Metamodel Construction Research Articles

Experimental Design and Modeling for Forward-Inverse Maps

In customer-driven design of systems or products, one has performance targets in mind and would like to determine values for product or system parameters that meet such targets. Engineering computer simulation models predict performance given design parameter values; meeting a target is done iteratively through an optimization search procedure, typically by optimizing a regression, neural network or other type of approximation metamodel of the computer model. We pose the thesis that, since forward metamodel construction is a key part of this strategy, constructing an inverse metamodel directly is advantageous. The inverse metamodel obviates the need for optimization in many settings. One can design experiments that allow simultaneous fitting of forward and inverse metamodels. We discuss the potential for this strategy, the connection with the calibration problem, and some of the issues that must be resolved to make the approach practical.

An active learning Kriging-based Bayesian framework for probabilistic structural model exploration

The Bayesian framework in structural health monitoring includes both modal identification and model exploration. Probabilistic model exploration, also named as model updating, can effectively estimate the structural parameters and quantify their uncertainties. However, it can be computationally intensive on application to real-world large-scale structures. Meta-models, e.g. Kriging models, can help tackle this challenge but they also introduce more uncertainties. In this paper, a novel Bayesian framework combining the active learning Kriging approach is proposed. The framework comprises three major components: the improved fast Bayesian spectral density approach for modal identification, the active learning Kriging method for meta-modelling, and the Bayesian structural model exploration. The Transitional Markov Chain Monte Carlo algorithm is implemented throughout the framework to sample the posterior distributions. The uncertainties from three aspects, i.e., (1) measurements, (2) meta-model construction and (3) finite element modelling, are considered in definition of the likelihood function adopted in both the active learning and model exploration processes. Compared with the ordinary Kriging model and adaptive Kriging approach using U function, the proposed active learning method significantly reduces the uncertainties of the Kriging predictor and improves its local prediction performance with fewer samples. The proposed framework is validated by a continuous test beam in the laboratory and applied to a real-world cable-stayed bridge using structural health monitoring data. A mode-matching criterion is used to overcome the difficulty of closely spaced modes in model exploration of the cable-stayed bridge. As the proposed framework is data-driven, no weighting hyperparameters are required. The active learning Kriging-based Bayesian framework can directly process structural dynamic time history response and conduct probabilistic model exploration with multiple uncertainties included, and therefore is promising in application to major structures.

Active-Learning Reliability Analysis of Automotive Structures Based on Multi-Software Interaction in the MATLAB Environment

The reliability design of automotive structures is characterized by numerous variables and implicit responses. The traditional design of experiments for metamodel construction often requires manual adjustment of model parameters and extensive finite element analysis, resulting in inefficiency. To address these issues, active learning-based reliability methods are effective solutions. This study proposes an active-learning reliability analysis method based on multi-software interaction. Firstly, through secondary development of different software and MATLAB (version 2023a)’s batch processing function, a multi-software interactive reliability analysis method is developed, achieving automation in structural parametric design, finite element analysis and post-processing. This provides a more efficient and convenient platform for the implementation of active learning. Secondly, the polynomial chaos–kriging (PCK) active-learning method is introduced, combining the advantages of polynomial chaos expansion (PCE) and kriging. The PCK method captures the global behavior of the computational model using regression-based PCE and local variations using interpolation-based kriging. This metamodel is constructed with fewer training samples, effectively replacing the real multi-dimensional implicit response relations, thereby improving the efficiency of modeling and reliability analysis. Finally, the specific implementation scheme is detailed. The accuracy and efficiency of the proposed method are verified by a reliability engineering example of body-in-white bending and torsional stiffness.

Meta-model-based shop-floor digital twin architecture, modeling and application

Digital twin is regarded as the virtual counterpart of physical entities, which can mirror the physical behavior and performance. Digital twin technology provides strong support for the achievement of cyber-physical system and intelligent manufacturing. Many investigations have been carried out for the digital twin of specific products. However, there are less researches on digital twin in the shop-floor domain, and there is a lack of model-driven digital twin comprehensive architecture. The modeling approach to the full lifecycle of digital twin is not considered enough. This paper proposes a meta-model-based shop-floor digital twin construction approach and a comprehensive architecture. A meta-model based on RAMI 4.0 is constructed, which provide a novel idea for the description of manufacturing resources and their status. The proposed shop-floor digital twin architecture consists of three key implementation elements: the meta-model construction, data modeling (including data interaction between cyber-physical spaces) and constructing different integration level models of shop-floor digital twin based on iteration feedback between the demands and models. The proposed approach is validated through a case study of the fischer learning factory 4.0.

