Efficient Design Optimization Research Articles

An EGO-based online model updating method for hybrid simulation

Hybrid simulation combines experimentally testing of physical substructures with computational simulation of numerical substructures to replicate structural responses under earthquakes. When numerical substructure involves parts that are similar to physical substructure, measured responses of physical substructure are often used to update similar parts within numerical substructure, aiming to improve accuracy of seismic assessment. This study proposes an efficient global optimization based approach for online model updating in hybrid simulation (HSMU-EGO) involving multiple key components yet with only one physically tested in laboratory. Kriging meta-model is constructed for the response error between the numerical model for updating and the experimental substructure, while efficient global optimization and optimal Latin hypercube design are integrated for parameter estimation to minimize the response error. Computational simulations are conducted for a simple steel braced frame and a complex concrete continuous bridge to comprehensively evaluate the performance of HSMU-EGO in the presence of constitutive parameter and model errors. The proposed method is demonstrated to effectively and efficiently improve the accuracy of hybrid simulation in almost all cases. Compared with Unscented Kalman Filter (UKF), this proposed HSMU-EGO provides more suitable alternative when prior information is limited for the physical substructure.

Genetic optimization of terahertz metamaterial absorber for improved absorption and quality factor

Terahertz metamaterial absorbers are typically comprised of an array of sub-wavelength meta-atoms, a dielectric spacer layer and a ground plane. The absorption and quality factor are two of the most important performance metrics for various advanced applications, such as THz communication, sensing, and imaging. However, a large number of structural parameters in the meta-atom make the design approach based on physical intuition and parameter sweep impractical and difficult. In this paper, we report an intelligent design methodology based on the genetic algorithm that facilitates the optimization of an air-spaced terahertz metamaterial absorber to improve its absorption and quality factor. The presented approach starts by randomly generating the size parameters of the meta-atom, and it iteratively obtains the optimized design of the dual narrow band terahertz metamaterial perfect absorber. The quality factor for the two near unity-absorption peaks are 23.8 at 0.5 THz and 60.3 at 0.7 THz, respectively. The device was fabricated using the surface and bulk-micromachining processes, and the measured absorption spectra agrees well with the simulated results. Not limited to this proof-of-concept demonstration, this methodology can be applied to all metamaterial-based photonic systems achieving efficient forward optimization design.

Transient topology optimization for efficient design of actively cooled microvascular materials

Microvascular materials containing internal microchannels are able to achieve multi-functionality by flowing different fluids through vasculature. Active cooling is one application to protect structural components and devices from thermal overload, which is critical to modern technology including electric vehicle battery packaging and solar panels on space probes. Creating thermally efficient vascular network designs requires state-of-the-art computational tools. Prior optimization schemes have only considered steady-state cooling, rendering a knowledge gap for time-varying heat transfer behavior. In this study, a transient topology optimization framework is presented to maximize the active-cooling performance and mitigate computational cost. Here, we optimize the channel layout so that coolant flowing within the vascular network can remove heat quickly and also provide a lower steady-state temperature. An objective function for this new transient formulation is proposed that minimizes the area beneath the average temperature versus time curve to simultaneously reduce the temperature and cooling time. The thermal response of the system is obtained through a transient Geometric Reduced Order Finite Element Model (GRO-FEM). The model is verified via a conjugate heat transfer simulation in commercial software and validated by an active-cooling experiment conducted on a 3D-printed microvascular metal. A transient sensitivity analysis is derived to provide the optimizer with analytical gradients of the objective function for further computational efficiency. Example problems are solved demonstrating the method’s ability to enhance cooling performance along with a comparison of transient versus steady-state optimization results. In this comparison, both the steady-state and transient frameworks delivered different designs with similar performance characteristics for the problems considered in this study. This latest computational framework provides a new thermal regulation toolbox for microvascular material designers.

