Search results for: probability bivariant models

Authors: Waqas Ali, Nadeem Majeed

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Requirement engineering is an essence of software development life cycle. The more time we spend on requirement engineering, higher the probability of success. Effective requirement engineering ensures and predicts successful software product. This paper presents the adaptation of requirement engineering practices in small and medium size companies of Pakistan. The study is conducted by questionnaires to show how much of requirement engineering models and practices are followed in Pakistan.

Keywords: requirement engineering, Pakistan, models, practices, organizations

Procedia PDF Downloads 706

Authors: Redouane Tlemsani, Redouane, Belkacem Kouninef, Abdelkader Benyettou

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In this paper, our system is a Markovien system which we can see it like a Dynamic Bayesian Networks. One of the major interests of these systems resides in the complete training of the models (topology and parameters) starting from training data. The Bayesian Networks are representing models of dubious knowledge on complex phenomena. They are a union between the theory of probability and the graph theory in order to give effective tools to represent a joined probability distribution on a set of random variables. The representation of knowledge bases on description, by graphs, relations of causality existing between the variables defining the field of study. The theory of Dynamic Bayesian Networks is a generalization of the Bayesians networks to the dynamic processes. Our objective amounts finding the better structure which represents the relationships (dependencies) between the variables of a dynamic bayesian network. In applications in pattern recognition, one will carry out the fixing of the structure which obliges us to admit some strong assumptions (for example independence between some variables).

Keywords: Arabic on line character recognition, dynamic Bayesian network, pattern recognition, networks

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Authors: Sean Sloan

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Probability Risk Assessments (PRA) can be a difficult concept for students to grasp. So in searching for different ways to describe PRA to relate it to their lives; COVID-19 came up. The parallels are amazing. Soon students began analyzing acceptable risk with the virus. This helped them to quantify just how dangerous is dangerous. The original lesson was dismissed and for the remainder of the period, the probability of risk, and the lethality of risk became the topic. Spreading events such as a COVID carrier on an airline became analogous to single fault casualties such as a Tsunami. Odds of spreading became odds of backup-diesel-generator failure – like with Fukashima Daiichi. Fatalities of the disease became expected fatalities due to radiation spread. Quantification from this discussion took it from hyperbole and emotion into one where we could rationally base guidelines. It has been one of the most effective educational devices observed.

Keywords: COVID, education, probability, risk

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Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Junling Li, Fang Meng, Yichun Zhang

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Image saliency detection has been long studied, while several challenging problems are still unsolved, such as detecting saliency inaccurately in complex scenes or suppressing salient objects in the image borders. In this paper, we propose a new saliency detection algorithm in order to solving these problems. We represent the image as a graph with superixels as nodes. By considering appearance similarity between the boundary and the background, the proposed method chooses non-saliency boundary nodes as background priors to construct the background probability model. The probability that each node belongs to the model is computed, which measures its similarity with backgrounds. Thus we can calculate saliency by the transformed probability as a metric. We compare our algorithm with ten-state-of-the-art salient detection methods on the public database. Experimental results show that our simple and effective approach can attack those challenging problems that had been baffling in image saliency detection.

Keywords: visual saliency, background probability, boundary knowledge, background priors

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Authors: Aleš Florian, Lenka Ševelová, Jaroslav Žák

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Formation of tensile cracks in concrete slabs of rigid pavement can be (among others) the initiation point of the other, more serious failures which can ultimately lead to complete degradation of the concrete slab and thus the whole pavement. Two measures can be used for reliability assessment of this phenomenon - the probability of failure and/or the reliability index. Different methods can be used for their calculation. The simple ones are called moment methods and simulation techniques. Two methods - FOSM Method and Simple Random Sampling Method - are verified and their comparison is performed. The influence of information about the probability distribution and the statistical parameters of input variables as well as of the limit state function on the calculated reliability index and failure probability are studied in three points on the lower surface of concrete slabs of the older type of rigid pavement formerly used in the Czech Republic.

Keywords: failure, pavement, probability, reliability index, simulation, tensile crack

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Authors: Mina Jafari, Kobra Hamraee, Saied Hossein Hosseini

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The prediction of breast cancer disease is one of the challenges in medicine. In this paper we collected 528 records of women’s information who live in Kabul including demographic, life style, diet and pregnancy data. There are many classification algorithm in breast cancer prediction and tried to find the best model with most accurate result and lowest error rate. We evaluated some other common supervised algorithms in data mining to find the best model in prediction of breast cancer disease among afghan women living in Kabul regarding to momography result as target variable. For evaluating these algorithms we used Cross Validation which is an assured method for measuring the performance of models. After comparing error rate and accuracy of three models: Decision Tree, Naive Bays and Rule Induction, Decision Tree with accuracy of 94.06% and error rate of %15 is found the best model to predicting breast cancer disease based on the health care records.

