Surrogate Model Research Articles

Harmonic Current Optimization for Torque Ripple Reduction in Permanent Magnet Synchronous Machine Drives Based on Torque Ripple Surrogate Model

Harmonic Current Optimization for Torque Ripple Reduction in Permanent Magnet Synchronous Machine Drives Based on Torque Ripple Surrogate Model

Handling noise and overfitting in surrogate models based on non-uniform rational basis spline entities

This paper proposes a general and systematic approach to generate a surrogate model based on non-uniform rational basis spline (NURBS) hyper-surfaces as a solution of a constrained non-linear programming problem, which is solved through a gradient-based algorithm by considering two formulations. The first formulation, which is the general one, is prone to the curse of dimensionality. The second one separates dimensions in the NURBS domain and allows saving computational time and resources. The optimisation process consists of three steps, which are solved sequentially. Each step is characterised by different design variables and solving strategies. The gradient of the cost function, for both formulations and for each optimisation step, is derived analytically by exploiting the properties of NURBS entities, hence enhancing computational efficiency and accuracy. One of the main features of the presented methodology lies the incorporation of a smoothing term in the problem formulation. This term plays a crucial role in controlling overfitting phenomenon and attenuating local oscillations within the dataset. These oscillations may be due to various sources, such as inherent noise, model instabilities, measurement uncertainties, or numerical precision limitations. The effectiveness of the proposed approach is tested on both analytical benchmark problems and real-world engineering problems taken from the literature.

Hybrid AI-Analytical Modeling of Droplet Dynamics on Inclined Heterogeneous Surfaces

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

Updating Nonlinear Stochastic Dynamics of an Uncertain Nozzle Model using Probabilistic Learning with Partial Observability and Incomplete dataset

Abstract This paper introduces a methodology for updating the nonlinear stochastic dynamics of a nozzle with uncertain computational model. The approach focuses on a high-dimensional nonlinear computational model constrained by a small target dataset. Challenges include the large number of degrees-of-freedom, geometric nonlinearities, material uncertainties, stochastic external loads, under-observability, and high computational costs. A detailed dynamic analysis of the nozzle is presented. An updated statistical surrogate model relating the observations of interest to the control parameters is constructed. Despite small training and target datasets, and partial observability, the study successfully applies Probabilistic Learning on Manifolds (PLoM) to address these challenges. PLoM captures geometric nonlinear effects and uncertainty propagation, improving conditional mean statistics compared to training data. The conditional confidence region demonstrates the ability of the methodology to accurately represent both observed and unobserved output variables, contributing to advancements in modeling complex systems.

Determining a musculoskeletal system's pre-stretched state using continuum-mechanical forward modelling and joint range optimization.

The subject-specific range of motion (RoM) of a musculoskeletal joint system is balanced by pre-tension levels of individual muscles, which affects their contraction capability. Such an inherent pre-tension or pre-stretch of muscles is not measureable with in vivo experiments. Using a 3D continuum mechanical forward simulation approach for motion analysis of the musculoskeletal system of the forearm with 3 flexor and 2 extensor muscles, we developed an optimization process to determine the muscle fibre pre-stretches for an initial arm position, which is given human dataset. We used RoM values of a healthy person to balance the motion in extension and flexion. The performed sensitivity study shows that the fibre pre-stretches of the m.brachialis, m.biceps brachii and m.triceps brachii with dominate the objective flexion ratio, while m.brachiradialis and m.anconeus amount and . Within the multi-dimensional space of the surrogate model, 3D sub-spaces of primary variables, namely the dominant muscles and the global objective, flexion ratio, exhibit a path of optimal solutions. Within this optimal path, the muscle fibre pre-stretch of two flexors demonstrate a negative correlation, while, in contrast, the primary extensor, m.triceps brachii correlates positively to each of the flexors. Comparing the global optimum with four other designs along the optimal path, we saw large deviations, e.g., up to 15 in motion and up to 40% in muscle force. This underlines the importance of accurate determination of fibre pre-stretch in muscles, especially, their role in pathological muscular disorders and surgical applications such as free muscle or tendon transfer.