Multiobjective aerostructural optimization for efficient transport wing conceptual design

The advantages of Multidisciplinary wing development are only gradually being exploited in an industrial level, largely halted by the inevitable design space complexity arising from the interacting disciplines and objective constraints. An industrial tool has to provide design space exploration early in the design process and be reliable enough to guide subsequent fine-tuning optimization studies. In this paper, we display how our methodology can be used in an industrially relevant constrained aerostructural problem described by the common research model and formulated by the asymmetric subspace optimization architecture. It uses multi fidelity analyses in a surrogate based optimization framework, offering more detailed information earlier in the design cycle. The results indicate efficient space exploration, particularly due to the system level dimensionality reduction associated with such a load balancing architecture.

Efficient Design Optimization of Cable-Stayed Bridges: A Two-Layer Framework with Surrogate-Model-Assisted Prediction of Optimum Cable Forces

Cable-stayed bridges have commonly been built for crossing large-span obstacles, such as rivers, valleys, and existing structures. Obtaining an optimum design for a cable-stayed bridge is challenging, due to the large number of design variables and design constraints that are typically nonlinear and usually conflict with each other. Therefore, it is a reasonable alternative to turn the large and complex optimization problem into two sub-problems, i.e., optimizing the internal force distribution by adjusting the cable prestressing forces, and optimizing the other sizing or geometrical parameters. However, conventional methods are lacking in efficiency when dealing with the problem of optimization of cable forces in the first sub-problem, under the circumstance that iteration between the two sub-problems is required. To address this, this paper presents a surrogate-model-assisted method to construct a cable forces predictor ahead of the structural optimization process, so that cable forces can be effectively predicted rather than optimized in each iterative round. Additionally, B-spline interpolation curve is adopted for variable condensation when sampling for the surrogate model. Finally, the structure optimization in the second sub-problem is performed by leveraging an optimization program based on particle swarm optimization method. The performance of the proposed framework is tested with a practical engineering application. Results show that the proposed method showcases good efficiency and accuracy. The theoretical raw material consumption of the towers and the cables is 32% lower than the original design.

Sequential simulated annealing for life-cycle optimization of nonlinear stochastic systems via arbitrary polynomial chaos expansion

Quantifying the uncertainties of engineering systems modeled as nonlinear oscillators subject to random excitation is a theoretically complex and computationally demanding task. Consequently, finding an optimal design of such systems considering their life-cycle performance is prohibitive with Monte Carlo simulation methods. In this paper, an efficient performance-based design optimization approach is developed for finding the optimal parameters of engineering systems modeled as nonlinear/hysteretic oscillators subject to stationary and non-stationary excitation. This novel approach utilizes an arbitrary polynomial chaos expansion to estimate the expected cost of failure without performing a computationally expensive integration over the hazard levels. Moreover, we introduce a novel sequential heuristic optimization scheme based on simulated annealing to minimize the total expected cost over the structure life-cycle. Three examples are included in the paper to assess the developed optimization scheme. First, we use the developed framework to optimize a linear single-degree-of-freedom oscillator subject to broadband excitation. Second, a multi-degree-of-freedom oscillator with cubic nonlinearity in damping and stiffness, subject to stationary broadband excitation, is optimized to show the influence of the problem dimensionality in the optimization process. In the last example, a multi-story reinforced concrete shear building modeled as a multi-degree-of-freedom Bouc-Wen oscillator with stiffness and strength degradation and subject to multi-hazards modeled as stationary (wind excitation) and non-stationary (earthquake) stochastic processes, is optimized.

A machine learning proxy based multi-objective optimization method for low-carbon hydrogen production

With industrial informatization, rich data frameworks provide the possibility of efficient design and global optimization of methane to hydrogen processes. However, the high coupling between mixed variables leads to the difficulty of first-principles modeling (FPM) to capture the optimal Pareto front in infeasible domains. In this paper, a machine learning proxy (MLP) method is proposed to minimize economic, exergy destruction, CO2 emissions, and maximize hydrogen production. First, process simulation as FPM is built using physical properties, energy balance, and reaction kinetics to analyze single variable effects and objective trade-offs. Then, datasets consisting of feed, heat transfer, and design variables are built by sampling the FPM in design and extended spaces. The eXtreme Gradient Boosting (XGBoost) with hyperparameter optimization is built as a proxy FPM, capturing the complex mapping between variables and objectives. Finally, the Pareto front is searched in design and extended spaces by combining the proxy model and genetic algorithm. The proposed method benefits 20.2%, 37.2%, 46.7%, and 2.3% in economic, exergy destruction, CO2 emissions and hydrogen production respectively compared to the heuristic design. XGBoost not only can effectively proxy FPM to capture the complex behavior of reforming techniques, but also can perform better in infeasible domains that are difficult to explore with FPM.

