Kriging-based Surrogate Model Research Articles

A surrogate-based flow-field prediction and optimization strategy for hypersonic thrust nozzle

The thrust nozzle is a component that directly generates thrust, which is of great importance in the design of a hypersonic propulsion system. In this study, a surrogate-based flow-field prediction and optimization strategy for hypersonic thrust nozzles is proposed based on reduced-order modeling of the flow field. The effects of various methods on flow field prediction accuracy are studied, including domain decomposition-based proper orthogonal decomposition and Kriging-based surrogate models. A high-precision prediction of the viscid flow field can be achieved when an arbitrary nozzle contour parametrized by non-uniform rational B-spline is given. It is revealed that domain decomposition methods and improvements to the orthogonal basis effectively enhance the accuracy of flow field reconstruction. Compared to the full flow field surrogates, the near-wall region surrogates predict wall pressure more effectively and yield higher thrust accuracy. A hybrid infill sampling criterion is also proposed to improve the prediction accuracy of the model. Combining that with the surrogate-based flow-field prediction model and the intelligent optimization algorithms, an optimized nozzle contour is obtained, whose performance is 0.5% higher than that designed using the Rao method.

Kriging-based surrogate data-enriching artificial neural network prediction of strength and permeability of permeable cement-stabilized base

Limited test data hinder the accurate prediction of mechanical strength and permeability of permeable cement-stabilized base materials (PCBM). Here we show a kriging-based surrogate model assisted artificial neural network (KS-ANN) framework that integrates laboratory testing, mathematical modeling, and machine learning. A statistical distribution model was established from limited test data to enrich the dataset through the combination of markov chain monte carlo simulation and kriging-based surrogate modeling. Subsequently, an artificial neural network (ANN) model was trained using the enriched dataset. The results demonstrate that the well-trained KS-ANN model effectively captures the actual data distribution characteristics. The accurate prediction of the mechanical strength and permeability of PCBM under the constraint of limited data validates the effectiveness of the proposed framework. As compared to traditional ANN models, the KS-ANN model improves the prediction accuracy of PCBM’s mechanical strength by 21%. Based on the accurate prediction of PCBM’s mechanical strength and permeability by the KS-ANN model, an optimization function was developed to determine the optimal cement content and compaction force range of PCBM, enabling it to concurrently satisfy the requirements of mechanical strength and permeability. This study provides a cost-effective and rapid solution for evaluating the performance and optimizing the design of PCBM and similar materials.

Robust active learning framework for structural reliability analysis using uncertainty quantification and flexible meta-model

Achieving highly accurate results in assessing structural reliability with reduced time complexity is an active and challenging engineering topic, especially when working with complex real-world structures. One of the most prominent methods addressing this issue is AK-MCS, which adaptively updates the Kriging-based surrogate model for forecasting structures’ behavior. While the Kriging model’s performance may be limited compared to multiple new machine learning models, it remains dominant in reliability analysis thanks to its distinctive ability to assess uncertainty along with prediction results. This ability is necessary to determine the potential candidate sample in the active learning procedure. This study proposes a novel method, dubbed AUQ-meta, that allows us to leverage the recent powerful machine learning models while still being able to produce uncertainty quantification. The AUQ-meta method consists of three main components: a machine learning-based predictor, a quantile regression module for uncertainty assessment, and an adaptive reliability analysis process. The effectiveness and efficiency of the proposed method are consistently validated through six examples with high dimensionality, nonlinearity, and time-varying elements. In addition, comparison and sensitivity studies are carried out, providing further insights into the AUQ-meta method’s operational mechanism.