Intelligent meta-model construction and global stochastic sensitivity analysis based on PSO-CNN

A large-scale simulation model is needed for the stochastic sensitivity analysis of structural uncertainty. The finite element method often exceeds the computing power and cannot meet the analysis requirements and computational efficiency of stochastic sensitivity analysis. With the development of artificial intelligence, the calculation efficiency problem can be solved by a combination of the finite element model and a mathematical model, but the accuracy of the analysis results depends on the accuracy of the mathematical model. However, using artificial neural networks to construct mathematical models also has numerous problems, such as falling into local extrema. Thus, to address the computational efficiency and calculation accuracy problems, the particle swarm optimization (PSO)-convolutional neural network (CNN) meta-model is presented in this paper. This model was used to improve the training and prediction accuracy of a small-sample CNN, where the initial learning rate of the CNN was optimized by PSO. Additionally, the PSO was combined with the Adam optimizer to automatically screen the optimal network structure. The global stochastic sensitivity analysis method based on the Sobol sensitivity method and the Monte Carlo method was used to quantify the degree of influence of the input parameters on the model output parameters and to analyze the influence trend of the parameter changes on the structural response combined with the positive and negative Spearman’s rank correlation coefficients. The accuracy, good adaptability, and extension ability of the PSO-CNN meta-model was verified using the high-dimensional function examples and the structural models. Global stochastic sensitivity analysis was carried out on the joint of an extended end plate. The influence degree of the parameters on the initial rotational stiffness of the joint was determined, and corresponding design suggestions were obtained. These suggestions were consistent with the design specifications and the research results of other scholars, which verified the reliability of this method and could be applied to other types of structural sensitivity analyses.

Multi-objective optimization algorithm assisted by metamodels with applications in aerodynamics problems

The optimization algorithms when used in real engineering problems involving high fidelity numeric simulations often require a large number of numerical assessments to achieve a good approximation of the optimal solution. The computational time needed to find this solution may be unfeasible in these problems. The metamodel assisted algorithms have been used to accelerate optimization problems using different strategies to find the optimum. For single objective problems, CORS (Constrained Optimization using Response Surfaces) was developed with basis on the iterative generation of distance constraints to explore and exploit the design space, such that convergence to a global optimum is mathematically guaranteed. In this paper, a multi-objective optimization strategy based on metamodel construction using radial basis functions, MO-CORS, is presented. It takes the advantage of the CORS strategy in multi-objective problems to perform the effective detection of the non-dominated set extreme points, for the subsequent filling of empty spaces between these extremes. Metamodels are used strategically in an iterative sampling process to guide the search for better solutions and to determine where in the domain the next objective function evaluations should be performed. The evaluations carried out on the expensive functions also allow improving metamodel construction in the promising regions at each iteration. Results obtained in test problems and in aerodynamic problems applications show that the developed algorithm is an effective tool to accelerate single and multi-objective optimization problems and that the use of the CORS strategy inside MO-CORS was relevant in helping it to attain solutions not found by other optimization algorithms.

Noise shielding surrogate models using dynamic artificial neural networks

The optimal design methodologies in aeronautics are known to be constrained by the computational burden required by direct simulations. Due to this reason, the development of efficient metamodelling techniques represents nowadays an imperative need for the designers. In fact, surrogate models has been demonstrated to significantly reduce the number of high-fidelity evaluations, thus alleviating the computing effort. Over the last years, the aeronautical designers community has switched from a design approach predominantly based on direct simulations to an extensive use of metamodels. Recently, to further improve the efficiency, several dynamic approaches based on parameters self-tuning have been developed to support the metamodel construction. This work deals with the use of surrogate models based on Artificial Neural Network for the noise shielding of unconventional aircraft configurations. Here, the insertion loss field of the a Blended Wing Body is reproduced by means of advanced machine learning techniques. The relevant framework is the calculation of the noise emitted by innovative aircraft configurations by means of suitable corrections of existing well-assessed noise prediction tools. The self-tuning algorithm has demonstrated to be accurate and efficient, and the observed performance discloses the possibility to implement numerical strategies for the reliable and robust unconventional aircraft optimal design

NeuroPred-FRL: an interpretable prediction model for identifying neuropeptide using feature representation learning.

