Robust Optimization Procedure Research Articles

Uncertainty Analysis and Robust Design for a Hybrid Rocket Upper Stage

An uncertainty analysis is performed for a hybrid rocket engine, and a robust design method is proposed and applied to a liquid-oxygen/paraffin–based fuel hybrid rocket engine that powers the third stage of a Vega-like launcher. An indirect method is used to optimize a mission-specific objective function, which takes into account both the payload mass and the ability of the rocket to reach the required final orbit despite uncertainties. First, a screening of uncertain model parameters is performed using the Morris method. The screening shows that three groups can be distinguished: parameters with negligible or no effect on model outputs, parameters with small linear effect on model outputs, and parameters with large nonlinear effect on model outputs. The robust optimization design process is then carried out by a particle swarm optimization algorithm considering only the uncertainties of the latter group, which includes six parameters. A fractional factorial design of experiment techniques is considered to characterize the robust performance index. Average launcher performance is considered and the best solution is found by means of Box–Behnken’s array. Finally, the identified robust solution is checked against the second group of parameters uncertainties previously neglected in the robust optimization procedure. The scattering of the robust solution is small, and the robustness of the selected optimal solution is confirmed.

Robust design and optimization procedure for piled-raft foundation to support tall wind turbine in clay and sand

A geotechnical design and optimization procedure for piled-raft foundations to support tall wind turbines in clayey and sandy soil are presented in this paper. From the conventional geotechnical design, it was found that the differential settlement controlled the final design and was considered as the response of concern in the optimization procedure. A parametric study was subsequently conducted to examine the effect of the soil shear strength parameters and wind speed (random variables) on the design parameters (number and length of piles and radius of raft). Finally, a robust design optimization procedure was conducted using a Genetic Algorithm coupled with a Monte Carlo simulation considering the total cost of the foundation and the standard deviation of differential settlement as the objectives. This procedure resulted in a set of acceptable designs forming a Pareto front which can be readily used to select the best design for given performance requirements and cost limitations.

Performance- and cost-based robust design optimization procedure for typical foundations for wind turbine

A cost- and performance-based robust design optimisation procedure considering the uncertainties in soil properties and wind speed for three typical foundations (raft, pile group and piled raft) for tall wind turbines on clayey and sandy soils is presented in this paper. From the conventional geotechnical designs, it was found that the design is controlled by differential settlement and therefore considered as the response of concern in the robust design optimisation. The robust design optimisation was performed using Non-dominated Sorting Genetic Algorithm II coupled with Monte Carlo simulation to systematically incorporate the uncertainties in the soil properties and wind speed that have a direct impact on the lateral and moment load acting on the foundation. The total construction cost of the foundation and the standard deviation of the differential settlement were considered as the objectives of interest to be minimised. This procedure resulted in a set of acceptable designs presented in a graphical form called Pareto front for each foundation type on clayey and sandy soils. The comparison of Pareto fronts for the three foundations showed that the pile group or piled raft foundation is economical with higher robustness while the raft foundation is economical with lower robustness. Further, the optimum designs of each type of foundation on clayey and sandy soils were determined using the knee point concept from the Pareto front. The easy-to-use Pareto fronts can be used for selecting suitable foundation type and corresponding design variables for a given performance and cost limitations.

Robust epipolar geometry estimation using noisy pose priors

Epipolar geometry estimation is fundamental to many computer vision algorithms. It has therefore attracted a lot of interest in recent years, yielding high quality estimation algorithms for wide baseline image pairs. Currently many types of cameras such as smartphones produce geo-tagged images containing pose and internal calibration data. These include a GPS receiver, which estimates the position, a compass, accelerometers, and gyros, which estimate the orientation, and the focal length. Exploiting this information as part of an epipolar geometry estimation algorithm may be useful but not trivial, since the pose measurement may be quite noisy. We introduce SOREPP (Soft Optimization method for Robust Estimation based on Pose Priors), a novel estimation algorithm designed to exploit pose priors naturally. It sparsely samples the pose space around the measured pose and for a few promising candidates applies a robust optimization procedure. It uses all the putative correspondences simultaneously, even though many of them are outliers, yielding a very efficient algorithm whose runtime is independent of the inlier fraction. SOREPP was extensively tested on synthetic data and on hundreds of real image pairs taken by smartphones. Its ability to handle challenging scenarios with extremely low inlier fractions of less than 10% was demonstrated. It outperforms current state-of-the-art algorithms that do not use pose priors as well as others that do.

