China
Africa
Explore chapters and articles related to this topic
Optimal Control
Published in T. Thyagarajan, D. Kalpana, Linear and Non-Linear System Theory, 2020
A function f(a,b) is said to be an extremum value of f(x,y), if it is either a maximum or a minimum. In other words, the maximum and minimum values of a function are together called extreme values or turing values. The points at which they are attained are called points of maxima and minima. The points at which a function has extreme values are called turning points.
Geophysics, Astronomy, and Acoustics
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
The words maximum and minimum are used in the sense that most measured values fall between these limits. Speeds of propagation are generally determined from photographic data and are "two-dimensional." Since many lightning flashes are not vertical, values stated are probably slight underestimates of actual values. First return strokes have longer times to current peak and generally larger charge transfer than do subsequent return strokes.
A novel extended crossing rate method for time-dependent hybrid reliability analysis under random and interval inputs
Published in Engineering Optimization, 2020
Chunyan Ling, Zhenzhou Lu, Kaixuan Feng
The hybrid reliability analysis under random and interval inputs (HRA-RI) has been widely investigated. In HRA-RI, the aleatory uncertainty is quantified as a random variable by the use of probabilistic theory, while the epistemic uncertainty is treated as an interval variable bounded by an interval. In contrast to the safety index (failure probability or reliability) in reliability analysis with only random inputs (Xu, Lu, and Xiao 2019; Yun, Lu, and Jiang 2019a), the failure probability in HRA-RI is also an interval variable with lower and upper bounds. The lower and upper bounds of failure probability ( and ) are, respectively, shown as follows (Du, Venigella, and Liu 2009): where denotes the probability operator, is the random input vector, and is the interval input vector. and are the lower and upper bounds of the interval variables. and are the global maximum and minimum of the performance function with respect to interval variables .
Multi-objective clustering: a kernel based approach using Differential Evolution
Published in Connection Science, 2019
Subrat Kumar Nayak, Pravat Kumar Rout, Alok Kumar Jagadev
For the selection of the best solution of the Pareto front in most of the cases, many authors have considered one validity index that returns good compact clusters. But by doing so, the selected validity index may not consider the importance of all the objectives that have been considered for optimisation. Because of this, a fuzzy concept (Abido, 2003) is followed in this article can be considered as a Decision Maker for determining the best compromised solution. A membership function that has been followed to assign a membership value to each individual of the Pareto front set is depicted as follows: Here, represents the set of membership values of the objective function, whereas symbolises the maximum and minimum value of that function.
Modified U-Net based 3D reconstruction model to estimate volume from multi-view images of a solid object
Published in The Imaging Science Journal, 2023
Radhamadhab Dalai, Kishore Kumar Senapati, Nibedita Dalai
This sub-section intends to determine the volume of generated 3D pixel cloud of an object in images. In the proposed model, the volume can be determined based on the point cloud using a volume calculation algorithm [28]. Here, the point cloud of is given as input, and the point cloud has 3D coordinate information. Then, the output of the volume calculation algorithm will be the numerical value for geometrical display and estimated volume. However, the steps involved to estimate volume can be given as follows: Initially, load the point cloud file and set number of slice, then find the maximum and minimum value of the point cloud and determine the width of slice.Then, across , cut the point cloud into number of slices and store.Further, bisect every slices over and divide every slice into same sub-intervals on over .Choose maximum and minimum points in every interval.Moreover, the model curve is computed using the chosen points for every slice to indicate the slice boundary and then combines the curve to determine the area for every slices.Then, the slice area is stored in a vectorFinally, integrate the area of slice and determine the volume of object.