Computationally Efficient Design Optimization of Multiband Antenna Using Deep Learning–Based Surrogate Models

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.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

This paper presents an engine sizing and cycle selection study of ultra high bypass ratio engines applied to a subsonic commercial aircraft in the N+2 (2025) timeframe. NASA has created the Environmentally Responsible Aviation (ERA) project to serve as a technology transition bridge between fundamental research (TRL 1–4) and potential commercial application (TRL 7). Specifically, ERA is focused on subsonic transport technologies that could reach TRL 6 by 2020 and can be integrated into an advanced vehicle concept to simultaneously meet the ERA project metrics for noise, emissions, and fuel burn. An important variable in exploring the technology trade space is the selection of the optimal engine cycle for use on the advanced aircraft. Previous literature demonstrated the cycle optimization using a design of experiments (DOE) to explore the engine cycle design space for a pre-defined technology package. However, since the optimal engine cycle is dependent upon the specific technology package, this process would have to be repeated to ensure optimal performance for each technology package. With more than 80 technologies to be analyzed, the combinatorial space of technology packages is enormous. As a result, executing a DOE to find the optimum engine cycle for each technology package is infeasible. To address this issue, it is proposed to use surrogate models that encompass the engine cycle and technology design space to enable fast and accurate optimization of the engine cycle for any given technology package. This paper describes the generation and analysis of surrogate models used for technology assessment and cycle optimization of an ultra high bypass geared turbofan engine architecture. The first study in the paper shows that a single surrogate model can be used to accurately simulate both a technology and cycle design space. To demonstrate the proposed surrogate modeling approach, the cycle design space for three different technology packages was analyzed. This study demonstrated that when an optimal cycle is found within the constrained interior of a design space, the surrogate modeling approach is quite accurate. The study also established that the surrogate models can also be used to assess potential cycles at the boundaries or even outside of the region for which they were trained.

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.

Computational speed is a major limiting factor for performing design sensitivity and optimization studies of total knee replacements. Much of this limitation arises from extensive geometry calculations required by contact analyses. This study presents a novel surrogate contact modeling approach to address this limitation. The approach involves fitting contact forces from a computationally expensive contact model (e.g., a finite element model) as a function of the relative pose between the contacting bodies. Because contact forces are much more sensitive to displacements in some directions than others, standard surrogate sampling and modeling techniques do not work well, necessitating the development of special techniques for contact problems. We present a computational evaluation and practical application of the approach using dynamic wear simulation of a total knee replacement constrained to planar motion in a Stanmore machine. The sample points needed for surrogate model fitting were generated by an elastic foundation (EF) contact model. For the computational evaluation, we performed nine different dynamic wear simulations with both the surrogate contact model and the EF contact model. In all cases, the surrogate contact model accurately reproduced the contact force, motion, and wear volume results from the EF model, with computation time being reduced from 13 min to 13 s. For the practical application, we performed a series of Monte Carlo analyses to determine the sensitivity of predicted wear volume to Stanmore machine setup issues. Wear volume was highly sensitive to small variations in motion and load inputs, especially femoral flexion angle, but not to small variations in component placements. Computational speed was reduced from an estimated 230 h to 4 h per analysis. Surrogate contact modeling can significantly improve the computational speed of dynamic contact and wear simulations of total knee replacements and is appropriate for use in design sensitivity and optimization studies.

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

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.

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.

Multi-fidelity modeling and analysis of a pressurized vessel-pipe-safety valve system based on MOC and surrogate modeling methods

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.

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.

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