Small sample analysis of a platform vibration via bootstrap method

2010 ◽  
Author(s):  
Zhongyu Wang ◽  
Jianyong Sun ◽  
Jianjun Zhang ◽  
Xintao Xia
Keyword(s):  
Bootstrap Method ◽  
Small Sample ◽  
Sample Analysis

scholarly journals Reliability estimation for drive axle of wheel loader under extreme small sample

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983684 ◽  
Author(s):  
Leilei Cao ◽  
Lulu Cao ◽  
Lei Guo ◽  
Kui Liu ◽  
Xin Ding
Keyword(s):  
Sample Size ◽  
Promising Result ◽  
Small Sample Size ◽  
Bootstrap Method ◽  
Estimation Method ◽  
Small Sample ◽  
Reliability Estimation ◽  
Fatigue Reliability ◽  
Drive Axle ◽  
Semi Empirical

It is difficult to have enough samples to implement the full-scale life test on the loader drive axle due to high cost. But the extreme small sample size can hardly meet the statistical requirements of the traditional reliability analysis methods. In this work, the method of combining virtual sample expanding with Bootstrap is proposed to evaluate the fatigue reliability of the loader drive axle with extreme small sample. First, the sample size is expanded by virtual augmentation method to meet the requirement of Bootstrap method. Then, a modified Bootstrap method is used to evaluate the fatigue reliability of the expanded sample. Finally, the feasibility and reliability of the method are verified by comparing the results with the semi-empirical estimation method. Moreover, from the practical perspective, the promising result from this study indicates that the proposed method is more efficient than the semi-empirical method. The proposed method provides a new way for the reliability evaluation of costly and complex structures.

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

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenguang Yang ◽  
Lianhai Lin ◽  
Hongkui Gao
Keyword(s):  
Similarity Measure ◽  
Bootstrap Method ◽  
Grey System Theory ◽  
Small Sample ◽  
Point Estimation ◽  
Small Samples ◽  
Content Type ◽  
Relational Similarity ◽  
Simulation Evaluation ◽  
Grey Relational

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.

scholarly journals Dynamic Assessment of Vibration of Tooth Modification Gearbox Using Grey Bootstrap Method

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hui-liang Wang ◽  
Xiao-zhong Deng ◽  
Ju-bo Li ◽  
Jian-jun Yang
Keyword(s):  
Systematic Error ◽  
Performance Optimization ◽  
Bootstrap Method ◽  
Dynamic Assessment ◽  
Grey System Theory ◽  
Small Sample ◽  
Error Measure ◽  
True Value ◽  
Dynamic Uncertainty ◽  
Tooth Modification

The correlation analysis between gear modification and vibration characteristics of transmission system was difficult to quantify; a novel small sample vibration of gearbox prediction method based on grey system theory and bootstrap theory was presented. The method characterized vibration base feature of tooth modification gearbox by developing dynamic uncertainty, estimated true value, and systematic error measure, and these parameters could indirectly dynamically evaluate the effect of tooth modification. The method can evaluate the vibration signal of gearbox with installation of no tooth modification gear and topological modification gear, respectively, considering that 100% reliability is the constraints condition and minimum average uncertainty is the target value. Computer simulation and experiment results showed that vibration amplitude of gearbox was decreased partly due to topological tooth modification, and each value of average dynamic uncertainty, mean true value, and systematic error measure was smaller than the no tooth modification value. The study provided an important guide for tooth modification, dynamic performance optimization.

Estimation of Measurement Upper Limit in Deriving the Vibration Environmental Test Conditions by Bootstrap Method

2012 ◽  
Vol 566 ◽  
pp. 11-14
Author(s):  
Jian Jun Zhang ◽  
Jian Yong Sun ◽  
Ming Li ◽  
Hai Juan Chang
Keyword(s):  
Bootstrap Method ◽  
Small Sample ◽  
Measure Data ◽  
Test Conditions ◽  
Power Spectral ◽  
Upper Limits ◽  
Environmental Test ◽  
Upper Tolerance Limit ◽  
Field Measure

For deriving the vibration environmental test conditions of materiels in the limited field measured data, a bootstrap method is firstly employed to evaluate the upper tolerance limit of the vibration power spectral density (PSD). Firstly for the simulation data from the normal distribution, the bias-corrected bootstrap method and the bootstrap-t method are validated to attain the appropriate upper limits for the small sample data through comparing the evaluations with the true values. Secondly for the 10 and 90 flight measurements of some aircraft, the upper tolerance limits of vibration PSD have been estimated by the above method and the traditional computation methods of MIL-STD-810F and GJB126. The result shows the bootstrap method fits the actual vibration environment better than other two methods and it has a wide application in the determination of vibration test conditions based on the small field measure data.

THE ASSAY OF CORTICOTROPHIN IN MICE

1963 ◽  
Vol 44 (2) ◽  
pp. 237-249 ◽  
Author(s):  
Claus Rerup ◽  
Pavo Hedner
Keyword(s):  
Subcutaneous Administration ◽  
Small Sample ◽  
Lower Body ◽  
Sample Analysis ◽  
Lower Body Weight ◽  
Increased Sensitivity ◽  
The Mean ◽  
The Difference ◽  
Response Line ◽  
Free Plasma

ABSTRACT The assay of corticotrophin was performed in mice by means of small sample analysis of free plasma corticosteroids. In this method hypophysectomy was replaced by dexamethasone pretreatment. The response was measured preferably in a single mouse weighing 20 g or more. When mice of a lower body weight were used the plasma of two randomly assigned mice was pooled. Corticosteroids (mainly corticosterone) were determined fluorometrically in 0.25 (0.20) ml samples of plasma from heparinized blood. The results show that valid corticotrophin assays can be performed in mice both by the intravenous and subcutaneous route. Compared with the adrenal ascorbic acid depletion method or the plasma corticosteroid method in the rat the assay in mice was found to be at least five times more sensitive. 40 micro-units of corticotrophin were consistently detectable. Precision was dependent on the route of administration, the mean index of precision (s/b) being 0.20 in the intravenous and 0.12 in the subcutaneous assay. The difference was due to a steeper slope of the logdose-response line after subcutaneous administration. Contrary to the findings in the rat, corticotrophin A (oxycel purified) did not differ significantly in potency estimates from subcutaneous and intravenous assays in mice, when crude corticotrophin (U. S. P. Corticotropin Reference Standard) was the basis of comparison. Accordingly results of subcutaneous assays of corticotrophin A samples in terms of the U. S. P. standard were lower in mice than in rats. The use of gelatine instead of saline as diluent in the subcutaneous assays yielded slightly but not significantly higher potency estimates (25 per cent). The interpretation of the results is that for intravenous corticotrophin assays the mouse method is comparable to the rat assay. For subcutaneous corticotrophin assays, however, the mouse method is not suitable, if crude corticotrophin (U. S. P. standard) is the basis of comparison, but if corticotrophin A (oxycel purified) is the standard of reference (e. g. the Third International Standard for Corticotrophin), the mouse method may justifiably be used. The advantages of the mouse method are increased sensitivity, precision, convenience, and economy.

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