Surrogate-based Design Optimization Research Articles

Sample-efficient and surrogate-based design optimization of underwater vehicle hulls

Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. For first approach, we investigate and compare the sample efficiency and convergence behavior of different optimization techniques with a standard CFD solver in the optimization loop. For the second approach, we develop a deep neural network (DNN) based surrogate model to approximate drag forces that would otherwise be computed via the CFD solver. The surrogate model is in turn used in the optimization loop of the hull design. Our study finds that the Bayesian Optimization—Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

Surrogate-based design optimization of the binder cover combining performance and production cost

AbstractThis study integrates surrogate models into combined design optimization of a binder cover, considering production cost and performance constraints. Results reveal that models trained on substantial datasets achieve designs close to the global optimum. Incorporating model variance into constraints prediction in surrogate-based optimization improves robustness and accuracy, especially with noisy functions. This modification enhances the likelihood of obtaining feasible designs, reducing computational demands and showcasing the potential of smaller datasets in predicting local optima.

Design Optimization of a Wafer Dough Blade Using Artificial Neural Network and Monte-Carlo Simulation

In this work, a systematic method to conduct the surrogate-based design optimization is proposed by utilizing Artificial Neural Network and Monte Carlo Simulation. To show its applicability, the design optimization of a wafer dough blade that is an important component in the food industry is carried out. In the optimization problem, design variables or inputs are totally six variables including distances, diameter and thickness, and design responses or outputs are the blade mass, the maximum stress occurred on it, and its surface area. When the results of the initial and optimum designs are compared, there is a significant decrease in the maximum stress (nearly 66%) whereas there was a reasonable low difference in both the mass and surface area. Thanks to the proposed method, it can be possible to take into account the experimental data instead of analytical data in a design problem. Moreover, the followed method provides engineers with a practical and systematic way to find the optimum solution for even nonlinear problems needs to be solved during engineering design process.

Geometric design of micro scale volumetric receiver using system-level inputs: An application of surrogate-based approach

Concentrating solar thermal power is an emerging renewable technology with accessible storage options to generate electricity when required. Central receiver systems or solar towers have the highest commercial potential in large-scale power plants because of reaching the highest temperature. With the increasing solar chemistry applications and new solar thermal power plants, various receiver designs require in micro or macro-scale, in materials, and temperature limits. The purpose of the article is computing the geometry of the receiver in various conditions and provide information during the conceptual design. This paper proposes a surrogate-based design optimization for a micro-scale volumetric receiver model in the literature. The study includes creating training data using the Latin Hypercube method, training five different surrogate models, surrogate model validation, selection procedure, and surrogate-based design optimization. Selected surrogates have over 98% R2 fit and less than 4% root mean square error. In final step, optimization performance compared with the base model. Because of the model complexity, surrogate models reached better objective values in a significantly shorter time.

Surrogate-Based Design Optimization of a H-Darrieus Wind Turbine Comparing Classical Response Surface, Artificial Neural Networks, and Kriging

Clean energy sources like wind energy have been receiving much attention, and great emphasis has been given to the design and optimization of horizontal axis wind turbines, but just as important are the vertical axis wind turbines that can be used for generating energy for small businesses, houses, and buildings. This article sought to study the optimal geometrical parameters of a H-Darrieus vertical axis wind turbine using surrogate-based optimization with three different types of surrogate models and compared them. Airfoil chord and thickness were chosen as the design variables and respective ranges set at 0.32-0.6 m and 0.04-0.16 m. All evaluations are carried out for a tip-speed ratio of 1.5. Three different surrogate models were used and compared, namely a quadratic polynomial response surface, an artificial neural network based on radial basis functions called Extreme Learning Machine and a Kriging interpolator. Surrogates were constructed based on an initial sample data distributed according to a full factorial design. A test set was designed to evaluate the accuracy of the surrogates. Both training and testing data sets were generated using 2D CFD modeling to reduce computational cost. From the test set, Extreme Learning Machine surrogate showed the smallest RMSE of 11.24%, followed by Kriging, at 17.64%, and Response Surface of 22.17%. For the optimal designs the same pattern ensued, with optimal power coefficient overestimated by 8.7% for the response surface surrogate, followed by 3.12% and 2.17% for the Kriging interpolator and the Extreme Learning Machine, respectively. Power coefficient curves comparing the three optimal geometries from each surrogate were calculated and plotted. Optimal turbine obtained from Kriging surrogate optimization process resulted in a 7.92% increase in the Cp, whilst Extreme Learning Machine and Response Surface resulted in a 7.86% and 4.29% increase, respectively, all when compared to baseline CFD model. Concluding guidelines are that the quadratic polynomial response surface may not be the best alternative when dealing with complex non-linear relationships as typically present in VAWT simulations. Superior techniques such as Extreme Learning Machine and Kriging could be more suitable for this application.

