Robust Design Optimization Method Research Articles

Multi-objective robust design optimization of a novel negative Poisson’s ratio bumper system

Negative Poisson’s ratio (NPR) structure has outstanding performances in lightweight and energy absorption, and it can be widely applied in automotive industries. By combining the front anti-collision beam, crash box and NPR structure, a novel NPR bumper system for improving the crashworthiness is first proposed in the work. The performances of the NPR bumper system are detailed studied by comparing to traditional bumper system and aluminum foam filled bumper system. To achieve the rapid design while considering perturbation induced by parameter uncertainties, a multi-objective robust design optimization method of the NPR bumper system is also proposed. The parametric model of the bumper system is constructed by combining the full parametric model of the traditional bumper system and the parametric model of the NPR structure. Optimal Latin hypercube sampling technique and dual response surface method are combined to construct the surrogate models. The multi-objective robust optimization results of the NPR bumper system are then obtained by applying the multi-objective particle swarm optimization algorithm and six sigma criteria. The results yielded from the optimizations indicate that the energy absorption capacity is improved significantly by the NPR bumper system and its performances are further optimized efficiently by the multi-objective robust design optimization method.

Sequential Monte Carlo simulation for robust optimal design of cooling water system with quantified uncertainty and reliability

Conventional design of cooling water systems mainly focused on the individual components of cooling water system, not the system as a whole. In this paper, a robust optimal design based on sequential Monte Carlo simulation is proposed to optimize the design of cooling water system. Monte Carlo simulation is used to obtain the cooling load distribution of required accuracy, power consumption and unmet cooling load. Convergence assessment is conducted to terminate the sampling process of Monte Carlo simulation. Under different penalty ratios and repair rates, this proposed design minimizes the annual total cost of cooling water system. A case study of a building in Hong Kong is conducted to demonstrate the design process and test the robust optimal design method. The results show that the minimum total cost could be achieved under various possible cooling load conditions considering the uncertainties of design inputs and reliability of system components.

Multilevel Robust Design Optimization of a Superconducting Magnetic Energy Storage Based on a Benchmark Study

Superconducting magnetic energy storage (SMES) systems with different superconducting materials are attracting great attentions and funding from the governments around the world because they are promising large-scale energy storage devices for future smart grid. Due to the high cost of SMES, its manufacturing quality and operation reliability have to be investigated in the design optimization stage. This paper presents a robust design optimization method to solve this issue based on a benchmark problem, TEAM problem 22. The proposed method is based on a technique called design for Six Sigma. Meanwhile, a three-level optimization framework is employed to reduce the computation cost of a finite-element analysis due to high-dimensional design space and Monte-Carlo analysis. As shown, the manufacturing reliability and quality of the investigated SMES after robust optimization have been increased greatly.

Surrogate-Based Robust Optimization and Design to Unsteady Low-Noise Open Rotors

An efficient, robust design optimization method based on surrogate models was developed and applied to a practical design problem of a low-noise, coaxial contrarotating rotor. A classical Monte Carlo simulation was carried out at greatly reduced computational cost through dual-level Kriging surrogate models, and it determines the variance of the simulation for uncertainty quantification. The accuracy and numerical stability of the Kriging model were improved by a mathematical indicator of the function trend. The numerical instabilities of the Kriging model in finding distribution parameters were also reduced by the approaches of penalization and cross-validation in a maximum likelihood evaluation. Finally, the robust design optimization framework was applied to a low-noise DLR, German Aerospace Center contrarotating open rotor at a nominal takeoff condition. The objective function was to minimize an overall sound power level at the baseline thrust level. An efficient computational-fluid-dynamics approach of the harmonic balance method solved unsteady open-rotor flows, and aeroacoustic characteristics were computed by Ffowcs-Williams–Hawkings equations. The design variables were the radii of the front and aft rotors, rotor spacing, and pitch angle of the aft rotor. Aleatory uncertainties were considered in both geometric design variables and the freestream Mach number. Noise reduction of 3.3 dB was achieved with reduced variance.

Robust optimal design of chilled water systems in buildings with quantified uncertainty and reliability for minimized life-cycle cost

Conventional design of chilled water systems is typically based on the peak cooling loads of buildings, while the cooling load reaches its peak level for only a small proportion of time in a year. This results in that design flow of chilled water system could be significantly oversized in actual operation and it thus causes significant energy wastes. In this paper, a robust optimal design based on minimized life-cycle cost is proposed to optimize the design of chilled water pump systems while concerning the uncertainties of design inputs and models as well as the component reliability in operation. Monte Carlo simulation is used to generate the cooling load distribution and hydraulic resistance distribution by quantifying the uncertainties. Markov method is used to obtain the probability distribution of the system state. Under different control methods, this proposed design method minimizes the annual total cost. A case study on a building in Hong Kong is conducted to demonstrate the design process and validate the robust optimal design method. Results show that the system could operate at a relatively high efficiency and the minimum total life-cycle cost could be achieved.

