Sequential robust optimization of a V-bending process using numerical simulations

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure.

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

ABSTRACTThe rapid development of renewable energy has promoted the research of the integrated energy system. In particular, the joint optimal scheduling of renewable energy and traditional thermal power units is the key technology to solve the current renewable energy integration and the source network load balance. At present, the total installed capacity of cogeneration units is huge, which hinders the integration of renewable energy and the flexibility of the power grid regulation. Therefore, this paper proposes a robust optimal scheduling strategy for the plant‐level integrated energy system considering electricity‐heat balance. The wind power and solar energy are connected in parallel with the heating network of cogeneration units to decouple heat and power in a more economical and flexible way, while improving the integration of renewable energy. Based on the principle of Kang's robust optimization, robust optimization, a linear robust optimization probability density bias prediction optimization method for the plant‐level integrated energy system considering the electric‐heat balance is proposed in this paper. The dynamic nonlinear constraints in the output process of thermal and electrical loads are transformed into linear, which takes into account the conservatism of robust optimization and the economy of the objective function. The proposed optimization algorithm facilitates the integration of a high proportion of renewable energy into the power grid and is also applicable to other integrated energy systems with nonlinear constraint characteristics.

Mars entry trajectory planning using robust optimization and uncertainty quantification

To succeed in a demanding and competitive market, great attention needs to be given to the process of product design. Incorporating optimization into the process enables the designer to find high-quality products according to their simulated performance. However, the actual performance may differ from the simulation results due to a variety of uncertainty factors. Robust optimization is commonly used to search for products that are less affected by the anticipated uncertainties. Changeability can improve the robustness of a product, as it allows the product to be adapted to a new configuration whenever the uncertain conditions change. This ability provides the changeable product with an active form of robustness. Several methodologies exist for engineering design of changeable products, none of which includes optimization. This study presents the Active Robust Optimization (ARO) framework that offers the missing tools for optimizing changeable products. A new optimization problem is formulated, named Active Robust Optimization Problem (AROP). The benefit in designing solutions by solving an AROP lies in the realistic manner adaptation is considered when assessing the solutions' performance. The novel methodology can be applied to optimize any product that can be classified as a changeable product, i.e., it can be adjusted by its user during normal operation. This definition applies to a huge variety of applications, ranging from simple products such as fans and heaters, to complex systems such as production halls and transportation systems. The ARO framework is described in this dissertation and its unique features are studied. Its ability to find robust changeable solutions is examined for different sources of uncertainty, robustness criteria and sampling conditions. Additionally, a framework for Active Robust Multi-objective Optimization is developed. This generalisation of ARO itself presents many challenges, not encountered in previous studies. Novel approaches for evaluating and comparing changeable designs comprising multiple objectives are proposed along with algorithms for solving multi-objective AROPs. The framework and associated methodologies are demonstrated on two applications from different fields in engineering design. The first is an adjustable optical table, and the second is the selection of gears in a gearbox.

Hybrid evolutionary robust optimization-based optimal control for time-delay nonlinear systems

Robustness, optimization and Finite Element (FE) simulations are of major importance for achieving better products and cost reductions in the metal forming industry. In this paper, a metamodel‐based robust optimization strategy is proposed for metal forming processes. The applicability of the strategy is demonstrated by application to an analytical test function and an industrial V‐bending process. The results of both applications underline the importance of including uncertainty and robustness explicitly in the optimization procedure.

This paper presents a new approach aims to solve robust multidisciplinary design optimization MDO problem called Improved Multi-objective Robust Collaborative Optimization . This method combines the Multi-objective Robust Collaborative Optimization method, the Worst Possible Point constraint cuts and the Genetic algorithm NSGA-II type as an optimizer to solve the robust optimization problem of complex structure named Y-stiffened panel under interval uncertainty . The proposed approach hierarchically decomposes the optimization problem into a structure level considered as an upper level in the Y-stiffened panel and a second level considered as a lower level of the studied panel. A robust multi-objective optimization problem intended to optimize the eigenfrequency, the global mass and the displacement at a fixed point of the Y-stiffened panel at the first level and each structure’s robust optimization problem allows optimizing its eigenfrequency and mass limited by their local constraint functions at the second one. Tor demonstrate our method, an engineering example of Y-stiffened panel is treated. A good performance of proposed method is proved by a comparison between obtained results and Non-Distributed Multi-objective Robust Optimization .

In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.

