In the recent years, the internet has been developed rapidly. By this convenient medium, the information can be spread easily all over the world. Using the convenience and variety of internet, e-learning has become a burgeoning and efficient way for learning. The main idea of e-learning is applying the concept of Asynchronous Course Delivery, and establishing a learning environment on the internet. With the connection between computer and the internet, user can learn more in a convenient environment. In order to apply the concept of e-learning to the course of statistics, we use the Java programming language to establish an on-line interactive environment. In addition to learn some fundamental concepts of statistics, learner can also strengthen the abilities of researching and surfing by themselves. In this paper we developed six interactive examples. Not only interpreting and illustrating, we also introduce the motive, goal, relative concepts and applications in detail for each example. Finally, we hope that user can easily learn more knowledge of statistics by this learning environment, then our e-learning to statistical education, can be achieved.

This thesis is concerned with investigations on two related issues of turbulent jet diffusion flame, namely (a) stabilization at liftoff and (b) autoignition in a turbulent jet diffusion flame. The approach of Conditional Moment Closure (CMC) has been taken. Fully elliptic first order CMC equations are solved with detailed chemistry to simulate lifted H2/N2 flame in vitiated coflow. The same approach is further used to simulate transient autoignition process in inhomogeneous mixing layers. In Chapter 1, difficulties involved in numerical simulation of turbulent combustion problems are explained. Different numerical tools used to simulate turbulent combustion are briefly discussed. Previous experimental, theoretical and numerical studies of lifted jet diffusion flames and autoignition are reviewed. Various research issues related to objectives of the thesis are discussed. In Chapter 2, the first order CMC transport equations for the reacting flows are presented. Various closure models that are required for solving the governing equations are given. Calculation of mean reaction rate term for detailed chemistry is given with special focus on the reaction rates for pressure dependent reactions. In Chapter 3, starting with the laminar flow code, further extension is carried to include kε turbulence model and PDF model. The code is validated at each stage of inclusion of different model. In this chapter, the code is first validated for the test problem of constant density, 2D, axisymmetric turbulent jet. Further, validation of PDF model is carried out by simulating the problem of nonreacting jet of cold air issuing into a vitiated coflow. The results are compared with the published data from experiments as well as numerical simulations. It is shown that the results compare well with the data. In Chapter 4, numerical results of lifted jet diffusion flame are presented. Detailed chemistry is modelled using Mueller mechanism for H2/O2 system with 9 species and 21 reversible reactions. Simulations are carried out for different jet velocities and coflow stream temperatures. The predicted liftoff generally agrees with experimental data, as well as joint PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for different coflow temperatures reveal that (1) Inside the flamezone, the chemical term balances the molecular diffusion term, and hence the structure is of a diffusion flamelet for both cases. (2) In the preflame zone, the structure depends on the coflow temperature: for low coflow temperatures, the chemical term being small, the advective term balances the axial diffusion term. However, for the high coflow temperature case, the chemical term is large and balances the advective term, the axial diffusion term being small. It is concluded that, liftoff is controlled (a) by turbulent premixed flame propagation for low cofflow temperature while (b) by autoignition for high coflow temperature. In Chapter 5, the numerical results of autoignition in inhomogeneous mixing layer are presented. The configuration consists of a fuel jet issued into hot air for which transient simulations are performed. It is found that the constants assumed in various modelling terms can severely influence the results, particularly the flame temperature. Hence, modifications to these constants are suggested to obtain improved predictions. Preliminary work is carried out to predict autoignition lengths (which may be defined by Tign × Ujet incase of jet- and coflowvelocities being equal) by varying the coflow temperature. The autoignition lengths show a reasonable agreement with the experimental data and LES results. In Chapter 6, main conclusions of this thesis are summarized. Possible future studies on this problem are suggested.

