A Comparison of Machine Learning Techniques for Modeling River Flow Time Series: The Case of Upper Cauvery River Basin

Models of river flow time series are essential in efficient management of a river basin. It helps policy makers in developing efficient water utilization strategies to maximize the utility of scarce water resource. Time series analysis has been used extensively for modeling river flow data. The use of machine learning techniques such as support-vector regression and neural network models is gaining increasing popularity. In this paper we compare the performance of these techniques by applying it to a long-term time-series data of the inflows into the Krishnaraja Sagar reservoir (KRS) from three tributaries of the river Cauvery. In this study flow data over a period of 30 years from three different observation points established in upper Cauvery river sub-basin is analyzed to estimate their contribution to KRS. Specifically, ANN model uses a multi-layer feed forward network trained with a back-propagation algorithm and support vector regression with epsilon intensive-loss function is used. Auto-regressive moving average models are also applied to the same data. The performance of different techniques is compared using performance metrics such as root mean squared error (RMSE), correlation, normalized root mean squared error (NRMSE) and Nash-Sutcliffe Efficiency (NSE).

COMPUTATIONAL MODELING OF A MULTI-LAYERED PIEZO-COMPOSITE BEAM MADE UP OF MFC

The Variational Asymptotic Method (VAM) is used for modeling a coupled non-linear electromechanical problem finding applications in aircrafts and Micro Aerial Vehicle (MAV) development. VAM coupled with geometrically exact kinematics forms a powerful tool for analyzing a complex nonlinear phenomena as shown previously by many in the literature 3 - 7] for various challenging problems like modeling of an initially twisted helicopter rotor blades, matrix crack propagation in a composite, modeling of hyper elastic plates and various multi-physics problems. The problem consists of design and analysis of a piezocomposite laminate applied with electrical voltage(s) which can induce direct and planar distributed shear stresses and strains in the structure. The deformations are large and conventional beam theories are inappropriate for the analysis. The behavior of an elastic body is completely understood by its energy. This energy must be integrated over the cross-sectional area to obtain the 1-D behavior as is typical in a beam analysis. VAM can be used efficiently to approximate 3-D strain energy as closely as possible. To perform this simplification, VAM makes use of thickness to width, width to length, width multiplied by initial twist and strain as small parameters embedded in the problem definition and provides a way to approach the exact solution asymptotically. In this work, above mentioned electromechanical problem is modeled using VAM which breaks down the 3-D elasticity problem into two parts, namely a 2-D non-linear cross-sectional analysis and a 1-D non-linear analysis, along the reference curve. The recovery relations obtained as a by-product in the cross-sectional analysis earlier are used to obtain 3-D stresses, displacements and velocity contours. The piezo-composite laminate which is chosen for an initial phase of computational modeling is made up of commercially available Macro Fiber Composites (MFCs) stacked together in an arbitrary lay-up and applied with electrical voltages for actuation. The expressions of sectional forces and moments as obtained from cross-sectional analysis in closed-form show the electro-mechanical coupling and relative contribution of electric field in individual layers of the piezo-composite laminate. The spatial and temporal constitutive law as obtained from the cross-sectional analysis are substituted into 1-D fully intrinsic, geometrically exact equilibrium equations of motion and 1-D intrinsic kinematical equations to solve for all 1-D generalized variables as function of time and an along the reference curve co-ordinate, x(1).

