Riccardo Pellegrini - Academia.edu (original) (raw)

Papers by Riccardo Pellegrini

The paper presents a study on four adaptive sampling methods of a multifidelity global metamodel ... more The paper presents a study on four adaptive sampling methods of a multifidelity global metamodel for expensive computer simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference between highand low-fidelity simulations. The multi-fidelity metamodel is trained selecting the fidelity to sample based on the prediction uncertainty and the computational cost ratio between the highand low-fidelity evaluations. The adaptive sampling methods are applied to the CFD-shape optimization of a NACA hydrofoil. The performance of the sampling methods is assessed in terms of convergence of the maximum uncertainty and the minimum of the function.

The paper presents some recent trends in multi-fidelity digital modelling for marine engineering ... more The paper presents some recent trends in multi-fidelity digital modelling for marine engineering applications. Digital modelling is achieved by machine learning methods, namely multi-fidelity surrogate models, trained by computational fluid dynamics (CFD). Adaptative approaches are discussed for radial basis functions and Gaussian process models. Simulation-based design optimisation problems are presented to discuss the use and effects of different adaptivity concepts: (1) adaptive refinement of the computational-domain discretization in CFD; (2) adaptive sampling of the design/operational space; (3) adaptive selection of the fidelity used for the surrogate model training in a multi-fidelity environment; (4) adaptivity of the models to noise. Model adaptation allows for the efficient training of machine learning models, reducing the computational cost associated to building the training sets and improving the overall accuracy of the digital representation.

AIAA AVIATION 2021 FORUM, 2021

Despite the increased computational resources, the simulation-based design optimization (SBDO) pr... more Despite the increased computational resources, the simulation-based design optimization (SBDO) procedure can be very expensive from a computational viewpoint, especially if highfidelity solvers are required. Multi-fidelity metamodels have been successfully applied to reduce the computational cost of the SBDO process. In this context, the paper presents the performance assessment of an adaptive multi-fidelity metamodel based on a Gaussian process regression (MF-GPR) for noisy data. The MF-GPR is developed to: (i) manage an arbitrary number of fidelity levels, (ii) deal with objective function evaluations affected by noise, and (iii) improve its fitting accuracy by adaptive sampling. Multi-fidelity is achieved by bridging a low-fidelity metamodel with metamodels of the error between successive fidelity levels. The MF-GPR handles the numerical noise through regression. The adaptive sampling method is based on the maximum prediction uncertainty and includes rules to automatically select the fidelity to sample. The MF-GPR performance are assessed on a set of five analytical benchmark problems affected by noisy objective function evaluations. Since the noise introduces randomness in the evaluation of the objective function, a statistical analysis approach is adopted to assess the performance and the robustness of the MF-GPR. The paper discusses the efficiency and effectiveness of the MF-GPR in globally approximating the objective function and identifying the global minimum. One, two, and three fidelity levels are used. The results of the statistical analysis show that the use of three fidelity levels achieves a more accurate global representation of the noise-free objective function compared to the use of one or two fidelities.

Machine Learning, Optimization, and Big Data, Dec 21, 2017

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-b... more A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) lineasearch method. Six MODHA formulations are discussed, based on two MODPSO formulations and three DFMO activation criteria. Forty five analytical test problems are solved, with two/three objectives and one to twelve variables. The performance is evaluated by two multi-objective metrics. The most promising formulations are finally applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions and compared to MODPSO and DFMO, showing promising results.

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

A multi-fidelity global metamodel is presented for uncertainty quantification of computationally ... more A multi-fidelity global metamodel is presented for uncertainty quantification of computationally expensive simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high-and low-fidelity simulations. The metamodel is based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are added where the prediction uncertainty is largest, according to an adaptive sampling procedure. The prediction uncertainty of both the low-fidelity and the error metamodel are considered for the adaptive training of the low-and high-fidelity metamodels, respectively. The method is applied to a steady fluid-structure interaction (FSI) problem of a 3D NACA 0009 stainless steel hydrofoil. Two functions are considered simultaneously, namely lift and drag coefficients, versus angle of attack and Reynolds number. Two problems are presented: in the first problem the high-fidelity evaluations are obtained through steady FSI computer simulations, whereas in the second problem they are given by available experimental data from literature. Low-fidelity evaluations are provided in both cases by steady hydrodynamic simulations. The overall uncertainty of the multi-fidelity metamodel is used as a convergence criterion.

