Use Of Surrogate Models Research Articles

Optimization and comparison of strut-braced and high aspect ratio wing aircraft configurations including flutter analysis with geometric non-linearities

Novel aircraft designs employing wings with high aspect ratio, such as the strut-braced wing (SBW), are one way to reduce their environmental impact. However, the flexibility of longer and more slender wings leads to higher deformations in cruise flight and off-design conditions. Therefore, the interdependence between aerodynamics and structure should be assessed in a multi-disciplinary design optimization (MDO) framework. Although MDO is computationally expensive, it can be mitigated by the use of surrogate models and efficient global optimization methods. This work aims to optimize a SBW aircraft using surrogate models considering flexibility effects. Another objective is to compare the resulting SBW aircraft with a similarly optimized conventional high aspect ratio wing (HARW) aircraft. Both optimized designs are compared regarding their potential fuel consumption and mass benefits under structural and aeroelastic constraints. Despite slightly heavier, the SBW design was found to improve the aerodynamic efficiency compared to an equally optimized HARW configuration. Further, non-linear aeroelastic analyses using multi-fidelity tools were carried out to assess if geometric non-linearities affect the optimized designs. These, while expensive to assess, offer further optimization potential for complex structures.

Adaptive RBF with hyperparameter optimisation for aeroacoustic applications

The present work reports an investigation on the use of adaptive metamodels based on radial basis functions (RBFs) for aeroacoustic applications of highly innovative configurations. The relevance of the topic lies on the paramount importance of metamodelling techniques within the design optimisation process of disruptive aircraft layouts. Indeed, the air traffic growth, consequently the hard environmental constraints imposed by regulations, will make a technological breakthrough, an imperative need within few years. As a consequence, the engineering community is paying particular attention to the development of innovative techniques for the design of unconventional configurations. For this class of applications, the designer cannot successfully rely on historical data or low-fidelity models, and the expensive direct simulations remain the only valuable design strategy. In this regard, it can be demonstrated that the use of surrogate models, i.e., metamodels, significantly reduces the computing costs, especially in view of a robust approach to the optimised design. In order to further improve the efficiency of metamodel-based techniques, dynamic approaches based on hyperparameter optimisation and adaptive sampling procedures have been recently developed. The case study presented here pertains the exploiting of dynamic RBF-based metamodels for noise shielding applications. The analysis of the metamodel performances and its convergence properties shows how the final number of direct simulations is significantly reduced by the hyperparameter optimisation algorithm, still strongly depending on the choice of the RBF kernel function.

A k‐means clustering machine learning‐based multiscale method for anelastic heterogeneous structures with internal variables

AbstractA new machine‐learning based multiscale method, called k‐means FE, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k‐means clustering—machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi‐brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions.

Metamodels’ Development for High Pressure Die Casting of Aluminum Alloy

Simulation is a very useful tool in the design of the part and process conditions of high-pressure die casting (HPDC), due to the intrinsic complexity of this manufacturing process. Usually, physics-based models solved by finite element or finite volume methods are used, but their main drawback is the long calculation time. In order to apply optimization strategies in the design process or to implement online predictive systems, faster models are required. One solution is the use of surrogate models, also called metamodels or grey-box models. The novelty of the work presented here lies in the development of several metamodels for the HPDC process. These metamodels are based on a gradient boosting regressor technique and derived from a physics-based finite element model. The results show that the developed metamodels are able to predict with high accuracy the secondary dendrite arm spacing (SDAS) of the cast parts and, with good accuracy, the misrun risk and the shrinkage level. Results obtained in the predictions of microporosity and macroporosity, eutectic percentage, and grain density were less accurate. The metamodels were very fast (less than 1 s); therefore, they can be used for optimization activities or be integrated into online prediction systems for the HPDC industry. The case study corresponds to several parts of aluminum cast alloys, used in the automotive industry, manufactured by high-pressure die casting in a multicavity mold.