Modeling Ultrasonic NDE and Guided Wave based Structural Health Monitoring

Structural Health Monitoring (SHM) systems require integration of non-destructive technologies into structural design and operational processes. Modeling and simulation of complex NDE inspection processes are important aspects in the development and deployment of SHM technologies. Ray tracing techniques are vital simulation tools to visualize the wave path inside a material. These techniques also help in optimizing the location of transducers and their orientation with respect to the zone of interrogation. It helps in increasing the chances of detection and identification of a flaw in that zone. While current state-of-the-art techniques such as ray tracing based on geometric principle help in such visualization, other information such as signal losses due to spherical or cylindrical shape of wave front are rarely taken into consideration. The problem becomes a little more complicated in the case of dispersive guided wave propagation and near-field defect scattering. We review the existing models and tools to perform ultrasonic NDE simulation in structural components. As an initial step, we develop a ray-tracing approach, where phase and spectral information are preserved. This enables one to study wave scattering beyond simple time of flight calculation of rays. Challenges in terms of theory and modelling of defects of various kinds are discussed. Various additional considerations such as signal decay and physics of scattering are reviewed and challenges involved in realistic computational implementation are discussed. Potential application of this approach to SHM system design is highlighted and by applying this to complex structural components such as airframe structures, SHM is demonstrated to provide additional value in terms of lighter weight and/or longevity enhancement resulting from an extension of the damage tolerance design principle not compromising safety and reliability.

Joint modeling of lithosphere and mantle dynamics: Evaluation of constraints from global tomography models

With the advances in technology, seismological theory, and data acquisition, a number of high-resolution seismic tomography models have been published. However, discrepancies between tomography models often arise from different theoretical treatments of seismic wave propagation, different inversion strategies, and different data sets. Using a fixed velocity-to-density scaling and a fixed radial viscosity profile, we compute global mantle flow models associated with the different tomography models and test the impact of these for explaining surface geophysical observations (geoid, dynamic topography, stress, and strain rates). We use the joint modeling of lithosphere and mantle dynamics approach of Ghosh and Holt (2012) to compute the full lithosphere stresses, except that we use HC for the mantle circulation model, which accounts for the primary flow-coupling features associated with density-driven mantle flow. Our results show that the seismic tomography models of S40RTS and SAW642AN provide a better match with surface observables on a global scale than other models tested. Both of these tomography models have important similarities, including upwellings located in Pacific, Eastern Africa, Iceland, and mid-ocean ridges in the Atlantic and Indian Ocean and downwelling flows mainly located beneath the Andes, the Middle East, and central and Southeast Asia.

Control of Large-size SiC Growth Process Using Modeling tool

Large size bulk silicon carbide (SiC) crystals are commonly grown by the physical vapor transport (PVT) method. The PVT growth of SiC crystals involves sublimation and condensation, chemical reactions, stoichiometry, mass transport, induced thermal stress, as well as defect and micropipes generation and propagation. The quality and polytype of as-grown SiC crystals are related to the temperature distribution inside the growth chamber during the growth process, it is critical to predict the temperature distribution from the measured temperatures outside the crucible by pyrometers. A radio-frequency induction-heating furnace was used for the growth of large-size SiC crystals by the PVT method in the present study. Modeling and simulation have been used to develop the SiC growth process and to improve the SiC crystal quality. Parameters such as the temperature measured at the top of crucible, temperature measured at the bottom of the crucible, and inert gas pressure are used to control the SiC growth process. By measuring the temperatures at the top and bottom of the crucible, the temperatures inside the crucible were predicted with the help of modeling tool. SiC crystals of 6H polytype were obtained and characterized by the Raman scattering spectroscopy and SEM, and crystals of few millimeter size grown inside the crucible were found without micropipes. Expansion of the crystals were also performed with the help of modeling and simulation.

Algorithm for simulating fracture processes in concrete by lattice modeling

To simulate fracture behaviors in concrete more realistically, a theoretical analysis on the potential question in the quasi-static method is presented, then a novel algorithm is proposed which takes into account the inertia effect due to unstable crack propagation and meanwhile requests much lower computational efforts than purely dynamic method. The inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, results may become questionable if a fracture process including unstable cracking is simulated by the quasi-static procedure excluding completely inertia effects. However, it requires much higher computational effort to simulate experiments with not very high loading rates by the dynamic method. In this investigation which can be taken as a natural continuation, the potential question of quasi-static method is analyzed based on the dynamic equations of motion. One solution to this question is the new algorithm mentioned above. Numerical examples are provided by the generalized beam (GB) lattice model to show both fracture processes under different loading rates and capability of the new algorithm.

