Hybrid neural network modeling of a full-scale industrial wastewater treatment process

In recent years, hybrid neural network approaches, which combine mechanistic and neural network models, have received considerable attention. These approaches are potentially very efficient for obtaining more accurate predictions of process dynamics by combining mechanistic and neural network models in such a way that the neural network model properly accounts for unknown and nonlinear parts of the mechanistic model. In this work, a full-scale coke-plant wastewater treatment process was chosen as a model system. Initially, a process data analysis was performed on the actual operational data by using principal component analysis. Next, a simplified mechanistic model and a neural network model were developed based on the specific process knowledge and the operational data of the coke-plant wastewater treatment process, respectively. Finally, the neural network was incorporated into the mechanistic model in both parallel and serial configurations. Simulation results showed that the parallel hybrid modeling approach achieved much more accurate predictions with good extrapolation properties as compared with the other modeling approaches even in the case of process upset caused by, for example, shock loading of toxic compounds. These results indicate that the parallel hybrid neural modeling approach is a useful tool for accurate and cost-effective modeling of biochemical processes, in the absence of other reasonably accurate process models.     

Combining model structure identification and hybrid modelling for photo-production process predictive simulation and optimisation

Integrating physical knowledge and machine learning is a critical aspect of developing industrially focused digital twins for monitoring, optimisation, and design of microalgal and cyanobacterial photo-production processes. However, identifying the correct model structure to quantify the complex biological mechanism poses a severe challenge for the construction of kinetic models, while the lack of data due to the time-consuming experiments greatly impedes applications of most data-driven models. This study proposes the use of an innovative hybrid modelling approach that consists of a simple kinetic model to govern the overall process dynamic trajectory and a data-driven model to estimate mismatch between the kinetic equations and the real process. An advanced automatic model structure identification strategy is adopted to simultaneously identify the most physically probable kinetic model structure and minimum number of data-driven model parameters that can accurately represent multiple data sets over a broad spectrum of process operating conditions. Through this hybrid modelling and automatic structure identification framework, a highly accurate mathematical model was constructed to simulate and optimise an algal lutein production process. Performance of this hybrid model for long-term predictive modelling, optimisation, and online self-calibration is demonstrated and thoroughly discussed, indicating its significant potential for future industrial application.     

A new generation of predictive models: The added value of hybrid models for manufacturing processes of therapeutic proteins

Due to the lack of complete understanding of metabolic networks and reaction pathways, establishing a universal mechanistic model for mammalian cell culture processes remains a challenge. Contrarily, data-driven approaches for modeling these processes lack extrapolation capabilities. Hybrid modeling is a technique that exploits the synergy between the two modeling methods. Although mammalian cell cultures are among the most relevant processes in biotechnology and indeed looks ideal for hybrid modeling, their application has only been proposed but never developed in the literature. This study provides a quantitative assessment of the improvement brought by hybrid models with respect to the state-of-the-art statistical predictive models in the context of therapeutic protein production. This is illustrated using a dataset obtained from a 3.5 L fed-batch experiment. With the goal to robustly define the process design space, hybrid models reveal a superior capability to predict the time evolution of different process variables using only the initial and process conditions in comparison to the statistical models. Hybrid models not only feature more accurate prediction results but also demonstrate better robustness and extrapolation capabilities. For the future application, this study highlights the added value of hybrid modeling for model-based process optimization and design of experiments.     

Modeling bird species distribution change in fire prone Mediterranean landscapes: incorporating species dispersal and landscape dynamics

Species distribution models (SDMs) have traditionally been founded on the assumption that species distributions are in equilibrium with environmental conditions and that these species–environment relationships can be used to estimate species responses to environmental changes. Insight into the validity of this assumption can be obtained from comparing the performance of correlative species distribution models with more complex hybrid approaches, i.e. correlative and process‐based models that explicitly include ecological processes, thereby accounting for mismatches between habitat suitability and species occupancy patterns. Here we compared the ability of correlative SDMs and hybrid models, which can accommodate non‐equilibrium situations arising from dispersal constraints, to reproduce the distribution dynamics of the ortolan bunting Emberiza hortulana in highly dynamic, early successional, fire driven Mediterranean landscapes. Whereas, habitat availability was derived from a correlative statistical SDM, occupancy was modeled using a hybrid approach combining a grid‐based, spatially‐explicit population model that explicitly included bird dispersal with the correlative model. We compared species occupancy patterns under the equilibrium assumption and different scenarios of species dispersal capabilities. To evaluate the predictive capability of the different models, we used independent species data collected in areas affected to different degree by fires. In accordance with the view that disturbance leads to a disparity between the suitable habitat and the occupancy patterns of the ortolan bunting, our results indicated that hybrid modeling approaches were superior to correlative models in predicting species spatial dynamics. Furthermore, hybrid models that incorporated short dispersal distances were more likely to reproduce the observed changes in ortolan bunting distribution patterns, suggesting that dispersal plays a key role in limiting the colonization of recently burnt areas. We conclude that SDMs used in a dynamic context can be significantly improved by using combined hybrid modeling approaches that explicitly account for interactions between key ecological constraints such as dispersal and habitat suitability that drive species response to environmental changes.     

