Jordi Pons-Prats

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Robust design optimization in aeronautics using stochastic analysis and evolutionary algorithms

Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take advantage of multi-point criteria to look for robust solutions accounting with uncertainty definition. From the computational point of view, the application to coupled problems, like computational fluid dynamics (CFD) or fluid–structure interaction (FSI), can be extremely expensive. This study presents a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. At first, a stochastic procedure is proposed to be applied into optimization problems. The proposed method has been applied to both CFD and FSI problems for the reduction of drag and flutter, respectively.

Double Shock Control Bump design optimization using hybridised evolutionary algorithms

The paper investigates two advanced optimisation methods for solving active flow control device shape design problem and also compares their optimisation efficiency in terms of computational cost and design quality. The first optimisation method uses Hierarchical Asynchronous Parallel Multi-Objective Evolutionary Algorithm (HAPMOEA) and the second uses Hybridized EA with Nash-Game strategies. Both optimisation method are based on a canonical evolution strategy and incorporates the concepts of parallel computing and asynchronous evaluation. For the practical test case, one of active flow control devices named Shock Control Bump (SCB) is considered and it is applied to Natural Laminar Flow (NLF) aerofoil. The concept of SCB is to decelerate supersonic flow on upper/lower surface of transonic aerofoil that leads delay of shock occurrence. Such active flow technique reduces a total drag at transonic speeds. Numerical results clearly show that Hybrid-Game helps EA to accelerate optimisation process, and also applying SCB on the suction and pressure sides significantly reduces transonic wave drag and improves lift on drag (L/D) value when compared to the baseline design.

Summary of UMRIDA Best Practices

Uncertainty quantification (UQ) is becoming a strategic step in the design phase. Robust Design Optimization (RDO) is the following step. The Technological Readiness Level (TRL) of intrusive and non-intrusive methodologies is increasing rapidly, although several limitations remain. Nowadays, UQ is a major trend in research, because there is a lot of room for improvement.

Monte Carlo-Based and Sampling-Based Methods and Their Range of Applicability

The present section will focus on the applicability issues of Monte Carlo-based methods, as well as those methods based on sampling techniques. Special focus will be put on the Multi-Level Monte Carlo method and the two implementations developed during the UMRIDA project, namely the Continuous MLMC and MLMC. All named methods have been described in the above sections of this book.

General Introduction to Monte Carlo and Multi-level Monte Carlo Methods

In this chapter, we present a general introduction to Monte Carlo (MC)-based methods, sampling methodologies, stratification methods, and variance reduction techniques. In the first part, we will discuss the theoretical basis and the convergence proprieties of MC methods. The next part is devoted to pseudorandom and quasi-random number generation, the generation of random variables and the application of stratification. It is followed by techniques for correlation and discrepancy control. The third part presents the concept of Latin Hypercube Sampling (LHS). The last part introduces the concept of Multi-Level Monte Carlo (MLMC).

Industrial Application of Genetic Algorithms to Cost Reduction of a Wind Turbine Equipped with a Tuned Mass Damper

Design optimization has already become an important tool in industry. The benefits are clear, but several drawbacks are still present, being the main one the computational cost. The numerical simulation involved in the solution of each evaluation is usually costly, but time and computational resources are limited. Time is key in industry. The present communication focuses on the methodology applied to optimize the installation and design of a Tuned Mass Damper. It is a structural device installed within the tower of a wind turbine aimed to stabilize the oscillations and reduce the tensions and the fatigue loads. The paper describes the decision process to define the optimization problem, as well as the issues and solutions applied to deal with a huge computational cost.

An implicit surface tension model for the analysis of droplet dynamics

Abstract A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.

Computational evaluation of cochlear implant surgery outcomes accounting for uncertainty and parameter variability

Cochlear implantation (CI) is a complex surgical procedure that restores hearing in patients with severe deafness. The successful outcome of the implanted device relies on a group of factors, some of them unpredictable or difficult to control. Uncertainties on the electrode array position and the electrical properties of the bone make it difficult to accurately compute the current propagation delivered by the implant and the resulting neural activation. In this context, we use uncertainty quantification methods to explore how these uncertainties propagate through all the stages of CI computational simulations. To this end, we employ an automatic framework, encompassing from the finite element generation of CI models to the assessment of the neural response induced by the implant stimulation. To estimate the confidence intervals of the simulated neural response, we propose two approaches. First, we encode the variability of the cochlear morphology among the population through a statistical shape model. This allows us to generate a population of virtual patients using Monte Carlo sampling and to assign to each of them a set of parameter values according to a statistical distribution. The framework is implemented and parallelized in a High Throughput Computing environment that enables to maximize the available computing resources. Secondly, we perform a patient-specific study to evaluate the computed neural response to seek the optimal post-implantation stimulus levels. Considering a single cochlear morphology, the uncertainty in tissue electrical resistivity and surgical insertion parameters is propagated using the Probabilistic Collocation method, which reduces the number of samples to evaluate. Results show that bone resistivity has the highest influence on CI outcomes. In conjunction with the variability of the cochlear length, worst outcomes are obtained for small cochleae with high resistivity values. However, the effect of the surgical insertion length on the CI outcomes could not be clearly observed, since its impact may be concealed by the other considered parameters. Whereas the Monte Carlo approach implies a high computational cost, Probabilistic Collocation presents a suitable trade-off between precision and computational time. Results suggest that the proposed framework has a great potential to help in both surgical planning decisions and in the audiological setting process.

Applying Multi-objective Robust Design Optimization Procedure to the Route Planning of a Commercial Aircraft

Aircraft emission targets worldwide and their climatic effects have put pressure in government agencies, aircraft manufacturers and airlines to reduce water vapour, carbon dioxide (\(CO_{2}\)) and oxides of nitrogen (\(NO_{x}\)) resulting from aircraft emissions. The difficulty of reducing emissions including water vapor, carbon dioxide (\(CO_{2}\)) and oxides of nitrogen (\(NO_{x}\)) is mainly due to the fact that a commercial aircraft is usually designed for a particular optimal cruise altitude but may be requested or required to operate and deviate at different altitudes and speeds to archive a desired or commanded flight plan, resulting in increased emissions. This is a multi- disciplinary problem with multiple trade-offs such as optimizing engine efficiency, minimizing fuel burnt and emissions while maintaining prescribed aircraft trajectories, altitude profiles and air safety. There are possible attempts to solve such problems by designing new wing/aircraft shape, new efficient engine, ATM technology, or modifying the aircraft flight plan. Based on the rough data provided by an air carrier company, who was willing to assess the methodology, this paper will present the coupling of an advanced optimization technique with mathematical models and algorithms for aircraft emission, and fuel burnt reduction through flight plan optimization. Two different approaches are presented; the first one describes a deterministic optimization of the flight plan and altitude profile in order to reduce the fuel consumption while reducing time and distance. The second approach presents the robust design optimization of the previous case considering uncertainties on several parameters. Numerical results will show that the methods are able to capture a set of useful trade-offs solutions between aircraft range and fuel consumption, as well as fuel consumption and flight time.