Robust design optimization method for centrifugal impellers under surface roughness uncertainties due to blade fouling

Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression (SVR) metamodel is combined with the Monte Carlo simulation (MCS) method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.

Sequential quadrature methods for RDO

Abstract This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.

Uncertainty-based MDO for aircraft conceptual design

Purpose – 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. Design/methodology/approach – 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 eva...

Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

Crashworthiness design of foam-filled bitubal structures with uncertainty

Structural optimization has been widely used to improve the crashworthiness of foam-filled thin-walled structures. However, majority of the existing optimization studies to date have not considered uncertainties for simplication. Its associated risk is that a deterministic optimization might deteriorate its optimality and/or violate design constraints when being present in uncertain environment. In this study, a multiobjective robust design optimization (MORDO) method is adopted to explore the design of foam-filled bitubal structures. To reduce the computational burden of highly-non-linear crash analysis, adaptive Kriging models are employed in the optimization process. In this strategy, sequential sampling points are generated over the design space and Kriging models are refitted in an iterative fashion. Based on the Kriging models, the multiobjective particle swarm optimization (MOPSO) algorithm is employed to perform the optimization, integrated with Monte Carlo simulation and descriptive sampling technique. The results demonstrate that the proposed method is capable of improving the robustness of Pareto solutions within the prescribed minimum requirements of reliability. Moreover, the influence of varying the emphasis on mean and standard deviation components is also analyzed, which can provide decision-makers with insightful design information.

Robust design of Mars entry micro-probe with evidence theory and multi-fidelity strategies

Purpose – A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry probe, not only the geometric configuration, but the trajectory and thermal protection system (TPS). In the design optimization, the uncertainties of atmospheric and aerodynamic parameters are taken into account. The probability distribution information of the uncertainties are supposed to be unknown in the design. To ensure accuracy levels, time-consuming numerical models are coupled in the optimization. Multi-fidelity approach is designed for model management to balance the computational cost and accuracy. Design/methodology/approach – Uncertainties which cannot defined by usual Gaussian probability distribution are modeled with degree of belief, and optimized through with multiple-objective optimization method. The optimization objectives are set to be the thermal performance of the probe TPS and the corresponding b...

A revised method for robust optimal design of energy supply systems based on minimax regret criterion

A robust optimal design method of energy supply systems under uncertain energy demands is revised so that it can be applied to systems with complex configurations and large numbers of periods for variations in energy demands. First, a robust optimal design problem is described by using the minimax regret criterion and considering the hierarchical relationship among design variables, energy demands, and operation variables, which is followed by a solution method. Especially, a novel solution method is proposed for efficiently evaluating an upper bound for the optimal value of the maximum regret. Then, a method of comparing two energy supply systems under uncertain energy demands is proposed by utilizing a part of the revised robust optimal design method. Finally, through a case study on a gas turbine cogeneration system for district energy supply, the validity and effectiveness of the revised optimal design method and features of the robust optimal design are clarified. In addition, the gas turbine cogeneration system is compared with a conventional energy supply system using the proposed comparison method.

Design of a Disturbance Observer for a Two-Link Manipulator With Flexible Joints

This brief proposes a method for designing a disturbance observer (DOB) to decouple joint interactions in robot dynamics with nonlinearity. The traditional DOB based on filter design theory has limited performance since the cut-off frequency of its Q-filter is the only tunable parameter to deal with disturbance suppression and model uncertainty. In this brief, a robust optimal design method is developed for the DOB, which can achieve optimal performance of suppressing disturbance by systematically shaping its Q-filter. Simulation results of application to a two-link manipulator with flexible joints show the improvements in disturbance suppression, which illustrates the validity of the proposed method.

Robust optimization of nonlinear impulsive rendezvous with uncertainty

The optimal rendezvous trajectory designs in many current research efforts do not incorporate the practical uncertainties into the closed loop of the design. A robust optimization design method for a nonlinear rendezvous trajectory with uncertainty is proposed in this paper. One performance index related to the variances of the terminal state error is termed the robustness performance index, and a two-objective optimization model (including the minimum characteristic velocity and the minimum robustness performance index) is formulated on the basis of the Lambert algorithm. A multi-objective, non-dominated sorting genetic algorithm is employed to obtain the Pareto optimal solution set. It is shown that the proposed approach can be used to quickly obtain several inherent principles of the rendezvous trajectory by taking practical errors into account. Furthermore, this approach can identify the most preferable design space in which a specific solution for the actual application of the rendezvous control should be chosen.

Robust design optimization of suspension system considering steering pull reduction

This paper presents robust design optimization method to reduce steering pull phenomenon. One of the biggest causes of steering pull phenomenon is tolerance of suspension system such as hard point, spring, damper and bush. Therefore, the relationship between suspension systems and steering pull phenomenon has as nonlinear characteristics. But, it can be very difficult to evaluate the analytical design sensitivity. Thus, it is impossible to directly apply a well-developed optimization algorithm based on gradient information. To avoid these difficulty, this study uses sequential approximation optimization process based on a meta-model. The robust design process has 28 random design variables with tolerance. For efficient design process, the sample variances for the design goals are approximated from meta-models. The proposed approach required only 62 evaluations until it converged. Optimal design reduced the drift by 80% and its deviation by 38.7%, respectively. This result proves that the suggested design method of suspension system is effective and useful.

