جستجوی مقالات مرتبط با کلیدواژه « تابع چگالی احتمال » در نشریات گروه « آب و خاک »

The cost of building dams is very high and their failure can be hazardous. On the other hand, they are vital for every country as freshwater storage. Deterministic and traditional algorithms can not answer the multidimensional and complex problems of dam construction, and it is necessary to use hybrid methods based on probabilities. The problems of fluid movement in their nature have a complexity that modeling and finding requires using an advanced algorithm that can finally interpret its non-deterministic nature. Earth dams have a porous, multiphase, and complex medium, and the hydraulic and mechanical variables in different parts are associated with uncertainty. For this reason, in recent years, the regulations for the design of dams have been reforming in the direction of applying non-deterministic and probabilistic variables in the calculations. A probabilistic engineering view leads to a more realistic understanding of design than deterministic approaches. In the research, artificial intelligence (AI) methods have been used to analyze the data, which provides a predictive model of behavior for seepage discharge flow through the earth dam. In general, the present research has two purposes a) to estimate the effect of uncertainty of the hydraulic conductivity dam on seepage discharge and b) to provide a model to estimate seepage discharge in a dimensionless way with the gene expression programming (GEP) and support vector machine (SVM) methods.

Monte Carlo simulation (MCS) with 2000 iterations was executed for stochastic analysis. The first step of the Monte Carlo simulation is the choice of the deterministic performance function. In the second step, the input variables were defined to the performance function and the probability distribution for variable/variables. By repeating the process n times, n random answers were extracted for the resulting problem, and finally, probability density function (PDF) and cumulative density function (CDF) graphs were drawn for the results. In the Fortran code of this research and to check the convergence, the hydraulic heads were compared to achieve the difference obtained in iteration n with the obtained value in iteration n-1, and if the difference is less than the tolerance error, then the program stops. In the next section of the algorithm, the obtained data (from the repeated execution of the MCS) are converted into a model for a description relationship between the effective seepage discharge (ESD) and the input variables by using the metaheuristic methods that include; gene expression programming (GEP) and support vector machine (SVM). After GEP and support vector regression (SVR) modeling the predicted and observed results were compared by statistical indexes such as MSE, RMSE, MAE, and Correlation coefficients.

The different models of earth dams were implemented in the Fortran program, and the average and standard deviation of the seepage discharge flow in the uncertainty state were obtained. To determine the relationship between the ESD value, indicators had been defined that these parameters used for the Gene Expression Programming model include; Kx/Ky, W/B, Bd/B, Bu/B, Hdam/B, Hu/Hdam, and Hd/Hu. These were the factors influencing the seepage discharge of the earth dam, and the discharge component is also defined as the effective seepage discharge (ESD) in a dimensionless manner. Kx and Ky are soil permeability in the direction of the horizontal and vertical axes respectively (m/s), W is the width of the crest, B is the width of the base of the earth dam, Bd is the horizontal distance of the dam tip from the downstream side from the crest, Bu is the horizontal distance of the dam tip from the upstream side crest, Hdam height of the dam, Hu height of the reservoir level, Hd water height downstream of the dam, all the variables are in meters. By increasing the Kx/Ky ratio of horizontal to vertical hydraulic conductivity by 49%, the Effective Seepage Discharge increases by 14%. If the horizontal variable of permeability is increased by 25%, the ESD rate increases by 4.56%, similarly, if the vertical variable is increased by 25%, the ESD decreases by 4.72%.

After finite element analysis, and modeling with two methods of gene expression programming (GEP) and support vector regression (SVR), the statistical analysis of the methods showed that the two calculation models had a good prediction of the ESD with a correlation coefficient above 0.9. Vertical hydraulic conductivity (Ky) has a greater effect on the ESD rate than horizontal hydraulic conductivity (Kx). The results of the geometric investigation of the dam also show that the increase in the ratio Hdam/B has a direct impact on the ESD and also the lower the slope downstream of the dam leads to the lower the ESD. The statistical analysis was used to compare the results of the data obtained from Fortran output for SVR and GEP models. In general, the SVR model is closer to the model resulting from the Fortran code rather than the GEP model, and it has a low root mean square error (RMSE) and a high correlation coefficient.

Estimation of temperature probability distribution function (PDF) is a basic step for risk and uncertainty analysis in hydrology and environment studies. Most researches on temperature PDF estimation have been based on parametric approach while non-parametric approach has been considered in recent years because of some its benefit. The Ortho-Normal Series (ONS) method is a novel non-parametric method with suitable features that has recently been considered in hydrology. This method uses a number of constants with default values for its calculation, but no independent research has taken place about the importance of the default values on the precision of PDF fitting. The objective of this study is sensitivity analysis of ONS constants for precision of temperature PDF estimation which leads to a better understanding of the importance of the coefficients of this method.
First, the precision of non-parametric ONS method beside four conventional parametric methods (i.e. Gamma, Gumbel, Exponential and Log-Normal) for annual maximum and minimum temperature PDF estimation of Isfahan, Shiraz, Zahedan and Ramsar stations were investigated using Akaike Information criteria (AIC) and Mean Square Error (MSE). The non-parametric ONS method uses CJ0, CJ1, CT and CM coefficients with their default values. The reasonable domains were determined for each coefficient and a certain number of values in each domain were selected. The precision criteria corresponding to the selected value in the domains of coefficients were calculated separately. The sensitivity analysis graphs were drawn using calculated values. The CV of fitting precision criteria of each coefficient was determined considering studied data series for comparison of magnitude of sensitivity of the coefficients.
The ONS coefficients sensitivity analysis show the CT coefficient is most sensitive coefficient to changes relative to its default value. The CM and CJO coefficients have similar magnitude of sensitivity and are less sensitive to CT coefficient while CJ1 coefficient is least sensitive coefficient among all coefficients. The analysis of sensitivity analysis graph reveled that increase in precision with decrease in coefficients values and decrease in pension with increase in coefficients.
The results show sensible decrease or increase on ONS precision with changes in default values of the coefficients. Moreover it is obvious the completely acceptable precision of ONS using its default values for the coefficients but the changes in CT coefficient led to sensible improvement in precision. Therefore it can be concluded that investigation of changes in default values of ONS coefficients are an important and suitable tool to increase the precision of PDF estimation by this method.

The most important factors about rainfall are its frequency, intensity and amount. The main goal of this study was estimating the time distribution of rainfall in some climatic regions of Iran. There are different methods in estimating time distribution of rainfall. Two of these are the Huff and Pilgrim methods in which real rainfall data are used to estimate rainfall temporal patterns. As the first step statistical analysis was performed to estimate the PDF curves. Then the minimum range for storm selection in each station was investigated. The results showed that the optimum rainfall range in each of the selected stations (Bam, Tehran, Shiraz and Gorgan) were 7.0, 10.5, 12.0 and 10.0 mm, respectively. Then the rainfall temporal pattern of the four climatic regions of Iran including sever arid (Bam), arid (Shiraz), semi- arid (Tehran) and semi humid (Gorgan) was identified applying the Huff and Pilgrim methods. Dimensionless curve fitting of the temporal patterns of the rainfall of each statin was also investigated. Comparison of the patterns of the two selected methods with the collected data indicated that the Huff method was superior to the Pilgrim method results