Nacelle optimisation through multi-fidelity neural networks

An improved adaptive sampling and experiment design method for aerodynamic optimization

Multi-fidelity surrogate modeling, by integrating high-fidelity (HF) and low-fidelity (LF) data, provides an efficient approximation framework for complex fluid dynamics problems, particularly those driven by numerical resolution discrepancies. However, under limited computational budgets, efficiently selecting HF samples remains a critical challenge. This study proposes a Nonlinear-Guided Active Learning Multi-Fidelity Surrogate (NG-AL-MFS) modeling method. The proposed framework employs a recursive Co-Kriging model combined with an adaptive sampling strategy to achieve hierarchical data fusion. In this approach, the adaptive sampling strategy introduces a local nonlinearity indicator derived from LF responses to identify complex regions and integrates a distance-based exploration criterion to balance exploitation and exploration during potential HF sampling. Throughout the process, NG-AL-MFS quantitatively extracts local nonlinear features from LF responses to iteratively and adaptively update HF samples, thereby constructing a multi-fidelity surrogate that achieves a superior trade-off between modeling accuracy and computational cost. The proposed framework is validated using three benchmark functions and two fluid engineering applications. Results demonstrate that NG-AL-MFS outperforms existing approaches in terms of prediction accuracy, convergence efficiency, and statistical robustness, offering notable advantages in multivariate nonlinear scenarios. Overall, NG-AL-MFS provides a data-efficient and reliable solution for budget-constrained surrogate modeling in fluid dynamics and other computation-intensive domains.

Design approach for tilt propellers of UAM/eVTOLs for cruise and hover considering aerodynamic and aeroacoustic characteristics via a multi-fidelity model

A physics-guided machine learning for multifunctional wave control in active metabeams

Recently, surrogate modeling methods have been explored for structural acoustics applications. These often involve evaluation of an “expensive” high-fidelity computational model to obtain training data. However, in many applications, models of varying fidelity and computational cost are available. In such situations, one can leverage multi-fidelity surrogate modeling, where the training data from models of varying fidelity are combined and simultaneously used to produce a surrogate model. A particularly popular class of multi-fidelity surrogate modeling techniques is known as co-Kriging, where simulation output from both “expensive” and “cheap” computational models are correlated and a correction process is obtained that maps between the results of these models of varying fidelity. This talk will review co-Kriging and demonstrate its utility on a canonical structural acoustics problem. [Work supported by the Office of Naval Research.]

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interest as a function of the design variables. The trend enables us to eciently and eectively nd an optimal design in appropriate areas of the design space. We apply this approach to the ONERA-M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. Given an initial set of 300 designs, the ASM discovered a low-dimensional linear subspace of the input space that explained the majority of the variability in the drag and lift coecients. This revealed a global trend that we exploited to nd an optimal design with reduced computational cost.

Multi-fidelity surrogate modeling (MFSM) methods are gaining recognition for their effectiveness in addressing simulation-based design challenges. Prior approaches have typically relied on recursive techniques, combining a limited number of high-fidelity (HF) samples with multiple low-fidelity (LF) datasets structured in hierarchical levels to generate a precise HF approximation model. However, challenges arise when dealing with non-level LF datasets, where the fidelity levels of LF models are indistinguishable across the design space. In such cases, conventional methods employing recursive frameworks may lead to inefficient LF dataset utilization and substantial computational costs. To address these challenges, this work proposes the extended hierarchical Kriging (EHK) method, designed to simultaneously incorporate multiple non-level LF datasets for improved HF model construction, regardless of minor differences in fidelity levels. This method leverages a unique Bayesian-based MFSM framework, simultaneously combining non-level LF models using scaling factors to construct a global trend model. During model processing, unknown scaling factors are implicitly estimated through hyperparameter optimization, resulting in minimal computational costs during model processing, regardless of the number of LF datasets integrated, while maintaining the necessary accuracy in the resulting HF model. The advantages of the proposed EHK method are validated against state-of-the-art MFSM methods through various analytical examples and an engineering case study involving the construction of an aerodynamic database for the KP-2 eVTOL aircraft under various flying conditions. The results demonstrated the superiority of the proposed method in terms of computational cost and accuracy when generating aerodynamic models from the given multi-fidelity datasets.

