So

Thickness of the gas-side boundary layer

(m)

Sl

Thickness of the liquid-side boundary layer

(m)

t%Xj Elasticity of reaction rate i with respect to concentration of metabolite Xj e Cell-mass specific production rate of P (l/h)

e Measurement error tj Cell-mass specific production rate of Pj (l/h)

Ejo Characteristic of a particular strain in Eq. 2.20 (l/h)

A = (A, B, C) The set of probabilities in an HMM Afc(r) Log-likelihood ratio

Aij (i, j)th element of the relative gain array (RGA), defined in Eq. 7.113

¡JL Specific cell growth rate (l/h)

/inet Net specific cell growth rate, defined in Eq. 2.10 (l/h)

fia, fis, fih Specific growth rates of apical, subapical, and hyphal cells, respectively, defined in Eq. 2.25 (l/h)

fj,0 Characteristic of a particular strain in Eq. 2.17 (l/h)

Vi Reaction rate of the ith reaction step lü Forcing frequency in forced periodic operation (cycles/h)

u>i, a>2 Forcing frequencies for U\ and U2, respectively, in forced periodic operation (cycles/h)

$ Wavelet scaling function

7Tj Classes of events such as distinct operation modes i — 1, • • • ,g

Mother wavelet ip{X) Functions in Eq. 2.17 and Table 2.1 ipj(Pj) Functions in Eq. 2.17 and Table 2.1

^fe(-Pfc) Functions in the expression for ej in Eq. 2.20 and Table 2.2 p Culture density (g/L)

pb Density of biomass (g/L) Pij (i, j)th element of II(u/), section 7.3

a Cell-mass specific uptake rate of limiting substrate S (Section

<Ji Cell-mass specific uptake rate of nutrient Ni (l/h)

<7j Standard deviation of summed mean contributions over time instances

(Tj jth singular value of a matrix fjfc Standard deviation of summed mean contributions over all process variables t Cycle period in forced periodic operation (h)

6 Model parameters vector

Subscripts abiotic Abiotic phase biotic Biotic phase

/ At the end of bioreactor operation (t — tj) F Bioreactor feed, gas feed or liquid feed as appropriate J Partial derivative with respect to J (Sections 7.2.5 and 7.3.2) m, max Maximum values of a variable min Minimum value of a variable r Reference state/value sp Set point syn, util Synthesis and utilization, respectively (Section 2.6.3)

0, 0 Initial conditions

0, 0 Steady-state conditions (Section 7.3)

Reciprocal of a scalar or inverse of a matrix

Superscripts c Complex conjugate T Transpose of a matrix

* Optimal trajectory/value or desired trajectory/value Abbreviations adj A Adjoint of a matrix A, Eqs. 7.119 and 7.120

AHPCA Adaptive hierarchical principal component analysis

AIC Akaike information criteria

ANN Artificial neural network

AO Additive outlier

AR Auto regressive

ARL Average run length

ARMA Auto regressive moving average

ARMAX Auto regressive moving average with exogenous inputs ARX Auto regressive model with exogenous inputs BJ Box-Jenkins

CCC Concentration control coefficient

CPCA Consensus principal components analysis

CUMPRESS Cumulative prediction sum of squares

CUSUM Cumulative sum

CV Canonical variate

CVA Canonical variates analysis

CVSS Canonical variate state space (models)

d.f. Degrees of freedom diag A Diagonal matrix containing the diagonal elements of a matrix A

DMC Dynamic-matrix control

DOE Design of experiments

DTW Dynamic time warping

ECM Expected cost of misclassification

EKF Extended Kalman filter

EWMA Exponentially weighted moving average

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