Index
adaptive partial least squares
see also moving-window principal component analysis; time-varying processes
alternative hypotheses
application delay
bootstrapping
broken stick model
canonical correlation analysis (CCA)
catalyst fluidization
central limit theorem
central moments
chemical reaction process example
correlation matrix construction
covariance matrix
fault diagnosis
temperature variables
variable reconstruction
Cholesky decomposition
column pressure
column temperature
common cause variation
see also t-score
computational efficiency
maximum regression partial least squares
moving window PCA
correlation matrix recalculation
partial least squares
computationally efficient algorithm
confidence limits
constraint NIPALS
contribution charts
distillation example
Q statistic
reliability
T2 statistic
control ellipse
construction
control limits
definition
monitoring statistics
moving window principal component analysis (MWPCA)
scatter chart
small data sets
specification limits
correlation see variable correlation
correlation coefficient
highly correlated variables
hypothesis testing
perfect correlation
uncorrelated variables
correlation matrix
chemical reaction process example
moving window PCA
computational adaptation cost
covariance
highly correlated variables
perfectly correlated variables
primary residuals
covariance matrix
adaptive PLS
distillation process example
effect of variable reconstruction
eigenvalues
partial least squares
estimation
MRPLS and
primary residuals
principal component analysis
error
t-score
reconstruction from loading vectors
t-scores
covariance structure changes
examples
detectable by standard methods
not detectable by standard methods
fault isolation
gearbox system example
monitoring statistics
Q statistic
simulated examples
T2 statistic
cross-correlation matrix
cross-covariance matrix
adaptive PLS
deflation procedure
primary residuals
cross-validation
bootstrapping
leave-one-out (LOO)
principal component analysis
R statistic
cumulative distribution function
cumulative percentage variance (CPV)
cumulative sum charts
data matrix
contribution of score vectors to
partial least squares
deflation
data reduction techniques
dual-block
partial least squares
single-block
deflation procedure
effect of error-in-variable data structure
MRPLS
distillation process example
error-in-variable model for maximum redundancy PLS
fault identification
column temperature
feed flow drops
monitoring model identification
covariance matrix
input variables
MRPLS model identification
divide and conquer algorithm
drift faults
eigendecomposition
changes in covariance structure
determination of primary residuals
effect on monitoring statistics
error-in-variable estimation
maximum likelihood PCA
moving window PCA
NIPALS algorithm
recursive PCA
simulation example
eigenvalue-one-rule
eigenvalues
changes in covariance structure and
chemical process example
improved residuals
maximum likelihood PCA
primary residuals
principal component analysis
equality of discarded
stopping rules
eigenvectors
control ellipse
primary residuals
covariance matrix for change in
see also loading vectors
embedded error function
error covariance matrix
error-in-variable data structure
distillation process example
known error covariance matrices
examples
fluid catalytic cracking see fluid catalytic cracking
gearbox system see gearbox system example
simulation see simulation examples
F-distribution
fault detection
gearbox
improved residuals
ramp changes
residuals-based tests
simulation example
scatter diagrams
fault diagnosis
chemical plant example
distillation process example
using primary residuals
fault direction
fault identification
improved residuals
variable reconstruction
fault isolation
primary residuals
feed flow
first order perturbation
floating point operations
Fluid Catalytic Cracking (FCC)
input sequences
loss in combustion air blower
process description
process variables
simulated examples
fluidization (catalyst)
Frobenius norm
furnace process
Gaussian distribution
gearbox system example
monitoring model
process description
schematic
tooth breakage
gradient descent
Gram-Schmidt orthogonalization
H-principle
Hotelling T2 statistic
changes in covariance structure undetectable by
chemical process example
contribution charts
distillation process example
effect of covariance structure changes
effect of variable reconstruction
F-distribution
improved residuals
maximum likelihood PCA
MLPCA
moving window PCA
partial least squares model
primary residuals
ramp error detection
small data sets
hypothesis testing
correlated variables
distillation example
