The general problem in the theoretical and practical examination of hazards coming into existence in case of real, complicated industrial systems is basically the approximation of complicated multivariable functions of input and output variables.
Optimization is carried out based on multivariable functions such as effectiveness and total cost.
A one-dimensional integral approach (ODIA) consisting of sampling, evaluation of statistical moments for multivariable functions, probability density function fitting, and simple integration of failure probability was developed through system integration.
To derive the equivalent affine form, we use the extreme value theory of multivariable functions [24] to estimate the upper and lower bounds of the difference in space, and the difference is introduced by the approximation of the first part.
For example, in [1] the strongly superlinearity is used to specify functions with specific behavior at 0 and ; in [2] the superlinearity and sublinearity are defined for multivariable functions.
Figure 2 d f, d emax, and d emin of the example in Section 3. The extreme value theory of multivariable functions is used to compare demax, dfimax, demin, and dfimin.
According to the extreme value theory of multivariable functions, the Hessian matrix of the function, H, and Jacobian matrix of the function, J, can be used to find the local maxima and the local minima.
The proposed equivalent affine form of AASEE is more accurate since the extreme value theory of multivariable functions is used to minimize the difference between the result of multiplication and the approximate affine form.
This identification approach utilizes the generalized form of a Padé Legendre approximation for studying multivariable functions.
The proposed approximation is based on the extreme value theory of multivariable functions [24].
