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In this work, the performance of a semicircular cylinder with the flat side parallel to the incoming flow has been studied experimentally in a wind-excited energy harvester. Preliminary sectional model wind tunnel tests have allowed the identification of the reduced velocity ranges howing appreciable wind-induced oscillations. Interestingly, vortex-induced vibration-galloping interferences have been identified for both heave and pitch degrees of freedom at low reduced wind speeds, as well as coupled galloping in the higher ranges of flow velocities. The impact on the aeroelastic response caused by the attachment of a small-diameter rod at different positions has been studied, finding an enhancement in the amplitude of the oscillations and an enlargement in the vortex-induced vibration excitation range for some of them. Based on these preliminary results, an energy harvester has been designed adopting a cantilever beam supporting the semicircular cylinder. The device has showed a good performance reaching 2.5 mW of averaged harvested power for the configuration with a small-diameter rod attached at γ=85º for 8 m/s flow speed.

[EN] One of the remaining challenges for the scientific-technical community is predicting preterm births, for which electrohysterography (EHG) has emerged as a highly sensitive prediction technique. Sample and fuzzy entropy have been used to characterize EHG signals, although they require optimizing many internal parameters. Both bubble entropy, which only requires one internal parameter, and dispersion entropy, which can detect any changes in frequency and amplitude, have been proposed to characterize biomedical signals. In this work, we attempted to determine the clinical value of these entropy measures for predicting preterm birth by analyzing their discriminatory capacity as an individual feature and their complementarity to other EHG characteristics by developing six prediction models using obstetrical data, linear and non-linear EHG features, and linear discriminant analysis using a genetic algorithm to select the features. Both dispersion and bubble entropy better discriminated between the preterm and term groups than sample, spectral, and fuzzy entropy. Entropy metrics provided complementary information to linear features, and indeed, the improvement in model performance by including other non-linear features was negligible. The best model performance obtained an F1-score of 90.1 ± 2% for testing the dataset. This model can easily be adapted to real-time applications, thereby contributing to the transferability of the EHG technique to clinical practice., This work was supported by the Spanish Ministry of Economy and Competitiveness, the European Regional Development Fund (MCIU/AEI/FEDER, UE RTI2018-094449-A-I00-AR), and by the Generalitat Valenciana (AICO/2019/220)

[Abstract:] In the present study, the aerodynamics of the flow fields around a static and vertically free-to-oscillate 4:1 rectangular cylinder are analysed by means of 3D LES simulations, adopting the OneEqEddy viscosity model. Integral parameters, pressure distributions, amplitudes of oscillation, coherences and correlations are obtained and compared with the available experimental data. Aiming to ascertain the impact of the boundary conditions and the grid resolution on the accuracy of results, five cases adopting 3 different meshes including two different spanwise discretisations have been considered. When studying the aerodynamics of the cylinder in static conditions, the influence of the spatial discretisation is very limited, and the agreement with experimental data is fairly good. On the other hand, for the free-to-oscillate cylinder, the structural response is dramatically dependent on the spanwise discretisation. The maximum amplitude of the structural response decreases as the mesh resolution increases, providing a closer fit with the experimental data. Also, the spanwise correlation of pressures is studied, finding remarkable differences depending on the level of spatial discretisation. Ministerio de Economía y Competitividad; BIA2016-76656-R Ministerio de Economía y Competitividad; BES-2014-068418 Ministerio de Economía y Competitividad; BIA2013-41965-P Ministerio de Economía y Competitividad; EEBB-I-17-11905 Xunta de Galicia; ED431C2017/72

Shape and size design of twin-box decks involves managing a number of highly sensitive deck features, including aerodynamic, stiffness, and mass properties, which leads to important and co...

