In this paper, we present an improved general methodology including four stages to designrobust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simul...
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In this paper, we present an improved general methodology including four stages to designrobust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simultaneously to propose the new formulation of reliability-based robust design optimization (RBRDO) problems. In order to generate reliable and robust Pareto-optimal solutions, the combination of genetic algorithm with reliability assessment loop based on the performance measure approach is applied as the second stage. Next, we develop two criteria to select a solution from obtained Pareto-optimal set to achieve the best possible implementation. Finally, the result verification is performed with Monte Carlo Simulations and also the quality improvement during manufacturing process is considered by identifying and controlling the critical variables. The effectiveness and applicability of this new proposed methodology is demonstrated through a case study. (C) 2014 Elsevier Ltd. All rights reserved.
In order to deal with main targets of design methodologies subject to uncertainties in design variables: reliability and robustness, the reliability-based robust design optimization (RBRDO) is developed by integrating...
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In order to deal with main targets of design methodologies subject to uncertainties in design variables: reliability and robustness, the reliability-based robust design optimization (RBRDO) is developed by integrating the performance robustness and constraint feasibility into a single optimization model. A new RBRDO algorithm is proposed based on the worst case scenario approximation for robustness assessment and the sensitivity-assisted Monte Carlo simulation method for effective reliability calculation. Furthermore, one multi-objective RBRDO formulation is suggested. Overall, an electromagnetic application-superconducting magnetic energy storage device (TEAM Problem 22) is used to investigate performances of the proposed RBRDO methods.
Time-variant reliability-based robust design optimization (TRBRDO) has achieved certain progress recently for its ability to ensure both robustness of design and feasibility of time-variant probabilistic constraints. ...
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Time-variant reliability-based robust design optimization (TRBRDO) has achieved certain progress recently for its ability to ensure both robustness of design and feasibility of time-variant probabilistic constraints. However, the existing TRBRDO methods have not specifically addressed the dynamic uncertainty of material degradation, and there is lack of a universal and efficient approach for this class of time-variant robustdesign problems. For this reason, this paper proposes three solution strategies, namely the reliability index based double-loop method, performance measure based double-loop method, and sequential single-loop method. In these approaches, the minimum reliability of each time-variant probabilistic constraint is considered by obtaining the extremum in a series system. With use of the first-order reliability analysis technique, two different single-loop multivariate optimization models are established to obtain the minimum reliabilities and minimum performance measures through sequential quadratic programming algorithm, respectively. Following this, two different double-loop models and a sequential single-loop model are developed. Furthermore, an augmented step length adjustment technique is proposed for inverse reliability analysis, which is integrated into the performance moment integration and percentile difference method to derive the robustness indicators for the design objective. Finally, three illustrative numerical examples and one engineering problem are provided to demonstrate the effectiveness of the proposed solution strategies for reliable and robustdesignoptimization with high computational efficiency.
In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliabilitybased...
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In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliabilitybaseddesignoptimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliabilitybasedrobustdesign in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method. [DOI: 10.1115/1.4005442]
We consider reliability-based robust design optimization (RRDO) where it is sought to optimize the mean of an objective function while satisfying constraints in probability. The high computational cost of the simulati...
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We consider reliability-based robust design optimization (RRDO) where it is sought to optimize the mean of an objective function while satisfying constraints in probability. The high computational cost of the simulations underlying the objective and constraints strongly limits the number of evaluations and makes this type of problems particularly challenging. The numerical cost issue and the parametric uncertainties have been addressed with Bayesian optimization algorithms which leverage Gaussian processes of the objective and constraint functions. Current Bayesian optimization algorithms call the objective and constraint functions simultaneously at each iteration. This is often not necessary and overlooks calculation savings opportunity. This article proposes a new efficient RRDO Bayesian optimization algorithm that optimally selects for evaluation, not only the usual design variables, but also one or several constraints along with the uncertain parameters. The algorithm relies on a multi-output Gaussian model of the constraints. The coupling of constraints and their separated selection are gradually implemented in three algorithm variants which are compared to a reference Bayesian approach. The results are promising in terms of convergence speed, accuracy and stability as observed on a two, a four and a 27-dimensional problem.
This study addresses the bi-level multi-objective optimization problems raised in reliability-based robust design optimization (RBRDO) of engineering applications through establishing a state-of-the-art game theoretic...
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This study addresses the bi-level multi-objective optimization problems raised in reliability-based robust design optimization (RBRDO) of engineering applications through establishing a state-of-the-art game theoretic scenario. A novel bi-level decentralized decision-making approach is proposed using the synergy of RBRDO, game theory, Monte Carlo simulation (MCS), and genetic programming (GP). The application of the proposed approach is elaborated in a case study of robust synthesis of high-speed path-generating four-bar mechanisms. The four performance criteria, namely, accuracy (TE), robustness ( mu TE and sigma 2 TE ), reliability (f G ) at the upper level, and quality of motion (TA) at the lower level are assigned to four players so that each of whom is in charge of one objective criterion. The peak input driving torque (T S ) is associated with the upper-level problem. The GP meta-model is used to capture the Stackelberg protocol that is, constructing the follower's rational reaction set (RRS) and the Nash bargaining function is hired to model the cooperative behavior. The obtained results show a considerable enhancement in reliability and robust behavior of mechanism, while the deterministic criteria of accuracy and quality of motion are preserved.