Keywords: decision tree, breast cancer, probability, data mining

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Authors: Francis Mugabi, Kevin Duffy, Joseph J. Y. T Mugisha, Obiora Collins

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Bluetongue virus (BTV) has 27 serotypes, with some of them coexisting in patchy (different) environments, which make its control difficult. Wind-aided midge movement is a known mechanism in the spread of BTV. However, its effects on the probability of coexistence of multiple BTV serotypes are not clear. Deterministic and stochastic models for r BTV serotypes in n discrete patches connected by midge and/or cattle movement are formulated and analyzed. For the deterministic model without midge and cattle movement, using the comparison principle, it is shown that if the patch reproduction number R0 < 1, i=1,2,...,n, j=1,2,...,r, all serotypes go extinct. If R^j_i0>1, competitive exclusion takes place. Using numerical simulations, it is shown that when the n patches are connected by midge movement, coexistence takes place. To account for demographic and movement variability, the deterministic model is transformed into a continuous-time Markov chain stochastic model. Utilizing a multitype branching process, it is shown that the midge movement can have a large effect on the probability of coexistence of multiple BTV serotypes. The probability of coexistence can be brought to zero when the control interventions that directly kill the adult midges are applied. These results indicate the significance of wind-aided midge movement and vector control interventions on the coexistence and control of multiple BTV serotypes in patchy environments.

Keywords: bluetongue virus, coexistence, multiple serotypes, midge movement, branching process

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Authors: Flavio Cordeiro Fontanella, Asla Medeiros e Sá, Moacyr Alvim Horta Barbosa da Silva

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In the present work, we analyse the performance of football results forecasting models. In order to do so, we have performed the data collection from eight different forecasting models during the 2021 Brazilian football season. First, we guide the analysis through visual representations of the data, designed to highlight the most prominent features and enhance the interpretation of differences and similarities between the models. We propose using a 2-simplex triangle to investigate visual patterns from the results forecasting models. Next, we compute the expected points for every team playing in the championship and compare them to the final league standings, revealing interesting contrasts between actual to expected performances. Then, we evaluate forecasts’ accuracy using the Ranked Probability Score (RPS); models comparison accounts for tiny scale differences that may become consistent in time. Finally, we observe that the Wisdom of Crowds principle can be appropriately applied in the context, driving into a discussion of results forecasts usage in practice. This paper’s primary goal is to encourage football forecasts’ performance discussion. We hope to accomplish it by presenting appropriate criteria and easy-to-understand visual representations that can point out the relevant factors of the subject.

Keywords: accuracy evaluation, Brazilian championship, football results forecasts, forecasting models, visual analysis

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Authors: Jerry Hu

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Let G = (V, E) with V = {1, 2, ..., k} be a graph, the k positive integers a₁, a₂, ..., ak are G-wise relatively prime if (aᵢ, aⱼ ) = 1 for {i, j} ∈ E. We use an inductive approach to give an asymptotic formula for the number of k-tuples of integers that are G-wise relatively prime. An exact formula is obtained for the probability that k positive integers are G-wise relatively prime. As a corollary, we also provide an exact formula for the probability that k positive integers have exactly r relatively prime pairs.

Keywords: graph, independent set, G-wise relatively prime, probability

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Authors: Bahareh Zare

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The theory of the investment model of dating infidelity maintains that loyalty is an essential power within romantic relationships. Loyalty signifies both motivation and psychological attachment to maintain a relationship. This study examined the relationship between the Big Five Personality Factors (Extraversion, Neuroticism, Openness, Conscientiousness, and Agreeableness), probability of marital infidelity, and risk of divorce. The participants completed NEO-FFI, INFQ (infidelity questionnaire) and were interviewed by OHI (Oral History Interview). The results demonstrated that extraversion and agreeableness traits were significant predictors for the probability of infidelity and risk of divorce. In addition, conscientiousness predicted the probability of infidelity, while neuroticism predicted the risk of divorce.

