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Time of Concentration (TC) is a widely utilized time variable in hydrological studies. Various approaches exist to estimate TC, including direct measurements, empirical relations, and graphical method (GM). The GM is commonly regarded as a standard by researchers. Nevertheless, this approach faces obstacles due to the scarcity of records in many watersheds.. This research explores a novel technique for TC estimation, focusing on the examination and recommendation of two-dimensional (2D) hydraulic modeling. The proposed method leverages available satellite data to obtain the necessary input for the 2D simulation. Additionally, several empirical relations were evaluated for TC determination. The GM served as reference point for evaluating the results obtained from empirical relations and hydraulic modeling. To accomplish this, analysis was conducted on four distinct watersheds in Iran, comprising a total of 28 recorded rainfall-runoff data.. In numerical modeling, TC was defined as the duration required for a water parcel to traverse from the headwater to the outlet of a basin. In all studied watersheds, the maximum relative error between the benchmark (GM) and the 2-D modeling was limited to less than 10%. This observation establishes the reliability of hydraulic modeling as a viable method for TC calculation, particularly in ungauged watersheds where the GM cannot be employed. [ABSTRACT FROM AUTHOR]

This paper introduces a more streamlined and convenient graphical approach to investigate the stability of fractional-order dynamical systems comprehensively. In particular, we focus on the utilization of Kharitonov theorem, renowned for robust stability analysis of incommensurate fractional-order systems in the presence of uncertainty. A novel graphical framework is illustrated, promising to streamline the stability analysis of such systems, which leads to reducing the computational burden. Using the proposed method, we can achieve the least possible Kharitonov polynomials among the existing methods to analyze the robust stability of the incommensurate fractional-order systems. To validate our approach, we perform numerical simulations on four illustrative examples, demonstrating its effectiveness. Simulation results underscore the real-world utility of our methodology, emphasizing its potential significance in fractional-order system analysis. [ABSTRACT FROM AUTHOR]

A four-bar mechanism is a basic kinematic chain in most of planar mechanisms. Four-bar chains are synthesized for a specific task. The output deviates from the desired one due to many reasons broadly from the group of systematic and random input sources. The work presented herewith deals with the error estimation in the four-bar path generation mechanism under link tolerance. The primary estimation of error is carried out using a Taylor series approximation with a modified error equation. The inaccuracy is estimated using sample independent variables. A geometrical method for the estimation of specific errors is developed. The results are verified using the CAD model. The appropriateness of the Taylor series approximation with modified error equation estimations is compared with exact solutions from the geometrical method. The methodology is demonstrated through a sample case of the four-bar mechanism presented to compare the capability of the two methods. The deviations due to single systematic inaccuracy are exposed, and one of the methods- i.e. the geometrical method is found to be the robust method of error evaluation. [ABSTRACT FROM AUTHOR]

This paper attempts to expand the graphical analysis concept proposed by Chen and Abousleiman (Géotechnique, 2022. https://doi.org/10.1680/jgeot.21.00172) to deduce the undrained expansion solution of a cylindrical cavity in shear strain-hardening Drucker–Prager frictional soil. Based on the geometrical representation of the stress state/path and strain increments in the deviatoric planes, it is shown that the deviatoric stress-Lode angle stress path can be desirably determined by solving a first-order differential equation for the stress ratio (deviatoric stress over mean effective stress) in term of the Lode angle. The essential cavity expansion curve may also be readily constructed by calculating the internal cavity pressure and the corresponding expanded cavity radius, respectively, through simple numerical integrations with respect to the same variable of stress ratio. In particular, the ultimate cavity pressure can be easily evaluated by directly integrating the expression for cavity pressure with the stress ratio up to its limiting value. Some numerical results obtained from the proposed graphical method are presented to illustrate the impacts on the cavity responses of the earth pressure coefficient at rest, K 0 , and the key plasticity hardening parameters, which have also been compared with alternative solutions that require dealing with a system of coupled differential equations involving three principal effective stress components. [ABSTRACT FROM AUTHOR]

