Operation planning of district heating and cooling plants using genetic algorithms for mixed integer programming

In recent years, an operation planning of a district heating and cooling (DHC) plant has been arousing interest as a result of development of cooling load or heat demand prediction methods for district heating and cooling systems. In this paper, we formulate an operation planning of a district heating and cooling plant as a mixed integer linear programming problem. Since the formulated problem involves hundreds of variables, we anticipate that it is difficult to strictly solve it by enumeration-based methods. Thereby, we propose an approximate solution method based on genetic algorithms for mixed integer programming problems. Furthermore, we show the feasibility and effectiveness of the proposed method by comparison with the branch-and-bound method through numerical experiments using actual plant data.     

Robust probabilistic PCA with missing data and contribution analysis for outlier detection

Principal component analysis (PCA) is a widely adopted multivariate data analysis technique, with interpretation being established on the basis of both classical linear projection and a probability model (i.e. probabilistic PCA (PPCA)). Recently robust PPCA models, by using the multivariate t-distribution, have been proposed to consider the situation where there may be outliers within the data set. This paper presents an overview of the robust PPCA technique, and further discusses the issue of missing data. An expectation-maximization (EM) algorithm is presented for the maximum likelihood estimation of the model parameters in the presence of missing data. When applying robust PPCA for outlier detection, a contribution analysis method is proposed to identify which variables contribute the most to the occurrence of outliers, providing valuable information regarding the source of outlying data. The proposed technique is demonstrated on numerical examples, and the application to outlier detection and diagnosis in an industrial fermentation process.     

Robust fixed-lag smoother for linear systems including outliers in the system and observation noises

We develop a robust fixed-lag smoother for linear discrete-time systems having outliers both in the process and the observation noises. By modifying the system equation to a linear regression model, a robust Kalman filter and a robust fixed-lag smoother are derived using an M-estimate. Then the robust smoother is constructed using a robust Kalman filter and two robust sub-smoothers; the outliers in the observation noise are detected by filtering, and those in the system noise are detected by smoothing. Monte Carlo simulations are also presented to show the effectiveness of the proposed algorithms.     

A Robust Missing Data-Recovering Technique for Mobility Data Mining

Based on location information, users’ mobility profile building is the main task for making different useful systems such as early warning system, next destination and route prediction, tourist guide, mobile users’ behavior-aware applications, and potential friend recommendation. For mobility profile building, frequent trajectory patterns are required. The trajectory building is based on significant location extraction and the user’s actual movement prediction. Previous works have focused on significant places extraction without considering the change in GSM (global system for mobile communication) network and is based on complete data analysis. Since network operators change the GSM network periodically, there are possibilities of missing values and outliers. These missing values and outliers must be addressed to ensure actual mobility and for the efficient extraction of significant places, which are the basis for users’ trajectory building. In this paper, we propose a methodology to convert geo-coordinates into semantic tags and we also purposed a clustering methodology for recovering missing values and outlier detection. Experimental results prove the efficiency and effectiveness of the proposed scheme.     

Imputation of missing values for compositional data using classical and robust methods

New imputation algorithms for estimating missing values in compositional data are introduced. A first proposal uses the k-nearest neighbor procedure based on the Aitchison distance, a distance measure especially designed for compositional data. It is important to adjust the estimated missing values to the overall size of the compositional parts of the neighbors. As a second proposal an iterative model-based imputation technique is introduced which initially starts from the result of the proposed k-nearest neighbor procedure. The method is based on iterative regressions, thereby accounting for the whole multivariate data information. The regressions have to be performed in a transformed space, and depending on the data quality classical or robust regression techniques can be employed. The proposed methods are tested on a real and on simulated data sets. The results show that the proposed methods outperform standard imputation methods. In the presence of outliers, the model-based method with robust regressions is preferable.     

