Parameter identification of structural dynamic models by inverse statistical analysis

Auf dem Gebiet der Strukturdynamik sind computergestützte Modellvalidierungstechniken inzwischen weit verbreitet. Dabei werden experimentelle Modaldaten, um ein numerisches Modell für weitere Analysen zu korrigieren. Gleichwohl repräsentiert das validierte Modell nur das dynamische Verhalten der getesteten Struktur. In der Realität gibt es wiederum viele Faktoren, die zwangsläufig zu variierenden Ergebnissen von Modaltests führen werden: Sich verändernde Umgebungsbedingungen während eines Tests, leicht unterschiedliche Testaufbauten, ein Test an einer nominell gleichen aber anderen Struktur (z.B. aus der Serienfertigung), etc. Damit eine stochastische Simulation durchgeführt werden kann, muss eine Reihe von Annahmen für die verwendeten Zufallsvariablengetroffen werden. Folglich bedarf es einer inversen Methode, die es ermöglicht ein stochastisches Modell aus experimentellen Modaldaten zu identifizieren. Die Arbeit beschreibt die Entwicklung eines parameter-basierten Ansatzes, um stochastische Simulationsmodelle auf dem Gebiet der Strukturdynamik zu identifizieren. Die entwickelte Methode beruht auf Sensitivitäten erster Ordnung, mit denen Parametermittelwerte und Kovarianzen des numerischen Modells aus stochastischen experimentellen Modaldaten bestimmt werden können.

How well do high resolution models reproduce tropical convection?

Cascade is a multi-institution project studying the temporal and spatial organization of tropical convective systems. While cloud resolving numerical models can reproduce the observed diurnal cycle of such systems they are sensitive to the chosen resolution. As part of this effort, we are comparing results from the Met. Office Unified Model to data from the Global Earth Radiation Budget satellite instrument over the African Monsoon Interdisciplinary Analyses region of North Africa. We use a variety of mathematical techniques to study the outgoing radiation and the evolution of properties such as the cloud size distribution. The effectiveness of various model resolutions is tested with a view to determining the optimum balance between resolution and the need to reproduce the observations.

Comparison between observations and models of the Mozambique Channel transport: Seasonal cycle and eddy frequencies

A time series of the observed transport through an array of moorings across the Mozambique Channel is compared with that of six model runs with ocean general circulation models. In the observations, the seasonal cycle cannot be distinguished from red noise, while this cycle is dominant in the transport of the numerical models. It is found, however, that the seasonal cycles of the observations and numerical models are similar in strength and phase. These cycles have an amplitude of 5 Sv and a maximum in September, and can be explained by the yearly variation of the wind forcing. The seasonal cycle in the models is dominant because the spectral density at other frequencies is underrepresented. Main deviations from the observations are found at depths shallower than 1500 m and in the 5/y–6/y frequency range. Nevertheless, the structure of eddies in the models is close to the observed eddy structure. The discrepancy is found to be related to the formation mechanism and the formation position of the eddies. In the observations, eddies are frequently formed from an overshooting current near the mooring section, as proposed by Ridderinkhof and de Ruijter (2003) and Harlander et al. (2009). This causes an alternation of events at the mooring section, varying between a strong southward current, and the formation and passing of an eddy. This results in a large variation of transport in the frequency range of 5/y–6/y. In the models, the eddies are formed further north and propagate through the section. No alternation similar to the observations is observed, resulting in a more constant transport.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

Numerical prediction of atmospheric blocking-A case study

A series of numerical models have been used to investigate the predictability of atmospheric blocking for an episode selected from FGGE Special Observing Period I. Level II-b FGGE data have been used in the experiment. The blocking took place over the North Atlantic region and is a very characteristic example of high winter blocking. It is found that the very high resolution models developed at ECMWF, in a remarkable way manage to predict the blocking event in great detail, even beyond 1 week. Although models with much less resolution manage to predict the blocking phenomenon as such, the actual evolution differs very much from the observed and consequently the practical value is substantially reduced. Wind observations from the geostationary satellites are shown to have a substantial impact on the forecast beyond 5 days, as well as an extension of the integration domain to the whole globe. Quasi-geostrophic baroclinic models and, even more, barotropic models, are totally inadequate to predict blocking except in its initial phase. The prediction experiment illustrates clearly that efforts which have gone into the improvement of numerical prediction models in the last decades have been worth while.

Parameterised diabatic processes in numerical simulations of an extratropical cyclone

The parameterisation of diabatic processes in numerical models is critical for the accuracy of weather forecasts and for climate projections. A novel approach to the evaluation of these processes in models is introduced in this contribution. The approach combines a suite of on-line tracer diagnostics with off-line trajectory calculations. Each tracer tracks accumulative changes in potential temperature associated with a particular parameterised diabatic process in the model. A comparison of tracers therefore allows the identification of the most active diabatic processes and their downstream impacts. The tracers are combined with trajectories computed using model-resolved winds, allowing the various diabatic contributions to be tracked back to their time and location of occurrence. We have used this approach to investigate diabatic processes within a simulated extratropical cyclone. We focus on the warm conveyor belt, in which the dominant diabatic contributions come from large-scale latent heating and parameterised convection. By contrasting two simulations, one with standard convection parameterisation settings and another with reduced parameterised convection, the effects of parameterised convection on the structure of the cyclone have been determined. Under reduced parameterised convection conditions, the large-scale latent heating is forced to release convective instability that would otherwise have been released by the convection parameterisation. Although the spatial distribution of precipitation depends on the details of the split between parameterised convection and large-scale latent heating, the total precipitation amount associated with the cyclone remains largely unchanged. For reduced parameterised convection, a more rapid and stronger latent heating episode takes place as air ascends within the warm conveyor belt.