Electrical machines surrogate‐based design optimization based on novel waveform targeting strategy with improvement of the computational efficiency

Electrical machine design optimization is an expensive procedure as it contains numerous variables and multiple objectives. Therefore, it might require hundreds of time-consuming finite element analyses (FEA). Surrogate models are one of the superior alternatives that can overcome the computational burden of FEA. However, in optimization problems with sensitive input-output relationships, surrogate models can lack accuracy or suffer from unreasonable initial FE-computational cost. To tackle this problem, this work presents a novel strategy called Waveform-Targeted Surrogate Modeling (WTSM) that improves the computational efficiency of surrogate-based design optimization of electrical machines by modifying the model construction process. In this paper, an Interior Permanent Magnet Machine (IPMSM) is studied to evaluate the proposed strategy's performance compared to the conventional Black Box Modeling (BBM) method. A two-step assessment procedure consisting of multiple scenarios has been developed to analyse the reliability of the WTSM concerning different training-validation datasets. Meanwhile, the Kriging model and Latin-Hypercube-Sampling (LHS) method are employed for surrogate model construction purposes. From the discussion and the results, it can be found that the proposed WTSM strategy can significantly increase the accuracy of the surrogate modelling procedure while the required computational cost can be reduced.

Surrogate-Based Design Optimization of Multi-Band Antenna

In this work, design optimization process of a multi-band antenna via the use of artificial neural network (ANN) based surrogate model and meta-heuristic optimizers are studied. For this mean, first, by using Latin-Hyper cube sampling method, a data set based on 3D full wave electromagnetic (EM) simulator is generated to train an ANN-based model. By using the ANN-based surrogate model and a meta-heuristic optimizer invasive weed optimization (IWO), design optimization of a multi-band antenna for (1) 2.4–3.6 GHz for ISM, LTE, and 5G sub-frequencies, and (2) 9–10 GHz for X-band applications is aimed. The obtained results are compared with the measured and simulated results of 3D EM simulation tool. Results show that the proposed methodology provides a computationally efficient design optimization process for design optimization of multi-band antennas.

3D EM data driven surrogate based design optimization of traveling wave antennas for beam scanning in X-band: an application example

3D EM data driven surrogate based design optimization of traveling wave antennas for beam scanning in X-band: an application example

Experimental surrogate-based design optimization of wing geometry and structure for flapping wing micro air vehicles

We present the experimental design optimization of a flapping wing and the development of a non-circular gear based flapping mechanism to enhance the propulsive efficiency of a flapping wing micro air vehicle (FWMAV). The proposed flapping mechanism consists of a very simple structure, which excludes any linkages but utilizes non-circular gears to achieve a desired flapping amplitude and angular velocity. An optimal wing was obtained via a surrogate-based global optimization reflecting the noise generated from the experiments. Compared to the baseline wing, the optimal wing was improved more than three times in terms of propulsive efficiency. The analysis showed that one of wing geometric parameters, the non-dimensional radius of second moment of area rˆ2, plays an essential role in designing an optimal wing. To achieve high efficiency, rˆ2 should decrease as the wing area increases. Simultaneously, rˆ2 determined other optimal values of geometry parameters such as aspect ratio and camber angle. Furthermore, rˆ2 was also closely related to an optimal vein position which not only generated a moderate wing angle of attack but also reduced the adverse effect of angle of attack fluctuation. Through the optimal wing and the proposed flapping mechanism, we could be able to achieve better efficiency and robust manufacturing compared with the previously reported tailless-FWMAVs.