Neural networks as effective surrogate models of radio-frequency quadrupole particle accelerator simulations

Radio-frequency quadrupoles (RFQs) are multi-purpose linear particle accelerators that simultaneously bunch and accelerate charged particle beams. They are ubiquitous in accelerator physics, especially as injectors to higher-energy machines, owing to their impressive efficiency. The design and optimization of these devices can be lengthy due to the need to repeatedly perform high-fidelity simulations. Several recent papers have demonstrated that machine learning can be used to build surrogate models (fast-executing replacements of computationally costly beam simulations) for order-of-magnitude computing time speedups. However, while these pilot studies are encouraging, there is room to improve their predictive accuracy. Particularly, beam summary statistics such as emittances (an important figure of merit in particle accelerator physics) have historically been challenging to predict. For the first time, we present a surrogate model trained on 200 000 samples that yields < 6% mean average percent error for the predictions of all relevant beam output parameters from defining RFQ design parameters, solving the problem of poor emittance predictions by identifying and including hidden variables which were not accounted for previously. These surrogate models were made possible by using the Julia language and GPU computing; we briefly discuss both. We demonstrate the utility of surrogate modeling by performing a multi-objective optimization using our best model as a callback in the objective function to select an optimal RFQ design. We consider trade-offs in RFQ performance for various choices of Pareto-optimal design variables—common issues for any multi-objective optimization scheme. Lastly, we make recommendations for input data preparation, selection, and neural network architectures that pave the way for future development of production-capable surrogate models for RFQs and other particle accelerators.

Surrogate modelling for ice accretion prediction on wind turbine blades based on support vector regression

AbstractIce accretion poses a significant challenge, threatening the safety and operational stability of wind turbines in extreme cold weather. Accurate estimation of ice accretion is essential in minimizing this concern. Data‐driven techniques typically rely on extensive historical datasets, and simulation‐based methods may be time‐consuming. To address these challenges, surrogate modelling for ice accretion prediction is proposed, utilizing support vector regression. This surrogate model undergoes rigorous evaluation to ensure reliability. The surrogate model reduces time consumption by four orders of magnitude compared to simulation, with only a 2.5% decrease in accuracy. The analysis reveals that real‐time pitch angle adjustments, informed by both the surrogate model and meteorological data, can effectively reduce ice accretion on wind turbine blades in cold climates.

Probabilistic assessment of existing shield tunnel longitudinal responses to tunnelling

AbstractThis paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second, the longitudinal beam‐spring model (LBSM), which can explicitly consider the circumferential joints, is applied to reflect the performances of the existing shield tunnel. Two well‐documented case histories are selected to validate the effectiveness of the deterministic analysis model. The predictions are also compared with previous analytical methods. Afterward, to improve the computational efficiency, a surrogate model is then established to replace deterministic model and perform the global sensitivity analysis (GSA). A probabilistic analysis is further performed to explore the tunnelling‐induced deformation characteristics of the shield tunnel by means of Monte Carlo simulation (MCS) method. Parametric analyses are further performed to explore the influences of key variables on the failure probabilities of the existing shield tunnel. The results show the proposed deterministic model gives a satisfactory prediction in tunnelling‐induced responses of the existing shield tunnel. The LBSM can reflect the segmental ring and joint deformations more realistically. The uncertainties in the ground elastic modulus, joint rotation stiffness and the joint shearing stiffness dominate the tunnel settlement, joint opening and dislocation, respectively. The failure probability of tunnel settlement is more sensitive to volume loss than that of the joint opening and dislocation. The whole system failure probability is identical to that of the tunnel settlement failure mode. By increasing the coefficient of variation (COV) of random variables, probability density function (PDF) curves for neutral and pessimistic conditions become lower and wider, and the maximum joint opening and dislocation positions corresponding to the peaks of PDF apparently deviate from that of the determinate results. Increasing the two tunnel clearances, the allowable volume loss for opening and dislocation increase linearly, but it has insignificant influence on the tunnel failure mode. However, enlarge the new tunnel diameter leads to rapid decrease in the allowable volume loss for all failure modes.

