Traditional Metamodel Research Articles

Net-HDMR Metamodeling Method for High-Dimensional Problems

Abstract Metamodel technology provides an efficient method to approximate complex engineering design problems. However, the approximation for high-dimensional problems usually requires a large number of samples for most traditional metamodeling methods, which leads to the difficulty of “curse of dimensionality.” To address the aforementioned issue, this paper presents the Net-high dimension model representation (HDMR) method based on the Cut-HDMR framework. Compared with traditional HDMR modeling, the Net-HDMR method incorporates two novel modeling approaches that improve the modeling efficiency of high-dimensional problems. The first approach enhances the modeling accuracy of HDMR by using the net function interpolation method to decompose the component functions into a series of one-dimensional net functions. The second approach adopts the CV-Voronoi sequence sampling method to effectively represent one-dimensional net functions with limited samples. Overall, the proposed method transforms complex high-dimensional problems into fitting finite one-dimensional splines, thereby increasing the modeling efficiency while ensuring approximate accuracy. Six numerical benchmark examples with different dimensions are examined to demonstrate the accuracy and efficiency of the proposed Net-HDMR. An engineering problem of thermal stress and deformation analysis for a jet engine turbine blade was introduced to verify the engineering feasibility of the proposed Net-HDMR.

Model Updating Using Bridge Influence Lines Based on an Adaptive Metamodel Global Optimization Method

Model updating seeks to update a finite-element model to reduce discrepancies between predicted and measured data. Metamodel-based model updating using bridge influence lines is a very promising method. However, the accuracy of traditional metamodel methods is not high due to the traditional metamodels being fitted in the entire parameter space using limited sample data. To address this problem, a model updating procedure based on the adaptive metamodel global optimization method is proposed. First, a systematic model updating theory using influence lines is developed, including three different objective functions and a selection of model updating parameters. Then, the adaptive metamodel-based global optimization method is proposed. The adaptive metamodel is iteratively fitted using the automatically added sample data by the mode-pursuing sampling method in the process of optimization. To improve the efficiency of finding the global optimal solution, a two-stage optimization strategy is presented. Finally, the proposed procedure is applied to numerical and practical examples of a long-span suspension bridge. In the numerical example, the global optimal solution is found successfully compared with the traditional metamodels. Excellent agreements are observed between the updated influence lines and measured influence lines in both numerical and practical examples. Based on the proposed theory, the accuracy and efficiency of model updating can well meet engineering requirements.

Multi-objective optimization of a multi-cellular aluminum extruded crush rail subjected to dynamic axial and oblique impact loading conditions

This work presents a multi-objective shape optimization study of a multi-cellular aluminum extrusion subjected to dynamic axial and oblique (20° angled) impact loading conditions. Finite element models are developed, validated with experimental data, parameterized, and used to exhaust the design space using a full factorial design of experiments. An analysis of different energy absorption characteristics, such as axial and oblique mean crush force, crush efficiency, and oblique impact coefficient, are presented. A multi-objective optimization problem is defined to generate new solutions that dominate a baseline profile in all aspects of performance, which produced a geometry with up to 16% improvements in energy absorption. The parametric study is used to define the “true” Pareto front, which is the set of non-dominated designs and the solution to the optimization problem. The response surface methodology (RSM) is used to perform the multi-objective optimization analysis. The traditional RSM approach is compared to an adaptive surrogate-assisted response surface method (ASA-RSM) in their speed and ability to identify the true Pareto front correctly. Using the traditional metamodel constraint, the traditional RSM approach could only identify 18% of the true Pareto front using up to 8% of the design domain. After relaxing the constraint, the traditional RSM approach still required approximately 63% of the entire domain to identify 67% of the true Pareto front accurately. In comparison, the ASA-RSM approach was able to identify 84.5% of the true Pareto front using 42% of the entire domain. In some instances, the ASA-RSM approach correctly identified 100% of the true Pareto front by using as little as 18% of the domain. However, the ASA-RSM approach’s peak performance is dependent on the initial sampling and resulting metamodel. This study provides a comprehensive understanding of the performance gains of multi-objective optimization in the application of structural crashworthiness considering various loading conditions.

Causal artificial neural network and its applications in engineering design

To reduce the computational cost in engineering design, expensive high-fidelity simulation models are approximated by mathematical models, named as metamodels. Typical metamodeling methods assume that expensive simulation models are black-box functions. In this paper, in order to improve the accuracy of metamodels and reduce the cost of building metamodels, knowledge about engineering design problems is employed to help develop a novel metamodel, named as causal artificial neural network (causal-ANN). Cause–effect relations intrinsic to the design problem are employed to decompose an ANN into sub-networks and values of intermediate variables are utilized to train these sub-networks. By involving knowledge of the design problem, the accuracy of causal-ANN is higher than the traditional metamodeling methods that assume black-box functions. Additionally, one can identify attractive subspaces from the causal-ANN by leveraging the structure of the causal-ANN and the theory of Bayesian Networks. The impacts of fidelity of causal graphs and design variable correlations are also discussed in the paper. The engineering case studies demonstrate that the causal-ANN can be accurately constructed with a small number of expensive simulations, and attractive design subspaces can be identified directly from the causal-ANN.