The standard, EN12354-1 describes a simplified statistical energy analysis (SEA) model to predict the apparent sound reduction index between two rooms inclusive of the contributions of the flanking paths. There is interest worldwide in applying the EN12354 model to lightweight building elements. However, lightweight elements typically do not meet the requirements of an SEA subsystem and therefore applying the EN12354 model to these elements may result in inaccurate predictions. The purpose of this investigation was to systematically evaluate the application of the EN12354 model to lightweight building constructions. The evaluation included the determination of the probability density functions and the propagated uncertainty of the calculations. Knowledge of the probability density functions resulted in alternative calculations of the structure-borne sound transmitted through the constructions. The uncertainty analysis revealed that the uncertainty of the predictions is directly affected by the variance of the vibratory field measured on the elements. The vibratory fields of lightweight elements typically show large variances and therefore the propagated uncertainty of the EN12354 predictions for these elements can be significant. The investigation included measurements both in the laboratory and in the field. The results of the laboratory measurements were compared to both predictions using the EN12354 methods and ESEA models which included higher order flanking paths and non-resonant transmission paths. The field measurements included in this investigation were unique because the flanking intensity sound reduction indices of the elements in the source room were measured. The measurements allowed for the EN12354 predictions for each flanking element to be assessed instead of just the apparent sound reduction index between the rooms. The study resulted in proposed correction factors for when reciprocity does not hold and proposed changes to ISO10848 to improve the accuracy of the predictions when the EN12354 method was applied to lightweight building elements. However, neither the proposed correction factors nor the proposed changed to ISO10848-1 could correct for the potentially large differences between the predicted and the measured results. Based on the findings of this study, the use of the EN12354 model for the calculation of the apparent sound reduction index of lightweight elements is not endorsed. Lightweight constructions may not be categorized as ideal SEA subsystems due to the lack of diffuseness of the vibratory field. Furthermore, in order for EN12354 to be applied to lightweight constructions, a reliable method of calculating the resonant component of the sound reduction index of double-leaf elements is required. Therefore, statistical methods including the EN12354 method may be unsuitable for use for the prediction of flanking noise for lightweight building constructions.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

<p>In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as &lsquo / mean-unbiased&rsquo / and &lsquo / medianunbiased&rsquo / estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1).</p> <p><br /> However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to&nbsp / compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the &lsquo / medianunbiased&rsquo / estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed / the &lsquo / most-probably-unbiased&rsquo / estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed / (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model / (3) the exact variance and MSE of LS estimator is determined / (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort / (5) an exact method of evaluating the density of the three estimators is described / (6) their exact bias, mean, variance and MSE are determined and analysed / and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed.</p> <p><br /> The discussion and results show that the estimators are still biased in the usual sense: &lsquo / in expectation&rsquo / . However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation.</p>

To navigate successfully in a previously unexplored environment, a mobile robot must be able to estimate the spatial relationships of the objects of interest accurately. A Simultaneous Localization and Mapping (SLAM) sys- tem employs its sensors to build incrementally a map of its surroundings and to localize itself in the map simultaneously. The aim of this research project is to develop a SLAM system suitable for self propelled household lawnmowers. The proposed bearing-only SLAM system requires only an omnidirec- tional camera and some inexpensive landmarks. The main advantage of an omnidirectional camera is the panoramic view of all the landmarks in the scene. Placing landmarks in a lawn field to define the working domain is much easier and more flexible than installing the perimeter wire required by existing autonomous lawnmowers. The common approach of existing bearing-only SLAM methods relies on a motion model for predicting the robot’s pose and a sensor model for updating the pose. In the motion model, the error on the estimates of object positions is cumulated due mainly to the wheel slippage. Quantifying accu- rately the uncertainty of object positions is a fundamental requirement. In bearing-only SLAM, the Probability Density Function (PDF) of landmark position should be uniform along the observed bearing. Existing methods that approximate the PDF with a Gaussian estimation do not satisfy this uniformity requirement. This thesis introduces both geometric and proba- bilistic methods to address the above problems. The main novel contribu- tions of this thesis are: 1. A bearing-only SLAM method not requiring odometry. The proposed method relies solely on the sensor model (landmark bearings only) without relying on the motion model (odometry). The uncertainty of the estimated landmark positions depends on the vision error only, instead of the combination of both odometry and vision errors. 2. The transformation of the spatial uncertainty of objects. This thesis introduces a novel method for translating the spatial un- certainty of objects estimated from a moving frame attached to the robot into the global frame attached to the static landmarks in the environment. 3. The characterization of an improved PDF for representing landmark position in bearing-only SLAM. The proposed PDF is expressed in polar coordinates, and the marginal probability on range is constrained to be uniform. Compared to the PDF estimated from a mixture of Gaussians, the PDF developed here has far fewer parameters and can be easily adopted in a probabilistic framework, such as a particle filtering system. The main advantages of our proposed bearing-only SLAM system are its lower production cost and flexibility of use. The proposed system can be adopted in other domestic robots as well, such as vacuum cleaners or robotic toys when terrain is essentially 2D.