Decision Tree-PLS (DT-PLS) algorithm for the development of process: Specific local prediction models

This work presents a novel multivariate statistical algorithm, Decision Tree-PLS (DT-PLS), to improve the prediction and understanding of dynamic processes based on local partial least square regression (PLSR) models for characteristic process groups defined based on Decision Tree (DT) analysis. The DT-PLS algorithm is successfully applied to two different cell culture data sets, one obtained from bioreactors of 3.5 L lab scale and the other obtained from the 15 ml ambr microbioreactor system. Substantial improvement in the predictive capabilities of the model can be achieved based on the localization compared to the classical PLSR approach, which is implemented in the commercially available packages. Additionally, the differences in the model parameters of the local models suggest that the governing process variables vary for the different process regimes indicating the different states of the cell under different process conditions.     

A hybrid mechanistic-empirical model for in silico mammalian cell bioprocess simulation

In cell culture processes cell growth and metabolism drive changes in the chemical environment of the culture. These environmental changes elicit reactor control actions, cell growth response, and are sensed by cell signaling pathways that influence metabolism. The interplay of these forces shapes the culture dynamics through different stages of cell cultivation and the outcome greatly affects process productivity, product quality, and robustness. Developing a systems model that describes the interactions of those major players in the cell culture system can lead to better process understanding and enhance process robustness. Here we report the construction of a hybrid mechanistic-empirical bioprocess model which integrates a mechanistic metabolic model with subcomponent models for cell growth, signaling regulation, and the bioreactor environment for in silico exploration of process scenarios. Model parameters were optimized by fitting to a dataset of cell culture manufacturing process which exhibits variability in metabolism and productivity. The model fitting process was broken into multiple steps to mitigate the substantial numerical challenges related to the first-principles model components. The optimized model captured the dynamics of metabolism and the variability of the process runs with different kinetic profiles and productivity. The variability of the process was attributed in part to the metabolic state of cell inoculum. The model was then used to identify potential mitigation strategies to reduce process variability by altering the initial process conditions as well as to explore the effect of changing CO₂ removal capacity in different bioreactor scales on process performance. By incorporating a mechanistic model of cell metabolism and appropriately fitting it to a large dataset, the hybrid model can describe the different metabolic phases in culture and the variability in manufacturing runs. This approach of employing a hybrid model has the potential to greatly facilitate process development and reactor scaling.     

Performance modeling and simulation of biochemical process sequences with interacting unit operations

Many biochemical processes consist of a sequence of operations for which optimal operating conditions (setpoints) have to be determined. If such optimization is performed for each operation separately with respect to objectives defined for each operation individually, overall process performance is likely to be suboptimal. Interactions between unit operations have to be considered, and a unique objective has to be defined for the whole process. This paper shows how a suitable optimization problem can be formulated and solved to obtain the best overall set of operating conditions for a process. A typical enzyme production process has been chosen as an example. In order to arrive at a demonstrative model for the entire sequence of unit operations, it is shown how interaction effects may be accommodated in the models. Optimal operating conditions are then determined subject to a global process objective and are shown to be different from those resulting from optimization of each separate operation. As this strategy may result in an economic benefit, it merits further research into interaction modeling and performance optimization.     

