Surrogate Modeling for Simultaneous Engine Cycle and Technology Optimization for Next Generation Subsonic Aircraft

In this paper, we present an optimal-control-based method for ageing-aware charging. A surrogate modeling approach is used to approximate ageing-related Doyle-Fuller-Newman (DFN) model states, where the surrogate model is a combination of a black-box finite-dimensional linear-time-invariant model and a static nonlinear model that is a function of state-of-charge. We formulate the optimal-control problem as minimizing the side reactions for a given charging time and subject to several ageing-related constraints that are commonly used in literature. We will show that the ageing-related DFN model states can be well approximated by the proposed surrogate model. Furthermore, we will show that with the surrogate modeling approach, even in an open-loop execution of the optimal-control-based method, the considered constraints are only marginally violated when applied to the DFN model. Finally, we will compare the Pareto front achieved with the proposed optimal-control-based method with the Pareto fronts achieved with various multi-stage charging protocols. Here, we will show that the proposed optimal-control-based method achieves a significantly improved Pareto front over the multistage charging protocols.

Surrogate modeling of parameterized multi-dimensional premixed combustion with physics-informed neural networks for rapid exploration of design space

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs.

A parametric study is carried out to optimize the design of a ducted rotor system. Computational Fluid Dynamics simulations were conducted for several designs to generate system performance characteristics data to develop surrogate models. Verfication of the accuracy of the surrogate models in representing the system performance was conducted and thereafter the surrogate models were used to investigate the design space to determine the optimum design. The study showed that the surrogate model approach is able to predict the performance within 3% of the computed data.

In this paper, we describe a strategy for modeling the feasible set of power-split continuously variable transmission (CVT) system designs for retrofitting rear-wheel-drive consumer automobiles. A design is considered feasible if it produces a higher fuel economy than the stock vehicle’s fuel economy rating. Towards modeling the feasible set of designs, we first model a vehicle with a power-split CVT system taking into account the system’s mass and CVT efficiency. In this model, the effective design variables are the mass of the transmission system, the CVT functional efficiency, and effective gear ratio defining the allowable power split through and around the CVT. We formulate the set of feasible design solutions utilizing a multiobjective optimization problem to define the boundaries of the maximum allowable system mass, minimum allowable efficiency, and minimum allowable effective gear ratio. We solve this multiobjective optimization problem using NSGA-II and fit a quadratic model to the NSGA-II results to define a surrogate model of the feasible design set. We show that this surrogate modeling approach is sufficient for predicting the feasibility of a candidate transmission design.

Optimizing conjunctive use of surface water and groundwater for irrigation to address human-nature water conflicts: A surrogate modeling approach

In this paper, deep learning–based data‐driven surrogate modeling approach is proposed for enhancing cost‐efficiency of multiband antenna design optimization. The proposed surrogate model–assisted design approach has achieved a computational cost reduction of almost 40% compared to the conventional direct electromagnetic solver–based design methodologies in case of single design example. As for the validation of the proposed method, the obtained optimal design parameters from the surrogate model are used to manufacture an antenna design. The obtained results from the experimental measurement are compared with counterpart results from the literature.

Significant progress in the oil and gas industry advances the application of pipeline into an intelligent era, which poses rigorous requirements on pipeline safety, reliability, and maintainability, especially when crossing seismic zones. In general, strike-slip faults are prone to induce large deformation leading to local buckling and global rupture eventually. To evaluate the performance and safety of pipelines in this situation, numerical simulations are proved to be a relatively accurate and reliable technique based on the built-in physical models and advanced grid technology. However, the computational cost is prohibitive, so one has to wait for a long time to attain a calculation result for complex large-scale pipelines. In this manuscript, an efficient and accurate surrogate model based on machine learning is proposed for strain demand prediction of buried X80 pipelines subjected to strike-slip faults. Specifically, the support vector regression model serves as a surrogate model to learn the high-dimensionally nonlinear relationship which maps multiple input variables, including pipe geometries, internal pressures, and strike-slip displacements, to output variables (namely tensile strains and compressive strains). The effectiveness and efficiency of the proposed method are validated by numerical studies considering different effects caused by structural sizes, internal pressure, and strike-slip movements.

Modern performance earthquake engineering practices frequently require a large number of time‐consuming non‐linear time‐history simulations to appropriately address excitation and structural uncertainties when estimating engineering demand parameter (EDP) distributions. Surrogate modeling techniques have emerged as an attractive tool for alleviating such high computational burden in similar engineering problems. A key challenge for the application of surrogate models in earthquake engineering context relates to the aleatoric variability associated with the seismic hazard. This variability is typically expressed as high‐dimensional or non‐parametric uncertainty, and so cannot be easily incorporated within standard surrogate modeling frameworks. Rather, a surrogate modeling approach that can directly approximate the full distribution of the response output is warranted for this application. This approach needs to additionally address the fact that the response variability may change as input parameter changes, yielding a heteroscedastic behavior. Stochastic emulation techniques have emerged as a viable solution to accurately capture aleatoric uncertainties in similar contexts, and recent work by the second author has established a framework to accommodate this for earthquake engineering applications, using Gaussian Process (GP) regression to predict the EDP response distribution. The established formulation requires for a portion of the training samples the replication of simulations for different descriptions of the aleatoric uncertainty. In particular, the replicated samples are used to build a secondary GP model to predict the heteroscedastic characteristics, and these predictions are then used to formulate the primary GP that produces the full EDP distribution. This practice, however, has two downsides: it always requires minimum replications when training the secondary GP, and the information from the non‐replicated samples is utilized only for the primary GP. This research adopts an alternative stochastic GP formulation that can address both limitations. To this end, the secondary GP is trained by measuring the square of sample deviations from the mean instead of the crude sample variances. To establish the primitive mean estimates, another auxiliary GP is introduced. This way, information from all replicated and non‐replicated samples is fully leveraged for estimating both the EDP distribution and the underlying heteroscedastic behavior, while formulation accommodates an implementation using no replications. The case study examples using three different stochastic ground motion models demonstrate that the proposed approach can address both aforementioned challenges.

