Suitable Probability Density Function Research Articles

An artificial gorilla troops optimizer for stochastic unit commitment problem solution incorporating solar, wind, and load uncertainties.

The unit commitment (UC) optimization issue is a vital issue in the operation and management of power systems. In recent years, the significant inroads of renewable energy (RE) resources, especially wind power and solar energy generation systems, into power systems have led to a huge increment in levels of uncertainty in power systems. Consequently, solution the UC is being more complicated. In this work, the UC problem solution is addressed using the Artificial Gorilla Troops Optimizer (GTO) for three cases including solving the UC at deterministic state, solving the UC under uncertainties of system and sources with and without RE sources. The uncertainty modelling of the load and RE sources (wind power and solar energy) are made through representing each uncertain variable with a suitable probability density function (PDF) and then the Monte Carlo Simulation (MCS) method is employed to generate a large number of scenarios then a scenario reduction technique known as backward reduction algorithm (BRA) is applied to establish a meaningful overall interpretation of the results. The results show that the overall cost per day is reduced from 0.2181% to 3.7528% at the deterministic state. In addition to that the overall cost reduction per day is 19.23% with integration of the RE resources. According to the results analysis, the main findings from this work are that the GTO is a powerful optimizer in addressing the deterministic UC problem with better cost and faster convergence curve and that RE resources help greatly in running cost saving. Also uncertainty consideration makes the system more reliable and realistic.

Elaboration of a Generalized Mixed Model for the wind speed distribution and an assessment of wind energy in Algerian Coastal regions and at the Capes

Understanding and evaluating wind energy involves various steps, including the observed temporal and directional variations in wind speed, choosing a suitable Probability Density Function (PDF) to describe wind regimes, and selecting an appropriate location for building wind farms. The wind speed data archived from nine meteorological stations along the northern coast of Algeria from 2017 to 2021 was used as a dataset to achieve these purposes. Zero-inflated mixed model (ZIMM) has been elaborated to model the wind speed regimes that combine two processes. The first process consists of mixing two PDFs that generate the counts data. The second process generates the residual zero-counts data. The estimation of ZIMM parameters is obtained with the Expectation–Maximization algorithm. ZIMM performances were evaluated at the selected sites using the commonly used goodness of fit (GOF) metrics: coefficient of determination (R2), root mean square error (RMSE), sum of square error (SSE), Kolmogorov–Smirnov (KS), Akaike information criterion (AIK), Bayesian Information Criterion (BIC), and compared with the widespread single PDFs: the two parameters Weibull, generalized extreme value (GEV) and Normal–Weibull mixed model. The datasets are used as input for assessing wind power and the feasibility of wind power plants in 24 Algerian Capes where the data is unavailable, using the Wind Atlas Analyses and Application Program (WAsP) and three different wind turbines, namely Nordex N50, Bonus B54, and Nordex N60. The results show significant variations in diurnal, monthly, and seasonal mean wind speed and power density. According to all GOF, the ZIMM PDF model outperforms conventional PDFs and the mixed model at the nine meteorological stations. The Bonus B54 wind turbine has the best capacity factor (Cp) with the lowest electrical production cost of all Algerian Capes, and the Cp exceeds 0.3 at 15 Capes from the 24 analyzed Capes. The highest Cp, about 0.467 with an annual electric production that reaches 4.09 GWh/year, is obtained at Cape Takouch with the lowest electrical production cost of 0.0414 $/kWh and 2.032 Kton/year of CO2 emission avoided.

Wind Power Potential of Kaniga Region, Rwanda

The purpose of this study was to investigate the potential of wind power in Kaniga, Rwanda. Wind speed and wind direction are the most important characteristics for assessing wind energy potential of a location using suitable probability density functions. In this study, a hybrid-Weibull probability density function was used to analyze data from Kaniga station. Kaniga is located in Gicumbi District, in the Northern Province of Rwanda. Onsite hourly wind speed and wind direction data for the year 2022 were analyzed using Computer programmes. The research was conducted to reveal the wind power potential of Kaniga and other major wind stations in the country as an approach to address energy shortage problem in the country. It was found that the average annual wind speed for Kaniga, Nyarwambu, and Byumba were 4.5m/s, 3.7m/s and 4.1m/s respectively, while corresponding dominant wind directions for the stations were 3200, 1800 and 1500 respectively. The average annual wind power density of Kaniga was found to be 1,285.4W/m2, while the annual power densities for Nyarwambu and Byumba were determined as 689.4W/m2 and 805.4W/m2 respectively. The other stations in Rwanda have the average annual power densities ranging from 6.99 W/m2 to 138.2W/m2. From these findings, it is clear that Kaniga has the greatest wind power potential among all other studied wind stations in the country.

