MODEL UPDATING AND STRUCTURAL HEALTH MONITORING OF HORIZONTAL AXIS WIND TURBINES VIA ADVANCED SPINNING FINITE ELEMENTS AND STOCHASTIC SUBSPACE IDENTIFICATION METHODS

Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Pollen records and lithology of profiles from Lobsigensee, Switzerland

Lobsigensee is a small kettle hole lake 15 km north-west of Bern on the Swiss Plateau, at an altitude of 514 m asl. Its surface is 2ha today, its maximum depth 2.7 m; it has no inlet and the overflow functions mainly during snow melting. The area was covered by Rhone ice during the Last Glaciation (map in Fig.2). Local geology, climate and vegetation are summarized in Figure 3A-C, the history of settlement in Figures 5-7. In order to reconstruct the vegetational and environmental history of the lake and its surroundings pollen analysis and other bio- and isotope stratigraphies were applied to twelve profiles cored across the basin with modified Livingstone corers (Fig.3 D). (1) The standard diagram: The central core LQ-90 is described as the standard pollen diagram (Chapter 3) with 10 local pollen assemblage zones of the Late-Glacial (local PAZ Ll to Ll0, from about 16'000(7) to 10'000 years BP) and 20 PAZ of the Holocene (local PAZ L11 to L30), see Figs. 8-10 and 20-24. Local PAZ L 1 to L3 are in the Late-Glacial clay and record the vegetational development after the ice retreat: L1 shows very low pollen concentration and high Pinus percentages due to long-distance transport and reworking; the latter mechanism is corroborated by the findings of thermophilous and pre-Quaternary taxa. Local PAZ L2 has a high di versi ty of non-arboreal pollen (NAP) and reflects the Late-Glacial steppe rich in heliophilous species. Local PAZ L3 is similar but additionally rich in Betula nana and Sal1x, thus reflecting a "shrub tundra". The PAZ L1 to L3 belong to the Oldest Dryas biozone. Local PAZ L4 to L 10 are found in the gyttja of the profundal or in the lake marl of the littoral and record the Late-Glacial forests. L4 is the shrub phase of reforestation with very high Junlperus and rapidly increasing Betula percentages. L5 is the PAZ with a first, L7 with a second dominance of tree-birches, separated by L6 showing a depression in the Betula curve. L4 to L7 can be assigned to the Balling biozone. Possible correlation of the Betula depression to the Older Dryas biozone is discussed. In local PAZ L8 Plnus immigrates and expands. L9 shows a facies difference in that Plnus dominates over Betula in littoral but not in profundal spectra. L8 and L9 belong to the Allerod biozone. In its youngest part the volcanic ash from Laach/Eifel is regularly found (11,000 BP). The local PAZ Ll0 corresponds to the Younger Dryas blozone. The merely slight increase of the NAP indicates that the pine forests of the lowland were not strongly affected by a cooler climate. In order to evaluate the significance of the littoral accumulation of coniferous pollen the littoral profile LQ-150 is compared to the profundal. Radiocarbon stratigraphies derived from different materials are presented in Figures 13 and 14 and in Tables 2 and 3. The hard-water errors in the gyttja samples and the carbonate samples are similar. The samples of terrestrial plant macrofossils are not affected by hard-water errors. Two plateaux of constant age appear in the age-depth relationship; their consequence for biostratigraphy as well as pollen concentration and influx diagrams are discussed. Radiocarbon ages of the Late-Glacial pollen zones are shown in Table 10. The Holocene vegetational history is recorded in the local PAZ L 11 to L30. After a Preboreal (PAZ L11) dominated by pine and birch the expansions of Corylus, Ulmus and Quercus are very rapid. Among these taxa Corylus dominates dur ing the Boreal (PAZ L 12 and L 1 3), whereas the components of the mixed oak forest dominate in the Older Atlantic (PAZ L14 to L16). In the Younger Atlantic (PAZ L 17 to L 19) Fagus and Alnus play an increasing, the mixed oak forest a decreasing role. During the period of local PAZ L19 Neolithic settlers lived on the shore of Lobsigensee. During the Subboreal (PAZ L20 and L21) and the Older Subatlantic (L22 to L25) strong fluctuations of Fagus and often antagonistic peaks of NAP, Alnus, Betula and Corylus can be interpreted as signs of human impact on vegetation. L23 is characterized not only by high values of NAP (especially apophytes and anthropochorous species) but also by the appearance of Juglans, Castanea and Secale which point to the Roman colonization of the area. For a certain period during the Younger Subatlantic (PAZ L26 to L30) the lake was used for retting hemp (Cannabis). Later the dominance of Quercus pollen indicates the importance of wood pastures. The youngest sediments reflect the wide-spread agricultural grass lands and the plantation of Pinus and Picea. Radiocarbon dates for the Holocene are given in Figure 23 and Table 4, the extrapolated ages of the Holocene pollen zones in Table 15. (2) The cross sections: