Surrogate Modelling

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and inthe-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting b...

This paper presents a concise state-of-the-art review along with an exhaustive comparative investigation on surrogate models for critical comparative assessment of uncertainty in natural frequencies of composite plates on the basis of computational efficiency and accuracy. Both individual and combined variations of input parameters have been considered to account for the effect of low and high dimensional input parameter spaces in the surrogate based uncertainty quantification algorithms including the rate of convergence. Probabilistic characterization of the first three stochastic natural frequencies is carried out by using a finite element model that includes the effects of transverse shear deformation based on Mindlin’s theory in conjunction with a layer-wise random variable approach. The results obtained by different metamodels have been compared with the results of traditional Monte Carlo simulation (MCS) method for high fidelity uncertainty quantification. The crucial issue regarding influence of sampling techniques on the performance of metamodel based uncertainty quantification has been addressed as an integral part of this article.

The numerical search for the optimum shape of airfoil/wing geometry is of great interest for aircraft and turbomachinery designers. However the conventional method of design and optimization, which is to repeat the process of modifying airfoil/wing geometry data based on the flow field calculation of initial geometry, is computationally intensive and time-costly. In lieu of this, this article introduces an applicable airfoil/wing inverse design method with the help of Artificial Neural Network and airfoil/wing database, so that a properly trained network should directly provide an airfoil/wing that fits the required aerodynamical features. Repeating the process itself being avoided, the design efficiency improves. This article will present the detail of setting up the airfoil/wing inverse design method and provide the verification of the applicability of the approach.

Problem of aircraft structural components (wing, fuselage, tail) optimization is considered. Solution of this problem is very computationally intensive, since it requires at each iteration a twolevel process: first from previous iteration, an update step at full component level must be performed in order to take into account internal loads and their sensitivities in the whole structure involved by changes in local geometry. Second, numerous local analyzes are run on isolated elements (for example, super stiffeners) of structural components in order to calculate mechanical strength criteria and their sensitivities, depending on current internal loads. An optimization step is then performed from combined global-local sensitivities. This bi-level global-local optimization process is then repeated until convergence of load distribution in the whole structure. Numerous calculations of mechanical strength criteria are necessary for local analyzes, resulting in great increase of the time b...

This study focuses on the development of a statistical model for buildings with infilled reinforced concrete frames. The cornerstone of this study is the nonlinear numerical model of a school building in Nepal. The model is developed based on the ASCE 14-17 guidelines, and it is extensively validated with field data. Then, it is used in a series of parametric studies conducted to identify the influential material parameters, and in incremental dynamic analyses conducted to provide data for the calibration of the statistical model. The three-staged least square statistical modeling approach is employed to relate the influential material parameters and ground motion intensity measures with important response quantities related to the peak and residual first story drift ratios.

This paper presents an enhanced version and the validation of a recently proposed methodology for earthquake-induced damage detection and localization in masonry towers by using long-term vibration monitoring data. The proposed enhanced method is based on continuous operational modal analysis through stochastic subspace identification, dynamic multiple linear regressive analysis to remove the effects of changing environmental conditions and finite element (FE) model updating. Any anomalous frequency deviation from normal conditions resulting from an earthquake triggers the damage localization process. This task is performed by solving an inverse FE model calibration problem, where equivalent elastic properties of macrostructural elements are identified by minimizing an objective function considering experimentally identified and numerically predicted damage induced decays in natural frequencies and changes in eigenvector components. To minimize the computational effort of this calibration procedure, a quadratic surrogate model is constructed using a tuned numerical FE model of the structure. The methodology is validated through application to the "Sciri Tower", an historic civic masonry tower located in Perugia, Italy, that has been continuously monitored by the authors for more than 1 year. The validation is carried out by using simulated damage scenarios and a set of real far-field earthquake data and is based on a FE model of the tower including surrounding buildings , calibrated on the basis of the measured data from ambient vibration tests. The results demonstrate that the proposed procedure is capable of correctly detecting and localizing earthquake-induced damages.