Computational Optimization and Applications, 2017

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems... more The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of "hard" nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

2016 IEEE Congress on Evolutionary Computation (CEC), 2016

The paper presents a multi-fidelity global metamodel for expensive computer simulations, develope... more The paper presents a multi-fidelity global metamodel for expensive computer simulations, developed as an essential part of efficient simulation-based design optimization under uncertainty. High- and low-fidelity solvers are managed through a multi-fidelity adaptive sampling procedure. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high- and low-fidelity simulations. The metamodels are based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are placed where the prediction uncertainty is maximum. The prediction uncertainty of both the low-fidelity and the error metamodel is considered for the adaptive refinement of the low- and high-fidelity training set, respectively. The method is demonstrated through three analytical test problems and one simple industrial application in ship hydrodynamics. The fitting error of the multi-fidelity metamodel is used as evaluation metric. The comparison with a high-fidelity-trained metamodel shows the effectiveness of the present method.

Engineering Optimization 2014, 2014

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean ... more A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal fourdimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivative-free multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multi-objective extensions of the deterministic particle swarm optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness.

A multi-fidelity (MF) active learning method is presented for design optimization problems charac... more 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...

Mathematics

The paper presents a multi-fidelity extension of a local line-search-based derivative-free algori... more The paper presents a multi-fidelity extension of a local line-search-based derivative-free algorithm for nonsmooth constrained optimization (MF-CS-DFN). The method is intended for use in the simulation-driven design optimization (SDDO) context, where multi-fidelity computations are used to evaluate the objective function. The proposed algorithm starts using low-fidelity evaluations and automatically switches to higher-fidelity evaluations based on the line-search step length. The multi-fidelity algorithm is driven by a suitably defined threshold and initialization values for the step length, which are associated to each fidelity level. These are selected to increase the accuracy of the objective evaluations while progressing to the optimal solution. The method is demonstrated for a multi-fidelity SDDO benchmark, namely pertaining to the hull-form optimization of a destroyer-type vessel, aiming at resistance minimization in calm water at fixed speed. Numerical simulations are based o...

An adaptive-fidelity approach to metamodeling from noisy data is presented for design-space explo... more An adaptive-fidelity approach to metamodeling from noisy data is presented for design-space exploration and design optimization. Computational fluid dynamics (CFD) simulations with different numerical accuracy (spatial discretization) provides metamodel training sets affected by unavoidable numerical noise. The-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of differences (errors) between higher-fidelity levels whose hierarchy needs to be provided. The approach encompasses two core metamodeling techniques, namely: i) stochastic radial-basis functions (SRBF) and ii) Gaussian process (GP). The adaptivity stems from the sequential training procedure and the auto-tuning capabilities of the metamodels. The method is demonstrated for an analytical test problem and a CFD-based optimization of a NACA airfoil, where the fidelity levels are defined by an adaptive grid refinement technique of a Reynolds-averaged Navier-Stokes (RANS) solver...

The aim of metamodelling in CFD-based automatic shape optimization is to replace expensive CFD co... more The aim of metamodelling in CFD-based automatic shape optimization is to replace expensive CFD computations in the optimization process by evaluations of a cheap surrogate model, created from a limited training set of simulations. Multi-fidelity metamodels [1] make this process even more efficient by basing a part of the metamodel on inexpensive low-fidelity simulations and introducing a correction based on a few high-fidelity simulations. To adaptively define the training sets of the low-fidelity and correction metamodels, different sampling strategies can be used [2]. However, the CFD results on which the metamodels are based contain numerical errors. Especially if new grids are generated for each simulation, the numerical errors for two similar geometries may be different. These differences manifest themselves as numerical noise in the training sets for the metamodels. Adaptive sampling strategies which determine new training points by evaluating the uncertainty of the metamodel,...

