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This study aims to propose an efficient method for solving reliability-based design optimization (RBDO) problems.

In the proposed algorithm, genetic algorithm (GA) is employed to search the global optimal solution of design parameters satisfying the reliability and deterministic constraints. The Kriging model based on U learning function is used as a classification tool to accurately and efficiently judge whether an individual solution in GA belongs to feasible region.

Compared with existing methods, the proposed method has two major advantages. The first one is that the GA is employed to construct the optimization framework, which is helpful to search the global optimum solutions of the RBDO problems. The other one is that the use of Kriging model is helpful to improve the computational efficiency in solving the RBDO problems.

Since the boundaries are concerned in two Kriging models, the size of the training set for constructing the convergent Kriging model is small, and the corresponding efficiency is high.

This paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary optimization problem of a safety transformer to highlight the most effective.

The RBDO and various approaches to calculate the probability of failure are is presented. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems.

The mathematical example shows that the six RBDO approaches have almost the same results except the approximate moment approach that is less accurate. The optimization of the safety transformer highlights that not all the methods can converge to the global solution. Performance measure approach, single-loop approach and sequential optimization and reliability assessment (SORA) method appear to be more stable. Considering both numerical examples, SORA is the most effective method among all RBDO approaches.

The comparison of six RBDO methods on the optimization problem of a safety transformer is achieved for the first time. The comparison in terms of precision and number of evaluations highlights the most effective ones.

This paper aims to present a dynamic reliability model of scraper chains based on the fretting wear process and propose a reasonable structural optimization method.

First, the dynamic tension of the scraper chain is modeled by considering the polygon effect of the scraper conveyor. Then, the numerical wear model of the scraper chain is established based on the tangential and radial fretting wear modes. The scraper chain wear process is introduced based on the diameter wear rate. Furthermore, the time-dependent reliability of scraper chains based on the fretting wear process is addressed by the third-moment saddlepoint approximation (TMSA) method. Finally, the scraper chain is optimized based on the reliability optimization design theory.

There is a correlation between the wear and the dynamic tension of the scraper conveyor. The unit sliding distance of fretting wear is affected by the dynamic tension of the scraper conveyor. The reliability estimation of the scraper chain with incomplete probability information is achieved by using the TMSA for the method needs only the first three statistical moments of the state variable. From the perspective of the chain drive system, the reliability-based optimal design of the scraper chain can effectively extend its service life and reduce its linear density.

The innovation of the work is that the physical model of the scraper chain wear is established based on the dynamic analysis of the scraper conveyor. And based on the physical model of wear, the time-dependent reliability and optimal design of scraper chains are carried out.

As 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.

This study presents a comprehensive review of the RBMDO theory, mainly including the reliability analysis methods of different uncertainties and the decoupling strategies of RBMDO.

First, 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.

The 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.

Kriging model has been widely adopted to reduce the high computational costs of simulations in Reliability-based design optimization (RBDO). To construct the Kriging model accurately and efficiently in the region of significance, a local sampling method with variable radius (LSVR) is proposed. The paper aims to discuss these issues.

In LSVR, the sequential sampling points are mainly selected within the local region around the current design point. The size of the local region is adaptively defined according to the target reliability and the nonlinearity of the probabilistic constraint. Every probabilistic constraint has its own local region instead of all constraints sharing one local region. In the local sampling region, the points located on the constraint boundary and the points with high uncertainty are considered simultaneously.

The computational capability of the proposed method is demonstrated using two mathematical problems, a reducer design and a box girder design of a super heavy machine tool. The comparison results show that the proposed method is very efficient and accurate.

The main contribution of this paper lies in: a new local sampling region computational criterion is proposed for Kriging. The originality of this paper is using expected feasible function (EFF) criterion and the shortest distance to the existing sample points instead of the other types of sequential sampling criterion to deal with the low efficiency problem.

