Metamodeling Techniques Research Articles

A new multi-objective discrete robust optimization algorithm for engineering design

• A novel multi-objective discrete robust optimization algorithm was proposed. • The presented method was verified by a mathematical example and a ten-bar truss design. • Robust optimization design for the crashworthiness design of full vehicle was conducted. This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.

Multiobjective constraints for climate model parameter choices: PragmaticPareto fronts in CESM1

AbstractGlobal climate models (GCMs) are examples of high‐dimensional input‐output systems, where model output is a function of many variables, and an update in model physics commonly improves performance in one objective function (i.e., measure of model performance) at the expense of degrading another. Here concepts from multiobjective optimization in the engineering literature are used to investigate parameter sensitivity and optimization in the face of such trade‐offs. A metamodeling technique called cut high‐dimensional model representation (cut‐HDMR) is leveraged in the context of multiobjective optimization to improve GCM simulation of the tropical Pacific climate, focusing on seasonal precipitation, column water vapor, and skin temperature. An evolutionary algorithm is used to solve for Pareto fronts, which are surfaces in objective function space along which trade‐offs in GCM performance occur. This approach allows the modeler to visualize trade‐offs quickly and identify the physics at play. In some cases, Pareto fronts are small, implying that trade‐offs are minimal, optimal parameter value choices are more straightforward, and the GCM is well‐functioning. In all cases considered here, the control run was found not to be Pareto‐optimal (i.e., not on the front), highlighting an opportunity for model improvement through objectively informed parameter selection. Taylor diagrams illustrate that these improvements occur primarily in field magnitude, not spatial correlation, and they show that specific parameter updates can improve fields fundamental to tropical moist processes—namely precipitation and skin temperature—without significantly impacting others. These results provide an example of how basic elements of multiobjective optimization can facilitate pragmatic GCM tuning processes.

Effects of coupling anisotropic yield functions with the optimization process of extruded aluminum front rail geometries in crashworthiness

Using advanced constitutive models in simulation tools can improve predictive capabilities of automotive structures in crashworthiness applications. This work presents the influences of coupling anisotropic yield functions into the size optimization of extruded front rails to maximize energy absorption characteristics. Finite element simulations of the extrusion crush response are performed using the von Mises (1913), Hosford (1972) and Barlat et al. (2005) Yld2004-18p yield functions. Each yield function is implemented into a 2-dimensional plane stress and 3-dimensional element formulation to highlight the modeling differences prior to optimization. The simulations are also compared to the experimental dynamic crush response of the extrusion. The response surface methodology (RSM) with the artificial neural network (ANN) metamodeling technique is coupled with the genetic algorithm (GA) optimization scheme to improve the specific energy absorption (SEA) through maximizing energy absorption and minimizing mass. A constrained and unconstrained mass optimization study is performed to identify the sensitivity of global optimization to yield surface choice. Analytical models are derived to explain the influence of the yield surface on the convergence of optimization. The results highlight the importance of incorporating anisotropic yield functions into the optimization process.

Performance of global metamodeling techniques in solution of structural reliability problems

Solution of structural reliability and uncertainty propagation problems can be a computationally intensive task, since complex mechanical models have to be solved thousands or millions of times. In this context, surrogate models can be employed in order to reduce the computational burden. This article compares the performance of three global surrogate modeling techniques in the solution of structural reliability problems. The paper addresses artificial neural networks, polynomial chaos expansions and Kriging metamodeling. Analytical and numerical problems of increasingly complexity are addressed, including an eight-hundred bar, 3D steel lattice tower. Implementation strategies concerning data mapping and optimization of Kriging hyper parameters are proposed and discussed. Advantages and limitations of each technique are addressed. Results show that the three techniques explored herein are reliable tools for approximating the response of complex mechanical models.

