Nonlinear Statistical Process Monitoring Based on Control Charts with Memory Effect and Kernel Independent Component Analysis

A novel nonlinear combination process monitoring method was proposed based on techniques with memory effect (multivariate exponentially weighted moving average (MEWMA)) and kernel independent component analysis (KICA). The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently developed statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of measurements and it is a two-phase algorithm: whitened kernel principal component analysis (KPCA) plus independent component analysis (ICA). The application to the fluid catalytic cracking unit (FCCU) simulated process indicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear relationship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for long-term performance deterioration.

Multi-state Information Dimension Reduction Based on Particle Swarm Optimization-Kernel Independent Component Analysis

The precision of the kernel independent component analysis( KICA) algorithm depends on the type and parameter values of kernel function. Therefore,it's of great significance to study the choice method of KICA's kernel parameters for improving its feature dimension reduction result. In this paper, a fitness function was established by use of the ideal of Fisher discrimination function firstly. Then the global optimal solution of fitness function was searched by particle swarm optimization( PSO) algorithm and a multi-state information dimension reduction algorithm based on PSO-KICA was established. Finally,the validity of this algorithm to enhance the precision of feature dimension reduction has been proven.

Application of Particle Swarm Optimization to Fault Condition Recognition Based on Kernel Principal Component Analysis

Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.

A deep kernel method for lithofacies identification using conventional well logs

How to fit a properly nonlinear classification model from conventional well logs to lithofacies is a key problem for machine learning methods.Kernel methods(e.g.,KFD,SVM,MSVM)are effective attempts to solve this issue due to abilities of handling nonlinear features by kernel functions.Deep mining of log features indicating lithofacies still needs to be improved for kernel methods.Hence,this work employs deep neural networks to enhance the kernel principal component analysis(KPCA)method and proposes a deep kernel method(DKM)for lithofacies identification using well logs.DKM includes a feature extractor and a classifier.The feature extractor consists of a series of KPCA models arranged according to residual network structure.A gradient-free optimization method is introduced to automatically optimize parameters and structure in DKM,which can avoid complex tuning of parameters in models.To test the validation of the proposed DKM for lithofacies identification,an open-sourced dataset with seven con-ventional logs(GR,CAL,AC,DEN,CNL,LLD,and LLS)and lithofacies labels from the Daniudi Gas Field in China is used.There are eight lithofacies,namely clastic rocks(pebbly,coarse,medium,and fine sand-stone,siltstone,mudstone),coal,and carbonate rocks.The comparisons between DKM and three commonly used kernel methods(KFD,SVM,MSVM)show that(1)DKM(85.7%)outperforms SVM(77%),KFD(79.5%),and MSVM(82.8%)in accuracy of lithofacies identification;(2)DKM is about twice faster than the multi-kernel method(MSVM)with good accuracy.The blind well test in Well D13 indicates that compared with the other three methods DKM improves about 24%in accuracy,35%in precision,41%in recall,and 40%in F1 score,respectively.In general,DKM is an effective method for complex lithofacies identification.This work also discussed the optimal structure and classifier for DKM.Experimental re-sults show that(m_(1),m_(2),O)is the optimal model structure and linear svM is the optimal classifier.(m_(1),m_(2),O)means there are m KPCAs,and then m2 residual units.A workflow to determine an optimal classifier in DKM for lithofacies identification is proposed,too.

NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS

In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.

Statistical Monitoring of Chemical Processes Based on Sensitive Kernel Principal Components

核主管部件分析(KPCA ) 方法采用开始的几个核主管部件(KPC ) ，它为过程监视显示正常观察的大多数变化信息，但是不能反映差错信息。在这研究，敏感内核主管部件分析(SKPCA ) 被建议改进监视性能的过程，即，错过了察觉率处理 T2 统计、摆平的预言错误 SPE 统计数值和还原剂的不和。T2 统计数值能被用来沿着每 KPC 直接测量变化并且分析察觉表演以及在一个过程捕获最有用的信息。随沿着每 KPC 的 T2 统计数值的变化率的计算， SKPCA 为进程监视选择敏感内核主管部件。一个模仿的简单系统和田纳西伊斯门过程被采用在联机监视上表明 SKPCA 的效率。结果显示监视表演显著地被改进。

Kernel Generalization of Multi-Rate Probabilistic Principal Component Analysis for Fault Detection in Nonlinear Process

In practical process industries,a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes,which indicates that the measurements coming from different sources are collected at different sampling rates.To build a complete process monitoring strategy,all these multi-rate measurements should be considered for data-based modeling and monitoring.In this paper,a novel kernel multi-rate probabilistic principal component analysis(K-MPPCA)model is proposed to extract the nonlinear correlations among different sampling rates.In the proposed model,the model parameters are calibrated using the kernel trick and the expectation-maximum(EM)algorithm.Also,the corresponding fault detection methods based on the nonlinear features are developed.Finally,a simulated nonlinear case and an actual pre-decarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL-BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.

