Missing data methods in PCA and PLS: Score calculations with incomplete observations

A very important problem in industrial applications of PCA and PLS models, such as process modelling or monitoring, is the estimation of scores when the observation vector has missing measurements. The alternative of suspending the application until all measurements are available is usually unacceptable. The problem treated in this work is that of estimating scores from an existing PCA or PLS model when new observation vectors are incomplete. Building the model with incomplete observations is not treated here, although the analysis given in this paper provides considerable insight into this problem. Several methods for estimating scores from data with missing measurements are presented, and analysed: a method, termed single component projection, derived from the NIPALS algorithm for model building with missing data; a method of projection to the model plane; and data replacement by the conditional mean. Expressions are developed for the error in the scores calculated by each method. The error analysis is illustrated using simulated data sets designed to highlight problem situations. A larger industrial data set is also used to compare the approaches. In general, all the methods perform reasonable well with moderate amounts of missing data (up to 20% of the measurements). However, in extreme cases where critical combinations of measurements are missing, the conditional mean replacement method is generally superior to the other approaches.     

自适应冗余提升小波降噪分析及其在轴承故障识别中的应用

为有效识别机械设备中滚动轴承的微弱故障信息,本文提出一种自适应冗余提升小波降噪方法。根据待分解低频尺度系数所含的不同特征,应用范数准则来自适应地选取最匹配于该尺度系数特征的小波函数。同时,引入多孔算法,用以通过冗余性来保证逐层分解后各尺度系数和小波系数所含有的丰富的信息量。接下来,对各层小波系数采用变尺度阈值降噪算法,并对降噪后的系数进行重构及包络谱分析,进而提取滚动轴承的故障特征。应用上述方法分别对轴承实验台轴承混合故障信号和现场实际信号进行分析,均较好地实现了故障识别,验证了本文方法的有效性。     

基于多尺度局部保持投影的轴承故障特征增强方法

针对轴承故障声发射信号的非线性特性,及易受背景噪声干扰的特点,提出一种多尺度局部保持投影方法。通过小波包分解实现一维信号的多尺度构造,利用近邻图保持信号局部流形信息,通过局部保持投影将信号变换到新的坐标空间下,实现故障特征增强。仿真和实验信号处理结果表明,多尺度局部保持投影方法在轴承故障增强检测中效果显著。     

基于DCT的微弱信号提取和识别

微弱信号提取一直是故障诊断领域的难点。结合离散余弦变换(DCT),将离散时间序列经过离散余弦变换处理成对应的系数向量,在阈值处理的基础上,重构信号提取出微弱故障信息。与小波降噪和低通滤波方法进行对比分析,该算法突出了信号的微弱故障特征信息,较好的再现了夹杂在信号中的微弱成分,参数设定简单,结果对参数不敏感。最后通过实验证实该方法的有效性。本算法速度快,简单易行,可用于实时故障监测。     

Fault diagnostic method of power transformers based on hybrid genetic algorithm evolving wavelet neural network

The main drawbacks of a back propagation algorithm of wavelet neural network (WNN) commonly used in fault diagnosis of power transformers are that the optimal procedure is easily stacked into the local minima and cases that strictly demand initial value. A fault diagnostic method is presented based on a real-encoded hybrid genetic algorithm evolving a WNN, which can be used to optimise the structure and the parameters of WNN instead of humans in the same training process. Through the process, compromise is satisfactorily made among network complexity, convergence and generalisation ability. A number of examples show that the method proposed has good classifying capability for single- and multiple-fault samples of power transformers as well as high fault diagnostic accuracy.     