Reliability-based robust design optimization using anchored ANOVA expansion and truncated Edgeworth series approximation

Based on the basic concept of reliability-based design optimization and robust design optimization, a reliability-based robust design optimization is achieved with the moment method in this work. At the first step, two methods, i.e. the anchored ANOVA expansion and truncated Edgeworth series approximation, are combined to solve the reliability constraints in the optimization procedure. The computational effort of the reliability analysis involved in the reliability-based design optimization is then reduced by the moment method. The reliability-based robust design optimization is then formulated by introducing the reliability sensitivity into the reliability-based design optimization as a sub-objective function, which is derived based on the truncated Edgeworth series expansion. The numerical examples illustrate the effectiveness and applicability of the proposed methodology and that the moment-based reliability-based robust design optimization satisfies (1) the reliability target of each constraint and (2) the minimum reliability sensitivity with respect to the mean value of the input random variables. The proposed reliability-based robust design optimization procedure could be applied to the product design under uncertain environment.

Optimum Arrangement of Film Cooling Holes Considering the Manufacturing Tolerance

Despite several studies on the optimum shape of film cooling holes, only a small number of research efforts have attempted to optimize the hole arrangement for film cooling. Moreover, although the manufacturing tolerance has substantial effects on the performance of film cooling, the studies on this issue are even scarcer. The present study proposed a robust design optimization procedure that takes the manufacturing uncertainties into account; it was subsequently applied to the film holes on a high-pressure turbine nozzle to obtain a high-performance array shape that is robust to the manufacturing tolerance. To this end, the hole array was parameterized using newly suggested shape functions and two representative manufacturing factors were considered for the film holes. Additionally, Monte Carlo simulation was employed using the kriging surrogate model for a probabilistic design procedure; design optimization was performed using a genetic algorithm. As a result of the optimization, it was possible to obtain a nozzle with superior cooling performance and a robustness maximum 7.66 and 52.53% higher than that of the baseline, respectively. Additionally, it was confirmed that the tolerance of the holes near the leading edge is more influential on the cooling performance than that of the other holes.

Robust design procedure for dielectric resonator metasurface lens array.

In this paper, we present a design strategy for single layer metasurface lenses based on dielectric resonators. This strategy is based on a robust optimization procedure for the resonator distribution in order to meet required performances (e.g. encircled energy, bandwidth, field of view, etc.). Possible deviations due to manufacturing errors are taken into account in the design procedure. This is applied to the design of array of microlenses for maskless lithography applications. The final design shows more uniform focusing performances (bandwidth 20 nm at 395 nm - 415 nm, field of view ±60 mrad) and increased robustness against manufacturing errors, compared to designs based on analytic phase projections.

Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017

An efficient and robust method to determine the optimal tap coefficients of high speed FIR equalizer

The FIR equalizer is a common way to compensate for the effect of ISI in high speed data transmission. One key issue for the FIR equalizer design is to find the optimal tap coefficient (TC) set. In this work, the TC search is formulated as an eye-diagram based global optimization problem and an efficient and robust multi-start point (MSP) optimizer is developed and applied to determine the optimal TC set. To guarantee a robust optimization procedure, an objective function based on the eye diagram is studied. It proves that a 330x speedup is provided by the proposed method as compared with the Monte Carlo method. With the proposed method, the optimal design point of the equalizer can be further estimated.

Sequential improvement for robust optimization using an uncertainty measure for radial basis functions

The performance of the sequential metamodel based optimization procedure depends strongly on the chosen building blocks for the algorithm, such as the used metamodeling method and sequential improvement criterion. In this study, the effect of these choices on the efficiency of the robust optimization procedure is investigated. A novel sequential improvement criterion for robust optimization is proposed, as well as an improved implementation of radial basis function interpolation suitable for sequential optimization. The leave-one-out cross-validation measure is used to estimate the uncertainty of the radial basis function metamodel. The metamodeling methods and sequential improvement criteria are compared, based on a test with Gaussian random fields as well as on the optimization of a strip bending process with five design variables and two noise variables. For this process, better results are obtained in the runs with the novel sequential improvement criterion as well as with the novel radial basis function implementation, compared to the runs with conventional sequential improvement criteria and kriging interpolation.

An efficient procedure for structural reliability-based robust design optimization

This paper focuses on the development of an optimization tool with the aim to obtain robust and reliable designs in short computational time. The robustness measures considered here are the expecte...

