Nomenclature
, , c, d, ϑ, | Constants or correction terms |
Correlation matrix for variable set z0 | |
χ2, | Cumulative chi-squared distribution function and critical value for significance α |
Projection matrix, (PCA model) | |
δij | Kronecker delta, δij = 1 for i = j and 0 for i ≠ j |
e, f, E, F | Residual vectors and matrices for input and output variables (PLS/MRPLS model) |
, | Error vector for input and variables (PLS/MRPLS model) |
f( · ), F( · ) | Probability density and cumulative distribution function |
, | Cumulative distribution and critical value of an F distribution with m1 and m2 degrees of freedom and a significance α |
g, G | Residual vector and matrix (PCA model) |
Error vector for process variables (PCA model) | |
Γ(m) | Gamma function, m > 0 |
H0,H1 | Null and alternative hypothesis |
i, j | Variable indices, e.g. zi or xj |
k, l | Sampling indices, e.g. z(k) is the kth sample of z |
Index set | |
K, and | Number of reference samples, application delay for adapted MSPC models and length of moving window |
Λ, λi | Diagonal matrix of eigenvalues, ith eigenvalue |
n | Number of retained pairs of latent variables (PCA and PLS/MRPLS models) |
nx, ny and nz | Number of input and output variables (PLS/MRPLS model), and number of process variables (PCA model) |
Cumulative Gaussian distribution function of mean and covariance matrix Szz | |
Ω, ω | General projection matrix and vector |
p, P | Loading vector and matrix for process variables (PCA model) and input variable sets (PLS/MRPLS model) |
q, , Q, | Weight and loading vectors and matrices for output variables (PLS/MRPLS model) |
Q, Qα | Residual Q statistic and its control limit for significance α |
rij | Correlation coefficient between ith and jth variable |
r, w, R, W | Loading vectors and matrices for input variables (PLS/MRPLS model) |
σ, Σ | Standard deviation and diagonal matrix storing standard deviations |
Covariance matrix of source variables and its eigendecomposition | |
t, T | Score vector and matrix for data vector of PCA model and input vector of PLS/MRPLS model |
T2, | Hotelling's T2 statistic and control limit for significance α |
u, U | Score vector and matrix for output vector (PLS model) |
Fault subspace | |
w, , W | Weight vectors and matrix for input variables (PLS/MRPLS model) |
x, X | Input vector and matrix (PLS/MRPLS model) |
Ξ and (, ) | Parameter matrices (PCA and PLS/MRPLS models) |
y, Y | Output vector and matrix (PLS/MRPLS model) |
z, Z | Data vector and matrix (PCA model) |
Parameter vector determining confidence interval for covariance matrix (Chapter 7) |
Metric conversions | |
1lb/s | 0.453 kb/s |
1scf/s | 0.0283m3/s |
1psi/psia | 6894.75732Pa |
Degrees in K | (80 × degrees in F − 32)/1.8 + 273.15 |
1 ICFM | 1.699 m3/h |
degrees in C | (80 × degrees in F − 32)/1.8 |
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