Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems

This paper proposes a new modeling approach that is experimentally validated on piezoelectric systems in order to provide a black‐box pseudolinear model for complex systems control. Most of the time, one uses physical based approaches. However, sometimes complex phenomena occur in the system due to atypical changes of the process behavior, output noise or some hard nonlinearities. Therefore, we adopt identification methods to achieve the modeling task. The microdisplacements of the piezoelectric systems generate atypical data named outliers, leading to large estimated prediction errors. Since these errors disturb the classical normal probability density function, we choose here, as corrupted distribution model, the gross error model (GEM). In order to deal more efficiently with the outliers, we use the Huber's function, as mixed L₂/L₁ norms in which the tuning threshold named scaling factor is extended. From this function, a cost function also named PREC as parameterized robust estimation criterion is established. The identification is performed by choosing an Output Error model structure. In order to express the asymptotic covariance matrix of the robust estimator, we present a L finite Taylor's expansion to linearize the gradient and the hessian of the PREC. Experimental results are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Use of a quantile regression based echo state network ensemble for construction of prediction Intervals of gas flow in a blast furnace

The usual huge fluctuations in the blast furnace gas (BFG) generation make the scheduling of the gas system become a difficult problem. Considering that there are high level noises and outliers mixed in original industrial data, a quantile regression-based echo state network ensemble (QR-ESNE) is modeled to construct the prediction intervals (PIs) of the BFG generation. In the process of network training, a linear regression model of the output matrix is reported by the proposed quantile regression to improve the generalization ability. Then, in view of the practical demands on reliability and further improving the prediction accuracy, a bootstrap strategy based on QR-ESN is designed to construct the confidence intervals and the prediction ones via combining with the regression models of various quantiles. To verify the performance of the proposed method, the practical data coming from a steel plant are employed, and the results indicate that the proposed method exhibits high accuracy and reliability for the industrial data. Furthermore, an application software system based on the proposed method is developed and applied to the practice of this plant.     

Alternative Hotelling's T2 Charts using Winsorized Modified One‐Step M‐estimator

Hotelling's T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive in the presence of outliers. To alleviate the problem, this paper proposed alternative Hotelling's T² charts for individual observations using robust location and scale matrix instead of the usual mean vector and the covariance matrix, respectively. The usual mean vector in the Hotelling T² chart is replaced by the winsorized modified one‐step M‐estimator (MOM) whereas the usual covariance matrix is replaced by the winsorized covariance matrix. MOM empirically trims the data based on the shape of the data distribution. This study also investigated on the different trimming criteria used in MOM. Two robust scale estimators with highest breakdown point, namely S_n and T_n were selected to suit the criteria. The upper control limits for the proposed robust charts were calculated based on simulated data. The performance of each control chart is based on the false alarm and the probability of outlier's detection. In general, the performance of an alternative robust Hotelling's T² charts is better than the performance of the traditional Hotelling's T² chart. Copyright © 2012 John Wiley & Sons, Ltd.     

An adaptive normal estimation method for scanned point clouds with sharp features

Normal estimation is an essential task for scanned point clouds in various CAD/CAM applications. Many existing methods are unable to reliably estimate normals for points around sharp features since the neighborhood employed for the normal estimation would enclose points belonging to different surface patches across the sharp feature. To address this challenging issue, a robust normal estimation method is developed in order to effectively establish a proper neighborhood for each point in the scanned point cloud. In particular, for a point near sharp features, an anisotropic neighborhood is formed to only enclose neighboring points located on the same surface patch as the point. Neighboring points on the other surface patches are discarded. The developed method has been demonstrated to be robust towards noise and outliers in the scanned point cloud and capable of dealing with sparse point clouds. Some parameters are involved in the developed method. An automatic procedure is devised to adaptively evaluate the values of these parameters according to the varying local geometry. Numerous case studies using both synthetic and measured point cloud data have been carried out to compare the reliability and robustness of the proposed method against various existing methods.     