Bayesian robust linear dynamic system approach for dynamic process monitoring

In this paper, a Bayesian robust linear dynamic system approach is proposed for process modeling. Traditional linear dynamic system (LDS) constructed with Kalman filter is designed by Gaussian assumption which can be easily violated in non-Gaussian modeling situations, especially those with outliers. To deal with this issue, the conventional Gaussian-based Kalman filter is modified with heavy tailed Student's t-distribution so as to deal with the non-Gaussian noise and modeling outliers. Then, a variational Bayesian expectation maximization (VBEM) algorithm is developed for learning parameters of the robust linear dynamic system. For process monitoring, traditional monitoring scheme are discussed and the residual space monitoring mechanism has been improved. To explore the feasibility and effectiveness, the proposed method is applied for fault detection, with detailed comparative studies with several other methods through the Tennessee Eastman benchmark.     

基于概率矩阵分解的不完整数据集特征选择方法

在机器学习理论与应用中,特征选择是降低高维数据特征维度的常用方法之一。传统的特征选择方法多数基于完整数据集,对实际应用中普遍存在缺失数据的情形研究较少。针对不完整数据中含有未被观察信息和存在异常值的特点,提出一种基于概率矩阵分解技术的鲁棒特征选择方法。使用基于分簇的概率矩阵分解模型对数据集中的缺失值进行近似估计,以有效测量相邻簇之间数据的相似性,缩小问题规模,同时降低填充误差。依据缺失数据值存在少量异常值的情形,利用基于l_2,1损失函数的方法进行特征选择,在此基础上给出不完整数据集的特征选择方法流程,并对其收敛性进行理论分析。该方法利用不完整数据集中的所有信息,有效应对不完整数据集中异常值带来的影响。实验结果表明,相比传统特征选择方法,该方法在合成数据集上选择更少的无关特征,可降低异常值带来的影响,在真实数据集上获得了较高的分类准确率,能够选择出更为准确的特征。     

Robust PLS approach for KPI-related prediction and diagnosis against outliers and missing data

In practical industrial applications, the key performance indicator (KPI)-related prediction and diagnosis are quite important for the product quality and economic benefits. To meet these requirements, many advanced prediction and monitoring approaches have been developed which can be classified into model-based or data-driven techniques. Among these approaches, partial least squares (PLS) is one of the most popular data-driven methods due to its simplicity and easy implementation in large-scale industrial process. As PLS is totally based on the measured process data, the characteristics of the process data are critical for the success of PLS. Outliers and missing values are two common characteristics of the measured data which can severely affect the effectiveness of PLS. To ensure the applicability of PLS in practical industrial applications, this paper introduces a robust version of PLS to deal with outliers and missing values, simultaneously. The effectiveness of the proposed method is finally demonstrated by the application results of the KPI-related prediction and diagnosis on an industrial benchmark of Tennessee Eastman process.     

基于稀疏表示的数据流异常数据预测方法

为了提高数据流中异常数据的预测速度与精度,提出一种基于稀疏表示的数据流异常数据预测方法。结合了小波噪声检测方法,采用新近发展起来的稀疏表示工具,对含有异常数据的数据流进行小波变换,并得到一组小波系数,然后对这些系数建立稀疏表示模型。引入随机测量矩阵对小波系数进行变换,恢复小波系数的稀疏性达到预测异常数据的目的。仿真结果表明,在一定条件下该方法可获得相当好的预测效果。     

带丢失观测和不确定噪声方差系统改进的鲁棒协方差交叉融合稳态Kalman滤波器

对带丢失观测和不确定噪声方差的线性定常多传感器系统,引入虚拟噪声将原系统转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理,用Lyapunov方程方法提出局部鲁棒稳态Kalman滤波器及其实际方差最小上界,并利用保守的局部滤波误差互协方差,提出一种改进的鲁棒协方差交叉(covariance intersection,CI)融合稳态Kalman滤波器及其实际方差最小上界.证明了所提出的鲁棒局部和融合滤波器的鲁棒性,并证明了改进的CI融合器鲁棒精度高于原始CI融合鲁棒精度,且高于每个局部滤波器的鲁棒精度.一个仿真例子验证所提出结果的正确性和有效性.     