Surrogate based design optimization of low noise amplifier for ISM band

Design optimization of microwave circuits is a crucial matter for microwave engineers. For the last decades, researchers had been studying surrogate models for a computationally efficient design optimization process. Artificial Intelligence based algorithms had been used for modelling of complex microwave stages such as antenna, amplifiers and frequency selective surfaces. In this study, design optimization of a Low Noise Amplifier (LNA) based on surrogate models for both transistor stage and input & output matching circuits had been presented. Support Vector Regression Machine had been used for creating surrogate models of a microwave transistor and a non-uniform transmission line for having a fast and accurate LNA design optimization process alongside a low profile and high performance LNA using on-uniform transmission lines. By using this methodology, not only designer can create a mapping for missing points in the sparse sample S parameter data points provided by manufacturers but also the overall simulation duration can be significantly reduced thanks to the fast nature of surrogates compared to EM simulators. Here, the proposed surrogate models had been used alongside of Particle Swarm Optimization algorithm to determine optimal geometrical values of input/output matching networks. Then the obtained designs are prototyped and measured. The measured results are also compared with the performance results of counterpart design in literature. As for results, not only the proposed methodology is an effective, fast and reliable method for computationally efficient design optimization process of LNA but also provides better results than the counterpart design in literature.

Design Optimization of a Dual-Bleeding Recirculation Channel to Enhance Operating Stability of a Transonic Axial Compressor

The present work performed a comprehensive investigation to find the effects of a dual-bleeding port recirculation channel on the aerodynamic performance of a single-stage transonic axial compressor, NASA Stage 37, and optimized the channel’s configuration to enhance the operating stability of the compressor. The compressor’s performance was examined using three parameters: The stall margin, adiabatic efficiency, and pressure ratio. Steady-state three-dimensional Reynolds-averaged Navier–Stokes analyses were performed to find the flow field and aerodynamic performance. The results showed that the addition of a bleeding channel increased the recirculation channel’s stabilizing effect compared to the single-bleeding channel. Three design variables were selected for optimization through a parametric study, which was carried out to examine the influences of six geometric parameters on the channel’s effectiveness. Surrogate-based design optimization was performed using the particle swarm optimization algorithm coupled with a surrogate model based on the radial basis neural network. The optimal design was found to increase the stall margin by 51.36% compared to the case without the recirculation channel with only 0.55% and 0.28% reductions in the peak adiabatic efficiency and maximum pressure ratio, respectively.

Stochastic Crashworthiness Optimization Accounting for Simulation Noise

Abstract Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as Non-Deterministic Kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as Modified Augmented Expected Improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an Occupant Restraint System (ORS) during a crash.

Design by adaptive infill sampling with multi-objective optimization for exploitation and exploration

A surrogate-based design optimization with an adaptive sampling technique based on the innovative infill sampling criteria (ISC) is developed, where key issues are mathematically formulated on where in the design space and how many sample points are infilled to guarantee desirable accuracy at minimal computational cost. The ISC developed in the study involve multi-objective optimization (MOO) to determine infilling sample points separately for exploitation and exploration of the design space, which represent the global and the local accuracy of the surrogate model, respectively. The infill samples are found by the MOO on the Pareto front in terms of variance of estimation uncertainty and a predicted function value. To dynamically control the location and the count of the infilling points per iteration for the sample infilling, two criteria of the balancing and the dynamic switching approach are developed.The balancing approach selects infill sample points equally from the two far ends of the Pareto front as well as on the middle of it. The dynamic switching approach uses cut-off variance of uncertainty estimation to dynamically switch the ISC exclusively from the exploration to the exploitation, or vice versa adaptively to the accuracy of the model. Solution optimality and computation efficiency of the present method for the EGO, are compared for two analytic functions with those of the EGO with a conventional, multi-point Expected Improvement (q-EI) ISC and a Latin Hypercube Sampling (LHS) method. The gradient-based optimization without using the surrogate model was also carried out independently for the comparison purpose on the solution accuracy and efficiency. The proposed method shows the greatest efficiency, requiring the smallest number sample points in the training set and becomes even compatible with the gradient-based optimization method. For the practical design problem, high-life multi-element airfoil is chosen to maximize a lift coefficient with non-increasing drag constraints. The proposed method showed about 18% increase of lift force.