Data-driven optimisation of wind farm layout and wake steering with large-eddy simulations

Abstract. Maximising the power production of large wind farms is key to the transition towards net zero. The overarching goal of this paper is to propose a computational method to maximise the power production of wind farms with two practical design strategies. First, we propose a gradient-free method to optimise the wind farm power production with high-fidelity surrogate models based on large-eddy simulations and a Bayesian framework. Second, we apply the proposed method to maximise wind farm power production by both micro-siting (layout optimisation) and wake steering (yaw angle optimisation). Third, we compare the optimisation results with the optimisation achieved with low-fidelity wake models. Finally, we propose a simple multi-fidelity strategy by combining the inexpensive wake models with the high-fidelity framework. The proposed gradient-free method can effectively maximise wind farm power production. Performance improvements relative to wake-model optimisation strategies can be attained, particularly in scenarios of increased flow complexity, such as in the wake steering problem, in which some of the assumptions in the simplified flow models become less accurate. The optimisation with high-fidelity methods takes into account nonlinear and unsteady fluid mechanical phenomena, which are leveraged by the proposed framework to increase the farm output. This paper opens up opportunities for wind farm optimisation with high-fidelity methods and without adjoint solvers.

A novel stability equation for the estimation of the factor of safety for homogeneous dry finite slopes

AbstractThis paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance to the limit state. It can be easily programmed into calculators or computers and accurately determines the minimum factor of safety based on the shear strength parameters and slope geometry—meaning that it is ideally suited for integration into reliability calculations. The equation is determined parametrically for various soil parameters and slope geometry using the Morgenstern–Price method and compares favorably with conventional techniques, such as slope stability charts, limit equilibrium, and strength reduction methods (SRM). From a practical perspective, the proposed equation greatly simplifies the analysis of the slope stability as the creation of a numerical model is not required and is suited to use in the feasibility stage of a project, for example, for large linear infrastructure projects with differing slope geometries or in situations where a quick assessment is desired.

Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor.

Compressive sensing-based construction of high-resolution mode shapes for updating bridge boundary constraints

AbstractIn this study, a method of finite element model updating is proposed to quantitatively identify bridge boundary constraints using the high-resolution mode shapes of a bridge. The high-resolution mode shapes are first identified from the responses measured by few randomly distributed sensors using the compressive sensing theory, which is innovatively implemented in the spatial domain with a proposed basis matrix. To speed up finite element updating, the frequency and modal assurance criterion Kriging models are then established to approximate the implicit relation between boundary constraints and bridge modal parameters including frequencies and mode shapes, serving as surrogate models for the bridge finite element model. By adopting the surrogate models in finite element updating, the objective functions of frequencies and mode shape indicators are optimized by a multi-objective genetic algorithm. The numerical examples as well as an actual laboratory experiment have shown that the mode shapes and boundary constraints of a bridge can be identified precisely and efficiently by the proposed method, even for a continuous and variable cross-sectional bridge.

From seasonal field study to surrogate modeling: Investigating the biomechanical dynamics of Elymus sp. in salt marshes

AbstractSalt marshes have been studied in the context of ecosystem services they can provide for coastal protection. In this study, monthly field campaigns focusing on Elymus spp. and its biomechanical properties were conducted from December 2021 to December 2022 on the German Barrier Island Spiekeroog. A total of 1390 specimens were investigated to determine their growth length, out of which 418 specimens were investigated mechanically with three‐point bending tests to determine their biomechanical properties. To evaluate the interaction of hydraulic loads and vegetation, the challenge of modeling biomechanical plant properties to scale is addressed by using resin 3D printing with flexible material, while focusing on the materials mechanical properties. Based on the field data acquired and additional literature (adding up to 1959 measurements), a cylindrical plant model with an outer diameter of (scale 1 : 1) was developed. It was manufactured mixing two resin components with varying volume ratios resulting in surrogates with different flexural stiffnesses. The surrogates were characterized using three‐point bending tests and image analysis of their bending behavior when subjected to currents between 0.4 and 1.2 m/s. With the average Young's modulus ranging from 8.45 to 1708.42 MPa, the bending angle varies from 0° to 77.4° displaying the influence of material stiffness and flow velocity. Applying the Cauchy scaling law, this study shows that resin 3D printing can be used to model Elymus sp. with respect to its biomechanical properties allowing for seasonally independent physical laboratory experiments with plant models.