Keywords: five factors personality, infidelity, risk of divorce, investment theory

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Authors: Martha E. Aguiar-Barrera, Humberto Gutierrez-Pulido, Veronica Vargas-Alejo

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Identifying and modeling random phenomena is a fundamental cognitive process to understand and transform reality. Recognizing situations governed by chance and giving them a scientific interpretation, without being carried away by beliefs or intuitions, is a basic training for citizens. Hence the importance of generating teaching-learning processes, supported using technology, paying attention to model creation rather than only executing mathematical calculations. In order to develop the student's knowledge about basic probability distributions and decision making; in this work a model eliciting activity (MEA) is reported. The intention was applying the Model and Modeling Perspective to design an activity related to civil engineering that would be understandable for students, while involving them in its solution. Furthermore, the activity should imply a decision-making challenge based on sample data, and the use of the computer should be considered. The activity was designed considering the six design principles for MEA proposed by Lesh and collaborators. These are model construction, reality, self-evaluation, model documentation, shareable and reusable, and prototype. The application and refinement of the activity was carried out during three school cycles in the Probability and Statistics class for Civil Engineering students at the University of Guadalajara. The analysis of the way in which the students sought to solve the activity was made using audio and video recordings, as well as with the individual and team reports of the students. The information obtained was categorized according to the activity phase (individual or team) and the category of analysis (sample, linearity, probability, distributions, mechanization, and decision-making). With the results obtained through the MEA, four obstacles have been identified to understand and apply the binomial distribution: the first one was the resistance of the student to move from the linear to the probabilistic model; the second one, the difficulty of visualizing (infering) the behavior of the population through the sample data; the third one, viewing the sample as an isolated event and not as part of a random process that must be viewed in the context of a probability distribution; and the fourth one, the difficulty of decision-making with the support of probabilistic calculations. These obstacles have also been identified in literature on the teaching of probability and statistics. Recognizing these concepts as obstacles to understanding probability distributions, and that these do not change after an intervention, allows for the modification of these interventions and the MEA. In such a way, the students may identify themselves the erroneous solutions when they carrying out the MEA. The MEA also showed to be democratic since several students who had little participation and low grades in the first units, improved their participation. Regarding the use of the computer, the RStudio software was useful in several tasks, for example in such as plotting the probability distributions and to exploring different sample sizes. In conclusion, with the models created to solve the MEA, the Civil Engineering students improved their probabilistic knowledge and understanding of fundamental concepts such as sample, population, and probability distribution.

Keywords: linear model, models and modeling, probability, randomness, sample

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Authors: Seon Soon Choi

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The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: crack size, fatigue crack propagation, magnesium alloys, probability distribution, specimen thickness

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Authors: Yanqi Yang, Chongshan Liao, Cheuk Hin Ho, Susan Bridges

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Aim: To investigate student’s perceptions of using e-models in an inquiry-based curriculum. Approach: 52 second-year dental students completed a pre- and post-test questionnaire relating to their perceptions of e-models and their use in inquiry-based learning. The pre-test occurred prior to any learning with e-models. The follow-up survey was conducted after one year's experience of using e-models. Results: There was no significant difference between the two sets of questionnaires regarding student’s perceptions of the usefulness of e-models and their willingness to use e-models in future inquiry-based learning. Most of the students preferred using both plaster models and e-models in tandem. Conclusion: Students did not change their attitude towards e-models and most of them agreed or were neutral that e-models are useful in inquiry-based learning. Whilst recognizing the utility of 3D models for learning, student's preference for combining these with solid models has implications for the development of haptic sensibility in an operative discipline.

Keywords: e-models, inquiry-based curriculum, education, questionnaire

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Authors: Mohammad Bakhshi, Firas Al Janabi

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High resolution rain data are very important to fulfill the input of hydrological models. Among models of high-resolution rainfall data generation, the temporal disaggregation was chosen for this study. The paper attempts to generate three different rainfall resolutions (4-hourly, hourly and 10-minutes) from daily for around 20-year record period. The process was done by DiMoN tool which is based on random cascade model and method of fragment. Differences between observed and simulated rain dataset are evaluated with variety of statistical and empirical methods: Kolmogorov-Smirnov test (K-S), usual statistics, and Exceedance probability. The tool worked well at preserving the daily rainfall values in wet days, however, the generated data are cumulated in a shorter time period and made stronger storms. It is demonstrated that the difference between generated and observed cumulative distribution function curve of 4-hourly datasets is passed the K-S test criteria while in hourly and 10-minutes datasets the P-value should be employed to prove that their differences were reasonable. The results are encouraging considering the overestimation of generated high-resolution rainfall data.