Surrogate Based Design Optimization of Multi-Band Antenna

In this work, design optimization process of a multiband antenna via the use of Artificial Neural Network (ANN) based surrogate model and meta-heuristic optimizers is studied. For this mean firstly, by using Latin-Hyper cube sampling method a data set based on 3D full wave EM simulator is generated to train an ANN based model. By using the ANN based surrogate model and a meta-heuristic optimizer Invasive Weed Optimization (IWO), design optimization of a multi-band antenna for (I) 2.4-3.6 GHz for ISM, LTE, and 5G sub frequencies, (II) 9–10 GHz for X band applications is aimed. Then the obtained results are compared with the simulated results of 3D EM simulation tool CST. Results show, that the proposed methodology provides a computationally efficient design optimization process for design optimization of multi-band antennas.

Surrogate-based design optimization of a centrifugal pump impeller

The input power to a centrifugal pump is optimized by changing the impeller blade exit angle. In the optimization, blade exit angles of three meridional profile layers are selected as the design variables, while pump shaft power and head developed are the multi-objective optimization functions obtained through a surrogate model. A multi-objective genetic algorithm is used to find the optimum design point. Computational fluid dynamics simulations are performed to solve Reynolds-averaged Navier–Stokes equations using a shear-stress transport turbulence model for the closure term. Manipulation of the impeller blade angle profile affects both shaft power and efficiency without affecting the head at the best efficiency point, corresponding to a mass flow rate of 1.75 kg/s. The optimum design point of the pump impeller shows an enhancement (>10%) in pump efficiency. Improved flow separation near the trailing edge of the impeller blade and uniform blade loading decreases the input power required at the shaft of the pump impeller.

An Automated Machine Learning-Genetic Algorithm Framework With Active Learning for Design Optimization

AbstractThe use of machine learning (ML)-based surrogate models is a promising technique to significantly accelerate simulation-driven design optimization of internal combustion (IC) engines, due to the high computational cost of running computational fluid dynamics (CFD) simulations. However, training the ML models requires hyperparameter selection, which is often done using trial-and-error and domain expertise. Another challenge is that the data required to train these models are often unknown a priori. In this work, we present an automated hyperparameter selection technique coupled with an active learning approach to address these challenges. The technique presented in this study involves the use of a Bayesian approach to optimize the hyperparameters of the base learners that make up a super learner model. In addition to performing hyperparameter optimization (HPO), an active learning approach is employed, where the process of data generation using simulations, ML training, and surrogate optimization is performed repeatedly to refine the solution in the vicinity of the predicted optimum. The proposed approach is applied to the optimization of a compression ignition engine with control parameters relating to fuel injection, in-cylinder flow, and thermodynamic conditions. It is demonstrated that by automatically selecting the best values of the hyperparameters, a 1.6% improvement in merit value is obtained, compared to an improvement of 1.0% with default hyperparameters. Overall, the framework introduced in this study reduces the need for technical expertise in training ML models for optimization while also reducing the number of simulations needed for performing surrogate-based design optimization.

