A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis

Process monitoring and fault diagnosis using profile data remains an important and challenging problem in statistical process control (SPC). Although the analysis of profile data has been extensively studied in the SPC literature, the challenges associated with monitoring and diagnosis of multichannel (multiple) nonlinear profiles are yet to be addressed. Motivated by an application in multioperation forging processes, we propose a new modeling, monitoring, and diagnosis framework for phase-I analysis of multichannel profiles. The proposed framework is developed under the assumption that different profile channels have similar structure so that we can gain strength by borrowing information from all channels. The multidimensional functional principal component analysis is incorporated into change-point models to construct monitoring statistics. Simulation results show that the proposed approach has good performance in identifying change-points in various situations compared with some existing methods. The codes for implementing the proposed procedure are available in the supplementary material.     

随机海洋环境下基于互相关函数和主成分分析的平台结构损伤辨识

为了确保海洋平台安全作业,及时辨识损伤以及进行损伤定位,海洋平台结构健康监测技术已成为学者研究关注的重要问题。针对某在役导管架平台,对平台在不同随机波浪激励下的动力响应分别进行了健康状态和损伤状态的数值模拟。在损伤辨识过程中,对结构不同位置的动力响应进行互相关分析,提取损伤敏感特征;利用主成分分析(principal component analysis,PCA)方法从复杂的数据中提取主成分;定义损伤指标并进行损伤辨识。针对传统PCA方法对某些杆件的损伤辨识精度不高等问题,提出了一种新的主成分选取方式,并在此基础上对传统PCA方法进行了改进。结果表明,改进后的PCA方法有效提高了损伤辨识的精度,可以对随机波浪条件下的结构损伤进行准确辨识。     

Estimation of Complicated Profiles in Phase I,Clustering and S‐estimation Approaches

Some quality characteristics are well defined when expressed as a function of an independent variable. This function is usually called a profile. If the functional form of the profile is known, parametric methods could be used to monitor the profile representing a process. However, some processes are complicated, and it is not suitable to use parametric models. In these cases, nonparametric methods may be used to monitor the profiles. One of the powerful nonparametric profile monitoring methods is to use wavelets. In this paper, the issue of estimating the complicated profiles in phase I is studied. In order to monitor the process using wavelets, it is required to estimate the vector of wavelet coefficients. Classical estimators are usually used to estimate the coefficients vector. These estimators should be used when the data do not contain outliers. However, it is possible that the data set is contaminated and includes some outliers. Thus, it is better to use robust estimators that are insensitive to the presence of outliers. In this paper, two robust estimators for estimating the complicated profiles using wavelets are proposed. In the first approach, the dimension of the coefficients vector is reduced by means of PCA incorporated into clustering. The second approach is based on the S‐estimation method. An extensive simulation study is performed using matlab ® software to evaluate the proposed methods and to compare the results with an existing classical method. The results show the well performance of the suggested methods in estimating the model parameters when the data set is not contaminated and in the presence of outliers. Copyright © 2016 John Wiley & Sons, Ltd.     

Evolving factor analysis,a new multivariate technique in chromatography

Overlapping peaks are a general problem in chromatography. Modern multichannel detectors such as the diode-array detector allow multivariate techniques for a computational resolution. Evolving factor analysis (EFA) is a recently developed method for a completely model-free resolution of overlapping peaks into concentration profiles and absorption spectra. EFA is successfully tested with real chromatograms. The requirements concerning the quality of the measured data are discussed and related to the scope and fields of application of EFA.     

A formulation development strategy for multivariate kinetic responses

The purpose of this paper was to evaluate a multivariate strategy for handling time-dependent kinetic data during formulation development. Dissolution profiles were evaluated by the Weibull equation, multiple linear regression (MLR), principal component analysis (PCA), alone and in combination. In addition a soft independent modeling of class analogy (SIMCA) was performed. Employing a typical kinetic model for solid formulations (here Weibull) showed difficulties with the model adaptation, resulting in increased model standard deviation and thereby failure in identifying significant variables. In general, the selection of a kinetic model is crucial for finding the significant formulation variables. Describing the dissolution profile based on MLR models of individual time points described the dissolution rates as a function of formulation variables with good precision. Establishing prediction models made it easy to evaluate effects on the entire dissolution profile. The use of PCA/MLR (PCR) reduced the influence of noise from single measurements in a kinetic profile, since they develop statistical parameters representing the profile without being dependent on a physicochemically-modeled profile. The use of PCA reduced the eight time-point variables to two latent variables (principal components), simplifying the classification of formulations and new samples as well as avoiding unwanted effects of model non-linearities between the factors and responses (model error). The group membership of new samples was demonstrated by SIMCA.     

Detecting the process changes for multivariate nonlinear profile data

In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out‐of‐control average run length (ARL₁ ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.     

