Metamodeling Techniques Research Articles

Optimal design of electrical machines assisted by hybrid surrogate model based algorithm

In this paper, for design of large-scale electromagnetic problems, a novel robust global optimization algorithm based on surrogate models is presented. The proposed algorithm can automatically select a proper meta-model technique among multiple alternatives. In this paper, three representative meta-modeling techniques including ordinary Kriging, universal Kriging, and response surface method with multi-quadratic radial basis functions are applied. In each optimization iteration, the above three models are used for parallel calculation. The proposed hybrid surrogate model optimization algorithm synthesizes advantages of these different meta-models. Without verification of a specific meta-model, a suitable one for the engineering problem to be analyzed is automatically selected. Therefore, the proposed algorithm intends to make a better trade-off between numerical efficiency and searching accuracy for solving engineering problems, which are characterized by stronger non-linearity, higher complexity, non-convex feasible region, and expensive performance analysis.

Non-Uniform Rational Basis Spline hyper-surfaces for metamodelling

This study presents an original metamodelling technique based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case. The shape of such a hyper-surface is tuned by several parameters: the number of control points (CPs), their coordinates and the related weights, the degrees of the blending functions and the knot-vector components defined along each direction. The goal of the proposed strategy is to automatically determine (i.e. without the user’s intervention) the full set of parameters defining the NURBS hyper-surface approximating a given set of TPs, without considering simplifying hypotheses. To this purpose, the problem is formulated as a constrained nonlinear programming problem (CNLPP) wherein the optimization variables are all the parameters tuning the shape of the NURBS hyper-surface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a changing dimension. This problem is solved by means of an original genetic algorithm able to determine, simultaneously, the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The effectiveness of the proposed approach is shown by means of two meaningful test cases. In addition, the proposed method has been applied to a benchmark taken from the literature and the results have been compared to those provided by the Proper Generalized Decomposition method.

Convergence rates of the efficient global optimization algorithm for improving the design of analog circuits

Optimal sizing of analog circuits is a hard and time-consuming challenge. Nowadays, analog designers are more than ever interested in developing solutions for automating such a task. In order to overcome well-known drawbacks of the conventional equation-based and simulation-based sizing techniques, analog designers are being attracted by the so-called metamodeling techniques and recently have used them for establishing accurate models of circuits’ performances. Metamodels have been associated to optimization routines to maximize circuits’ performances. In this work we deal with the newly proposed efficient global optimization (EGO) algorithm that intrinsically offers both the metamodel generation and the optimization routine. Furthermore, it performs the requested task by using a relatively very small number of performance evaluations. Firstly, we focus on the convergence rates of the EGO technique via twenty benchmark test problems. Then, we use EGO for the optimal design of a couple of analog CMOS circuits. Comparison between EGO performances and those obtained using two surrogate-assisted metaheuristics is provided to show potentialities of the proposed approach. Finally, The case of muti-objective problems is also considered. The multi-objective efficient global optimization algorithm is used for generating Pareto fronts of conflicting perormances of two analog circuits. Obtained results are compared to those of the conventional in-loop optimization technique.

Estimation of in-situ maximum horizontal principal stress magnitudes from borehole breakout data using machine learning

This paper presents a technique for in-situ horizontal stress prediction in vertical boreholes based on borehole breakout data using a machine learning-based meta-modelling technique, i.e. Kriging. This model is generated based on the deterministic mean function and a stationary Gaussian process function derived from the 106 data points from published experimental studies. To examine the reliability of the model, a leave-one-out cross-validation process is conducted against the published experimental results. The Kriging prediction gives an average error of 10.59% on maximum horizontal principal stress (σH). A total of 23 field data were also extracted from both literature and mine site A with stress measurements conducted at the similar depth. The model yields an average prediction error of 8.4% in comparison with field stress measurement results on σH, which is remarkable considering its simplicity, reliability and low cost. This study limits the scope to σH estimation only due to the nature of the experimental setup, in which minimum horizontal principal stress (σh) values are often kept constant while changing σH. This results in a lot of repetition σh values in training data and it makes the prediction of σh unreliable. By collecting a broader range of data on breakout geometries, stress magnitudes and the rock strength, it is expected that the accuracy and the parameter coverage of this technique can be further improved in practical conditions.