This paper presents a comparison of two methods for the forward uncertainty quantification (UQ) o... more This paper presents a comparison of two methods for the forward uncertainty quantification (UQ) of complex industrial problems. Specifically, the performance of Multi-Index Stochastic Collocation (MISC) and adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF) surrogates is assessed for the UQ of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties, namely the ship speed and draught. The estimation of expected value, standard deviation, and probability density function of the (model-scale) resistance is presented and discussed obtained by multi-grid Reynolds averaged Navier-Stokes (RANS) computations. Both MISC and SRBF use as multi-fidelity levels the evaluations on different grid levels, intrinsically employed by the RANS solver for multi-grid acceleration; four grid levels are used here, obtained as isotropic coarsening of the initial finest mesh. The results suggest that MISC could be preferred when only limited data...

ArXiv, 2021

This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quanti... more This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, kurtosis), and the probability density function for such quantity of interest (QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index Stochastic Collocation (MISC) method and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF) algorithm. The QoI is evaluated via computational fluid dynamics simulations, which are performed with the in-house unsteady Reynolds-Averaged NavierStokes (RANS) multi-grid solver χnavis. The different fidelities employed by both methods are obtained by stopping the RANS solver at different grid leve...

2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Mathematics

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algori... more The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based o...

Applied Soft Computing

Global derivative-free deterministic algorithms are particularly suitable for simulation-based op... more Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization , where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive , thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-b... more A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) linesearch method. Six MODHA formulations are discussed, based on two MODPSO formulations and three DFMO activation criteria. Forty five analytical test problems are solved, with two/three objectives and one to twelve variables. The performance is evaluated by two multi-objective metrics. The most promising formulations are finally applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions and compared to MODPSO and DFMO, showing promising results.

The paper presents a study on four adaptive sampling methods of a multifidelity global metamodel ... more The paper presents a study on four adaptive sampling methods of a multifidelity global metamodel for expensive computer simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference between highand low-fidelity simulations. The multi-fidelity metamodel is trained selecting the fidelity to sample based on the prediction uncertainty and the computational cost ratio between the highand low-fidelity evaluations. The adaptive sampling methods are applied to the CFD-shape optimization of a NACA hydrofoil. The performance of the sampling methods is assessed in terms of convergence of the maximum uncertainty and the minimum of the function.

The paper presents some recent trends in multi-fidelity digital modelling for marine engineering ... more The paper presents some recent trends in multi-fidelity digital modelling for marine engineering applications. Digital modelling is achieved by machine learning methods, namely multi-fidelity surrogate models, trained by computational fluid dynamics (CFD). Adaptative approaches are discussed for radial basis functions and Gaussian process models. Simulation-based design optimisation problems are presented to discuss the use and effects of different adaptivity concepts: (1) adaptive refinement of the computational-domain discretization in CFD; (2) adaptive sampling of the design/operational space; (3) adaptive selection of the fidelity used for the surrogate model training in a multi-fidelity environment; (4) adaptivity of the models to noise. Model adaptation allows for the efficient training of machine learning models, reducing the computational cost associated to building the training sets and improving the overall accuracy of the digital representation.

AIAA AVIATION 2021 FORUM, 2021

Despite the increased computational resources, the simulation-based design optimization (SBDO) pr... more Despite the increased computational resources, the simulation-based design optimization (SBDO) procedure can be very expensive from a computational viewpoint, especially if highfidelity solvers are required. Multi-fidelity metamodels have been successfully applied to reduce the computational cost of the SBDO process. In this context, the paper presents the performance assessment of an adaptive multi-fidelity metamodel based on a Gaussian process regression (MF-GPR) for noisy data. The MF-GPR is developed to: (i) manage an arbitrary number of fidelity levels, (ii) deal with objective function evaluations affected by noise, and (iii) improve its fitting accuracy by adaptive sampling. Multi-fidelity is achieved by bridging a low-fidelity metamodel with metamodels of the error between successive fidelity levels. The MF-GPR handles the numerical noise through regression. The adaptive sampling method is based on the maximum prediction uncertainty and includes rules to automatically select the fidelity to sample. The MF-GPR performance are assessed on a set of five analytical benchmark problems affected by noisy objective function evaluations. Since the noise introduces randomness in the evaluation of the objective function, a statistical analysis approach is adopted to assess the performance and the robustness of the MF-GPR. The paper discusses the efficiency and effectiveness of the MF-GPR in globally approximating the objective function and identifying the global minimum. One, two, and three fidelity levels are used. The results of the statistical analysis show that the use of three fidelity levels achieves a more accurate global representation of the noise-free objective function compared to the use of one or two fidelities.

