Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs

The basic characteristic of a chaotic system is its sensitivity to the infinitesimal changes in its initial conditions. A limit to predictability in chaotic system arises mainly due to this sensitivity and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha basin, India for the period 1955-2000 is used for the study. It is found to exhibit a low dimensional chaotic nature with the dimension varying from 5 to 7. A multivariate phase space is generated, considering a climate data set of 16 variables. The chaotic nature of each of these variables is confirmed using false nearest neighbor method. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to eight principal components (PCs). This multivariate series (rainfall along with eight PCs) is found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction employing local approximation method is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is decreased or in other words predictability is increased by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be altered by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. (C) 2011 Elsevier B.V. All rights reserved.

PROMIDS: A PROtotype multi-rIng data flow system for functional programming languages

This paper presents a detailed description of the hardware design and implementation of PROMIDS: a PROtotype Multi-rIng Data flow System for functional programming languages. The hardware constraints and the design trade-offs are discussed. The design of the functional units is described in detail. Finally, we report our experience with PROMIDS.

The 26 July 2005 heavy rainfall event over Mumbai: numerical modeling aspects

The performance of the Advanced Regional Prediction System (ARPS) in simulating an extreme rainfall event is evaluated, and subsequently the physical mechanisms leading to its initiation and sustenance are explored. As a case study, the heavy precipitation event that led to 65 cm of rainfall accumulation in a span of around 6 h (1430 LT-2030 LT) over Santacruz (Mumbai, India), on 26 July, 2005, is selected. Three sets of numerical experiments have been conducted. The first set of experiments (EXP1) consisted of a four-member ensemble, and was carried out in an idealized mode with a model grid spacing of 1 km. In spite of the idealized framework, signatures of heavy rainfall were seen in two of the ensemble members. The second set (EXP2) consisted of a five-member ensemble, with a four-level one-way nested integration and grid spacing of 54, 18, 6 and 1 km. The model was able to simulate a realistic spatial structure with the 54, 18, and 6 km grids; however, with the 1 km grid, the simulations were dominated by the prescribed boundary conditions. The third and final set of experiments (EXP3) consisted of a five-member ensemble, with a four-level one-way nesting and grid spacing of 54, 18, 6, and 2 km. The Scaled Lagged Average Forecasting (SLAF) methodology was employed to construct the ensemble members. The model simulations in this case were closer to observations, as compared to EXP2. Specifically, among all experiments, the timing of maximum rainfall, the abrupt increase in rainfall intensities, which was a major feature of this event, and the rainfall intensities simulated in EXP3 (at 6 km resolution) were closest to observations. Analysis of the physical mechanisms causing the initiation and sustenance of the event reveals some interesting aspects. Deep convection was found to be initiated by mid-tropospheric convergence that extended to lower levels during the later stage. In addition, there was a high negative vertical gradient of equivalent potential temperature suggesting strong atmospheric instability prior to and during the occurrence of the event. Finally, the presence of a conducive vertical wind shear in the lower and mid-troposphere is thought to be one of the major factors influencing the longevity of the event.

A novel neural network design for long range prediction of rainfall pattern

The importance of long-range prediction of rainfall pattern for devising and planning agricultural strategies cannot be overemphasized. However, the prediction of rainfall pattern remains a difficult problem and the desired level of accuracy has not been reached. The conventional methods for prediction of rainfall use either dynamical or statistical modelling. In this article we report the results of a new modelling technique using artificial neural networks. Artificial neural networks are especially useful where the dynamical processes and their interrelations for a given phenomenon are not known with sufficient accuracy. Since conventional neural networks were found to be unsuitable for simulating and predicting rainfall patterns, a generalized structure of a neural network was then explored and found to provide consistent prediction (hindcast) of all-India annual mean rainfall with good accuracy. Performance and consistency of this network are evaluated and compared with those of other (conventional) neural networks. It is shown that the generalized network can make consistently good prediction of annual mean rainfall. Immediate application and potential of such a prediction system are discussed.

Predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach

Perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one. Even though the sensitivity of initial conditions limits the predictability in chaotic systems, an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor. This paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters, i.e., embedding dimension and delay time to quantify the uncertainty in initial conditions. The ensemble approach is implemented through a local learning wavelet network model with a global feed-forward neural network structure for the phase space prediction of chaotic streamflow series. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times. The ensemble approach is proved to be 50% more efficient than the single prediction for both local approximation and wavelet network approaches. The wavelet network approach has proved to be 30%-50% more superior to the local approximation approach. Compared to the traditional local approximation approach with single initial condition, the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated.