Vibrational spectroscopic and ultrasound analysis for in-process characterization of high-density polyethylene/polypropylene blends during melt extrusion

Spectroscopic techniques such as Raman, mid-infrared (MIR), and near-infrared (NIR) have become indispensable analytical tools for rapid chemical quality control and process monitoring. This paper presents the application of in-line Fourier transform near-infrared (FT-NIR) spectroscopy, Raman spectroscopy, and ultrasound transit time measurements for in-line monitoring of the composition of a series of high-density polyethylene (HDPE)/polypropylene (PP) blends during single-screw extrusion. Melt composition was determined by employing univariate analysis of the ultrasound transit time data and partial least squares (PLS) multivariate analysis of the data from both spectroscopic techniques. Each analytical technique was determined to be highly sensitive to changes in melt composition, allowing accurate prediction of blend content to within +/- 1% w/w (1sigma) during monitoring under fixed extrusion conditions. FT-NIR was determined to be the most sensitive of the three techniques to changes in melt composition. A four-factor PLS model of the NIR blend spectra allowed determination of melt content with a standard prediction error of +/- 0.30% w/w (1sigma). However, the NIR transmission probes employed for analysis were invasive into the melt stream, whereas the single probes adopted for Raman and ultrasound analysis were noninvasive, making these two techniques more versatile. All three measurement techniques were robust to the high temperatures and pressures experienced during melt extrusion, demonstrating each system's suitability for process monitoring and control.     

基于多尺度Kalman数据融合滤波

本文通过分析基于小波变换的动态系统模型,提出一种基于小波多尺度的Kalman数据滤波方法,本文利用小波的多尺度特点,把初始估计序列多尺度分解,并在不同尺度层上进行Kalman滤波估计,再利用小波重构来融合各层的估计信息,把标准Kalman滤波只在单一尺度和时间轴上对状态估计值和误差协方差进行数据更新,改进为基于小波变换的尺度轴和时间轴上的双向数据更新,该算法将小波多尺度分解去噪和Kalman滤波相结合,对实际中含较强噪声的动态系统的状态估计效果较好.算法也可用于多分辨率多传感器数据融合.     

基于小波包变换和随机森林算法的光伏系统故障分类

针对光伏系统故障分类问题,提出一种小波包变换和随机森林算法相结合的故障分类方法。采集光伏系统的故障电压数据,利用小波包变换对电压信号进行分解,提取各频带能量作为故障特征,将特征样本送入随机森林算法中进行分类。随机森林算法是结合集成学习理论和随机子空间方法的一种算法,可以对多种故障做出准确分类。使用PSCAD/EMTDC搭建独立光伏发电系统,选取12种故障进行模拟,得到600个故障样本,选取其中360个样本用于训练分类器,240个样本用于测试分类器的分类性能。仿真结果表明:该方法可有效辨别光伏系统的12种故障,分类准确率达到97.92%。与RBF神经网络分类器相比,故障分类准确率提高了4.17%,对进一步实现光伏系统故障诊断研究具有重要意义。     

A fault diagnosis prototype for a bioreactor for bioinsecticide production

The objective of this work is to develop an algorithm for fault diagnosis in a process of animal cell cultivation, for bioinsecticide production. Generally, these processes are batch processes. It is a fact that the diagnosis for a batch process involves a division of the process evolution (time horizon) into partial processes, which are defined as pseudocontinuous blocks. Therefore, a PCB represents the evolution of the system in a time interval where it has a qualitative behavior similar to a continuous one. Thus, each PCB, in which the process is divided, can be handled in a conventional way (like continuous processes). The process model, for each PCB, is a Signed Directed Graph (SDG). To achieve generality and to allow the computational implementation, the modular approach was used in the synthesis of the bioreactor digraph. After that, the SDGs were used to carry out qualitative simulations of faults. The achieved results are the fault patterns. A special fault symptom dictionary —SM—has been adopted as data base organization for fault patterns storage. An effective algorithm is presented for the searching process of fault patterns. The system studied, as a particular application, is a bioreactor for cell cultivation for bioinsecticide production. During this work, we concentrate on the SDG construction, and 3btaining real fault patterns by the elimination of spurious patterns. The algorithm has proved to be effective in both senses, resolution and accuracy, to diagnose different kinds of simulated faults.     

