Surrogate Modeling Method Research Articles

WEIGHT MINIMIZATION OF SHIP CHAMBER STRUCTURE IN VERTICAL SHIP LIFT DESIGN BASED ON MULTI-LEVEL STRUCTURAL OPTIMIZATION METHOD

Weight reduction of ship chamber is a main concern of ship lift design for improving the load capacity. The structure of ship chamber is typical of beam-plate structure. To deal with structural optimization problem of beam-plate structure, a multilevel structural optimization method was developed based on combining an improved bi-directional evolutionary structural optimization (BESO) method and surrogate model method, which covers three optimization levels, as dimension optimization, topology optimization and section optimization. The aim of the proposed optimization method is to determine global design parameters, integral structural topology, and locations and sectional parameters of structural members from an oversized ground structure. The kernel optimization procedure (KOP) is using BESO to obtain the optimal topology from a ground structure. In order to deal with beam-plate structures, cubic box is adopted as the unit cell to construct ground structure for BESO. In the first optimization level, based on different dimensional parameter combinations, a series of ground structures are generated and used to perform KOP. Response surface (RS) model is used to simulate the nonlinear relationship between the optimal objective values and dimension parameters, then the optimal dimensional parameters can be obtained. In the second optimization level, the optimal dimension parameters are used to generate the ground structure, and the optimal topology could be obtained by using KOP. In the third optimization level, RS model is also used to determine the section parameters. The proposed method is applied to structural design of ship chamber of a 500-ton class ship lift. The results show that the proposed method leads to a greater weight saving, compared with the original design and generic algorithm (GA)-based optimization results.

Probabilistic assessment of pile group response considering superstructure stiffness and three-dimensional soil spatial variability

This note presents the probabilistic analyses of pile groups considering spatially variable soil properties and superstructure-foundation interaction effects. Condensed stiffness matrices for the superstructure and spatially variable subsurface domain are evaluated individually, and coupled with foundation elements for holistic analyses of the system. Probabilistic assessments are then performed using surrogate modeling method. Parametric studies show that common assumptions of perfect or no spatial correlations in the soil may not represent the critical scenario for pile groups. Two presented foundation case studies also reveal the significance of interactions between superstructure and soil variability, and potentials of foundation tilting due to spatially variable soil properties.

Surrogate modeling for liquid-gas interface determination under microgravity

In recent years the advent of on-orbital refueling technology and the accompanying interest in liquid management in space have rekindled attention to the study of the liquid-gas interface determination. So far, a series of numerical methods, such as the Shooting method, are used to calculate the mathematical model of liquid-gas interface. However, these methods have some drawbacks in common, such as poor convergence, dependence on initial value and instability. As a result, long calculation time and sudden calculation interruption are inevitable. Although satisfactory results can be achieved, it requires human intervention. As an important intermediary of capillary flow and liquid management device design, liquid-gas interface calculations need to be done thousands of times. Therefore, the quickness and robustness of liquid-gas interface calculations are needed. Surrogate modeling method arising with the development of aerospace technology in recent years provides a new way to solve this problem. Combining with the characteristics of liquid-gas interface calculation, a double-layer radial basis function surrogate model is proposed to approximate the mathematical model of liquid-gas interface. This surrogate model is approximately equivalent to the mathematical model of liquid-gas interface but is much easier to solve. Compared with the Shooting method, the efficiency of the surrogate model is improved by 99.46%, and the success rate is increased to 100% from 35%.

Strategies for efficient machine learning of surrogate drag models from three-dimensional mesoscale computations of shocked particulate flows

Macroscale simulations of shocked particulate flows rely on closure laws to model momentum transfer between the fluid and dispersed particles phase. Developing closure models from experimental data is expensive. Robust and accurate closures laws can be obtained through surrogate modeling using high-resolution mesoscale simulations. However, development of surrogate models for drag from 3D high-fidelity simulations of shock interaction with clusters of particles can be computationally prohibitive. This paper explores various strategies to efficiently construct surrogate models for drag on particles in the shocked flow. The cost of generating training data is reduced by selecting optimal grid resolutions, particle arrangements in clusters, and size of particle clusters, i.e., by selecting suitable representative volumes (RVEs). Different surrogate modeling strategies such as multi-fidelity and parameter-by-parameter construction approaches are examined. The surrogate models obtained from the different methods are compared to determine the most cost-effective machine learning based surrogate modeling method in the context of shock-particle interactions.