Multi-fidelity expected improvement based on multi-level hierarchical kriging model for efficient aerodynamic design optimization

To reduce the computational burden of aerodynamic design optimization, a multi-fidelity expected improvement (MFEI) method is developed, based on the error analysis of a multi-level hierarchical kriging (MHK) model for accelerating optimization convergence. By maximizing the MFEI function, a new sample of arbitrary fidelity level is determined to ameliorate the accuracy of the MHK model, and convergence to the high-fidelity optimum is ensured. The proposed optimization method based on MFEI and MHK is demonstrated by two analytical function cases and verified by two aerodynamic design optimizations: drag minimizations of an RAE2822 aerofoil and an ONERA M6 wing in transonic flows. It is shown that the MFEI method tends to infill more gainful samples of lower fidelities during optimization, so fewer highest-fidelity samples are required. This confirms that the proposed method can obtain optimal results within a limited computational budget and is more efficient than the existing single-fidelity or two-fidelity methods.

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

An Efficient Optimization Design Framework for Low-Resistance Shape of Bionic Amphibious Robot

An Efficient Optimization Design Framework for Low-Resistance Shape of Bionic Amphibious Robot

Use of GIS and BIM for the integration of tunnel design and construction process in conventional tunneling

This paper presents the development of a framework for the parametric design of tunnels using geographic information system (GIS) mapping and building information modelling (BIM). According to the framework, a parametric representation of each system component (e.g., layers of rock mass, size of excavation, topography, fault geometry, primary lining, secondary lining, rock bolts, etc.) can be incorporated in the GIS model with high levels of detail and used for the automatic generation of numerical models for the design of tunnel construction. This parametric evaluation allows the designer to consider several levels of detail for each component, for the efficient design and process optimization in conventional tunneling. Information between parametric analysis and numerical simulations can be freely exchanged with significantly reduced computational effort while results can be exported into BIM. It is anticipated that the proposed framework could lead to a comprehensive, yet efficient analysis of complex conventional tunneling project using parametric evaluations at the early design stages.

Exploring Multiple-Objective Optimization for Efficient and Effective Test Paper Design with Dynamic Programming Guided Genetic Algorithm.

Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

Optimal Design of a Surface Permanent Magnet Machine for Electric Power Steering Systems in Electric Vehicle Applications Using a Gaussian Process-Based Approach

The efficient design optimization of electric machines for electric power steering (EPS) applications poses challenges in meeting demanding performance criteria, including high power density, efficiency, and low vibration. Traditional optimization approaches often fail to find a global solution or suffer from excessive computation time. In response to the limitations of traditional approaches, this paper introduces a novel methodology by incorporating a Gaussian process-based adaptive sampling technique into a surrogate-assisted optimization process using a metaheuristic algorithm. Validation on a 72-slot/8-pole interior permanent magnet (IPM) machine demonstrates the superiority of the proposed approach, showcasing improved exploitation–exploration balance, faster convergence, and enhanced repeatability compared to conventional optimization methods. The proposed design process is then applied to two surface PM (SPM) machine configurations with 9-slot/6-pole and 12-slot/10-pole combinations for EPS applications. The results indicate that the 12-slot/10-pole SPM design surpasses the alternative design in torque density, efficiency, cogging torque, torque ripple, and manufacturability.