A 27 day persistence model of near-Earth solar wind conditions: a long lead-time forecast and a benchmark for dynamical models

Geomagnetic activity has long been known to exhibit approximately 27 day periodicity, resulting from solar wind structures repeating each solar rotation. Thus a very simple near-Earth solar wind forecast is 27 day persistence, wherein the near-Earth solar wind conditions today are assumed to be identical to those 27 days previously. Effective use of such a persistence model as a forecast tool, however, requires the performance and uncertainty to be fully characterized. The first half of this study determines which solar wind parameters can be reliably forecast by persistence and how the forecast skill varies with the solar cycle. The second half of the study shows how persistence can provide a useful benchmark for more sophisticated forecast schemes, namely physics-based numerical models. Point-by-point assessment methods, such as correlation and mean-square error, find persistence skill comparable to numerical models during solar minimum, despite the 27 day lead time of persistence forecasts, versus 2–5 days for numerical schemes. At solar maximum, however, the dynamic nature of the corona means 27 day persistence is no longer a good approximation and skill scores suggest persistence is out-performed by numerical models for almost all solar wind parameters. But point-by-point assessment techniques are not always a reliable indicator of usefulness as a forecast tool. An event-based assessment method, which focusses key solar wind structures, finds persistence to be the most valuable forecast throughout the solar cycle. This reiterates the fact that the means of assessing the “best” forecast model must be specifically tailored to its intended use.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

Parameterization Of Turbulence Models Using 3DVAR Data Assimilation

In this research the 3DVAR data assimilation scheme is implemented in the numerical model DIVAST in order to optimize the performance of the numerical model by selecting an appropriate turbulence scheme and tuning its parameters. Two turbulence closure schemes: the Prandtl mixing length model and the two-equation k-ε model were incorporated into DIVAST and examined with respect to their universality of application, complexity of solutions, computational efficiency and numerical stability. A square harbour with one symmetrical entrance subject to tide-induced flows was selected to investigate the structure of turbulent flows. The experimental part of the research was conducted in a tidal basin. A significant advantage of such laboratory experiment is a fully controlled environment where domain setup and forcing are user-defined. The research shows that the Prandtl mixing length model and the two-equation k-ε model, with default parameterization predefined according to literature recommendations, overestimate eddy viscosity which in turn results in a significant underestimation of velocity magnitudes in the harbour. The data assimilation of the model-predicted velocity and laboratory observations significantly improves model predictions for both turbulence models by adjusting modelled flows in the harbour to match de-errored observations. 3DVAR allows also to identify and quantify shortcomings of the numerical model. Such comprehensive analysis gives an optimal solution based on which numerical model parameters can be estimated. The process of turbulence model optimization by reparameterization and tuning towards optimal state led to new constants that may be potentially applied to complex turbulent flows, such as rapidly developing flows or recirculating flows.

Analysis of Mediterranean ocean variability using five numerical simulations

Programa de oceanografía

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

Extension and Partitioning in an Oblique Subduction Zone, New Zealand: Constraints from Three-Dimensional Numerical Modeling

Contraction, strike slip, and extension displacements along the Hikurangi margin northeast of the North Island of New Zealand coincide with large lateral gradients in material properties. We use a finite- difference code utilizing elastic and elastic-plastic rheologies to build large- scale, three-dimensional numerical models which investigate the influence of material properties on velocity partitioning within oblique subduction zones. Rheological variation in the oblique models is constrained by seismic velocity and attenuation information available for the Hikurangi margin. We compare the effect of weakly versus strongly coupled subduction interfaces on the development of extension and the partitioning of velocity components for orthogonal and oblique convergence and include the effect of ponded sediments beneath the Raukumara Peninsula. Extension and velocity partitioning occur if the subduction interface is weak, but neither develops if the subduction interface is strong. The simple mechanical model incorporating rheological variation based on seismic observations produces kinematics that closely match those published from the Hikurangi margin. These include extension within the Taupo Volcanic Zone, uplift over ponded sediments, and dextral contraction to the south.

Development of FEM/BEM and SEA models from experimental results for structural elements with attached equipment

This work focuses on the analysis of a structural element of MetOP-A satellite. Given the special interest in the influence of equipment installed on structural elements, the paper studies one of the lateral faces on which the Advanced SCATterometer (ASCAT) is installed. The work is oriented towards the modal characterization of the specimen, describing the experimental set-up and the application of results to the development of a Finite Element Method (FEM) model to study the vibro-acoustic response. For the high frequency range, characterized by a high modal density, a Statistical Energy Analysis (SEA) model is considered, and the FEM model is used when modal density is low. The methodology for developing the SEA model and a compound FEM and Boundary Element Method (BEM) model to provide continuity in the medium frequency range is presented, as well as the necessary updating, characterization and coupling between models required to achieve numerical models that match experimental results.

A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.