Neuropeptides (NPs) are the most versatile neurotransmitters in the immune systems that regulate various central anxious hormones. An efficient and effective bioinformatics tool for rapid and accurate large-scale identification of NPs is critical in immunoinformatics, which is indispensable for basic research and drug development. Although a few NP prediction tools have been developed, it is mandatory to improve their NPs' prediction performances. In this study, we have developed a machine learning-based meta-predictor called NeuroPred-FRL by employing the feature representation learning approach. First, we generated 66 optimal baseline models by employing 11 different encodings, six different classifiers and a two-step feature selection approach. The predicted probability scores of NPs based on the 66 baseline models were combined to be deemed as the input feature vector. Second, in order to enhance the feature representation ability, we applied the two-step feature selection approach to optimize the 66-D probability feature vector and then inputted the optimal one into a random forest classifier for the final meta-model (NeuroPred-FRL) construction. Benchmarking experiments based on both cross-validation and independent tests indicate that the NeuroPred-FRL achieves a superior prediction performance of NPs compared with the other state-of-the-art predictors. We believe that the proposed NeuroPred-FRL can serve as a powerful tool for large-scale identification of NPs, facilitating the characterization of their functional mechanisms and expediting their applications in clinical therapy. Moreover, we interpreted some model mechanisms of NeuroPred-FRL by leveraging the robust SHapley Additive exPlanation algorithm.

A fast-convergence algorithm for reliability analysis based on the AK-MCS

In the field of reliability engineering, assessing the probability of failure of an event is usually a computationally demanding task. One way of tackling this issue is by metamodelling, in which the original computational-expensive model is approximated by a simpler metamodel. A method called AK-MCS for Active learning reliability method combining Kriging and Monte Carlo Simulation, was developed for the metamodel construction, and proved effective in reliability analysis. However, the performance of the AK-MCS algorithm is sensitive to the candidate size and the Kriging trend. Moreover, it cannot take advantage of parallel computing, a highly efficient way to speed up the simulation process. Focusing on the identified issues, this study proposes three methods to improve algorithm performance: the candidate size control method, multiple trends method, and weighted clustering method. These three methods are integrated into the AK-MCS structure, with their individual and combined performances being tested using four examples. Results suggest that all three methods contribute to the improvement of algorithm efficiency. When the three methods working together, the computational time is reduced significantly, and in the meantime, higher accuracy can be achieved.

Rapidtolerance‐awaredesign of miniaturized microwave passives by means ofconfined‐domainsurrogates

AbstractThe effects of uncertainties, primarily manufacturing tolerances but also incomplete information about operating conditions or material parameters, can be detrimental to the performance of microwave components. Quantification of such effects is essential to ensure a meaningful evaluation of the structure, in particular, its reliability under imperfect fabrication procedures. The improvement of the circuit robustness can be achieved by reducing sensitivity to geometry/material parameter deviations, which requires optimization of suitably chosen statistical performance metrics such as the yield. The prerequisite for the latter is statistical analysis. In the case of compact circuits, it is executed through full‐wave electromagnetic (EM) analysis. The fundamental difficulty, that is, the high CPU cost, can be alleviated by the employment of fast surrogate models, which is the method of choice for the majority of contemporary approaches. Despite its advantages, a practical challenge of surrogate‐assisted design is the initial computational overhead related to metamodel construction. As a workaround, this work proposes the employment of a recently introduced concept of constrained modelling, where the surrogate domain is confined only to contain the essential subsets of the parameter space. In the context of yield optimization, the domain needs to correspond to directions featuring maximum variability of the circuit responses (particularly the parts thereof that affect the yield value in the most significant way) with respect to its geometry parameters. The small volume of the domain spanned by such directions permits setting up an accurate model using a fraction of training data samples required by conventional methods. The proposed technique is demonstrated using a miniaturized microstrip rat‐race coupler with its yield optimized at the cost of just a few dozen of EM simulations of the circuit. EM‐based Monte Carlo simulations corroborate the reliability of the approach.

A new hybrid reliability‐based design optimization method under random and interval uncertainties

SummaryThis article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI.

Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

Project Management Metamodel Construction Regarding IT Departments

Given the fast technological progress, the need for project management continues to grow in terms of methodology and new concepts. In this article, we will build a framework of generating a metamodel that we will apply on the project management to generate a generic metamodel of project management, in this approach we will be based on two methodologies of project management; predictive method (ex: PRINCE 2), Agile method (ex: SCRUM). The goal of this research is to validate and apply this methodology on all the components of IT Governance then to aggregate the metamodels to restore a global metamodel for all IT Governance domains.

A Robust Predicted Performance Analysis Approach for Data-Driven Product Development in the Industrial Internet of Things.