Robust optimization based optimal chiller loading under cooling demand uncertainty

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

Summary Shale oilgains much attention as an unconventional resource, which has a potential of significant oil production. Moreover, the technology of horizontal drilling and hydraulic fracturing has encouraged the exploration and development of shale oil reservoirs. An optimal hydraulic fracturing design is essential to achieve a high oil production rate. However, industry is still faced with many challenging issues in hydraulic fracturing optimization, especially under geological and economic uncertainties. These uncertainties can result in a significant increase in capital costs and negative effects on project revenue. This paper presents innovative hydraulic fracturing robust optimization fordevelopment of unconventional reservoirs to reduce the current challenges and minimize the future investment expenses. We first address a sensitivity analysis for creatingmultiple scenerios of a simulation model, consideringuncertainties of geology and reservoir properties. Most of the previous hydraulic fracturing optimization workflows often ignoredthese uncertainty parameters; therefore, the conventional optimal solution obtained based on a single realization may deviate severely from the actual optimality. To capture geological and reservoir uncertainties, a large number of geological reservoir realizations must be generated honoring geological constraints. Hydraulic fracturing parameters (e.g., fracture half-length, fracture spacing, and fracture height), injection composition and operating conditions are optimized simultaneously based on these multiple geological realizations. The sensitivity analysis results indicate that the four parameters that strongly affect the shale oil production include matrix permeability, fracture half-length, fracture spacing and rock compressibility. To maximize oil recovery, a series of physics-based optimizations have been performed for a hydraulic fracturing design by applying the Partical Swarm Optimization algorithm in a robust optimizer. Both the conventional optimization, based on a single geological realization and robust optimization, based on multiple geological realizations have been conducted. After the conventional optimization process, the ultimate oil recovery yields about 18.63% OOIP. Then the robust optimization procedure is applied with 210 realizations. Due to the high computational cost of shale oil simulations, it is impractical to use all generated models in the robust optimization workflow. Thus we propose a method for the robust optimization of hydraulic fracturing (HF) and gas injection composition based on a small set of geological realizations that represent the overall uncertainty of a reservoir. This is achieved by ranking all realizations according to the performance of each realization in terms of cumulative oil production. The comparison shows that the robust optimization increases all the NPV percentile values. This indicates the increased robustness of the optimal solution under uncertainties and thus an adoption of the robust optimization procedure can significantly reduce the project risk. This research is to present an innovative optimization approach which is fast and robust and can be used to efficiently capture the uncertainties of the key factors including geology, reservoir properties, and economic variation.

Optimization for crashworthiness is of vast importance in automobile industry. Recent advancement in computational prowess has enabled researchers and design engineers to address vehicle crashworthiness, resulting in reduction of cost and time for new product development. However, a deterministic optimum design often resides at the boundary of failure domain, leaving little or no room for modeling imperfections, parameter uncertainties, and/or human error. In this study, an operational model-based robust design optimization (RDO) scheme has been developed for designing crashworthiness of vehicle against side impact. Within this framework, differential evolution algorithm (DEA) has been coupled with polynomial correlated function expansion (PCFE). An adaptive framework for determining the optimum basis order in PCFE has also been presented. It is argued that the coupled DEA–PCFE is more efficient and accurate, as compared to conventional techniques. For RDO of vehicle against side impact, minimization of the weight and lower rib deflection of the vehicle are considered to be the primary design objectives. Case studies by providing various emphases on the two objectives have also been performed. For all the cases, DEA–PCFE is found to yield highly accurate results.

The uncertainties of design variables, noise parameters, and metamodel are important factors in simulation-based robust design optimization. Most conventional metamodel construction methods only consider one or two uncertainties. In this paper, a new surrogate modeling method simultaneously measuring all the uncertainties is proposed for simulation-based robust design optimization of complex product. The effect of metamodel uncertainty on product performance uncertainty is quantified through uncertainty propagation analysis among design variables uncertainty, noise parameters uncertainty, metamodel uncertainty, and performance uncertainty. Then, the sampling points are selected and the metamodel is constructed based on the predictive interval of product performance and mean square error of the Kriging metamodel. The constructed metamodel is applied to robust design optimization considering multiple uncertainties. Results of two mathematical examples show that the proposed metamodel considering multiple uncertainties increases the result accuracy of robust design optimization. Finally, the proposed algorithm is applied to robust design optimization of a heat exchanger, and the total heat transfer rate is enhanced under uncertainties of fin structural parameters, operation conditions parameters and simulation metamodel.

The majority of the opportunistic spectrum access schemes in cognitive radio networks (CRNs) rely on the Listen-Before-Talk (LBT) model due to the half-duplex nature of conventional wireless radios. In this paper, we consider the problem of optimal opportunistic multi-channel spectrum sensing and access using full-duplex (FD) radios in the presence of uncertain primary user (PU) activity statistics. A joint learning and spectrum access scheme is proposed. To optimize its throughput, the SU sensing period has to be carefully tuned. However, in absence of exact knowledge of the PU activity statistics, the PU's performance may be adversely affected. To address this problem, we formulate a robust optimization problem. Our analysis shows that under some non-restrictive simplifying assumptions, the robust optimization problem is convex. We analyze the impact of the sensing period on the PU collision probability and the SU throughput, and find the optimal sensing period via convex optimization. We show that sublinear regrets can be attained by the proposed estimation and robust optimization strategy. Simulation studies also demonstrate that the resulting robust solution provides a good trade-off between optimizing the SU's throughput and protecting the PU.