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Reliability-based design optimization (RBDO) offers a powerful tool to handle optimization problems with inherently unavoidable uncertainty factors. However, solving the engineering systems with high fidelity remains a great challenge. In this study, a novel fidelity transformation framework is proposed to address this issue, where an arbitrary high-fidelity RBDO method can be converted into an arbitrary low-fidelity RBDO method without sacrificing the accuracy. The fidelity transformation factor plays the central role. Furthermore, two fidelity transformation strategies are developed to solve the RBDO problem efficiently and accurately. In addition, the well-known performance measure approach and sequential optimization and reliability assessment method are employed as the low-fidelity RBDO methods. In this way, six new methods are developed based on three high-fidelity RBDO methods and two low-fidelity RBDO methods. One highly mathematical example, two numerical examples, and a stiffened panel with cutouts are used to demonstrate the generality, fidelity, and superiority of the proposed methods.

The problems of reliability-based design optimization (RBDO) can generally be solved by double-loop methods, single-loop methods or decoupled methods. The sequence optimization and reliability assessment (SORA) method is a widely used decoupled method due to its good efficiency and stability. However, most research on SORA is the most probable point (MPP) based, which may cause the unavoidable error or even fail in convergence, especially for the problems with high nonlinearity, multiple MPPs, and nonnormally distributed variables. This paper presents a new decoupled method based on quantile instead of MPP to overcome the intrinsic shortcomings of MPP-based methods. In comparison with SORA which decouples RBDO in the design space, the proposed method decouples RBDO in the probability space. The quantile is obtained by sampling methods with the Kriging model, in which a sample updating strategy is utilized by choosing the updating samples in the region significant for solving the RBDO problem. The proposed method is compared with SORA and the performance measure approach (PMA) using several examples, and the results show that the proposed method can solve the RBDO problems efficiently and accurately with high nonlinearity, multiple MPPs, or high dimensions.

A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

In this paper, a novel reliability-based topology optimization (RBTO) framework integrating fail-safe is first presented to boost reliability levels and load path redundancy for complex marine structures. The sequential optimization and reliability assessment (SORA) approach using the conjugate gradient (CG) algorithm (SORACG) is proposed to decouple the RBTO procedure into sequential deterministic topology optimization (DTO) loops and reliability assessment (RA) loops. The computational efficiency and solution accuracy are enhanced benefiting from the decoupling feature of SORA. A popular fail-safe model simulating the local material failure using damaged zones with prescribed shape and size is introduced into DTO. Non-differentiable fail-safe worst-case problem is transformed into an equivalent bound formulation via the β -method. Combing the three-stage continuation technique (3SCT) which considers both iterative efficiency and global optimality, a multi-model optimization strategy is suggested to address the fail-safe model. In RA, the CG algorithm is developed to derive the most probable point (MPP) for the optimal fail-safe DTO design. Numerical cases concerning a cantilever beam and engineering applications for a long-span open deck and 10,000-ton container ship demonstrate the effectiveness of the framework.

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.

Reliability-based design optimization (RBDO) has been an important research field with the increasing demand for product reliability in practical applications. This paper presents a new RBDO method combining adaptive surrogate model and Importance Sampling-based Modified Sequential Optimization and Reliability Assessment (IS-based modified SORA) method, which aims to reduce the number of calls to the expensive objective function and constraint functions in RBDO. The proposed method consists of three key stages. First, the samples are sequentially selected to construct Kriging models with high classification accuracy for each constraint function. Second, the samples are obtained by Markov Chain Monte Carlo in the safety domain of design space. Then, another Kriging model for the objective function is sequentially constructed by adding suitable samples to update the Design of Experiment (DoE) of the objective function. Third, the expensive objective and constraint functions of the original optimization problem are replaced by the surrogate models. Then, the IS-based modified SORA method is performed to decouple reliability optimization problem into a series of deterministic optimization problems that are solved by a Genetic Algorithm. Several examples are adopted to verify the proposed method. The optimization results show that the proposed method can reduce the number of calls to the original objective function and constraint functions without loss of precision compared to the alternative methods, which illustrates the efficiency and accuracy of the proposed method.

Due to lack of sufficient data and information in engineering practice, it is often difficult to obtain precise probability distributions of some uncertain variables and parameters in reliability-based design optimization (RBDO). In this paper, distributional probability-box (p-box) model is employed to quantify these uncertain variables and parameters. To reduce the computational cost in RBDO associated with expensive and time-consuming constraints, an active learning Kriging-assisted method is proposed. In this method, the sequential optimization and reliability assessment (SORA) method is extended for RBDO under distributional p-box model. Kriging metamodels are constructed to make the replacement of actual constraints. To remove unnecessary computational expense on constructing Kriging metamodels, a screening criterion is built and employed for the judgment of active constraints in RBDO. Then, an active learning function is defined to find out update samples, which are adopted for sequentially refining Kriging metamodel of each active constraint by focusing on its limit-state surface (LSS) around the most probable target point (MPTP) at the solution of SORA. Several examples, including a welded beam problem and a piezoelectric energy harvester design, are provided to test the accuracy and efficiency of the proposed active learning Kriging-assisted method.

This paper focuses on the reliability of complex system that has been measured as a complex system using minimal paths. The reliability of this system has been assigned to research the possible approaches of the assignment reliability values based on reducing the total cost of this method. The results originally included: (i) Three cost functions were used to measure the cost of the complex system: First, the exponential behavior model with the feasibility factor model. Second, the exponential behavior model. Third, the logarithm model. (ii) The reliability of every component of the system was calculated using Particle Swarm algorithm to solve the problems of optimizing the given reliability of the complex system.

This paper focuses on the reliability of Reduction Oxygen Supply System (ROSS) of a Spacecraft which was calculated as a complex system using probability theory. The reliability of this system was assigned to study the possible approaches of the allocation of reliability values based on the minimization of the total cost in this system. The original results was included:(i) a critical point is a fixed purpose of a appropriate application.(ii) Using the reduction oxygen supply system of a spacecraft of with the cost of exponential behavior model.(iii) The results also obtained by genetic algorithim to solve the optimization problems of the given reliability network.

This study investigates efficient design optimization frameworks for composite structures with uncertainties related to material properties and loading. The integration of two decoupled reliability-based design optimization methodologies with a decoupled discrete material optimization is proposed to determine material and fiber orientation for three-dimensional composite structures. First, a deterministic and decoupled discrete material optimization is used for baseline comparison. The objective is to minimize the cost of composite structures with the design variables comprising of the piecewise patch orientations and material properties of the fiber reinforced composites. The reliability-based design optimization includes a hybrid method, and also the sequential optimization and reliability assessment method. In the sequential optimization and reliability assessment method, the inverse reliability analysis is evaluated using a stochastic response surface method and a first order reliability approach. Comparing the methods based on the optimal material and fiber orientations, the uncertainties in loads and material properties lead to different optimal layouts compared to the deterministic solutions. The numerical results also reveal that the hybrid method applied in reliability based designs results in negligible additional computational cost.