The morphometry of abdominal aortic aneurysms (AAA) has been recognized as one of the main factors that may predispose them to rupture. The need to quantify the morphometry of AAA on a patient-specific basis constitutes a valuable tool for assisting in rupture risk prediction. Previous results of this research group have determined the correlations between hemodynamic stresses and aneurysm morphometry by means of the Pearson coefficient. The present work aims to find how the AAA morphology correlates with the hemodynamic stresses acting on the arterial wall. To do so, the potential of the bootstrap technique has been explored. Bootstrap works appropriately in applications where few data are available (13 patient-specific AAA models were simulated). The methodology developed can be considered a contribution to predicting the hemodynamic stresses from the size and shape indices. The present work explores the use of a specific statistical technique (the bootstrap technique) to predict, based on morphological correlations, the patient-specific aneurysm rupture risk, provide greater understanding of this complex phenomenon that can bring about improvements in the clinical management of aneurysmatic patients. The results obtained using the bootstrap technique have greater reliability and robustness than those obtained by regression analysis using the Pearson coefficient, thus allowing to obtain more reliable results from the characteristics of the samples used, such as their small size and high variability. Additionally, it could be an indicator that other indices, such as AAA length, deformation rate, saccular index, and asymmetry, are important.

[Abstract] The wind flow around twin-box decks is particularly complex due to the very important role played by the slot distance between girders and the presence of the downwind box that is immersed in the wake of the upwind box. Detailed experimental studies on the three-dimensional flow features of this deck typology are certainly challenging, and CFD simulations have not tackled this problem so far. The goal of this 3D LES piece of research is to shed some light on the complex flow features around twin-box decks, particularly when the deck geometry is fully three-dimensional due to the presence of the transversal beams linking together the deck girders. Integral parameters, mean and instantaneous flow structures and spanwise correlations are studied for a segment of the Stonecutters Bridge. It has been found that the presence of the transversal beam plays a key role in the flow correlation loss, identifying, for instance, the out-of-phase shedding of vortices at different sides of the transversal beam. The numerical results agree well with experimental data in the literature, and offer a richer and more comprehensive explanation for the identified aerodynamic responses. This research has been funded by the Spanish Ministry of Economy and Competitiveness in the frame of the research project with reference BIA2016-76656-R and the Galician regional government with reference ED431C 2017/72. The first of the authors has been funded by the Spanish Ministry of Economy and Competitiveness in the frame of the National Program for Promotion of Talent and Employability through the BES-2014-068418 predoctoral contract grant, associated with the BIA2013-41965-P research project Xunta de Galicia; ED431C2017/72

[Abstract] The phenomenon of turbulence is present in almost every type of flow in practical applications. Depending on its level of intensity and length scale, it can modify both the aerodynamic and aeroelastic performance of a body under flow action. In wind tunnel tests, the desired turbulence level is achieved by placing obstacles, spires, grids and extra roughness generators upwind the tested model. On the other hand, when trying to reproduce turbulence effects by means of a computational fluid dynamics (CFD) approach, two options have usually been considered: synthetic turbulence generation and the reproduction of velocity and pressure fluctuations recorded from previous simulations or wind tunnel tests. Another option, whose feasibility in CFD applications is addressed in this work by means of a 2D URANS (unsteady Reynolds averaged Navier–Stokes) consists of placing a rod upstream of the studied body, near the stagnation line. This approach is based on the generation of small scale turbulence upstream of the studied body, so that the turbulent wake generated by an upwind rod impinges on the body located downwind. In the present study, by means of 2D URANS simulations, the smooth flow over a circular cylinder (the upwind rod) is studied focusing on its wake turbulence characteristics. Furthermore, the aerodynamic performance of a square cylinder, first under smooth flow, and later immersed in the turbulent wake of the upstream rod, are analysed. A substantial effort has been devoted in the verification studies of the numerical models. It has been found that the adopted numerical approach is able to reproduce the turbulent characteristics of the rod wake and assess the impact of the turbulent flow on a square cylinder, providing a promising agreement with experimental data. Xunta de Galicia; ED431C2017/72

[Abstract] In computational fluid dynamics (CFD) simulations, verification is the process of identifying both the spatial and the temporal discretisations providing relatively insensitive model results. The underlying goal of this task is to identify the mesh with a lower number of elements and the longer time step size compatible with the purposes of the study. In this manner, the computational burden associated with CFD methods may be decreased without compromising the accuracy of the numerical results. In general, this process is accomplished by studying three meshes with increasing discretisation levels (coarse, medium and fine), expecting that the medium one would provide satisfactory results. Once the satisfactory spatial discretisation level is selected, the different time step sizes are studied, taking into account that a Courant number (Co) of 1 is usually considered the maximum allowable value for numerical stability when adopting a LES (Large Eddy Simulation) approach. In this study, a detailed verification study considering two different approaches, providing the uncertainty level of several parameters of interest depending on the spatial and temporal discretisation is reported. The first of them consists in the curve fitting of linear or quadratic curves to selected model outputs; meanwhile the second approach relies on the Richardson extrapolation principle. These two different approaches are applied in the frame of the 3D LES numerical simulations of the Stonecutters bare deck geometry. In the study the focus is put on the sensitivity of the integral parameters, that is the force coefficients and Strouhal number, with the spatial and temporal discretisations. This research has been funded by the Spanish Ministry for Science and Innovation in the frame of the research project with reference PID2019-110786GB-I00 and the Galician regional Government with reference ED431C2017/72. The computations have been carried out in the computer cluster Breogan and in the Galician Supercomputing Center (CESGA) Xunta de Galicia; ED431C2017/72

