If the number of samples is the same as that of population, an exact probability distribution can be found. Based on this review, weight function and distribution parameters can be defined in a reasonable way.
#Median latin hypercube sampling how to
In order to see how to extend LHS to propose WLHS, it is helpful for us to review on LHS. 2.Weighted Latin Hypercube Sampling (WLHS) and WLHS proposed in this paper, respectively, are compared to investigate the effect of choosing different sampling techniques. In this application, clearance-to-stops (CSs) calculated using LHS proposed by Huang et al. is used in this paper with the site-specific ground motions of the nuclear power plant in Diablo Canyon, which is western region in the USA. The same numerical example as Huang et al. considered the uncertainties using LHS for a study on seismic performance evaluation of seismically isolated structures in NPPs. The proposed WLHS is also applied to seismically isolated structures in nuclear power plants. This study establishes equations necessary to apply weight function to WLHS, and verifies WLHS through numerical examples. This method is called Weighted Latin Hypercube Sampling (WLHS). In a case where intervals with different probability areas are used, it is necessary to make a correction using proper weight function. This study proposes extension of LHS to avoid the necessity of using intervals with the same probability area. For this reason, LHS is preferred in probabilistic structural design for an efficient calculation. LHS can estimate the probability distribution approximately using a far smaller sample than RS, and is effective in estimating the distribution parameters in a case where the type of the probability distribution of random variable is known or properly assumable. Latin Hypercube Sampling (LHS) is a method for dividing the whole interval of random variables into several intervals with the same probability area and for selecting samples from each interval. When there is a need to calculate the probability in the tail, Importance Sampling is a method for selecting, randomly in the tail area, a far smaller sample than RS. As Random Sampling (RS) uses samples selected randomly among population, it has a disadvantage of a lengthy calculation time because a large number of samples are required especially in a case where a probability to be calculated is located in the tail of probability distribution. To estimate the mentioned uncertainties, one can use well known techniques such as 1) Random Sampling, 2) Importance Sampling, and 3) Latin Hypercube Sampling. Nevertheless, in probabilistic design for nuclear power plants associated to ASCE 43, the probability distribution of outputs produced by the system is properly assumed in order to increase the efficiency in calculation through an allowance for some degree of error. Even if the inputs are fortunately known as normal distribution, the outputs produced by a system may have other types of distribution than normal distribution if the correlation between random variables is nonlinear or the system itself has a nonlinear feature. It is often difficult to define the probability distribution of inputs entered in a system to define problems in sociology and engineering. Also, in a case where the type of probability distribution of population is known or properly assumable, it is possible to calculate the occurrence probability of subset based on the distribution parameters of population estimated through sampling. As the type of probability distribution of population is unknown in most sociology and engineering problems, the expectation of random variable or the occurrence probability of subset can be directly calculated through sampling. Sampling technique is used to estimate uncertainty inherent in population. The proposed WLHS is applied to seismically isolated structures in nuclear power plants. Accuracy of WLHS estimation on distribution parameters is depending on the selection of weight function. WLHS provides more flexible way on selecting samples than LHS. WLHS is verified through numerical examples by comparing the estimated distribution parameters with those from other methods such as Random Sampling and Latin Hypercube Sampling. This paper describes equations and detail procedure necessary to apply weight function to WLHS. This paper proposes extension of Latin Hypercube Sampling (LHS) to avoid the necessity of using intervals with the same probability area where intervals with different probability areas are used.
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