A Comparative Study of Deep Neural Network and Meta-Model Techniques in Behavior Learning of Microgrids

Behavior learning of microgrids (MGs) is a necessary and challenging task for multi-MGs cooperation and energy pricing of distribution energy market. With the increasing demand for user privacy, this problem becomes more severe because of much less limited access to device parameters and models behind the Point of Common Coupling (PCC), which hinders conventional model-based power management methods. In this paper, to address this problem, some novel model-free data-driven methods including Deep Neural Network (DNN) and Meta-model techniques, such as Radial Basis Function (RBF), Response Surface Methods (RSM), and Kriging methods are introduced. These methods can predict the behavior of MGs through continuous iterative learning by accessing merely the historical active power measurements at the PCCs as well as public electricity price and weather information behind the PCCs, without full system identification and no prior knowledge on the system. A comparative study has been fully carried out by comparing with the conventional model-based model to better understand their advantages, drawbacks and limitations. The validity and applicability of the proposed methods is verified by numerical experiments. This paper can provide some references for future MGs interactive operation under incomplete information.

Meta-model based generation of solution spaces in sheet-bulk metal forming

Sheet-bulk metal forming (SBMF) is an emerging manufacturing technology that offers vast potential for lightweight design and functional integration. However, product designers often lack information about the required manufacturing parameters for their specific design. This problem is currently tackled by a knowledge acquisition process from manufacturing experts in combination with meta-modelling techniques. These meta-models predict resulting manufacturing parameters for given part design properties. When employing this design-for-manufacturing approach, it is key for product designers to evaluate many design alternatives that are all manufacturable with given forming machines. This is currently done by a genetic algorithm-based optimization of the meta-models with regard to manufacturing features. This papers proposes a novel approach for generating many design alternatives based on the meta-models and gathering them in a solution space. In doing so it is possible to review all manufacturable sheet-bulk metal forming part variants and let the product designers decide which part design fits best. The approach is applied to a locking teeth part, which highlights the usability of the new method.

Transit interchange discount optimization using an agent-based simulation model

Transit interchange discounts encourage people to travel by public transport, increasing the revenue of the operators. This research develops a transit assignment model, which takes account of the actual travel time, congestion and fare of the public transport, using an agent-based simulation model MATSim. Then, a simulation-based optimization problem is formulated to optimize the interchange discount to maximize profit. For computational efficiency, a metamodeling technique is further proposed and the metamodel can serve as a surrogate of the expensive simulation process. Transfer hubs are set up in a Hong Kong Island scenario and the interchange discount for bus-bus interchanges is optimized. The optimization result shows that the optimal interchange discount optimized by the proposed metamodel-based method increases the bus operators’ profit by 12%.

A Meta-Model for Strategic Educational Goals

Metamodeling technique is adopted widely in different fields related to software and system engineering. A meta-model represents the abstraction of a detailed design at multiple level. It is used in any structured environment ruled by a certain constraints and obligations and instantiate different platform specific domains from a single platform independent domain. This paper proposes a new model-driven approach for generating and analyzing automatically the outcome measures of strategic educational goals model. A new meta-model augmented with arithmetic semantics is created for Strategic Educational Goals where a set of outlines defines the enhancement framework of an academic organization. The vision, mission, program educational objectives and student outcomes are the four common strategic educational goals. These Goals support the performance roadmap to measures the institution situation and progress. The proposed meta-model is used to evaluate the strategic educational goals in a formal way, improve the continuous improvement process in academic organizations and allows the assessment at different level of management.