Figures 25 and 26 give a summary of the litho- and palynostratigraphy of the two cross sections. Based on 11 Late-Glacial and 9 Holocene pollen diagrams (in addition to the standard ones), the consistency of the criteria for the definition of the pollen zones is examined in Tables 7 and 8 for the Late-Glacial and in Tables 11 to 14 for the Holocene. Sediment thicknesses across the basin for each pollen zone are presented in these tables as well as in Figures 43 to 45 for the Late-Glacial and in Figures 59 to 65 for the Holocene. Sediment focusing can explain differences between the gyttja cores of the profundal. Focusing is more than compensated for through "stretching" by carbonate precipitation on the littoral terrace. Pollen influx to the cross section are discussed (Chapters 4.1.5. and 4.2.3.). (3) The regional pollen zones: Based on some selected sites between Lake Geneva and Lake Constance regional pollen zones are proposed (Table 16, 17 and 19). (4) Paleoecology: Climatic change in the Late-Glacial can be inferred from Coleoptera, Trichoptera, Chironomidae and d18O of carbonates: a distinct warming is recorded around 12' 600 BP and around 10' 000 BP. The Younger Dryas biozone (10'700-10'000 BP) was the only cooling found in the Late-Glacial. The Betula depression often correlated wi th the Older Dryas biozone was possibl not colder but dryer than the previous period. During the Holocene the lowland site is not very sensitive to the minor climatic changes. Table 22 summarizes climatic and trophic changes before 8'000 BP as deduced from various biostratigraphies studied by a number of authors. Ostracods, Chironomids and fossil pigments indicate that anoxic conditions prevailed during the BoIling (possibly meromixis). Changes in the lake level are illustrated in Figure 74. A first lake-level lowering occurred in the early Holocene (10'000 to 9'000 BP), a second during the Atlantic (about 6'800 to 5'200 BP). The first "shrinking" of the lake volume resulted in a eutrophication recorded by laminations in the profundal and by pigments of Cyanophyceae. The second fall in water level corresponds to an increase of Nymphaeaceae. Human impact can be inferred in three ways: eutrophication of the lake (since the Neolithic), changes of terrestrial vegetation by deforestations (cyclicity of Fagus, see Figures 78 to 80), and enhanced erosion (increasing sedimentation rates by inwashed clay, particularly since the Roman Colonization, see Figures 49 and 81). Summary: This paper was planned as the final report on Lobsigensee. However, a number of issues are not answered but can only be asked more precisely, for example: (1) For the two periods with the highest rates of change, Le. the Bolling and the Preboreal biozones, pollen influx may reflect vegetation dynamics. Detailed investigations of these periods in annually laminated sediments are planned. (2) Biostratigraphies other than palynostratigraphy are needed to estimate the degree of linkage or independence in the development of terrestrial and lacustrine ecosystems. Often our sampling intervals were not identical, thus influencing our temporal resolution. (3) 6180- and 14C-stratigraPhies with high resolution will elucidate the leads and lags of these dynamic periods. Plateaux of constant age in the age-depth relationship have a strong bearing on both biological and geophysical understanding of Late-Glacial and early Holocene developments. (4) Numerical methods applied to the pollen diagrams of the cross section will help to quantify the significance of similari ties and dissimilarities across a single basin (with Prof. Birks). (5) Numerical methods applied to different sites on the Swiss Plateau and on the transect across the Alps will be helpful in evaluating the influence of different environmental factors (with Prof. Birks). (6) A new map 1: 1000 with 50cm-contour lines prov ided by Prof. Zurbuchen will be combined with a grid of cores sampling the transition from lake marl to peat enabling us to calculate paleo-volumes of the lake. This is interesting for the two "shrinking periods" (in Fig. 74A numbers 2-6 and 7-10), both accompanied by eutrophication. The pal eo-volume during the Neoli thic set tlement of the Cortaillod culture linked wi th an est l.mate of trophic change derived from diatoms (Prof. Smol in prep.) could possibly give an indication of the size of the human population of this period. (7) For the period with the antagonism between Fagus peaks and ABC-peaks close collaboration between palynologists, geochemists and archeologists should enable us to determine the influence of prehistoric and historic people on vegetation (collaboration with Prof. Stockli and Prof. Herzig). (8) The core LL-75 taken with a "cold letter box" will be analysed for major and trace elements by Dr. Sturm for 210pb and 137Cs by Prof.von Gunten and for pollen. We will see if our local PAZ L30 really corresponds to the surface sediment and if the small seepage lake reflects modern pollution.