Industrial Internet of Things (IoT) is a ubiquitous network integrating various sensing technologies and communication technologies to provide intelligent information processing and smart control abilities for the manufacturing enterprises. The aim of applying industrial IoT is to assist manufacturers manage and optimize the entire product manufacturing process to improve product quality and production efficiency. Data-driven product development is considered as one of the critical application scenarios of industrial IoT, which is used to acquire the satisfied and robust design solution according to customer demands. Performance analysis is an effective tool to identify whether the key performance have reached the requirements in data-driven product development. The existing performance analysis approaches mainly focus on the metamodel construction, however, the uncertainty and complexity in product development process are rarely considered. In response, this paper investigates a robust performance analysis approach in industrial IoT environment to help product developers forecast the performance parameters accurately. The service-oriented layered architecture of industrial IoT for product development is first described. Then a dimension reduction approach based on mutual information (MI) and outlier detection is proposed. A metamodel based on least squares support vector regression (LSSVR) is established to conduct performance prediction process. Furthermore, the predicted performance analysis method based on confidence interval estimation is developed to deal with the uncertainty to improve the robustness of the forecasting results. Finally, a case study is given to show the feasibility and effectiveness of the proposed approach.

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

PurposeIn real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).Design/methodology/approachIn this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.FindingsThe efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.Originality/valueThe authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

Metamodel of Transformations of Concepts to Support the Object-Relational Mapping

The paper considers the problem of searching for the origin of objects and/or their sources necessary to support the object-relational mapping. The solution is presented as a variant of a specialized semantic search that takes into account the possibility of transformations of conceptual constructions of the domain description while working with the system. To take into account such transformations, a metamodel of transformations of concepts is proposed, which also takes into account the transformation of the connections between them. The basic metamodel is a specialized system of applicative type, based on the combination of domain theory methods and object theory. The metamodel is created in the category of functors, which allows us to consider transformable concepts as variants of the functor-as-object construction. The choice of the basic category ensures the possibility of parametrization of the metamodel construction, which provides a set of specialized models for a given class of subject areas. Identification of the properties of basic category requires involving of difficultly formalized criteria and is cognitive in nature.

An efficient reliability method combining adaptive Support Vector Machine and Monte Carlo Simulation

To enhance computational efficiency in reliability analysis, metamodeling has been widely adopted for reliability assessment. This work develops an efficient reliability method which takes advantage of the Adaptive Support Vector Machine (ASVM) and the Monte Carlo Simulation (MCS). A pool-based ASVM is employed for metamodel construction with the minimum number of training samples, for which a learning function is proposed to sequentially select informative training samples. Then MCS is employed to compute the failure probability based on the SVM classifier obtained. The proposed method is applied to four representative examples, which shows great effectiveness and efficiency of ASVM-MCS, leading to accurate estimation of failure probability with rather low computational cost. ASVM-MCS is a powerful and promising approach for reliability computation, especially for nonlinear and high-dimensional problems.

An adaptive sampling method for variable-fidelity surrogate models using improved hierarchical kriging

ABSTRACTVariable-fidelity (VF) modelling methods have been widely used in complex engineering system design to mitigate the computational burden. Building a VF model generally includes two parts: design of experiments and metamodel construction. In this article, an adaptive sampling method based on improved hierarchical kriging (ASM-IHK) is proposed to refine the improved VF model. First, an improved hierarchical kriging model is developed as the metamodel, in which the low-fidelity model is varied through a polynomial response surface function to capture the characteristics of a high-fidelity model. Secondly, to reduce local approximation errors, an active learning strategy based on a sequential sampling method is introduced to make full use of the already required information on the current sampling points and to guide the sampling process of the high-fidelity model. Finally, two numerical examples and the modelling of the aerodynamic coefficient for an aircraft are provided to demonstrate the approximation capability of the proposed approach, as well as three other metamodelling methods and two sequential sampling methods. The results show that ASM-IHK provides a more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.

Metamodel construction for sensitivity analysis

We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study.

Efficient VaR and CVaR Measurement via Stochastic Kriging

In this paper, stochastic kriging (SK) is considered as a metamodeling tool to capture risk-related properties of complex stochastic system outputs. To better assess the tail behavior of the underlying distribution of a system output, we specifically focus on global prediction of value-at-risk and conditional value-at-risk. Going beyond the standard SK framework intended for metamodeling of mean response surfaces, we rethink the original formulation to allow for the flexibility of utilizing different estimation methods for metamodel construction. The resulting impact on the predictive performance of SK is examined in detail. In parallel with the study by Chen et al. [Chen X, Ankenman BE, Nelson BL (2013) Enhancing stochastic kriging metamodels with gradient estimators. Oper. Res. 61(2):512–528], we further consider the situation in which noisy gradient information can be incorporated into SK metamodel construction and prediction. The theoretical results are illustrated by two numerical examples.