Multivariate Gaussian process surrogates for predicting basic structural parameters of refractory non-dilute random alloys

Refractory non-dilute random alloys consist of two or more principal refractory metals with complex interactions that modify their basic structural properties such as lattice parameters and elastic constants. Atomistic simulations (ASs) are an effective method to compute such basic structural parameters. However, accurate predictions from ASs are computationally expensive due to the size and number of atomistic structures required. To reduce the computational burden, multivariate Gaussian process regression (MVGPR) is proposed as a surrogate model that only requires computing a small number of configurations for training. The elemental atom percentage in the hyper-spherical coordinates is demonstrated to be an effective feature for surrogate modeling. An additive approximation of the full MVGPR model is also proposed to further reduce computations. To improve surrogate accuracy, active learning is used to select a small number of alloys to simulate. Numerical studies based on AS data show the accuracy of the surrogate methodology and the additive approximation, as well as the effectiveness and robustness of the active learning for selecting new alloy designs to simulate.

Numerical assessment and optimization of photovoltaic-based hydrogen-oxygen Co-production energy system: A machine learning and multi-objective strategy

Green hydrogen production technology based on photovoltaic (PV), battery energy storage system (BESS) and proton exchange membrane (PEM) water electrolysis plays a crucial part in the transition process of energy to zero carbon technology. But few studies have focused on achieving all-day continuous hydrogen production, which is the key to large-scale hydrogen utilization. In this study, we developed an off-grid PV-BESS-PEM system for hydrogen and oxygen production. Firstly, the PV, BESS and PEM water electrolysis components were modeled and model validation was performed. Secondly, an energy management strategy (EMS) is proposed to achieve the goal of continuous and stable hydrogen production. Then, a surrogate model between design variables and optimization objectives is established based on machine learning methods, and a multi-objective optimization algorithm is used to drive the optimization process. Finally, a case study of the PV-BESS-PEM system is presented based on solar irradiation data in Lhasa, where there is sufficient solar resources and oxygen demand. The results demonstrate that the EMS can satisfy the purpose of all-day continuous and stable hydrogen production. The number of cells in the electrolyzer and the water temperature have a significant effect on the hydrogen production and the electrolysis efficiency. And the optimal system has increased the hydrogen production by 16.80 % and the electrolysis efficiency of PEM by 12.08 %, respectively. Herein, the methodological framework is expected to provide theoretical guidance for large-scale water electrolysis hydrogen production applications based on solar energy.

Co-Pyrolysis of biomass and plastic waste: Process prediction and optimization based on Artificial Intelligence and response optimizer surrogate model

Co-pyrolysis process prediction and optimization has been done through different artificial intelligence processes and response optimizer surrogate model. Neural network and machine learning-based different prediction models have been evaluated to predict the co-pyrolysis output based on the experimental data from literature. While multi-objective optimization has been done through response optimizer. According to prediction models results, CatBoost Regressor (CatB) and Extreme Gradient Boosting (XGB) models’ performance is better than other (seven) models with CatB co-efficient of determinant (R2) 0.92–0.98 while it is 0.91–0.98 for XGB in different scenarios. Therefore, CatB and XGB both models can provide an optimal result for co-pyrolysis prediction. Surrogate-model for multi-objective optimization results concluded that lower portion of biomass waste and higher plastic waste in the feedstock has the optimum co-pyrolysis process output around 550 °C and 60 min of resident time for higher portion of liquid yield with lower gases production. Overall higher portion of the plastic waste in feedstock at high temperature and low resident time promotes more liquid yield. While solid (biochar) production is optimal when there is a higher amount of biomass waste in the feedstock at lower temperature, and longer resident time.

