Adaptive Surrogate Model Research Articles

Adaptive AI-based surrogate modelling via transfer learning for DEM simulation of multi-component segregation

Segregation of granular materials is a critical challenge in many industries, often aimed at being controlled or minimised. The discrete element method (DEM) offers valuable insights into this phenomenon. However, calibrating DEM models is a crucial, albeit time-consuming, step. Recently, using machine learning (ML)-based surrogate models (SMs) in the calibration process has emerged as a promising solution. Nevertheless, developing such SMs is challenging due to the high number of DEM simulations required for training. Additionally, choosing a suitable ML model is not trivial. This study aims to develop SMs that effectively link particle-particle and particle-wall DEM interaction parameters to segregation of a multi-component mixture. We evaluate several ML models, ranging from artificial neural networks to ensemble learning, that are trained on a very cost-effective dataset, employing Bayesian optimisation with cross-validation to tune their hyperparameters. Next, we introduce a novel transfer learning (TL)-based approach that leverages knowledge from a few scenarios to handle new “unseen” ones. This method enables the construction of adaptive SMs for unseen scenarios, such as a new initial configuration (IC) of granular mixtures, without the need for a full-sized dataset. Our findings indicate that Gaussian process regression (GPR) efficiently builds accurate SMs on a very small dataset. We also demonstrate that only a few samples are required to build an accurate SM for the unseen IC, which significantly reduces the data preparation burden. By incorporating one and five samples from unseen scenarios to update the TL-GPR-based surrogate model, the SM’s performance (based on \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{R}^{2}$$\\end{document}) on unseen scenarios improves by 17 and 47%, respectively. The insights and methodology presented in this study will facilitate and accelerate the development of accurate SMs for DEM calibration, assisting in developing reliable DEM models in a shorter timeframe.

Pulsar Signal Adaptive Surrogate Modeling

As the number of spacecraft heading beyond Earth’s orbit increased in recent years, autonomous navigation solutions have become increasingly important. One such solution is pulsar-based navigation. The availability of pulsar signals for simulations and HIL testing is essential for the development of pulsar-based navigation. This study proposes a method to develop a surrogate model of pulsar signals based on radio pulsar observations. The selection of suitable pulsars for the radio telescope is discussed, and a series of observations are conducted. The collected data are processed using the PRESTO software, and the pulsar parameters for the model are derived. Unlike current pulsar signal models, the proposed model anticipates pulsar signal parameters to change over time. It can provide dynamic input parameters for known synthetic pulsar signal generators, resulting in a more realistic signal.

Hydrodynamic optimization and performance verification of fairings for round-ended cofferdams using dam-break wave experiments and numerical simulations

Round-ended cofferdams are crucial for large-scale marine projects but are vulnerable to the complex marine environment, including waves, tides, and storms. Enhancing the hydrodynamic performance of these cofferdams is essential for improving safety and efficiency in marine construction. This study introduces a novel fairing design aimed at reducing water flow resistance during the quasi-stable stage of a tsunami. The flow field is analyzed using computational fluid dynamics (CFD) simulations, and an adaptive surrogate model is employed to optimize the parameterized fairing shape. The results demonstrate that the optimized shape significantly suppresses vortex shedding, leading to a 16.59 % reduction in the drag coefficient and a 44.3 % reduction in the lift coefficient under flow conditions. Experimental and numerical simulations of dam-break waves are conducted for two designs, R1 and R0. By comparing their flow field and force characteristics, it is found that R1 effectively separates waves during the impulse stage, reduces wave climb height, and decreases impact loads. In the quasi-stable stage, R1 mitigates the blockage effect, reducing the liquid level difference between the front and back, and thus lowering flow forces. Experimental data further reveals that when the downstream is a dry riverbed, R1′s load reduction is particularly notable, with maximum reductions of 45.62 % in the impulse stage and 28.75 % in the quasi-stable stage. When the riverbed is wet, the maximum load reduction rates are 18.04 % and 8.72 %, respectively. Therefore, R1 not only reduces the resistance of round-end cofferdams under water currents but also under extreme wave forces, providing valuable insights for advancing ocean engineering design.