MODELING EVOLUTION OF INTERNAL WAVES IN SOUTH CHINA SEA

Internal waves are an important factor in the design of drill operations and production in deep water, because the waves have very large amplitude and may induce large horizontal velocity. How the internal waves occur and propagate over benthal terrain is of great concern for ocean engineers. In the present paper, we have formulated a mathematical model of internal wave propagation in a two-layer deep water, which involves the effects of friction, dissipation and shoaling, and is capable of manifesting the variation of the amplitude and the velocity pattern. After calibration by field data measured at the Continental Slope in the Northern South China Sea, we have applied the model to the South China Sea, investigating the westward propagation of internal waves from the Luzon Strait, where internal waves originate due to the interaction of benthal ridge and tides. We find that the internal wave induced velocity profile is obviously characterized by the opposite flow below and above the pycnocline, which results in a strong shear, threatening safety of ocean structures, such as mooring system of oil platform, risers, etc. When internal waves propagate westwards, the amplitude attenuates due to the effects of friction and dissipation. The preliminary results show that the amplitude is likely to become half of its initial value at Luzon Strait when the internal waves propagate about 400 kilometers westwards.

The Madden-Julian Oscillation : observation, modeling, and theory

The Madden-Julian Oscillation (MJO) is a pattern of intense rainfall and associated planetary-scale circulations in the tropical atmosphere, with a recurrence interval of 30-90 days. Although the MJO was first discovered 40 years ago, it is still a challenge to simulate the MJO in general circulation models (GCMs), and even with simple models it is difficult to agree on the basic mechanisms. This deficiency is mainly due to our poor understanding of moist convection—deep cumulus clouds and thunderstorms, which occur at scales that are smaller than the resolution elements of the GCMs. Moist convection is the most important mechanism for transporting energy from the ocean to the atmosphere. Success in simulating the MJO will improve our understanding of moist convection and thereby improve weather and climate forecasting.

We address this fundamental subject by analyzing observational datasets, constructing a hierarchy of numerical models, and developing theories. Parameters of the models are taken from observation, and the simulated MJO fits the data without further adjustments. The major findings include: 1) the MJO may be an ensemble of convection events linked together by small-scale high-frequency inertia-gravity waves; 2) the eastward propagation of the MJO is determined by the difference between the eastward and westward phase speeds of the waves; 3) the planetary scale of the MJO is the length over which temperature anomalies can be effectively smoothed by gravity waves; 4) the strength of the MJO increases with the typical strength of convection, which increases in a warming climate; 5) the horizontal scale of the MJO increases with the spatial frequency of convection; and 6) triggered convection, where potential energy accumulates until a threshold is reached, is important in simulating the MJO. Our findings challenge previous paradigms, which consider the MJO as a large-scale mode, and point to ways for improving the climate models.

Complexity of rupture propagation in large earthquakes in relation to tectonic environment

Complexity in the earthquake rupture process can result from many factors. This study investigates the origin of such complexity by examining several recent, large earthquakes in detail. In each case the local tectonic environment plays an important role in understanding the source of the complexity.

Several large shallow earthquakes (M_s > 7.0) along the Middle American Trench have similarities and differences between them that may lead to a better understanding of fracture and subduction processes. They are predominantly thrust events consistent with the known subduction of the Cocos plate beneath N. America. Two events occurring along this subduction zone close to triple junctions show considerable complexity. This may be attributable to a more heterogeneous stress environment in these regions and as such has implications for other subduction zone boundaries.

An event which looks complex but is actually rather simple is the 1978 Bermuda earthquake (M_s ~ 6). It is located predominantly in the mantle. Its mechanism is one of pure thrust faulting with a strike N 20°W and dip 42°NE. Its apparent complexity is caused by local crustal structure. This is an important event in terms of understanding and estimating seismic hazard on the eastern seaboard of N. America.

