Estimation of heavy rainfall during cyclonic storms from microwave observations using nonlinear approach over Indian Ocean

In this study, an effort has been made to study heavy rainfall events during cyclonic storms over Indian Ocean. This estimate is based on microwave observations from tropical rainfall measuring mission (TRMM) Microwave Imager (TMI). Regional scattering index (SI) developed for Indian region based on measurements at 19-, 21- and 85-GHz brightness temperature and polarization corrected temperature (PCT) at 85 GHz have been utilized in this study. These PCT and SI are collocated against Precipitation Radar (PR) onboard TRMM to establish a relationship between rainfall rate, PCT and SI. The retrieval technique using both linear and nonlinear regressions has been developed utilizing SI, PCT and the combination of SI and PCT. The results have been compared with the observations from PR. It was found that a nonlinear algorithm using combination of SI and PCT is more accurate than linear algorithm or nonlinear algorithm using either SI or PCT. Statistical comparison with PR exhibits the correlation coefficients (CC) of 0.68, 0.66 and 0.70, and root mean square error (RMSE) of 1.78, 1.96 and 1.68 mm/h from the observations of SI, PCT and combination of SI and PCT respectively using linear regressions. When nonlinear regression is used, the CC of 0.73, 0.71, 0.79 and RMSE of 1.64, 1.95, 1.54 mm/h are observed from the observations of SI, PCT and combination of SI and PCT, respectively. The error statistics for high rain events (above 10 mm/h) shows the CC of 0.58, 0.59, 0.60 and RMSE of 5.07, 5.47, 5.03 mm/h from the observations of SI, PCT and combination of SI and PCT, respectively, using linear regression, and on the other hand, use of nonlinear regression yields the CC of 0.66, 0.64, 0.71 and RMSE of 4.68, 5.78 and 4.02 mm/h from the observations of SI, PCT and combined SI and PCT, respectively.

Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

On Regression Methods for Virtual Metrology in Semiconductor Manufacturing

Virtual metrology (VM) aims to predict metrology values using sensor data from production equipment and physical metrology values of preceding samples. VM is a promising technology for the semiconductor manufacturing industry as it can reduce the frequency of in-line metrology operations and provide supportive information for other operations such as fault detection, predictive maintenance and run-to-run control. The prediction models for VM can be from a large variety of linear and nonlinear regression methods and the selection of a proper regression method for a specific VM problem is not straightforward, especially when the candidate predictor set is of high dimension, correlated and noisy. Using process data from a benchmark semiconductor manufacturing process, this paper evaluates the performance of four typical regression methods for VM: multiple linear regression (MLR), least absolute shrinkage and selection operator (LASSO), neural networks (NN) and Gaussian process regression (GPR). It is observed that GPR performs the best among the four methods and that, remarkably, the performance of linear regression approaches that of GPR as the subset of selected input variables is increased. The observed competitiveness of high-dimensional linear regression models, which does not hold true in general, is explained in the context of extreme learning machines and functional link neural networks.

On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots. The framework proposed combines nonlinear dimensionality reduction, nonlinear regression under noise, and variational Bayesian learning to create consistent probabilistic representations of places from images. These generative models are learnt from a few images and used for multi-class place recognition where classification is computed from a set of feature-vectors. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions and blurring. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

A bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots that can be used for planning and navigation tasks. The proposed framework combines nonlinear dimensionality reduction, nonlinear regression under noise, and Bayesian learning to create consistent probabilistic representations of places from images. These generative models are incrementally learnt from very small training sets and used for multi-class place recognition. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions, blurring and moving objects. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images, respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Prediction of frequency and amplitude of foundations at resonance

This note presents the statistical analysis carried out on some of the available experimental results to predict the resonant frequency and maximum displacement amplitude of a machine foundation – soil system under vertical vibration as a function of the size and weight of the foundation and of the excitation level. A total of 442 experimental results of Fry, Novak, and Raman have been analysed using nonlinear regression analysis. The results obtained compared well with predictions obtained from the popular theoretical models, and the coefficient of correlation obtained from the analysis was satisfactory in most of the cases.