Forecasting Ionospheric TEC Changes Associated with the December 2019 and June 2020 Solar Eclipses: A Comparative Analysis of OKSM, FFNN, and DeepAR Models

This paper presents forecast and investigation of the variation in ionospheric Total Electron Content (TEC) during the solar eclipses (SEs) of December 2019 and June 2020 using three different methods: Deep Autoregressive model (DeepAR), Feed-Forward Neural Network (FFNN), and Ordinary Kriging-based Surrogate Model (OKSM), and the TEC data predicted by DeepAR, FFNN, and OKSM were compared with the actual TEC during the observation days. The study was conducted based on GPS data taken from the IISC receiver located in Bangalore, India, during the SEs which happened on 26.12.2019 and 21.06.2020. The TEC data were examined to assess the effect of solar eclipses on TEC values. Eighty-day prior TEC data for the IISC station are gathered from IONOLAB servers along with the other parameter data like Dst, Ap, F10.7, and Kp taken from OMNIWEB servers which were used to predict TEC. The reliability of the forecasted results is evaluated using numerical factors like Normalized Root Mean Square Error (NRMSE), Correlation Coefficient (CC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R-squared. The study demonstrates the usefulness of combining multiple methods for analyzing TEC variations during SEs and highlights the potential of OKSM, FFNN, and DeepAR models for studying TEC variation in the same context. The findings may be useful for satellite broadcasting and navigational services and for further research into the influence of solar eclipses on the TEC changes.

Investigating adaptive sampling strategies for optimal building energy performance using artificial neural networks and kriging surrogate models

Recent studies highlight surrogate models as efficient alternatives to energy simulation tools, reducing computational burden. However, accurate metamodels often require extensive evaluations, leading to high computational costs. Adaptive sampling approaches offer a promising solution by constructing accurate surrogate models at a lower computational expense compared to static sampling. The selection of an appropriate adaptive sampling criterion is crucial in sequential sampling strategies, as it determines how new sample points are chosen based on previous iterations. However, concerns remain regarding the impact of the sampling infill criterion on surrogate model accuracy. Additionally, a lack of studies exists comparing artificial neural networks (ANN) and Kriging models in terms of potential computational improvements through sequential sampling. This study aims to explore the potential of adaptive sampling strategies to estimate optimal building energy consumption within a reasonable computational budget, thus reducing the number of energy simulation model runs required. Furthermore, a comprehensive comparison between sequential sampling techniques employing ANN-based and Kriging-based surrogate models is conducted. Four different sampling criteria are evaluated to understand the relationship between sampling strategies and accuracy. The findings contribute to a more efficient resolution of building optimization problems. The results indicate that the choice of a sampling strategy depends on the model's requirements and the specific problem. Each strategy has distinct strengths and weaknesses, necessitating careful consideration of the model's needs. Selecting the appropriate sampling strategy improves model accuracy and reduces training time. Adaptive sampling methods yield significant improvements, saving 25 %–68 % of simulation samples compared to static approaches.

A novel tri-semicircle shaped submerged breakwater for mitigating wave loads on coastal bridges part Ⅱ: Application perspective

In Part I of this study, the effectiveness of the new breakwater in terms of the attenuation of wave forces on coastal bridges, was comprehensively substantiated. In the present paper (Part Ⅱ), three key practical aspects concerning the development of the new breakwater are further investigated. Firstly, numerical simulations employing the Volume of Fluid (VOF) methodology are conducted to elucidate wave–breakwater interactions. These simulations are validated through comparisons with existing experimental data, thereby affirming the reliability of the numerical model. Subsequent wavelet analysis reveals a noteworthy phenomenon that the wave energy redistribution across the time–frequency domain significantly contributes towards the reduction of transient impacting forces. Following that, a validated ANSYS finite element model is employed to scrutinize the dynamic responses of the new breakwater under varying wave conditions. The analysis underscores that tensile stress, typically peaking at the arch foot region, dominates in governing the safety of the new breakwater, thus necessitating particular attention in this specific area. Furthermore, for the studied scenarios, the maximum tensile stress remains well below 1.33 MPa, suggesting that commonly used concrete materials such as C40 are more than sufficient for construction purposes. Finally, an adaptive Kriging-based surrogate model is established using machine learning techniques. This prediction model achieves determination coefficients of 98.19% and 98.63% when assessing the horizontal and vertical protective efficacy of the new breakwater, respectively, thus indicating a high degree of confidence in its predictions. Based on the prediction model, it is advisable to deploy the new breakwater in water depths that are less than 1.25 times its height, as such implementation could achieve a reduction of wave loads by 20% or more.