The Multi-Layer Perceptron (MLP) is one of the most widely applied and researched Artificial Neural Network model. MLP networks are normally applied to performing supervised learning tasks, which involve iterative training methods to adjust the connection weights within the network. This is commonly formulated as a multivariate non-linear optimization problem over a very high-dimensional space of possible weight configurations. Analogous to the field of mathematical optimization, training an MLP is often described as the search of an error surface for a weight vector which gives the smallest possible error value. Although this presents a useful notion of the training process, there are many problems associated with using the error surface to understand the behaviour of learning algorithms and the properties of MLP mappings themselves. Because of the high-dimensionality of the system, many existing methods of analysis are not well-suited to this problem. Visualizing and describing the error surface are also nontrivial and problematic. These problems are specific to complex systems such as neural networks, which contain large numbers of adjustable parameters, and the investigation of such systems in this way is largely a developing area of research. In this thesis, the concept of the error surface is explored using three related methods. Firstly, Principal Component Analysis (PCA) is proposed as a method for visualizing the learning trajectory followed by an algorithm on the error surface. It is found that PCA provides an effective method for performing such a visualization, as well as providing an indication of the significance of individual weights to the training process. Secondly, sampling methods are used to explore the error surface and to measure certain properties of the error surface, providing the necessary data for an intuitive description of the error surface. A number of practical MLP error surfaces are found to contain a high degree of ultrametric structure, in common with other known configuration spaces of complex systems. Thirdly, a class of global optimization algorithms is also developed, which is focused on the construction and evolution of a model of the error surface (or search spa ce) as an integral part of the optimization process. The relationships between this algorithm class, the Population-Based Incremental Learning algorithm, evolutionary algorithms and cooperative search are discussed. The work provides important practical techniques for exploration of the error surfaces of MLP networks. These techniques can be used to examine the dynamics of different training algorithms, the complexity of MLP mappings and an intuitive description of the nature of the error surface. The configuration spaces of other complex systems are also amenable to many of these techniques. Finally, the algorithmic framework provides a powerful paradigm for visualization of the optimization process and the development of parallel coupled optimization algorithms which apply knowledge of the error surface to solving the optimization problem.