Conformance probability in the assessment of Calibration and Measurement Capabilities

We argue that the assessment of the Calibration and Measurement Capabilities, CMCs, by means of the results of a Key Comparison is a bona fide exercise of conformity assessment, and as such should be treated, using the appropriate tools, including risk assessment. This position contrasts with the current practice, in which acceptance or rejection of a CMC claim are based on the normalised error. We show that, behind this seemingly unique acceptance criterion, different decision rules – guarded acceptance, simple acceptance and guarded rejection – exist in reality, depending on the characteristics of the comparison. This variety of decision rules impairs the fairness of the current equivalence arrangement. We suggest that the conformance probability should be the key parameter to be considered in the assessment of a CMC claim. Using a suitable Probability Density Function, PDF, for the measurand, we calculate the conformance probability for the possible scenarios, and show that using the current acceptance criterion the conformance probability can attain unacceptably low values. Therefore, we maintain that the current acceptance criterion is ambiguous and inadequate, and suggest to rather adopt a criterion based on the calculation of the conformance probability and the establishment of a minimum threshold for acceptance. We demonstrate our proposal by applying it to a practical case and to a fictitious example in mass metrology.

Investigation on the statistical distribution of PM2.5 concentration in Chiang Mai, Thailand

Recently, it is found that Northern Thailand has very high levels of airborne particulates known as PM2.5. PM2.5 particulates can cause breathing problems and may raise the risks of heart disease and even some cancers. According to AirVisual, Chiang Mai, the capital of Northern Thailand which offers for tourists in both business and cultural center, had the highest levels of smog in the world in March 2018, reaching at least 183 on the PM2.5 Air Quality Index scale. The daily average PM2.5 concentration data are determined from July 2016 – June 2018 at two stations in Chiang Mai at Yupparaj Wittayalai school and City Hall. The Weibull, Gamma, Lognormal and Inverse Gaussian distributions are considered for finding the most appropriate probability functions of the daily average PM2.5 concentration. The results show that, as evaluated with the goodness- of-fit measures; Komolgorov-Smirnov and Anderson-Darling test statistics, the Inverse Gaussian distribution is the most suitable probability density functions of the daily average PM2.5 concentration for two stations. Furthermore, the return periods of the PM2.5 concentration are predicted by using the Largest Extreme Value distribution, which can be further applied in air quality management and related policy making.

Droplet size distributions and batch separation of oil-in-water dispersions created by the two-phase flow through perforated plates

The design of liquid/liquid gravity separators requires extensive research and optimization. In this context, the current contribution provides experimental insights into the droplet size distributions and the separation behavior of paraffin oil-in-water dispersions. The investigated dispersions result from the two-phase flow through perforated plates, which are placed inside the dispersion unit of a continuous mixer-settler. The droplet sizes are examined in relation to the geometry and number of perforated plates, the specific energy dissipation rates and the dispersed phase concentrations. A self-similar state, to which all normalized droplet size distributions converge, is approximated using a large sample of experimental data and modeled with suitable probability density functions. Finally, the influence of the Sauter mean diameter and the aforementioned process parameters on batch separation time is examined. It is suggested that the ratio between sedimentation and total separation time is analogous to a power-law decrease of the Sauter mean diameter and that the correlation is characteristic of the perforated plates geometry.

