed method provides a practical and effective reliability design method for multidisciplinary system.

An efficient single-loop strategy for reliability-based multidisciplinary design optimization under non-probabilistic set theory

Non-probabilistic reliability based multidisciplinary design optimization (NRBMDO) offers a powerful tool for making reliable decisions with the consideration of uncertain-but-bounded uncertainties for complex engineering systems. However, the prohibitive computation and convergence difficulties caused by the directly coupling of uncertainty based multidisciplinary analysis (UMDA), non-probabilistic reliability analysis (NRA) and MDO would seriously hamper the application of NRBMDO. In this paper, an efficient single loop strategy for NRBMDO (SLS_NRBMDO) is developed to decouple the nested issue and thus improve the computational efficiency. The key idea of the proposed strategy is decoupling NRBMDO with several cycles of sequential MDO, UMDA, NRA and translating distance calculation (TDC). For UMDA, three methods, i.e., the first order interval Taylor expansion method, the interval vertex theorem, the direct optimization approach are formulated. Besides, NRA is conducted on the basis of the expanded non-probabilistic stress–strength interference model and the volume ratio thought, which provides a clear and definite assessment criterion for the structural safety with uncertain-but-bounded parameters. Furthermore, the translating strategy based on the performance measure approach is proposed to shift and update the constraints, and the expression of the translating distance is mathematically derived to accelerate the design procedure. Eventually, the effectiveness and efficiency of the proposed method are illustrated with one numerical case and one practical supersonic wing optimization design problem.

Hybrid reliability-based multidisciplinary design optimization with random and interval variables

This article presents a procedure for reliability-based multidisciplinary design optimization with both random and interval variables. The sign of performance functions is predicted by the Kriging model which is constructed by the so-called learning function in the region of interest. The Monte Carlo simulation with the Kriging model is performed to evaluate the failure probability. The sample methods for the random variables, interval variables, and design variables are discussed in detail. The multidisciplinary feasible and collaborative optimization architectures are provided with the proposed method. The method is demonstrated with three examples.