An efficient dynamic reliability method for maglev vehicle-bridge systems and its application in random controller parameters analysis

This article presents an efficient method for analyzing the dynamic reliability of maglev vehicle-bridge coupled systems by combining a theoretical model with an adaptive surrogate model and the probability density evolution method (PDEM). First, a refined theoretical model of a maglev vehicle-bridge coupling system is established. Next, an adaptive surrogate model of the equivalent extreme value of the system dynamic response is established by combining an adaptive sampling method with radial basis functions. Finally, the adaptive surrogate model and PDEM are combined to further improve the efficiency of the dynamic reliability analysis. In the numerical example, the theoretical model of the maglev vehicle-guideway system was first validated by comparing with the measured data from the Shanghai high-speed maglev line. Then, by treating the controller parameters as normally distributed random variables, the accuracy and efficiency of the proposed reliability method were verified through comparison with the Monte Carlo method and the one-stage sampling surrogate model. Additionally, the impact of the randomness of each controller parameter and the coefficient of variation of the controller parameters on the system’s dynamic reliability was discussed.

A Fast Multi-Objective Optimization Method for Control Parameters of High-Speed Maglev Vehicle-Bridge System

A fast multi-objective optimization method (FMOOM) is proposed by optimizing control parameters to improve the dynamic performance of a high-speed maglev vehicle–bridge system. This approach involves generating the corresponding dynamic response to the sampled control parameters using a theoretical model of a high-speed maglev vehicle–bridge system, followed by establishing an adaptive surrogate model for the relationship between the control parameters and the dynamic response extrema. In the second step, we combine the adaptive surrogate model and the multi-objective gradient-based optimizer (MOGBO) algorithm to obtain the Pareto solution set satisfying different performance indexes. Additionally, the control parameters are optimized using the fuzzy comprehensive evaluation method. In the numerical simulation, we investigate five maglev trains and ten-span simply supported beam bridges and the theoretical model is verified by comparing the calculations with the measured results. The optimization effect of FMOOM is analyzed under different working conditions. The results show that the adaptive surrogate model has good prediction accuracy based on the radial basis function. Furthermore, the Pareto solution distribution of different schemes using FMOOM is reasonable, and the optimization results are as expected. Compared with the reference scheme, the dynamic response of the maglev vehicle–bridge system is smaller after being subjected to FMOOM optimization, and the six performance indexes are dramatically improved.

An active learning approach for reliability assessment of passive systems combining polynomial chaos expansion and adaptive sampling

Passive safety system is extensively employed in newly designed reactors to increase their inherent safety. However, the driving force is smaller, and the uncertainty of the thermal–hydraulic (T-H) process may potentially result in the inability of system to perform its intended function, which is often known as functional failure. Therefore, the passive systems reliability has received increasing attention. Unfortunately, the assessment of system failure probability utilizing Monte Carlo simulation (MCS) methods necessitates a significant quantity of repeated calculations employing the thermal–hydraulic code, which may be impractical in terms of computational cost. To enhance the assessment calculation efficiency, an adaptive surrogate model is proposed. The bootstrap method was employed to introduce an error estimate into the polynomial chaos expansion (PCE) model, which solves the obstacle of the PCE model in reliability evaluation applications due to the lack of error estimation. The method constructs an active learning approach through error estimation, strategically identifies and selects the best candidate samples, and iteratively updates the initial experimental design. The effectiveness of the method was verified through three benchmark cases, and it was employed for assessing the passive residual heat removal system (PRHRS) reliability within integral-type pressurized water reactor (IPWR200). The results demonstrated that the proposed method significantly diminishes the frequency of invocations to the T-H code and improves computational efficiency to a large extent. Furthermore, it can serve as a valuable guide for the design, operation, and reliability evaluation of the passive system.

Active learning for adaptive surrogate model improvement in high-dimensional problems

This paper investigates a novel approach to efficiently construct and improve surrogate models in problems with high-dimensional input and output. In this approach, the principal components and corresponding features of the high-dimensional output are first identified. For each feature, the active subspace technique is used to identify a corresponding low-dimensional subspace of the input domain; then a surrogate model is built for each feature in its corresponding active subspace. A low-dimensional adaptive learning strategy is proposed to identify training samples to improve the surrogate model. In contrast to existing adaptive learning methods that focus on a scalar output or a small number of outputs, this paper addresses adaptive learning with high-dimensional input and output, with a novel learning function that balances exploration and exploitation, i.e., considering unexplored regions and high-error regions, respectively. The adaptive learning is in terms of the active variables in the low-dimensional space, and the newly added training samples can be easily mapped back to the original space for running the expensive physics model. The proposed method is demonstrated for the numerical simulation of an additive manufacturing part, with a high-dimensional field output quantity of interest (residual stress) in the component that has spatial variability due to the stochastic nature of multiple input variables (including process variables and material properties). Various factors in the adaptive learning process are investigated, including the number of training samples, range and distribution of the adaptive training samples, contributions of various errors, and the importance of exploration versus exploitation in the learning function.