Aero structure damage growth prediction using age-based state transition models

Flaw growth in aero-structures is a stochastic phenomenon as the structure is subjected to random stresses and varying environmental conditions. Accurate prediction of flaw growth enables maintenance managers to undertake correct decision making leading to timely repair/ replacement actions. The flaw growth rate varies with respect to age of the structure making it difficult to predict using classical prognosis techniques. A statistical framework based on sequential Monte Carlo technique known as particle filter (PF) is used in this study for predicting flaw growth. PF implementation involves degradation prediction step and update step at each instant. The selection of a suitable probability density function as a state transition model for predicting flaw growth plays a vital role in prediction accuracy. Different prediction densities represent varying rates of flaw growth during the structure’s lifecycle. The use of a single prediction density at every prediction stage throughout the life of the aero structure is inappropriate and leads to inaccuracy. Therefore, dynamic flaw prediction density is proposed to accurately predict the flaw growth. The suitable candidate for dynamic prediction density is Weibull density as it is equivalent to different densities by changing the value of shape parameter. The shape parameter is estimated by applying the Maximum Likelihood Estimation (MLE) technique on the available database of measurements at each life stage, spanning 1000 loading cycles, throughout the life. A case study of crack growth around the countersunk rivet holes of an in-service passenger aircraft’s wing structure is used to validate the accuracy of the proposed technique. The database is divided into training and validation segments. The proposed prognosis technique and classical prognosis technique (with single/constant prediction density throughout the lifecycle) are compared to showcase the efficacy of the proposed technique for prognostics of aero-structures.

Ku-Band scintillation over Akure, Nigeria

Relationship between scintillation intensity (σ χ ) and peak-to-peak amplitude (χ pp) is important for mitigating scintillation effects on any communication link. This study employs linear, logarithmic and polynomial functions for fitting σ χ and χ pp in order to determine the best model for describing the variation of the former with the latter. It also examines the frequency of occurrence of scintillation intensity and the suitable probability density function for characterizing its distribution. Data used spanned 24 months, and were obtained from measurement of EUTELSAT W4/W7 satellite beacons on 12.245 GHz frequency, 1 s integration time and 53° elevation angle, at the Department of Physics, Federal University of Technology, Akure (07°17′N, 005°18′E, 358 m) Nigeria. Results show that logarithmic function performed best in modelling χ pp from σ χ as indicated by high coefficient of determination and minimal root mean sqaure error values. Strong scintillation events (σ χ > 0.5) were also found to occur less frequently as sample interval increased. Lastly, lognornal, gamma and generalised extreme value (GEV) models were found suitable for describing σ χ distribution.

Optimal placement and sizing of FACTS devices for optimal power flow in a wind power integrated electrical network

Optimal power flow (OPF) is one of the challenging optimization problems in power domain. The complexity of the problem escalates with incorporation of uncertain and intermittent renewable sources into the electrical network. Flexible AC transmission system (FACTS) devices are also becoming more commonplace in modern power system to mitigate growing demand and to relieve congestion from the network. This paper aims to solve the OPF where the generation cost is optimized with incorporation of stochastic wind power and several types of FACTS devices such as static VAR compensator, thyristor-controlled series compensator and thyristor-controlled phase shifter. Case studies with both fixed and uncertain load demands are performed. The stochastic wind energy and load demand are modeled using suitable probability density functions. Optimization objective considers cost of thermal generation, direct cost of scheduled wind power, penalty cost for underestimation and reserve cost for overestimation of the wind power. In addition, both locations and ratings of the FACTS devices are optimized to minimize total generation cost of the system. Success history-based adaptive differential evolution (SHADE), a powerful evolutionary algorithm, is adopted to perform the optimization task. The constraints of OPF problem are handled using superiority of feasible solutions (SF) method. The integration approach of SF method with several popular metaheuristic algorithms has been proposed in this work, and a detailed comparative analysis among various algorithms establishes SHADE algorithm to be the best performer.

Estimation of Performance with the Two Truncated Probability Density Functions, Case Study: Using Mixco Column to Extract Samarium and Gadolinium

ABSTRACT A hydrodynamic performance by the variation in the droplet size and distribution was moreover considered in the recording of experimental data for the extraction of rare-earth ions. The percentage of stripping and extraction efficiency for rare earth ions increases directly proportional to rotation speed. The identification of a suitable probability density function is carried out by utilizing the mixture of two normal probability density functions. By separation factor exceeding 5.9, extraction efficiency and percentage of stripping up to 95% could be achieved in the continuous Mixco column, which has superior hydrodynamic characteristics with a great prospect of application.

