Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Stabilizing controller design for uncertain nonlinear systems using fuzzy models

A Lyapunov-based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed. The controller is constructed using a design model of the dynamical process to be controlled. The design model is obtained from the truth model using a fuzzy modeling approach. The truth model represents a detailed description of the process dynamics. The truth model is used in a simulation experiment to evaluate the performance of the controller design. A method for generating local models that constitute the design model is proposed. Sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state-feedback controllers are given. The results obtained are illustrated with a numerical example involving a four-dimensional nonlinear model of a stick balancer.

Study of stayability in Nellore cows using a threshold model

The objectives of the current study were to assess the feasibility of using stayability traits to improve fertility of Nellore cows and to examine the genetic relationship among the stayabilities at different ages. Stayability was defined as whether a cow calved every year up to the age of 5 (Stay5), 6 (Stay6), or 7 (Stay7) yr of age or more, given that she was provided the opportunity to breed. Data were analyzed based on a maximum a posteriori probit threshold model to predict breeding values on the liability scale, whereas the Gibbs sampler was used to estimate variance components. The EBV were obtained using all animals included in the pedigree or bulls with at least 10 daughters with stayability observations, and average genetic trends were obtained in the liability and transformed to the probability scale. Additional analyses were performed to study the genetic relationship among stayability traits, which were compared by contrasting results in terms of EBV and the average genetic superiority as a function of the selected proportion of sires. Heritability estimates and SD were 0.25 +/- 0.02, 0.22 +/- 0.03, and 0.28 +/- 0.03 for Stay5, Stay6, and Stay7, respectively. Average genetic trends, by year, were 0.51 +/- 0.34, and 0.38% for Stay5, Stay6, and Stay7, respectively. Estimates of EBV SD, in the probability scale, for all animals included in the pedigree and for bulls with at least 10 daughters with stayability observations were 7.98 and 12.95, 6.93 and 11.38, and 8.24 and 14.30% for Stay5, Stay6, and Stay7, respectively. A reduction in the average genetic superiorities in Stay7 would be expected if the selection were based on Stay5 or Stay6. Nonetheless, the reduction in EPD, depending on selection intensity, is on average 0.74 and 1.55%, respectively. Regressions of the sires' EBV for Stay5 and Stay6 on the sires' EBV for Stay7 confirmed these results. The heritability and genetic trend estimates for all stayability traits indicate that it is possible to improve fertility with selection based on a threshold analysis of stayability. The SD of EBV for stayability traits show that there is adequate genetic variability among animals to justify inclusion of stayability as a selection criterion. The potential linear relationship among stayability traits indicates that selection for improved female traits would be more effective by having predictions on the Stay5 trait.

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

A Multi-Stage Stochastic Non-Linear Model for Reactive Power Planning Under Contingencies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Contribution of electrical parameters on the dynamical behaviour of a nonlinear electromagnetic damper

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The use of nonlinear programming as a tool for maximum profit feed formulation of broilers

The purpose of this study was to compare linear and nonlinear programming models for feed formulation, for maximum profit, considering the real variation in the prices of the corn, soybean meal and broilers during the period from January of 2008 to October of 2009, in the São Paulo State, Brazil. For the nonlinear formulation model, it was considered the following scenarios of prices: a) the minimum broiler price and the maximum prices of the corn and soybean meal during the period, b) the mean prices of the broiler, corn and soybean meal in the period and c) the maximum broiler price and the minimum prices of the corn and soybean meal, in the considered period; while for the linear formulation model, it was considered just the prices of the corn and the soybean. It was used the Practical Program for Feed Formulation 2.0 for the diets establishment. A total of 300 Cobb male chicks were randomly assigned to the 4 dietary treatments with 5 replicate pens of 15 chicks each. The birds were fed with a starter diet until 21 d and a grower diet from 22 to 42 d of age, and they had ad libitum access to feed and water, on floor with wood shavings as litter. The broilers were raised in an environmentally-controlled house. Body weight, body weight gain, feed intake, feed conversion ratio and profitability (related to the prices variation of the broilers and ingredients) were obtained at 42 d of age. It was found that the broilers fed with the diet formulated with the linear model presented the lowest feed intake and feed conversion ratio as compared with the broilers fed with diets from nonlinear formulation models. There were no significant differences in body weight and body weight gain among the treatments. Nevertheless, the profitabilities of the diets from the nonlinear model were significantly higher than that one from the linear formulation model, when the corn and soybean meal prices were near or below their average values for the studied period, for any broiler chicken price.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Transformer Operation at Deep Saturation: Model and Parameter Determination

This paper proposes a model that adequately describes the operation of the transformer at deep saturation, suitable for power-electronics applications, and a method for determining its parameters. Simulation and experimental results are presented to confirm the validity of the model and the method.

Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Study of tissue damage during mechanical peeling of tough skinned vegetables

Peeling is an essential phase of post harvesting and processing industry; however the undesirable losses and waste rate that occur during peeling stage are always the main concern of food processing sector. There are three methods of peeling fruits and vegetables including mechanical, chemical and thermal, depending on the class and type of fruit. By comparison, the mechanical method is the most preferred; this method keeps edible portions of produce fresh and creates less damage. Obviously reducing material losses and increasing the quality of the process has a direct effect on the whole efficiency of food processing industry which needs more study on technological aspects of this industrial segment. In order to enhance the effectiveness of food industrial practices it is essential to have a clear understanding of material properties and behaviour of tissues under industrial processes. This paper presents the scheme of research that seeks to examine tissue damage of tough skinned vegetables under mechanical peeling process by developing a novel FE model of the process using explicit dynamic finite element analysis approach. In the proposed study a nonlinear model which will be capable of simulating the peeling process specifically, will be developed. It is expected that unavailable information such as cutting force, maximum shearing force, shear strength, tensile strength and rupture stress will be quantified using the new FEA model. The outcomes will be used to optimize and improve the current mechanical peeling methods of this class of vegetables and thereby enhance the overall effectiveness of processing operations. Presented paper aims to review available literature and previous works have been done in this area of research and identify current gap in modelling and simulation of food processes.