Comparison of experimental and numerical sloshing loads in partially filled tanks

Sloshing describes the movement of liquids inside partially filled tanks, generating dynamic loads on the tank structure. The resulting impact pressures are of great importance in assessing structural strength, and their correct evaluation still represents a challenge for the designer due to the high level of nonlinearities involved, with complex free surface deformations, violent impact phenomena and influence of air trapping. In the present paper, a set of two-dimensional cases, for which experimental results are available, is considered to assess the merits and shortcomings of different numerical methods for sloshing evaluation, namely two commercial RANS solvers (FLOW-3D and LS-DYNA), and two academic software (Smoothed Particle Hydrodynamics and RANS). Impact pressures at various critical locations and global moment induced by water motion in a partially filled rectangular tank, subject to a simple harmonic rolling motion, are evaluated and predictions are compared with experimental measurements. 2012 Copyright Taylor and Francis Group, LLC.

FE–BE Coupling Methods for Elastoplasticity

Non-linear physical systems of infinite extent are conveniently modelled using FE–BE coupling methods. By the combination of both methods, suitable use of the advantages of each one may be obtained. Several possibilities of FEM–BEM coupling and their performance in some practical cases are discussed in this paper. Parallelizable coupling algorithms based on domain decomposition are developed and compared with the most traditional coupling methods.

Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation

It is well known that the evaluation of the influence matrices in the boundary-element method requires the computation of singular integrals. Quadrature formulae exist which are especially tailored to the specific nature of the singularity, i.e. log(*- x0)9 Ijx- JC0), etc. Clearly the nodes and weights of these formulae vary with the location Xo of the singular point. A drawback of this approach is that a given problem usually includes different types of singularities, and therefore a general-purpose code would have to include many alternative formulae to cater for all possible cases. Recently, several authors1"3 have suggested a type independent alternative technique based on the combination of standard Gaussian rules with non-linear co-ordinate transformations. The transformation approach is particularly appealing in connection with the p.adaptive version, where the location of the collocation points varies at each step of the refinement process. The purpose of this paper is to analyse the technique in eference 3. We show that this technique is asymptotically correct as the number of Gauss points increases. However, the method possesses a 'hidden' source of error that is analysed and can easily be removed.