Least Square Saliency Transformation of Capsule Endoscopy Images for PDF Model Based Multiple Gastrointestinal Disease Classification

Wireless capsule endoscopy (WCE) is an effective video technology to diagnose gastrointestinal (GI) diseases, such as bleeding, ulcer, and tumor. In order to avoid a tedious manual review process of long duration WCE video recordings, automatic disease detection schemes have received significant attention from the researchers. In particular, instead of the conventional approach of dealing with a single disease, developing a unified scheme, which is capable of detecting multiple GI diseases, is getting more importance while being challenging. In this paper, a unified computer-aided scheme is developed for detecting multiple GI diseases from WCE videos based on a proposed least-square saliency transformation (LSST) followed by a probabilistic model-fitting approach. Commonly in the training phase, image-level labeling of images is used, as pixel-level annotations are available only for a small number of images. In view of utilizing the knowledge from pixel-level annotated diseased images, an LSST scheme is proposed to extract a set of optimum prior coefficient-vectors which is later used to capture the salient pixels of interest (POI) in a larger WCE image dataset that do not have pixel-annotations. The intensity distributions of salient POI are modeled by a suitable probability density function (PDF) and the fitted PDF parameters are utilized as features in the proposed supervised hierarchical classification scheme. A large number of WCE images obtained from publicly available WCE videos are used for performance evaluation and it is found that the result obtained by the proposed method outperforms the results obtained in case of some state-of-the-art methods.

Metaheuristic optimization algorithms to estimate statistical distribution parameters for characterizing wind speeds

An accurate analysis of wind speeds is vital to justify wind energy projects. Statistical distributions can be used to characterize wind speeds through considering uncertainty in wind resources. However, the selection of the most suitable probability density function (PDF) is still a challenging task. Therefore, this study aims at developing a framework to accurately evaluate the performance of different PDFs to fit wind speeds, as well as presenting a new metaheuristic optimization algorithm method, called Social Spider Optimization (SSO), for wind characterization purposes. Seven sites in Saudi Arabia are used as case studies. Results indicate that combined PDFs outperform single PDFs in representing the observed wind speeds frequencies at all considered sites. Weibull distribution appears to be the most prevalent single distribution while no combined PDF dominates the others. In addition, the proposed SSO method is found to be the most efficient method for estimating PDFs parameters in Saudi Arabia. Overall, this proposed framework can be used to evaluate different wind PDFs in other countries.

Probability density function based modeling of spatial feature variation in capsule endoscopy data for automatic bleeding detection

Wireless capsule endoscopy (WCE) is a video technology to inspect abnormalities, like bleeding in the gastrointestinal tract. In order to avoid a complex and long duration manual review process, automatic bleeding detection schemes are developed that mainly utilize features extracted from WCE images. In feature-based bleeding detection schemes, either global features are used which produce averaged characteristics ignoring the effect of smaller bleeding regions or local features are utilized that cause large feature dimension. In this paper, pixels of interest (POI) in a given WCE image are determined using a linear separation scheme, local spatial features are then extracted from the POI and finally, a suitable characteristic probability density function (PDF) is fitted over the resulting feature space. The proposed PDF model fitting based approach not only reduces the computational complexity but also offers more consistent representation of a class. Details analysis are carried out to find the best suitable PDF and it is found that fitting of Rayleigh PDF model to the local spatial features is best suited for bleeding detection. For the purpose of classification, the fitted PDF parameters are used as features in the supervised support vector machine classifier. Pixels residing in the close vicinity of the POI are further classified with the help of an unsupervised clustering-based scheme to extract more precise bleeding regions. A large number of WCE images obtained from 30 publicly available WCE videos are used for performance evaluation of the proposed scheme and the effects on classification performance due to the changes in PDF models, block statistics, color spaces, and classifiers are experimentally analyzed. The proposed scheme shows satisfactory performance in terms of sensitivity (97.55%), specificity (96.59%) and accuracy (96.77%) and the results obtained by the proposed method outperforms the results reported for some state-of-the-art methods.

Weibull Probability Distribution of Wind Speed for Gaza Strip for 10 Years

The need of clean and renewable energy, as well as the power shortage in Gaza strip with few wind energy studies conducted in Palestine, provide the importance of this paper. Probability density function is commonly used to represent wind speed frequency distributions for the evaluation of wind energy potential in a specific area. This study shows the analysis of the climatology of the wind profile over the State of Palestine; the selections of the suitable probability density function decrease the wind power estimation error percentage. A selection of probability density function is used to model average daily wind speed data recorded at for 10 years in Gaza strip. Weibull probability distribution function has been estimated for Gaza based on average wind speed for 10 years. This assessment is done by analyzing wind data using Weibull probability function to find out the characteristics of wind energy conversion. The wind speed data measured from January 1996 to December 2005 in Gaza is used as a sample of actual data to this study. The main aim is to use the Weibull representative wind data for Gaza strip to show how statistical model for Gaza Strip over ten years. Weibull parameters determine by author depend on the pervious study using seven numerical methods, Weibull shape factor parameter is 1.7848, scale factor parameter is 4.3642 ms-1, average wind speed for Gaza strip based on 10 years actual data is 2.95 ms-1 per a day so the behavior of wind velocity based on probability density function show that we can produce energy in Gaza strip.