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG [Abstract] An efficient method for analyzing the nonlinear aerostatic stability of long-span bridges using a modal formulation is proposed. First, a simplified linear version defined as modal-based approach is introduced, which evaluates the bridge displacements using the modal properties of the bridge and speeds up the assessment of the critical velocity by applying a root-finding algorithm. Then, this scheme is further developed to identify the instability limit point in nonlinear structures by combining nonlinear FEM analyses with the linear version of the modal-based approach and a root-finding algorithm in an outer loop. The effects of considering the three components of the wind loads, the stays sag effect, structural nonlinearities, aerodynamic nonlinearities, and the initial wind angle of attack, are analyzed and discussed. The computational advantages of the proposed method and its accuracy are demonstrated through three application examples, including a simplified linear 1 DoF system, and linear and nonlinear FEM models of a full cable-stayed bridge. The collapse mechanism of the cable-stayed bridge is driven by the stiffness degradation of the stays caused by the deck vertical upward displacements. It has been found that the influence of the nonlinear aerodynamic features is very low when the structural nonlinearities control the bridge collapse. Xunta de Galicia; ED481B2018/053 Xunta de Galicia; ED431C 2017/72 EEUU. National Science Foundation; CMMI #1562244 M. Cid Montoya is funded by the Xunta de Galicia (Galician regional government) and the Fulbright Scholar Program with reference ED481B2018/053. S. Hernández, F. Nieto, and M. Cid Montoya have been funded by the Spanish Ministry of Economy and Competitiveness in the frame of the research project with reference PID2019-110786 GB-I00, and the Xunta de Galicia, including FEDER funding, with reference ED431C 2017/72. A. Kareem especially thanks NSF for in part support under grant CMMI #1562244.

Structural optimization techniques have the potential to become a powerful tool in the design of long-span bridges. The search for more efficient and reliable designs involves considering shape variations in the deck cross-section, which is one of the key features of the bridge. This affects the deck aerodynamics and its mechanical properties, and consequently to the aeroelastic response of the bridge. A numerical approach pursuing to optimize a long-span bridge needs to explore changes in the deck shape, including structural and aeroelastic responses as design constraints. Therefore, the flutter response of the bridge must be computed numerically for every candidate proposed by the optimization algorithm. This work presents a novel approach to conduct the optimization of deck shape and cables size of a long-span cable-stayed bridge considering simultaneously aeroelastic and structural constraints. The design variables are the cross-section area and prestressing force of each stay, the deck plates thickness and the width and depth of a streamlined box deck. The aeroelastic constraint is evaluated based on the fully numerical procedure developed in an authors' previous work. A series of parameter variation studies, that are instrumental for the sound interpretation of the optimum designs, are also reported.

The classical approach currently used in the bridge engineering industry for the structural and aeroelastic design of bridges is based on an iterative heuristic process which includes wind tunnel testing. The dependency on experimental techniques for the aeroelastic characterization of the bridge deck cross-section requires a substantial amount of resources, and consequently the number of potential candidate designs must be limited. The fast improvements in Computational Fluid Dynamics (CFD) techniques in recent years have led to its use in the industrial field, and consequently bridge design methods must be updated. This paper proposes a fully numerical strategy to overcome the classical iterative process in bridge deck shape design. Firstly, it consists in constructing a surrogate model of the aerodynamic response of the baseline cross-section and the allowed shape variations by conducting a set of CFD simulations of several sample designs. Then, the force coefficients and their slopes can be obtained for every design included in the design domain, the flutter derivatives can be approximated by the quasi-steady formulation, and the flutter velocity can be computed. This procedure is applied to two cable-stayed bridges with different spans, and the reported results are validated with wind tunnel tests.