Numerical analysis of shell and spatial structures

Since the advent of the computer into the engineering field, the application of the numerical methods to the solution of engineering problems has grown very rapidly. Among the different computer methods of structural analysis the Finite Element (FEM) has been predominantly used. Shells and space structures are very attractive and have been constructed to solve a large variety of functional problems (roofs, industrial building, aqueducts, reservoirs, footings etc). In this type of structures aesthetics, structural efficiency and concept play a very important role. This class of structures can be divided into three main groups, namely continuous (concrete) shells, space frames and tension (fabric, pneumatic, cable etc )structures. In the following only the current applications of the FEM to the analysis of continuous shell structures will be discussed. However, some of the comments on this class of shells can be also applied to some extend to the others, but obviously specific computational problems will be restricted to the continuous shells. Different aspects, such as, the type of elements,input-output computational techniques etc, of the analysis of shells by the FEM will be described below. Clearly, the improvements and developments occurring in general for the FEM since its first appearance in the fifties have had a significative impact on the particular class of structures under discussion.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Numerical modeling of electromagnetic coupling phenomena in the vicinities of overhead power transmission lines.

Electromagnetic coupling phenomena between overhead power transmission lines and other nearby structures are inevitable, especially in densely populated areas. The undesired effects resulting from this proximity are manifold and range from the establishment of hazardous potentials to the outbreak of alternate current corrosion phenomena. The study of this class of problems is necessary for ensuring security in the vicinities of the interaction zone and also to preserve the integrity of the equipment and of the devices there present. However, the complete modeling of this type of application requires the three- -dimensional representation of the region of interest and needs specific numerical methods for field computation. In this work, the modeling of problems arising from the flow of electrical currents in the ground (the so-called conductive coupling) will be addressed with the finite element method. Those resulting from the time variation of the electromagnetic fields (the so-called inductive coupling) will be considered as well, and they will be treated with the generalized PEEC (Partial Element Equivalent Circuit) method. More specifically, a special boundary condition on the electric potential is proposed for truncating the computational domain in the finite element analysis of conductive coupling problems, and a complete PEEC formulation for modeling inductive coupling problems is presented. Test configurations of increasing complexities are considered for validating the foregoing approaches. These works aim to provide a contribution to the modeling of this class of problems, which tend to become common with the expansion of power grids.

Models and methods for the direct simulation of rough and micropatterned surfaces

Friction in hydrodynamic bearings are a major source of losses in car engines ([69]). The extreme loading conditions in those bearings lead to contact between the matching surfaces. In such conditions not only the overall geometry of the bearing is relevant, but also the small-scale topography of the surface determines the bearing performance. The possibility of shaping the surface of lubricated bearings down to the micrometer ([57]) opened the question of whether friction can be reduced by mean of micro-textures, with mixed results. This work focuses in the development of efficient numerical methods to solve thin film (lubrication) problems down to the roughness scale of measured surfaces. Due to the high velocities and the convergent-divergent geometries of hydrodynamic bearings, cavitation takes place. To treat cavitation in the lubrication problem the Elrod- Adams model is used, a mass-conserving model which has proven in careful numerical ([12]) and experimental ([119]) tests to be essential to obtain physically meaningful results. Another relevant aspect of the modeling is that the bearing inertial effects are considered, which is necessary to correctly simulate moving textures. As an application, the effects of micro-texturing the moving surface of the bearing were studied. Realistic values are assumed for the physical parameters defining the problems. Extensive fundamental studies were carried out in the hydrodynamic lubrication regime. Mesh-converged simulations considering the topography of real measured surfaces were also run, and the validity of the lubrication approximation was assessed for such rough surfaces.

Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

Numerical solution of flood prediction and river regulation problems; report.

Reports 2 and 3 by E. Isaacson, J. J. Stoker, and A. Troesch.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.