This paper presents a surrogate model-based computationally efficient optimization scheme for design problems with multiple, probabilistic objectives estimated through stochastic simulation. It examines the extension of the previously developed MODU-AIM (Multi-Objective Design under Uncertainty with Augmented Input Metamodels) algorithm, which performs well for bi-objective problem but encounters scalability difficulties for applications with more than two objectives. Computational efficiency is achieved by using a single surrogate model, adaptively refined within an iterative optimization setting, to simultaneously support the uncertainty quantification and the design optimization, and the MODU-AIM extension is established by replacing the originally used epsilon-constraint optimizer with a multi-objective evolutionary algorithm (MOEA). This requires various modifications to accommodate MOEA’s unique traits. For uncertainty quantification, a clustering-based importance sampling density selection is introduced to mitigate MOEA’s lack of direct control on Pareto solution density. To address the potentially large solution set of MOEAs, both the termination criterion of the iterative optimization scheme and the design of experiment (DoE) strategy for refinement of the surrogate model are modified, leveraging efficient performance comparison indicators. The importance of each objective in the different parts of the Pareto front is further integrated in the DoE to improve the adaptive selection of experiments.

A hybrid finite element and surrogate modelling approach for simulation and monitoring supported TBM steering

Modern neural architecture search (NAS) is inherently multi-objective balancing trade-offs such as accuracy, parameter count, and computational cost. This complexity makes NAS computationally expensive and nearly impossible to solve without efficient approximations. To address this, we propose a novel surrogate modelling approach that leverages an ensemble of Siamese network blocks to predict dominance relationships between candidate architectures. Lightweight and easy to train, the surrogate achieves 92% accuracy and replaces the crowding distance calculation in the survivor selection strategy with a heuristic rule based on model size. Integrated into a framework termed SiamNAS, this design eliminates costly evaluations during the search process. Experiments on NAS-Bench-201 demonstrate the framework's ability to identify Pareto-optimal solutions with significantly reduced computational costs. The proposed SiamNAS identified a final non-dominated set containing the best architecture in NAS-Bench-201 for CIFAR-10 and the second-best for ImageNet, in terms of test error rate, within 0.01 GPU days. This proof-of-concept study highlights the potential of the proposed Siamese network surrogate model to generalise to multi-tasking optimisation, enabling simultaneous optimisation across tasks. Additionally, it offers opportunities to extend the approach for generating Sets of Pareto Sets (SOS), providing diverse Pareto-optimal solutions for heterogeneous task settings.

Electromagnetic levitation experiments in space are an essential tool for thermophysical property measurement and solidification studies. In light of the need for material properties as inputs to industrial process modeling, investigators need new tools for efficient experiment planning. MHD surrogate modeling is a parametric method for prediction of flow conditions during processing using the ISS-EML facility. Flow conditions in model Au, Zr, and Ti39.5Zr39.5Ni21 samples are predicted using the surrogate model. For Au, flow is shown be turbulent in nearly all experimental conditions, making property measurement difficult. For Zr, the flow is turbulent with the heater on and laminar with the heater off, allowing for property measurement during free-cooling experiments only. For TiZrNi, the flow is laminar under all experimental conditions, indicating that TiZrNi is an excellent candidate for EML experiments. This surrogate modeling approach can be easily applied to other materials of interest, enabling investigators to choose materials that will perform well in levitation and to tailor experiment parameters to achieve desirable flow conditions.

We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically, we represent the model output with a truncated Karhunen-Lo\`eve (KL) expansion, screen the structure of the input space with respect to each KL mode via the active subspace method, and finally form an overall surrogate model of the output by combining surrogates of individual output KL modes. To ensure scalable computation of the gradients of the output KL modes, needed in active subspace discovery, we rely on adjoint-based gradient computation. The proposed method combines benefits of active subspace methods for input dimension reduction and KL expansions used for spectral representation of the output field. We provide a mathematical framework for the proposed method and conduct an error analysis of the mixed KL active subspace approach. Specifically, we provide an error estimate that quantifies errors due to active subspace projection and truncated KL expansion of the output. We demonstrate the numerical performance of the surrogate modeling approach with an application example from biotransport.

In this study, in order to characterize the buried object via deep-learning-based surrogate modeling approach, 3-D full-wave electromagnetic simulations of a GPR model have been used. The task is to independently predict characteristic parameters of a buried object of diverse radii allocated at different positions (depth and lateral position) in various dispersive subsurface media. This study has analyzed variable data structures (raw B-scans, extracted features, consecutive A-scans) with respect to computational cost and accuracy of surrogates. The usage of raw B-scan data and the applications for processing steps on B-scan profiles in the context of object characterization incur high computational cost so it can be a challenging issue. The proposed surrogate model referred to as the deep regression network (DRN) is utilized for time frequency spectrogram (TFS) of consecutive A-scans. DRN is developed with the main aim being computationally efficient (about 13 times acceleration) compared to conventional network models using B-scan images (2D data). DRN with TFS is favorably benchmarked to the state-of-the-art regression techniques. The experimental results obtained for the proposed model and second-best model, CNN-1D show mean absolute and relative error rates of 3.6 mm, 11.8 mm and 4.7%, 11.6% respectively. For the sake of supplementary verification under realistic scenarios, it is also applied for scenarios involving noisy data. Furthermore, the proposed surrogate modeling approach is validated using measurement data, which is indicative of suitability of the approach to handle physical measurements as data sources.