Aerodynamic Shape Optimization of Natural-Laminar-Flow Wing Using Surrogate-Based Approach

Aerodynamic shape optimization of a swept natural-laminar-flow wing in the transonic regime is still challenging. The difficulty is associated with reliable prediction of laminar–turbulence transition and reasonable compromise of viscous and wave drags. This paper proposes to use efficient global optimization based on surrogate models to address this problem. The Reynolds-averaged Navier–Stokes flow solver features automatic transition prediction via a full method, in which dual factors are used for Tollmien–Schlichting and crossflow instabilities, respectively. The optimizer is based on the kriging surrogate model and parallel infill-sampling method. The baseline natural-laminar-flow wing for short- and medium-range transport aircraft is designed at a cruise Mach number 0.75. Then, drag minimization with up to 42 design variables is carried out, and significant drag reduction (8.79%) has been achieved. A close examination of the optimal wing shows that the drag reduction mainly comes from shock-wave weakening on the upper surface and laminar flow extending via suppression of crossflow instability on the lower surface. Robustness of the optimal wing is investigated, and multipoint optimization is further exercised to improve the robustness to the Mach number variation. It is demonstrated that surrogate-based optimization is feasible and effective for aerodynamic shape optimization of transonic natural-laminar-flow wings.

Dynamic Centrifuge Testing Method for Large Embankment Dams: Limitations and Alternative Methods

The performance and safety of large embankment dams subjected to strong earthquake ground motion is one of the major risks in new construction projects. The design and performance of the structure are generally verified by numerical methods in most of engineering practice, and reduced scale physical modeling is often carried out for the same purpose. In general, physical model tests are designed and carried out according to rigorous scaling principles. However, it is sometimes difficult to follow these principles due to various limitations; equipment, boundary conditions, characteristics of prototype structures, etc. This paper reviews the limitations of physical modeling and its effects in seismic performance evaluation of large embankment dams. It also introduces alternative modelling and testing methods to overcome the limitations. A test with a reduced scale embankment dam model have been carried out to examine the limitations and to verify the applicability of alternative modeling method. Keywords: Physical Modeling, Centrifuge, Generalized Scaling, Embankment Dam

Shape optimisation method based on the surrogate models in the parallel asynchronous environment

This paper proposes a new optimisation method, the Parallel Asynchronous Surrogate Model (PASM) method, which is based on the surrogate models approximation and takes advantage of the asynchronous, parallel processing threads. Additionally, it introduces the Cornering technique (PASM+C), which by using values from the corners of the design space provides a rapid drop of the value of the objective function and a significant reduction of the processing time.An overview and characteristics of the main reference optimisation methods, like Particle Swarm Optimisation PSO and Genetic Algorithm (GA), is presented, together with the results of the computer experiments involving optimisation of the generic car body shape. Significant attention is devoted to the time and computational effort needed for drag minimization by using different optimisation schemes.Finally, the benefits and limitations of the proposed methods are discussed together with their potential impact on the optimisation process workflow.

Design and landing dynamic analysis of reusable landing leg for a near-space manned capsule

To improve the landing performance of a near-space manned capsule under various landing conditions, a novel landing system is designed that employs double chamber and single chamber dampers in the primary and auxiliary struts, respectively. A dynamic model of the landing system is established, and the damper parameters are determined by employing the design method. A single-leg drop test with different initial pitch angles is then conducted to compare and validate the simulation model. Based on the validated simulation model, seven critical landing conditions regarding nine crucial landing responses are found by combining the radial basis function (RBF) surrogate model and adaptive simulated annealing (ASA) optimization method. Subsequently, the adaptability of the landing system under critical landing conditions is analyzed. The results show that the simulation effectively results match the test results, which validates the accuracy of the dynamic model. In addition, all of the crucial responses under their corresponding critical landing conditions satisfy the design specifications, demonstrating the feasibility of the landing system.

Predicting the distribution of Encephalartos latifrons, a critically endangered cycad in South Africa

This study evaluates how a modelling approach to determine areas of suitable habitat for the Critically Endangered Albany cycad Encephalartos latifrons can assist in systematic conservation planning for this and other rare and threatened cycads. A map distinguishing suitable from unsuitable habitat for E. latifrons was produced and important environmental predictors (climate, geology, topography and vegetation) influencing the suitable habitat were estimated. The maximum entropy (MaxEnt) modelling technique was chosen for this study as it has consistently performed well compared with alternative modelling methods and is also an appropriate model choice when the sample size is small and locality records are relatively few. Predicted habitat suitability showed that some locations chosen for translocation and restoration of E. latifrons specimens are not suitable. This revealed that modelling suitable habitat can guide relocation and regeneration of E. latifrons and perhaps other threatened cycads with restricted distributions and few locality records. The species distribution model constructed for E. latifrons is the first reported habitat model for a Critically Endangered cycad in South Africa. The results may be incorporated into conservation planning and structured decision-making about translocations and restoration programmes involving vulnerable cycads, which are among the most threatened organisms globally.