Data-driven method of solving computationally expensive combined economic/emission dispatch problems in large-scale power systems: an improved kriging-assisted optimization approach

Combined economic/emission dispatch (CEED) is generally studied using analytical objective functions. However, for large-scale, high-dimension power systems, CEED problems are transformed into computationally expensive CEED (CECEED) problems, for which existing approaches are time-consuming and may not obtain satisfactory solutions. To overcome this problem, a novel data-driven surrogate-assisted method is introduced firstly. The fuel cost and emission objective functions are replaced by improved Kriging-based surrogate models. A new infilling sampling strategy for updating Kriging-based surrogate models online is proposed, which improves their fitting accuracy. Through this way, the evaluation time of the objective functions is significantly reduced. Secondly, the optimization of CECEED is executed by an improved non-dominated sorting genetic algorithm-II (NSGA-II). The above infilling sampling strategy is also used to reduce the number of evaluations for original mathematic fitness functions. To improve their local convergence ability and global search abilities, the individuals that exhibit excellent performance in a single objective are cloned and mutated. Finally, information about the Pareto front is used to guide individuals to search for better solutions. The effectiveness of this optimization method is demonstrated through simulations of IEEE 118-bus test system and IEEE 300-bus test system.

Deterministic and probabilistic-based model updating of aging steel bridges

Numerical modeling is a very useful tool in different fields of bridge engineering, such as load-carrying capacity assessment or structural health monitoring. Developing a reliable computational model that accurately represents the actual bridge mechanical behavior entails advanced FEM-based modeling complemented by a comprehensive experimental campaign that provides the necessary supporting information and allows validating simulation outcomes. This paper proposes a unified approach aimed at the experimental characterization and FE model updating of aging steel bridges. It first involves the realization of an extensive experimental campaign aimed at the bridge's geometrical, material, and dynamic behavior characterization. Then, a model calibration framework is developed, where deterministic (optimization) and probabilistic (Bayesian inference) approaches are employed, and techniques such as global variance-based sensitivity analysis and Kriging-based surrogate modeling are further implemented in order to enhance the identification process and reduce the overall computational burden. The methodology has been validated in a historical riveted steel bridge in O Barqueiro, north of Galicia, Spain. The results show a good agreement in the identified model parameter values and a noticeable correlation between numerical and experimental modal properties, with an average relative error in frequencies of 0.34% and 0.44% for the deterministic and probabilistic approaches and an average MAC (Modal Assurance Criterion) ratio of 0.96.

Conceptual Design of a Nonconstant Swept Flying Wing Unmanned Combat Aerial Vehicle

The design of unmanned combat aerial vehicles (UCAVs) is primarily governed by the low-observability requirement for military applications rather than aerodynamic performance. The conceptual design and optimization of UCAV models via size and shape variables for different missions in different flow regimes form a research area for military vehicle design. Flying wing UCAVs experience flow separation during takeoff and landing, and furthermore exhibit stability issues. The aerodynamic performance of these UCAVs can be significantly improved by redesigning their leading-edge sweep angle and wing planform. In the present work, the initial weight determination, aerodynamic sizing, and planform with and without inlet lip integration, and the conceptual design of a nonconstant leading-edge flying wing UCAV configuration are performed. Next, the obtained conceptual design is downscaled 1:20 to be used as a wind-tunnel model and optimized for low-speed conditions using a kriging-based surrogate model with a vortex-lattice method to maximize the lift-to-drag ratio. Later, the optimized design is validated using an open-source computational fluid dynamics code, OpenFOAM 8.0, to verify the accuracy of the surrogate model and to investigate the aerodynamic characteristics. The optimized UCAV design exhibited improved aerodynamic characteristics in terms of the lift-to-drag ratio. Furthermore, the aerodynamic performance and flowfield of the optimized UCAV model with and without inlet lip integration have been evaluated at low and high speeds.

