Surrogate Modeling Method Research Articles

Requirements for the application of the Digital Twin Paradigm to offshore wind turbine structures for uncertain fatigue analysis

The Digital Twin (DT) paradigm offers an extension of simulation model utility into the operational phase of an engineering asset. The goal is a simulation “twinned” with observed data that reflects the actual performance of the asset. However, exploring sources of uncertainty for both the physical asset and the simulation model are a challenge. For example, random metocean conditions, and uncertainty on model parameters and response behaviour of offshore wind turbine (OWT) structures, contribute to uncertainty for predicted life under fatigue. In-service assessment of OWT structures will benefit from twinning simulations and observed data, where a framework to treat this uncertainty is defined. The DT needs to capture state, condition, and behaviour to a level that allows quantification and propagation of uncertainty for reliability analysis. Using a DT, built for fatigue assessment of bolted ring-flanges on OWT support structures, this paper explores the challenges and opportunities in defining uncertainties of interest. We propagate these uncertainties through the DT in a coherent manner using a Gaussian Process (GP) surrogate modelling approach, efficiently emulating a computationally expensive numerical simulator. The GP is an attractive surrogate model method given this computational efficiency, in addition to providing an estimate of prediction uncertainty at unobserved points in the output space. The use of the GP surrogate model is included within a definition of the Surrogate DT, a framework including “fast” and “slow” twinning processes. We define six requirements to apply DTs to OWT structures which provide practical guidelines for modelling this complex asset under uncertainty.

Surrogate modeling method for multi-objective optimization of the inlet channel and the basin of a gravitational water vortex hydraulic turbine

This work presents a high-fidelity surrogate model for generating a multi-objective genetic algorithm to allow the search for the optimal geometry of the inlet channel and the basin of a gravitational water vortex hydraulic turbine. Six parameters were considered for the optimization: the relations between the basin diameter (D) and the basin height (H), H/D; the wrap-around angle (γ), the outlet diameter (d) and D, d/D; the inlet channel width (w) and D, w/D; the inlet channel height (h) and D, h/D; and the inlet channel length (L) and D, L/D. Two conflicting objectives were studied: maximizing the vortex strength (Γ) and minimizing the volume flow rate (Q). The multi-objective optimization problem was resolved by applying the gamultiobj function in Matlab R2018b software. The optimization combines the genetic algorithm with Kriging interpolation to obtain the Pareto front. To train the gamultiobj function, an initial population of 40 individuals was used. As a stopping criterion, the maximum generation of 500 individuals was established. To improve the Pareto front, 20 optimization cycles (60 new samples) were required, reaching a final population of 100 individuals. It was found from the Pareto front that the values of the six variables providing the compromise solution, between Γ and Q, were H/D=1.572, L/D=1.518, h/D=0.565, w/D=0.361, d/D=0.108, and γ=92.141°. This solution reaches a Q of 0.00305 m3/s and a Γ of 1.699 m2/s. The results of this study were compared with the results reported by other authors, who optimized this type of turbine by applying the response surface methodology. The difference between these results was less than 9.61%.

Surrogate model for 3D ground and structural deformations in tunneling by the sequential excavation method

Ground deformation control is one of the key challenges faced during urban tunneling when using the sequential excavation method (SEM). Three-dimensional (3D) numerical analysis is a powerful and essential tool to assess SEM-induced ground and structural deformations. The main challenge in numerical modeling is the uncertainties in data needed to build a model. Various analyses are needed, such as parametric and back-analysis. However, such analyses require thousands to millions of repeated model evaluations making 3D numerical simulations expensive. One technique to make the modeling more manageable is reducing the model size by using a surrogate model that captures the main elements of a full 3D model. This paper examines the capability of four surrogate modeling methods, namely the Polynomial Chaos Expansion (PCE), Kriging, sequential Polynomial-Chaos-Kriging (PCK-SEQ), and optimal Polynomial-Chaos-Kriging (PCK-OPT), to accurately and efficiently capture the ground and structural deformations induced by SEM tunneling. A 3D finite-difference model using FLAC3D was developed to simulate an actual SEM project's excavation and initial support process. A sensitivity analysis was performed to determine the most influential geotechnical input parameters. The Sobol sequence sampling strategy was utilized to conduct a design of experiments. The overall and individual output accuracy of surrogate models, the robustness of training and testing, and the accuracy distribution throughout the input parameter space were evaluated and compared.