Keywords: DiMoN Tool, disaggregation, exceedance probability, Kolmogorov-Smirnov test, rainfall

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Authors: A. Bayaga

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This research provides a technical account of estimating Transition Probability using Time-homogeneous Markov Jump Process applying by South African HIV/AIDS data from the Statistics South Africa. It employs Maximum Likelihood Estimator (MLE) model to explore the possible influence of Transition Probability of mortality cases in which case the data was based on actual Statistics South Africa. This was conducted via an integrated demographic and epidemiological model of South African HIV/AIDS epidemic. The model was fitted to age-specific HIV prevalence data and recorded death data using MLE model. Though the previous model results suggest HIV in South Africa has declined and AIDS mortality rates have declined since 2002 – 2013, in contrast, our results differ evidently with the generally accepted HIV models (Spectrum/EPP and ASSA2008) in South Africa. However, there is the need for supplementary research to be conducted to enhance the demographic parameters in the model and as well apply it to each of the nine (9) provinces of South Africa.

Keywords: AIDS mortality rates, epidemiological model, time-homogeneous markov jump process, transition probability, statistics South Africa

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Authors: Gabriel Calvo, Carmen Armero, Luigi Spezia

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A basketball player is said to have a hot hand if his/her performance is better than expected in different periods of time. A way to deal with this phenomenon is to make use of latent variables, which can indicate whether the player is ‘on fire’ or not. This work aims to model the hot hand phenomenon through a Bayesian hidden Markov model (HMM) with two states (cold and hot) and two different probability of success depending on the corresponding hidden state. This task is illustrated through a comprehensive simulation study. The simulated data sets emulate the field goal attempts in an NBA season from different profile players. This model can be a powerful tool to assess the ‘streakiness’ of each player, and it provides information about the general performance of the players during the match. Finally, the Bayesian HMM allows computing the posterior probability of any type of streak.

Keywords: Bernoulli trials, field goals, latent variables, posterior distribution

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Authors: Carlson Murray, Ali Lazrak

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Robust experimental evidence of systematic violations of expected utility (EU) establishes that individuals facing risk overweight utility from low probability gains and losses when making choices. These findings motivated development of models of preferences with probability weighting functions, such as rank dependent utility (RDU). We solve for the optimal investing strategy of an RDU investor in a dynamic binomial setting from which we derive implications for investing behavior. We show that relative to EU investors with constant relative risk aversion, commonly measured probability weighting functions produce optimal RDU terminal wealth with significant downside protection and upside exposure. We additionally find that in contrast to EU investors, RDU investors optimally choose a portfolio that contains fair bets that provide payo↵s that can be interpreted as lottery outcomes or exposure to idiosyncratic returns. In a calibrated version of the model, we calculate that RDU investors would be willing to pay 5% of their initial wealth for the freedom to trade away from an optimal EU wealth allocation. The dynamic trading strategy that supports the optimal wealth allocation implies portfolio weights that are independent of initial wealth but requires higher risky share after good stock return histories. Optimal trading also implies the possibility of non-participation when historical returns are poor. Our model fills a gap in the literature by providing new quantitative and qualitative predictions that can be tested experimentally or using data on household wealth and portfolio choice.

Keywords: behavioral finance, probability weighting, portfolio choice

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Authors: Suparat Niwitpong, Sa-aat Niwitpong

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Statistical inference of normal mean with known coefficient of variation has been investigated recently. This phenomenon occurs normally in environment and agriculture experiments when the scientist knows the coefficient of variation of their experiments. In this paper, we constructed new confidence intervals for the normal population mean with known coefficient of variation. We also derived analytic expressions for the coverage probability of each confidence interval. To confirm our theoretical results, Monte Carlo simulation will be used to assess the performance of these intervals based on their coverage probabilities.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation

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Authors: Seon Soon Choi

Abstract:

It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to present the good probability distribution fit for the fatigue crack propagation life at a specified fatigue crack size in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed and the good probability distribution fit for the fatigue crack propagation life is presented. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: fatigue crack propagation life, load ratio, magnesium alloys, probability distribution

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Authors: Moses Mwangi, Geert Verbeke, Geert Molenberghs

