Point estimation method

An excellent comprehensive review by Dearden (1999) describes how most melting point estimation methods involve correlations with other physical properties. Table 1 lists several examples of these from his review. 

Availability of Boiling Point Estimation Methods for Specific Chemical Classes.1... 

Overview of Boiling Point Estimation Methods Described in this Chapter... 

Lai et al. (1987) have developed what is likely the most accurate boiling point estimation method using a nonlinear group contribution method. The method is applicable to com-... 

One method to finding the minimum of a function is to search over all possible values of x and find the minimum based on the corresponding values of Y. These algorithms include region elimination methods, such as the Golden Search algorithm or point-estimation methods, such as Powell s method, neither of which require calculation of the derivatives. However, these types of methods often assume unimodality, and in some cases, continuity of the function. The reader is referred to Reklaitis Ravindran, and Ragsdell (1983) or Rao (1996) for details. 

The one-fluid approach can be used with some of the models presented earlier. In the method of Mehrotra [II], the one-fluid model can be used to obtain the needed normal boiling temperature, T, from = [ZxjT y ], if the mixture is well defined. This proposal has not been tested in that method. However, Orbey and Sandler [ 13] found this boiling-point estimation method to be suitable for use in their viscosity model as discussed later. 

Rosenblueth point estimate method, which is proposed by Rosenblueth in 1975, can compute the mean value and S.D. of Factor of Safety (FOS). 

To get detailed data on soil properties, exploratory wells dug in the study area, made new loess, old loess and silty clay samples each 15 groups. Then, they were tested on the GDS advanced dynamic triaxial test system in State Key Laboratory of Continental Dynamics, Northwest University. Show in Figure 5. Finally, we got series of the effective cohesion and effective friction angle. Because of the variation of c which made the greater impact of slope stability than other parameters, we obtain the mean and standard deviation to used in Rosenblueth point estimate method. Table 1 summarizes the values of soil properties obtained from laboratory tests in the study area. 

Table 1 Values for the application of the Point Estimate method with stochastic Kanai-Tajimi spectrum. ...

Figure 6 On the accuracy of the Point Estimate technique for calculating the spectrum of the unconditional standard deviation of SDOF displacement. Solid line Point Estimate method. Dashed line Monte Carlo simulation (1,000 samples). The dotted line corresponds to the standard deviation without considering uncertainties in the Kanai-Tajimi model and using the mean values of the parameters.

The above discussion suggests that the Point Estimate method in the version reported in (Hong 1998) constitutes an excellent means to evaluate the unconditional structural robustness in Earthquake Engineering, with or without active control. 

Christian, J.T. Baecher, G.B. 1998. Point-estimate method and numerical quadrature. 

Hong, H.P. 1998. An efficient point estimate method for probabilistic analysis. Reliability... 

Practically, the integral in Eq. (34) cannot be evaluated analytically because of the high dimensionality and the complicated integration. In order to avoid this problem, in the present paper, the point estimate method (Zhao Ono 2000) is used to determine the moments of the performance function such as Eq. 11 for a series system. For a function of only one random variable y = y(x), the moments of y can be point-estimated as... 

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