Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have signi...Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.展开更多
Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significa...Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.展开更多
为了能够更加准确地实现地铁客流预测,提出了一种基于经验模态分解算法(empirical mode decomposition,EMD)优化非线性自回归(nonlinear auto regressive,NAR)动态神经网络的地铁客流量短时预测模型.分析地铁客流量数据后发现日客流量...为了能够更加准确地实现地铁客流预测,提出了一种基于经验模态分解算法(empirical mode decomposition,EMD)优化非线性自回归(nonlinear auto regressive,NAR)动态神经网络的地铁客流量短时预测模型.分析地铁客流量数据后发现日客流量具有一定的变化规律,为此使用了基于时间序列的NAR动态神经网络,该网络具有优秀的非线性动态拟合能力和反馈记忆的功能.结合EMD经验模态分解算法优化NAR动态神经网络预测模型,以此来减少预测误差,提高预测精度.结果显示,EMD-NAR神经网络组合预测模型适用于地铁客流的短时预测,预测精度可达93%,具有较好的应用价值.展开更多
In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlJnear autoregressive models. We show that under certain conditions that ensu...In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlJnear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.展开更多
The response of the train–bridge system has an obvious random behavior.A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge...The response of the train–bridge system has an obvious random behavior.A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge,and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track.Firstly,the coupling model of train–bridge systems is reviewed.Then,an ensemble method is presented,which can estimate the small probabilities of a dynamic system with stochastic excitations.The main idea of the ensemble method is to use the NARX(nonlinear autoregressive with exogenous input)model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution.Finally,the efficiency of the suggested method is compared with the direct Monte Carlo simulation method,and the probability exceedance of train responses under the vertical track irregularity is discussed.The results show that when the small probability of train responses under vertical track irregularity is estimated,the ensemble method can reduce both the calculation time of a single sample and the required number of samples.展开更多
We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail...We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.展开更多
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive predicti...A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.展开更多
Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis.Traditional causality inference methods have a salient limitation that the model must be linear...Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis.Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise.Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series,it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations.This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models,which extends the additive nonlinear times series to nonlinear structural vector autoregressive models.An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables.Simulations demonstrate the effectiveness of the proposed method.展开更多
In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution w...In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.展开更多
为探究不同训练函数对于非线性自回归(nonlinear auto regressive,NAR)高铁沉降预测模型影响,研究选择以我国某段高铁沉降数据作为研究对象,探究不同训练函数对于NAR高铁沉降预测模型的影响。试验结果表明:在本次数据预测模型研究中,弹...为探究不同训练函数对于非线性自回归(nonlinear auto regressive,NAR)高铁沉降预测模型影响,研究选择以我国某段高铁沉降数据作为研究对象,探究不同训练函数对于NAR高铁沉降预测模型的影响。试验结果表明:在本次数据预测模型研究中,弹性反向传播算法表现出更优的预测水平,其预测结果的RMSE=0.52 mm,MRE=0.04 mm,ME=0.40 mm,MSE=0.31 mm。动量梯度下降法算法表现出更快的训练速度,其完成参数训练平均时间为42.42 s,研究结果可为后续对于NAR高铁沉降预测模型的训练模型选取提供参考。展开更多
A new prediction method based on the nonlinear autoregressive model is proposed to improve the accuracy of medium-term and long-term predictions of Satellite Clock Bias(SCB).Forecast experiments for three time periods...A new prediction method based on the nonlinear autoregressive model is proposed to improve the accuracy of medium-term and long-term predictions of Satellite Clock Bias(SCB).Forecast experiments for three time periods were implemented based on the precision SCB published on the International GNSS Server(IGS)server.The results show that the medium-term and long-term prediction accuracy of the proposed approach is significantly better compared to other traditional models,with the training time being much shorter than the wavelet neural network model.展开更多
文摘Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.
文摘Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.
文摘为了能够更加准确地实现地铁客流预测,提出了一种基于经验模态分解算法(empirical mode decomposition,EMD)优化非线性自回归(nonlinear auto regressive,NAR)动态神经网络的地铁客流量短时预测模型.分析地铁客流量数据后发现日客流量具有一定的变化规律,为此使用了基于时间序列的NAR动态神经网络,该网络具有优秀的非线性动态拟合能力和反馈记忆的功能.结合EMD经验模态分解算法优化NAR动态神经网络预测模型,以此来减少预测误差,提高预测精度.结果显示,EMD-NAR神经网络组合预测模型适用于地铁客流的短时预测,预测精度可达93%,具有较好的应用价值.
文摘In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlJnear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51978589,51778544,and 51525804).
文摘The response of the train–bridge system has an obvious random behavior.A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge,and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track.Firstly,the coupling model of train–bridge systems is reviewed.Then,an ensemble method is presented,which can estimate the small probabilities of a dynamic system with stochastic excitations.The main idea of the ensemble method is to use the NARX(nonlinear autoregressive with exogenous input)model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution.Finally,the efficiency of the suggested method is compared with the direct Monte Carlo simulation method,and the probability exceedance of train responses under the vertical track irregularity is discussed.The results show that when the small probability of train responses under vertical track irregularity is estimated,the ensemble method can reduce both the calculation time of a single sample and the required number of samples.
基金supported by the National Natural Science Foundation of China(Grant No.10471005).
文摘We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
基金Project supported by the Scientific Research Foundation for the Returned 0verseas Chinese Scholars of China （Grant No 2004.176.4） and the Natural Science Foundation of Shandong Province of China （Grant No Z2004G01）.
文摘A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
基金supported by the National Natural Science Foundation of China under Grant Nos.60972150 and 10926197
文摘Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis.Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise.Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series,it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations.This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models,which extends the additive nonlinear times series to nonlinear structural vector autoregressive models.An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables.Simulations demonstrate the effectiveness of the proposed method.
文摘In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.
基金2022 Basic Scientific Research Project supported by Liaoning Provincial Education Department(No.LJKMZ20221686)。
文摘A new prediction method based on the nonlinear autoregressive model is proposed to improve the accuracy of medium-term and long-term predictions of Satellite Clock Bias(SCB).Forecast experiments for three time periods were implemented based on the precision SCB published on the International GNSS Server(IGS)server.The results show that the medium-term and long-term prediction accuracy of the proposed approach is significantly better compared to other traditional models,with the training time being much shorter than the wavelet neural network model.
