The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outsid...The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.展开更多
In real-life freeway transportation system, a few number of incident observation （very rare event） is available while there are large numbers of normal condition dataset. Most of researches on freeway incident detec...In real-life freeway transportation system, a few number of incident observation （very rare event） is available while there are large numbers of normal condition dataset. Most of researches on freeway incident detection have considered the incident detection problem as classification one. However, because of insufficiency of incident events, most of previous researches have utilized simulated incident events to develop freeway incident detection models. In order to overcome this drawback, this paper proposes a wavelet-based Hotelling 7a control chart for freeway incident detection, which integrates a wavelet transform into an abnormal detection method. Firstly, wavelet transform extracts useful features from noisy original traffic observations, leading to reduce the dimensionality of input vectors. Then, a Hotelling T2 control chart describes a decision boundary with only normal traffic observations with the selected features in the wavelet domain. Unlike the existing incident detection algorithms, which require lots of incident observations to construct incident detection models, the proposed approach can decide a decision boundary given only normal training observations. The proposed method is evaluated in comparison with California algorithm, Minnesota algorithm and conventional neural networks. The experimental results present that the proposed algorithm in this paper is a promising alternative for freeway automatic incident detections.展开更多
多变量统计过程控制(Multivariate Statistical Process Control,MSPC)是对经典的单变量的统计过程控制(Statistical Process Control,SPC)的拓展,通过对多个质量特征参数联合分析,达到控制生产过程的目的。传统的MSPC方法都是基于数据...多变量统计过程控制(Multivariate Statistical Process Control,MSPC)是对经典的单变量的统计过程控制(Statistical Process Control,SPC)的拓展,通过对多个质量特征参数联合分析,达到控制生产过程的目的。传统的MSPC方法都是基于数据服从多元正态分布的假设,在实际生产过程中数据会呈现非正态特性。针对这一问题,提出基于高斯混合模型(Gaussian Mixture Model,GMM)的非参数T^(2)控制图,记为G-T^(2)控制图,通过基于密度初始化的GMM对原始数据进行多元正态转化,用计算得出的均值μ和协方差σ代替样本均值和样本协方差,并引入混合权重系数α对μ进行修正,计算得到样本的T^(2)统计量,并用T^(2)控制图判断过程是否处于统计控制状态下。通过蒙特卡洛(Monte Carlo)仿真方法测试控制图的性能,结果表明:G-T^(2)控制图相比于普通多元控制图在非正态情况下有更好的性能表现。展开更多
为了满足传统的统计过程控制理论中统计量彼此独立的基本假设,研究了多元自相关过程的残差T2控制图的控制方法及其控制性能。针对一般多元自相关过程,在参数已知的条件下,讨论了多元自相关过程的残差T2控制图,给出多元自相关过程偏移量...为了满足传统的统计过程控制理论中统计量彼此独立的基本假设,研究了多元自相关过程的残差T2控制图的控制方法及其控制性能。针对一般多元自相关过程,在参数已知的条件下,讨论了多元自相关过程的残差T2控制图,给出多元自相关过程偏移量的定义。通过M on te C arlo模拟,得出该控制图在不同偏移量时的平均链长,在残差T2控制图的适用范围内给出平均链长与偏移量之间的经验公式。结果表明,残差T2控制图可以有效控制出现大偏移的多元自相关过程。展开更多
多元自相关过程不满足现行多元质量控制理论的前提假设。该文探讨了两个随机变量相互独立,其中一个随机变量的观测值相互独立、另一随机变量服从一阶自回归模型的二元自相关过程。在参数已知的条件下,提出了二元自相关过程的残差T2控制...多元自相关过程不满足现行多元质量控制理论的前提假设。该文探讨了两个随机变量相互独立,其中一个随机变量的观测值相互独立、另一随机变量服从一阶自回归模型的二元自相关过程。在参数已知的条件下,提出了二元自相关过程的残差T2控制图。通过M on te C arlo模拟,得到了一族该二元自相关过程在不同偏移量下的平均链长。分析结果表明残差T2控制图的适用范围由自相关的强弱和偏移量的大小决定,可以有效监控大部分该类二元自相关过程。展开更多
基金Supported by National Natural Science Foundation of China (No.70931004 and No. 70802043)
文摘The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.
文摘In real-life freeway transportation system, a few number of incident observation （very rare event） is available while there are large numbers of normal condition dataset. Most of researches on freeway incident detection have considered the incident detection problem as classification one. However, because of insufficiency of incident events, most of previous researches have utilized simulated incident events to develop freeway incident detection models. In order to overcome this drawback, this paper proposes a wavelet-based Hotelling 7a control chart for freeway incident detection, which integrates a wavelet transform into an abnormal detection method. Firstly, wavelet transform extracts useful features from noisy original traffic observations, leading to reduce the dimensionality of input vectors. Then, a Hotelling T2 control chart describes a decision boundary with only normal traffic observations with the selected features in the wavelet domain. Unlike the existing incident detection algorithms, which require lots of incident observations to construct incident detection models, the proposed approach can decide a decision boundary given only normal training observations. The proposed method is evaluated in comparison with California algorithm, Minnesota algorithm and conventional neural networks. The experimental results present that the proposed algorithm in this paper is a promising alternative for freeway automatic incident detections.
文摘多变量统计过程控制(Multivariate Statistical Process Control,MSPC)是对经典的单变量的统计过程控制(Statistical Process Control,SPC)的拓展,通过对多个质量特征参数联合分析,达到控制生产过程的目的。传统的MSPC方法都是基于数据服从多元正态分布的假设,在实际生产过程中数据会呈现非正态特性。针对这一问题,提出基于高斯混合模型(Gaussian Mixture Model,GMM)的非参数T^(2)控制图,记为G-T^(2)控制图,通过基于密度初始化的GMM对原始数据进行多元正态转化,用计算得出的均值μ和协方差σ代替样本均值和样本协方差,并引入混合权重系数α对μ进行修正,计算得到样本的T^(2)统计量,并用T^(2)控制图判断过程是否处于统计控制状态下。通过蒙特卡洛(Monte Carlo)仿真方法测试控制图的性能,结果表明:G-T^(2)控制图相比于普通多元控制图在非正态情况下有更好的性能表现。
文摘为了满足传统的统计过程控制理论中统计量彼此独立的基本假设,研究了多元自相关过程的残差T2控制图的控制方法及其控制性能。针对一般多元自相关过程,在参数已知的条件下,讨论了多元自相关过程的残差T2控制图,给出多元自相关过程偏移量的定义。通过M on te C arlo模拟,得出该控制图在不同偏移量时的平均链长,在残差T2控制图的适用范围内给出平均链长与偏移量之间的经验公式。结果表明,残差T2控制图可以有效控制出现大偏移的多元自相关过程。
文摘多元自相关过程不满足现行多元质量控制理论的前提假设。该文探讨了两个随机变量相互独立,其中一个随机变量的观测值相互独立、另一随机变量服从一阶自回归模型的二元自相关过程。在参数已知的条件下,提出了二元自相关过程的残差T2控制图。通过M on te C arlo模拟,得到了一族该二元自相关过程在不同偏移量下的平均链长。分析结果表明残差T2控制图的适用范围由自相关的强弱和偏移量的大小决定,可以有效监控大部分该类二元自相关过程。