small data sets
Type I error
Type II error
see also T2 statistic, Q statistic
ideal process
improved residuals
covariance matrix
change in eigenvectors
change in score variables
for eigenvalues
gearbox system example
sensitivity to sensor bias
indicator function
inverse iteration
Isserlis theorem
Kernel algorithm
Kronecker delta
Lanczos tridiagonalization
latent variables (LV)
adaptive PLS
distillation process example
estimation
see also stopping rules
retention stopping rules
least median of squares (LMS)
least trimmed squares (LTS)
leave-one-out (LOO) cross-validation
Liapounoff theorem
loading matrix
loading plots
loading vectors
computation
error-in-variable data structure
distillation process example
producing score variables of maximum variance
reconstruction of covariance matrix
small data sets
see also p-loading; q-loading
M-estimator
matrix deflation see deflation procedure
maximum likelihood principal component analysis (MLPCA)
eigenvectors
examples
Hotelling T2 statistic
model and residual subspace estimate properties
PLS error-in-variable
simulated examples
application to data
stopping rules
unknown error covariance matrix
maximum redundancy partial least squares (MRPLS)
algorithm
computationally efficient algorithm
distillation example
error-in-variable model
process variables
error-in-variable data structure
geometric analysis of data structure
model identification
model properties
deflation procedure
relationship between weight vectors for input variables
t-and u-score vector orthogonality
monitoring statistics
simultaneous algorithm for LV sets
maximum redundancy PLS (MRPLS) objective function simplification
mean value
trends
means squared error
measurement bias
minimum covariance distance estimator (MCD)
Minimum Description Length
minimum volume estimator (MVE)
model estimation see deflation procedure
model subspace
estimation
estimate properties
simulation example
monitoring statistics
covariance structure change sensitivity
maximum regression PLS (MRPLS)
moving-window PCA
partial least squares (PLS)
primary residuals
principal component analysis (PCA)
Monte Carlo simulations
moving window partial least squares (MWPLS)
moving window principal component analysis (MWPCA)
application delay
control limits
correlation matrix
downdating
updating
eigendecomposition
example
model determination
simulated example
fluid catalytic cracking
simulation example
source signal determination
window length
multivariate trimming (MVT)
NIPALS
see also constraint NIPALS
non-negative quadratic monitoring statistics see monitoring statistics
null hypothesis
ordinary least squares (OLS)
compared to PLS
parameter estimation
regression parameters
outliers
trimming
p-loading vectors
orthogonality to w-weight vectors
orthonormality
see also loading vectors
parallel analysis
parameter estimation
least median of squares (LMS)
M-estimator
ordinary least squares
partial least squares
distillation process example
projection pursuit
robust estimation of moments
small sample sets
trimming
Pareto Maxim
partial least squares (PLS)
adaptive
model adaptation
algorithm overview
compared to ordinary least squares (OLS)
computational efficiency
contrasted with maximum redundancy PLS
core algorithm
data structure assumptions
deflation procedure
distillation process example
error-in-variable structure
loading vectors
maximum redundancy
model identification
model properties
matrix-vector product properties
regression coefficient calculation
relationship between q-weight and q-loading vectors
t-and u-score vector orthogonality
t-score vector calculation from data matrix
t-score vector orthogonality
w-weight to p-loading vector orthogonality
monitoring statistics
non-negative quadratic process monitoring
partial least squares
parameter estimation
parameter estimation bias and variance
regression model accuracy
score variables
simulation example
input variable set
latent variables
PLS model determination
weight and loading matrices
simulation examples, limitations
stopping rules
bootstrapping
variable sets
weight vectors
see also maximum likelihood partial least squares
Powerforming
prediction sum of squares (PRESS)
predictor variable sets
primary residuals
covariance
covariance matrix
change in score values
eigenvectors non-orthogonal to model
degrees of freedom
distribution function
eigenvectors
fault isolation
gearbox example
residual subspace
sensitivity
simulation examples
statistical properties
variance
principal component analysis (PCA)
algorithm summary
chemical process example
computation
core algorithm
scaling matrix