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Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment with respect to a reference treatment (placebo or standard). The main advantage of using cross-over design over conventional parallel design is its flexibility, where every subject become its own control, thereby reducing confounding effect. Jones & Kenward, discuss in detail more recent developments in the analysis of cross-over trials. We revisit the simple piecewise linear mixed-effects model, proposed by Mwangi et. al, (in press) for its first application in the analysis of cross-over trials. We compared performance of the proposed piecewise linear mixed-effects model with two commonly cited statistical models namely, (1) Grizzle model; and (2) Jones & Kenward model, used in estimation of the treatment effect, in the analysis of randomized cross-over trial. We estimate two performance measurements (mean square error (MSE) and coverage probability) for the three methods, using data simulated from the proposed piecewise linear mixed-effects model. Piecewise linear mixed-effects model yielded lowest MSE estimates compared to Grizzle and Jones & Kenward models for both small (Nobs=20) and large (Nobs=600) sample sizes. It’s coverage probability were highest compared to Grizzle and Jones & Kenward models for both small and large sample sizes. A piecewise linear mixed-effects model is a better estimator of treatment effect than its two competing estimators (Grizzle and Jones & Kenward models) in the analysis of cross-over trials. The data generating mechanism used in this paper captures two time periods for a simple 2-Treatments x 2-Periods cross-over design. Its application is extendible to more complex cross-over designs with multiple treatments and periods. In addition, it is important to note that, even for single response models, adding more random effects increases the complexity of the model and thus may be difficult or impossible to fit in some cases.

Keywords: Evaluation, Grizzle model, Jones & Kenward model, Performance measures, Simulation

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Authors: Julio Vicente Cateia

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This paper aims to assess the role of informality and trade facilitation on the export probability of Guinea-Bissau. We include informality in the Féchet function, which gives the expression for the country's supply probability. We find that Guinea-Bissau is about 7.2% less likely to export due to the 1% increase in informality. The export's probability increases by about 1.7%, 4%, and 1.1% due to a 1% increase in trade facilitation, R&D stock, and year of education. These results are significant at the usual levels. We suggest a development agenda aimed at reducing the level of informality in this country.

Keywords: development, trade, informality, trade facilitation, economy of Guinea-Bissau

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Authors: Tomoaki Hashimoto

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In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research field. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method with the unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with the unknown probability distribution.

Keywords: optimal control, stochastic systems, discrete time systems, probabilistic constraints

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Authors: H. Jung, N. Kim, B. Kang, J. Choe

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History matching is a crucial procedure for predicting reservoir performances and making future decisions. However, it is difficult due to uncertainties of initial reservoir models. Therefore, it is important to have reliable initial models for successful history matching of highly heterogeneous reservoirs such as channel reservoirs. In this paper, we proposed a novel scheme for regenerating geological models using support vector machine (SVM) and principal component analysis (PCA). First, we perform PCA for figuring out main geological characteristics of models. Through the procedure, permeability values of each model are transformed to new parameters by principal components, which have eigenvalues of large magnitude. Secondly, the parameters are projected into two-dimensional plane by multi-dimensional scaling (MDS) based on Euclidean distances. Finally, we train an SVM classifier using 20% models which show the most similar or dissimilar well oil production rates (WOPR) with the true values (10% for each). Then, the other 80% models are classified by trained SVM. We select models on side of low WOPR errors. One hundred channel reservoir models are initially generated by single normal equation simulation. By repeating the classification process, we can select models which have similar geological trend with the true reservoir model. The average field of the selected models is utilized as a probability map for regeneration. Newly generated models can preserve correct channel features and exclude wrong geological properties maintaining suitable uncertainty ranges. History matching with the initial models cannot provide trustworthy results. It fails to find out correct geological features of the true model. However, history matching with the regenerated ensemble offers reliable characterization results by figuring out proper channel trend. Furthermore, it gives dependable prediction of future performances with reduced uncertainties. We propose a novel classification scheme which integrates PCA, MDS, and SVM for regenerating reservoir models. The scheme can easily sort out reliable models which have similar channel trend with the reference in lowered dimension space.

