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Simulation Runs and Output Analysis
Published in Raymond J. Madachy, Daniel X. Houston, What Every Engineer Should Know About Modeling and Simulation, 2017
Raymond J. Madachy, Daniel X. Houston
We desire to know the true value of a simulation output parameter based on the results of many observations. The accuracy of the statistical estimate is expressed as a range called a confidence interval. The upper and lower bounds define a range of values where the true value of an estimated parameter is expected to exist. A confidence interval (e.g. for a mean value) is produced from multiple runs and it can be updated after the result of each simulation run. The confidence level used in hypothesis testing is the probability that the interval contains the true value of the parameter.
Fuzzy Logic Control
Published in Clarence W. de Silva, Intelligent Control, 2018
in which p denotes a PID parameter. The subscript “new” denotes the updated value and “old” denotes the previous value. The incremental action taken by the fuzzy controller is denoted by Δp. Upper and lower bounds for a parameter are denoted by the subscripts max and min. A sensitivity parameter psen is also introduced for adjusting the sensitivity of tuning, when needed. A fuzzy tuner of this type will be used in the application, which is described in Chapter 6.
Applicability of sunspot activity on the climatic conditions of Gilgit-Baltistan region using fractal dimension rescaling method
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2021
Ali Khan, Syed Muhammad Murshid Raza, Sajjad Ali
To start with the relation , the upper and lower bounds of the intervals can be represented by the inequality, . This implies that when the value of Hurst exponent goes over and close enough to 0, the time series behavior will show more jagged structure. The other way to expressing Hurst exponent is that it measures the dimensional smoothness of a fractal time series created by the rescaled range (R/S) analysis of the process of the asymptotic behavior. The estimation of Hurst exponent can be made by the expression, , in that case represents duration of the sample data and R/S is the corresponding value of the rescaled range. Rescaled range also measures the divergence of time series in the form as the range of the mean-centered values for a given time period divided by the standard deviation for that duration. In the compact form Hurst suggested how to compute the rescaled range as , in this relation k stands for a constant depending on the nature of a time series, (Kale and Butar Butar 2011).
Customized bus routing problem with time window restrictions: model and case study
Published in Transportmetrica A: Transport Science, 2019
Rongge Guo, Wei Guan, Wenyi Zhang, Fanting Meng, Zixian Zhang
The branch-and-cut algorithm is the same approach introduced for the travelling salesman problem (Padberg and Rinaldi 1991). As a combination of branch-and-bound and cutting planes, the branch-and-cut algorithm addresses the problem by solving a series of relaxation problems of integer linear programming (Fischetti et al. 1997; Lysgaard, Letchford, and Eglese 2004). The branch-and-cut algorithm contains several steps: (i) pre-processing initial integer programming problem and setting upper and lower bounds; (ii) solving the relaxation problem to determine whether it is feasible; (iii) cutting the unfeasible part and adjusting the two bounds to find a feasible solution; and (iv) obtaining the optimal solution (Mitchell and John 2011).
Enhancement of wind energy resources assessment using Multi-Objective Genetic algorithm: A case study at Gabal Al-Zayt wind farm in Egypt
Published in International Journal of Green Energy, 2021
Mohamed L. Shaltout, Moaz A. Mostafa, Sayed M. Metwalli
where is the design vector , is the real frequency of wind speed, is the value of Weibull PDF at wind speed, and is the total number of wind speed bins. The design vector is subject to a set of inequality constraints representing upper and lower bounds on the values of and . The minimization of the first objective function will minimize and maximize , thus improving the accuracy of the Weibull PDF to represent the actual wind speed distribution. The minimization of the second objective function will minimize , thus improving the estimation of the wind power density. The solution of the formulated multi-objective optimization problem in Eq. (25) will generate a set of noninferior optimal solutions called the Pareto solution set. A preferred optimal solution can then be selected from the Pareto set according to a criterion specified by the assessment individuals, thus providing an important degree of flexibility in the decision-making process.