基于Mallat算法与ARMA模型的露天矿卡车故障率预测
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摘要
为提高露天矿山运输卡车故障率预测精度、降低因非平稳时间序列数据造成的精度损失及有效解决模型参数估计困难等问题,提出一种基于小波分析与自回归滑动平均模型(ARMA)的露天矿山卡车故障率预测方法。首先,根据矿山时间序列数据的非平稳特征,采用Mallat算法分频处理原始数据,将原始的时间序列分解为一组近似系数和多组细节系数;然后,采用ARMA模型拟合与预测单支重构后的小波系数;其次,引入模型的相关变量,将ARMA模型的参数估计问题转化为带有相关变量的多维高斯分布参数估计问题;最后,通过计算模型中的典型相关变量实现ARMA模型的定阶与参数估计并与其他算法模型进行对比。结果表明:采用此法预测测试集数据,绝对误差的平均值为0. 322,相对误差的平均值为5. 49%;这说明此种组合模型具有更高的拟合精度,应用该模型进行卡车故障率预测是可行且有效的。
In order to improve the predictive accuracy of open-pit mine transport trucks failure rate,reduce accuracy loss caused by the non-stationary time series data and solve difficulty in the model parameter estimation,this paper puts forward a new method for predicting the failure rate of trucks based on wavelet analysis and ARMA. First of all,according to the characteristics of the non-stationary time series data,this paper first uses Mallat algorithm to process the original data,at the same time,the original time series is decomposed into a set of approximation coefficients and sets of detail coefficients.Then,the wavelet coefficients after single branch reconstruction are fitted and predicted by ARMA model.To effectively solve the ARMA model identification and parameter estimation problem, this paper introduces the relevant variables of the original model,and parameter estimation problem can be converted to the parameter estimation problem of multi-dimensional Gauss distribution with the related variables.Finally,ordering and parameter estimation of ARMA model are realized by calculating the typical correlation variables in the model. Simulation results show that the mean value of absolute error is 0. 322,and the mean value of relative error is 5. 49%, that compared with other algorithm models, this combination model has higher fitting precision,and that the model is feasible and effective in predicting the failure rate of trucks.
In order to improve the predictive accuracy of open-pit mine transport trucks failure rate,reduce accuracy loss caused by the non-stationary time series data and solve difficulty in the model parameter estimation,this paper puts forward a new method for predicting the failure rate of trucks based on wavelet analysis and ARMA. First of all,according to the characteristics of the non-stationary time series data,this paper first uses Mallat algorithm to process the original data,at the same time,the original time series is decomposed into a set of approximation coefficients and sets of detail coefficients.Then,the wavelet coefficients after single branch reconstruction are fitted and predicted by ARMA model.To effectively solve the ARMA model identification and parameter estimation problem, this paper introduces the relevant variables of the original model,and parameter estimation problem can be converted to the parameter estimation problem of multi-dimensional Gauss distribution with the related variables.Finally,ordering and parameter estimation of ARMA model are realized by calculating the typical correlation variables in the model. Simulation results show that the mean value of absolute error is 0. 322,and the mean value of relative error is 5. 49%, that compared with other algorithm models, this combination model has higher fitting precision,and that the model is feasible and effective in predicting the failure rate of trucks.
引文
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[15]齐越.结合小波分析的非平稳时间序列预测方法研究[D].秦皇岛:燕山大学,2014.QI Yue. Studies of non-stationary time series prediction method based on wavelet analysis[D]. Qinhuangdao:Yanshan University,2014.
[16]王振龙,顾岚.时间序列分析[M].北京:中国统计出版社,2000:22-43.
[17]安鸿志.时间序列分析及应用[M].北京:科学出版社,1983:33-69.
[18] BOX G E P,Time series analysis forecasting and control[M]. California:Holden-Day Inc,1976:18-27.
[19]张尧庭.多元统计分析引论[M].北京:科学出版社,1976:23-51.
[2]杨琦,曹显兵.基于ARMA-GARCH模型的股票价格分析与预测[J].数学的实践与认识,2016,46(6):80-86.YANG Qi,CAO Xianbing. Analysis and prediction of stock price based on ARMA-GARCH model[J]. Mathematics in Practice and Theory,2016,46(6):80-86.
