This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Robust Model-Based Fault Diagnosis for Dynamic Systems

Matrix Differential Calculus with Applications in Statistics and Econometrics

This paper provides an overview and analysis of statistical process monitoring methods for fault detection, identification and reconstruction. Several fault detection indices in the literature are analyzed and unified. Fault reconstruction for both sensor and process faults is presented which extends the traditional missing value replacement method. Fault diagnosis methods that have appeared recently are reviewed. The reconstruction-based approach and the contribution-based approach are analyzed and compared with simulation and industrial examples. The complementary nature of the reconstruction- and contribution-based approaches is highlighted. An industrial example of polyester film process monitoring is given to demonstrate the power of the contribution- and reconstruction-based approaches in a hierarchical monitoring framework. Finally we demonstrate that the reconstruction-based framework provides a convenient way for fault analysis, including fault detectability, reconstructability and identifiability conditions, resolving many theoretical issues in process monitoring. Additional topics are summarized at the end of the paper for future investigation. Copyright © 2003 John Wiley & Sons, Ltd.

Statistical process monitoring: basics and beyond

Conventional approaches to chemical sensors have
traditionally made use of a “lock-and-key” design,
wherein a specific receptor is synthesized in order to
strongly and highly selectively bind the analyte of
interest.1-6 A related approach involves exploiting a
general physicochemical effect selectively toward a
single analyte, such as the use of the ionic effect in
the construction of a pH electrode. In the first
approach, selectivity is achieved through recognition
of the analyte at the receptor site, and in the second,
selectivity is achieved through the transduction
process in which the method of detection dictates
which species are sensed. Such approaches are appropriate
when a specific target compound is to be
identified in the presence of controlled backgrounds
and interferences. However, this type of approach
requires the synthesis of a separate, highly selective
sensor for each analyte to be detected. In addition,
this type of approach is not particularly useful for
analyzing, classifying, or assigning human value
judgments to the composition of complex vapor
mixtures such as perfumes, beers, foods, mixtures of
solvents, etc.

/pdf/cross-reactive-chemical-sensor-arrays-38dz1buu0b.pdf

Cross-reactive chemical sensor arrays.

The process chemometrics approach to process monitoring and fault detection

Multivariate statistical process control (MSPC) tools have been developed for monitoring a Lam 9600 TCP metal etcher at Texas Instruments. These tools are used to determine if the etch process is operating normally or if a system fault has occurred. Application of these methods is complicated because the etch process data exhibit a large amount of normal systematic variation. Variations due to faults of process concern can be relatively minor in comparison. The Lam 9600 used in this study is equipped with several sensor systems including engineering variables (e.g. pressure, gas flow rates and power), spatially resolved optical emission spectroscopy (OES) of the plasma and a radio-frequency monitoring (RFM) system to monitor the power and phase relationships of the plasma generator. A variety of analysis methods and data preprocessing techniques have been tested for their sensitivity to specific system faults. These methods have been applied to data from each of the sensor systems separately and in combination. The performance of the methods on a set of benchmark fault detection problems is presented and the strengths and weaknesses of the methods are discussed, along with the relative advantages of each of the sensor systems. Copyright © 1999 John Wiley & Sons, Ltd.

A comparison of principal component analysis, multiway principal component analysis, trilinear decomposition and parallel factor analysis for fault detection in a semiconductor etch process

A data pre-processing method is presented for multichannel ‘spectra’ from process spectrophotometers and other multichannel instruments. It may be seen as a ‘pre-whitening’ of the spectra, and serves to make the instrument ‘blind’ to certain interferants while retaining its analyte sensitivity. Thereby the instrument selectivity may be improved already prior to multivariate calibration. The result is a reduced need for process perturbation or sample spiking just to generate calibration samples that span the unwanted interferants. The method consists of shrinking the multidimensional data space of the spectra in the off-axis dimensions corresponding to the spectra of these interferants. A ‘nuisance’ covariance matrix Σ is first constructed, based on prior knowledge or estimates of the major interferants' spectra, and the scaling matrix G = Σ−1/2 is defined. The pre-processing then consists of multiplying each input spectrum by G. When these scaled spectra are analysed in conventional chemometrics software by PCA, PCR, PLSR, curve resolution, etc., the modelling becomes simpler, because it does not have to account for variations in the unwanted interferants. The obtained model parameter may finally be descaled by G−1 for graphical interpretation. The pre-processing method is illustrated by the use of prior spectroscopic knowledge to simplify the multivariate calibration of a fibre optical vis/NIR process analyser. The 48-dimensional spectral space, corresponding to the 48 instrument wavelength channels used, is shrunk in two of its dimensions, defined by the known spectra of two major interferants. Successful multivariate calibration could then be obtained, based on a very small calibration sample set. Then the paper shows the pre-whitening used for reducing the number of bilinear PLSR components in multivariate calibration models. Nuisance covariance Σ is either based on the prior knowledge of interferants' spectra or based on estimating the interferants' spectral subspace from the calibration data at hand. The relationship of the pre-processing to weighted and generalized least squares from classical statistics is outlined. Copyright © 2003 John Wiley & Sons, Ltd.

Pre-whitening of data by covariance-weighted pre-processing

http://www.eigenvector.com/Docs/robustness.pdf

Development and Benchmarking of Multivariate Statistical Process Control Tools for a Semiconductor Etch Process: Improving Robustness through Model Updating

Four hydrogen bond acidic polymers are examined as sorbent layers on acoustic wave devices for the detection of basic vapors. A polysiloxane polymer with pendant hexafluoro-2-propanol groups and polymers with hexafluorobisphenol groups linked by oligosiloxane spacers yield sensors that respond more rapidly and with greater sensitivity than fluoropolyol, a material used in previous SAW sensor studies. Sensors coated with the new materials all reach 90% of full response within 6 s of the first indication of a response. Unsupervised learning techniques applied to pattern-normalized sensor array data were used to examine the spread of vapor data in feature space when the array does or does not contain hydrogen bond acidic polymers. The radial distance in degrees between pattern-normalized data points was utilized to obtain quantifiable distances that could be compared as the number and chemical diversity of the polymers in the array were varied. The hydrogen bond acidic polymers significantly increase the dis...

Barry M. Wise

Papers

The process chemometrics approach to process monitoring and fault detection

A comparison of principal component analysis, multiway principal component analysis, trilinear decomposition and parallel factor analysis for fault detection in a semiconductor etch process

Pre-whitening of data by covariance-weighted pre-processing

Development and Benchmarking of Multivariate Statistical Process Control Tools for a Semiconductor Etch Process: Improving Robustness through Model Updating

Hydrogen Bond Acidic Polymers for Surface Acoustic Wave Vapor Sensors and Arrays