Numerical simulation and fragility analysis of coastal bridges with tension-compression bearings under extreme waves

The bearing connection between the bridge girder and substructure plays a crucial role in resisting wave forces. Previous works pointed out that the box-girder bridge with laminated rubber bearings is susceptible to unseating, sliding, and overturning under extreme waves. This study develops a tension-compression (TC) bearing system to enhance the structural resistance against wave impact. A three-dimensional (3D) finite element (FE) model considering the nonlinear rubber material is established for investigating the dynamic behavior of coastal box-girder bridges, where the wave forces are imported from the computational fluid dynamics (CFD) simulations. By tracking the time histories of the reaction forces and efficient stress, four damage status levels are identified to assess the vulnerability of coastal bridges. To improve calculation efficiency, the Kriging-based surrogate model is adopted for the fragility analysis of coastal box-girder bridges under extreme waves. The results indicate that the lower plate of the bearing on the seaward side (R1) is more prone to yield under the uplifting wave forces, while the upper plate of the bearing on the landward side (R2) is more sensitive to the horizontal forces. The vertical wave force is the key influential factor of bridge damage under extreme waves. In addition, the structural capacity of the bridge with the proposed bearing system is enhanced compared with the one using the traditional laminated rubber bearing.

Generalized uncertainty in surrogate models for concrete strength prediction

Applied soft computing has been widely used to predict material properties, optimal mixture, and failure modes. This is challenging, especially for the highly nonlinear behavior of brittle materials such as concrete. This paper proposes three surrogate modeling techniques (i.e., polynomial chaos expansion, Kriging, and canonical low-rank approximation) in concrete compressive strength regression analysis. A benchmark database of high-performance concrete is used with over 1,000 samples, and various sources of uncertainties in surrogate modeling are quantified, including meta-modeling assumptions, solvers, and sampling size. Two generalized extreme value distributional models are developed for error metrics using an extensive database of collected data in the literature. Bias and dispersion in the developed surrogate models are empirically compared with those distributions to quantify the overall accuracy and confidence level. Overall, the Kriging-based surrogate models outperform 80%–90% of the existing predictive models, and they illustrate more stable results. The selection of a proper optimization algorithm is the most important factor in surrogate modeling. For any practical purposes, the Kriging regression outperforms the polynomial chaos expansion and the low-rank approximation. The Kriging model is reliable for the pilot database and is less sensitive to modeling uncertainties. Finally, a series of composite error metrics is discussed as a decision-making tool that facilitates the selection of the best surrogate model using multiple criteria.

Surrogate modeling of open-celled metal foam sound absorbers with stepwise property gradients

In this paper, we develop a Kriging-based surrogate model to predict the sound absorption performance of open-celled metal foams with user-defined stepwise relative density gradients. An experimentally validated transfer matrix model is used to generate training data capturing the absorption profiles of metal foams with various geometrical parameters. We deploy a spatial analysis method to create influence surfaces around each sample data point and depict its effect on the observed output by using Kriging's basis functions. The surrogate model has an in-built machine learning framework that uses a genetic algorithm and a maximum likelihood function to tune the weights that define these influence surfaces. Using this approach, we successfully developed a data-fed, supervised prediction model that estimates absorption coefficient of a virtual metal foam sample. Post-validation predicted values for unknown sample configurations show satisfactory agreement with their actual absorption coefficients. Finally, we implement the developed metamodel as an iOS application as a potential low-cost tool to reduce testing costs and enable rapid design iterations for acoustic design problems.

Response surface based reliability analysis of critical lateral buckling force of subsea pipelines

Pipeline lateral Out-of-Straightness (OoS) can act as buckle trigger in unburied (exposed) subsea pipelines. Determining the Critical Buckling Force (CBF) of the pipeline is a computationally challenging task due to the inherent uncertainties in contributing parameters which requires utilising reliability-based approaches. This implies the need for a novel framework to develop the response surface (RS) of the CBF of a nominally straight pipeline with rogue lateral OoS which is the subject of this paper and so far, has not been fully explored in the literature. The contributing parameters in CBF are narrowed down through sensitivity studies and the trend of the CBF variation versus OoS curvature and soil lateral mobilisation is established. A novel and structured approach is taken to select the RS sample points. To calculate the CBF of a pipeline with arbitrary design variables, a kriging-based surrogate model is adopted and automated by deploying a Visual Basic Application script. The framework is fully implemented for 6″ to 14” pipelines. Monte Carlo simulation is utilised to show some applications of the RS such as reliability of the buckle initiation at engineered buckling sites and susceptibility of lateral buckling considering target reliability limits.