Optimal Design of Droplet Ejection for PZT Printhead Based on Surrogate Model

Droplet ejection technology is widely used in green and intelligent manufacturing. A stable jetting can be defined as no obvious satellite droplets during the whole ejection process, which is of great importance to ensure the quality and efficiency of the printed products; However, due to the multi-parameter features and the interaction between different physics, using traditional analytical-based approaches to analyze and/or optimize is usually difficult and even unfeasible. Experimental tests using a PZT printhead design-optimization method based on surrogate modeling are proposed in this paper to overcome this challenge, which can synthesize the advantages of numerical simulation. The basic data for surrogate model construction was obtained by the Computational Fluid Dynamics (CFD) numerical-based model, which was developed to predict the flow characteristic under different parameter settings of the printhead. The accuracy of the developed numerical model was validated by performing experimental tests; thereby, the predictive ability of the numerical model in droplet ejection was verified. With the validated numerical model, the Design of Experiments (DoE) was performed to generate the necessary training and validation sample dataset required by the surrogate modeling. Thereafter, four surrogate modeling methods were adopted to construct the relationship between the design parameters and flow features, where the Kriging (KRG) was identified as the optimal modeling method. Based on the developed KRG model, global sensitivity analysis (GSA) of the parameters was carried out with Sobol’s method; thereby, the influence of different parameters can be quantified. Finally, a genetic algorithm (GA) was used to optimize the structure of the droplet printhead. Through validation, the optimized design model increases the droplet ejection speed by 20.84% while keeping no satellite droplet formation, confirming the efficient and stable printhead ejection, and verifying the feasibility and effectiveness of the analysis/optimization method proposed in this paper.

Accelerating multimodal gravitational waveforms from precessing compact binaries with artificial neural networks

Gravitational waves from the coalescences of black hole and neutron stars afford us the unique opportunity to determine the sources' properties, such as their masses and spins, with unprecedented accuracy. To do so, however, theoretical models of the emitted signal that are i) extremely accurate and ii) computationally highly efficient are necessary. The inclusion of more detailed physics such as higher-order multipoles and relativistic spin-induced orbital precession increases the complexity and hence also computational cost of waveform models, which presents a severe bottleneck to the parameter inference problem. A popular method to generate waveforms more efficiently is to build a fast surrogate model of a slower one. In this paper, we show that traditional surrogate modelling methods combined with artificial neural networks can be used to build a computationally highly efficient while still accurate emulation of multipolar time-domain waveform models of precessing binary black holes. We apply this method to the state-of-the-art waveform model SEOBNRv4PHM and find significant computational improvements: On a traditional CPU, the typical generation of a single waveform using our neural network surrogate SEOBNN_v4PHM_4dq2 takes 18ms for a binary black hole with a total mass of $44 M_{\odot}$ when generated from 20Hz. In comparison to SEOBNRv4PHM itself, this amounts to an improvement in computational efficiency by two orders of magnitude. Utilising additional GPU acceleration, we find that this speed-up can be increased further with the generation of batches of waveforms simultaneously. Even without additional GPU acceleration, this dramatic decrease in waveform generation cost can reduce the inference timescale from weeks to hours.

Tolerance Optimization of Antenna Structures by Means of Response Feature Surrogates

Fabrication tolerances and other types of uncertainties, e.g., the lack of precise knowledge of material parameters, have detrimental effects on the electrical and field performance of antenna systems. In the case of input characteristics, these are particularly noticeable for narrowband and multiband antennas where deviations of geometry parameters from their nominal values lead to frequency shifts of the operating frequency bands. Improving design robustness is therefore important yet challenging. On the one hand, it is numerically demanding as it involves uncertainty quantification (UQ), in particular, estimation and improvement of appropriately defined statistical performance metrics. On the other hand, it has to be carried out at the level of full-wave electromagnetic (EM) simulation models, which incurs considerable computational expenses. Executing UQ tasks at practically acceptable costs can be realized using surrogate modeling methods; however, the construction of reliable metamodels is hindered by the curse of dimensionality. This article proposes a novel approach to the robust design of antenna structures, where the task is formulated to increase the maximum values of parameter deviations for which 100% fabrication yield is ensured. Low cost of the optimization process is enabled by incorporating feature-based regression models for rapid yield estimation, as well as the employment of the trust-region framework for adaptive adjustment of design relocation but also as a convergence safeguard. Our methodology is validated using three microstrip antennas, including two dual-band and a triple-band structure.