This paper presents the results of numerical and experimental investigations on the force coefficients and Strouhal numbers of circular segments considering different corner angles or chord to sagitta ratios. The research is motivated because these geometries are becoming increasingly popular in several engineering disciplines. The so-called D-section (semi-circular cylinder with a corner angle of $ 90^{\circ } $ ) has been experimentally studied in the past, since it is a galloping prone geometry. However, there is a lack of research for cases with different corner angles, and the numerical investigations related to this topic are particularly scarce. In this work, a 2D Unsteady Reynolds Averaged Navier–Stokes approach has been adopted aiming to study the circular segments at the sub-critical regime, considering corner angles from $ 40^{\circ } $ to $ 90^{\circ } $ , and the flow parallel to the rectilinear side. These sections were found to be particularly challenging since they present massive flow separation on the rectilinear side, alongside the inherent difficulties related to modeling the flow along curved surfaces at high Reynolds numbers. The impact of introducing low-Reynolds-number and curvature corrections in the $ k-\omega $ SST turbulence model and the performance of the Transition SST model have been extensively studied.

The quality of aeroelastic tests of long-span bridges is highly influenced by the ability of the reduced-scale models to reproduce the dynamic response of the real bridge. Hence, the design of the models is one important component in the process, as differences between the dynamic properties of the model and the prototype typically arise due to inherent limitations when constructing the reduced-scale model. This paper reviews the design process of full bridge reduced-scale models and explores sources of inaccuracies. A method based on optimization algorithms is proposed to reduce these inaccuracies in the model dynamic responses. This method is applied to a modified version of a real project consisting of a cable-stayed bridge with two diamond-shaped towers, single-box deck, 176 stays, and four piers. The optimization of the dynamic properties of the full bridge reduced-scale model is conducted in two phases: the first one optimizes the standalone tower, and the second one the complete bridge model. The results show the capabilities of the method, which nearly eliminates the inaccuracies in the natural frequencies of the model. The effects on other dynamic properties, such as variations in the generalized masses and in the modal shapes, are studied and commented upon.

Structures Congress 2020. 5-8 abril, 2020. St. Louis, Missouri [Abstract] This paper describes the evolution of deck shape of long span bridges since the Tacoma Narrows collapse trying to avoid undesirable aerodynamic behavior under wind flow and the trend in the last decades to increase the length of the main span of suspension and cable stayed bridges. The necessity to use advanced technologies to help the engineer to obtain the best possible design is highlighted and the advantages of applying optimization methodologies is encouraged. It is explained that this approach requires to use only numerical tools and hence to eliminate experimental studies, as wind tunnel tests using reduced models of full bridge of a segment of the deck, and their substitution by computational fluid dynamics (CFD) simulations. After doing so, the current capabilities of this approach are presented and, finally, the problems that need to be solved to have a fully operational methodology able to be implemented in real structures are outlined. This research has been funded by the Spanish Ministry of Economy and Competitiveness in the frame of the research project BIA2016-76656-R and the Galician regional government (including FEDER Funding) reference ED431C 2017/72. M. Cid Montoya has been funded by the Galician regional government (Xunta de Galicia) with reference ED481B 2018/053 and the Fulbright postdoctoral scholarship program Xunta de Galicia; ED431C 2017/72 Xunta de Galicia; ED481B 2018/053

Structures Congress 2020. 5-8 abril, 2020. St. Louis, Missouri [Abstract] Optimization techniques have demonstrated their capability to obtain economic and sustainable designs while meeting the performance and safety requirements in a number of engineering disciplines. In the bridge engineering field, the increasing main span length of super-long span bridges makes the wind-resistant design a top priority. However, it has been traditionally conducted following heuristic rules based on experimental analyses. Alternatively, the last advances in CFD and metamodeling techniques enables the development of optimization frameworks. The right conception of the aerostructural optimization problem is crucial to achieve noticeable reductions in the required amount of material and comprehensive safe designs. This paper reports the last advances in the authors’ line of research that pursues the definition of a numerical methodology for the full aerostructural optimization of long-span bridges considering shape and size design variables. The capabilities of the method are presented, and the necessity of considering uncertainty in the process is discussed. This research has been funded by the Spanish Ministry of Economy and Competitiveness in the frame of the research project with reference BIA2016-76656-R, and the Galician regional government, including FEDER funding, with reference ED431C 2017/72. M. Cid Montoya is funded by the Galician regional government with reference ED481B 2018/053 and the Fulbright postdoctoral scholarship program. A. Kareem especially thanks NSF support under grant CMMI #1612843. Fei Ding is supported by a grant from the Center for Informatics and Computational Sciences Xunta de Galicia; ED431C 2017/72 Xunta de Galicia; ED481B 2018/053 EEUU. National Sanitation Foundation (NSF); CMMI #1612843