Machine Learning, Optimization, and Big Data, Dec 21, 2017

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-b... more A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) lineasearch method. Six MODHA formulations are discussed, based on two MODPSO formulations and three DFMO activation criteria. Forty five analytical test problems are solved, with two/three objectives and one to twelve variables. The performance is evaluated by two multi-objective metrics. The most promising formulations are finally applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions and compared to MODPSO and DFMO, showing promising results.

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

A multi-fidelity global metamodel is presented for uncertainty quantification of computationally ... more A multi-fidelity global metamodel is presented for uncertainty quantification of computationally expensive simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high-and low-fidelity simulations. The metamodel is based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are added where the prediction uncertainty is largest, according to an adaptive sampling procedure. The prediction uncertainty of both the low-fidelity and the error metamodel are considered for the adaptive training of the low-and high-fidelity metamodels, respectively. The method is applied to a steady fluid-structure interaction (FSI) problem of a 3D NACA 0009 stainless steel hydrofoil. Two functions are considered simultaneously, namely lift and drag coefficients, versus angle of attack and Reynolds number. Two problems are presented: in the first problem the high-fidelity evaluations are obtained through steady FSI computer simulations, whereas in the second problem they are given by available experimental data from literature. Low-fidelity evaluations are provided in both cases by steady hydrodynamic simulations. The overall uncertainty of the multi-fidelity metamodel is used as a convergence criterion.

Computational Optimization and Applications, 2017

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems... more The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of "hard" nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

2016 IEEE Congress on Evolutionary Computation (CEC), 2016

The paper presents a multi-fidelity global metamodel for expensive computer simulations, develope... more The paper presents a multi-fidelity global metamodel for expensive computer simulations, developed as an essential part of efficient simulation-based design optimization under uncertainty. High- and low-fidelity solvers are managed through a multi-fidelity adaptive sampling procedure. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high- and low-fidelity simulations. The metamodels are based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are placed where the prediction uncertainty is maximum. The prediction uncertainty of both the low-fidelity and the error metamodel is considered for the adaptive refinement of the low- and high-fidelity training set, respectively. The method is demonstrated through three analytical test problems and one simple industrial application in ship hydrodynamics. The fitting error of the multi-fidelity metamodel is used as evaluation metric. The comparison with a high-fidelity-trained metamodel shows the effectiveness of the present method.

Engineering Optimization 2014, 2014

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean ... more A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal fourdimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivative-free multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multi-objective extensions of the deterministic particle swarm optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness.

A multi-fidelity (MF) active learning method is presented for design optimization problems charac... more 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...

Mathematics

The paper presents a multi-fidelity extension of a local line-search-based derivative-free algori... more The paper presents a multi-fidelity extension of a local line-search-based derivative-free algorithm for nonsmooth constrained optimization (MF-CS-DFN). The method is intended for use in the simulation-driven design optimization (SDDO) context, where multi-fidelity computations are used to evaluate the objective function. The proposed algorithm starts using low-fidelity evaluations and automatically switches to higher-fidelity evaluations based on the line-search step length. The multi-fidelity algorithm is driven by a suitably defined threshold and initialization values for the step length, which are associated to each fidelity level. These are selected to increase the accuracy of the objective evaluations while progressing to the optimal solution. The method is demonstrated for a multi-fidelity SDDO benchmark, namely pertaining to the hull-form optimization of a destroyer-type vessel, aiming at resistance minimization in calm water at fixed speed. Numerical simulations are based o...