A Single- and Multi-objective Optimization Algorithm for Electromagnetic Devices Assisted by Adaptive Kriging Based on Parallel Infilling Strategy

A computationally efficient surrogate model is suggested to approximate the objective and constraint function values, which replace expensive evaluation of the objective and constraint function values in numerical simulation-based optimization. Kriging surrogate model has been widely used in surrogate-based design optimization (SBDO) to replace the highly nonlinear black-box functions. In this paper, a novel adaptive Kriging model based on parallel infilling strategy is proposed to improve both the numerical accuracy and efficiency of the SBDO methods. The parallel infilling strategy consists of two parts: local sampling and globaluthor sampling. In the local sampling, new additional sampling points are generated only within a limited region that is determined according to the optimal point at the last iteration, while in global sampling they are generated based on the fitting error estimation in the whole region. The effectiveness of the proposed algorithm is verified through applications to analytical functions. Then the algorithm is applied to the multi-objective optimal design of an ironless permanent magnet synchronous linear motor.

Efficient Surrogate-Based NVH Optimization of a Full Vehicle Using FRF Based Substructuring

<div class="section abstract"><div class="htmlview paragraph">The computer simulation with the Finite Element (FE) code for the structural dynamics becomes more attractive in the industry. However, it normally takes a prohibitive amount of computation time when design optimization is performed with running a large-scale FE simulation many times. Exploiting Dynamic Structuring (DS) leads to alleviating the computational complexity since DS necessities iterative reanalysis of only the substructure(s) to be optimally designed. In this research, Frequency Response Function (FRF) based substructuring is implemented to realize the benefits of DS for fast single- and multi-objective evolutionary design optimization. Also, Differential Evolution (DE) is first combined with two sorting approaches of Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Infeasibility Driven Evolutionary Algorithm (IDEA) for effective constrained single- and multi-objective evolutionary optimization. The effectiveness of the proposed algorithm (NSGA-II/DE-IDEA) is verified using several test functions for constrained single- and multi-objective optimization. To circumvent the need for frequent time-consuming simulation runs, Kriging surrogate models are established by interpolating the responses simulated at the sample points, which are generated by executing an Optimal LHS algorithm. Besides, the Morris method is implemented to leave out unimportant design variables. A constrained single-objective and a constrained multi-objective NVH design optimization of a truck are carried out to demonstrate the surrogate-based design optimization process involving FRF based substructuring and the proposed algorithm.</div></div>

Surrogate modeling in design optimization of structures with discontinuous responses

Advances in computational technology have resulted in the dramatic reduction of computational time for crashworthiness analysis, hence enabling its structural design optimization. Surrogate modeling has been shown to further reduce computational effort as well as to smooth noisy responses. Crashworthiness optimization problems are, though, ill posed as they include nonlinear, noncontinuous and noisy responses. This violates the Hadamard conditions for well-posed problems and therefore the applicability of gradient-based algorithms is limited. Here, discontinuities in the responses with respect to the design variables will be handled that result in large changes in the system functions with only small changes in the design variables using a novel surrogate modeling technique. The applicability of typical global surrogate models is limited when critical discontinuities are present. An efficient method has been developed here to identify the number of discontinuities and their position in the design domain. Previous works assume a said number of discontinuities; here though, the number of discontinuities is not given a priori. The discontinuities are identified by examining the relative difference in the response value of samples in immediate proximity of each other. Samples in the same continuous subdomain are clustered and a support vector machine for classification is exploited to locate discontinuities. Local approximations are then used for the continuous subspaces between the discontinuities. Lastly, a surrogate-based design optimization is carried out. Starting with a two-bar truss, demonstrating a snap-through discontinuity, this method is shown to account for such discontinuities. This is then integrated into an optimization framework. Further academic example, namely a six-bar truss is modeled using the open-source framework Kratos Multiphysics and then optimized, showing the applicability of the method to problems with multiple discontinuities. Finally, a crash-absorbing tube is optimized that is impacted with an angle resulting in a noncontinuous design space: desired axial crushing and undesirable global buckling. After summarizing the results, advantages and possible limitations are discussed.

Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias

In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.