A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows

In this study, we investigate the implementation of a Proper Orthogonal Decomposition (POD) Polynomial Chaos Expansion (PCE) POD-PCE surrogate model for the propagation and quantification of the uncertainty in hydraulic modelling. The considered model consists of a system of multilayer shallow water equations with a mass exchange between the layers and over stochastic beds. As a numerical solver, we propose a finite volume characteristics method that does not require eigenstructure of the system in its implementation. The method is fast, accurate and can be used for both slowly and rapidly hydraulic simulations. The propagation and influence of several uncertainty parameters are quantified in the considered numerical methods for multilayer shallow water flows. To reduce the required number of samples for uncertainty quantification, we combine the proper orthogonal decomposition method with the polynomial Chaos expansions for efficient uncertainty quantification of complex hydraulic problems with a large number of random variables. Numerical results are shown for several test examples including a dam-break problem over a flat bed, and a wind-driven recirculation flow on flat and non-flat bottoms. Results are also presented for the case study of a recirculation flow problem in the Strait of Gibraltar. The results demonstrate the robustness of the uncertainty quantification method compared to the standard Monte-Carlo simulations. The results presented in this study suggest that the use of surrogate modelling may save a considerable amount of the necessary computational cost for all the considered cases.

Noise shielding surrogate models using dynamic artificial neural networks

The optimal design methodologies in aeronautics are known to be constrained by the computational burden required by direct simulations. Due to this reason, the development of efficient metamodelling techniques represents nowadays an imperative need for the designers. In fact, surrogate models has been demonstrated to significantly reduce the number of high-fidelity evaluations, thus alleviating the computing effort. Over the last years, the aeronautical designers community has switched from a design approach predominantly based on direct simulations to an extensive use of metamodels. Recently, to further improve the efficiency, several dynamic approaches based on parameters self-tuning have been developed to support the metamodel construction. This work deals with the use of surrogate models based on Artificial Neural Network for the noise shielding of unconventional aircraft configurations. Here, the insertion loss field of the a Blended Wing Body is reproduced by means of advanced machine learning techniques. The relevant framework is the calculation of the noise emitted by innovative aircraft configurations by means of suitable corrections of existing well-assessed noise prediction tools. The self-tuning algorithm has demonstrated to be accurate and efficient, and the observed performance discloses the possibility to implement numerical strategies for the reliable and robust unconventional aircraft optimal design

Building surrogate models for engineering problems by integrating limited simulation data and monotonic engineering knowledge

The use of surrogate models to replace expensive computations with computer simulations has been widely studied in engineering problems. However, often only limited simulation data is available when designing complex products due to the cost of obtaining this kind of data. This presents a challenge for building surrogate models because the information contained in the limited simulation data is incomplete. Therefore, a method for building surrogate models by integrating limited simulation data and engineering knowledge with evolutionary neural networks (eDaKnow) is presented. In eDaKnow, a neural network uses an evolutionary algorithm to integrate the simulation data and the monotonic engineering knowledge to learn its weights and structure synchronously. This method involves converting both limited simulation data and engineering knowledge into the respective fitness functions. Compared with the previous work of others, we propose a method to train the surrogate model by combining data and knowledge through evolutionary neural network. We take knowledge as fitness function to train the model, and use a network structure self-learning method, which means that there is no need to adjust the network structure manually. The empirical results show that: (1) eDaKnow can be used to integrate limited simulation data and monotonic knowledge into a neural network, (2) the prediction accuracy of the newly constructed surrogate model is increased significantly, and (3) the proposed eDaKnow outperforms other methods on relatively complex benchmark functions and engineering problems.