A Novel Hybrid Algorithm for Solving Multiobjective Optimization Problems with Engineering Applications

An effective hybrid algorithm is proposed for solving multiobjective optimization engineering problems with inequality constraints. The weighted sum technique and BFGS quasi-Newton’s method are combined to determine a descent search direction for solving multiobjective optimization problems. To improve the computational efficiency and maintain rapid convergence, a cautious BFGS iterative format is utilized to approximate the Hessian matrices of the objective functions instead of evaluating them exactly. The effectiveness of the proposed algorithm is demonstrated through a comparison study, which is based on numerical examples. Meanwhile, we propose an effective multiobjective optimization strategy based on the algorithm in conjunction with the surrogate model method. This proposed strategy has been applied to the crashworthiness design of the primary energy absorption device’s crash box structure and front rail under low-speed frontal collision. The optimal results demonstrate that the proposed methodology is promising in solving multiobjective optimization problems in engineering practice.

Dynamic Reliability Design of Multicomponent Structure with Improved Weighted Regression Distributed Collaborative Surrogate Model Method

For dynamic reliability design of complex structures with multiple components, an improved weighted regression distributed collaborative surrogate model method (IWRDCSMM) is developed from the extremum response surface method (ERSM), decomposed‐coordinated thought, and improved weighted regression principle. The ERSM is used to address the dynamic reliability and sensitivity analyses of multicomponent structures and enhance the computing efficiency. The decomposed‐coordinated thought is applied to handle the relationship among multiple components. The improved weighted regression method is used to find the efficient samples with smaller errors to improve the modeling accuracy. The proposed method is first introduced for dynamic probabilistic analysis (including reliability analysis and sensitivity analysis) of multicomponent structures. The method is then mathematically modeled by adopting the efficient samples selected based on the improved weighted regression method. Finally, the radial deformation dynamic probabilistic analysis of an aeroengine turbine blisk assembled by blade and disk is accomplished, in respect of the IWRDCSMM, fluid‐thermal‐structure interaction, and the randomness of input parameters within the time domain [0, T]. The results illustrate that the reliability degree of turbine blisk radial deformation is 0.9951 when the allowable value uallow is 2.30 × 10−3 m, and all the input parameters affecting the turbine blisk radial deformation are gas temperature, angular speed, inlet velocity, outlet pressure, material density, and inlet pressure, successively. As revealed by the comparison of different methods, the IWRDCSMM has high fitting speed and simulation efficiency with the guarantee of accuracy. The efforts of this study provide a promising dynamic probabilistic analysis technique for complex structures with multiple components and enrich mechanical reliability theory.

Optimization of the aerodynamic configuration of a tubular projectile based on blind Kriging

Based on optimal Latin hypercube design for computer experiments, blind Kriging surrogate model and sequential quadratic programming method, the optimal design of the aerodynamic configuration of a 30mm tubular projectile is carried out with the use of commercial softwares, such as UG, ICEM CFD, FLUENT etc. The aerodynamic configuration has been optimized to minimize the drag coefficients at different Mach numbers and maximize the kinetic energies at given flight ranges. The optimal configuration is obtained and discussed. Finally, the similarities and differences of the flow structure and aerodynamic characteristics between the original and optimal tubular projectiles are compared. The numerical optimal method proposed in this paper for optimizing the tubular projectile can provide important guidances for the aerodynamic configuration design of projectiles.

Verification, validation, and uncertainty quantification of a sub-grid model for heat transfer in gas-particle flows with immersed horizontal cylinders

In previous work we developed and implemented a sub-grid model for the efficient simulation of heat transfer in gas-particle flows around immersed horizontal cylinders. In this study we apply verification, validation, and uncertainty quantification methods to the developed model to rigorously examine its capabilities and limitations. Numerical verification with small, unit-cell problems shows excellent transient and steady-state behavior. Validation of a bubbling bed and a turbulent bed showed good agreement with high-resolution simulations. To quantify the error of the constitutive model predictions two methods were used to calculate confidence intervals, showing an error of approximately ±20%, well within the range of typical Nusselt number approximations. The sub-grid model was applied to a conceptual pilot-scale 1 MWe carbon capture reactor to compare with alternative modeling methods. Results show fair predictions of hydrodynamics, heat transfer, and carbon capture rates with significant savings in computational runtimes.