Source characterisation by mixing long-running tsunami wave numerical simulations and historical observations within a metamodel-aided ABC setting

Uncertainty related to the source parameters of earthquake can largely impact the tsunami-induced wave characteristics, especially in the case of near-field tsunami source. The combination of numerical simulations and historical eyewitness accounts can be used to better constrain those uncertainties. In the present study, we propose a Bayesian procedure to infer (i.e. learn) the probability distribution of the source parameters of the earthquake. The strategy is based on the combination of: (1) kriging-based metamodelling techniques to overcome the high computation time cost of the numerical simulator; and (2) Approximate Bayesian Computation (ABC) procedure to perform the Bayesian inference. The procedure is applied to the Ligurian (North West of Italy) 1887 tsunami case, for which tsunami-induced sea surface elevations at the coast have been reported at four locations, namely Marseille, Imperia, Diano-Marina and Genoa. The kriging metamodels are trained using only 300 long-running numerical simulations that were performed using the FUNWAVE-TVD code. Contrary to recent inversion exercises that can benefit from current modern observation networks (like tide gauges, sea bottom pressure gauges, GPS-mounted buoys), the case of historical tsunami like Liguria is complicated by the imprecision and scarcity of the observations: this is accounted for by conducting the combined ABC-kriging procedure a large number of times (i.e. 1000); each time a new set of observations being randomly generated to account for this observational error. The combined analysis of the inference results and of the observation uncertainty reveals that: (1) the coseismic slip is the most important source parameter with a very peaky density distribution around low values ranging from 0.3 to 0.6 m; (2) The fault width has a peaky density distribution around low values ranging from 10 to 12 km; (3) The rake and azimuth distribution only slightly deviate from the uniform prior, hence indicating a low influence of those parameters; (4) The bi-modal distribution of the dip is also evidenced.

Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Benchmark Datasets

Metamodeling techniques have recently been proposed to address the computational issues related to the valuation of large portfolios of variable annuity contracts. However, it is extremely difficult, if not impossible, for researchers to obtain real datasets from insurance companies in order to test their metamodeling techniques on such real datasets and publish the results in academic journals. Even if a researcher can obtain real datasets from insurance companies, it is difficult for the re- searcher to share the datasets with the public at large. To facilitate the development and dissemination of research related to the efficient valuation of large variable annuity portfolios, this paper creates a large synthetic portfolio of variable annuity contracts based on the properties of real portfolios of variable annuities and implements a Monte Carlo simulation engine for valuing the synthetic portfolio. In addition, this paper develops benchmark datasets of fair market values and Greeks, which are important quantities for managing the financial risks associated with variable annuities. The resulting datasets provide researchers with a common basis for testing and comparing the performance of various metamodeling techniques.

When Learners Escape Models of Their Behavior

Modeling and measurement are stable in many domains, such as ballistics. So why are new models continually needed in other domains, such as macro-economic policy and spam filtering? Models always include unmeasured dimensions, but people (or any learners) can escape into those unmeasured dimensions. People don’t always try to escape, so we look for conditions where escape is likely, prompted by the insight that too much striving for measured goals hurts unmeasured goals. For example, science hiring’s quantity demands led to a drop in quality, eventually visible in the reproducibility crisis. We can also identify macro-level indicators such as increasing prices, new products, and divergent profits. Under the pressure of high protein prices, manufacturers of pet food (normally a commodity) substituted melamine for protein, gaming the way protein was measured. What can modelers do? First, modelers can try to change the conditions that caused escape pressure. Failing that, we can either speed up the evolution of our own models or slow down the evolution of others’ models. Techniques to speed up include better feedback, models that are simple or explainable or modular, and using multiple models (an ensemble). Techniques to slow down others include obscuring our own model so that it cannot be backward-engineered. In sum, domains that continually need new models typically have pressure for learners to escape the models. We should study conditions that make escape likely and better meta-modeling techniques to deal with it.

A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects

In this paper, recent optimisation techniques have been used to improve crash performance of a thin-walled tube considering influence of the forming history. In the optimisation study, weight and amount of the energy absorption of the thin-walled tubes are chosen as objective function and constraint, respectively. Radial basis functions (RBFs) metamodelling technique was used to approximate the structural responses selected in crash and forming analyses. The performances of recent optimisation algorithms which are particle swarm algorithm, cuckoo search algorithm, gravitational search algorithm (GSA), hybrid gravitational search-Nelder Mead algorithm (HGSANM), league championship algorithm (LCA), firefly algorithm, bat algorithm, interior search algorithm (ISA) and imperialist competitive algorithm (ICA) were investigated to find the optimal thin-walled tube design. The lowest mass of the components is obtained at 1000 function evaluation number (FEN) using hybrid GSA.

