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.

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.

Fusion Method for True Value Estimation of Manufacturing Quality under Condition of Poor Information (Part I: Theory)

2010 ◽  
Vol 34-35 ◽  
pp. 157-161
Author(s):  
Xin Tao Xia ◽  
Lei Lei Gao ◽  
Jian Feng Chen
Keyword(s):  
Bootstrap Method ◽  
Small Sample ◽  
Point Estimation ◽  
Fusion Method ◽  
Insufficient Information ◽  
Manufacturing Quality ◽  
Large Samples ◽  
Grade Method ◽  
True Value ◽  
Value Estimation

Poor information means incomplete and insufficient information, such as small sample and unknown distribution. For point estimation under the condition of poor information, the statistical methods relied on large samples and known distributions may become ineffective. For this end, a fusion method is proposed. The fusion method develops five methods, three concepts, and one rule. The five methods include the rolling mean method, the membership function method, the maximum membership grade method, the moving bootstrap method, and the arithmetic mean method. The three concepts comprise the solution set on the estimated true value, the fusion series, and the final estimated true value. The rule is the range rule. The method proposed can supply a foundation for the true value estimation of manufacturing quality under the condition of poor information.

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.

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 Evaluation of Dynamic Uncertainty of Rolling Bearing Vibration Performance

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Liang Ye ◽  
Xintao Xia ◽  
Zhen Chang
Keyword(s):  
Time Series ◽  
Chaos Theory ◽  
Maximum Entropy Method ◽  
Bootstrap Method ◽  
Rolling Bearing ◽  
Entropy Method ◽  
Performance Time ◽  
Dynamic Uncertainty ◽  
Bearing Vibration ◽  
Vibration Performance

The variation trend, failure trajectory, probability distribution, and other information vary with time and working conditions for rolling bearing vibration performance, which makes the evaluation and prediction of the evolution process difficult for the performance reliability. In view of this, the chaos theory, grey bootstrap method, and maximum entropy method were effectively fused to propose a mathematical model for the dynamic uncertainty evaluation of rolling bearing vibration performance. After reconstructing the phase space of the vibration performance time series, four local prediction methods were applied to predict the vibration values of bearings to verify the effectiveness and validity of chaos theory. The estimated true value and estimated interval were calculated using the grey bootstrap method (GBM) and maximum entropy method. Finally, the validity of the proposed model was verified by comparing the probability that the original data fall into the estimated interval with the given confidence level. The experimental results show that the proposed method can effectively predict the variation trend and failure trajectory of the vibration performance time series so as to realize the dynamic monitoring of the evolution process for rolling bearing vibration performance online.

scholarly journals A SIEVE BOOTSTRAP TEST FOR COINTEGRATION IN A CONDITIONAL ERROR CORRECTION MODEL

2009 ◽  
Vol 26 (3) ◽  
pp. 647-681 ◽  
Author(s):  
Franz C. Palm ◽  
Stephan Smeekes ◽  
Jean-Pierre Urbain
Keyword(s):  
Error Correction ◽  
Single Equation ◽  
Error Correction Model ◽  
Small Sample ◽  
Bootstrap Test ◽  
Correction Model ◽  
Sieve Bootstrap ◽  
Asymptotic Test ◽  
True Value ◽  
Deterministic Components

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic components included are insensitive to the true value of the trends in the model and retain correct size.

A REPAIRABLE SYSTEM MODELLING: COMBINING GREY SYSTEM THEORY WITH INTERVAL-VALUED FUZZY SET THEORY

2005 ◽  
Vol 12 (03) ◽  
pp. 241-266 ◽  
Author(s):  
R. GUO
Keyword(s):  
System Theory ◽  
Fuzzy Sets ◽  
Underlying Mechanism ◽  
Grey System Theory ◽  
Small Sample ◽  
System Modelling ◽  
Repairable System ◽  
Type I ◽  
Grey System ◽  
Interval Valued

A fundamental but impossible to be addressed problem in repairable system modelling is how to estimate the system repair improvement (or damage) effects because of the large-sample requirements from the standard statistical inference theory. On the other hand, repairable system operating and maintenance data are often imprecise and vague and therefore Type I fuzzy sets defined by point-wise membership functions are often used for the modelling repairable systems. However, it is more logical and natural to argue that Type II fuzzy sets defined by interval-valued membership function, called interval-valued fuzzy sets (IVFS), should be used in characterizing the underlying mechanism of repairable system. In this paper, we explore a small-sample based GM(1,1) modelling approach rooted in the grey system theory to extract the system intrinsic functioning times from the seemly lawless functioning-failure time records and thus to estimate the repair improvement (damage) effects. We further explore the role of interval-valued fuzzy sets theory in the analysis of the system underlying mechanism. We develop a framework of the GM(1,1)-IVFS mixed reliability analysis and illustrate our idea by an industrial example.

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.

scholarly journals BIAS CORRECTION OF SEMIPARAMETRIC LONG MEMORY PARAMETER ESTIMATORS VIA THE PREFILTERED SIEVE BOOTSTRAP

2016 ◽  
Vol 33 (3) ◽  
pp. 578-609 ◽  
Author(s):  
D. S. Poskitt ◽  
Gael M. Martin ◽  
Simone D. Grose
Keyword(s):  
Bias Correction ◽  
Long Memory ◽  
Bootstrap Method ◽  
Bias Reduction ◽  
Sieve Bootstrap ◽  
True Value ◽  
Bootstrap Simulation ◽  
Parameter Estimators ◽  
Memory Parameter ◽  
The Bootstrap Method

This paper investigates bootstrap-based bias correction of semiparametric estimators of the long memory parameter, d, in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data prefiltered by a preliminary semiparametric estimate of the long memory parameter. Theoretical justification for using the bootstrap technique to bias adjust log periodogram and semiparametric local Whittle estimators of the memory parameter is provided in the case where the true value of d lies in the range 0 ≤ d < 0.5. That the bootstrap method provides confidence intervals with the correct asymptotic coverage is also proven, with the intervals shown to adjust explicitly for bias, as estimated via the bootstrap. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias-correction techniques is presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which some degree of bias reduction has already been accomplished by analytical means.

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