A Metamodel for the Management of Large Databases: Toward Industry 4.0 in Metal Forming

Metal forming machines can be servo-controlled and their numerical control can easily record and monitor several on-line process signals and loading curves, as a function of time, with a given sampling frequency. If these signals are collected and stored inside a designed database, any single forming process can generate a large amount of information that can be preciously used for process improvement and optimization. The database can be generated and stored locally at the machine, but it becomes more useful if it is transferred to a centralized big database. In both cases, if sampling frequencies are selected in order to follow the actual process dynamics, the amount of data stored can very easily and rapidly reach unpractical and unfeasible dimensions, in the order of magnitude of terabytes. A smart, designed and comprehensive strategy is therefore required for large data collecting and processing. Such a comprehensive strategy is difficult to be generalized for any forming process, but it must be specifically designed for each type of operation. In this paper, a framework for the management of large databases in the rotary draw tube bending process is proposed. A metamodeling technique for data compression is described and tested with actual process data, obtained during several rotary-draw bending of round stainless-steel tubes. Tube bending tests have been performed with CN controlled benders, where 12 axes can be actuated and 16 simultaneous output signals or loading curves have been recorded. The proposed method is able, for some of the selected signals, to reduce the amount of required data with a 75:1 ratio, with no significant loss of technological information.

The effects of digital predistortion in a CO-OFDM system – a stochastic approach

Digital predistortion is topic of significant interest in telecommunications – both in the wireless radio field and, more recently, in photonics. In the present letter, the authors undertake a sensitivity analysis of various digital predistortion algorithms. Using recent metamodeling techniques designed for efficient stochastic analysis, the authors show that using predistortion not only leads to a reduction of the error vector magnitude in general but can also make the system less sensitive to uncertainties.

Experimental and numerical study on the thermal control strategy for a gas foil bearing enhanced with thermoelectric modules

The authors report the method for temperature gradient control in gas foil bearings with the use of thermoelectric modules. The paper presents a prototype installation consisting of a gas foil bearing with integrated 36 thermoelectric modules, an electric spindle, measurement and control system. The results of a preliminary qualitative and quantitative assessment of the investigated temperature gradient control are shown, making use of the carried out numerical simulations. Steady state thermal analyses were performed for the defined control currents assigned to the Peltier modules. The metamodeling technique improved the search for a suboptimal choice on the control currents values in terms of temperature gradient control efficiency. Consideration of simultaneous forward and backward heat pumping directions for the selected thermoelectric modules improved temperature gradient reduction by additional 10%.Moreover, the paper is complemented with the results of an experimental test performed for a prototype installation of a gas foil bearing. A straightforward adaptive algorithm, dedicated to control thermal parameters of the bearing’s foil, was successfully tested. The control algorithm allowed for a significant temperature gradient reduction, however considerable oscillations in the temperature profile were observed. In order to eliminate these oscillations, a PID controller was implemented into the algorithm. Consequently, the magnitude of the temperature oscillations was reduced by 60%.

A Convolutional Neural Network for Impact Detection and Characterization of Complex Composite Structures.

This paper reports on a novel metamodel for impact detection, localization and characterization of complex composite structures based on Convolutional Neural Networks (CNN) and passive sensing. Methods to generate appropriate input datasets and network architectures for impact localization and characterization were proposed, investigated and optimized. The ultrasonic waves generated by external impact events and recorded by piezoelectric sensors are transferred to 2D images which are used for impact detection and characterization. The accuracy of the detection was tested on a composite fuselage panel which was shown to be over 94%. In addition, the scalability of this metamodelling technique has been investigated by training the CNN metamodels with the data from part of the stiffened panel and testing the performance on other sections with similar geometry. Impacts were detected with an accuracy of over 95%. Impact energy levels were also successfully categorized while trained at coupon level and applied to sub-components with greater complexity. These results validated the applicability of the proposed CNN-based metamodel to real-life application such as composite aircraft parts.

Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation

This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge from a catchment area during a precipitation event is considered. The goal of the case study is to perform a global sensitivity analysis and to identify the unknown model parameters as well as the measurement and prediction errors. These objectives can only be achieved by cheapening the incurred computational costs, that is, lowering the number of necessary model runs. With this in mind, a regularity-exploiting metamodeling technique is proposed that enables fast uncertainty quantification. Principal component analysis is used for output dimensionality reduction and sparse polynomial chaos expansions are used for the emulation of the reduced outputs. Sobol’ sensitivity indices are obtained directly from the expansion coefficients by a mere post-processing. Bayesian inference via Markov chain Monte Carlo posterior sampling is drastically accelerated.