Decomposition-Assisted Computational Technique Based on Surrogate Modeling for Real-Time Simulations

The development of complex simulation systems is extremely costly as it requires high computational capability and expensive hardware. As cost is one of the main issues in developing simulation components, achieving real-time simulation is challenging and it often leads to intensive computational burdens. Overcoming the computational burden in a multidisciplinary simulation system that has several subsystems is essential in producing inexpensive real-time simulation. In this paper, a surrogate-based computational framework was proposed to reduce the computational cost in a high-dimensional model while maintaining accurate simulation results. Several well-known metamodeling techniques were used in creating a global surrogate model. Decomposition approaches were also used to simplify the complexities of the system and to guide the surrogate modeling processes. In addition, a case study was provided to validate the proposed approach. A surrogate-based vehicle dynamic model (SBVDM) was developed to reduce computational delay in a real-time driving simulator. The results showed that the developed surrogate-based model was able to significantly reduce the computing costs, unlike the expensive computational model. The response time in surrogate-based simulation was considerably faster than the conventional model. Therefore, the proposed framework can be used in developing low-cost simulation systems while yielding high fidelity and fast computational output.

Multi-objective micro-geometry optimization of gear tooth supported by response surface methodology

This paper shows the application of response surface methodology for gear optimization using micro-geometry profile modifications. The suitability of three distinct metamodeling techniques is studied in this paper: Gaussian Process (stochastic), Shepard k-Nearest (nonparametric deterministic) and Polynomial (parametric deterministic). The described optimization strategy is implemented and tested on a case study consisting of a pair of identical spur gears, in which the goal is to find optimal micro-geometry modifications of tooth profile, providing decreased values of peak-to-peak transmission error and maximal contact stress along the meshing cycle, while maintaining the safety coefficient linked to tooth bending fatigue above a required threshold. The gear pair is analyzed under three different loading scenarios. It is shown that the described optimization strategy allows finding optimal micro-geometry modifications of tooth profile that enable significant improvements in all the observed performance indices with respect to the unmodified gear design, as confirmed by detailed numerical simulations of the optimal gears.

Heat pump and PV impact on residential low-voltage distribution grids as a function of building and district properties

Heating electrification powered by distributed renewable energy generation is considered among potential solutions towards mitigation of greenhouse gas emissions. Roadmaps propose a wide deployment of heat pumps and photovoltaics in the residential sector. Since current distribution grids are not designed to accommodate these loads, potential benefits of such policies might be compromised. However, in large-scale analyses, often grid constraints are neglected. On the other hand, grid impact of heat pumps and photovoltaics has been investigated without considering the influence of building characteristics. This paper aims to assess and quantify in a probabilistic way the impact of these technologies on the low-voltage distribution grid, as a function of building and district properties. The Monte Carlo approach is used to simulate an assortment of Belgian residential feeders, with varying size, cable type, heat pump and PV penetration rates, and buildings of different geometry and insulation quality. Modelica-based models simulate the dynamic behavior of both buildings and heating systems, as well as three-phase unbalanced loading of the network. Additionally, stochastic occupant behavior is taken into account. Analysis of neighborhood load profiles puts into perspective the importance of demand diversity in terms of building characteristics and load simultaneity, highlighting the crucial role of back-up electrical loads. It is shown that air-source heat pumps have a greater impact on the studied feeders than PV, in terms of loading and voltage magnitude. Furthermore, rural feeders are more prone to overloading and under-voltage problems than urban ones. For large rural feeders, cable overloading can be expected already from 30% heat pump penetration, depending on the cable, while voltage problems start usually at slightly higher percentages. Additionally, building characteristics show high correlations with the examined grid performance indicators, revealing promising potential for statistical modeling of the studied indicators. Further work will be directed to the assessment of meta-modeling techniques for this purpose. The presented models and methodology can easily incorporate other technologies or scenarios and could be used in support of policy making or network design.

Power macromodeling technique and its application to SoC‐based design

AbstractLow power is becoming a more crucial performance metrics in system‐on‐chip (SoC) design. Power function is largely determined by input patterns. The characteristics of these patterns have a major influence on power dissipation.This paper demonstrates power estimation technique using input patterns with the predefined statistical characteristics that helps to analyze the average power consumption of the different intellectual property (IP) cores and the interconnects/buses in SoC design. Genetic algorithm is implemented for the generation of sequences of input signals during the power estimation procedure. The genetic algorithm concurrently optimizes the input signal characteristics that influence the final solution of the pattern. Then, a Monte Carlo zero‐delay simulation is performed for individual IP core and bus at a high level. By the simple addition of these cores/buses, power is predicted by a novel macromodel function. The metamodeling technique is adopted to improve accuracy of the samples of realistic data for the quality of results. In the experiments with the IP‐based SoC system, the average error is estimated at 11.42%.