An adaptive-fidelity approach to metamodeling from noisy data is presented for design-space explo... more An adaptive-fidelity approach to metamodeling from noisy data is presented for design-space exploration and design optimization. Computational fluid dynamics (CFD) simulations with different numerical accuracy (spatial discretization) provides metamodel training sets affected by unavoidable numerical noise. The-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of differences (errors) between higher-fidelity levels whose hierarchy needs to be provided. The approach encompasses two core metamodeling techniques, namely: i) stochastic radial-basis functions (SRBF) and ii) Gaussian process (GP). The adaptivity stems from the sequential training procedure and the auto-tuning capabilities of the metamodels. The method is demonstrated for an analytical test problem and a CFD-based optimization of a NACA airfoil, where the fidelity levels are defined by an adaptive grid refinement technique of a Reynolds-averaged Navier-Stokes (RANS) solver...

The aim of metamodelling in CFD-based automatic shape optimization is to replace expensive CFD co... more The aim of metamodelling in CFD-based automatic shape optimization is to replace expensive CFD computations in the optimization process by evaluations of a cheap surrogate model, created from a limited training set of simulations. Multi-fidelity metamodels [1] make this process even more efficient by basing a part of the metamodel on inexpensive low-fidelity simulations and introducing a correction based on a few high-fidelity simulations. To adaptively define the training sets of the low-fidelity and correction metamodels, different sampling strategies can be used [2]. However, the CFD results on which the metamodels are based contain numerical errors. Especially if new grids are generated for each simulation, the numerical errors for two similar geometries may be different. These differences manifest themselves as numerical noise in the training sets for the metamodels. Adaptive sampling strategies which determine new training points by evaluating the uncertainty of the metamodel,...

This paper presents a comparison of two methods for the forward uncertainty quantification (UQ) o... more This paper presents a comparison of two methods for the forward uncertainty quantification (UQ) of complex industrial problems. Specifically, the performance of Multi-Index Stochastic Collocation (MISC) and adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF) surrogates is assessed for the UQ of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties, namely the ship speed and draught. The estimation of expected value, standard deviation, and probability density function of the (model-scale) resistance is presented and discussed obtained by multi-grid Reynolds averaged Navier-Stokes (RANS) computations. Both MISC and SRBF use as multi-fidelity levels the evaluations on different grid levels, intrinsically employed by the RANS solver for multi-grid acceleration; four grid levels are used here, obtained as isotropic coarsening of the initial finest mesh. The results suggest that MISC could be preferred when only limited data...

ArXiv, 2021

This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quanti... more This paper presents a comparison of two multi-fidelity methods for the forward uncertainty quantification of a naval engineering problem. Specifically, we consider the problem of quantifying the uncertainty of the hydrodynamic resistance of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties (ship speed and payload). The first four statistical moments (mean, variance, skewness, kurtosis), and the probability density function for such quantity of interest (QoI) are computed with two multi-fidelity methods, i.e., the Multi-Index Stochastic Collocation (MISC) method and an adaptive multi-fidelity Stochastic Radial Basis Functions (SRBF) algorithm. The QoI is evaluated via computational fluid dynamics simulations, which are performed with the in-house unsteady Reynolds-Averaged NavierStokes (RANS) multi-grid solver χnavis. The different fidelities employed by both methods are obtained by stopping the RANS solver at different grid leve...

2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Mathematics

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algori... more The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based o...

Applied Soft Computing

Global derivative-free deterministic algorithms are particularly suitable for simulation-based op... more Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization , where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive , thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-b... more A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) linesearch method. Six MODHA formulations are discussed, based on two MODPSO formulations and three DFMO activation criteria. Forty five analytical test problems are solved, with two/three objectives and one to twelve variables. The performance is evaluated by two multi-objective metrics. The most promising formulations are finally applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions and compared to MODPSO and DFMO, showing promising results.

A multi-fidelity (MF) active learning method is presented for design optimization problems charac... more 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.