A Novel Multi-Fidelity Surrogate for Efficient Turbine Design Optimization

Abstract To solve the turbine design optimization problems efficiently, surrogate-based optimization algorithms are frequently used. To further reduce the cost of turbine design, the multi-fidelity surrogate (MFS)-based optimization is proposed by the researchers, who resort to augmenting the small number of expensive high-fidelity (HF) samples by a large portion of low-fidelity (LF) but cheap samples in surrogate modeling and optimization process. Nonetheless, according to our observations, the MFS-based optimization sometimes can only have better convergence rate at the early stage of optimization process, but yielding worse final solution than the single-fidelity surrogate (SFS)-based optimization that uses high-fidelity samples alone. The reason behind can be explained as follows. With the increase of HF samples in the optimization process, the LF samples can cause negative effect and therefore misleading the optimization search. To address the above issue, an ensemble weighted multi-fidelity surrogate (EMFS) is proposed. Specifically, the density-based spatial clustering of applications with noise is used to detect the region where the MFS cannot build a more accurate surrogate, and a local SFS is built there. Then, an EMFS is built by combining the MFS and SFS with adaptive weights, which is used to guide the optimization process. The related algorithm is named as multi- and single-fidelity surrogate fused optimization (MSFO). Through tests on GE-E3 blade optimization and the film cooling layout design of a turbine endwall, the effectiveness of proposed MSFO is well demonstrated.

A novel method for fast computation of the temperature rise and optimal design of GIL based on thermal network model

Accurate and fast computation of the temperature rise of gas-insulated transmission lines (GIL) is of great significance to its efficient operation and optimal design. This study proposes a novel method for efficient and accurate computation of the temperature rise and optimal design of GIL based on the thermal network method (TNM). The proposed TNM considers different heat transfer processes between the upper and lower parts of the GIL and the corresponding thermodynamic differential equations are derived. When applied to numerical simulation of GIL, the TNM can save more than three orders of magnitude in computational time compared to computational fluid dynamics (CFD) simulations, and good agreement with experimental data is also achieved. Then a fast optimal design model for GIL current-carrying structures is established based on the TNM, where it is convenient to consider factors including temperature rise and cost objectives, as well as electrical and mechanical field constraints. This optimal design approach circumvents the highly time-consuming electromagnetic-thermal-fluid coupled numerical computations. It is concluded that the proposed TNM provides an accurate way for temperature rise calculation and optimal design of GIL with really high efficiency.

Computational Design of Flexible Planar Microstructures

Mechanical metamaterials enable customizing the elastic properties of physical objects by altering their fine-scale structure. A broad gamut of effective material properties can be produced even from a single fabrication material by optimizing the geometry of a periodic microstructure tiling. Past work has extensively studied the capabilities of microstructures in the small-displacement regime, where periodic homogenization of linear elasticity yields computationally efficient optimal design algorithms. However, many applications involve flexible structures undergoing large deformations for which the accuracy of linear elasticity rapidly deteriorates due to geometric nonlinearities. Design of microstructures at finite strains involves a massive increase in computation and is much less explored; no computational tool yet exists to design metamaterials emulating target hyperelastic laws over finite regions of strain space. We make an initial step in this direction, developing algorithms to accelerate homogenization and metamaterial design for nonlinear elasticity and building a complete framework for the optimal design of planar metamaterials. Our nonlinear homogenization method works by efficiently constructing an accurate interpolant of a microstructure's deformation over a finite space of macroscopic strains likely to be endured by the metamaterial. From this interpolant, the homogenized energy density, stress, and tangent elasticity tensor describing the microstructure's effective properties can be inexpensively computed at any strain. Our design tool then fits the effective material properties to a target constitutive law over a region of strain space using a parametric shape optimization approach, producing a directly manufacturable geometry. We systematically test our framework by designing a catalog of materials fitting isotropic Hooke's laws as closely as possible. We demonstrate significantly improved accuracy over traditional linear metamaterial design techniques by fabricating and testing physical prototypes.