Variable-Fidelity Surrogate Model-Based Airfoil Optimization at a Moderate Reynolds Number

Airfoil shape optimization for enhanced aerodynamic performance at a moderate Reynolds number is carried out using a novel technique for constrained optimization of expensive engineering functions. The proposed method is a co-kriging surrogate model using two levels of fidelity in conjunction with a gradient-free trust-region method to drive the model towards the global optimum. The methodology is first applied on a generic test function to demonstrate its efficiency. Later, the proposed optimization framework is applied on constrained airfoil shape optimization problems involving maximizing the lift-to-drag ratio, maximizing the endurance factor, and minimizing the drag coefficient of an Eppler E214 airfoil. The optimal lift-to-drag ratio and the endurance factor are found to be 13.25% and 16.05%, respectively, higher than the baseline airfoil. The optimal drag coefficient is 6.86% lower than the baseline airfoil. The flow transition is also delayed for the some of the optimal airfoils. The present results show that the proposed optimization methodology is successful in improving the aerodynamic characteristics in the sensitive low/moderate Reynolds number regime.

Plasma surrogate modelling using Fourier neural operators

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier neural operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (Mean Squared Error in the normalised domain ≈10−5 ). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations, and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e. cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

Identification of parameter importance for benzene transport in the unsaturated zone using global sensitivity analysis

Abstract. One of the greatest threats to groundwater is contamination from fuel derivatives. Benzene, a highly mobile and toxic fuel derivative, can easily reach groundwater from fuel sources and lead to extensive groundwater contamination and drinking water disqualification. Modelling benzene transport in the unsaturated zone can quantify the risk for groundwater contamination and provide needed remediation strategies. Yet, characterization of the problem is often complicated, due to typical soil heterogeneity, numerous unknown site and solute parameters, and the difficulty of distinguishing important from non-important parameters. Thus, sensitivity analysis (SA) methods, such as global SA (GSA), are applied to reduce uncertainty and detect key parameters for groundwater contamination and remediation. Nevertheless, studies devoted to identifying the parameters that determine transport of fuel derivatives in the unsaturated zone are scarce. In this study, we performed GSA to assess benzene transport in the unsaturated zone. First, a simple GSA (Morris) screening method was used for a homogenous sandy vadose zone. Then, a more computationally demanding (Sobol) variance-based GSA was run on the most influential parameters. Finally, the Morris method was tested for a heterogeneous medium containing clay layers. To overcome model crashes during GSA, several methods were tested for imputation of missing data. The GSA results indicate that benzene degradation rate (λk) is the utmost influential parameter controlling benzene mobility, followed by aquifer depth (z). The adsorption coefficient (Kd) and the van Genuchten n parameter of the sandy soil (n1) were also highly influential. The study emphasizes the significance of λk and the presence of clay layers in predicting aquifer contamination. The study also indicates the importance of heterogenous media representation in the GSA. Though identical parameters control the transport in the different soil types, in the presence of both sand and clay, parameters directly affecting the solute concentration like λk and Kd have increased influence in clay, whereas n is more influential for sand comprising most of the profile. Overall, GSA is demonstrated here as an important tool for the analysis of transport models. The results also show that in higher dimensionality models, the radial basis function (RBF) is an efficient surrogate model for missing data imputation.

A novel morphing nose cone for underwater gliders: Performance analysis, parameter optimization, and driving mechanism design

As an autonomous underwater vehicle with low energy consumption, underwater glider has been widely applied to long-term ocean exploration missions. To better deal with complex working environments and various mission requirements, morphing underwater gliders are receiving increasing attention. This paper attempts to introduce the morphing nose cone that can achieve length and bending angle adjustments into the glider to improve its comprehensive performance. The performance indicators of the glider include energy utilization rate, static stability, and voyage velocity. Based on dynamic analysis and CFD simulation, performance evaluation models of a glider are established, and the effect of morphing nose cone configurations on the glider's hydrodynamic characteristics is discussed. Then, mathematical optimization models for morphing parameters of the nose cone are established, and they are solved by a multi-objective optimization algorithm and surrogate model technology. Especially, the diving and ascending motion processes of the glider are separately considered in the above optimization. Finally, the multi-objective optimization results are used for guiding the driving mechanism design of the morphing nose cone, and the principle prototype of a novel design scheme is manufactured to verify the feasibility. The research methods and results will provide new development direction for the morphing underwater glider technology.