Application of ensemble surrogates and adaptive sequential sampling to optimal groundwater remediation design at DNAPLs-contaminated sites

In this study, we aimed to develop an optimal groundwater remediation design for sites contaminated by dense non-aqueous phase liquids by using an ensemble of surrogates and adaptive sequential sampling. Compared with previous approaches, our proposed method has the following advantages: (1) a surrogate surfactant-enhanced aquifer remediation simulation model is constructed using a Gaussian process; (2) the accuracy of the surrogate model is improved by constructing ensemble surrogates using five different surrogate modelling techniques, i.e., polynomial response surface, radial basis function, Kriging, support vector regression, and Gaussian process; (3) we conducted comparisons and analyses based on 31 surrogate models derived from different combinations of the five surrogate modelling techniques; and (4) the reliability of the optimal solution was improved by implementing adaptive sequential sampling. The two proposed methods were applied to a hypothetical perchloroethylene-contaminated site in order to demonstrate their performance. The results showed that the best surrogate model integrated all five of the surrogate modelling methods, with an R2 value of 0.9913 and a root mean squared error of 0.0159, thereby demonstrating the advantage of using ensemble surrogates. In addition, the reliability of the optimization model solution was improved by adaptive sequential sampling, which avoided false solutions.

Fitting semi‐empirical drying models using a tool based on wavelet neural networks: Modeling a maize drying process

AbstractMaize drying is an important process, especially for storage and conservation. For this study, the experimental stage was carried out using a forced convection dryer with air heated at different temperature conditions (306.05–441.85 K) and flow (0.13–0.256 m3/hr), totalizing 15 drying curves. Then the performances of the classic drying kinetics methodology and the approach proposed in this paper, in which the increase in moisture content of the product with time was represented combining exponential models and neural networks based on wavelets, were compared. Good performance was obtained in predictions using the proposed approach. One of the main differentials of the methodology adopted was the obtainment of a model that has a global predictive capacity, within the range of tested operating conditions, which can be used in predicting drying curves for different operating conditions.Practical applicationsThe drying process is also one of the most widely used methods for preserving food, and has the advantage of reducing the costs of storage and transport because of the low volume and weight of the end product. During the last years, this topic has attracted a broad industrial interest, resulting in many research studies investigating the drying process. Usually, with regard to the classic approach for modeling of the drying process, the kinetics of drying curves obtained in different operating conditions is affected separately, that is, the parameters are estimated independently, resulting in different regression problems. With the classical approach, in general, it is not possible to obtain a comprehensive prediction model with regards to operating conditions. We have proposed an alternative modeling method. Aiming to obtain a modeling tool with an overall predictive ability, an approach for drying kinetics prediction that combines exponential models and neural networks was proposed. The proposed modeling method was able to predict drying curves for different operating conditions.

ANOVA-based transformed probabilistic collocation method for Bayesian data-worth analysis

Abstract Bayesian theory provides a coherent framework in quantifying the data worth of measurements and estimating unknown parameters. Nevertheless, one common problem in Bayesian methods is the considerably high computational cost since a large number of model evaluations is required in the likelihood evaluation. To address this issue, a new surrogate modeling method, i.e., ANOVA (analysis of variance)-based transformed probabilistic collocation method (ATPCM), is developed in this work. To cope with the strong nonlinearity, the model responses are transformed to the arrival times, which are then approximated with a set of low-order ANOVA components. The validity of the proposed method is demonstrated by synthetic numerical cases involving water and heat transport in the vadose zone. It is shown that, the ATPCM is more efficient than the existing surrogate modeling methods (e.g., PCM, ANOVA-based PCM and TPCM). At a very low computational cost, the ATPCM-based Bayesian data-worth analysis provides a quantitative metric in comparing different monitoring plans, and helps to improve the parameter estimation. Although the flow and heat transport in vadose zone is considered in this work, the proposed method can be equally applied in any other hydrologic problems.