Identification of control chart patterns using wavelet filtering and robust fuzzy clustering

This paper proposes a hybrid framework composed of filtering module and clustering module to identify six common types of control chart patterns, including natural pattern, cyclic pattern, upward shift, downward shift, upward trend, and downward trend. In particular, a multi-scale wavelet filter is designed for denoising and its performance is compared to single-scale filters, including mean filter and exponentially weighted moving average (EWMA) filter. Moreover, three fuzzy clustering algorithms, based on fuzzy c means (FCM), entropy fuzzy c means (EFCM) and kernel fuzzy c means (KFCM), are adopted to compare their performance of pattern classification. Experimental results demonstrate that the excellent performance of EFCM and KFCM against outliers, especially in the case of high noise level embedded in the input data. Therefore, a hybrid framework combining wavelet filter with robust fuzzy clustering is suggested and proposed in this paper. Compared to neural network based approaches, the proposed method provides a promising way for the on-line recognition of control chart patterns because of its efficient computation and robustness against outliers.     

基于最大相关熵准则的2维主成分分析

目的 本文针对基于最小均方差准则的主成分分析算法(如2DPCA-L₂(two-dimensional PCA with L₂-norm)算法和2DPCA-L₁(two-dimensional PCA with L₁-norm)算法)对外点敏感、识别率低的问题,结合信息论中的最大相关熵准则,提出了一种基于最大相关熵准则的2DPCA(2DPCA-MCC)。方法 2DPCA-MCC算法采用最大相关熵表示目标函数,通过半二次优化技术解决相关熵问题,降低了外点在目标函数评价中的贡献,从而提高了算法的鲁棒性和识别精度。结果 通过对比2DPCA-MCC算法和2DPCA-L₂、2DPCA-L₁在ORL人脸数据库上的识别效果,表明了2DPCA-MCC算法的识别率比2维主成分分析算法的识别率最低提高了近10%,最高提高了近30%。结论 提出了一种基于最大相关熵的2DPCA算法,通过半二次优化技术解决非线性优化问题,实验结果表明,本算法能够较好地解决外点问题,显著提高识别精度,适用于解决人脸识别中的外点问题。     

基于自适应抗差卡尔曼滤波的UWB室内定位

在UWB室内定位中,测距中存在的NLOS误差和测距异常值会大幅降低其定位的精度和可靠性.针对这一问题,提出了一种自适应抗差卡尔曼滤波方法.该方法首先在UWB距离模型的基础上,利用新息向量和LOS环境下的阈值所构造的抗差因子鉴别并削弱NLOS测距误差和测距异常值的影响,同时利用Sage-Husa滤波对系统噪声进行实时估计和修正,在此基础上推导UWB定位的线性模型,利用卡尔曼滤波进行UWB定位解算.实验结果表明,该方法能有效地抑制并消除UWB测距中的NLOS测距误差和测距异常值的影响,进而能提高UWB定位的精度和可靠性.     

A Bayesian robust CP decomposition approach for missing traffic data imputation

The inevitable problem of missing data is ubiquitous in the real transportation system, which makes the data-driven intelligent transportation system suffer from incorrect response. We propose a Bayesian robust Candecomp/Parafac (CP) tensor decomposition (BRCP) approach to deal with missing data and outliers by integrating the general form of transportation system domain knowledge. Specifically, when the lower rank tensor captures the global information, the sparse tensor is added to capture the local information, which can robustly predict the distribution of missing items and under the fully Bayesian treatment, the effective variational reasoning can prevent the over fitting problem. Real and reliable traffic data sets are used to evaluate the performance of the model in two data missing scenarios, which the experimental results show that the proposed BRCP model achieves the best imputation accuracy and is better than the most advanced baseline (Bayesian Gaussian CP decomposition (BGCP), high accuracy low-rank tensor completion (HaLRTC) and SVD-combined tensor decomposition (STD)), even in the case of high missed detection rate, the model still has the best performance and robustness.