Λαμβάνοντας υπόψη, ότι η αποδοτική σχεδίαση, αξιολόγηση και εγκατάσταση ενός ασύρματου δικτύου επικοινωνιών, απαιτούν τον ακριβή χαρακτηρισμό του καναλιού διάδοσης και ειδικότερα των διαλείψεων μικρής και μεγάλης κλίμακας, το αντικείμενο μελέτης της παρούσας Διδακτορικής Διατριβής (ΔΔ) εστιάζεται στη μοντελοποίηση των διαλείψεων με νέα γενικότερα στατιστικά μοντέλα και απαρτίζεται από τρεις θεματικές ενότητες που αφορούν α) μοντέλα παρουσία συνιστώσας Οπτικής Επαφής (ΟΕ), β) μοντέλα που χαρακτηρίζονται από απουσία συνιστώσας ΟΕ καθώς και γ) χρήσιμες στατιστικές εκφράσεις για τη περιγραφή του τυχαίου θορύβου FM και της μέσης χωρητικότητας του καναλιού για μερικά από τα νέα κανάλια (α-μ, α-η-μ, α-κ-μ και α-λ-η-μ). Με βάση την υφιστάμενη διεθνή βιβλιογραφία, οι κατανομές που περιγράφουν κανάλια διαλείψεων δεν είναι αρκετά ευέλικτες και πολλές φορές είναι ανεπαρκείς για τη προσαρμογή αυτών σε δεδομένα προερχόμενα από πειραματικές μετρήσεις της έντασης ανά μονάδα επιφάνειας του ηλεκτρομαγνητικού πεδίου, τόσο για κανάλια εσωτερικών, όσο και για κανάλια υπαίθριων (εξωτερικών) χώρων. Έτσι, αρχικά δίδεται ο φυσικός μηχανισμός για την ερμηνεία κάθε νέου παρουσιαζόμενου μοντέλου. Χρησιμοποιώντας το μαθηματικό φορμαλισμό που προκύπτει από την μοντελοποίηση του ασύρματου καναλιού μέσω διαφόρων μιγαδικών Gaussian διεργασιών με διαφορετικές ιδιότητες, παρέχονται χρήσιμες εκφράσεις για την περιγραφή και αξιολόγηση των ψηφιακών συστημάτων επικοινωνιών που λειτουργούν σε περιβάλλοντα διαλείψεων. Στη συνέχεια, παρουσιάζεται η μελέτη που αφορά μοντέλα που υποθέτουν ότι η συνιστώσα πολυδιόδευσης συνυπάρχει με συνιστώσα. Έπειτα, πραγματοποιείται μελέτη μοντέλων που λειτουργούν σε συνθήκες διαλείψεων, όπου δεν υφίσταται συνιστώσα ΟΕ. Στη συνέχεια της ΔΔ, αναφορικά με κάποια από τα μοντέλα που παρουσιάστηκαν, πραγματοποιείται μελέτη και διερεύνηση του τυχαίου θορύβου FM και της Μέσης Χωρητικότητας του Καναλιού (ΜΧΚ). / The effective design, assessment, and installation of a wireless radio network require an accurate characterization of the propagation channel and, in particular, the small and large scale fading. By taking this into consideration, the subject of this Philosophy Diploma (PhD) dissertation is summarized in the characterization of fading with new more general statistical models and it is composed from three thematic units that concern: a) models under LOS conditions, v) models that are characterized by lack of a LOS component as well as c) useful statistical expressions for the description of random noise FM and average channel capacity for some of the new channels. A important amount of scientific work shows that the existing distributions are not enough flexible and many times are insufficient for the adaptation in data coming from experimental measurements of intensity per unit of surface of the electromagnetic field for both indoor and outdoor channels. Based on this fact, the objective of the Thesis was the production of new more general models with always natural background. Thus, initially, the natural mechanism is given for the interpretation of each new presented model. Using the mathematic formalism that results from the modelling of wireless channel via various complex Gaussian processes with different attributes, useful expressions are provided for the description and evaluation of digital communication systems that operate in fading environments. Consequently, initially, the basic theoretical background is presented that is rendered useful and essential for the study of fading channels. Next, a study is presented that concerns models that assume that the mulitpath part coexists with a LOS component. Then, a study of models, which assume NLOS conditions, takes place. In the next part of the PhD, in regard to some of the presented models, a study of random noise FM and ACC takes place.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Maize is a main crop in Brazil. Maize yield can be decreased by water deficit. Irrigation is an alternative to overcome this problem and avoid the low soil water availability. In order to efficiently irrigate a crop it is necessary to know some parameters and irrigation and crop requirements in each region. The objective of this study was to determine the most likely values the duration of developmental phases, water depth and the number of irrigations required for maize crop sown at different sowing dates, considering the water storage capacity of main soils of the Central Area of Rio Grande do Sul State and its variation with simulated developmental stage. Crop development for three maturation groups was simulated using the thermal time, for 14 sowing dates, from August until mid-February, every during the period from 1968 to 