形态非抽样小波及其在冲击信号特征提取中的应用

针对形态小波分解过程的抽样引起信号长度逐层递减的问题,提出一种基于多尺度Top-Hat变换的形态非抽样小波构造方法。利用形态非抽样小波的一般框架,分别采用形态学开运算和多尺度Top-Hat变换作为形态非抽样小波分解的近似信号和细节信号的分析算子,使形态小波分解过程中信号长度保持不变,从而保证了形态分析时所需的信息量。结合转子振动冲击特征信号提取试验,验证所提方法在故障诊断中应用的可行性与有效性。     

小波函数性质及其对小波分析结果的影响

分析了小波变换在图像处理、语音处理领域和设备故障诊断领域的应用特点 ,指出了两者的不同之处。并进一步讨论了小波函数的性质及其对小波变换结果的影响 ,指出在用小波变换进行诊断信号分析和特征提取时 ,小波函数的影响是不容忽视的     

Multivariate monitoring of batch process startup

A batch process is finite in duration and can be separated into two stages: startup and production. We develop a methodology to monitor a batch process during the startup stage to reduce the length of the startup stage. We focus on processes that are characterized by multiple process parameters and product characteristics. Because of the complex interdependencies characterizing the process parameters and product characteristics, it is more effective to evaluate them simultaneously. To address the multivariate nature of the process we use a multivariate statistical model: PLS (Projection to Latent Structures). PLS has been applied to several applications in statistical process monitoring. We present a new application of PLS to the startup stage of a batch process. Iterative adjustments made during startup in search of an acceptable production zone consume considerable amounts of material, labor and equipment time. We develop a monitoring procedure to reduce the time as well as the number of iterations and adjustments needed for startup. A PLS model is constructed, using baseline data, to characterize the relationship among process parameters during good production. The startup stage is monitored using the PLS characterization to determine if the process is consistent with good production. We illustrate the improved startup operations with an example from a batch process in filament extrusion, the application that motivates this work. Copyright © 2001 John Wiley & Sons, Ltd.     

Partial least squares based decomposition of five spectrally overlapping factors

The development of a multi-sensory fiber-optic based fluence rate probe (MSP) for light monitoring and dosimetry during photodynamic therapy (PDT) created the need for a robust multivariate signal analysis algorithm capable of quantifying the intensity of five component spectra, representing the sensors, which display a large degree of spectral overlap. Partial least squares (PLS) analysis, as an option for such an analysis algorithm, was evaluated through simulations in the presence of three types of noise, which experimentally may limit the accuracy of PLS quantification of component spectra contributions. Random, or white noise, background was varied over a range of 0-15% relative intensity. A non-random (Gaussian) background vector was simulated, as an experimentally relevant spectral interferent, over a range of 0-7% relative intensity. Spectral variation was modeled by a spectral shift of +/-1-5 nm. Procedures for selecting preferred combinations of fluorophores, with minimum possible spectral overlap, were developed. To illustrate the importance of this selection process, PLS performance results were compared for two possible combinations of five fluorophores, as well as for the combination of three fluorophores currently in experimental use with MSPs. Experimentally anticipated worst-case quantifications were identified for all three types of simulated noise (5% random background, 0.5% Gaussian background, and +/-2 nm spectral shift). The effects of single and combined types of noise were evaluated by independently varying each type of simulated noise over the experimentally relevant range. The mean percentage error in determining the fluorophore contributions and hence quantification of the fluence rate were compared with the required performance standard of better than 10% error for optical power meters in medical use. The PLS algorithm provided an accuracy of 7 +/- 2% for five fluorophores and 3.3 +/- 0.8% for three fluorophores, indicating that PLS is an appropriate choice for this application.     

基于局部均值分解多尺度模糊熵和灰色相似关联度的滚动轴承故障诊断

提出了一种基于局部均值分解多尺度模糊熵和灰色相似关联度相结合的滚动轴承故障诊断方法。该方法将故障信号自适应地分解为若干乘积函数,并从中选取包含主要故障信息的PF分量计算多尺度模糊熵作为特征向量,通过计算待识别样本与标准故障模式的灰色相似关联度,对滚动轴承故障类型和损伤程度进行判断。将该方法与LMD模糊熵和灰色相似关联度相结合的方法进行了对比,实验表明,基于LMD多尺度模糊熵和灰色相似关联度的滚动轴承故障诊断方法,能够有效地识别滚动轴承运行状态,实现对滚动轴承的故障诊断。     

Fault mode analysis and detection for gear tooth crack during its propagating process based on dynamic simulation method