covariance matrix
data correlation matrix
data structure assumptions
eigendecomposition of covariance matrix
Fluid Catalytic Cracking example
geometric analysis of data structure
limitations regarding time-varying processes
loading vectors
model identification
model properties
asymptotic distribution of t-score
covariance matrix exhaustion
data matrix exhaustion
orthogonality of t-score vectors
orthonormality of p-loading vectors
t-score vector computation
non-negative quadratic process monitoring
residual subspace, primary residuals
residuals-based tests
robust parameter estimation
simulated examples
simulation example
stopping rules
cross-validation based
eigenvalue-based
information-based
time-varying processes
see also moving window principal component analysis, maximum likelihood principal component analysis
probability density function
improved residuals
perfectly correlated variables
uncorrelated variables
process monitoring
see also monitoring statistics
process types
projection pursuit
projection-based adaptation
promising process
propane
Q statistic
changes in covariance structure undetectable by
contribution charts
effect of variable reconstruction
maximum likelihood PCA
moving window PCA
primary residuals
small data sets
q-loading
see also loading vectors
q-weight
maximum redundancy PLS
quadratic monitoring statistics see monitoring statistics
R statistic
r-weight vectors
ramp error detection
random variables
cumulative distribution function
mean and variance
probability density function
Shewhart charts
trends
rank one modification
recursive principal component analysis (RPCA)
regression coefficient
residual percentage variance test
residual subspace
effect of variable reconstruction
estimation
estimate properties
simulation examples
fault detection based on
maximum likelihood PCA
primary residuals
sensitivity
statistical properties
see also improved residuals; primary residuals
residual sum of squares (RSS)
RSS
sample generation
scaling matrix
scatter diagram
weaknesses
scatter diagrams
distillation example
score variables
weaknesses
see also t-score, u-score
score vectors, contribution to data matrix
SCREE test
sensor bias
sensitivity of improved residuals
Shewhart charts
significance
SIMPLS algorithm
simulation examples
adaptive MSPC
covariance structure changes
Fluid Catalytic Cracking
PCA application
maximum likelihood PCA
model and residual subspace estimation
partial least squares (PLS)
weaknesses of conventional MSPC
singular value decomposition (SVD)
source signal adaptation
source signal determination
time variant
special cause variation
specification limits
squared prediction error see Q statistic
Stahel-Donoho location estimator
standard deviation
statistical fingerprinting
statistical local approach
statistical process control (SPC)
basic principles
history
motivations for use of multivariate techniques
overview
step faults
stochastic variables see random variables
stopping rules
maximum likelihood PCA (MLPCA)
partial least squares (PLS)
adaptive
analysis of variance
bootstrapping
cross-validation
principal component analysis (PCA)
cross-validation based
eigenvalue-based
information-based
Student t-score see t-score
t-score
asymptotic distribution of variables
distillation process example ,
error-in-variable data structure
maximum regression PLS
MRPLS models
partial least squares models
asymptotic distribution
computation
orthogonality
orthogonality with u-score
vector computation
vector orthogonality
see also score variables
t’-score
distillation process example,
see also score variables
time-varying processes
application delays
minimum window length
partial least squares methods
source signal determination
tooth breakage
total quality management (TQM)
treacherous process
trends in mean value
see also drift faults
trimming
turbulent process
Type I errors
Type II errors
u-score
maximum regression PLS
orthogonality with t-score vectors
see also score variables
variable correlation
perfect correlation
uncorrelated variables
see also correlation coefficient; correlation matrix
variable reconstruction
chemical process example
influence on model plane
influence on residual subspace
projection-based
geometric analysis
limitations
linear dependency of projection residuals
maximum dimension of fault subspace
optimality
reconstruction subspace
regression formulation
single sample
regression-based
variable reconstruction error
variance
primary residuals
trends
variance of reconstruction error (VRE)
Velicer Partial Correlation Correction (VPC)
vibration
W statistic
w-weight
weight vectors
Wishart distribution