Optimization of a Tip Appendage for the Control of Tip Leakage Vortices in Axial Flow Fans

Abstract This paper presents the numerical optimization of a tip appendage design for the passive control of tip leakage vortices in subsonic axial flow cooling fans. The studied class of fan was designed in the conventional manner without the consideration of tip clearance effects. As such, the objective of this investigation is the improvement of the aerodynamic performance characteristics of the datum fan through consideration of the blade tip geometry. Based on previous studies involving fan performance enhancement using various tip end-plate configurations, the most promising end-plate geometry which is found to best improve the fan’s performance characteristics is selected for further development through optimization. Before the optimization process can begin, initialization of the chosen end-plate’s design space using the design of experiments (DoEs) technique is performed. Formulation of the response surface is based on a multi-objective multi-point objective function which considers the fan’s various performance metrics. Considering the optimization process, the design and analysis of computer aided experiments method is used in the development of the Kriging-based surrogate model’s database. The resulting database is coupled with an efficient global optimization algorithm which completes the workflow of the optimization routine. The Pareto-front of non-dominated solutions is used to guide the optimal design selection, on which the experimental evaluations are based. The experimental results of the optimized design indicate improved fan performance characteristics at greater than peak efficiency flowrates. This design is found to increase the datum fan’s design point performance characteristics by a value of 32.90% in total-to-static pressure rise and a 7.66 percentage point increase in total-to-static efficiency at the fan’s design speed of 722 rpm.

Multi-objective surrogate model-based optimization of a small aircraft engine air-intake duct

Aviation industry is constantly striving for more efficient design processes in respect to optimal time, human and computational resources utilization. This implies a need for application of an approximation techniques enabling for fast responses generation with maintained level of results quality. This study focuses on an advancement of aerodynamic shape optimization process of a small aircraft engine intake system by introduction of a surrogate modelling step into the design loop. The multi-objective metamodel assisted optimization is carried out in order to reduce pressure losses along the engine intake duct and increase flow homogeneity at the engine compressor intake plane. Latin Hypercube Design method is utilized in order to sample the design space. A set of initial objective function evaluations is generated with application of Reynolds-averaged Navier–Stokes solver. The ensemble of samples is further used to train a Kriging-based surrogate model. The Efficient Global Optimization algorithm basing on the Expected Improvement function is employed to gradually increase the metamodel prediction quality by usage of sequential sampling technique. Finally, the optimal point predicted by the Kriging surrogate is validated against the high-fidelity model with usage of the Computational Fluid Dynamics code. The paper presents an application of the abovementioned methodology to the design process of the I-31T aircraft turboprop engine intake system. Proposed Kriging-based optimization workflow is utilized in order to reduce pressure losses and improve flow homogeneity in the engine air-intake duct.

Multidisciplinary design approach for solar-powered tri-lobed HALESA

In the recent years, there has been a lot of interest in developing hybrid airships as aerial platforms for various applications because of their several advantageous features. This paper presents a multi-disciplinary design optimization based methodology for an airship with a tri-lobed envelope. The proposed methodology involves five disciplines, viz., Geometry, Environment, Energy, Aerodynamics and Structures. To reduce computational complexity involved in evaluating the aerodynamic characteristics of the tri-lobed envelope, a Kriging-based surrogate model was developed to estimate the envelope drag coefficient and coupled to the optimization framework to achieve the optimal solutions for different operating conditions. The surrogate model predicts the drag coefficient of the tri-lobed envelope with less than ±3% error with respect to the results obtained through CFD. Since the problem follows a multi-disciplinary design approach, a composite objective function is formulated based on volume of the envelope, area of the solar array, and total mass of the airship, which isminimized using Particle Swarm Optimization (PSO) Algorithm. This study reveals that for meeting the same mission requirements, a tri-lobed airship powered by regenerative fuel cells requires half the volume and 33.5% lower solar array area, and has ~46% lower mass compared to the one powered by rechargeable batteries.