Robust Design Optimization of PM-SMC Motors for Six Sigma Quality Manufacturing

In our previous work, soft magnetic composite (SMC) material was employed to design cores for two kinds of permanent magnet (PM) motors, namely transverse flux machine (TFM) and claw pole motor. Compared with motors designed by traditional silicon steel sheets, these motors require 3D flux design with new material and new manufacturing method. Meanwhile, the performances of these motors highly depend on the material and manufacturing parameters besides structure parameters. Therefore, we present a robust design optimization method for high quality manufacturing of these PM-SMC motors to improve their industrial applications. Thereafter, from the design analysis of a PM-SMC TFM, it can be found that the proposed method can significantly improve the manufacturing quality and reliability of the motor, and reduce the manufacturing cost.

Robust design optimization by polynomial dimensional decomposition

This paper introduces four new methods for robust design optimization (RDO) of complex engineering systems. The methods involve polynomial dimensional decomposition (PDD) of a high-dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. New closed-form formulae are presented for the design sensitivities that are simultaneously determined along with the moments. The methods depend on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompassing direct, single-step, sequential, and multi-point single-step design processes. Numerical results indicate that the proposed methods provide accurate and computationally efficient optimal solutions of RDO problems, including an industrial-scale lever arm design.

Analysis of transfer orbit deviation propagation mechanism and robust design for manned lunar landing

Earth-moon transfer orbit for manned lunar landing needs a long flight time, complex, nonlinear and variable coefficient dynamics model, and asks for a high reliability. Analysis of deviation propagation mechanism and robust design of transfer orbit are investigated in this paper. It is not only practical for projecting, but also significant for exploring the role of earth-moon space gravitational field upon transfer orbit deviation. This paper analyses firstly the boundary and the amplitude of the sun, earth, and moon central gravitation, the earth J2 perturbation that affect the transfer orbit deviation transmission. And then a method to analyse the deviation propagation mechanism based on nominal orbital data is obtained analytically. A robust indicator of transfer orbit based on deviation transition matrix is proposed,and a robust optimization design method that employs NSGA-II(nondominated sorting genetic algorithms) for earth-moon transfer orbit with robust indicator is proposed.Simulation shows that the analysis of transfer orbit deviation propagation mechanism can obtain earth-moon transfer orbit deviation propagation matrix quickly and precisely, and the deviation propagation matrix can be used to obtain the covariance matrix and mid-course correction delta V analytically and exactly. The quality of nominal transfer orbit is improved by optimizing with robust indicator.

Robust Optimal Design of Fiber-Reinforced Composite Cylinder with Metallic Liner

An enhanced robust optimal design method dealing with both property and material uncertainties is established in this paper. The method is applied to the robust optimal design of fiber-reinforced composite cylinder with reinforced composite patches and metallic liner subjected to uniform pressure and local loadings. Instead of the traditional numerical approach, modified constraints are used to analytically solve the antioptimization subproblem by a maximizing procedure in the developed method, consequently the computation time for robust optimal design problem can be significantly reduced. The effectiveness and accuracy of the developed method are verified by a degenerated example. Analysis result shows the optimal weight increases significantly with property and material uncertainties as expected. It is also found that the optimal thickness of metallic liner is affected by the utilized design rules of metallic liner. For plastic design, the thickness of metallic liner should be kept as small as possible for a minimal weight optimal design provided that manufacturing and nonleakage constraints can be met. On the contrary the optimal thickness of metallic liner depends on the relative ratio of allowable strain of metallic liner and composite material if elastic design is used.

Robust Design Optimization of Dual Thrust Solid Propellant Motors due to Burning Rate Uncertainties

Solid rocket motor design becomes a clamant task where fusion of design and non-design parameters may lead to various design configurations, especially under uncertainties. This paper proposes a robust design optimization method for the performance of a dual thrust solid rocket motor under investigation of the propellant burning rate and grain geometry uncertainties. It was found that due to uncertainties, the burning rate varies erratically during burning surface area regression, which may lead to catastrophic failure. The present approach aims at uncertainty quantification associated with burning rate and its influence on dual thrust motor performance. A first-order orthogonal design is applied to estimate the worst case deviation coupled with motor internal ballistics. The robustness assessment is measured directly by a mean-variance and average difference approach. A sensitivity analysis of performance parameters is performed to analyze the effects of variation of the design parameters. A hybrid genetic algorithm and simulated annealing approach is used as optimizer. The robust design solution obtained in the form of insensitive design and performance parameters shows the effectiveness and efficiency of the proposed methodology.