     

基于抗差自适应容积卡尔曼滤波的超紧耦合跟踪方法

为降低基于单一调节回路的超紧耦合结构存在的反作用影响,设计了一种基于双回路的超紧耦合结构.基于此,为解决所设计结构中跟踪环路的非线性滤波问题,针对测量异常误差和动力学模型误差,提出了一种基于抗差自适应容积卡尔曼滤波(Robust adaptive cubature Kalman filter,RACKF)的超紧耦合跟踪算法.该算法采用稳健M估计调整容积卡尔曼滤波 (Cubature Kalman filter,CKF)算法,对观测量中粗差的影响“程度”进行探测和处理,以减小观测量异常误差产生的影响,同时利用自适应调节因子对算法进行调节修正,以处理动态扰动误差引入的影响.实验结果表明: 所提出的方法能有效地处理模型不准确所引入的误差,较好地实现全球定位系统(Global positioning system,GPS)卫星信号的高精度和稳定跟踪,其跟踪性能远优于基于单一回路的跟踪方法,同时优于基于无迹卡尔曼滤波(Unscented Kalman filter,UKF)和基于CKF的跟踪方法,提升了导航系统在高动态条件下的适应性能.     

Hybrid robust support vector machines for regression with outliers

In this study, a hybrid robust support vector machine for regression is proposed to deal with training data sets with outliers. The proposed approach consists of two stages of strategies. The first stage is for data preprocessing and a support vector machine for regression is used to filter out outliers in the training data set. Since the outliers in the training data set are removed, the concept of robust statistic is not needed for reducing the outliers’ effects in the later stage. Then, the training data set except for outliers, called as the reduced training data set, is directly used in training the non-robust least squares support vector machines for regression (LS-SVMR) or the non-robust support vector regression networks (SVRNs) in the second stage. Consequently, the learning mechanism of the proposed approach is much easier than that of the robust support vector regression networks (RSVRNs) approach and of the weighted LS-SVMR approach. Based on the simulation results, the performance of the proposed approach with non-robust LS-SVMR is superior to the weighted LS-SVMR approach when the outliers exist. Moreover, the performance of the proposed approach with non-robust SVRNs is also superior to the RSVRNs approach.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

Hybrid online sensor error detection and functional redundancy for systems with time-varying parameters

Supervision and control systems rely on signals from sensors to receive information to monitor the operation of a system and adjust manipulated variables to achieve the control objective. However, sensor performance is often limited by their working conditions and sensors may also be subjected to interference by other devices. Many different types of sensor errors such as outliers, missing values, drifts and corruption with noise may occur during process operation. A hybrid online sensor error detection and functional redundancy system is developed to detect errors in online signals, and replace erroneous or missing values detected with model-based estimates. The proposed hybrid system relies on two techniques, an outlier-robust Kalman filter (ORKF) and a locally-weighted partial least squares (LW-PLS) regression model, which leverage the advantages of automatic measurement error elimination with ORKF and data-driven prediction with LW-PLS. The system includes a nominal angle analysis (NAA) method to distinguish between signal faults and large changes in sensor values caused by real dynamic changes in process operation. The performance of the system is illustrated with clinical data continuous glucose monitoring (CGM) sensors from people with type 1 diabetes. More than 50,000 CGM sensor errors were added to original CGM signals from 25 clinical experiments, then the performance of error detection and functional redundancy algorithms were analyzed. The results indicate that the proposed system can successfully detect most of the erroneous signals and substitute them with reasonable estimated values computed by functional redundancy system.     

Combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling

Linear subspace methods that provide sufficient reconstruction of the data, such as PCA, offer an efficient way of dealing with missing pixels, outliers, and occlusions that often appear in the visual data. Discriminative methods, such as LDA, which, on the other hand, are better suited for classification tasks, are highly sensitive to corrupted data. We present a theoretical framework for achieving the best of both types of methods: an approach that combines the discrimination power of discriminative methods with the reconstruction property of reconstructive methods which enables one to work on subsets of pixels in images to efficiently detect and reject the outliers. The proposed approach is therefore capable of robust classification with a high-breakdown point. We also show that subspace methods, such as CCA, which are used for solving regression tasks, can be treated in a similar manner. The theoretical results are demonstrated on several computer vision tasks showing that the proposed approach significantly outperforms the standard discriminative methods in the case of missing pixels and images containing occlusions and outliers.