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In the past three decades, various computational frameworks for the modelling of the intracellular isotopic distribution have been proposed by different research groups. Among them the cascaded linear systems are the most popular approaches since they can transfer the nonlinear isotopomer labeling system into cascaded linear sub-systems. In this work, a novel two-step decomposition algorithm to model isotopomer labeling system is proposed. It can be utilized to decompose large metabolic networks. For convenience purpose, a new concept of isotopomer decomposition units (IDUs) is defined to distinguish the approach from others. Comparing to other cascaded linear systems, the IDU method follows a different decomposition procedure and results in another set of cascaded linear systems with different coefficients. Two variants of IDU algorithms are proposed, while one variant of them (IDU-B) has fewer number of balance equations than that of EMU balance equations. The efficiency of the IDU approach is demonstrated through two simulated examples.

The selection of informative variables in partial least squares (PLS) is important in process analytical technology (PAT) applications in the pharmaceutical industry, for example, the calibration of spectrometers. In the past, numerous approaches have been proposed to select the variables in partial least squares. In this work, a new variable selection method for PLS with the weighted variable contribution (PLS-WVC) to the first singular value of the covariance matrix for each PLS component is proposed. Several variants of PLS-WVC with different weighting factors are proposed. One variant of PLS-WVC is equivalent to the PLS with variable importance in projection (PLS-VIP). However, the variants with the correlation between X γ w γ and Y γ q γ as the weighting factor are preferred based on the results of the simulation cases studies. The proposed PLS-WVCs are integrated with interval PLS (iPLS) further to select the informative wavelength intervals for spectroscopic modelling. The utility of the proposed WVC based variable selection methods in PLS is demonstrated with the real spectral data sets.

Aimed at the determination of the number of mixtures for finite mixture models (FMMs), in this work, a new method called the penalized histogram difference criterion (PHDC) is proposed and evaluated with other criteria such as Akaike information criterion (AIC), the minimum message length (MML), the information complexity (ICOMP) and the evidence of data criterion (EDC). The new method, which calculates the penalized histogram difference between the data generated from estimated FMMs and those for modeling purpose, turns out to be better than others for data with complicate mixtures patterns. It is demonstrated in this work that the PHDC can determine the optimal number of clusters of the FMM. Furthermore, the estimated FMMs asymptotically approximate the true model. The utility of the new method is demonstrated through synthetic data sets analysis and the batch-wise comparison of citric acid fermentation processes.

Multi-batch bioprocesses data, unlike the data from other industries, are highly correlated due to the operation characteristics of the industry. In this work, pairwise Fisher discriminant analysis (FDA) is successfully utilized to reveal the similarity between two batches. In order to handle the mixture pattern for the data projected into the reduced feature subspace represented by the first several generalized eigenvectors, the finite Gaussian mixture model is adopted here to calculate the confidence region of each mixture. There are several challenges facing application engineers when estimate finite mixture models (FMMs), such as initialization of the expectation-maximization (EM) algorithm and determination of number of mixtures. In this work, an initialization method based on the uniform prior distribution assumption and a new method to determine the number of components of FMMs based on estimated density histogram are proposed. The utility of the proposed method has been demonstrated in simulation studies. Combined with the pairwise FDA, the method has been successfully applied to a large scale multi-batch bioprocess data set.

Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input-output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A,B,C,D) and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles.

In this paper, we analyze two recently proposed closed-loop subspace identification methods, referred to as innovation estimation method and whitening filter approach respectively. The similarity and difference between them are investigated in detail. It turns out that all closed-loop subspace identification methods can be classified as one-step, two-step, or multi-stage projection methods. A SISO closed-loop simulation shows that to identify a consistent model the whitening filter approach might require longer future and past horizons than the innovation estimation method.

The mean activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water) were determined experimentally in the temperature range 293.15 K to 308.15 K at four NaHCO 3 molality fractions (0.1, 0.3, 0.5, and 0.7). The measurements were made with an electrochemical cell, using a Na + glass ion-selective electrode and a Cl − solid-state ion-selective electrode. The experimental values reported by Butler and Huston are found to be higher than those calculated from the Pitzer equation using the existing parameters while the experimental results of this work are close to the calculated values, up to an NaHCO 3 molality fraction of 0.5. At the NaHCO 3 molality fraction of 0.7, the experimental data are much lower than the calculated values, implying that the interference of HCO 3 − on the Na + glass ion-selective electrode can only be neglected up to a molality fraction of NaHCO 3 of 0.5, an observation which is consistent with that of Butler and Huston.

The mean activity coefficients of NaCl in the NaCl‐NH 4HCO3‐H2O system, measured by an electrochemical cell using ion-selective electrodes, were used to calculate the mean activity coefficients of NH 4HCO3 in the system through a thermodynamic model. The measurements were made at four temperatures from 293.15 to 308.15 K up to 1.8 mol kg 1 ,a t NH 4HCO3 molality fractions of 0.2 and 0.4. Both sets of values agree with those obtained from Pitzer equation incorporated with chemical reactions. This observation supports the applicability of the existing parameters for calculating mean activity coefficients of this system. © 2001 Elsevier Science B.V. All rights reserved.

This paper outlines an object/agent based system model for the Computer Integrated Process Operation System (CIPOS). Most previous studies have focused on the Computer Aided Process Operation system (CAPO), while they are standalone and not good at communication with each other. The system model proposed in this work can solve some key integrated problems in CIPOS, which are problem integration, task integration, tools integration and personnel involvement. An instantiated system, TE_CIPOS, is implemented to give further explanation and verification of the proposed object/agent based system model and its integrating environment.