Bayesian Optimization of a Low-Boom Supersonic Wing Planform

A surrogate-assisted methodology to accelerate the design space exploration process and multi-objective optimization of a notional low-drag, low-boom supersonic transport planform using Euler computational fluid dynamics with an empirical parasite drag addition and an augmented Burgers equation solver is demonstrated. The use of Kriging-based surrogate models, coupled with expected hypervolume improvement in a Kriging believer framework, allows efficient global optimization of the selected wing design parameters. The use of effective nondominated sampling is used to further improve the solutions found. The effects of parameterizing the planform of a baseline model (NASA’s 69 deg wing–body) with 6- and 11-variables are explored. Genetic and local optimizers are used to search the Kriging surrogates. The results show the tradeoff between planform shapes that efficiently use compression lift to increase the lift-to-drag ratio and a smooth undertrack pressure signature to reduce ground-level noise. Furthermore, correctly positioned wingtips may also be used to smooth the undertrack signature, reducing the sonic boom.

3D probabilistic landslide run-out hazard evaluation for quantitative risk assessment purposes

The quantitative risk assessment of landslides requires the spatial impact probability of their run-out processes to conduct vulnerability assessments and prioritize mitigation measures. Hence, a general framework for three-dimensional (3D) probabilistic landslide run-out hazard evaluation is presented in this paper. In the proposed framework, a continuum mechanics concept-based dynamic numerical model, called Massflow, is used to conduct run-out analyses. A multi-observation Bayesian back analysis method with Markov chain Monte Carlo simulation is used to calibrate the uncertainties of the input parameters based on a past landslide event, which integrates the prior information, observation information, and model bias factor to yield posterior distributions of the input parameters. Then, the posterior distributions are used as inputs for a future event to estimate the exceedance probabilities of run-out intensities (i.e., maximum run-out height and velocity) on a 3D terrain and produce run-out hazard maps for quantitative landslide risk assessments purposes. To improve the computational efficiency of the proposed framework without losing accuracy, a multi-response Kriging-based surrogate model with a sequential adaptive sampling strategy is developed for both the back analysis and forward prediction. Finally, two sequential slides of landslide CJ#8 located in the Heifangtai terrain, Gansu, China are employed to test the performance of the proposed framework, with its advantages and potential drawbacks discussed in detail. Results show that the proposed framework can effectively calibrate the model input parameters to evaluate the run-out hazard of similar landslides, and the predicted results can be employed in landslide risk assessments and mitigations.

A Novel Risk Evaluation Procedure Using a Kriging-Based Surrogate Modeling for Offshore Structures

An innovative reliability estimation procedure for Jacket-type offshore platforms is proposed. The information on risk is extracted using multiple deterministic analyses using advanced mathematical theories resulting in compounding beneficial effects. The platforms are modeled by finite elements. Nonlinearity and major sources of uncertainty are incorporated. The wave loading model is realistically developed to satisfy the underlying physics. It is applied in three-dimension in time domain incorporating the uncertainties in the parameters. Implicit performance functions are expressed explicitly using several advanced factorial schemes and significantly improved response surface method. The efficiency and accuracy of the method are improved using a comprehensively improved Kriging-based surrogate modeling technique. The risk is evaluated for the serviceability and strength limit state functions for a jacket-type offshore platform using about two hundred nonlinear finite element analyses. The procedure was verified using simulation techniques. The concept can be considered an alternative to the conventional random vibration techniques and the standard Monte Carlo simulation procedure.

An improved Kriging-based approach for system reliability analysis with multiple failure modes

Reliability analysis with multiple failure modes is needed because more than one failure mode exists in many engineering applications. Kriging-based surrogate model is widely adopted for component reliability analysis because of its high computational efficiency. Compared with Kriging-based component reliability analysis, selecting the sample points that affect the system performance is more difficult than that of a single failure mode in system reliability analysis. Therefore, how to select suitable sample points is a key problem in system reliability analysis. Meanwhile, reducing the number of calls to the performance functions is challenging, especially for systems with time-consuming performance functions. In this paper, an improved Kriging-based system reliability analysis approach is proposed based on the two strategies. In strategy 1, the initial sample points are determined by considering only two different cases: (a) the candidate samples are selected from the safe regions only for series systems; (b) the candidate samples are selected from the failure regions only for parallel systems. Therefore, samples having little contributions to the composite performance function are avoided. In strategy 2, the sample points determined in strategy 1 will be further optimized by interpolating. From comparisons with three reported methods in numerical examples, the efficiency and accuracy of the proposed method are illustrated.