Juan Redmond presents an inferential conception of scientific representation based on the ludic perspective of dialogical pragmatism. He conceives of his 3 proposal as an answer to the question How models are used to represent the world?" Consequently, he lines up with the host of pragmatic approaches that stress the importance of the notion of use and users for representing and modeling. The main point of his proposal is that users or agents use models to represent their targets doing inferences concerning those targets on the basis of reasoning dialogically about the models.

Surrogate modelling is becoming a necessary modelling tool in engineering analysis and synthesis. This is, especially, true when mathematical models are not available. The capability of response surface methodology is explored with single unconstrained/constrained linear and non-linear problems. Problems with special features or with highly non-linear nature are dealt with. A further development with multi-objective problems starts with bi-objective functions and continues to deal with higher number of objective functions. A simple multi-objective problem is taken to initiate the development. Orthogonal arrays and response surface models are combined and used to explore the sets of Pareto Frontiers. One important result is that various array sizes are able to explore the Pareto set at no or little cost change with comparable accuracy. Except for one array, the optimum solution is typical for all arrays employed. One development is using the first derivative of the two objective functions to obtain the starting point for model construction. Design of experiments and analysis of variance (ANOVA) are employed to verify the relative significance of variables. Results of ANOVA guide the modeller in the model building process. We attempt to achieve a 'local accurate model' rather than a 'global accurate model'. Computational experience with different classes of problems is given.

Organizational change management is concerned with realizing strategies using models, methods and prescriptions that seek to guide the three key elements of strategic management process: strategic analysis (what is our current configuration?), strategic choice (what is our desired configuration?) and strategic implementation (how to realize the desired configuration?). To address these strategic management issues, this paper presents an evolutionary and structural approach that uses a classification technique (cladistics) and a method from algebraic topology (q-analysis) to identify and understand different organizational configurations, along with the relationships and connectivity (change route) between a current and desired configuration. A simple example data set is used to introduce and describe the cladistic and q-analysis methods. This is followed by an application of the technique to a data set from the automotive assembly industry.

The traditional crashworthiness optimisation problem is augmented by inclusion of additional design criterion associated with vehicle vibration characteristics. Through finite element (FE) simulations, full frontal, offset frontal and side crashes of a full vehicle model are analysed for peak acceleration, intrusion distance and internal energy. Moreover, the FE crash model of the vehicle is modified to develop a vibration-analysis model for evaluation of natural frequencies and mode shapes. Design of computer experiments through Latin hypercube sampling is used to sample the design space defined by the wall thicknesses of 22 parts. Radial basis functions are used to generate separate surrogate models for the selected crash responses measured at multiple sites as well as the fundamental natural frequencies in bending and torsion. A nonlinear surrogate-based mass minimisation problem is formulated and solved under crash and vibration constraints with the results verified through FE simulations. The optimum vehicle design under multiple design criteria is presented and the vehicle's characteristics are compared with those of the baseline design as well as those associated with the optimum design based on crash responses alone.

This paper presents a novel mechanism to adapt surrogateassisted population-based algorithms. This mechanism is
applied to ACM-ES, a recently proposed surrogate-assisted
variant of CMA-ES. The resulting algorithm, s∗ACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters.
Both heuristics significantly improve the quality of the
surrogate model, yielding a significant speed-up of
s∗ACMES compared to the ACM-ES and CMA-ES baselines. The
empirical validation of s∗ACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems

A Simulation Based Design Optimization method for marine propellers design using a two-fidelity levels metamodel for global design space exploration and optimization is presented. Response surfaces are built using the co-Kriging approximation, i.e. a multi-output Gaussian process that combines large low-fidelity dataset with few, costly, high-fidelity data. The method is applied for the hydrodynamic shape optimization of the E779A propeller using, as fidelity levels, two different physical models for the propeller performances prediction, namely an inviscid, potential based Boundary Element Method (low-fidelity) and a viscous, finite volume RANS solver (high-fidelity). Results demonstrate the feasibility of multi-objective, constrained, design procedures, like those involving marine propellers, using these multi-fidelity response surfaces. At the same time, the need of good correlations between low-and high-fidelity data feeding the response surfaces is highlighted as a requisite for robust and reliable predictions using these approximated methods.