The inverse medium problem for Timoshenko beams and frames: damage detection and profile reconstruction in the time-domain

We discuss a systematic methodology that leads to the reconstruction of the material profile of either single, or assemblies of one-dimensional flexural components endowed with Timoshenko-theory assumptions. The probed structures are subjected to user-specified transient excitations: we use the complete waveforms, recorded directly in the time-domain at only a few measurement stations, to drive the profile reconstruction using a partial-differential- equation-constrained optimization approach. We discuss the solution of the ensuing state, adjoint, and control problems, and the alleviation of profile multiplicity by means of either Tikhonov or total variation regularization. We report on numerical experiments using synthetic data that show satisfactory reconstruction of a variety of profiles, including smoothly and sharply varying profiles, as well as profiles exhibiting localized discontinuities. The method is well suited for imaging structures for condition assessment purposes, and can handle either diffusive or localized damage without need for a reference undamaged state.     

Shape-dependent regularization for the retrieval of atmospheric state parameter profiles

We present an adaptive regularization approach to retrieve vertical state parameter profiles from limb-sounding measurements with high accuracy. This is accomplished by introducing a dedicated regularization functional based on a reasonable assumption of the profile characteristics. The approach results in shape-dependent weighting during least-squares computations and relies on a Cholesky decomposition of a preselected L(T)L matrix. Our method is compared with established regularization functionals such as optimal estimation and Tikhonov with respect to errors and achievable height resolution. The results show an improved height resolution of the retrieved profiles together with a reduction of absolute and relative errors obtained by test-bed simulations.     

Functional Process Capability Indices for Circular Profile

Profile is a relation between one response variable and one or more explanatory variables that represent quality of a product or performance of a process. On the other hand, process capability indices are measures to help practitioners in improving the processes to satisfy the customer's expectations. Few researches are done to account for the process capability index in the areas of profile monitoring. All of these researches are focused on process capability index in simple linear profile. In all of these methods, response variables in different levels of explanatory variable are considered, and the relationship in all range of explanatory variable is neglected. In this paper, a functional method is proposed to measure process capability index of circular profiles in all range of explanatory variable. The proposed method follows the traditional definition of process capability indices. The functional method uses reference profile, functional specification limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability in each level of explanatory variable in circular profile as well as a unique value of process capability index for circular profile. The application of the proposed method is illustrated through a real case in automotive industry. Copyright © 2013 John Wiley & Sons, Ltd.     

小波信号消噪及阈值函数的一种改进方法

对于非平稳信号,小波多尺度分解是一种有效的信号去噪方法。介绍了阈值计算的Stein的无偏风险估计子(SURE)阈值、多分辨率SURE阈值和平移不变阈值,以及硬取阈值、软取阈值估计子,同时提出了一种新的小波消噪阈值选取方法,提出了相关参数的确定原则;并与硬取阈值、软取阈值进行比较,仿真结果表明,消噪效果有明显的改观。     

Digital programmable light spectrum synthesis system using a digital micromirror device

We present a digital programmable light spectrum synthesis system based on a digital micromirror device (DMD) from Texas Instruments. A DMD pattern-scanning calibration method is developed and applied to the synthesis of various infrared C-band (1530-1565 nm) spectral profiles, including a fast programmable tunable light source with a bandwidth of approximately 3.8 nm, a square profile, a sawtooth waveform, and a triangular spectrum profile. The experimental results show that the wavelength resolution of the DMD spectrum synthesis system is approximately 0.076 nm/pixel. The proposed spectrum synthesis system has a number of key advantages, including a rapid and stable performance and multichannel compatibility. The spectrum synthesis system is suitable for various applications, including pulse shaping for coherent control and harmonic generation, a tunable light source, an equalizer for erbium-doped fiber amplifiers, and a wavelength scanner.     

基于主成分分析马氏距离的支腿控制阀健康评估

支腿控制阀的性能是影响起重机支腿系统伸缩性能的重要因素之一。为了准确的评估支腿控制阀的健康性能,提出一种支腿系统的性能衰退与健康状态的评估方法,该方法基于PCA降维与马氏距离相结合的分析模型,建立不同状态下传感器信号与关键零部件的映射关系,从而达到对起重机支腿系统性能衰退量化评估的目的。该方法应用于起重机支腿控制阀的压力信号,通过对传感器信号内蕴关系及起重机在各年份提取的特征在特征空间的相关性分析,以得到量化性能评估结果。与常见的其他方法相比,该模型能够准确地反映起重机支腿系统历年来的性能衰退趋势,具有更好的鲁棒性与泛化性。     

Using independent component analysis to monitor 2‐D geometric specifications

Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.     