多个粗差剔除前后的平差值转换

本文从观测值中含有多个粗差的平差值入手，采用文献[1]中的F－T检验法剔除多个粗差，导出了剔除多个粗差后的平差值转换公式．与文献[2]中的转换公式比较可知，本文所提出的是一通用公式，而文献[2]中转换公式仅是文中的特冽。文中的其例说明，这一转换公式在理论上是严密的，实用起来方便、可行．     

Application of a rice field experimental error distribution function to nitrogen-phosphorus-potassium fertilizer response model analysis

A distribution function of rice yield deviations from the mean was developed from field experiments with 555 plots at 16 sites in Zhejiang province, China, for three years. The deviation distribution in interval of 50kg/ha appeared as a symmetrical distribution with a high peak (Mean=0.279 [kg/ha], SD=240.686 [kg/ha]). Normality test using Kolmogrove-Smirnov test between the observed cumulative distribution and the normal cumulative distribution function indicates that the observed deviation distribution is not normal. An empirical exponential cumulative distribution function was developed. The distribution function was used to remove outliers during the development of a rice yield fertilizer response model, based on data from a non-replicated NPK field experiment.     

一种基于自然最近邻的离群检测算法

任何涉及k近邻求解问题的算法被应用于处理不同特征的数据集时,参数k值的选择都会明显影响算法的性能和结果。因而,如何选择k近邻算法中敏感参数k值一直是一个研究难点。提出了一种新的近邻关系———自然最近邻,它不需要设置参数k,每个节点的邻居是由算法自适应计算而形成的。针对离群点检测的特殊性,通过确定自然最近邻居搜索算法的终止条件,提出一种基于自然最近邻的新的离群检测算法ODb3N。实验表明,该算法不仅避免了k近邻中参数的选择问题,而且能够更有效地发现离群簇。     

基于最小二乘支持向量机算法的测量数据时序异常检测方法

将最小二乘支持向量机方法引入火电厂DCS的测量数据时序异常检测领域,该方法很好地建立了火电厂DCS的测量数据时序预测模型,具有预测真实值能力强、全局优化及泛化性好等优点。将该方法应用于某600 MW超临界火电机组DCS测量数据中,经过训练后的LS-SVM模型对再热蒸汽温度数据的检验样本进行不良值检测与真实值预测,均方根误差和平均相对误差分别为0.067%和0.050%,均方根误差是BP网络模型、RBF网络模型的8.756%和8.272%,平均相对误差是BP网络模型、RBF网络模型的7.541%和7.236%。应用结果表明,最小二乘支持向量机方法优于多层BP与RBF神经网络法,能很好地满足异常检测与真实值预测要求。     

Range Unit‐Root (RUR) Tests: Robust against Nonlinearities,Error Distributions,Structural Breaks and Outliers

Abstract. Since the seminal paper by Dickey and Fuller in 1979, unit‐root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long‐wave patterns observed not only in unit‐root time series but also in series following more complex data‐generating mechanisms. To this end, our testing device analyses the unit‐root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit‐root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit‐root tests on near‐unit‐root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward–backward range unit‐root (FB‐RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey–Fuller unit‐root test on exchange rate series.     

State space models for time series with patches of unusual observations

Abstract. An alternative to leave‐k‐out diagnostics for detecting patches of outlying points in time series is developed. We propose that unusual behaviour should be modelled by the addition of shocks. By including shocks in the transition equation of a state space model, we admit the possibility of a persistent change associated with a patch of outliers. Persistent change may take the form of a level shift or a change in seasonal pattern. We provide an efficient mechanism for computing diagnostic statistics associated with the addition of k shocks using a simple adaptation of the Kalman filter. Statistics for detecting unspecified patterns of shocks and an interpretation of the output of the associated smoothing algorithm are derived. Illustrations using real series are given.