Leakage and pressurization risk assessment of CO2 reservoirs: A metamodeling modeling approach

Monitoring of pressure build-up can provide explicit information on reservoir integrity. This work evaluated pressurization of a CO2 reservoir system in the presence of leakage pathways as well as exploring the effects of compartmentalization of the reservoir utilizing metamodeling techniques (e.g. Design of Experiments (DoE) and Response Surface Methodology (RSM)). Two simulation models were developed (1) an idealized scenario for the evaluation of multiple DoE methods, and (2) a complex scenario implementing the best performing DoE method to investigate pressurization of the reservoir system. The evaluation of the idealized scenario determined that the Central Composite design would be suitable for the complex scenario. The complex scenario evaluated 5 uncertain factors such as the permeabilities of the reservoir, seal, leakage pathway and fault, and finally the location of the pathway. A total of 36 response surface equations (RSEs) were developed for the complex scenario with a coefficient of determination (R2) of 0.95 and a Normalized Root Mean Square Error (NRMSE) of 0.060. Sensitivities of RSEs to the input factors were dynamic through space and time. At the earliest time, the impact of the reservoir permeability was dominant, whereas the fault permeability became dominant for later times (>0.5years). The RSEs were implemented in a Monte Carlo Analysis to analyze leakage and pressurization risks. At the earliest time, the permeability of the leakage pathway had a sufficiently high influence on the above-zone pressure (i.e., the change in pressure in an aquifer overlying the sealing formation) allowing for adequate determination of leakage risk. At later times, the fault permeability became dominate inhibiting the determination of leakage risk while allowing for sufficient determination of pressurization risk.

Global optimization method using ensemble of metamodels based on fuzzy clustering for design space reduction

For most engineering design optimization problems, it is difficult or even impossible to find the global optimum due to the unaffordable computational cost. To overcome this difficulty, a global optimization method that integrates the ensemble of metamodels and fuzzy clustering is proposed to deal with the optimization problems involving the computation-intensive, black-box computer analysis and simulation. The ensemble of metamodels combining three representative metamodeling techniques with optimized weight factors is used to decrease the computational expense during the optimization procedure and the fuzzy clustering technique is applied to obtain the reduced design space. In this way, the efficiency and capability of capturing the global optimum will be improved in the reduced design space. To demonstrate the superior performance of the proposed global optimization method over existing methods, it is examined using various benchmark optimization problems and applied to solve an engineering design optimization problem. The results show that the proposed global optimization method is robust and efficient in capturing the global optimum.

Post-injection trapping of mobile CO 2 in deep aquifers: Assessing the importance of model and parameter uncertainties

Predicting the fate of the injected CO2 is crucial for the safety of carbon storage operations in deep saline aquifers: especially the evolution of the position, the spreading and the quantity of the mobile CO2 plume during and after the injection has to be understood to prevent any loss of containment. Fluid flow modelling is challenging not only given the uncertainties on subsurface formation intrinsic properties (parameter uncertainty) but also on the modelling choices/assumptions for representing and numerically implementing the processes occurring when CO2 displaces the native brine (model uncertainty). Sensitivity analysis is needed to identify the group of factors which contributes the most to the uncertainties in the predictions. In this paper, we present an approach for assessing the importance of model and parameter uncertainties regarding post-injection trapping of mobile CO2. This approach includes the representation of input parameters, the choice of relevant simulation outputs, the assessment of the mobile plume evolution with a flow simulator and the importance ranking for input parameters. A variance-based sensitivity analysis is proposed, associated with the ACOSSO-like meta-modelling technique to tackle the issues linked with the computational burden posed by the use of long-running simulations and with the different types of uncertainties to be accounted for (model and parameter). The approach is tested on a potential site for CO2 storage in the Paris basin (France) representative of a project in preliminary stage of development. The approach provides physically sound outcomes despite the challenging context of the case study. In addition, these outcomes appear very helpful for prioritizing the future characterisation efforts and monitoring requirements, and for simplifying the modelling exercise.