Efficient aero-structure coupled wing optimization using decomposition and adaptive metamodeling techniques

This paper proposes an efficient decomposition-based optimization framework using adaptive metamodeling for expensive aero-structure coupled wing optimization problems. First, high-fidelity aero-structure coupled analysis method is presented through spatial interpolations of distributed aerodynamic loads and structural deformation. The proposed optimization framework decomposes the original complex coupled optimization problem into 2-D airfoil optimization (i.e., Stage-I) and 3-D wing optimization (i.e., Stage-II) to alleviate the expensive computational costs. In Stage-II, a two-level optimization strategy is tailored to further decompose the 3-D wing optimization into system-level and subsystem-level for dimension reduction. An adaptive response surface method using intelligent space exploration strategy is used to perform optimization tasks involving CFD simulations (i.e., 2-D airfoil optimization and system-level optimization in Stage-II), while sequential quadratic programming is employed to optimize the massive subsystem structure sizing variables. The effectiveness of two-level optimization strategy is validated on a numerical testing problem and a simplified wing optimization case. Finally, the developed models and proposed methods are successfully applied to aero-structure coupled optimization of a high aspect ratio wing. The optimization results demonstrate the effectiveness of the developed aero-structural analysis models and efficiency of the proposed optimization methods.

Reliability analysis of concrete barriers under vehicular crashes using augmented RBFs

A reliability analysis approach was studied for the assessment of roadside barriers under vehicular crashes. It was achieved using computational mechanics and a simulation-based reliability analysis method. Traditionally, the evaluation of roadside barriers has been conducted based on limited crash tests. With the development of high-performance computer hardware and software, numerical crash simulations can be performed using high-fidelity finite element (FE) methods. Based on the crash simulation results, various barrier systems can be assessed. Due to the high nonlinearity and implicit nature of crash responses, approximate models such as metamodels become useful to replace numerical crash analyses. In this work, augmented radial basis functions (RBFs) were used to generate approximate models of limit state functions, which represented crash responses exceeding certain limit values. With explicit limit state functions, failure probabilities or probabilities of exceedance were calculated using Monte Carlo simulations (MCS). The combination of crash simulations and a metamodeling technique allows an efficient reliability analysis, when expensive numerical analyses are required. A New Jersey concrete barrier example was analyzed and various crash responses and their limits were considered. The probability-based analysis method provides a useful tool to improve transportation safety. It can potentially replace the prescriptive pass/fail approach traditionally employed in barrier evaluation and design.

Onboard satellite visibility prediction using metamodeling based framework

Satellite autonomous systems are employed to address complex space applications through onboard data processing and mission planning. To take advantage of onboard autonomous systems, rapid onboard satellite visibility predictions are necessary for certain decision-making missions, including Earth observation resource allocation and satellite data transmission. We consider this visibility prediction process as a roots-finding problem for a multiple hump function, and design a metamodeling-based framework with a self-adaptive interpolation method. Metamodels are developed as surrogates for visibility prediction functions to reduce expensive computational costs. Our proposed framework has a broad range of applications for all orbital types and orbit propagators. We conduct the experiments using different metamodeling techniques, radial basis functions, Kriging, and support vector regression based upon real China's satellites. Numerical simulations indicate that the proposed framework outperforms existing interpolation methods, efficiently reducing the onboard computational cost.

Probabilistic analysis of strip footings based on enhanced Kriging metamodeling

SummaryTwo advanced Kriging metamodeling techniques were used to compute the failure probability of geotechnical structures involving spatially varying soil properties. These methods are based on a Kriging metamodel combined with a global sensitivity analysis that is called in literature Global Sensitivity Analysis‐enhanced Surrogate (GSAS) modeling for reliability analysis. The GSAS methodology may be used in combination with either the Monte Carlo simulation (MCS) or importance sampling (IS) method. The resulting Kriging metamodeling techniques are called GSAS‐MCS or GSAS‐IS. The objective of these techniques is to reduce the number of calls of the mechanical model as compared with the classical Kriging‐based metamodeling techniques (called AK‐MCS and AK‐IS) combining Kriging with MCS or IS. The soil uncertain parameters were assumed as non‐Gaussian random fields. EOLE methodology was used to discretize these random fields. The mechanical models were based on numerical simulations. Some probabilistic numerical results are presented and discussed.