Gearbox is one of the most important parts of rotating machinery, therefore, it is vital to carry out health monitoring for gearboxes. However, it is still an unsolved problem to disclose the impact of gear tooth crack fault on gear system vibration features during the crack propagating process, besides effective crack fault mode detection methods are lacked. In this study, an analytical model is proposed to calculate the time varying mesh stiffness of the meshing gear pair, and in this model the tooth bending stiffness, shear stiffness, axial compressive stiffness, Hertzian contact stiffness and fillet-foundation stiffness are taken into consideration. Afterwards, the vibration mechanism and effects of different levels of gear tooth crack on the gear system dynamics are investigated based on a 6 DOF dynamic model. Then, the crack fault vibration mode is studied, and a parametrical-Laplace wavelet method is presented to describe the crack fault mode. Furthermore, based on the maximum correlation coefficient (MCC) criterion, the optimized Laplace wavelet base is determined, which is then designed as a health indicator to detect the crack fault. The results show that the proposed method is effective in fault diagnosis of severe tooth crack as well as the early stage tooth crack.     

Gearbox Fault Detection Using Real Coded Genetic Algorithm and Novel Shock Response Spectrum Features Extraction

This paper presents an intelligent fault detection method for gearbox. The method uses band-pass and wavelet filtering with real coded genetic algorithm (RCGA) and shock response spectrum (SRS) for features extraction. Vibration data acquired from gearbox are adaptively filtered through a band-pass and wavelet filters optimized by the RCGA. The filtering process unveils the fault pulses buried under huge background noise. Shock response spectrum is used to calculate the amount of shock produced by these pulses over a frequency band of interest for features extraction. The proposed method is a combination of intelligent and conventional search techniques, which shows a high performance and accurate fault detection results. The effectiveness, feasibility, and robustness of the proposed method are demonstrated on experimental data. The RCGA has successfully achieved an average speed up factor of 74 %, as compared to conventional genetic algorithms (GA) while preserving the quality of results.     

基于SVDD和距离测度的齿轮泵故障诊断方法研究

提出了一种基于支持向量域描述和距离测度的齿轮泵故障诊断方法。该方法首先对齿轮泵各种工况下的振动信号进行小波包分解,提取各频带能量百分比作为特征向量;然后仅利用正常工况下的特征向量训练SVDD超球模型,通过定义绝对距离测度检测齿轮泵状态是否出现异常;最后针对每类工况下的特征向量单独训练SVDD超球模型,通过定义相对距离测度准确定位齿轮泵的不同故障工况。试验结果表明,采用小波包频带能量降低了数据维数,有效浓缩了故障信息;基于绝对距离测度和相对距离测度的SVDD故障诊断方法既能检测异常状态,又能区分各种故障工况,达到了状态监测和故障分类识别的目的。     

基于多尺度降维的柴油机信号信息熵增强方法

针对柴油机曲轴轴承磨损故障信号特征微弱,易被噪声湮没且不同故障程度信号较难区分的特点,提出了一种基于压缩小波和局部保持投影的柴油机信息熵增强方法。利用压缩小波对信号多尺度重构减弱噪声干扰,通过局部保持映射对多尺度信号进行降维,消除冗余信息并增强信号的冲击特性,最终以时域、频域以及时频域的三种信息熵表征信号特征。仿真和实例信号表明,该方法对故障信号特征增强明显,依据信息熵值实现了曲轴磨损状态的分类识别。     

多尺度表面肌电信号的广义判别分析

提出一种融合小波特征和广义判别分析的特征解析方法,并对动作表面肌电信号的多尺度特征进行有效降维描述。首先,通过对表面肌电信号进行小波分解,提取各尺度上小波系数绝对值均值作为原始特征向量,然后用广义判别分析方法进行降维,得到低维的新特征向量,用贝叶斯分类器进行降维有效性检验。结果显示,对选用的三种小波,通过选取恰当的小波分解层数,核参数以及新特征向量的维数,对三名受试者前臂6种动作模式（内翻,外翻,握拳,展拳,上切和下切）的正确识别率可以达到97 %以上。研究表明,该方法能很好地获取表面肌电信号的多尺度主要成分及其特性。