Using structural decomposition and refinements for deep modeling of software architectures

Traditional metamodeling in two levels gets to its limits when model elements of a domain should be described as instances of other model elements. For example in architecture description languages, components may be instances of their component types. Although workarounds to model such instance relations between model elements exist, they require many validation constraints and imply a cumbersome interface. To obtain more elegant metamodels, deep modeling seeks ways to represent non-transitive instantiation chains directly. However, existing concepts cannot be applied in some situations we refer as composite instantiation patterns. Further, these concepts make existing technologies for model transformation and analysis obsolete as these languages have to be adapted. In this paper, we present an approach to realize deep modeling through structural decomposition and refinements that can be implemented as a noninvasive extension to EMOF-like meta-metamodels. As a consequence, existing tools need not be adapted and composite instantiation patterns are fully supported. We validate our concept by creating a deep modeling architecture description language based on the Palladio Component Model and demonstrate its advantages by modeling a synthetic web application. We show that existing tools for incremental model analysis can be reused and manifest several orders of speedup for a synthetic example analysis.

Adaptive metamodel-assisted shape optimization for springback in metal forming processes

This paper aims to propose a shape optimization strategy for springback shape in metal forming processes based on the adaptive metamodel of the spatial field that can reduce the computational time and cost. The first stage includes solving metal forming problem using finite element simulation and building of Reduction Order Model of spatial field based on Proper Orthogonal Decomposition. Then, the metamodel of spatial field is built using the combination of Reduction Order Model and Kriging method to replace the expensive high fidelity model. In the second stage, the metamodel of spatial field is used within the iterative optimization procedure to find the optimal design for the final shape after springback in the metal forming processes. This strategy allows reducing computational cost to achieve the optimal design with respect to the approach based on the traditional metamodel. The proposed methodology is illustrated with the “U-shape bending” from the Numisheet2011 benchmark problem. Two parameters: the blank holder force and the die radius are chosen to optimize the springback effect.

Optimal Parallel Machine Allocation Problem in IC Packaging Using IC-PSO: An Empirical Study

We model and apply a stochastic-simulation-based methodology to optimize the machine allocation of a flexible flow shop (FFS) dedicated to integrated circuit (IC) packaging. This contrasts with most previous research on non-deterministic FFS problems wherein stochastic simulation is mostly used to estimate throughput, cycle time, delay cost, or some other measure(s) in order to compare the performances of already-existing heuristic-based algorithms. The methodology applied in this research, called progressive simulation metamodeling for IC Packaging (IC-PSO), while rooted in the traditional metamodeling technique known as Response Surface Methodology (RSM), contrasts with RSM in that it is equipped with well-designed mechanisms to ensure an ever-increasing solution quality in an attempt to achieve the desirable optimality. The computational efficiency that IC-PSO affords IC packaging companies is demonstrated via a numerical study. Meanwhile, an empirical study based on real data was conducted to validate the viability of the proposed methodology in real settings.

A matter-element method for risk identification of technology innovation

With the rapid development of IT, technology innovation has attracted increasing attentions from governments, enterprises and researchers. It is notable that the failure rate of technology innovation is high and the risk cannot be ignored. Risk identification is a critical step of risk management and to identify risk accurately and effectively is important for technology innovation organizations. However, the extant risk identification approaches cannot be directly applied, due to the characteristics of technology innovation risk such as uncertainty and fuzziness. In this paper we introduce matter-element model, which is developed from extension theory, and can be employed to support the characteristics of technology innovation risk. On the basis of the traditional meta-model, this paper attempts to improve the schema, through constructing indicator system of technology innovation risk. We present a method of determining the weights of indicators based on minimum deviation, which integrates the AHP weight and entropy weight. Through the calculating process and sensitivity analysis, the risk factors of technology innovation with different features can be identified, and technology innovation organizations can formulate and perform targeted strategies toward different risk factors. Finally, based on an instance, we discuss the effectiveness of our method and draw the conclusions.

A Computationally Efficient Simulation-Based Optimization Algorithm for Large-Scale Urban Transportation Problems

This paper proposes a computationally efficient simulation-based optimization (SO) algorithm suitable to address large-scale generally constrained urban transportation problems. The algorithm is based on a novel metamodel formulation. We embed the metamodel within a derivative-free trust region algorithm and evaluate the performance of this SO approach considering tight computational budgets. We address a network-wide traffic signal control problem using a calibrated microscopic simulation model of evening peak period traffic of the full city of Lausanne, Switzerland, which consists of more than 600 links and 200 intersections. We control 99 signal phases of 17 intersections distributed throughout the entire network. This SO problem is a high-dimensional nonlinear constrained problem. It is considered large-scale and complex in the fields of derivative-free optimization, traffic signal optimization, and simulation-based optimization. We compare the performance of the proposed metamodel method to that of a traditional metamodel method and that of a widely used commercial signal control software. The proposed method systematically and efficiently identifies signal plans with improved average city-wide travel times.

Process optimization via neural network metamodeling

Queuing systems are often used to model manufacturing or communication systems. Simulation models have been the most accurate models of such systems, but when optimizing the systems it is often impractical to simulate all possible configurations to identify the “best” choice. In the absence of mathematical approximations, one may turn to simulation metamodeling. Traditional metamodeling schemes would involve a simulation model of the entire system run over some subset of the possible configurations. A regression model is then typically fit to the results of these runs and used to predict results for the many configurations that were not simulated. Our approach is to develop an artificial neural network (ANN) metamodel of components of the entire system rather than of the entire system. The entire system is then modeled by interconnecting the ANN metamodels. Specifically, we propose the following approach. An ANN is trained via simulation to act as a single “generic” queuing node. The ANN accepts input data on inter-arrival and service distributions in the form of histograms and generates a departure distribution and a performance measure. A network of queues is then modeled by interconnecting copies of the generic queuing node. To illustrate the process, a simple manufacturing system is modeled. The ANN network model is used to select the buffer sizes in front of each process that provide a desired mix of product throughput rates, while minimizing average system sojourn time.