An integrated beam-plate structure multi-level optimal design framework based on bi-directional evolutionary structural optimization and surrogate model

Lots of endeavors have been made to apply optimization techniques to real design problems for various engineering beam-plate structures, however, due to the limitation of traditional topological form and the difficulty of finding the optimal topology in numerous optional design plans, many beam-plate structure designs are not the optimal solution but only a feasible solution. This paper proposes an integrated optimal design framework for beam-plate structure based on combining bi-directional evolutionary structural optimization (BESO) and surrogate model method, which covers three optimization levels, as dimension optimization, topology optimization and section optimization. BESO is used for topology optimization. In order to deal with beam-plate structures, the traditional BESO method is improved by using cubic box as the unit cell instead of solid unit to construct periodic lattice structure. Requirements for the framework are discussed based on the features of beam-plate structure design process first. The proposed framework consists of automated finite element modeling module, structure optimization module and post-processing module. Usefulness of the designed framework is examined through a cantilever beam structure design.

System Margining Surrogate-Based Optimization in Post-Silicon Validation

There is an increasingly higher number of mixed-signal circuits within microprocessors. A significant portion of them corresponds to high-speed input/output (HSIO) links. Post-silicon validation of HSIO links is critical to provide a release qualification decision. One of the major challenges in HSIO electrical validation is the physical layer (PHY) tuning process, where equalization techniques are typically used to cancel any undesired effect. Current industrial practices for PHY tuning in HSIO links are very time-consuming, since they require massive laboratory measurements. On the other hand, surrogate modeling techniques allow to develop an approximation of a system response within a design space of interest. In this paper, we analyze several surrogate modeling methods and design of experiments techniques to identify the best approach to efficiently optimize a receiver equalizer. We evaluate the models performance by comparing with actual measured responses on a real server HSIO link. We then perform a surrogate-based optimization on the best model to obtain the optimal PHY tuning settings of an HSIO link. Our methodology is validated by measuring the real functional eye diagram of the physical system using the optimal surrogate model solution.

Structure-material integrated multi-objective lightweight design of the front end structure of automobile body

This paper proposes a hybrid method combining the Contribution Analysis Method, the Radial Basis Function Neutral Network (RBFNN)-Response Surface Method (RSM) hybrid surrogate modeling method, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), used for structure-material integrated multi-objective lightweight design of the front end structure of an automobile body. First, Contribution Analysis Method provides an effective approach to determine the final parts for lightweight design, and fourteen thickness variables and thirteen material variables are finally selected. Second, RBFNN-RSM hybrid surrogate modeling method successfully constructs the mapping between the input thickness-material variables and the output lightweight controlling quotas of the automobile body. Third, the MOPSO solves the multi-objective lightweight design process, considering the total mass and the torsional stiffness of the automobile body, the maximum impact acceleration at lower end of the B-pillar and the total material cost of the selected design parts as four conflicting objective functions. Accordingly, a set of Pareto-optimal solutions are obtained. Finally, a decision-making procedure based on TOPSIS method ranks all these Pareto-optimal solutions from the best to the worst for determining the best compromise solution. In addition, the proposed lightweight design method is demonstrated by the comparison among the baseline design, the actual experiment and the optimal design. The results show that the automobile body is lightweight designed with a mass reduction of 4.12 kg while other mechanical performance are well guaranteed. Hence, the proposed lightweight design method could be well applied to the lightweight design of the automobile body.

Robust aerodynamic shape design based on an adaptive stochastic optimization framework

Optimization techniques combined with uncertainty quantification are computationally expensive for robust aerodynamic optimization due to expensive CFD costs. Surrogate model technology can be used to improve the efficiency of robust optimization. In this paper, non-intrusive polynomial chaos method and Kriging model are used to construct a surrogate model that associate stochastic aerodynamic statistics with airfoil shapes. Then, global search algorithm is used to optimize the model to obtain optimal airfoil fast. However, optimization results always depend on the approximation accuracy of the surrogate model. Actually, it is difficult to achieve a high accuracy of the model in the whole design space. Therefore, we introduce the idea of adaptive strategy to robust aerodynamic optimization and propose an adaptive stochastic optimization framework. The surrogate model is updated adaptively by increasing training airfoils according to historical optimization results to guarantee the accuracy near the optimal design point, which can greatly reduce the number of training airfoils. The proposed method is applied to a robust aerodynamic shape optimization for drag minimization considering uncertainty of Mach number in transonic region. It can be concluded that the proposed method can obtain better optimal results more efficiently than the traditional robust optimization method and global surrogate model method.