Recent findings have shown that maximum diameter of abdominal aortic aneurysm (AAA) and its growth rate are not entirely reliable indicators of rupture potential. The AAA geometrical shape and size may be related to the rupture risk which is a clinical manifestation of the balance between the forces generated by blood flow within the AAA and its strength. This study aims at assessing the hemodynamic features associated with the geometry of AAAs.

While it is well known that the gap between twin-box decks is a key design variable that impacts the onset flutter velocity of a bridge, further research is required to ascertain how modifications in several bridge design variables affect other aeroelastic responses. This paper utilizes aero-structural optimization techniques for the design of long-span bridges with short gap twin-box decks considering simultaneously structural, flutter and buffeting constraints. The optimization helps to reduce the material volume of the structure while maintaining all the performance and safety requirements below the imposed thresholds. It has been found that the geometry of the individual box cross-section is an important feature for the control of the buffeting response, particularly the vertical acceleration. On the other hand, flutter and torsional buffeting constraints require designs with larger gap distance and alternative box geometries, leading to a trade-off between conflicting design demands. Hence, depending on the expected wind load conditions and the specific requirements of a particular project, an optimum aero-structural bridge design with a particular deck shape can be identified. The framework presented in this study is an effective tool to achieve sustainable and safe bridge designs that seeks a most efficient balance between all the design constraints.

The design of long-span bridges under wind places multiple demands that are frequently contradictory in regard to the resulting deck configuration. The structural demand requires that the deck contributes to the bridge stiffness, which results in bluff geometry. Conversely, aeroelastic aspects demand that the deck shape be more streamlined to reduce the aerodynamic and aeroelastic load effects. This requires that the design of long-span bridges be carried out as an aero-structural design problem, where the goal is to obtain designs with the lowest cost that simultaneously fulfill the structural and aeroelastic constraints. This study presents a numerical framework for the aero-structural design of long-span bridges under buffeting focusing on the deck shape. In this paper, the relationship between the buffeting response of a cable-stayed bridge and its deck shape is analyzed by means of parametric studies that help to better understand the role played by each involved parameter. This information is used to tailor the deck shape aiming at keeping the buffeting response under a given threshold. By building upon this framework, the design problem can be recast as an aero-structural optimization problem.

Reliability based design optimization (RBDO) for deck shape and thicknesses of the steel plates that form a box girder of long-span suspension bridges is performed considering probabilistic flutter constraint. The entire process was carried out fully computationally including the definition of flutter derivatives. Surrogate models were constructed to estimate the aerodynamic response of the bridge for different deck shapes based on the results from a series of CFD simulations. Some of the aerodynamic coefficients were validated by wind tunnel tests. Flutter derivatives were then estimated using quasi-steady approach for the evaluation of critical flutter velocity. Uncertainty in the aerodynamic coefficients from CFD simulations as well as the extreme wind speed at the bridge site were considered. The formulated methodology was applied to the Great Belt East Bridge.

The design of long-span bridges consists of dealing with a large number of design variables and it is conditioned by responses of structural and aeroelastic nature. A deep knowledge about the influence of these variables governing the bridge responses is crucial to achieve efficient and safe designs. Apart from heuristic rules, numerical approaches, such as parameter variation studies, sensitivity analysis and optimization algorithms, can provide reliable information to improve designs. This work studies the effects on the flutter and structural responses of a cable-stayed bridge when the mechanical, mass, aerodynamic and aeroelastic properties of a streamlined mono-box deck are modified. These results are used to understand qualitatively and quantitatively the effects caused by the variation of the deck plate thickness and cross-section shape on the bridge responses.