State-of-the-Art: AI-Assisted Surrogate Modeling and Optimization for Microwave Filters

Microwave filters are indispensable passive devices for modern wireless communication systems. Nowadays, electromagnetic (EM) simulation-based design process is a norm for filter designs. Many EM-based design methodologies for microwave filter design have emerged in recent years to achieve efficiency, automation, and customizability. The majority of EM-based design methods exploit low-cost models (i.e., surrogates) in various forms, and artificial intelligence techniques assist the surrogate modeling and optimization processes. Focusing on surrogate-assisted microwave filter designs, this article first analyzes the characteristic of filter design based on different design objective functions. Then, the state-of-the-art filter design methodologies are reviewed, including surrogate modeling (machine learning) methods and advanced optimization algorithms. Three essential techniques in filter designs are included: 1) smart data sampling techniques; 2) advanced surrogate modeling techniques; and 3) advanced optimization methods and frameworks. To achieve success and stability, they have to be tailored or combined together to achieve the specific characteristics of the microwave filters. Finally, new emerging design applications and future trends in the filter design are discussed.

KUALITAS LAYANAN, CUSTOMER VALUE, DIGITALISASI BANK, KEPUASAN NASABAH DAN LOYALITAS NASABAH BPR


 This study aims to determine the effect of service quality, customer value, bank digitization, customer satisfaction and customer loyalty of Rural Banks. The population in this study were all customers of PT BPR Lestari Bali. The sampling method used in this research is non-probability sampling with purposive sampling technique. The sample was obtained from the customers of 9 offices of PT BPR Lestari Bali. Instruments in data collection using a questionnaire measured by a 5-point Likert scale. This study uses an alternative structural equation modeling (SEM) method of PLS ??(Partial Least Square) with the SmartPLS 3.0 M3 program. The results of this study indicate that service quality, customer value, and bank digitization have a positive and significant effect on customer satisfaction. Service quality, customer value, and bank digitization have a positive but not significant effect on customer loyalty. Service quality has a positive and significant effect on loyalty mediated by BPR customer satisfaction. Customer value has a positive and significant effect on customer loyalty which is mediated by BPR customer satisfaction. Bank digitalization has a significant positive effect on customer loyalty through customer satisfaction. The presence of the customer satisfaction variable as a mediating variable is very important to increase customer loyalty.

Effect of preoperative statins on respiratory complications after coronary artery bypass grafting.

Limited data exist on the effect of preoperative statin therapy on postoperative respiratory complications. Machine learning algorithms (MLA) can process large, heterogenous data, and have immensely improved the ability for risk prediction. In this study, we sought to examine the role of preoperative statins on respiratory complications in patients undergoing coronary artery bypass grafting(CABG) using MLA. The study population contained the data of patients who underwent CABG between the years 2015 and 2019 (n = 5638). Three hundred and thirty-seven independent variables were recorded and the data was randomly split with stratified sampling into training and testing data with 20% of the data (1113 records) reserved for model testing. Various models including linear models, Random forest, SVM, and XGboostwere trained to predict the incidence of postoperative respiratory complications. Forty-seven important features were found to impact model prediction (p ≤ .05) using the global surrogate model method. A conventional multivariable linear regression model was then used to identify predictors of respiratory complications. One thousand three hundred sixty-two(24.5%) patients developed a respiratory complication in our series. The respiratory complication was seen in 561 (29.7%) of the patients who were not on statin compared to only 801 (21.8%) who were on a statin, p < .0001.The area under the curvefor receiver operating characteristiccurve using statins and respiratory complications was 0.706. Statins showed positive feature importance in all the MLA models. MLA showed that statins impacted the prediction of respiratory complications in all the models studied. The study confirmed that preoperative statins reduced the risk of respiratory complications by 21%.

On the combination of dynamic substructuring and surrogate modeling for the design and study of complex systems

For decades, dynamic substructuring approaches have been successfully utilized for the modeling and simulation of complex systems. More recently, surrogate modeling methods have emerged as a way to reduce the computational cost of simulating for design. This talk will introduce a paradigm in which these two techniques may be combined for the design and study of complex systems. For illustration, a simple example is put forward in which a mass-spring system is broken into subsystems and parameterized. The open-source Python package SMT (Surrogate Modeling Toolbox) developed and maintained by Bouhel et al. is used to construct surrogate models for each subsystem in which the component parameters are taken as inputs and the frequency response functions (FRFs) of the interface degrees of freedom are output. These FRFs are then used to construct the response of the fully coupled system by utilizing a dual Frequency Based Substructuring technique. In many real-world applications, this manner of calculating the effect of varying design parameters on the system response is likely more practical and computationally feasible than the alternative of directly simulating the coupled system response for many parameter sets and training a surrogate model from that output for further design space exploration and optimization. [Work supported by the Office of Naval Research]

A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain

In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.

