Search results for: probability%20formula

Authors: Ahmet Kaya

Abstract:

Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

Procedia PDF Downloads 299

Authors: Naoyuki Sugihashi, Toshiharu Kishi

Abstract:

The probability of occurrence of thermal cracks in mass concrete in Japan is evaluated by the cracking probability diagram that represents the relationship between the thermal cracking index and the probability of occurrence of cracks in the actual structure. In this paper, we propose a method to directly calculate the cracking probability, following a probabilistic theory by modeling the variance of tensile stress and tensile strength. In this method, the relationship between the variance of tensile stress and tensile strength, the thermal cracking index, and the cracking probability are formulated and presented. In addition, standard deviation of tensile stress and tensile strength was identified, and the method of calculating cracking probability in a general construction controlled environment was also demonstrated.

Keywords: thermal crack control, mass concrete, thermal cracking probability, durability of concrete, calculating method of cracking probability

Procedia PDF Downloads 296

Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

Abstract:

The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

Procedia PDF Downloads 120

Authors: Ahmet Kaya

Abstract:

Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

Procedia PDF Downloads 294

Authors: Toby Li, Julian Zhu

Abstract:

In this paper, a model based on a simplified geometry is introduced to give a very conservative collision probability prediction for the Starlink satellite in its most densely clustered region. Under the model in this paper, the probability of collision for Starlink satellite where it clustered most densely is found to be 8.484 ∗ 10^−4. It is found that the predicted collision probability increased nonlinearly with the increased safety distance set. This simple model provides evidence that the continuous development of maneuver avoidance systems is necessary for the future of the orbital safety of satellites under the harsher Lower Earth Orbit environment.

Keywords: Starlink, collision probability, debris, geometry model

Procedia PDF Downloads 45

Authors: Yuan-Lin Chen

Abstract:

This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

Procedia PDF Downloads 252

Authors: Karim Hamidi Machekposhti, Hossein Sedghi

Abstract:

This study was designed to find the best-fit probability distribution of annual rainfall based on 50 years sample (1966-2015) in the Karkheh river basin at Iran using six probability distributions: Normal, 2-Parameter Log Normal, 3-Parameter Log Normal, Pearson Type 3, Log Pearson Type 3 and Gumbel distribution. The best fit probability distribution was selected using Stormwater Management and Design Aid (SMADA) software and based on the Residual Sum of Squares (R.S.S) between observed and estimated values Based on the R.S.S values of fit tests, the Log Pearson Type 3 and then Pearson Type 3 distributions were found to be the best-fit probability distribution at the Jelogir Majin and Pole Zal rainfall gauging station. The annual values of expected rainfall were calculated using the best fit probability distributions and can be used by hydrologists and design engineers in future research at studied region and other region in the world.

Keywords: Log Pearson Type 3, SMADA, rainfall, Karkheh River

Procedia PDF Downloads 163

Authors: Komeil Valipourian

Abstract:

Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)

Procedia PDF Downloads 92

Authors: Yuanjin Liu

Abstract:

Retirement withdrawal strategies are very important to minimize the probability of ruin in retirement. The ruin probability is modeled as a function of initial withdrawal age, gender, asset allocation, inflation rate, and initial withdrawal rate. The ruin probability is obtained based on the 2019 period life table for the Social Security, IRS Required Minimum Distribution (RMD) Worksheets, US historical bond and equity returns, and inflation rates using simulation. Several popular machine learning algorithms of the generalized additive model, random forest, support vector machine, extreme gradient boosting, and artificial neural network are built. The model validation and selection are based on the test errors using hyperparameter tuning and train-test split. The optimal model is recommended for retirees to monitor the ruin probability. The optimal withdrawal strategy can be obtained based on the optimal predictive model.

Keywords: ruin probability, retirement withdrawal strategies, predictive models, optimal model

Procedia PDF Downloads 39

Authors: Quznetsov Gunn

Abstract:

In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

Procedia PDF Downloads 264

Authors: Sean Sloan

Abstract:

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

Procedia PDF Downloads 127

Authors: Sule Sahin, Basak Bulut Karageyik

Abstract:

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

Procedia PDF Downloads 355

Authors: Junling Li, Fang Meng, Yichun Zhang

Abstract:

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

Procedia PDF Downloads 393

Authors: Aleš Florian, Lenka Ševelová, Jaroslav Žák

Abstract:

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

Procedia PDF Downloads 513

Authors: Jerry Hu

Abstract:

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

Procedia PDF Downloads 55

Authors: Bahareh Zare

Abstract:

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

Procedia PDF Downloads 63

Authors: Seon Soon Choi

Abstract:

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

Procedia PDF Downloads 468

Authors: Mohd Aftar Abu Bakar, Noratiqah Mohd Ariff, Abdul Aziz Jemain

Abstract:

Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.