A study of several large strike-slip continental earthquakes identifies characteristics which are common to them and may be useful in determining what to expect from the next great earthquake on the San Andreas fault. The events are the 1976 Guatemala earthquake on the Motagua fault and two events on the Anatolian fault in Turkey (the 1967, Mudurnu Valley and 1976, E. Turkey events). An attempt to model the complex P-waveforms of these events results in good synthetic fits for the Guatemala and Mudurnu Valley events. However, the E. Turkey event proves to be too complex as it may have associated thrust or normal faulting. Several individual sources occurring at intervals of between 5 and 20 seconds characterize the Guatemala and Mudurnu Valley events. The maximum size of an individual source appears to be bounded at about 5 x 10²⁶ dyne-cm. A detailed source study including directivity is performed on the Guatemala event. The source time history of the Mudurnu Valley event illustrates its significance in modeling strong ground motion in the near field. The complex source time series of the 1967 event produces amplitudes greater by a factor of 2.5 than a uniform model scaled to the same size for a station 20 km from the fault.

Three large and important earthquakes demonstrate an important type of complexity --- multiple-fault complexity. The first, the 1976 Philippine earthquake, an oblique thrust event, represents the first seismological evidence for a northeast dipping subduction zone beneath the island of Mindanao. A large event, following the mainshock by 12 hours, occurred outside the aftershock area and apparently resulted from motion on a subsidiary fault since the event had a strike-slip mechanism.

An aftershock of the great 1960 Chilean earthquake on June 6, 1960, proved to be an interesting discovery. It appears to be a large strike-slip event at the main rupture's southern boundary. It most likely occurred on the landward extension of the Chile Rise transform fault, in the subducting plate. The results for this event suggest that a small event triggered a series of slow events; the duration of the whole sequence being longer than 1 hour. This is indeed a "slow earthquake".

Perhaps one of the most complex of events is the recent Tangshan, China event. It began as a large strike-slip event. Within several seconds of the mainshock it may have triggered thrust faulting to the south of the epicenter. There is no doubt, however, that it triggered a large oblique normal event to the northeast, 15 hours after the mainshock. This event certainly contributed to the great loss of life-sustained as a result of the Tangshan earthquake sequence.

What has been learned from these studies has been applied to predict what one might expect from the next great earthquake on the San Andreas. The expectation from this study is that such an event would be a large complex event, not unlike, but perhaps larger than, the Guatemala or Mudurnu Valley events. That is to say, it will most likely consist of a series of individual events in sequence. It is also quite possible that the event could trigger associated faulting on neighboring fault systems such as those occurring in the Transverse Ranges. This has important bearing on the earthquake hazard estimation for the region.

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in themixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective-reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected. © 2011 Taylor & Francis.

Fem modeling of periodic arrays of multi-walled carbon nanotubes

Multiwalled carbon nanotubes display dielectric properties similar to those of graphite, which can be calculated using the well known Drude-Lorentz model. However, most computational softwares lack the capacity to directly incorporate this model into the simulations. We present the finite element modeling of optical propagation through periodic arrays of multiwalled carbon nanotubes. The dielectric function of nanotubes was incorporated into the model by using polynomial curve fitting technique. The computational analysis revealed interesting metamaterial filtering effects displayed by the highly dense square lattice arrays of carbon nanotubes, having lattice constants of the order few hundred nanometers. The curve fitting results for the dielectric function can also be used for simulating other interesting optical applications based on nanotube arrays.