An adaptive sampling surrogate model building framework for the optimization of reaction systems

Many industrial engineering problems involve complex formulations and are assisted by simulation tools. Although these tools provide highly accurate solutions, they may not be suitable for large scale problems and for optimization applications. Looking for alternatives to complex formulations that often lead to convergence issues and to time consuming solutions, the use of surrogate modeling for reaction systems is addressed herein. We propose a novel adaptive sampling algorithm that iteratively explores the solution space and incorporates ideas from adaptive sampling, trust region methods, and successive linear programming approaches. The surrogates are iteratively embedded into optimization problems to check feasibility and to collect insights to the following adaptive sampling iteration. The methodology is applied to a reaction system network and the surrogates are built to predict the reactor outputs. The adaptive sampling algorithm builds highly accurate surrogates that can be embedded into the reaction system optimization leading to near optimal solutions.

A low-query black-box adversarial attack based on transferability

Artificial intelligence systems suffer from black-box adversarial attacks recently. To prevent this kind of attack, a large amount of researches that reveal the nature of this attack has emerged. However, the query count, success rate, and distortion in the existing works cannot fully satisfy the practical purposes. In this paper, we propose a low-query black-box adversarial attack based on transferability by combining the optimization-based method and the transfer-based method. Our approach aims to improve the black-box attack with a lower number of queries, higher success rate, and lower distortion. In addition, we make full use of surrogate models and optimize the objective function to further improve the performance of our algorithm. We verified our method on MNIST (Lecun and Bottou, 1998) [1], CIFAR-10 (Krizhevsky et al., 2009) [2], and ImageNet (Deng et al. 2009) [3], respectively. Experimental results demonstrate that our method can implement a black-box attack with more than 98.5% success rate and achieve specific distortion with less than 5% queries comparing with other state-of-the-art methods.

A machine-learning-based method for thermal design optimization of residential buildings in highly urbanized areas of Turkey

In 2008, the Turkish government legislated a new regulation mandating the retrofit of existing buildings and construction of energy-efficient buildings. Owing to the requirements of the legislated regulations and environmental concerns, constructing energy-efficient buildings has become a necessity. Researchers working in this field have proposed various optimization techniques to determine energy-optimal design solutions. However, the proposed techniques require a large number of simulations thereby reducing the practicality and inhibiting the wider diffusion of the technique into the industry. Recent studies have demonstrated that the use of surrogate models as alternatives to commercial energy simulation tools significantly reduces the time required for optimization, and a large number of buildings can be optimized in a shorter period. In this study, we aimed at developing a surrogate model-based integrated optimization system to obtain energy-optimal thermal designs for residential buildings in the most urbanized cities in Turkey under different levels of budget constraints. For this purpose, an integrated system consisting of a genetic algorithm optimization technique and gradient boosting machine based surrogate model was developed. The results indicate that the proposed surrogate model-based optimization system is an effective method of overcoming the difficulties of simulation-based optimization methods and it can be integrated into the daily workflow of designers. This study reveals the performance of the scarcely used gradient boosting machine based surrogate model in predicting the thermal loads of buildings. The outcomes of this research will guide designers in finding energy-optimal design alternatives for residential buildings.

Use of Bayesian Model Averaging to Estimate Model Uncertainty for Predicting Strain in a Four-Layered Flexible Pavement

AbstractBecause most of the numerical approaches are intensive in terms of computational effort and time, researchers have resorted to the use of surrogate models. For example, surrogate models for...

From package and design surfaces to optimization - how to apply shape optimization under geometrical constraints