Prior work has shown Convolutional Neural Networks (CNNs) trained on surrogate Computer Aided Design (CAD) models are able to detect and classify real-world artefacts from photographs. The applications of which support twinning of digital and physical assets in design, including rapid extraction of part geometry from model repositories, information search & retrieval and identifying components in the field for maintenance, repair, and recording. The performance of CNNs in classification tasks have been shown dependent on training data set size and number of classes. Where prior works have used relatively small surrogate model data sets (< 100 models), the question remains as to the ability of a CNN to differentiate between models in increasingly large model repositories. This paper presents a method for generating synthetic image data sets from online CAD model repositories, and further investigates the capacity of an off-the-shelf CNN architecture trained on synthetic data to classify models as class size increases. 1,000 CAD models were curated and processed to generate large scale surrogate data sets, featuring model coverage at steps of 10 • , 30 • , 60 • , and 120 • degrees. The findings demonstrate the capability of computer vision algorithms to classify artefacts in model repositories of up to 200, beyond this point the CNN's performance is observed to deteriorate significantly, limiting its present ability for automated twinning of physical to digital artefacts. Although, a match is more often found in the top-5 results showing potential for information search and retrieval on large repositories of surrogate models.

Surrogate modelling is becoming a necessary modelling tool in engineering analysis and synthesis. This is, especially, true when mathematical models are not available. The capability of response surface methodology is explored with single unconstrained/constrained linear and non-linear problems. Problems with special features or with highly non-linear nature are dealt with. A further development with multi-objective problems starts with bi-objective functions and continues to deal with higher number of objective functions. A simple multi-objective problem is taken to initiate the development. Orthogonal arrays and response surface models are combined and used to explore the sets of Pareto Frontiers. One important result is that various array sizes are able to explore the Pareto set at no or little cost change with comparable accuracy. Except for one array, the optimum solution is typical for all arrays employed. One development is using the first derivative of the two objective functions to obtain the starting point for model construction. Design of experiments and analysis of variance (ANOVA) are employed to verify the relative significance of variables. Results of ANOVA guide the modeller in the model building process. We attempt to achieve a 'local accurate model' rather than a 'global accurate model'. Computational experience with different classes of problems is given.

Current design and analysis increasingly uses computer simulations to evaluate candidate designs. In such setups there will often exist candidate designs for the simulation fails thereby hampering the process. To effectively handle this obstacle this study presents an algorithm which uses ensembles of both metamodels and classifiers to predict which candidate designs are expected to cause such failures and to divert the search accordingly. An extensive numerical evaluation shows the effectiveness of the proposed algorithm.

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and in-the-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting both the design points and the required fidelity level via an active learning approach. This is based on the lower confidence bounding method, which combines performance prediction and associated uncertainty to select the most promising design regions. The fidelity levels are selected considering the benefit-cost ratio associated with their use in the training. The method’s performance is assessed and discussed using four analytical tests and three SDD problems based on computational fluid dynamics (CFD) simulations, namely the shape optimization of a NACA hydrofoil, the DTMB 5415 destroyer, and a roll-on/roll-off passenger ferry. Fidelity levels are provided by both adaptive grid refinement and multi-grid resolution approaches. Under the assumption of a limited budget of function evaluations, the proposed MF method shows better performance in comparison with the model trained by high-fidelity evaluations only.