New application of temperature-dependent modelling of high temperature superconductors: Quench propagation and pulse magnetization

We present temperature-dependent modeling of high-temperature superconductors (HTS) to understand HTS electromagnetic phenomena where temperature fluctuation plays a nontrivial role. Thermal physics is introduced into the well-developed H-formulation model, and the effect of temperature-dependent parameters is considered. Based on the model, we perform extensive studies on two important HTS applications: quench propagation and pulse magnetization. A micrometer-scale quench model of HTS coil is developed, which can be used to estimate minimum quench energy and normal zone propagation velocity inside the coil. In addition, we study the influence of inhomogeneity of HTS bulk during pulse magnetization. We demonstrate how the inhomogeneous distribution of critical current inside the bulk results in varying degrees of heat dissipation and uniformity of final trapped field. The temperature- dependent model is proven to be a powerful tool to study the thermally coupled electromagnetic phenomena of HTS. © 2012 American Institute of Physics.

Modeling of cyanobacterial blooms in hypereutrophic Lake Dianchi, China

Compared with other approaches for modeling and predicting, artificial neural networks are more effective in describing complex and non-linear systems. The occurrence of cyanobacterial blooms has been a continuous and serious problem over the past decades in hypereutrophic Lake Dianchi. Yet, the main factor(s) initiating these blooms remain(s) unclear. During 2001-2002 at 40 sampling sites in Lake Dianchi, physicochemical parameters possibly relating to the blooms were measured. Parameters directly or indirectly relating to the cyanobacterial blooms were used as driving factors in a back-propagation network to model the concentration of chlorophyll a. According to sensitivity analysis, chemical oxygen demand was identified as a very significant environmental factor for algal growth in Lake Dianchi.

Modeling and optimizing of high-concentration erbium-doped fiber amplifiers with consideration of ion-clusters

Starting from the modeling of isolated ions and ion-clusters, a closed form rate and power evolution equations for high-concentration erbium-doped fiber amplifiers are constructed. Based on the equations, the effects of the fraction of ion-clusters in total ions and the number of ions per cluster on the performance of high-concentration erbium-doped fiber amplifiers are analyzed numerically. The results show that the presence of the ion-clusters deteriorates amplifier performance, such as the signal power, signal gain, the threshold pump power for zero gain, saturated signal gain, and the maximum gain efficiency, etc. The optimum fiber length or other parameters should be modified with the ion-clusters being taken into account for the amplifiers to achieve a better performance. (c) 2007 Elsevier B.V. All rights reserved.

APPLICATION OF THE KHOKHLOV-ZABOLOTSKAYA-KUZNETSOV EQUATION TO MODELING HIGH-INTENSITY FOCUSED ULTRASOUND BEAMS

High-intensity focused ultrasound is a form of therapeutic ultrasound which uses high amplitude acoustic waves to heat and ablate tissue. HIFU employs acoustic amplitudes that are high enough that nonlinear propagation effects are important in the evolution of the sound field. A common model for HIFU beams is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation which accounts for nonlinearity, diffraction, and absorption. The KZK equation models diffraction using the parabolic or paraxial approximation. Many HIFU sources have an aperture diameter similar to the focal length and the paraxial approximation may not be appropriate. Here, results obtained using the “Texas code,” a time-domain numerical solution to the KZK equation, were used to assess when the KZK equation can be employed. In a linear water case comparison with the O’Neil solution, the KZK equation accurately predicts the pressure field in the focal region. The KZK equation was also compared to simulations of the exact fluid dynamics equations (no paraxial approximation). The exact equations were solved using the Fourier-Continuation (FC) method to approximate derivatives in the equations. Results have been obtained for a focused HIFU source in tissue. For a low focusing gain transducer (focal length 50λ and radius 10λ), the KZK and FC models showed excellent agreement, however, as the source radius was increased to 30λ, discrepancies started to appear. Modeling was extended to the case of tissue with the appropriate power law using a relaxation model. The relaxation model resulted in a higher peak pressure and a shift in the location of the peak pressure, highlighting the importance of employing the correct attenuation model. Simulations from the code that were compared to experimental data in water showed good agreement through the focal plane.