RRI-GBT MULTI-BAND RECEIVER: MOTIVATION, DESIGN, AND DEVELOPMENT

We report the design and development of a self-contained multi-band receiver (MBR) system, intended for use with a single large aperture to facilitate sensitive and high time-resolution observations simultaneously in 10 discrete frequency bands sampling a wide spectral span (100-1500 MHz) in a nearly log-periodic fashion. The development of this system was primarily motivated by need for tomographic studies of pulsar polar emission regions. Although the system design is optimized for the primary goal, it is also suited for several other interesting astronomical investigations. The system consists of a dual-polarization multi-band feed (with discrete responses corresponding to the 10 bands pre-selected as relatively radio frequency interference free), a common wide-band radio frequency front-end, and independent back-end receiver chains for the 10 individual sub-bands. The raw voltage time sequences corresponding to 16 MHz bandwidth each for the two linear polarization channels and the 10 bands are recorded at the Nyquist rate simultaneously. We present the preliminary results from the tests and pulsar observations carried out with the Robert C. Byrd Green Bank Telescope using this receiver. The system performance implied by these results and possible improvements are also briefly discussed.

Framework for enabling highly available distributed applications for utility computing

The move towards IT outsourcing is the first step towards an environment where compute infrastructure is treated as a service. In utility computing this IT service has to honor Service Level Agreements (SLA) in order to meet the desired Quality of Service (QoS) guarantees. Such an environment requires reliable services in order to maximize the utilization of the resources and to decrease the Total Cost of Ownership (TCO). Such reliability cannot come at the cost of resource duplication, since it increases the TCO of the data center and hence the cost per compute unit. We, in this paper, look into aspects of projecting impact of hardware failures on the SLAs and techniques required to take proactive recovery steps in case of a predicted failure. By maintaining health vectors of all hardware and system resources, we predict the failure probability of resources based on observed hardware errors/failure events, at runtime. This inturn influences an availability aware middleware to take proactive action (even before the application is affected in case the system and the application have low recoverability). The proposed framework has been prototyped on a system running HP-UX. Our offline analysis of the prediction system on hardware error logs indicate no more than 10% false positives. This work to the best of our knowledge is the first of its kind to perform an end-to-end analysis of the impact of a hardware fault on application SLAs, in a live system.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

Fault-Tolerant Average Execution Time Optimization for General Purpose Multi-Processor System-on Chips

Fault-tolerance is due to the semiconductor technology development important, not only for safety-critical systems but also for general-purpose (non-safety critical) systems. However, instead of guaranteeing that deadlines always are met, it is for general-purpose systems important to minimize the average execution time (AET) while ensuring fault-tolerance. For a given job and a soft (transient) error probability, we define mathematical formulas for AET that includes bus communication overhead for both voting (active replication) and rollback-recovery with checkpointing (RRC). And, for a given multi-processor system-on-chip (MPSoC), we define integer linear programming (ILP) models that minimize AET including bus communication overhead when: (1) selecting the number of checkpoints when using RRC, (2) finding the number of processors and job-to-processor assignment when using voting, and (3) defining fault-tolerance scheme (voting or RRC) per job and defining its usage for each job. Experiments demonstrate significant savings in AET.

A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter. (C) 2013 Elsevier B.V. All rights reserved.

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

A parallel-serial binary arbitration scheme for collision-free multi-access techniques

Multi-access techniques are widely used in computer networking and distributed multiprocessor systems. On-the-fly arbitration schemes permit one of the many contenders to access the medium without collisions. Serial arbitration is cost effective but is slow and hence unsuitable for high-speed multiprocessor environments supporting very high data transfer rates. A fully parallel arbitration scheme takes less time but is not practically realisable for large numbers of contenders. In this paper, a generalised parallel-serial scheme is proposed which significantly reduces the arbitration time and is practically realisable.

Priority-oriented reservation multiple access scheme for data communication through satellites

A multi-access scheme is proposed for handling priority-based messages in data communication systems through satellites. The different schemes by which time slots are alloted by the satellite are based on a ‘priority index’. The performance characteristics of the system using these schemes under different traffic conditions are discussed.

CAE-based prediction of projectile residual velocity for impact on single and multi-layered metallic armour plates

The present, paper deals with the CAE-based study Of impact of jacketed projectiles on single- and multi-layered metal armour plates using LS-DYNA. The validation of finite element modelling procedure is mainly based on the mesh convergence study using both shell and solid elements for representing single-layered mild steel target plates. It, is shown that the proper choice of mesh density and the strain rate-dependent material properties are essential for all accurate prediction of projectile residual velocity. The modelling requirements are initially arrived at by correlating against test residual velocities for single-layered mild steel plates of different depths at impact velocities in the ran.-c of approximately 800-870 m/s. The efficacy of correlation is adjudged, in terms of a 'correlation index', defined in the paper: for which values close to unity are desirable. The experience gained for single-layered plates is next; used in simulating projectile impacts on multi-layered mild steel target plates and once again a high degree of correlation with experimental residual velocities is observed. The study is repeated for single- and multi-layered aluminium target plates with a similar level of success in test residual velocity prediction. TO the authors' best knowledge, the present comprehensive study shows in particular for the first time that, with a. proper modelling approach, LS-DYNA can be used with a great degree of confidence in designing perforation-resistant single and multi-layered metallic armour plates.