During the product development process, the engineer needs to design mechanical structures regarding package and design surface restrictions. Accordingly, the use of package definitions and design surfaces results in a constraining volume. Shape optimization algorithms can be applied for component or assembly optimization. By variation and setting of the upper and lower boundaries, the shape of the optimized part is restricted. The optimization result needs to stay within this design space. Hence, the engineer or designer sets the design variables in such a way, that none of the created designs reaches beyond the design variable boundaries. This manual method is not able to prevent every infeasible design, due to the vast amount of possible designs in the solution space. As well, the effort to set the design variables by hand is high for the designer. To avoid this manual and vulnerable process, the authors introduced and implemented a method for the automated detection of geometric infeasibility. The process is also named optimization under geometric infeasibility.This paper applies this method to a more complex example, which includes the detection of complex constraining geometries. It demonstrates the benefits of the method and how it can be applied in the product development process. Therefore, a generic b-pillar has been designed in SFE CONCEPT. The structural performance of this b-pillar is thought to be increased by a shape optimization. From a literature review, the dimensions of a parametric package and design surface are derived. In-between the surface definition, the algorithm creates feasible designs. Penalized designs are detected if a surface penetration of the assembly/component and the enveloping surface takes place. Hence, this method enables the optimization of structural performance with an NSGA-II, while the designs are geometrically feasible. Besides the validation of the method for population-based algorithms, this paper introduces and discusses the use of surrogate models for optimization under the geometrical constraint.

Technical Theme Topics

In previous themes we have addressed issues related to a probabilistic approach to addressing EMC problems. The need for such an approach is due to the inherent uncertainty of system parameters and configurations which make a deterministic approach difficult to justify. The implication of this is that full physical models of complete systems are hard to identify. In the current issue we examine how probabilistic approaches and the use of surrogate models, coupled with machine learning (ML) techniques, can help in making predictions of the behaviour of systems where uncertainties are built into models. ML is part of what is described as artificial intelligence (AI) and therefore likely to receive a lot of attention in future EMC studies.

A machine learning framework for predicting the shear strength of carbon nanotube-polymer interfaces based on molecular dynamics simulation data

Modern aerospace applications require lightweight materials with exceptionally high strength and stiffness. Carbon nanotube (CNT)-reinforced composites have great potential in addressing these requirements. However, one critical factor limiting the potential of CNT-reinforced composites is the limited load transfer capability between CNTs through a polymer matrix, which arises due to low CNT-polymer interfacial shear strength at a molecular scale. While molecular dynamics (MD) simulations can be employed to investigate the CNT-polymer interface, such simulations are computationally expensive. It is thus intractable to explore a sufficiently large design space for interface modifications and optimization using MD simulations alone, motivating the use of surrogate models to efficiently map CNT-polymer interfacial configurations to interfacial strength. In this paper, we develop a surrogate machine learning model trained with MD models of functionalized CNT-epoxy and the corresponding interfacial shear strength. The proposed ML model consists of (i) a feature representation of CNT-epoxy based on radial distribution functions; (ii) a convolutional neural network model to map feature representations to a metric of interfacial shear strength; and (iii) a data augmentation method to maximize the use of limited training data. The proposed ML model can predict the CNT pullout force quite well despite a large variation associated with the pullout force.

The role of surrogate models in the development of digital twins of dynamic systems

Digital twin technology has significant promise, relevance and potential of widespread applicability in various industrial sectors such as aerospace, infrastructure and automotive. However, the adoption of this technology has been slower due to the lack of clarity for specific applications. A discrete damped dynamic system is used in this paper to explore the concept of a digital twin. As digital twins are also expected to exploit data and computational methods, there is a compelling case for the use of surrogate models in this context. Motivated by this synergy, we have explored the possibility of using surrogate models within the digital twin technology. In particular, the use of Gaussian process (GP) emulator within the digital twin technology is explored. GP has the inherent capability of addressing noisy and sparse data and hence, makes a compelling case to be used within the digital twin framework. Cases involving stiffness variation and mass variation are considered, individually and jointly, along with different levels of noise and sparsity in data. Our numerical simulation results clearly demonstrate that surrogate models, such as GP emulators, have the potential to be an effective tool for the development of digital twins. Aspects related to data quality and sampling rate are analysed. Key concepts introduced in this paper are summarised and ideas for urgent future research needs are proposed.