Electric drive mining trucks, which are of heavy loads and high efficiencies, are widely used for off-road applications such as large-scale open-pit metal mines, coal mines, and water conservancy constructions. Unlike on-road trucks, off-road mining trucks usually work with fixed routes and in the mode of full-load uphill and no-load downhill along a high slope. The recoverable potential energy accounts for more than one-third of the uphill driving work. If this part of the energy can be recovered and reused, the vehicle fuel consumption and CO₂ emission can be significantly reduced.
As most of China’s large open-pit mines are located in cold areas, the low temperature will aggravate the degradation mechanism of the batteries, resulting in the high cost of the mining dump truck with a battery energy storage system. Therefore, it is necessary to develop a new energy storage system with large capacity, high power, high efficiency, and low-temperature resistance.
This paper takes the high-capacity composite pressure energy storage systems as the research objects, analyzes the influence of layouts on the performance of energy storage systems, and puts forward the method of using the oil-circulating hydro-pneumatic energy storage system to recover the downhill potential energy of mining trucks through layout comparison study; The thermal process model of circulating hydro-pneumatic energy storage system is established, its thermal effect mechanism is explored, and an effective coupling heat dissipation method with low energy consumption is proposed; Then, the multi-objective nested optimization method based on the adaptive hybrid surrogate model is used to obtain the optimal structure of circulating hydro-pneumatic energy storage system under the corresponding optimal energy management strategy with less computation cost; Finally, through the real vehicle test of the electric mining truck and the bench test of its composite powertrain, it is verified that the optimal structure and energy management strategy of the system can effectively reduce the fuel consumption and CO₂ emission of the mining truck.
Firstly, based on the hydraulic and compressed air energy storage systems, four basic hydro-pneumatic energy storage layouts are established: open volume layout, open mass layout, closed volume layout, and closed mass layout. Taking energy density and minimum specific power as the evaluation indicators, the energy and power characteristics of four basic layouts are analyzed, and their vehicle applicability is evaluated. According to the demand for braking energy recovery and energy storage of mining trucks in cold areas, the circulating hydro-pneumatic energy storage system model is established. The analysis results show that the system has good power and energy characteristics at the same time, which provides a feasible method for energy recovery and utilization of large mining trucks in cold environments.
Aiming at the overheating problem of circulating hydro-pneumatic energy storage system during high-capacity and high-power energy recovery, the thermal process model of the energy storage system is established, the factors that lead to overheating are explored, and the coupling heat dissipation method is proposed. By combining the surplus cold potential in the downhill process and the surplus heat potential in the uphill process of the mining truck, the temperature potential coupling heat dissipation is realized in the way of low energy consumption. The calculation results show that the maximum temperature of hydraulic oil is reduced to 52.79℃, and 28% of heat can be released through the cooling system, which effectively solves the overheating problem in the energy storage process of circulating hydro-pneumatic energy storage system.
Aiming at the efficient energy recovery and utilization of the system in the uphill process of the mining truck, an energy management strategy of the circulating hydro-pneumatic energy storage system is proposed. Aiming at the minimum fuel consumption of the whole vehicle, the power distribution strategy of the composite powertrain is obtained based on the dynamic programming algorithm. Through the real vehicle test of the electric mining truck under its working conditions and the bench test of its composite powertrain, it is verified that the energy management strategy can effectively reduce the fuel consumption of the mining truck.
Finally, to further improve the energy density of the circulating hydro-pneumatic energy storage system, the nested optimization method based on the adaptive hybrid surrogate model is adopted by using the Pareto optimal solution set. And combining the contradictory objectives of energy density and energy storage efficiency into the global normalized optimization objective, the optimal structure of the circulating hydro-pneumatic energy storage is obtained with less computation cost, which provides a basis for the design and application of the energy storage system for mining trucks.

Exploration of design tradeoffs for aerodynamic surfaces requires solving of multi-objective optimization (MOO) problems. The major bottleneck here is the time-consuming evaluations of the computational fluid dynamics (CFD) model used to capture the nonlinear physics involved in designing aerodynamic surfaces. This, in conjunction with a large number of simulations necessary to yield a set of designs representing the best possible tradeoffs between conflicting objectives (referred to as a Pareto front), makes CFD-driven MOO very challenging. This paper presents a computationally efficient methodology aimed at expediting the MOO process for aerodynamic design problems. The extreme points of the Pareto front are obtained quickly using single-objective optimizations. Starting from these extreme points, identification of an initial set of Pareto-optimal designs is carried out using a sequential domain patching algorithm. Refinement of the Pareto front, originally obtained at the level of the low-fidelity CFD model, is carried out using local response surface approximations and adaptive corrections. The proposed algorithm is validated using a few multi-objective analytical problems and an aerodynamic problem involving MOO of two-dimensional transonic airfoil shapes where the figures of interest are the drag and pitching moment coefficients. A multifidelity model is constructed using CFD model and control points parameterizing the shape of the airfoil. The results demonstrate that an entire or a part of the Pareto front can be obtained at a low cost when considering up to eight design variables.