A concurrent design optimization framework for IMSFRP composite structures considering material and structural parameters simultaneously

Injection molded short fiber reinforced polymer (IMSFRP) composite is a widely used lightweight material in the automobile industry. Due to the integrated molding characteristics of IMSFRP composite structures, its lightweight potential can be fully exploited through the simultaneous design of material and structural parameters. However, the efficient material-structure parallel optimization design method for IMSFRP composite structures has not been fully investigated. In this study, a framework of lightweight design containing the concurrent optimization of material and structure parameters is proposed, and it has been successfully applied to an automobile IMSFRP composite liftgate inner. Firstly, considering the skin-core-skin (SCS) structure of the material, a layered model is built up and a parameterized constitutive model is established to efficiently obtain material properties for various material parameters. Then, a parameter extraction and mapping method is proposed to map fiber distribution information to the structural analysis model to improve the accuracy of structural analysis. In addition, based on the Kriging model and a newly developed parallel boundary search particle swarm optimization algorithm, a lightweight design framework of composite liftgate inner is proposed to consider the material and structural design variables simultaneously. The results show that the proposed framework can solve the concurrent optimization design problem effectively and achieve a weight reduction of 10.5 % for the composite liftgate inner under multiple working conditions.

Efficient optimization design of flue deflectors through parametric surrogate modeling with physics-informed neural networks

In engineering applications, deflectors play a vital role in regulating the uniformity of flow field distribution in the selective catalytic reduction (SCR) system, and their optimal design is a topic of great concern. However, traditional optimal design methods often suffer from insufficient prediction accuracy or too high computational cost. This paper develops and verifies an efficient and robust parametric surrogate model for SCR systems based on the physics-informed neural networks (PINNs) framework. This study comprises three progressive steps. (1) We predicted the flow field distribution in the original flue based on the PINNs framework and compared the results qualitatively and quantitatively with the traditional computational fluid dynamics (CFD) method. The results show that the maximum relative error of velocity is 12.6%, and the relative error is within 5% in most areas. (2) For the optimal design of the deflector in the SCR system, a parametric surrogate model based on the PINNs framework is developed, and the model inputs include not only the coordinate variables but also the position parameters of the deflector. The accuracy and efficiency of this parametric surrogate model are also compared with the traditional CFD method. (3) Based on the parametric surrogate model developed above, the deflector optimal position for the research object of this study is found through two quantitative indicators (uniformity coefficient and flue gas energy loss). The results demonstrate that the parameterized model based on PINNs can reduce the computational time to about 14% compared to traditional methods. Finally, the sensitivity analysis of the deflector position parameters is carried out. Overall, the results of this study demonstrate that the parametric surrogate model based on the PINNs framework is an efficient and robust tool for system optimization, design, and autonomous control.

Efficient and robust optimal design for quantile regression based on linear programming

When informing decisions with experimental data, it is often necessary to quantify the distribution tails of uncertain system responses using limited data. To maximize the information content of the data, one is naturally led to use experimental design. However, common design techniques minimize global statistics such as the average estimation or prediction variance. Novel methods for optimal experimental design that target distribution tails are developed. To achieve this, pre-asymptotic estimates of the data uncertainty are produced via an upper bound on a prescribed quantile, computed using quantile regression. Two optimal design problems are formulated: (i) Minimize the variance of the upper bound; and (ii) Minimize the Conditional Value-at-Risk of the upper bound. Additionally, each design problem is augmented with an added cardinality constraint to bound the number of experiments. These optimal design problems are reduced to continuous and mixed-integer linear programming problems. Consequently, the proposed methods are extremely efficient, even when applied to large datasets. The application of the proposed design formulation is demonstrated through a sensor placement problem in direct field acoustic testing.

A flexible and efficient optimization design framework for the shape of blend-wing-body underwater glider

Shape optimization design plays an important role in improving the gliding performance of blended-wing-body underwater glider (BWBUG), but it faces the challenges of how to handle the geometric constraints and improve the optimization efficiency when building the surrogate-based optimization (SBO) framework. To address these issues, a flexible and efficient optimization design framework for the shape of BWBUG is proposed to perform the shape optimization design of BWBUG. In the framework, an axis-driven geometric free-form deformation method is presented to reduce cost of the BWBUG shape deformation by reasonably controlling the scale of optimization variables, and the rapid calculation method of geometric constraints are derived for the proposed shape deformation method. Based on these, a constrained SBO optimization strategy is developed to directly employ the geometric constraints into the training dataset generation and infill criteria. Finally, the shape of one BWBUG example is optimized, and the results show the flexibility and efficiency of the proposed optimization framework.