Propagation of two independent sources of uncertainty in the electrocardiography imaging inverse solution

This study investigates the effects of the input parameter uncertainties (organ conductivities, boundary data, etc.) on the electrocardiography (ECG) imaging problem. These inputs are very important for the construction of the torso potential for the forward problem and for the non-invasive electrical potential on the heart surface in the case of the inverse problem. We propose a new stochastic formulation that allows us to combine both sources of errors. We formulate the forward and inverse stochastic problems by considering the input parameters as random fields and a stochastic optimal control formulation. In order to quantify multiple independent sources of uncertainties on the forward and inverse solutions, we attribute suitable probability density functions for each randomness source and apply stochastic finite elements based on generalized polynomial chaos method. The efficiency of this approach to solve the forward and inverse ECG problems and the usability to quantify the effect of organ conductivity and epicardial boundary data uncertainties in the torso are demonstrated by a number of numerical simulations on a two-dimensional computational mesh of a realistic torso geometry.

A Bayesian approach to rapid seismic vulnerability assessment at urban scale

ABSTRACTThe seismic vulnerability of city centers is commonly assessed by extending the study methods applied to single buildings to urban aggregations. This approach is not always applicable at territorial scale, as it is uneconomical in terms of time and costs. An innovative method provides reasonable large-scale a priori estimation of parameters not directly evaluable from the exterior of buildings by elaborating values which can be measured from the outside. Those parameters are treated as continuous variables, by assigning them a suitable probability density function. The Bayesian approach is adopted, which allows the update of initial hypotheses by using new data gathered during on-site surveys. In this regard, a rapid survey form for the on-site data collection is proposed. An example of its application to a façade of a building structural unit in Santo Stefano di Sessanio in L’Aquila province (Italy) is proposed, showing promising preliminary results for buildings belonging to Italian historical centers.

Estimation of wind speed probability density function using a mixture of two truncated normal distributions

Probability density functions (PDFs) are normally used to describe wind speed distribution for the proper selection of wind turbines in a given location. The identification of a suitable PDF is fundamental for accurately assessing the wind energy potential and designing the wind farms.To achieve this objective, the use of a mixture of two truncated normal distributions (MTTND), defined for v ≥ 0 and obtained by linearly combining two normal distributions with different means and variances, is proposed in this work for the representation of the wind speed PDF. The distribution is a function of five parameters, does not require a high computational burden and allows the representation of wind calm hours (v = 0). The use of the MTTND allows an accurate estimation to be obtained of the experimental discrete distribution of the probability density and cumulative probability, and the characteristic statistical quantities used to estimate the available energy and the performance indicators in the selection of both the site and wind turbine.The validity of the use of the MTTND was verified by comparison with the most widespread PDFs in the scientific literature: Weibull, Rayleigh, lognormal, gamma, inverse Gaussian and Burr. This comparison was developed using experimental wind speed data relating to five Italian locations and a location in Colorado (USA) belonging to the National Renewable Energy Laboratory. For each location, the parameters of each PDF were obtained with the least squares non-linear regression method. The results of the comparisons, in terms of the coefficient of determination R2 and root mean square error (RMSE) for goodness of fit and in terms of relative error in the calculation of the statistical quantities, show that the use of the MTTND gives rise to greater accuracy than a conventional wind speed PDF.

A Model of Self-Monitoring Blood Glucose Measurement Error.

