Inverse modelling of an aneurysm's stiffness using surrogate-based optimization and fluid-structure interaction simulations

Characterization of the mechanical properties of arterial tissues is highly relevant. In this work, we apply an inverse modelling approach to a model accounting for an aneurysm and the distal part of the circulation which can be modified using two independent stiffness parameters. For given values of these parameters, the position of the arterial wall as a function of time is calculated using a forward simulation which takes the fluid-structure interaction (FSI) into account. Using this forward simulation, the correct values of the stiffness parameters are obtained by minimizing a cost function, which is defined as the difference between the forward simulation and a measurement. The minimization is performed by means of surrogate-based optimization using a Kriging model combined with the expected improvement infill criterion. The results show that the stiffness parameters converge to the correct values, both for a zero-dimensional and for a three-dimensional model of the aneurysm

ooDACE toolbox: a flexible object-oriented Kriging implementation

When analyzing data from computationally expensive simulation codes, surrogate modeling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualization and optimization. Kriging is a popular surrogate modeling technique used for the Design and Analysis of Computer Experiments (DACE). Hence, the past decade Kriging has been the subject of extensive research and many extensions have been proposed, e.g., co-Kriging, stochastic Kriging, blind Kriging, etc. However, few Kriging implementations are publicly available and tailored towards scientists and engineers. Furthermore, no Kriging toolbox exists that unifies several Kriging flavors. This paper addresses this need by presenting an efficient object-oriented Kriging implementation and several Kriging extensions, providing a flexible and easily extendable framework to test and implement new Kriging flavors while reusing as much code as possible

A constrained multi-objective surrogate-based optimization algorithm

Surrogate models or metamodels are widely used in the realm of engineering for design optimization to minimize the number of computationally expensive simulations. Most practical problems often have conflicting objectives, which lead to a number of competing solutions which form a Pareto front. Multi-objective surrogate-based constrained optimization algorithms have been proposed in literature, but handling constraints directly is a relatively new research area. Most algorithms proposed to directly deal with multi-objective optimization have been evolutionary algorithms (Multi-Objective Evolutionary Algorithms -MOEAs). MOEAs can handle large design spaces but require a large number of simulations, which might be infeasible in practice, especially if the constraints are expensive. A multi-objective constrained optimization algorithm is presented in this paper which makes use of Kriging models, in conjunction with multi-objective probability of improvement (PoI) and probability of feasibility (PoF) criteria to drive the sample selection process economically. The efficacy of the proposed algorithm is demonstrated on an analytical benchmark function, and the algorithm is then used to solve a microwave filter design optimization problem

Strategies for balancing exploration and exploitation in electromagnetic optimisation

The paper focuses on the advantages and drawbacks of different strategies which may be used to assist kriging surrogate modelling with the purpose of selecting multiple design vectors for evaluation when stepping forward in optimisation routines. The combined criteria include the efficiency of finding the global optimum but also the quality of the approximation of the shape of the objective function; the latter may be used to make judgements about the robustness of the optimised design

Active learning for feasible region discovery

Often in the design process of an engineer, the design specifications of the system are not completely known initially. However, usually there are some physical constraints which are already known, corresponding to a region of interest in the design space that is called feasible. These constraints often have no analytical form but need to be characterised based on expensive simulations or measurements. Therefore, it is important that the feasible region can be modeled sufficiently accurate using only a limited amount of samples. This can be solved by using active learning techniques that minimize the amount of samples w.r.t. what we try to model. Most active learning strategies focus on classification models or regression models with classification accuracy and regression accuracy in mind respectively. In this work, regression models of the constraints are used, but only the (in) feasibility is of interest. To tackle this problem, an information-theoretic sampling strategy is constructed to discover these regions. The proposed method is then tested on two synthetic examples and one engineering example and proves to outperform the current state-of-the-art

Towards efficient multiobjective optimization: multiobjective statistical criterions

The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, "real-world" problems often consist of multiple, conflicting objectives leading to a set of equivalent solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of making those decisions upfront). Most of the work in multiobjective optimization is focused on MultiObjective Evolutionary Algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as MultiObjective Surrogate-Based Optimization (MOSBO), may prove to be even more worthwhile than SBO methods to expedite the optimization process. In this paper, the authors propose the Efficient Multiobjective Optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the expected improvement and probability of improvement criterions to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II and SPEA2 multiobjective optimization methods with promising results

Surrogate-based optimization of tidal turbine arrays: a case study for the Faro-Olhão inlet

This paper presents a study for estimating the size of a tidal turbine array for the Faro-Olhão Inlet (Potugal) using a surrogate optimization approach. The method compromises problem formulation, hydro-morphodynamic modelling, surrogate construction and validation, and constraint optimization. A total of 26 surrogates were built using linear RBFs as a function of two design variables: number of rows in the array and Tidal Energy Converters (TECs) per row. Surrogates describe array performance and environmental effects associated with hydrodynamic and morphological aspects of the multi inlet lagoon. After validation, surrogate models were used to formulate a constraint optimization model. Results evidence that the largest array size that satisfies performance and environmental constraints is made of 3 rows and 10 TECs per row.Eduardo González-Gorbeña has received funding for the OpTiCA project (http://msca-optica.eu/) from the Marie Skłodowska-Curie Actions of the European Union's H2020-MSCA-IF-EF-RI-2016 / GA#: 748747. The paper is a contribution to the SCORE pro-ject, funded by the Portuguese Foundation for Science and Technology (FCT–PTDC/AAG-TEC/1710/2014). André Pacheco was supported by the Portuguese Foun-dation for Science and Technology under the Portuguese Researchers’ Programme 2014 entitled “Exploring new concepts for extracting energy from tides” (IF/00286/2014/CP1234).info:eu-repo/semantics/publishedVersio