Design space exploration can reveal the underlying structure of design problems of interest. In a set-based approach, for example, exploration can identify sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. Techniques have been introduced to map high-dimensional design spaces to low-dimensional, visualizable spaces. Before the promising regions can be visualized, however, the first task is to identify how many clusters of promising designs exist in the high-dimensional design space. Unsupervised machine learning methods, such as spectral clustering, have been utilized for this task. Spectral clustering is generally accurate but becomes computationally intractable with large sets of candidate designs. Therefore, in this paper a technique for accurately identifying clusters of promising designs is introduced that remains viable with large sets of designs. The technique is based on spectral clustering but reduces its computational impact by leveraging the Nyström Method in the formulation of self-tuning spectral clustering. After validating the method on a simplified example, it is applied to identify clusters of high performance designs for a high-dimensional negative stiffness metamaterials design problem.

Finite element models of whole gas turbine engines, also known as whole engine models (WEMs), which consist of three-dimensional solid elements are not commonly used in design optimization studies due to the high computational cost of solving them for many designs. WEMs consisting of two-dimensional shell elements can be a suitable replacement for high-fidelity solid WEMs as they approximate the responses well while being significantly quicker to solve. However, in a surrogate-assisted optimization study, the accumulation of errors in the shell WEM evaluations can result in the construction of a surrogate model that can be somewhat misleading compared to the solid WEM response surface. Such a surrogate model could return promising designs that, when validated using solid WEMs, turn out to be suboptimal or infeasible. A novel approach which combines medial meshing and multi-fidelity surrogate modelling techniques is proposed to increase the feasibility of conducting whole engine optimization studies. We demonstrate the workflow for generating medial meshes on an engine intercasing geometry. The accuracy of medial mesh simulations with respect to solid mesh simulations is evaluated and discussed in the context of their suitability as a source of low-fidelity structural information for multi-fidelity surrogate models. The impact of this combination of techniques is subsequently illustrated using two case studies. The first case study is the optimization of an intermediate compressor casing for minimum mass with constraints on the casing stiffness. The results show that the multi-fidelity approach is able to find optimum designs that are equivalent to the expensive single-fidelity approach of using only solid mesh evaluations but at a significantly lower computational cost. The second case study is the optimization of a whole engine geometry. This case study serves to demonstrate the effectiveness of the multi-fidelity approach for solving realistic design problems.

Aerodynamic shape optimization of large-span coal sheds for wind-induced effect mitigation using surrogate models

Application of deep learning based multi-fidelity surrogate model to robust aerodynamic design optimization

<div>Continuous rubber track systems for heavy applications are typically designed using multiple iterations of full-scale physical prototypes. This costly and time-consuming approach limits the possibility of exploring the design space and understanding how the design space of that kind of system is governed. A multibody dynamic simulation has recently been developed, but its complexity (due to the number of model’s inputs) makes it difficult to understand and too expensive to be used with multi-objective optimization algorithms (approximately 3 h on a desktop computer).</div> <div>This article aims to propose a first design space exploration of continuous rubber track systems via multi-objective optimization methods. Using an existing expensive multibody dynamic model as original function, surrogate models (artificial neural networks) have been trained to predict the simulation responses. These artificial neural networks are then used to explore the design space efficiently by using optimization algorithms. Sensitivity studies and multi-objective optimization were carried out on surrogate models to identify high-impact design parameters and potential improvements ranging from 2.24% to 17.2% compared to the current design of reference (CTS halftrack system) on wheel load, track pinch, and maximum required torque to cross a bump.</div>