This paper, by taking randomness and uncertainty of structural systems into account aims to implement a combined reliability‐based robust design optimization (RRDO) formulation. The random variables to be considered include the cross section dimensions, modulus of elasticity, yield stress, and applied loading. The RRDO problem is to be formulated as a multi‐objective optimization problem where the construction cost and the standard deviation of the structural response are the objectives to be minimized.

The solution of the optimization problem is performed with the non‐dominant cascade evolutionary algorithm with the weighted Tchebycheff metric, while the probabilistic analysis required is carried out with the Monte Carlo simulation method. Despite the computational advances, the solution of a RRDO problem for real‐world structures is extremely computationally demanding and for this reason neurocomputing estimations are implemented.

The obtained estimates with the neural network predictions are shown to be very satisfactory in terms of accuracy for performing this type of computation. Furthermore, the present numerical results manage to achieve a reduction in computational time up to four orders of magnitude, for low probabilities of violation, compared to the conventional procedure making thus feasible the reliability‐robust design optimization of realistic structures under probabilistic constraints.

The novel parts of the present work include the implementation of neurocomputing strategies in RRDO problems for reducing the computational cost and the comparison of the results given by RRDO and robust design optimization formulations, where the significance of taking into account probabilistic constraints is emphasized.

The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.

The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.

New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.

In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

The performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability index approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, the purpose of this paper is to propose an efficient PMA-based reliability analysis technique using radial basis function (RBF).

The RBF is adopted to approximate the implicit limit state functions in combination with latin hypercube sampling (LHS) strategy. The advanced mean value method is applied to obtain the most probable point (MPP) with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained MPP and reconstruct RBF until a criteria is satisfied.

The method is shown to be better in the computation time to the PMA based on the actual model. The analysis results of probabilistic performance measure are accurately close to the reference solution. Five numerical examples are presented to demonstrate the effectiveness of the proposed method.

The main contribution of this paper is to propose a new reliability analysis technique using reconstructed RBF approximate model. The originalities of this paper may lie in: investigating the PMA using metamodel techniques, using RBF instead of the other types of metamodels to deal with the low efficiency problem.

The purpose of this paper is a development of a virtual flight test framework with derivative design optimization. Aircraft manufactures and engineers have been putting significant effort into the design process to lower the cost of development and time to a minimum. In terms of flight tests and aircraft certification, implementing simulation and virtual test techniques may be a sufficient method in achieving these goals. In addition to simulation and virtual test, a derivative design can be implemented to satisfy different market demands and technical changes while reducing development cost and time.

In this paper, a derivative design optimization was applied to Expedition 350, a small piston engine powered aircraft developed by Found Aircraft in Canada. A derivative that changes the manned aircraft to an Unmanned Aerial Vehicle for payload delivery was considered. An optimum configuration was obtained while enhancing the endurance of the UAV. The multidisciplinary design optimization module of the framework represents the optimized configuration and additional parameters for the simulator. These values were implemented in the simulator and generated the aircraft model for simulation. Two aircraft models were generated for the flight test.

The optimization process delivered the UAV derivative of Expedition E350, and it had increased endurance up to 21.7 hours. The original and optimized models were implemented into virtual flight test. The cruise performance exhibited less than 10 per cent error on cruise performance between the original model and Pilots Operating Handbook (POH). The dynamic stability of original and optimized models was tested by checking Phugoid, short period, Dutch roll and spiral roll modes. Both models exhibited stable dynamic stability characteristics.

The original Expedition 350 was generated to verify the accuracy of the simulation data by comparing its result with actual flight test data. The optimized model was generated to evaluate the optimization results. Ultimately, the virtual flight test framework with an aircraft derivative design was proposed in this research. The additional module for derivative design optimization was developed and its results were implemented to commercial off-the-shelf simulators.

This paper proposed the application of UAV derivative design optimization for the virtual flight test framework. The methodology included the optimization of UAV derivative utilizing MDO and virtual flight testing of an optimized result with a flight simulator.