[3]宋博,陈万义.基于HP滤波和ARMA-GARCH模型的人民币汇率趋势预测[J].数学的实践与认识,2017,47(1):70-78.SONG Bo,CHEN Wanyi. Trend prediction of RMB exchange rate based on the HP filter and ARMA-GARCH model[J].Mathematics in Practice and Theory,2017,47(1):70-78.
[4]雷明,韩崇昭,郭文艳,等.非线性时间序列的小波分频预测[J].物理学报,2005,54(5):1 988-1 993.LEI Ming,HAN Chongzhao,GUO Wenyan,et al. A novel subband forecast method for nonlinear time series using wavelet transform[J]. Acta Physical Sinica,2005,54(5):1 988-1 993.
[5]黎志勇,李宁.基于小波的非平稳时间序列预测方法研究[J].计算机工程与应用,2014,50(10):38-43.LI Zhiyong,LI Ning. Research on non-stationary time series forecasting method based on wavelet[J]. Computer Engineering and Applications,2014,50(10):38-43.
[6]彭乃驰,党婷.基于ARMA-GM-BP组合预测模型及应用[J].统计与决策,2016(2):80-82.PENG Naichi,DANG Ting. Based on ARMA-GM-BP combination forecasting model and its application[J]. Statistics&Decision,2016(2):80-82.
[7]丁玲娟.基于小波分析和ARMA-SVM模型的股票指数预测分析[D].上海:华东师范大学,2012.DING Lingjuan. Forecasting of stock price index based on wavelet analysis and ARMA-SVM model[D]. Shanghai:East China Normal University,2012.
[8] BAPTISTA M,SANKARARAMAN S,MEDEIROS IVO P De,et al. Forecasting fault events for predictive maintenance using data-driven techniques and ARMA modeling[J].Computers&Industrial Engineering,2018,115:41-53.
[9]任国恒,朱变,朱海.马特拉算法在遥测数据短期预测中的应用[J].武汉工程大学学报,2014,36(2):73-78.REN Guoheng,ZHU Bian,ZHU Hai. Application of Mallat algorithm in short-term forecasting of telemetry data[J].Journal of Wuhan Institute of Technology,2014,36(2):73-78.
[10]丛玉良,王宏志,赵晓晖.数字信号处理原理及其Matlab实现[M].北京:电子工业出版社,2009:56-77.
[11]方清城. Matlab R2016a小波分析22个算法实现[M].北京:电子工业出版社,2018,1:79-83.
[12]孔玲军. Matlab小波分析超级学习手册[M].北京:人民邮电出版社,2014:24-27.
[13]钟丽辉,魏贯军.基于Mallat算法的小波分解重构的心电信号处理[J].电子设计工程,2012,20(2):57-59.ZHONG Li Hui,WEI Guanjun. Wavelet decomposition and reconstruction denoising based on the Mallat algorithm[J].Electronic Design Engineering,2012,20(2):57-59.
[14]高鹏,周松林.基于小波Mallat算法和BP神经网络的空气质量指数预测的研究[J].池州学院学报,2017,31(3):42-44.GAO Peng,ZHOU Songlin. Air quality index prediction based on Mallat wavelet algorithm and BP neural network[J].Journal of Chizhou University,2017,31(3):42-44.
[15]齐越.结合小波分析的非平稳时间序列预测方法研究[D].秦皇岛:燕山大学,2014.QI Yue. Studies of non-stationary time series prediction method based on wavelet analysis[D]. Qinhuangdao:Yanshan University,2014.
[16]王振龙,顾岚.时间序列分析[M].北京:中国统计出版社,2000:22-43.
[17]安鸿志.时间序列分析及应用[M].北京:科学出版社,1983:33-69.
[18] BOX G E P,Time series analysis forecasting and control[M]. California:Holden-Day Inc,1976:18-27.
[19]张尧庭.多元统计分析引论[M].北京:科学出版社,1976:23-51.