Keywords: daily probability model, monsoon seasons, regions, storm events

Procedia PDF Downloads 313

Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

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

Procedia PDF Downloads 354

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

Procedia PDF Downloads 610

Authors: Mohammed A. Hajeeh

Abstract:

This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: repairable models, imperfect, availability, exponential distribution

Procedia PDF Downloads 260

Authors: Julio Vicente Cateia

Abstract:

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

Procedia PDF Downloads 129

Authors: Tomoaki Hashimoto

Abstract:

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

Procedia PDF Downloads 549

Authors: Mustapha Kamel Mihoubi, Mohamed Essadik Kerkar

Abstract:

Probabilistic risk analysis models are used to provide a better understanding of the reliability and structural failure of works, including when calculating the stability of large structures to a major risk in the event of an accident or breakdown. This work is interested in the study of the probability of failure of concrete dams through the application of reliability analysis methods including the methods used in engineering. It is in our case, the use of level 2 methods via the study limit state. Hence, the probability of product failures is estimated by analytical methods of the type first order risk method (FORM) and the second order risk method (SORM). By way of comparison, a level three method was used which generates a full analysis of the problem and involves an integration of the probability density function of random variables extended to the field of security using the Monte Carlo simulation method. Taking into account the change in stress following load combinations: normal, exceptional and extreme acting on the dam, calculation of the results obtained have provided acceptable failure probability values which largely corroborate the theory, in fact, the probability of failure tends to increase with increasing load intensities, thus causing a significant decrease in strength, shear forces then induce a shift that threatens the reliability of the structure by intolerable values of the probability of product failures. Especially, in case the increase of uplift in a hypothetical default of the drainage system.

Keywords: dam, failure, limit-state, monte-carlo, reliability, probability, simulation, sliding, taylor

Procedia PDF Downloads 292

Authors: Mehran Naghizaderokni, Asscar Janalizadechobbasty

Abstract:

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

Procedia PDF Downloads 435

Authors: Safia Hocine, Djamil Aïssani

Abstract:

Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: heavy-tailed distribution, large claims, regenerative process, risk model, ruin probability, stability

Procedia PDF Downloads 324

Authors: Karim Hamidi Machekposhti, Hossein Sedghi

Abstract:

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

Procedia PDF Downloads 165

Authors: Hamid Ahmadi, Amirreza Ghaffari

Abstract:

Fatigue life of tubular joints in offshore structures is not only dependent on the value of hot-spot stress, but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). The DoB exhibits considerable scatter calling for greater emphasis in accurate determination of its governing probability distribution which is a key input for the fatigue reliability analysis of a tubular joint. Although the tubular X-joints are commonly found in offshore jacket structures, as far as the authors are aware, no comprehensive research has been carried out on the probability distribution of the DoB in tubular X-joints. What has been used so far as the probability distribution of the DoB in reliability analyses is mainly based on assumptions and limited observations, especially in terms of distribution parameters. In the present paper, results of parametric equations available for the calculation of the DoB have been used to develop probability distribution models for the DoB in the chord member of tubular X-joints subjected to four types of bending loads. Based on a parametric study, a set of samples was prepared and density histograms were generated for these samples using Freedman-Diaconis method. Twelve different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood method was utilized to determine the parameters of fitted distributions. In each case, Kolmogorov-Smirnov test was used to evaluate the goodness of fit. Finally, after substituting the values of estimated parameters for each distribution, a set of fully defined PDFs have been proposed for the DoB in tubular X-joints subjected to bending loads.

Keywords: tubular X-joint, degree of bending (DoB), probability density function (PDF), Kolmogorov-Smirnov goodness-of-fit test

Procedia PDF Downloads 694

Authors: Naci Büyükkaracığan

Abstract:

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

Procedia PDF Downloads 243

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

Abstract:

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

Procedia PDF Downloads 275