Multi-model Comprehensive Forecasting Method Combined with Bootstrap and Variable Weight
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摘要: 为了更好地估计构件的疲劳寿命,一种较好的策略是将几个合适模型进行合并预测,但传统合并预测的权重值为确定值,随着对预测精度要求的提高,变权重模型合并预测方法逐渐受到重视。但在工程中仅估计出预测结果还不足以提供充分的决策信息,进一步得到置信区间显得很有必要。本文提出一种基于Bootstrap与变权重的多模型综合置信区间预测方法,运用Bootstrap对合并数据进行再抽样,依据再抽样样本,采用变权重合并方法得到各项模型的权重函数,将各预测模型合并起来,最后通过百分位数法预测得到预测置信区间。将该方法用于工程算例中进行了验证,说明本文方法的合理性和可行性。
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关键词:
- Bootstrap方法 /
- 合并预测 /
- 变权重 /
- 置信区间
Abstract: To predict the fatigue life of the component accurately, a good strategy is to combine several suitable models for the prediction, but the weight value of the traditional method is a determined value. In order to improve the prediction accuracy, weight changeable combination forecasting method has been paid more and more attention. However, estimating the predicted results in the project is not sufficient to provide adequate decision information, and it is necessary to estimate the confidence interval. This paper presents a multi-model comprehensive confidence interval forecasting method based on Bootstrap and variable weight. Bootstrap is used to sample the combined data, based on the re-sampling samples, the weights of each model are obtained by variable weight combining method, and finally the confidence interval is predicted by the quantile method. The method is applied to the engineering example to verify the rationality and feasibility of the proposed method.-
Key words:
- Bootstrap /
- model combination /
- variable weight /
- confidence interval
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[1] Bunn D. Forecasting with more than one model[J]. Journal of Forecasting, 1989,8(3):161-166 [2] Park I, Grandhi R V. A Bayesian statistical method for quantifying model form uncertainty and two model combination methods[J]. Reliability Engineering & System Safety, 2014,129:46-56 [3] Vamos T. Epistemic background problems of uncertainty[C]//Proceedings of 1990 First International Symposium on Uncertainty Modeling and Analysis. College Park:IEEE, 1990:3-5 [4] Draper D. Assessment and propagation of model uncertainty[J]. Journal of the Royal Statistical Society. Series B, 1995,57(1):45-97 [5] Bunn D W. Combining forecasts[J]. European Journal of Operational Research, 1988,33(3):223-229 [6] Bates J M, Grange C W J. The combination of forecasts[J]. Journal of the Operational Research Society, 1969,20(4):451-468 [7] Spanos A. Akaike-type criteria and the reliability of inference:Model selection versus statistical model specification[J]. Journal of Econometrics, 2010,158(2):204-220 [8] Lian H. Semiparametric bayesian information criterion for model selection in ultra-high dimensional additive models[J]. Journal of Multivariate Analysis, 2014,123:304-310 [9] Hansen B E. Least squares model averaging[J]. Journal of the Econometric Society, 2007,75(4):1175-1189 [10] Picard R R, Cook R D. Cross-validation of regression models[J]. Journal of the American Statistical Association, 1984,79(387):575-583 [11] Claeskens G, Hjort N L, Hjort N L. Minimizing average risk in regression models[J]. Econometric Theory, 2008,24(2):493-527 [12] 石凯凯,蔡力勋,包陈.预测疲劳裂纹扩展的多种理论模型研究[J].机械工程学报,2014,50(18):50-58 Shi K K, Cai L X, Bao C. Various theoretical models study of prediction fatigue crack growth[J]. Journal of Mechanical Engineering, 2014,50(18):50-58(in Chinese) [13] 唐小我.最优组合预测方法及其应用[J].数理统计与管理,1992,11(1):31-35 Tang X W. Variable weight combination of forecasting model[J]. Application of Statistics and Management, 1992,11(1):31-35(in Chinese) [14] 王福林,张晋国.变权组合预测模型中最优权系数估计问题的研究[J].系统工程理论与实践,1996,16(10):49-52 Wang F L, Zhang J G. Study on the estimation of optional weight coefficients of weight changeable combination forecast model[J]. Systems Engineering Theory & Practice, 1996,16(10):49-52(in Chinese) [15] Zhang C, Zhang Q. Weight changeable combination forecast method based on ACA[C]//Proceedings of 2010 IEEE 17th International Conference on Industrial Engineering and Engineering Management. Xiamen:IEEE, 2010:29-31 [16] Efron B. Bootstrap methods:another look at the jackknife[J]. The Annals of Statistics, 1979,7(1):1-26 [17] Efron B. Nonparametric standard errors and confidence intervals:rejoinder[J]. The Canadian Journal of Statistics, 1981,9(2):170-172 [18] Efron B, Tibshirani R. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy[J]. Statistical Science, 1986,1(1):54-75 [19] Timmerman M E, Braak C J F T. Bootstrap confidence intervals for principal response curves[J]. Computational Statistics & Data Analysis, 2008,52(4):1837-1849 [20] Davision A C, Hinkley D V. Bootstrap methods and their application[M]. Cambridge:Cambridge University Press, 1997 [21] Park I S. Quantification of multiple types of uncertainty in physics-based simulation[D]. Dington:Wright State University, 2012 [22] 王卫国.轮盘低循环疲劳寿命预测模型和试验评估方法研究[D].南京:南京航空航天大学,2006:102-114 WANG W G. Research on prediction model for disc LCF life and experiment assessment methodology[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2006:102-114(in Chinese) [23] Han W, Wang J, Zhang X H. Application research of combined forecasting based on induced ordered weighted averaging operator[J]. Management Science and Engineering, 2014,8(3):23-26 [24] Samuels J D, Sekkel R M. Model confidence sets and forecast combination[J]. International Journal of Forecasting, 2017,33(1):48-60 [25] Zeng W, Yang Y, Xie H, et al. CF-Kriging surrogate model based on the combination forecasting method[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2016,230(18):3274-3284 [26] Jiang Y, Chen X Y, Yu K, et al. Short-term wind power forecasting using hybrid method based on enhanced boosting algorithm[J]. Journal of Modern Power Systems and Clean Energy, 2017,5(1):126-133 [27] 袁修开,吕震宙,岳珠峰.小样本下分位数函数的Bootstrap置信区间估计[J].航空学报,2012,33(10):1842-1849 Yuan X K, Lü Z Z, Yue Z F. Bootstrap confidence interval of quantile function estimation for small samples[J]. Acta Aeronautica et Astronautica Sinica, 2012,33(10):1842-1849(in Chinese) [28] 吕召燕,吕震宙,李贵杰,等.基于密度权重的可靠性灵敏度分析方法[J].航空学报,2014,35(1):179-186 Lü Z Y, Lü Z Z, Li G J, et al. Reliability sensitivity analysis method based on weight index of density[J]. Acta Aeronautica et Astronautica Sinica, 2014,35(1):179-186(in Chinese)
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