Abundance quantification by independent component analysis of hyperspectral imagery for oil spill coverage calculation

The estimation of oil spill coverage is an important part of monitoring of oil spills at sea.The spatial resolution of images collected by airborne hyper-spectral remote sensing limits both the detection of oil spills and the accuracy of estimates of their size.We consider at-sea oil spills with zonal distribution in this paper and improve the traditional independent component analysis algorithm.For each independent component we added two constraint conditions:non-negativity and constant sum.We use priority weighting by higher-order statistics,and then the spectral angle match method to overcome the order nondeterminacy.By these steps,endmembers can be extracted and abundance quantified simultaneously.To examine the coverage of a real oil spill and correct our estimate,a simulation experiment and a real experiment were designed using the algorithm described above.The result indicated that,for the simulation data,the abundance estimation error is 2.52% and minimum root mean square error of the reconstructed image is 0.030 6.We estimated the oil spill rate and area based on eight hyper-spectral remote sensing images collected by an airborne survey of Shandong Changdao in 2011.The total oil spill area was 0.224 km^2,and the oil spill rate was 22.89%.The method we demonstrate in this paper can be used for the automatic monitoring of oil spill coverage rates.It also allows the accurate estimation of the oil spill area.

Comparison of Kernel Entropy Component Analysis with Several Dimensionality Reduction Methods

Dimensionality reduction techniques play an important role in data mining. Kernel entropy component analysis( KECA) is a newly developed method for data transformation and dimensionality reduction. This paper conducted a comparative study of KECA with other five dimensionality reduction methods,principal component analysis( PCA),kernel PCA( KPCA),locally linear embedding( LLE),laplacian eigenmaps( LAE) and diffusion maps( DM). Three quality assessment criteria, local continuity meta-criterion( LCMC),trustworthiness and continuity measure(T&C),and mean relative rank error( MRRE) are applied as direct performance indexes to assess those dimensionality reduction methods. Moreover,the clustering accuracy is used as an indirect performance index to evaluate the quality of the representative data gotten by those methods. The comparisons are performed on six datasets and the results are analyzed by Friedman test with the corresponding post-hoc tests. The results indicate that KECA shows an excellent performance in both quality assessment criteria and clustering accuracy assessing.

Two Dimensional Spatial Independent Component Analysis and Its Application in fMRI Data Process

One important application of independent component analysis （ICA） is in image processing. A two dimensional （2-D） composite ICA algorithm framework for 2-D image independent component analysis （2-D ICA） is proposed. The 2-D nature of the algorithm provides it an advantage of circumventing the roundabout transforming procedures between two dimensional （2-D） image deta and one-dimensional （l-D） signal. Moreover the combination of the Newton （fixed-point algorithm） and natural gradient algorithms in this composite algorithm increases its efficiency and robustness. The convincing results of a successful example in functional magnetic resonance imaging （fMRI） show the potential application of composite 2-D ICA in the brain activity detection.

FSS-kernel与FastICA融合的盲源分离算法研究

Fast ICA算法有着比传统ICA算法更快、更稳健的收敛速度,但由于其选用的非线性函数不能很好地符合源信号的统计特性,恢复结果并不理想。针对该问题,提出了一种有限支持样本核函数(FSS-kernel)与Fast ICA融合的盲源分离算法。该方法是通过FSS-kernel算法估计得出源信号概率密度函数,结合Fast ICA算法,实现混合信号的盲分离。仿真结果表明,该方法能够有效地完成混叠信号的分离,通过与传统ICA算法及Fast ICA算法比较,证明了该方法具有更高的分离精度和自适应能力。

SIGNAL FEATURE EXTRACTION BASED UPON INDEPENDENT COMPONENT ANALYSIS AND WAVELET TRANSFORM

It is an important precondition for machine fault diagnosis that vibrationsignal can be extracted effectively. Based on the characteristic of noise interfused during thecourse of sampling vibration signal, independent component analysis (ICA) method is combined withwavelet to de-noise. Firstly, The sampled signal can be separated with ICA, then the function offrequency band chosen with multi-resolution wavelet transform can be used to judge whether thestochastic disturbance singular signal is interfused. By these ways, the vibration signals can beextracted effectively, which provides favorable condition for subsequent feature detection ofvibration signal and fault diagnosis.