Black-box combinatorial optimization using models with integer-valued minima

When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and a Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

Surrogate-assisted Bayesian inversion for landscape and basin evolution models

Abstract. The complex and computationally expensive nature of landscape evolution models poses significant challenges to the inference and optimization of unknown model parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing that can feature dozens of processing cores running in parallel to enhance computational efficiency. Nevertheless, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape evolution problems, a single model evaluation can take from several minutes to hours and in some instances, even days or weeks. Surrogate-assisted optimization has been used for several computationally expensive engineering problems which motivate its use in optimization and inference of complex geoscientific models. The use of surrogate models can speed up parallel tempering Bayeslands by developing computationally inexpensive models to mimic expensive ones. In this paper, we apply surrogate-assisted parallel tempering where the surrogate mimics a landscape evolution model by estimating the likelihood function from the model. We employ a neural-network-based surrogate model that learns from the history of samples generated. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelism. The results show that the proposed methodology is effective in lowering the computational cost significantly while retaining the quality of model predictions.

Multiobjective optimization of the groundwater exploitation layout in coastal areas based on multiple surrogate models.

Seawater intrusion is a common problem in coastal areas. The rational distribution of groundwater exploitation can minimize the scope of seawater intrusion and maximize groundwater exploitation. In this study, an optimization method for the groundwater exploitation layout in coastal areas was proposed. Based on the numerical simulation model of variable-density groundwater, a multiobjective groundwater management model was constructed with the objectives of maximizing groundwater exploitation and minimizing seawater intrusion. The optimization model was solved by nondominated sorted genetic algorithm-II (NSGA-II). To improve the computational efficiency of the optimization model, the surrogate models of the groundwater simulation model were built by using three different methods: kriging, support vector regression (SVR), and kernel extreme learning machines (KELM). Finally, the above methods were tested in Longkou City of China. The results show that the use of surrogate models can greatly reduce the computing time for solving seawater intrusion management problems. The surrogate model of the variable-density groundwater simulation model based on the SVR method has the best performance. The groundwater exploitation layout optimized by the above method is reasonable and can reflect the actual hydrogeological conditions in the study area. This study provides a reliable way to optimize the groundwater exploitation layout in coastal areas.

Global sensitivity analysis in high dimensions with PLS-PCE

Global sensitivity analysis is a central part of uncertainty quantification with engineering models. Variance-based sensitivity measures such as Sobol’ and total-effect indices are amongst the most popular and commonly used tools for global sensitivity analysis. Multiple sampling-based estimators of these measures are available, but they often come at considerable computational cost due to the large number of required model evaluations. If the computational model is expensive to evaluate, these approaches are quickly rendered infeasible. An alternative is the use of surrogate models, which reduce the computational cost per sample significantly. This contribution focuses on a recently introduced latent-variable-based polynomial chaos expansion (PCE) based on partial least squares (PLS) analysis, which is particularly suitable for high-dimensional problems. We develop an efficient way of computing variance-based sensitivities with the PLS-PCE surrogate. By back-transforming the surrogate model from its latent variable space-basis to the original input variable space-basis, we derive analytical expressions for the sought sensitivities. These expressions depend on the surrogate model coefficients exclusively. Thus, once the surrogate model is built, the variance-based sensitivities can be computed at negligible computational cost and no additional sampling is required. The accuracy of the method is demonstrated with two numerical experiments of an elastic truss and a thin steel plate.

Robust design optimization using surrogate models

Abstract The use of surrogate models (response surface models, curve fits) of various types (radial basis functions, Gaussian process models, neural networks, support vector machines, etc.) is now an accepted way for speeding up design search and optimization in many fields of engineering that require the use of expensive computer simulations, including problems with multiple goals and multiple domains. Surrogates are also widely used in dealing with uncertainty quantification of expensive black-box codes where there are strict limits on the number of function evaluations that can be afforded in estimating the statistical properties of derived performance quantities. Here, we tackle the problem of robust design optimization from the direction of Gaussian process models (Kriging). We contrast two previously studied models, co-Kriging and combined Kriging (sometimes called level 1 Kriging), and propose a new combined approach called combined co-Kriging that attempts to make best use of the key ideas present in these methods.