A parallel multi-objective optimization based on adaptive surrogate model for combined operation of multiple hydraulic facilities in water diversion project

A parallel multi-objective optimization based on adaptive surrogate model for combined operation of multiple hydraulic facilities in water diversion project

Plug‐and‐play adaptive surrogate modeling of parametric nonlinear dynamics in frequency domain

AbstractWe present an algorithm for constructing efficient surrogate frequency‐domain models of (nonlinear) parametric dynamical systems in a non‐intrusive way. To capture the dependence of the underlying system on frequency and parameters, our proposed approach combines rational approximation and smooth interpolation. In the approximation effort, locally adaptive sparse grids are applied to effectively explore the parameter domain even if the number of parameters is modest or high. Adaptivity is also employed to build rational approximations that efficiently capture the frequency dependence of the problem. These two features enable our method to build surrogate models that achieve a user‐prescribed approximation accuracy, without wasting resources in “oversampling” the frequency and parameter domains. Thanks to its non‐intrusiveness, our proposed method, as opposed to projection‐based techniques for model order reduction, can be applied regardless of the complexity of the underlying physical model. Notably, our algorithm for adaptive sampling can be used even when prior knowledge of the problem structure is not available. To showcase the effectiveness of our approach, we apply it in the study of an aerodynamic bearing. Our method allows us to build surrogate models that adequately identify the bearing's behavior with respect to both design and operational parameters, while still achieving significant speedups.

Accelerating sampling-based tolerance–cost optimization by adaptive surrogate models

ABSTRACT High numbers of function evaluations are inevitable to guarantee the reliability and optimality of sampling-based tolerance–cost optimization. Despite using different countermeasures to increase its efficiency, unreasonably long computation times and unreliable results currently hinder its profitable application. Motivated to overcome this shortcoming, this article presents a novel strategy harmonizing metaheuristic optimization and surrogate modelling. It is based on the idea of adaptive surrogate model-based optimization substituting the tolerance analysis subroutine with a surrogate model, which is iteratively re-modelled with intermediate optimization results to improve its accuracy continuously in potential optima regions. On the one hand, a directed intensification of promising solutions and, on the other hand, an accelerated exploration of the search space is achieved. Optimization studies prove its positive effect on overall efficiency, where a case study with multiple nonlinear assembly response functions and geometrical tolerances serves as a use case.

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene.

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. In this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

Flow Investigation and Optimization Design of a Radial Outflow Liquid Turbine Expander for Liquid CO2 Energy Storage System

Abstract The radial outflow liquid turbine expander (LTEROF) draws increasing attention for enhancing the efficiency of the liquid CO2 energy storage (LCES) system. However, the detrimental cavitation deteriorates the flow behavior, which demands an in-depth study of the flow physics and then effective attenuation. This study aims to effectively mitigate thermosensitive fluid cavitation and reduce energy dissipation. First, a preliminary expander design methodology taking into account the large specific volume variation of working fluid is implemented. Next, the entropy production analysis method (EPAM) is proposed to characterize energy dissipation and cavitation. Furthermore, the improved cavitation and turbulence models are validated through simulating Hord's liquid hydrogen hydrofoil. To suppress the cavitation and energy dissipation, the optimization design method based on the particle swarm optimization (PSO) algorithm together with the Kriging-based adaptive surrogate model is developed. Among them, the nonuniform relational B-splines and free form deformation (NURBS-FFD) method is applied to flexibly deform the profiles of nozzle and rotor, and a novel objective function incorporating vapor volume fraction and local entropy production rate (LEPR) is constructed to capture the cavitation and energy dissipation. During optimization, the optimizer is driven by the objective function to search globally toward the cavitation-resistance and low-dissipation geometry. With the optimization, the LEPR region shrinks and the cavitation is obviously weakened, the performance significantly improves both under design condition and under off-design conditions.