Anomaly Detection of UAV State Data Based on Single-Class Triangular Global Alignment Kernel Extreme Learning Machine

Unmanned Aerial Vehicles(UAVs)are widely used and meet many demands in military and civilian fields.With the continuous enrichment and extensive expansion of application scenarios,the safety of UAVs is constantly being challenged.To address this challenge,we propose algorithms to detect anomalous data collected from drones to improve drone safety.We deployed a one-class kernel extreme learning machine(OCKELM)to detect anomalies in drone data.By default,OCKELM uses the radial basis(RBF)kernel function as the kernel function of themodel.To improve the performance ofOCKELM,we choose a TriangularGlobalAlignmentKernel(TGAK)instead of anRBF Kernel and introduce the Fast Independent Component Analysis(FastICA)algorithm to reconstruct UAV data.Based on the above improvements,we create a novel anomaly detection strategy FastICA-TGAK-OCELM.The method is finally validated on the UCI dataset and detected on the Aeronautical Laboratory Failures and Anomalies(ALFA)dataset.The experimental results show that compared with other methods,the accuracy of this method is improved by more than 30%,and point anomalies are effectively detected.

Independent component analysis approach for fault diagnosis of condenser system in thermal power plant

A statistical signal processing technique was proposed and verified as independent component analysis(ICA) for fault detection and diagnosis of industrial systems without exact and detailed model.Actually,the aim is to utilize system as a black box.The system studied is condenser system of one of MAPNA's power plants.At first,principal component analysis(PCA) approach was applied to reduce the dimensionality of the real acquired data set and to identify the essential and useful ones.Then,the fault sources were diagnosed by ICA technique.The results show that ICA approach is valid and effective for faults detection and diagnosis even in noisy states,and it can distinguish main factors of abnormality among many diverse parts of a power plant's condenser system.This selectivity problem is left unsolved in many plants,because the main factors often become unnoticed by fault expansion through other parts of the plants.

Study of engine noise based on independent component analysis

Independent component analysis was applied to analyze the acoustic signals from diesel engine. First the basic prin-ciple of independent component analysis (ICA) was reviewed. Diesel engine acoustic signal was decomposed into several inde-pendent components (ICs); Fourier transform and continuous wavelet transform (CWT) were applied to analyze the independent components. Different noise sources of the diesel engine were separated, based on the characteristics of different component in time-frequency domain.

Relationships between changes of kernel nutritive components and seed vigor during development stages of F_1 seeds of sh_2 sweet corn

The changes of kernel nutritive components and seed vigor in F1 seeds of sh2 sweet corn during seed development stage were investigated and the relationships between them were analyzed by time series regression (TSR) analysis. The results show that total soluble sugar and reducing sugar contents gradually declined, while starch and soluble protein contents increased throughout the seed development stages. Germination percentage, energy of germination, germination index and vigor index gradually increased along with seed development and reached the highest levels at 38 d after pollination (DAP). The TSR showed that, during 14 to 42 DAP, total soluble sugar content was independent of the vigor parameters determined in present experiment, while the reducing sugar content had a significant effect on seed vigor. TSR equations between seed reducing sugar and seed vigor were also developed. There were negative correlations between the seed reducing sugar content and the germination percentage, energy of germination, germination index and vigor index, respectively. It is suggested that the seed germination, energy of germination, germination index and vigor index could be predicted by the content of reducing sugar in sweet corn seeds during seed development stages.

Online Batch Process Monitoring Based on Just-in-Time Learning and Independent Component Analysis

A new method was developed for batch process monitoring in this paper.In the developed method,just-in-time learning(J1TL) and independent component analysis(ICA) were integrated to build JITL-ICA monitoring scheme.JITL was employed to tackle with the characteristics of batch process such as inherent timevarying dynamics,multiple operating phases,and especially the case of uneven length stage.According to new coming test data,the most correlated segmentation was obtained from batch-wise unfolded training data by JITL.Then,ICA served as the principal components extraction approach.Therefore,the non-Gaussian distributed data can also be addressed under this modeling framework.The effectiveness and superiority of JITL-ICA based monitoring method was demonstrated by fed-batch penicillin fermentation.

Independent Component Analysis Based Blind Adaptive Interference Reduction and Symbol Recovery for OFDM Systems

To overcome the inter-carrier interference(ICI) of orthogonal frequency division multiplexing(OFDM) systems subject to unknown carrier frequency offset(CFO) and multipath, this paper develops a blind adaptive interference suppression scheme based on independent component analysis(ICA). Taking into account statistical independence of subcarriers' signals of OFDM, the signal recovery mechanism is investigated to achieve the goal of blind equalization. The received OFDM signals can be considered as the mixed observation signals. The effect of CFO and multipath corresponds to the mixing matrix in the problem of blind source separation(BSS) framework. In this paper, the ICAbased OFDM system model is built, and the proposed ICA-based detector is exploited to extract source signals from the observation of a received mixture based on the assumption of statistical independence between the sources. The blind separation technique can increase spectral efficiency and provide robustness performance against erroneous parameter estimation problem. Theoretical analysis and simulation results show that compared with the conventional pilot-based scheme, the improved performance of OFDM systems is obtained by the proposed ICA-based detection