Robust inverse identification of the effective three-dimensional elastic behaviour of a piezoceramic patch bonded to a multilayer unidirectional fibre composite

The effective three-dimensional elastic behaviour of a rectangular piezoceramic patch centrally surface-bonded to a free multilayer unidirectional carbon-fibre reinforced plastic composite plate is inversely identified from three potential ones: orthotropic, quasi transversely isotropic (QTI) or transversely isotropic. This is reached through minimizing the finite element-experimental frequency relative deviations of the first eight short-circuit modes of the smart composite structure using a robust multi-objective evolutionary optimization procedure. The latter combines full factorial design of experiments (DoE)-based surface response meta-modelling of the frequency dependence on the patch’s elastic engineering constants and a non-sorting genetic algorithm of second generation. The inverse identification robustness comes from considering large uncertainties (±20%) of the design parameters nominal (initial) values. DoE-based sensitivities of the considered frequencies to the investigated piezoceramic patch’s elastic behaviour engineering constants are analyzed in order to identify the most influent design parameters. The latter are used for reducing the DoE plans and corresponding finite element computations. It is found that the bonded patch’s effective elastic behaviour is QTI (or orthotropic) when all (or the most influent) engineering constants are optimized.

Development of Robust Optimization Procedure for Casting Conditions

Development of Robust Optimization Procedure for Casting Conditions

Robust Rank Reduction Algorithm with Iterative Parameter Optimization and Vector Perturbation

In dynamic propagation environments, beamforming algorithms may suffer from strong interference, steering vector mismatches, a low convergence speed and a high computational complexity. Reduced-rank signal processing techniques provide a way to address the problems mentioned above. This paper presents a low-complexity robust data-dependent dimensionality reduction based on an iterative optimization with steering vector perturbation (IOVP) algorithm for reduced-rank beamforming and steering vector estimation. The proposed robust optimization procedure jointly adjusts the parameters of a rank reduction matrix and an adaptive beamformer. The optimized rank reduction matrix projects the received signal vector onto a subspace with lower dimension. The beamformer/steering vector optimization is then performed in a reduced dimension subspace. We devise efficient stochastic gradient and recursive least-squares algorithms for implementing the proposed robust IOVP design. The proposed robust IOVP beamforming algorithms result in a faster convergence speed and an improved performance. Simulation results show that the proposed IOVP algorithms outperform some existing full-rank and reduced-rank algorithms with a comparable complexity.

Example Based Repetitive Structure Synthesis

AbstractWe present an example based geometry synthesis approach for generating general repetitive structures. Our model is based on a meshless representation, unifying and extending previous synthesis methods. Structures in the example and output are converted into a functional representation, where the functions are defined by point locations and attributes. We then formulate synthesis as a minimization problem where patches from the output function are matched to those of the example. As compared to existing repetitive structure synthesis methods, the new algorithm offers several advantages. It handles general discrete and continuous structures, and their mixtures in the same framework. The smooth formulation leads to employing robust optimization procedures in the algorithm. Equipped with an accurate patch similarity measure and dedicated sampling control, the algorithm preserves local structures accurately, regardless of the initial distribution of output points. It can also progressively synthesize output structures in given subspaces, allowing users to interactively control and guide the synthesis in real‐time. We present various results for continuous/discrete structures and their mixtures, residing on curves, submanifolds, volumes, and general subspaces, some of which are generated interactively.

Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures

Foam-filled multi-cell thin-walled structure has recently gained attentions for its excellent energy absorption capacity. Tapered thin-walled structure is less likely to fail by global buckling, and is more capable of bearing oblique impact loads. Thus, foam-filled tapered multi-cell thin-walled structure (FTMTS) may be an extremely excellent energy absorber candidate in future vehicle body. This paper focuses on the crashworthiness of four kinds of axisymmetric FTMTSs with different cell numbers. According to our study, we find that FTMTSs have very excellent energy absorption capacity as well as strong capacity of avoiding global buckling. According to our investigation, it was found that the crashworthiness of FTMTS was largely affected by design parameters such as geometric sizes and foam density. In order to find optimal designs of FTMTSs, it is very essential to carry out crashworthiness optimization for FTMTSs. However, the conventional deterministic design is likely to become less meaningful or even unacceptable when considering the uncertainties of design parameters due to the manufacturing or installation deviation. In order to overcome this drawback, a multi-objective robust optimization procedure which employs Kriging metamodels, multi-objective particle swarm optimization (MOPSO) algorithm, "k-sigma" robust design theory and Monte Carlo simulation (MCS) was developed. The comparison of the Pareto fronts obtained by the developed multi-objective robust optimization procedure and the traditional multi-objective deterministic optimization algorithm shows that the robust optimization result is more reliable than the deterministic optimization result. The robust optimal design of FTMTS not only has very excellent crashworthiness but also has very high reliability when considering the uncertainty of design parameters.