A combined shear strength reduction and surrogate model method for efficient reliability analysis of slopes

Surrogate models are often used to alleviate extensive computational burden for slope reliability analysis. How to efficiently train a surrogate model with high precision is always a nontrivial task. This paper proposes a novel method, which combines the shear strength reduction (SSR) technique, the surrogate model and the adaptive pool-based sampling strategy for efficient slope reliability analysis. The surrogate model is used to replace the time-consuming slope stability model in simulation-based reliability analysis, while the SSR technique coupled with an adaptive pool-based sampling strategy is innovatively adopted to search for the most informative samples to train the surrogate model, which can improve the computational efficiency significantly. Further, an expanded sampling method is suggested to improve the local prediction of surrogate model in other design space, enabling an efficient evaluation of the slope failure probability corresponding to different threshold safety factors. The main feature of the proposed method is that it takes advantage of SSR technique to efficiently generate training samples in the region of interest. Several slope examples are analyzed to validate the accuracy, computational efficiency as well as the applicability of the proposed method. The results show that proposed method outperforms other approaches in computational efficiency and can give accurate estimation of slope failure probability as well.

A reanalysis-based multi-fidelity (RBMF) surrogate framework for efficient structural optimization

In recent years, research on multi-fidelity (MF) surrogate modeling, which integrates high-fidelity (HF) and low-fidelity (LF) models, has been conducted to improve efficiency in structural optimization. However, even the latest well-developed MF surrogate models inevitably require a certain number of samples to maintain the fidelity of the surrogate models. To overcome this issue, in this paper, a reanalysis-based multi-fidelity (RBMF) surrogate framework, which combines the MF surrogate modeling and a structural reanalysis method, is developed to reduce the computational cost for each sample, not the number of samples. The core idea of the developed framework is to approximately obtain a large number of samples based on a small number of exactly calculated data as prior knowledge. Each sub-strategy for RBMF surrogate framework is developed to maximize the performances of the reanalysis method. Specifically, a reanalysis sample classification method, reanalysis sample infilling method, and local convergence criteria are proposed to effectively reflect the characteristics of the reanalysis method. Therefore, the coupling between MF surrogate modeling and reanalysis method is strengthened. Finally, two numerical examples show that the developed framework outperforms the conventional one.

An AI-Based Adaptive Surrogate Modeling Method for the In-Service Response of UVLED Modules

The response forecasting of in-service complex electronic systems remains a challenge due to its uncertainty. An AI-based adaptive surrogate modeling method, including offline and online learning procedures, is proposed in this research for different systems with significant variety. The offline learning aims to abstract the knowledge from the known information and represent it as root models. The in-service response is modeled by a linear combination of the online learning of these root models against the continuous new measurement. This research applies a performance measurement dataset of the UVLED modules with considerable deviation to verify the proposed method. Part of the datasets is selected to generate the root models by offline learning, and these root models are applied to the online learning procedures for the adaptive surrogate model (ASM) of the different systems. The results show that after approximately 10 online learning iterations, the ASM achieves the capability of predicting 1000 h of response.

Deep Transfer Learning-Based Sizing Method of Permanent Magnet Synchronous Motors Considering Axial Leakage Flux

The sizing process is necessary to analyze the electromagnetic characteristics according to the major shape parameters during the early design stage of permanent magnet synchronous motors (PMSMs). However, predicting the performance of PMSMs with 2-D finite element analysis (FEA) has errors due to axial leakage flux. Therefore, the axial leakage flux should be considered in the sizing process. The most accurate way to consider the axial leakage flux is to perform 3-D FEA, but it has a disadvantage of high computational cost. In this view, we propose a deep transfer learning-based surrogate modeling method to reduce the computational cost for calculating 3-D FEA-based motor parameters. The transfer learning is conducted using a large amount of 2-D FEA-based and small amount of 3-D FEA-based motor parameters. Using the proposed process, it is possible to accurately predict the motor characteristics according to size-related variables that satisfy the required specifications with small amount of 3-D FEA-based motor parameters. The proposed method was verified through 3-D FEA and experiments for pancake-type PMSMs, which is highly affected by axial leakage flux.