Keywords: history matching, principal component analysis, reservoir modelling, support vector machine

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Authors: Mehran Naghizaderokni, Asscar Janalizadechobbasty

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This paper explores probabilistic method for assessing the liquefaction potential of sandy soils. The current simplified methods for assessing soil liquefaction potential use a deterministic safety factor in order to determine whether liquefaction will occur or not. However, these methods are unable to determine the liquefaction probability related to a safety factor. A solution to this problem can be found by reliability analysis.This paper presents a reliability analysis method based on the popular certain liquefaction analysis method. The proposed probabilistic method is formulated based on the results of reliability analyses of 190 field records and observations of soil performance against liquefaction. The results of the present study show that confidence coefficient greater and smaller than 1 does not mean safety and/or liquefaction in cadence for liquefaction, and for assuring liquefaction probability, reliability based method analysis should be used. This reliability method uses the empirical acceleration attenuation law in the Chalos area to derive the probability density distribution function and the statistics for the earthquake-induced cyclic shear stress ratio (CSR). The CSR and CRR statistics are used in continuity with the first order and second moment method to calculate the relation between the liquefaction probability, the safety factor and the reliability index. Based on the proposed method, the liquefaction probability related to a safety factor can be easily calculated. The influence of some of the soil parameters on the liquefaction probability can be quantitatively evaluated.

Keywords: liquefaction, reliability analysis, chalos area, civil and structural engineering

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.

Keywords: Karkheh River, Log Pearson Type III, probability distribution, residual sum of squares

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Authors: Naci Büyükkaracığan

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Today, the need for water sources is swiftly increasing due to population growth. At the same time, it is known that some regions will face with shortage of water and drought because of the global warming and climate change. In this context, evaluation and analysis of hydrological data such as the observed trends, drought and flood prediction of short term flow has great deal of importance. The most accurate selection probability distribution is important to describe the low flow statistics for the studies related to drought analysis. As in many basins In Turkey, Gediz River basin will be affected enough by the drought and will decrease the amount of used water. The aim of this study is to derive appropriate probability distributions for frequency analysis of annual minimum flows at 6 gauging stations of the Gediz Basin. After applying 10 different probability distributions, six different parameter estimation methods and 3 fitness test, the Pearson 3 distribution and general extreme values distributions were found to give optimal results.

Keywords: Gediz Basin, goodness-of-fit tests, minimum flows, probability distribution

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Authors: Ernesto Pineda Leon, Dante Tolentino Lopez, Janis Zapata Lopez

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The current paper shows the application of the boundary element method for the analysis of plates under shear stress causing plasticity. In this case, the shear deformation of a plate is considered by means of the Reissner’s theory. The probability of failure of a Reissner’s plate due to a proposed index plastic behavior is calculated taken into account the uncertainty in mechanical and geometrical properties. The problem is developed in two dimensions. The classic plasticity’s theory is applied and a formulation for initial stresses that lead to the boundary integral equations due to plasticity is also used. For the plasticity calculation, the Von Misses criteria is used. To solve the non-linear equations an incremental method is employed. The results show a relatively small failure probability for the ranges of loads between 0.6 and 1.0. However, for values between 1.0 and 2.5, the probability of failure increases significantly. Consequently, for load bigger than 2.5 the plate failure is a safe event. The results are compared to those that were found in the literature and the agreement is good.

Keywords: boundary element method, failure, plasticity, probability

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Authors: A. B. M. Rezaul Islam, Ernur Karadogan

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Shape memory alloys (SMAs) are known for their shape memory effect and pseudoelasticity behavior. Their thermomechanical behaviors are modeled by numerous researchers using microscopic thermodynamic and macroscopic phenomenological point of view. Tanaka, Liang-Rogers and Ivshin-Pence models are some of the most popular SMA macroscopic phenomenological constitutive models. They describe SMA behavior in terms of stress, strain and temperature. These models involve material parameters and they have associated uncertainty present in them. At different operating temperatures, the uncertainty propagates to the output when the material is subjected to loading followed by unloading. The propagation of uncertainty while utilizing these models in real-life application can result in performance discrepancies or failure at extreme conditions. To resolve this, we used probabilistic approach to perform the sensitivity and uncertainty analysis of Tanaka, Liang-Rogers, and Ivshin-Pence models. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods have been used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. As per the results, it is evident that the models vary due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most significant parameters at several temperatures. This work highlights the sensitivity and uncertainty analysis results and shows comparison of them at different temperatures and loading conditions for all these models. The analysis presented will aid in designing engineering applications by eliminating the probability of model failure due to the uncertainty in the input parameters. Thus, it is recommended to have a proper understanding of sensitive parameters and the uncertainty propagation at several operating temperatures and loading conditions as per Tanaka, Liang-Rogers, and Ivshin-Pence model.

Keywords: constitutive models, FAST sensitivity analysis, sensitivity analysis, sobol, shape memory alloy, uncertainty analysis

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Authors: Kailash C. Madan

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We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

Keywords: a three server queue, Bernoulli schedule server vacations, queue size distribution at a random epoch, steady state

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