2008, covered by metereorological data at Santa Maria RS (EMPSM). To 13 soils, were grouped into six groups with similar water storage capacity (CAD) and infiltration capacity. Daily water balance was calculated when soil reached a minimum fraction of available water, according to four management levels (water withdrawn from the soil reached 20%, 30%, 40% and 50% of CAD). Data analysis consisted of analysis of variance, mean comparison tests and probability distribution analysis of the duration of crop developmental phases and the entire developmental cycle, water depth and number of irrigations. Developmental until tasseling are larger in the earliest sowing date (01/08). After tasseling, the greater duration of developmental phases occurs in the latest sowing (15/02). The normal and lognormal distributions represent better the variation of the duration of maize development both for the duration of the phases and the entire cycle. Sowing dates from early October to early November result a greater need water depth considering the entire cycle, regardless of the soil and maturation group. The mid maturation group needs more water during the entire cycle for all sowing dates, and the very early maturation group has the lowest water requirement. The variation of water depth and the number of irrigations follow the normal, lognormal, gamma and Weibull probability distribution functions. For the 90% probability level the water depth varies between 31 and 171 mm and the number of irrigations varies between one and nineteen during the developmental cycle, depending on sowing date, maize maturation group and soil. / O milho é uma das principais culturas da Agricultura Brasileira. A cultura sofre grandes perdas quando submetida a deficiência hídrica. Para contornar esse problema e evitar a baixa disponibilidade de água no solo, a irrigação do milho é a principal alternativa. Mas para isso ocorrer de forma satisfatória é necessário conhecer os parâmetros de irrigação e a necessidade de irrigação do milho em cada região. O objetivo desse trabalho foi determinar os valores mais prováveis de duração dos subperíodos do ciclo de desenvolvimento, de lâmina de irrigação e de número de irrigações necessários para o milho semeado em diferentes épocas, considerando-se a capacidade de armazenamento de água disponível dos principais solos da Região Central do Estado do Rio Grande do Sul e sua variação com o desenvolvimento simulado das plantas. O desenvolvimento da cultura para os três grupos de maturação foi realizado através da soma térmica, para as 14 épocas de semeadura, do início do mês de agosto até meados de fevereiro, para cada ano do banco de dados da Estação Meteorológica Principal de Santa Maria RS (EMPSM), utilizando o período de 1968 a 2008. Para simular a irrigação, os 13 solos da região de abrangência da EMPSM, foram agrupados em seis grupos que apresentam características semelhantes de capacidade de armazenamento de água disponível (CAD) e capacidade de infiltração. O balanço hídrico diário determinou a variação da água disponível e o momento da irrigação. O momento da irrigação foi determinado quando os solos alcançavam a fração mínima de água disponível a ser mantida. Para isso, foram utilizados quatro manejos que representaram a condição de quando a água retirada do solo alcançava a fração 20%, 30%, 40% e 50% da CAD. A análise dos dados consistiu de análise de variância, teste de comparação de médias e análise de distribuição de probabilidade para as variáveis: duração dos subperíodos e do ciclo de desenvolvimento do milho, lâmina de irrigação e o número de irrigações. Os subperíodos que ocorrem da semeadura até o pendoamento são maiores na primeira semeadura (01/08). Após o pendoamento a maior duração dos subperíodos ocorre na semeadura mais tardia (15/02). As distribuições normal e lognormal representam melhor o desenvolvimento do milho podem ser usadas para a duração dos subperíodos e do ciclo total. As épocas de semeadura do início de outubro até o início de novembro necessitam de maiores lâminas de irrigação considerando todo o ciclo, independente do solo e grupo de maturação. O grupo de maturação normal necessita maior lâmina de irrigação durante o ciclo de cultivo para todas as épocas de semeadura, e o grupo de maturação superprecoce tem a menor lâmina. A lâmina de irrigação e o número de irrigações são representadas pelas funções de distribuição de probabilidade normal, lognormal, gamma e Weibull. Para a probabilidade de 90% de ocorrência, a lâmina de irrigação varia entre 31 e 171 mm e o número de irrigações entre uma e dezenove durante o ciclo de desenvolvimento da cultura, dependendo da época de semeadura, grupo de maturação do milho e do solo de cultivo.