The paper shows how cost-reduction methods can be synergistically combined to enable high-fidelity hull-form optimization under stochastic conditions. Specifically, a multi-objective hull-form optimization is presente...
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The paper shows how cost-reduction methods can be synergistically combined to enable high-fidelity hull-form optimization under stochastic conditions. Specifically, a multi-objective hull-form optimization is presented, where (a) physics-informed design-space dimensionality reduction, (b) adaptive metamodeling, (c) uncertainty quantification (UQ) methods, and (d) global multi-objective algorithm are efficiently and effectively combined to achieve high-fidelity simulation-baseddesignoptimization (SBDO) solutions. The application pertains to the multi-objective optimization for resistance and seakeeping (operational efficiency and effectiveness) of a destroyer-type vessel. Two hierarchical multi-objective SBDO problems are presented, with a level of complexity decreasing from the most general (stochastic sea state, heading, and speed) to the least general (deterministic regular wave, at fixed sea state, heading, and speed). design-space dimensionality reduction is based on a generalized Karhunen-Loeve expansion of the shape modification vector combined with low-fidelity-based physical variables. A multi-objective deterministic particle swarm optimization algorithm is applied to a stochastic radial-basis-function metamodel that provides objective predictions. UQ methods include Gaussian quadrature and metamodel-based importance sampling. Numerical simulations are based on unsteady Reynolds-averaged Navier-Stokes and potential flow solvers. The paper shows and discusses the joint effort of computational-cost reduction methods in enabling high-fidelity SBDO, providing guidelines for future research directions in this area.
The main objective of this paper is to enhance the robustness of an on-off attitude control under uncertainties while limiting the probability of failure in attitude control. To do this, the concept of system optimiza...
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The main objective of this paper is to enhance the robustness of an on-off attitude control under uncertainties while limiting the probability of failure in attitude control. To do this, the concept of system optimization is utilized for detailed engineering of spacecraft control using reliability-based robust design optimization (RBRDO). The probability of failure of the attitude control is chosen by the system designer as the input of the RBRDO algorithm. The single-axis spacecraft attitude is controlled using a combination of the observer-based anti-windup modified PI-D with pulse-width pulse-frequency modulator in the presence of external disturbance. The on-off thruster is modeled with a delay followed by a second-order transfer function. The input frequency of the thruster is limited to 50 Hz. The uncertain parameters are given as the spacecraft moment of inertia, thrust level, and thruster delay. The controller gains are determined by using traditional, robust, and reliability-based robust design optimizations under uncertainties and disturbance. The simulations are carried out using quasi-normalized equations, along with reducing problem variables and computational burden, to obtain more applicable results for a preliminary design. The traditional optimization gives the highest pointing accuracy without uncertainty, whereas the robustoptimization obtains an approximately flat behavior for the mean of absolute pointing error under uncertainties. Under this situation, RBRDO could satisfy the prescribed reliability with a small loss in accuracy for the on-off attitude control of spacecraft, but under system limitations.
The present paper investigates the reliable and robust optimum design of a higher-order sandwich composite beam under the effect of uncertainty in material properties. The sandwich beam is modeled using the extended h...
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The present paper investigates the reliable and robust optimum design of a higher-order sandwich composite beam under the effect of uncertainty in material properties. The sandwich beam is modeled using the extended higher-order sandwich panel theory. The optimization approaches employed in this work are reliability-baseddesignoptimization, robustdesignoptimization, and a hybrid reliability-based robust design optimization. The efficiency of the optimization process is enhanced by using a novel time domain spectral element methodbased polynomial chaos surrogate model. The performance of the surrogate model is further improved by using Sobol indices based sensitivity analysis. The optimization procedure is performed using an accelerated particle swarm optimization. The numerical results of the reliable and robust optimal design are presented for both the soft and stiff core sandwich beam. Furthermore, the effect of load density and allowable deflection on the optimal design is also examined.
A study to evaluate the effects of different sources of uncertainty in the reliability-basedrobustdesign (RBRDO) of composite laminate structures is performed. The goal is to understand how the set of Pareto-optimal...
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A study to evaluate the effects of different sources of uncertainty in the reliability-basedrobustdesign (RBRDO) of composite laminate structures is performed. The goal is to understand how the set of Pareto-optimal solutions will change and the interaction between the design search and the reliability constraint. The RBRDO is executed by a newly proposed methodology exclusively based on Genetic Algorithms (GA), to guarantee higher levels of accuracy in the optimization procedure, avoiding local minima, common to gradient methods. designoptimization is considered as the bi-objective minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix (robustness). reliability assessment is made by a mathematical reformulation of the Performance Measure Approach, suitable for GA's, as an inner-cycle of the designoptimization. A numerical example of a fuselage-like composite laminate structure is presented. In the reliability assessment, the uncertainty of the system is considered only through the group of mechanical parameters. It is plausible that there exists an implicit functional relationship between feasibility robustness and the reliability constraint, on which the latter constrains the former, at least for the evaluated numerical example. Optimized weights vary between the same values. Tsai numbers and reliability indexes have similar distributions, for different sources of uncertainty. Only the thickness variables and the ply-angle seem to be affected by the structural feasibility robustness assessment. The distribution the Tsai numbers is affected by the reliability constraint, to respect the imposed reliability level.
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