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Optimization of structural systems under reliability‐based performance constraints is an important problem at present receiving too little attention. This problem is investigated in this paper. In developing the reliability‐based optimization approach to the design of framed structures, we review first the general formulation of the deterministic optimization problem and present some of the main features of two general‐purpose deterministic optimization programs. A computer‐automated reliability‐based optimum design procedure is then presented by which the concept of reliability analysis with regard to both serviceability and ultimate performance constraints is combined with that of the minimum weight design to achieve an optimum trade‐off between the global reliability and the total cost. The procedure is feasible for application in system optimization of both steel and reinforced concrete structures.

The paper attempts to establish the connection between structural reliability and structural optimization for the particular case of plastic structures. Along this line, the paper outlines a reliability‐based optimization approach to design plastic structures with uncertain interdependent strengths and acted on by random interdependent loads. The importance of such interdependencies, and of some of the other statistical parameters used as input data in probabilistic computations, is demonstrated by several examples of sensitivity studies on both the probability of collapse failure as well as the reliability‐based optimum solution.

The paper proposed a fast procedure for solving the reliability-based robust design optimization (RBRDO) by modifying the RBRDO formulation and transforming it into a series of RBRDO subproblems. Then for each subproblem, the objective function, constraint function and reliability index are approximated using Taylor series expansion, and their approximate forms depend on the deterministic design vector rather than the random vector and the uncertain estimation in the inner loop of RBRDO can be avoided. In this way, it can greatly reduce the evaluation number of performance function. Lastly, the trust region method is used to manage the above sequential RBRDO subproblems for convergence.

As is known, RBRDO is nested optimization, where the outer loop updates the design vector and the inner loop estimate the uncertainties. When solving the RBRDO, a large evaluation number of performance functions are needed. Aiming at this issue, the paper proposed a fast integrated procedure for solving the RBRDO by reducing the evaluation number for the performance functions. First, it transforms the original RBRDO problem into a series of RBRDO subproblems. In each subproblem, the objective function, constraint function and reliability index caused are approximated using simple explicit functions that solely depend on the deterministic design vector rather than the random vector. In this way, the need for extensive sampling simulation in the inner loop is greatly reduced. As a result, the evaluation number for performance functions is significantly reduced, leading to a substantial reduction in computation cost. The trust region method is then employed to handle the sequential RBRDO subproblems, ensuring convergence to the optimal solutions. Finally, the engineering test and the application are presented to illustrate the effectiveness and efficiency of the proposed methods.

The paper proposes a fast procedure of solving the RBRDO can greatly reduce the evaluation number of performance function within the RBRDO and the computation cost can be saved greatly, which makes it suitable for engineering applications.

The standard deviation of the original objective function of the RBRDO is replaced by the mean and the reliability index of the original objective function, which are further approximated by using Taylor series expansion and their approximate forms depend on the deterministic design vector rather than the random vector. Moreover, the constraint functions are also approximated by using Taylor series expansion. In this way, the uncertainty estimation of the performance functions (i.e. the mean of the objective function, the constraint functions) and the reliability index of the objective function are avoided within the inner loop of the RBRDO.

The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used.

Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research evaluates and compares the characteristics of each method in both cases.

The RBDO result can be improved when the amount of data concerning uncertain parameters is increased. Conversely, increasing information regarding uncertain parameters does not improve the PBDO result. The PBDO provides a conservative result when less information about uncertain parameters is available.

The formulation of RDO is more complex than other methods. If the uncertainty information is increased in aircraft conceptual design case, the accuracy of RBDO will be enhanced.

This research increases the probability of a feasible design when it considers the uncertainty. This result gives more practical optimization results on a conceptual design level for fabrication.

It is RBDO, PBDO and RDO methods combined with MDO that satisfy the target probability when the uncertainties of low fidelity analysis models are considered.

The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements.

The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem.

For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage.

Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data.

This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle.

While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.

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 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 purpose of this paper is to optimize the key dimensions parameters of the missile suspension structure to ensure the structural fatigue life (>10000 cycles) with the reliability of 0.995.

The design objective is the fatigue life reliability of the structure, while the design variables are the four fatigue‐sensitive dimensions. The nominal stress approach is introduced to predict the fatigue life, and it was verified by comparing with experimental data. The second respond surface method is applied to solve the reliability in a finite element‐supported analysis using software MSC Patran/Nastran. A Sequential quadratic programming (SQP) algorithm is used for structure optimization.

The fillet radius r is the most important factor that influences the fatigue life reliability of the structure. The four optimal dimensions parameters are obtained by a reliability‐based design optimization process with the fatigue life and reliability fulfilling the demands.

The optimal result can be used as the design values for missile suspension structure. The feasibility of the reliability‐based design optimization method is validated for the design of missile suspension structure.

The purpose of this paper is to propose a multi-objective optimization algorithm, which can improve both the performance robustness and the constraint feasibility when the uncertainty in design variables is considered.

Multi-objective robust optimization by gradient index combined with the reliability-based design optimization (RBDO).

It is shown that searching for the optimal design of the TEAM problem 22, which can minimize the magnetic stray field by keeping the target system energy (180 MJ) and improve the feasibility of superconductivity constraint (quenching condition), is possible by using the proposed method.

RBDO method applied to the electromagnetic problem cooperated with the design sensitivity analysis by the finite element method.

The purpose of this paper is to optimize the design of a hybrid tether using probabilistic approach considering inherent random variation in the stress developed and the strength it has. The variation in strength is mostly because of variation in diameter of the tether and the properties of the material along the length of the tether. As a result, classical design approach for the tether may not serve the purpose. For this purpose, a reliability-based design of hybrid tether is discussed in this paper.

A literature review was carried out on the design of tether and its operational reliability. It has been shown that the classical design approach does not serve the purpose, as the strategic operation has to be reliable enough, often requiring a measure of reliability required. A reliability-based approach has been presented to achieve the optimum design of a hybrid tether.

The optimization problem was carried out for different values of the safety factor to investigate the effect on the optimal design of tether. An analysis is carried out to show that one should not target a very high value of reliability or factor of safety, as it causes the self-weight of the tether to increase tremendously and its cost significantly.

The present work has been carried out considering the limited data and can further be extended to determine more accurate reliability measures by considering more number of sample test data. The measured data is collected from limited required trials for demo; do not represent the exact population data.

Lab strength test and flight trials were conducted to acquire data for the present analysis. In field use, it was noticed that the tether degraded from top portion attached toward the balloon end because of maximum exposure and repeated usage.