Adaptive stochastic configuration network ensemble for structural reliability analysis

This paper develops a new adaptive surrogate model method for structural reliability analysis, which is constructed by approximating the limit state function (LSF) using stochastic configuration network (SCN) ensemble model. The proposed ensemble model integrates three SCN base models and sets weights for each prediction result, reducing outliers and greatly improving the output accuracy and stability of the algorithm. In constructing a surrogate model for reliability analysis, a new adaptive sampling strategy is designed, including a novel learning function. The new strategy enables the most informative sample points are selected and significantly reduce the number of required sample point. Without further calls to the LSF, the structural failure probability is quickly evaluated using Monte Carlo simulation in terms of the constructed SCN ensemble surrogate model. Three benchmark problems, including a highly nonlinear problem with small failure probability and two multi-variable engineering structural problems, are used to verify the effectiveness of the proposed method.

Fast and reliable reduced‐order models for cardiac electrophysiology

AbstractMathematical models of the human heart increasingly play a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The ultimate aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modeling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. Apart from modeling attempts, the pursuit of efficient, reliable, and fast solution algorithms has been of great importance in this context. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The numerical treatment of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the electrical activity in the heart under varying parameters and inputs much faster than the finely resolved models. In this work, we develop an adaptive, projection‐based reduced‐order surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate model is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization.

Multi-objective multidisciplinary design optimization of liquid-propellant engines thrust chamber based on a surrogate model

The design of liquid-propellant engines (LPEs) has several challenges in setting the performance parameters. Accordingly, optimizing the design of a thrust chamber is of considerable importance that has been considered in several research projects. Previous research has focused on multidisciplinary design optimization (MDO). However, despite these efforts, the main issues remain. The present paper proposes a multi-objective multidisciplinary design optimization based on an efficient adaptive surrogate model of the thrust chamber to address these issues. The proposed method introduces a practical multidisciplinary optimization method based on an adaptive surrogate model that uses the moving least squares methodology, CCM, sensitivity analysis, and the elite multi-objective genetic algorithm (NSGAII). Due to the high importance of specific impulse and thrust-to-weight ratio, these two functions were used as target functions and in the NSGAII framework, the Pareto frontier was drawn for them. The proposed method is applied to a thrust-chamber engine test case. The results show that the target performance of the engine is improved, the specific impulse value is increased by 3.4 s, and the thrust-to-weight ratio is increased by 4%. These values represent significant advances in LPE engine design. The results obtained in this study indicate the potential of the proposed method in solving large-scale thrust-chamber design optimization problems.

Data-driven electronic packaging structure inverse design with an adaptive surrogate model

PurposeThe conventional design method relies on a priori knowledge, which limits the rapid and efficient development of electronic packaging structures. The purpose of this study is to propose a hybrid method of data-driven inverse design, which couples adaptive surrogate model technology with optimization algorithm to to enable an efficient and accurate inverse design of electronic packaging structures.Design/methodology/approachThe multisurrogate accumulative local error-based ensemble forward prediction model is proposed to predict the performance properties of the packaging structure. As the forward prediction model is adaptive, it can identify respond to sensitive regions of design space and sample more design points in those regions, getting the trade-off between accuracy and computation resources. In addition, the forward prediction model uses the average ensemble method to mitigate the accuracy degradation caused by poor individual surrogate performance. The Particle Swarm Optimization algorithm is then coupled with the forward prediction model for the inverse design of the electronic packaging structure.FindingsBenchmark testing demonstrated the superior approximate performance of the proposed ensemble model. Two engineering cases have shown that using the proposed method for inverse design has significant computational savings while ensuring design accuracy. In addition, the proposed method is capable of outputting multiple structure parameters according to the expected performance and can design the packaging structure based on its extreme performance.Originality/valueBecause of its data-driven nature, the inverse design method proposed also has potential applications in other scientific fields related to optimization and inverse design.