Genetic algorithms are efficient global optimizers, but they are weak in performing finegrained local searches. In this paper, the local search capability of genetic algorithm is improved by hybridizing real coded genetic algorithm with 'uniform random' local search to form a hybrid real coded genetic algorithm termed 'RCGAu'. The incorporated local technique is applied to all newly created offspring so that each offspring solution is given the opportunity to effectively search its local neighborhood for the best local optimum. Numerical experiments show that the performance of RCGA is remarkably improved by the uniform random local search technique.

Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low-and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high-and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES-RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES-RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

An essential issue in surrogate model-based reliability analysis is the selection of training points. Approaches such as efficient global reliability analysis (EGRA) and adaptive Kriging Monte Carlo simulation (AK-MCS) methods have been developed to adaptively select training points that are close to the limit state. Both the learning functions and convergence criteria of selecting training points in EGRA and AK-MCS are defined from the perspective of individual responses at Monte Carlo samples. This causes two problems:

The problem of pumping optimization of coastal unconfined aquifers is investigated. The Sequential Quadratic Programming (SQP) optimization method is combined with a numerical flow model based on the sharp interface assumption and Ghyben-Herzberg approximation. The objective is to maximize the total pumping rate, considering aquifer spatial variability and drought conditions due to climate changes, while protecting the aquifer from seawater intrusion. Using Monte-Carlo simulation, optimal pumping rates were calculated for different statistical properties of hydraulic conductivity and for various drought recharge scenarios. The results indicate that the maximum allowed pumping rates are significantly affected by the variance and correlation length of hydraulic conductivity random fields while recharge reduction leads to a significant reduction of maximum pumping.

Water resource management (WRM) through dams or reservoirs is worldwide necessary to support key human-related activities, ranging from hydropower production to water allocation and flood risk mitigation. Designing of reservoir operations aims primarily to fulfill the main purpose (or purposes) for which the structure has been built. However, it is well known that reservoirs strongly influence river geomorphic processes, causing sediment deficits downstream, altering water, and sediment fluxes, leading to riverbed incision and causing infrastructure instability and ecological degradation. We propose a framework that, by combining physically based modeling, surrogate modeling techniques, and multiobjective (MO) optimization, allows to include fluvial geomorphology into MO optimization whose main objectives are the maximization of hydropower revenue and the minimization of riverbed degradation. The case study is a run-of-the-river power plant on the River Po (Italy). A 1-D mobile-bed hydro-morphological model simulated the riverbed evolution over a 10 year horizon for alternatives operation rules of the power plant. The knowledge provided by such a physically based model is integrated into a MO optimization routine via surrogate modeling using the response surface methodology. Hence, this framework overcomes the high computational costs that so far hindered the integration of river geomorphology into WRM. We provided numerical proof that river morphologic processes and hydropower production are indeed in conflict but that the conflict may be mitigated with appropriate control strategies.

Genetic algorithms are efficient global optimizers, but they are weak in performing finegrained local searches. In this paper, the local search capability of genetic algorithm is improved by hybridizing real coded genetic algorithm with 'uniform random' local search to form a hybrid real coded genetic algorithm termed 'RCGAu'. The incorporated local technique is applied to all newly created offspring so that each offspring solution is given the opportunity to effectively search its local neighborhood for the best local optimum. Numerical experiments show that the performance of RCGA is remarkably improved by the uniform random local search technique.

Genetic algorithms are efficient global optimizers, but they are weak in performing finegrained local searches. In this paper, the local search capability of genetic algorithm is improved by hybridizing real coded genetic algorithm with 'uniform random' local search to form a hybrid real coded genetic algorithm termed 'RCGAu'. The incorporated local technique is applied to all newly created offspring so that each offspring solution is given the opportunity to effectively search its local neighborhood for the best local optimum. Numerical experiments show that the performance of RCGA is remarkably improved by the uniform random local search technique.

Organizational change management is concerned with realizing strategies using models, methods and prescriptions that seek to guide the three key elements of strategic management process: strategic analysis (what is our current configuration?), strategic choice (what is our desired configuration?) and strategic implementation (how to realize the desired configuration?). To address these strategic management issues, this paper presents an evolutionary and structural approach that uses a classification technique (cladistics) ...