Otimização via simulação por metamodelagem: um estudo em casos da área médica

O uso combinado da simulação a eventos discretos e otimização vem crescendo nos últimos anos. No entanto, esta forma de otimização ainda é pouco utilizada, devido principalmente a seu elevado custo computacional. Nesse sentido, vários trabalhos visam desenvolver novos métodos de otimização, buscando acelerar este procedimento. Este trabalho faz uso da técnica de metamodelagem, para criar um modelo matemático, que represente uma determinada saída de um modelo de simulação, e proceder com sua otimização sem a necessidade da utilização do modelo simulado. Para exemplificar o método empregado foram utilizados modelos de simulação ligados à área médica. O uso da metamodelagem permitiu otimizar os modelos de simulação, alcançando soluções estatisticamente iguais as encontradas por um otimizador comercial, com a vantagem de reduzir o tempo computacional do processo em mais de 68% em média. Desta forma, a metamodelagem se apresenta como uma potencial técnica de otimização para a simulação, ao prover soluções de elevada qualidade em um tempo computacional reduzido, quando comparado a métodos de otimização via simulação tradicionais.

Efficient power analysis approach and its application to system-on-chip design

Low-power is becoming more crucial performance metrics in system-on-chip (SoC) design. Power function is largely determined by input patterns. The characteristics of these patterns have a major influence on power dissipation.This paper demonstrates power estimation technique using input patterns with the predefined statistical characteristics that helps to analyze the average power consumption of the different intellectual-property (IP) cores and the interconnects/buses in SoC design. Genetic algorithm (GA) is implemented for the generation of sequences of input signals during the power estimation procedure. The GA concurrently optimizes the input signal characteristics that influence the final solution of the pattern. Then, a Monte-Carlo zero-delay simulation is performed for individual IP core and bus at high-level. By the simple addition of these cores/buses, power is predicted by a novel macro-model function. The meta-modeling technique is adopted to improve accuracy of the samples of realistic data for the quality of results. In experiments with the IP-based SoC system, the average error is estimated 11.42%.

Passive Sensing of Sensorized Composite Panels: Support Vector Machine

Strain readings recorded by surface mounted piezoelectric sensors due to impact events on composite panel are used to detect and characterize the impact. Sensor signals on a composite stiffened panels have been simulated by a valid numerical model. Applicability of least square support vector machines (LSSVM) on creating a meta-model to detect and characterize impact event has been investigated. In particular, the main advantage of LSSVM over other meta-modeling technique was found to be the smaller number of training data that is required. Experimental results on a composite panel has been used to validate the findings.

대량 데이터를 위한 제한거절 기반의 회귀부스팅 기법

The purpose of this study is to challenge a computational regression-type problem, that is handling large-size data, in which conventional metamodeling techniques often fail in a practical sense. To solve such problems, regression-type boosting, one of ensemble model techniques, together with bootstrapping-based re-sampling is a reasonable choice. This study suggests weight updates by the amount of the residual itself and a new error decision criterion which constructs an ensemble model of models selectively chosen by rejection limits. Through these ideas, we propose AdaBoost.RMU.R as a metamodeling technique suitable for handling large-size data. To assess the performance of the proposed method in comparison to some existing methods, we used 6 mathematical problems. For each problem, we computed the average and the standard deviation of residuals between real response values and predicted response values. Results revealed that the average and the standard deviation of AdaBoost.RMU.R were improved than those of other algorithms.

Reliability analysis of high-dimensional models using low-rank tensor approximations

Engineering and applied sciences use models of increasing complexity to simulate the behavior of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may become intractable in cases when a single simulation is time demanding. Particularly challenging is the reliability analysis of systems represented by computationally costly models, because of the large number of model evaluations that are typically required to estimate small probabilities of failure. In this paper, we demonstrate the potential of a newly emerged meta-modeling technique known as low-rank tensor approximations to address this limitation. This technique is especially promising for high-dimensional problems because: (i) the number of unknowns in the generic functional form of the meta-model grows only linearly with the input dimension and (ii) such approximations can be constructed by relying on a series of minimization problems of small size independent of the input dimension. In example applications involving finite-element models pertinent to structural mechanics and heat conduction, low-rank tensor approximations built with polynomial bases are found to outperform the popular sparse polynomial chaos expansions in the estimation of tail probabilities when small experimental designs are used. It should be emphasized that contrary to methods particularly targeted to reliability analysis, the meta-modeling approach also provides a full probabilistic description of the model response, which can be used to estimate any statistical measure of interest.