Reliability analysis of tape based chip-scale packages based metamodel

In the mechatronic devices, finite element methods (FEM) are widely used to determine the fatigue response of solder joints subjected to thermal loading. These life cycle analyses are often deterministic. However, experience shows that design variables present variability that affects prediction quality. This paper describes a method for predicting the solder joints reliability in Tape based Chip Scale Packaging (T-CSP) with consideration of uncertainties in material properties. The proposed approach, which is based on the metamodeling techniques, combines FEM, metamodels and Monte Carlo simulation (MCS). Once validated, the constructed metamodel is used to perform the MCS. This probabilistic method has sufficient efficiency and accuracy to analyze the reliability of T-CSPs.

Performance evaluation of metamodelling methods for engineering problems: towards a practitioner guide

Metamodelling or surrogate modelling techniques are frequently used across the engineering disciplines in conjunction with expensive simulation models or physical experiments. With the proliferation of metamodeling techniques developed to provide enhanced performance for specific problems, and the wide availability of a diverse choice of tools in engineering software packages, the engineering task of selecting a robust metamodeling technique for practical problems is still a challenge. This research introduces a framework for describing the typology of engineering problems, in terms of dimensionality and complexity, and the modelling conditions, reflecting the noisiness of the signals and the affordability of sample sizes, and on this basis presents a systematic evaluation of the performance of frequently used metamodeling techniques. A set of metamodeling techniques, selected based on their reported use for engineering problems (i.e. Polynomial, Radial Basis Function, and Kriging), were systematically evaluated in terms of accuracy and robustness against a carefully assembled set of 18 test functions covering different types of problems, sampling conditions and noise conditions. A set of four real-world engineering case studies covering both computer simulation and physical experiments were also analysed as validation tests for the proposed guidelines. The main conclusions drawn from the study are that Kriging model with Matérn 5/2 correlation function performs consistently well across different problem types with smooth (i.e. not noisy) data, while Kriging model with Matérn 3/2 correlation function provides robust performance under noisy conditions, except for the very high noise conditions, where the Kriging model with nugget appears to provide better models. These results provide engineering practitioners with a guide for the choice of a metamodeling technique for problem types and modelling conditions represented in the study, whereas the evaluation framework and benchmarking problems set will be useful for researchers conducting similar studies.

Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem

The increasing demands for travelling comfort and reduction of carbon dioxide emissions have been considered substantially in the stage of conceptual aircraft design. However, the design of a modern aircraft is a multidisciplinary process, which requires the coordination of information from several specific disciplines, such as structures, aerodynamics, control, etc. To address this problem with adequate accuracy, the multidisciplinary analysis and optimization (MAO) method is usually applied as a systematic and robust approach to solve such complex design issues arising from industries. Since MAO method is tedious and computationally expensive, genetic programming (GP)-based metamodeling techniques incorporating MAO are proposed as an effective approach to minimize the wing stiffness of a large aircraft subject to aerodynamic, aeroelastic and stability constraints in the conceptual design phase. Based on the linear small-disturbance theory, the state-space equation is employed for stability analysis. In the process of multidisciplinary analysis, aeroelastic response simulations are performed using Nastran. To construct metamodels representing the responses of the interests with high accuracy as well as less computational burden, optimal Latin hypercube design of experiments (DoE) is applied to determine the optimized distribution of sampling points. Following that, parametric optimization is carried out on metamodels to obtain the optimal wing geometry shape, elastic axis positions and stiffness distribution, and then the solution is verified by finite element simulations. Finally, the superiority of the GP-based metamodel technique over genetic algorithm is demonstrated by multidisciplinary design optimization of a representative beam-frame wing structure in terms of accuracy and efficiency. The results also show that GP metamodel-based strategy for solving MAO problems can provide valuable insights to tailoring parameters for the effective design of a large aircraft in the conceptual phase.