Reliability-based robust design optimization of vehicle components, Part I: Theory

The reliability-based design optimization, the reliability sensitivity analysis and robust design method are employed to present a practical and effective approach for reliability-based robust design optimization of vehicle components. A procedure for reliability-based robust design optimization of vehicle components is proposed. Application of the method is illustrated by reliability-based robust design optimization of axle and spring. Numerical results have shown that the proposed method can be trusted to perform reliability-based robust design optimization of vehicle components.

Robust optimal design of tuned mass dampers for tall buildings with uncertain parameters

In this paper a newly proposed approach to robust optimization is adopted in order to study the influence of uncertain structural parameters on the design of a passive control system The control devices are Tuned Mass Dampers placed on a tall building subjected to wind load. The uncertain structural variables are the floors' mass and stiffness. The spatial variability of the mass over the floor's surface is considered by ideally dividing each floor into a certain number of partitions in which the mass varies as a random variable. The robust optimization procedure is based on an enhanced Monte Carlo simulation technique and the genetic algorithm. The Latin Hypercube Sampling is employed to reduce the number of samples. The optimization of stiffnesses and dampings of the devices is carried out for each sample set of structural mass and stiffness matrices, allowing the evaluation of the probability distributions of the optimal parameters and the objective function. The robust designs are those having corresponding values of the objective function lying in the neighborhood of the expected value of the distribution The robust optimization is applied to a tall building controlled by a Tuned Mass Damper and subjected to wind loads obtained from wind tunnel tests. Several numerical analyses are carried out considering different numbers of surface partitions. Both the separate and joint influence of the mass and stiffness uncertainty is considered. The results show that the selected designs are robust, as they guarantee a small variability of structural performance caused by uncertainties.

MO‐E‐BRE‐01: Determination, Minimization and Communication of Uncertainties in Radiation Therapy

Medical Physicists have a general understanding of uncertainties in the radiation treatment process, both with respect to dosimetry and geometry. However, there is a desire to be more quantitative about uncertainty estimation. A recent International Atomic Energy Agency (IAEA) report (about to be published) recommends that we should be as “accurate as reasonably achievable, technical and biological factors being taken into account”. Thus, a single recommendation as a goal for accuracy in radiation therapy is an oversimplification. That report also suggests that individual clinics should determine their own level of uncertainties for their specific treatment protocols. The question is “how do we implement this in clinical practice”? AAPM Monograph 35 (2011 AAPM Summer School) addressed many specific aspects of uncertainties in each of the steps of a course of radiation treatment. The intent of this symposium is: (1) to review uncertainty considerations in the entire radiation treatment process including uncertainty determination for each step and uncertainty propagation for the total process, (2) to consider aspects of robust optimization which optimizes treatment plans while protecting them against uncertainties, and (3) to describe various methods of displaying uncertainties and communicating uncertainties to the relevant professionals. While the theoretical and research aspects will also be described, the emphasis will be on the practical considerations for the medical physicist in clinical practice.Learning Objectives: To review uncertainty determination in the overall radiation treatment process. To consider uncertainty modeling and uncertainty propagation. To highlight the basic ideas and clinical potential of robust optimization procedures to generate optimal treatment plans that are not severely affected by uncertainties. To describe methods of uncertainty communication and display.

Optimization Algorithms Based on Combining FD Approximations and Stochastic Gradients Compared With Methods Based Only on a Stochastic Gradient

Summary Optimization algorithms that incorporate a stochastic gradient [such as simultaneous-perturbation stochastic approximation (SPSA), simplex, and EnOpt] are easy to implement in conjunction with any reservoir simulator. However, for realistic problems, a stochastic gradient provides only a rough approximation of the true gradient, and, in particular, the angle between a stochastic gradient and the associated true gradient is typically far from zero even though a properly computed stochastic gradient usually represents an uphill direction. This paper develops a more robust optimization procedure by replacing the components of largest magnitude of the stochastic gradient with a finite-difference (FD) approximation of the pertinent partial derivatives. In essence, the objective of the method is to determine which components of the unknown true gradient are most important and then replace the corresponding components of the stochastic gradient with more-accurate FD approximations. This modified gradient can then be used in a gradient-based optimization algorithm to find the minimum or maximum of a given cost function. Our focus application is the estimation of optimal well controls, but it is clear that the method could also be used for other applications, including history matching.