The demand for fast and accurate electromagnetic solutions to support current and emerging technologies has fueled the rapid development of various machine learning techniques for applications such as antenna design and optimization, microwave imaging, device diagnostics, and more. Multi-fidelity (MF) surrogate modeling methods have shown great promise in significantly reducing computational costs associated with surrogate modeling while maintaining high model accuracy. This work offers a comprehensive review of the available MF surrogate modeling methods in electromagnetics, focusing on specific methodologies, related challenges, and the generation of variable-fidelity datasets. The article is structured around the two main types of electromagnetic problems: forward and inverse. It begins by summarizing key machine learning concepts and limitations. This transitions to discussing multi-fidelity surrogate model architectures and low-fidelity data techniques for the forward problem. Subsequently, the unique challenges of the inverse problem are presented, along with traditional solutions and their limitations. Following this, the review examines MF surrogate modeling approaches tailored to the inverse problem. In conclusion, the review outlines promising future directions in MF modeling for electromagnetics, aiming to provide fundamental insights into understanding these developing methods.

This research work deals with aspects concerned with delamination detection in composite structures as revealed by an approach based on vibration measurements. Variations in vibration characteristics generated in composite laminates indicate the existence of delaminations because degradation due to delamination causes reduction in flexural stiffness and strength of the material and as a result vibration parameters like natural frequency responses are changed. Hence, it is possible to monitor the variation in natural frequencies to identify the presence of delamination, and assess its size and location for online structural health monitoring (SHM). The approach to this paper, therefore, typically depends on undertaking the analysis of structural models implemented by finite element analysis (FEA). The numerical solutions using FE models known as the simulator computes the natural frequencies for the delaminated and undelaminated specimens of composite laminates. However, these FE models are computationally expensive, and surrogate (approximation) models are introduced to curtail the computational expense. The simulator is employed to solve the inverse problem using algorithms based on computational intelligence concepts. An artificial neural network (ANN) model is developed to also solve the inverse problem for delamination detection directly and to provide surrogate models integrated with optimization algorithms (the gradient-based local search and non-dominated sorting genetic algorithm-II) to contain the computationally expensive simulations by FEA. This approach is termed as surrogate assisted optimization and it is seen that the engagement of surrogate models in lieu of the FE models in the optimization loop greatly enhances the accuracy of delamination detection results within an affordable computational cost and provides control over handling different variables. Meanwhile, to aid with the building of effective surrogate models using substantial number of training datasets, K-means clustering algorithm is harnessed and this effectively reduces the large training datasets usually required for ANN training. This paper demonstrated that ANN and optimization algorithms with surrogates show immense potentialities for use in delamination damage detection scenarios. Prediction errors of the algorithms were quantified and they were shown to be satisfactory when applied to previously experimental data. The algorithms in their inverse formulations are capable of predicting accurately delamination parameters. Hence, these algorithms should be employed for application in the domain of SHM where their small computational requirements could be exploited for online damage detection.

This paper presents the development and evaluation of Artificial Neural Networks (ANN) based models and optimally selected surrogate models to provide the day-ahead forecast of the hourly-averaged energy load of buildings, by relating it to eight weather parameters as well as the hour of the day. Although ANN and other surrogate models have been used to predict building energy loads in the past, there is a limited understanding of what type of model prescriptions impact their performance as well as how un-recorded impact factors (e.g., human behavior and building repair work) should be accounted for. Here, the recorded energy data of three university buildings, from 9/2013–12/2015, is cleaned and synchronized with the local weather data. The data is then classified into eight classes; weekends and weekdays of Fall/Winter/Spring/Summer semesters. Both Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) NNs are explored. Differing number of hidden layers and transfer function choices are also explored, leading to the choice of the hyperbolic-tangent-sigmoid transfer function and 60 hidden layers. Similarly, an automated surrogate modeling framework is used to select the best models from among a pool of Kriging, RBF, and SVR models. A baseline concept, that uses energy information from the previous day as an added input to the ANN, helps to account for otherwise unrecorded recent changes in the building behavior, leading to improvement in fidelity of up to 30%.