Simulation evaluation of small samples based on grey estimation and improved bootstrap

Abstract

PurposeTo solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.Design/methodology/approachBased upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.FindingsThe new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.Originality/valueThis research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.

A study on modified P‐S‐N curve of notched specimens based on small sample under multiaxial loading

“…With the development of computer technology, many scholars have studied the Bootstrap method and gradually improved the algorithm. 20 For the original Bootstrap method, the resampled data coincide with the original data, while we can get any value between the maximum value and the minimum value of the original data by the improved Bootstrap method. Currently, the commonly used Bootstrap method is implemented as follows:…”

“…However, since the resampling subsamples in this method are derived from the original samples, the subsample data and the original data are largely coincident. With the development of computer technology, many scholars have studied the Bootstrap method and gradually improved the algorithm 20 . For the original Bootstrap method, the resampled data coincide with the original data, while we can get any value between the maximum value and the minimum value of the original data by the improved Bootstrap method.…”

A new multiaxial fatigue life prediction method based on grey theory under small sample condition

“…Do the reduction transformation on Equation (10), and the cumulative reduction value is calculated by Equation (11), that is the grey prediction value of the fatigue life.…”

“…Thus, it provides a new idea for the study of fatigue problems and the prediction of fatigue life. Besides, the method is established based on the regeneration and development of partially known information, extracting valuable information, and achieving a correct description and effective monitoring of the system's operational behavior and evolution law 11–13 . The fatigue problem of specimens can be seen as an uncertain system problem with few samples and poor information.…”

“…Besides, the method is established based on the regeneration and development of partially known information, extracting valuable information, and achieving a correct description and effective monitoring of the system's operational behavior and evolution law. [11][12][13] The fatigue problem of specimens can be seen as an uncertain system problem with few samples and poor information. The fatigue life prediction by establishing a gray system model is more consistent with the objective law than the traditional fatigue life prediction method based on the deterministic theory.…”