A High-Precision Surrogate Modeling Method Based on Parallel Multipoint Expected Improvement Point Infill Criteria for Complex Simulation Problems

In order to overcome the problem of the low fitting accuracy of the expected improvement point infill criteria (EI) and the improved expected improvement point infill criteria (IEI), a high-precision surrogate modeling method based on the parallel multipoint expected improvement point infill criteria (PMEI) is presented in this paper for solving large-scale complex simulation problems. The PMEI criterion takes full advantage of the strong global search ability of the EI criterion and the local search ability of the IEI criterion to improve the overall accuracy of the fitting function. In the paper, the detailed steps of the PMEI method are introduced firstly, which can add multiple sample points in a single iteration. At the same time, in the process of constructing the surrogate model, it is effective to avoid the problem of the low fitting accuracy caused by adding only one new sample point in each iteration of the EI and IEI criteria. The numerical examples of the classical one-dimensional function and two-dimensional function clearly demonstrate the accuracy of the fitting function of the proposed method. Moreover, the accuracy of the multi-objective optimization surrogate model of a truck cab constructed by the PMEI method is tested, which proves the feasibility and effectiveness of the proposed method in solving high-dimensional modeling problems. All these results confirm that the Kriging model developed by the PMEI method has high accuracy for low-dimensional problems or high-dimensional complex problems.

Non-parametric surrogate model method based on machine learning with application on low-pressure steam turbine exhaust system

Current surrogate model methods that are widely used in optimization and design processes rely on manual parameterization to describe the geometry of objects. The loss of geometric information in this process limits the prediction accuracy of surrogate model. To tackle this problem, the new method directly picks important geometric features from surface meshes of fluid domain using Graph Neural Networks (GNNs) and predicts contours of fluid variables based on extracted information with Convolutional Neural Networks (CNNs). The prediction error of CNNs propagates backwards to train GNNs to select sensitive features from surface meshes. This framework reduces uncertainties introduced by manual parameterization and the loss of geometric information because the input of this new method is from the meshes used in the numerical simulations. With CNN and larger amount of extracted geometric information, this method can also predict higher dimensions distributions of flow variables rather than only several performance metrics. The nature of non-parametric representation of geometry also allows users to access designs defined by other parameterization methods to create a larger database. Additionally, thanks to the generic nature of the new method, it can be used for any other design or optimization processes governed by partial differential equations involving complicated geometries. To demonstrate this new method, a non-parametric surrogate model is built for a low-pressure steam turbine exhaust system (LPES). The new surrogate model uses 10 surfaces meshes of the LPES as input and it is used to predicts the energy flux contours at the exit of the last stage of the turbine. Altogether 582 designs have been generated, which contains two types of geometries defined by different methods. Among them, 550 cases are used for training, and 32 cases for testing. The power output of the last two stages of the turbine predicted by the surrogate model has average 0.86% difference compared with those of numerical simulations over a wide range of power ratings. The structural similarity index measure (SSIM) is used to measure the differences between the simulated and predicted contours at the exit of the last rotor, where the average SSIM of 640 contours is 0.9594 (1.0 being identical).

Mobility Prediction of Off-Road Ground Vehicles Using a Dynamic Ensemble of NARX Models

Abstract Mobility prediction of off-road autonomous ground vehicles (AGV) in uncertain environments is essential for their model-based mission planning, especially in the early design stage. While surrogate modeling methods have been developed to overcome the computational challenge in simulation-based mobility prediction, it is very challenging for a single surrogate model to accurately capture the complicated vehicle dynamics. With a focus on vertical acceleration of an AGV under off-road conditions, this article proposes a surrogate modeling approach for AGV mobility prediction using a dynamic ensemble of nonlinear autoregressive models with exogenous inputs (NARX) over time. Synthetic vehicle mobility data of an AGV are first collected using a limited number of high-fidelity simulations. The data are then partitioned into different segments using a variational Gaussian mixture model to represent different vehicle dynamic behaviors. Based on the partitioned data, multiple surrogate models are constructed under the NARX framework with different numbers of lags. The NARX models are then assembled together dynamically over time to predict the mobility of the AGV under new conditions. A case study demonstrates the advantages of the proposed method over the classical NARX models for AGV mobility prediction.

Inversion of ocean sound speed profiles from travel time measurements using a ray-gradient-enhanced surrogate model

ABSTRACT Sound Speed Profiles (SSPs) are critical environmental parameters for many ocean applications. A novel Ray-Gradient-Enhanced Surrogate Model (RGE-SM) method is proposed for SSP inversion by matching the predicted acoustic travel times with the measured acoustic travel times. The surrogate model is adopted as the framework to search for the global solution of SSP parameters. Instead of approximating the objective function, the proposed method constructs the surrogate of the objective function’s lower envelope by finding local minima based on the ray gradient of the objective function. The RGE-SM method is verified using SSP data in the South China Sea, and the results show that the RGE-SM method exhibits a smaller estimation error than the genetic algorithm with less than one-twentieth of the calculation time.

Multi-Fidelity Low-Rank Approximations for Uncertainty Quantification of a Supersonic Aircraft Design

Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.