Metamodel Selection Research Articles

Predicting viscosity for steelmaking slag: A stacking regression approach

The viscosity of steel slag plays a pivotal role in steelmaking, impacting various aspects of the steelmaking operation and product quality. This paper introduces a novel approach for predicting the viscosity of turndown slag from a basic oxygen furnace using a stacking regression model. The stacking model in this approach incorporates four base models: multiple linear regression (LR), random forest (RF), k-nearest neighbour (KNN) and AdaBoost (ADB), while random forest is selected as a meta-model. The selection of meta-models is done through a systematic framework provided for identifying suitable meta-models in a stacking model. Similarly, the framework also demonstrated the workflow for constructing and evaluating a series of stacking models with different configurations. On the evaluation of 20 stacking models (including two and three-layers), the optimal configuration is found to be LR + KNN with R2 value of 0.993 and the shortest training time. Additionally, a correlation analysis of slag viscosity with composition and temperature is done, which will help the operators of steel melting shops in optimize the steelmaking process based on the required slag viscosity. Ultimately, this study emphasizes the efficacy of optimal-configured stacking regression models in industrial applications, achieving both maximum accuracy and minimal computational time.

A novel ensemble of metamodels using improved stepwise metamodel selection and two-layer pointwise ensemble

Although an independent metamodel may be used to accurately describe certain response relationships, it can be challenging to find suitable metamodels for various problems. The ensembled metamodel, in contrast, is a more universal method. The key to enhancing the performance of the ensembled metamodel is determining how to select the optimal set of metamodels to be ensembled (MBEs) and how to ensemble them to obtain a better fit. However, existing methods face challenges in exploring the fitting ability of individual metamodels within a pre-set sample set, often requiring prior knowledge or additional sample sets for assistance to get optimal MBEs, and they struggle to fully utilize the fitting ability of individual metamodels at each sample point. To address these challenges, this paper proposes a novel ensemble of metamodels using improved stepwise metamodel selection and two-layer pointwise ensemble (OSF-TLPE) through research in three aspects: model selection, weight calculation, and residual compensation. Firstly, the Leave-P-Out Prediction (LPOP) proposed in this paper reconstructs the response of the metamodel to the problem, which reduces the complexity of model selection. Then, considering the redundancy of the metamodel during ensemble, the Out-of-Bag Estimation (OOBE) based Stepwise Fit (OSF) eliminates redundancy as feature selection, which is a globally optimal method for metamodel selection. The two-layer pointwise ensemble of metamodels (TLPE), which consists of weight metamodels (WMs) and a residual metamodel (RM) provide a more robust ensemble strategy by assigning weights point by point and compensating for residuals. Finally, the performances of OSF and TLPE are evaluated on 12 benchmark functions using 6 and 13 typical metamodels, respectively. A performance comparison was also conducted on an aircraft final assembly line performance prediction problem. The results demonstrate that OSF-TLPE can deliver more flexible and reliable performances compared to common ensemble methods.

Effect of mooring line layout on the loads of ship-shaped offshore installations

An offshore mooring system stations a ship-shaped offshore installation in place while withstanding incoming loads from the marine environment with short-term and long-term uncertainties. This study aims to develop a novel framework for analysing the loads on floating systems, namely mooring line tension, mooring line fatigue damage, and hull bending moment, as a function of the mooring layout design variables and environmental random variables. The nonlinear influence of those variables is assessed by means of advanced techniques using response charts, response divergence charts, and Sobol's total-effect sensitivity indexes. The developed procedure includes a probabilistic selection of mooring scenarios, station-keeping numerical analyses, and metamodel selection to define input loads. An example of a hypothetical floating production storage and offloading (FPSO) unit with taut legs in the Gulf of Mexico illustrates the procedure. The details of the computations are documented, and the findings show that the mooring line top-tension has a high total-effect index for the wave-induced bending moment and the total mooring line tension, whereas the fatigue damage is mostly affected by the chain diameter. The results of this research offer useful insights to designers and propose the use of a surrogate model to be used in the reliability-based design of mooring systems.

Mechanical MNIST: A benchmark dataset for mechanical metamodels

Metamodels, or models of models, map defined model inputs to defined model outputs. Typically, metamodels are constructed by generating a dataset through sampling a direct model and training a machine learning algorithm to predict a limited number of model outputs from varying model inputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to multi-scale simulation. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data has not been thoroughly explored. Drawing inspiration from the benchmark datasets available to the computer vision research community, we introduce a benchmark data set (Mechanical MNIST) for constructing metamodels of heterogeneous material undergoing large deformation. We then show examples of how our benchmark dataset can be used, and establish baseline metamodel performance. Because our dataset is readily available, it will enable the direct quantitative comparison between different metamodeling approaches in a pragmatic manner. We anticipate that it will enable the broader community of researchers to develop improved metamodeling techniques for mechanical data that will surpass the baseline performance that we show here.