[Abstract:] Flexible structures, such as cable-supported bridges, are prone to suffer from vortex-induced vibrations (VIV) under wind flow, as their span lengths are steadily growing in the last decades. VIV is a phenomenon that takes place at reduced wind speeds. The movements of the structure at VIV are self-limited and their frequency corresponds with the natural frequency of the structure (lock in). Therefore, VIV affects the structure’s serviceability and can cause fatigue related damage. Hence, the need for identifying and avoiding this phenomenon at the early design stages is a key issue in long-span bridges design. In the present study a rectangular cylinder of width to depth ratio 4:1, which is a common simplification of a bridge deck cross section, is analysed for the static case as well as undergoing free vibration in the vertical direction under wind flow. These analyses have been carried out by 2D URANS CFD simulations, adopting two different turbulence models: the k − ω SST, which is based upon the Boussinesq eddy-viscosity approximation, and the Reynolds Stress Model, which directly calculates the components of the specific Reynolds stresses. For the static case the force coefficients, Strouhal number and the pressure coefficient distributions were calculated and compared with the available experimental data. In the case of the free-to-oscillate 4:1 rectangular cylinder, the oscillation amplitudes are compared with wind tunnel data reported in the literature. In addition, the frequencies and phase-lags between the time-dependent lift coefficient and the vertical oscillations are studied. Ministerio de Economía y Competitividad; BIA2016-76656-R Ministerio de Economía y Competitividad; BES-2014-068418 Ministerio de Economía y Competitividad; BIA2013-41965-P Xunta de Galicia; ED431C 2017/72

[Abstract:] 2D URANS simulations are conducted aiming to study the aerodynamic performance under smooth flow of twin-box decks depending on the gap distance between girders. The Stonecutters Bridge is taken as the reference geometry. In this parametric study, 14 gap to depth ratios in the range 0 ≤ G/D ≤ 9.70 are investigated, and for each geometry, 11 angles of attack in the range −10 ◦ ≤ α ≤ 10 ◦ are considered. Specific goals of this research have been: identification of the fundamental flow features, study of mean and fluctuating pressure coefficients distributions, identification of the vortex shedding mechanisms and general aerodynamic characterisation based on force coefficients. The numerical results provided herein are validated with wind tunnel data previously reported in the literature, finding a good agreement. A critical gap to depth ratio at G/D = 2.35, in terms of aerodynamic response, was identified, which is consistent with the value reported in the literature for a different bridge based on wind tunnel tests. The obtained set of data provide a general picture of the expected aerodynamic performance of a twin-box deck depending on the gap distance and could be of great value at the early design stage of long-span cable-supported bridges. Ministerio de Economía y Competitividad; BIA2016-76656-R Ministerio de Economía y Competitividad; BES-2014-068418 Ministerio de Economía y Competitividad; BIA2013-41965-P Xunta de Galicia; ED431C 2017/72

Design techniques based upon sensitivity analysis are not usual in the current design of suspension bridges. However, sensitivity analysis has been proved to be a useful tool in the car and aircraft industries. Evaluation of sensitivity analysis is a mandatory step in the way towards an efficient automated optimum design process which would represent a huge jump in the conception of long span bridges. Some of the authors of this paper were pioneers in establishing a methodology for obtaining the sensitivity analysis of flutter speed in suspension bridges a few years ago. That approach was completely analytical and required the evaluation of many matrices related to the phenomenon. In those works the total mass of the deck was considered as constant and such a circumstance supposed a limitation of the method. In the present paper the complete analytical formulation of the sensitivity analysis problem in bridges considering variable deck mass is presented, as well as its application to the design problem of the Great Belt Bridge. Analytical evaluation of sensitivities is a time demanding task, and in order to avoid excessive computation times, distributed computing strategies have been implemented which can be considered as an additional benefit of this approach. For the application example, it has been found that deck cross-section area and torsional inertia are the structural properties with the greatest influence on the flutter performance.

This document describes an optimization problem of cable cross section of a cable stayed bridge considering constraints of cable stress and deck displacement. Since the bridge is still in the design phase, the geometry and the mechanical characteristics are subjected to changes. In order to avoid creating different structural models, a computer code was written to produce a model from geometrical and mechanical data and solve the optimization problem. At the end of the document, two examples are included to show the capabilities of the methodology presented.