Comparison of the impact of six heat-load management strategies on thermal responses and milk production of feed-pad and pasture fed dairy cows in a subtropical environment

Exposure to hot environments affects milk yield (MY) and milk composition of pasture and feed-pad fed dairy cows in subtropical regions. This study was undertaken during summer to compare MY and physiology of cows exposed to six heat-load management treatments. Seventy-eight Holstein-Friesian cows were blocked by season of calving, parity, milk yield, BW, and milk protein (%) and milk fat (%) measured in 2 weeks prior to the start of the study. Within blocks, cows were randomly allocated to one of the following treatments: open-sided iron roofed day pen adjacent to dairy (CID) + sprinklers (SP); CID only; non-shaded pen adjacent to dairy + SP (NSD + SP); open-sided shade cloth roofed day pen adjacent to dairy (SCD); NSD + sprinkler (sprinkler on for 45 min at 1100 h if mean respiration rate >80 breaths per minute (NSD + WSP)); open-sided shade cloth roofed structure over feed bunk in paddock + 1 km walk to and from the dairy (SCP + WLK). Sprinklers for CID + SP and NSD + SP cycled 2 min on, 12 min off when ambient temperature >26°C. The highest milk yields were in the CID + SP and CID treatments (23.9 L cow−1 day−1), intermediate for NSD + SP, SCD and SCP + WLK (22.4 L cow−1 day−1), and lowest for NSD + WSP (21.3 L cow−1 day−1) (P < 0.05). The highest (P < 0.05) feed intakes occurred in the CID + SP and CID treatments while intake was lowest (P < 0.05) for NSD + WSP and SCP + WLK. Weather data were collected on site at 10-min intervals, and from these, THI was calculated. Nonlinear regression modelling of MY × THI and heat-load management treatment demonstrated that cows in CID + SP showed no decline in MY out to a THI break point value of 83.2, whereas the pooled MY of the other treatments declined when THI >80.7. A combination of iron roof shade plus water sprinkling throughout the day provided the most effective control of heat load.

Analysis of oxide and vanadate supports for catalytic hydrogen combustion: Kinetic and mechanistic investigations

Combustion synthesized oxide and vanadate compounds (CeO2, Fe2O3, CeVO4, and FeVO4) were tested for catalytic hydrogen combustion. The compounds were characterized by X-ray diffraction and X-ray photoelectron spectroscopy. All the four compounds showed good activity and stability for catalytic hydrogen combustion and more than 95% conversion was observed over all the compounds within 500 degrees C. The mechanisms for the reaction over the different classes of compounds (cerium-based and iron-based compounds) were proposed on the basis of spectroscopic observations. The main difference in the mechanisms was in the nature of adsorption of H2 over the sites. The elementary processes for the reaction were proposed, corresponding rate expressions were derived, and the rate parameters for the reaction were estimated using nonlinear regression. Langmuir-Hinshelwood and Eley-Rideal mechanisms were also tested for the reaction and the proposed mechanism was compared with these mechanisms. (c) 2011 American Institute of Chemical Engineers AIChE J, 2012

Temporal Envelope Fit of Transient Audio Signals

We address the problem of temporal envelope modeling for transient audio signals. We propose the Gamma distribution function (GDF) as a suitable candidate for modeling the envelope keeping in view some of its interesting properties such as asymmetry, causality, near-optimal time-bandwidth product, controllability of rise and decay, etc. The problem of finding the parameters of the GDF becomes a nonlinear regression problem. We overcome the hurdle by using a logarithmic envelope fit, which reduces the problem to one of linear regression. The logarithmic transformation also has the feature of dynamic range compression. Since temporal envelopes of audio signals are not uniformly distributed, in order to compute the amplitude, we investigate the importance of various loss functions for regression. Based on synthesized data experiments, wherein we have a ground truth, and real-world signals, we observe that the least-squares technique gives reasonably accurate amplitude estimates compared with other loss functions.