An effective method for quantifying and incorporating uncertainty in metamodel selection

In complex engineering systems, metamodels are extensively used to replace the computationally expensive simulation and analysis process. Different metamodels can be constructed by using different metamodeling techniques. Uncertainty exists in selecting the best metamodel among a set of alternatives. This study introduces an effective method based on Bayes’ theorem and additive adjustment factor for quantifying and incorporating this uncertainty in metamodel selection. In this method, the posterior probability of each metamodel evaluated by Bayes’ theorem is employed to quantify the uncertainty. The metamodel with the largest posterior probability is considered as the best. Then, the uncertainty in metamodel selection is accounted for by an additive adjustment factor and incorporated into the prediction of the best metamodel. Mathematical examples and the resistance and volume prediction example of a submersible are presented to showcase the introduced method. In these examples, metamodels are constructed by different metamodeling techniques, such as polynomial response surface (PRS), locally weighted regression (LWP), k-nearest neighbors (KNN), radial basis functions (RBF), multivariate adaptive regression splines (MARS) and Kriging. Results indicate that the introduced method can effectively quantify the uncertainty in metamodel selection and incorporate it into the prediction of a system output, hence achieving a prediction with good accuracy and small uncertainty.

Kriging Metamodeling-Based Monte Carlo Simulation for Improved Seismic Fragility Analysis of Structures

ABSTRACT The polynomial response surface method (RSM) is mostly adopted to overcome computational challenge of Monte Carlo Simulation (MCS)-based seismic fragility analysis (SFA) of structure. However, such SFA approach is primarily based on dual RSM involving lognormal assumption which lacks desired accuracy. The present study explores the advantage of adaptive nature of Kriging approach for improved SFA by random selection of metamodel to implicitly consider record to record variations of earthquakes. Without additional computational burden, the approach avoids a prior distribution assumption unlike dual RSM. The effectiveness of the approach over the usual polynomial RSM for SFA is elucidated numerically.

Machine learning of fire hazard model simulations for use in probabilistic safety assessments at nuclear power plants

This study explored the application of machine learning to generate metamodel approximations of a physics-based fire hazard model. The motivation to generate accurate and efficient metamodels is to improve modeling realism in probabilistic safety assessments where computational burden has prevented broader application of high fidelity models. The process involved scenario definition, generating training data by iteratively running the fire hazard model called CFAST over a range of input space using the RAVEN software, exploratory data analysis and feature selection, an initial testing of a broad set of metamodel methods, and finally metamodel selection and tuning using the R software.Twenty-five metamodel methods ranging in class and complexity were investigated. Linear models struggled because the physics of fire are non-linear. A k-nearest neighbor (kNN) model fit the vast majority of calculations within ±10% for maximum upper layer temperature and its timing.The resulting kNN model was compared to an algebraic model typically used in fire probabilistic safety assessments. This comparison illustrated the potential of metamodels to improve modeling realism over simpler models selected for computational feasibility. While the kNN metamodel is a simplification of the higher fidelity model, the error introduced is quantifiable and can be explicitly considered.

Support vector regression based metamodeling for seismic reliability analysis of structures

• Improved seismic reliability analysis by support vector regression based metamodel. • A simple effective algorithm to minimize the mean square error to obtain the model parameters. • Generating a suite of metamodels to implicitly takes into account the record to record variation. • Simulation by random metamodel selection with no additional computational burden and distribution assumption. • Numerical elucidation of the effectiveness of the proposed approach for seismic reliability analysis. The present study deals with support vector regression-based metamodeling approach for efficient seismic reliability analysis of structure. Various metamodeling approaches e.g. response surface method, Kriging interpolation, artificial neural network, etc. are usually adopted to overcome computational challenge of simulation based seismic reliability analysis. However, the approximation capability of such empirical risk minimization principal-based metamodeling approach is largely affected by number of training samples. The support vector regression based on the principle of structural risk minimization has revealed improved response approximation ability using small sample learning. The approach is explored here for improved estimate of seismic reliability of structure in the framework of Monte Carlo Simulation technique. The parameters necessary to construct the metamodel are obtained by a simple effective search algorithm by solving an optimization sub-problem to minimize the mean square error obtained by cross-validation method. The simulation technique is readily applied by random selection of metamodel to implicitly consider record to record variations of earthquake. Without additional computational burden, the approach avoids a prior distribution assumption about approximated structural response unlike commonly used dual response surface method. The effectiveness of the proposed approach compared to the usual polynomial response surface and neural network based metamodels is numerically demonstrated.

Multiobjective reliability-based design optimisation for front structure of an electric vehicle using hybrid metamodel accuracy improvement strategy-based probabilistic sufficiency factor method

ABSTRACTThe determinate multiobjective optimisation (DMOO) without considering effects of uncertainties on vehicle body design may fail to satisfy the desired property in practice. In this paper, a multiobjective reliability-based design optimisation (MORBDO) procedure is proposed to perform the design for front structure of an electric vehicle. In which, body performances including full-lap frontal crashworthiness, modal characteristic and lightweight level are involved and coordinated, and the thickness of five key components with geometric tolerances are selected as design variables. Probabilistic constraint in MORBDO is addressed by Monte Carlo simulation (MCS) technique-based probabilistic sufficiency factor (PSF) method. To improve the accuracy of optimisation results, a closed-loop system named hybrid metamodel accuracy improvement strategy is presented here by organising adaptive optimum metamodel selection and the max–min distance approach-based new samples addition technique together. The optimisation problem is solved by the multiobjective particle-swarm-optimisation algorithm. The effectiveness of the proposed procedure is certified by successfully obtaining more accurate and reliable alternative optimum schemes in the design for the front body structure in comparison with DMOO, normal PSF method and safety factor method.

Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive training time of surrogate models, or the optimal use of many-core computers to approximate efficiently multiple objectives simultaneously. Thinking out of the box, complexity can also be shifted from approximating the individual objective functions to approximating the entire Pareto front. This leads to further complexities, namely, how to validate statistically and apply the techniques developed to real-world problems. In this paper, we discuss emerging complexity-related topics in surrogate-assisted multicriteria optimization that may not be prevalent in nonsurrogate-assisted single-objective optimization. These complexities are motivated using several real-world problems in which the authors were involved. We then discuss several promising future research directions and prospective solutions to tackle emerging complexities in surrogate-assisted multicriteria optimization. Finally, we provide insights from an industrial point of view into how surrogate-assisted multicriteria optimization techniques can be developed and applied within a collaborative business environment to tackle real-world problems.

Metamodel selection based on stepwise regression

Metamodels are often used to replace expensive simulations of engineering problems. When a training set is given, a series of metamodels can be constructed, and then there are two strategies to deal with these metamodels: (1) picking out the best one with the highest accuracy as an approximation of the computationally intensive simulation; and (2) combining all of them into an ensemble model. However, since the choice of approximate model depends on design of experiments (DOEs), employing of the first strategy thus increases the risk of adopting an inappropriate model. Nevertheless, the second strategy also seems not to be a good choice, since adding redundant metamodels may lead to loss of accuracy. Therefore, it is a necessary step to eliminate the redundant metamodels from the set of the candidates before constructing the final ensemble. Illuminated by the method of variable selection widely used in polynomial regression, a metamodel selection method based on stepwise regression is proposed. In our method, just a subset of n ones (n ≤ p, where p is the number of all of the candidate metamodels) is used. In addition, a new ensemble technique is proposed from the view of polynomial regression in this work. This new ensemble technique, combined with metamodel selection method, has been evaluated using six benchmark problems. The results show that eliminating the redundant metamodels before constructing the ensemble can provide more ideal prediction accuracy than directly constructing the ensemble by utilizing all of the candidates.

Enhanced similarity-based metamodel updating strategy for reliability-based design optimization

Metamodels are becoming increasingly popular for handling large-scale optimization problems in product development. Metamodel-based reliability-based design optimization (RBDO) helps to improve the computational efficiency and reliability of optimal design. However, a metamodel in engineering applications is an approximation of a high-fidelity computer-aided engineering model and it frequently suffers from a significant loss of predictive accuracy. This issue must be appropriately addressed before the metamodels are ready to be applied in RBDO. In this article, an enhanced strategy with metamodel selection and bias correction is proposed to improve the predictive capability of metamodels. A similarity-based assessment for metamodel selection (SAMS) is derived from the cross-validation and similarity theories. The selected metamodel is then improved by Bayesian inference-based bias correction. The proposed strategy is illustrated through an analytical example and further demonstrated with a lightweight vehicle design problem. The results show its potential in handling real-world engineering problems.

Supporting model-driven development using a process-centered software engineering environment

The adoption of Model-Driven Development (MDD) is increasing and it is widely recognized as an important approach for building software systems. In addition to traditional development process models, an MDD process requires the selection of metamodels and mapping rules for the generation of the transformation chain which produces models and application code. In this context, software process tasks should be performed in a specific sequence, with the correct input artifacts to produce the output ones. However, existing support tools and transformation engines for MDD do not have a process-centered focus that addresses different kinds of software process activities, such as application modeling and testing to guide the developers. Furthermore, they do not enable process modeling nor the (semi) automated execution of activities during process enactment. The MoDErNE (Model Driven Process-Centered Software Engineering Environment) uses process-centered software engineering environment concepts to improve MDD process specification and enactment by using a metamodeling foundation. In MoDErNE, a software process model may be enacted several times in different software projects. This paper details the MoDErNE environment, its approach and architecture and also the case studies through which the tool was evaluated.

Performance Measures for Selection of Metamodels to be Used in Simulation Optimization

ABSTRACTThis paper points out the need for performance measures in the context of simulation optimization and suggests six such measures. Two of the measures are indications of absolute performance, whereas the other four are useful in assessing the relative performance of various candidate metamodels. The measures assess performance on three fronts: accuracy of placing optima in the correct location, fit to the response, and fit to the character of the surface (expressed in terms of the number of optima). Examples are given providing evidence of the measures' utility—one in a limited scenario deciding which of two competing metamodels to use as simulation optimization response surfaces vary, and the other in a scenario of a researcher developing a new, sequential optimization search procedure.