Physics-based corrosion reliability analysis of miter gates using multi-scale simulations and adaptive surrogate modeling

Stress corrosion cracking (SCC) initiation is usually simulated at the mesoscale, and these computations are usually expensive. This is made more computationally challenging or impossible when such simulations are coupled with a macroscale structural model required for reliability analysis, due to the sources of uncertainty from both scales. This paper tackles this computational barrier to perform physics-based corrosion reliability analysis of large structures using mesoscale simulations via a novel, adaptive surrogate modeling framework. A global surrogate model of the structure is first constructed from a finite element (FE) mechanical model to propagate various sources of input uncertainty at the macroscale to the local stress responses. After that, a mesoscale surrogate model is constructed from phase-field (PF) simulations to predict the failure probability of a given location by accounting for uncertainty in both the macroscale and mesoscale models. In order to guarantee the accuracy of the mesoscale surrogate model and reduce the number of PF simulations, an adaptive surrogate modeling method is proposed using importance sampling (IS) and active learning to refine iteratively the surrogate model in critical regions. Corrosion reliability analysis of a miter gate structure is adopted to demonstrate the efficacy of the proposed method. The result shows that the proposed framework can efficiently and accurately generate a failure probability map for a large structure like a miter gate based on computationally expensive mesoscale PF simulations. In addition, the proposed method is more accurate and converges faster than existing surrogate model-based reliability analysis algorithms.

Efficient adaptive reliability-based design optimization for geotechnical structures with multiple design parameters

Reliability-based design optimization (RBDO) aims to improve the reliability of geotechnical systems while minimizing the cost of design. However, the conventional RBDO method suffers from a large computational cost and intractable convergence problem due to the double-loop structure involving numerical optimization and repeated reliability analysis. To address this issue, this paper proposes an efficient adaptive RBDO framework for geotechnical structure with multiple design parameters. The proposed framework mainly includes two parts: a novel expanded inverse first-order reliability method (E-IFORM) for dealing with the inverse reliability problem with multiple design parameters, and an adaptive surrogate model to decouple the double-loop structure and improve the efficiency. The proposed methodology is applied to four geotechnical systems (i.e., a soil slope, an excavation pit, a strip footing and a retaining wall), and the results demonstrate the effectiveness and efficiency of the proposed framework.

A comparative study for adaptive surrogate-model-based reliability evaluation method of automobile components

PurposeThis study conducts a comparative study on the performance of reliability assessment methods based on adaptive surrogate models to accurately assess the reliability of automobile components, which is critical to the safe operation of vehicles.Design/methodology/approachIn this study, different adaptive learning strategies and surrogate models are combined to study their performance in reliability assessment of automobile components.FindingsBy comparing the reliability evaluation problems of four automobile components, the Kriging model and Polynomial Chaos-Kriging (PCK) have better robustness. Considering the trade-off between accuracy and efficiency, PCK is optimal. The Constrained Min-Max (CMM) learning function only depends on sample information, so it is suitable for most surrogate models. In the four calculation examples, the performance of the combination of CMM and PCK is relatively good. Thus, it is recommended for reliability evaluation problems of automobile components.Originality/valueAlthough a lot of research has been conducted on adaptive surrogate-model-based reliability evaluation method, there are still relatively few studies on the comprehensive application of this method to the reliability evaluation of automobile component. In this study, different adaptive learning strategies and surrogate models are combined to study their performance in reliability assessment of automobile components. Specially, a superior surrogate-model-based reliability evaluation method combination is illustrated in this study, which is instructive for adaptive surrogate-model-based reliability analysis in the reliability evaluation problem of automobile components.

A finite element model updating method based on the trust region and adaptive surrogate model

The traditional finite element (FE) model updating method based on a static surrogate model often suffers from high calculation costs and low updating accuracy. To address these problems, an FE model updating method based on the trust region (TR) and an adaptive surrogate model is proposed in this study, and the inverse identification of model parameters is realized through sampling. First, an average sensitivity method is introduced to select the parameters to be updated as the inputs of the surrogate model. Second, the residuals between the calculated responses and the experimental responses are taken as the outputs of the surrogate model, and the objective function measuring the misfit between the FE model and the actual structure is constructed. The FE model updating problem is directly converted into a surrogate model optimization problem. Then, during the iterations, adaptive sampling is carried out through the multi-prediction value (MPV) infill criterion, and the TR method is adopted to restrict the sampling space and improve the prediction accuracy of the surrogate model while reducing the calculation efforts of FE model updating to guide the surrogate model to find the global optimal solution. Finally, the proposed method is verified using a simply supported beam and steel truss bridge test. The results reveal that under a limited number of calls to the FE model, the proposed method can not only obtain the updated parameters with physical meaning but also provide high updated accuracy and efficiency.