A reliable model of the probability density function (PDF) of self-monitoring of blood glucose (SMBG) measurement error would be important for several applications in diabetes, like testing in silico insulin therapies. In the literature, the PDF of SMBG error is usually described by a Gaussian function, whose symmetry and simplicity are unable to properly describe the variability of experimental data. Here, we propose a new methodology to derive more realistic models of SMBG error PDF. The blood glucose range is divided into zones where error (absolute or relative) presents a constant standard deviation (SD). In each zone, a suitable PDF model is fitted by maximum-likelihood to experimental data. Model validation is performed by goodness-of-fit tests. The method is tested on two databases collected by the One Touch Ultra 2 (OTU2; Lifescan Inc, Milpitas, CA) and the Bayer Contour Next USB (BCN; Bayer HealthCare LLC, Diabetes Care, Whippany, NJ). In both cases, skew-normal and exponential models are used to describe the distribution of errors and outliers, respectively. Two zones were identified: zone 1 with constant SD absolute error; zone 2 with constant SD relative error. Goodness-of-fit tests confirmed that identified PDF models are valid and superior to Gaussian models used so far in the literature. The proposed methodology allows to derive realistic models of SMBG error PDF. These models can be used in several investigations of present interest in the scientific community, for example, to perform in silico clinical trials to compare SMBG-based with nonadjunctive CGM-based insulin treatments.

A new stochastic multi source approach to improve the accuracy of the sales forecasts

PurposeThe aim of this paper is to suggest a new approach to the problem of sales forecasting for improving forecast accuracy. The proposed method is capable of combining, by means of appropriate weights, both the responses supplied by the best-performing conventional algorithms, which base their output on historical data, and the insights of company’s forecasters which should take account future events that are impossible to predict with traditional mathematical methods.Design/methodology/approachThe authors propose a six-step methodology using multiple forecasting sources. Each of these forecasts, to consider the uncertainty of the variables involved, is expressed in the form of suitable probability density function. A proper use of the Monte Carlo Simulation allows obtaining the best fit among these different sources and to obtain a value of forecast accompanied by a probability of error known a priori.FindingsThe proposed approach allows the company’s demand forecasters to provide timely response to market dynamics and make a choice of weights, gradually ever more accurate, triggering a continuous process of forecast improvement. The application on a real business case proves the validity and the practical utilization of the methodology.Originality/valueForecast definition is normally entrusted to the company’s demand forecasters who often may radically modify the information suggested by the conventional prediction algorithms or, contrarily, can be too influenced by their output. This issue is the origin of the methodological approach proposed that aims to improve the forecast accuracy merging, with appropriate weights and taking into account the stochasticity involved, the outputs of sales forecast algorithms with the contributions of the company’s forecasters.

Markov Chain 모형을 이용한 시단위 모의강우특성 분석

우를 입력 자료로 해석되는 수문시스템 및 수공구조물 등은 강우의 형태와강 특성에 따라 각기 다르게 해석될 수 있다. 따라서 본 연구에서는 시간단위 강우자료를 이용하여 Markov Chain 모의 발생기법을 이용하여 강우를 모의 발생하였다. 모의 발생을 위해 1985년~2014년 30개년의 6월~10월의 시간단위 강우자료를 수집하고, Markov Chain 모의 발생기법을 이용하여 강우를 모의 발생시켰다. 또한, 과거 강우가 발생한 시간만을 모아 적합한 확률밀도함수를 선정하고 선정된 확률밀도함수에 난수를 발생시켜 강우강도를 생성하여 발생된 모의 강우자료에 적용하였다. 이렇게 발생된 모의 강우와 과거 발생한 과거 강우의 특성을 비교한 결과 전체적으로 유사한 특성을 보였으나 첨두 강우강도는 다소 과소 추정(4.88~9.28%)되는 결과를 보였다. 이러한 시간강우 모의는 도시 홍수방재 예측에 도움을 주리라 판단된다. Hydrological systems and hydraulic structures design of rainfall are used as input data. Accordingly shows the different analysis results. In this study, an hour unit of time rainfall occurred simulation using the Markov Chain model. Simulation was used for the time unit of rainfall in 1985~2014 year, 6~10 month. Simulated rainfall was generated using a Markov Chain model. In addition, selection of suitable probability density function using Rainfall occurrence time. Accordingly applied to simulated rainfall data generated by creating rainfall. The past rainfall and rainfall simulation characteristic comparison. Overall, rainfall characteristics showed a similar peak rainfall expression showed a slight underestimation (4.88~9.28%) results. One of the problems of all simulation model does not represent a peak rainfall. Rainfall simulation overall it was similar using time unit rainfall. But, will be helpful to describe the rainfall determined if supplement the rainfall estimation methods.