基于近邻元分析的滚动轴承故障诊断方法

提出基于近邻元分析（Neighborhood Component Analysis, NCA）的滚动轴承故障诊断模型。利用NCA技术对滚动轴承信号的时、频域特征向量降维,并对降维后向量分类,成功区分滚动轴承四种状态。通过Fisher判别函数定量分析目标维数对NCA降维效果影响,确定最佳特征约简目标维数。为突出NCA方法优势,将NCA与PCA两种不同降维方法进行对比。实验结果表明,NCA作为监督式降维方法,其聚类效果好于PCA。     

Random forest and rotation forest ensemble methods for classification of epileptic EEG signals based on improved 1D‐LBP feature extraction

In this study, an efficient method for extracting and selecting features of unrefined Electroencephalogram (EEG) signals according to the one‐dimensional local binary pattern (1D‐LBP) is presented. Considering that taking a correct decision on various issues particularly in the field of diagnosing diseases, such as epilepsy, is of paramount importance, a functional approach is designed to extract the optimal features of EEG signals. The proposed method is comprised of two main steps: First, extraction and selection of features is performed based on a novel improved 1D‐LBP model followed by data normalization through principal component analysis (PCA); as combining 1D‐LBP neighboring models and PCA (1D‐LBP^c2p) method. The second step includes classification using two of the best ensemble classification algorithms, that is, random forest and rotation forest. A comparative evaluation is performed between the proposed methods and 13 distinct reported approaches including uniform and non‐uniform 1D‐LBP. The results are demonstrating that the combining method presented in our approaches has superiority along with efficiency by providing higher accuracy compared to the other models and classifiers. The proposed method in this paper can be considered as a new method for feature extraction and selection of other kinds of EEG signals and data sets.     

Process Capability Analysis for NonLinear Profiles Using Depth Functions

There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, which is called profile. Such profiles frequently can be represented adequately using linear or nonlinear models. While there are several studies in monitoring profiles, there are few studies to evaluate the capability of a process with profile quality characteristic; specifically, there is no method in the literature to analyze process capability characterized by nonlinear profiles. In this paper, we propose two methods to measure the capability of these processes, based on the concept of functional depth. These methods do not have distributional assumptions and extend to functional data the Process Capability Indexes proposed by Clements 1 to measure the capability of a process characterized by a random variable. Performance of the proposed methods is evaluated through simulation studies. An example illustrates the applicability of these methods. Copyright © 2013 John Wiley & Sons, Ltd.     

超声多普勒信号降噪新方法的研究

本提出了利用离散小波框架结合软阈值的方法对超声多普勒信号进行降噪。通过对模拟多普勒信号和临床信号的降噪实验,发现利用小波框架的降噪方法可以获得比标准正交小波变换的降噪方法更好的降噪效果。     

Comparison of measurements made with two different instruments of the same atmospheric vertical profile

The validation of atmospheric remote-sensing measurements involves the comparison of vertical profiles of atmospheric constituents obtained by different instruments. This operation is a complex one because it has to take into account the measurement errors that are described by the variance-covariance matrices and the different features of the two observing systems that are described by the averaging kernels. The procedure is discussed and a method of comparison that is rigorous and does not involve degradation of the available information is developed by use of the formalism of functional spaces. The functional spaces that can be used for representation of the two profiles are reviewed, and criteria are determined for the choice of the most convenient functional space to minimize degradation of the measurements. Once the functional spaces are chosen, the components of the profiles are compared in the intersection space of these two functional spaces. If the intersection space coincides with the null vector, a pseudointersection space with useful geometrical properties can be used instead. A test of the method is made with a realistic simulation. In the test the profiles retrieved by two real instruments are simulated and quantitatively compared.     

Progress of the prompt (n, γ)-spectrometry for theAvogadro-project

The spectrometry of promptly emitted γ rays after thermal neutron capture is used for a complete, nondestructive, isotopic material analysis developed at the Physikalisch-Technische Bundesanstalt (PTB). This method is independent of the sample dimensions and its state of aggregation. Furthermore all isotopes are detected by multichannel analysis, simultaneously. Isotopic mass differences have been determined up to now with a relative uncertainty of 3×10^-10 [1]     

Robust profile alignment based on penalised-spline smoothing

In quality engineering practice, profiles that are used for quality monitoring or evaluation are sometimes unaligned due to engineering constraints. In such cases, profiles have to be registered (aligned) through shifting, time warping or coordinate alignment such that samples are comparable and easy to handle. Among the different registration algorithms, time warping, or alignment of profiles with unequal lengths, is a challenging task. In quality engineering, a typical phenomenon observed in profile alignment is that neighbours of an aligned pair have a high possibility of being similar, which means that a large jump in a warping path is less likely. In this article, a penalised-spline smoothing method is proposed for profile alignment to handle this problem. The newly proposed nonparametric alignment strategy attempts to capture the smoothness and spatially correlated features of warping shifts, and is proven more robust than existing algorithms. A dynamic programming algorithm is developed to obtain the optimal path. Both simulation studies and a real example demonstrate the effectiveness of the proposed method.