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The Bayesian approach is applied to estimation of the Weibull-power law process (WPLP) parameters as an alternative to the maximum likelihood (ML) method in the case when the number of events is small. For the process model considered we propose to apply the independent Jeffreys prior distribution and we argue that this is a useful choice. Comparisons were also made between the accuracy of the estimators obtained and those obtained by using other priors—informative and weakly informative. The investigations show that the Bayesian approach in many cases of a fairly broad collection of WPLP models can lead to the Bayes estimators that are more accurate than the corresponding ML ones, when the number of events is small. The problem of fitting the WPLP models, based on ML and Bayes estimators, to some real data is also considered. It is shown that the TTT-concept, used in the reliability theory, is not fully useful for the WPLP models, and it may be so for some other trend-renewal processes. In order to assess the accuracy of the fitting to the real data considered, two other graphical methods are introduced. [ABSTRACT FROM AUTHOR]

Reinforced concrete beams lose resistance at high temperatures and so as to guarantee their good performance, it is mandatory to consider this accidental action in design. As an alternative to the methods proposed by the European and Brazilian standards, above all the tabular method that, despite its simple application, limits calculations to a few pre-defined values, a new tool for fire design of these beams is proposed herein. A graphical method was developed with the Temperature Calculation and Design (TCD) software, which performs transient bi-dimensional thermo-structural analysis using the finite element method. The main variable of this method consists of the resistance to the bending moment of a heated cross-section. For its validation, the moment of four rectangular sections was determined according to four simplified methods. These results were compared among themselves and to those obtained by a more advanced method. They were all verified to lead to similar results. With regard to the TCD, whose results were used for the preparation of the graphical method, the maximum difference compared to a more advanced method was approximately 2.5%. After validation, graphs that associate the ratio between the applied moment in fire and the resistance to bending moment at ambient temperature to the fire resistance for different beams were created. These graphs present design solutions for more than 2300 beam models with T-shaped cross-sections in assorted lengths, heights, covers and reinforcement arrangements, both positive and negative. In the application examples, the results from the graphical method were generally more economic when compared to the tabular method of the fire design standards. [ABSTRACT FROM AUTHOR]

In this study, the coefficients of Weibull Distribution Function (WDF) were calculated at two different heights using by six different methods. One-year wind data were used to determine the coefficients of WDF at different heights, and the wind data were obtained from a metrology station with a height of 10 m and a real wind turbine with a height of 80 m in Turkey's Hatay region. The used methods in this study were Graphical Method (GM), Empirical Method, Energy Pattern Method (EPM), Energy Trend Method, Maximum Likelihood Method and Moment Method.\ Three different statistical error analysis tests were used to compare the performance of the used methods at two different heights. Estimated mean wind speed and power values are the most important indicators to evaluate the performance of the used methods. In this study, mean wind speeds and powers were estimated in all methods for both heights using the WDF. These obtained values were compared with the actual real data and the best performing method was determined at both different heights for selected region. When the results were evaluated in general at both different heights, it was seen that the best performance method was the EPM and the worst performance method was the GM. [ABSTRACT FROM AUTHOR]

Issues are examined in the calculation of the secondary currents of an arc in the implementation of single-phase auto-reclosing (SPAR) for elimination of unstable single-phase faults of 500 and 750-kV ultra-high-voltage lines. Dependences are shown for the backfeed arc extinguishment time, and the SPAR currentless pause recommended in the references, on the amplitude of the forced component of the secondary arc current. A graphical method is proposed for the calculation of secondary arc currents in ultra-high-voltage lines under the condition of SPAR currentless pause. The adequacy of the modeling of a backfeed arc was confirmed by a comparison of the calculated and experimental data from a 750-kV 525-km line. Examples are presented of the application of the graphical method proposed in this article for calculation of secondary backfeed arc currents in 500 kV lines of various length. The features of the implementation of SPAR in 300 and 1000 km lines are noted, and in particular, the effect of zero-power reactors connected to the neutral of the shunt reactors. An example of the implementation of SPAR using automatic phase shunting (APS) in a 500 km line is also examined. [ABSTRACT FROM AUTHOR]