Modelling and optimization of a recombinant BHK-21 cultivation process using hybrid grey-box systems

In this work a model-based optimization study of fed-batch BHK-21 cultures expressing the human fusion glycoprotein IgG1-IL2 was performed. It was concluded that due to the complexity of the BHK metabolism it is rather difficult to develop a kinetic model with sufficient accuracy for optimization studies. Many kinetic expressions and a large number of parameters are involved resulting in a complex identification problem. For this reason, an alternative more cost-effective methodology based on hybrid grey-box models was adopted. Several model structures combining the a priori reliable first principles knowledge with black-box models were investigated using data from batch and fed-batch experiments. It has been reported in previous studies that the BHK metabolism exhibits modulation particularities when compared to other mammalian cell lines. It was concluded that these mechanisms were effectively captured by the hybrid model, this being of crucial importance for the successful optimization of the process operation. A method was proposed to monitor the risk of hybrid model unreliability and to constraint the optimization results to acceptable risk levels. From the optimization study it was concluded that the process productivity may be considerably increased if the glutamine and glucose concentrations are maintained at low levels during the growth phase and then glutamine feeding is increased.     

Simulating invasions in fragmented habitats: theoretical considerations,a simple example and some general implications

This contribution discusses two entirely different methodologies for spatially explicit modeling of population dynamics. A hybrid Petri net and a partial differential equation model are used to study the intrusion of a non-endemic species into patched habitats. A detailed comparison of both models based on an application for the Galápagos archipelago in terms of simulation results, methodology, as well as structure shows how different building blocks of ecological models can be. Results of the investigation give a detailed insight into the problem of scaling ecological models and the core question of what processes should be considered in which scale in terms of space, time or complexity and show that model structure depends on spatial configuration, and on the landscape pattern of the investigation area.     

Partly functional temporal process regression with semiparametric profile estimating functions

Summary .  Marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models. Recent work on fully functional temporal process regression (TPR) offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying. The existing estimation procedure, however, prevents successive goodness-of-fit test for covariate coefficients in comparing a sequence of nested models. This article proposes a partly functional TPR model in the line of marginal mean models. Some covariate effects are time independent while others are completely unspecified in time. This class of models is very rich, including the fully functional model and the semiparametric model as special cases. To estimate the parameters, we propose semiparametric profile estimating equations, which are solved via an iterative algorithm, starting at a consistent estimate from a fully functional model in the existing work. No smoothing is needed, in contrast to other varying-coefficient methods. The weak convergence of the resultant estimators are developed using the empirical process theory. Successive tests of time-varying effects and backward model selection procedure can then be carried out. The practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients.     

Statistical methods for panel data from a semi-Markov process, with application to HPV

Continuous-time, multistate processes can be used to represent a variety of biological processes in the public health sciences; yet the analysis of such processes is complex when they are observed only at a limited number of time points. Inference methods for such panel data have been developed for time homogeneous Markov models, but there has been little research done for other classes of processes. We develop likelihood-based methods for panel data from a semi-Markov process, where transition intensities depend on the duration of time in the current state. The proposed methods account for possible misclassification of states. To illustrate the methods, we investigate a three- and a four-state models in detail and apply the results to model the natural history of oncogenic genital human papillomavirus infections in women.     

Biocatalytic process optimization based on mechanistic modeling of cholic acid oxidation with cofactor regeneration

Reduction and oxidation of steroids in the human gut are catalyzed by hydroxysteroid dehydrogenases of microorganisms. For the production of 12-ketochenodeoxycholic acid (12-Keto-CDCA) from cholic acid the biocatalytic application of the 12α-hydroxysteroid dehydrogenase of Clostridium group P, strain C 48-50 (HSDH) is an alternative to chemical synthesis. However, due to the intensive costs the necessary cofactor (NADP(+) ) has to be regenerated. The alcohol dehydrogenase of Thermoanaerobacter ethanolicus (ADH-TE) was applied to catalyze the reduction of acetone while regenerating NADP(+) . A mechanistic kinetic model was developed for the process development of cholic acid oxidation using HSDH and ADH-TE. The process model was derived by identifying the parameters for both enzymatic models separately using progress curve measurements of batch processes over a broad range of concentrations and considering the underlying ordered bi-bi mechanism. Both independently derived kinetic models were coupled via mass balances to predict the production of 12-Keto-CDCA with HSDH and integrated cofactor regeneration with ADH-TE and acetone as co-substrate. The prediction of the derived model was suitable to describe the dynamics of the preparative 12-Keto-CDCA batch production with different initial reactant and enzyme concentrations. These datasets were used again for parameter identification. This led to a combined model which excellently described the reaction dynamics of biocatalytic batch processes over broad concentration ranges. Based on the identified process model batch process optimization was successfully performed in silico to minimize enzyme costs. By using 0.1 mM NADP(+) the HSDH concentration can be reduced to 3-4 μM and the ADH concentration to 0.4-0.6 μM to reach the maximal possible conversion of 100 mM cholic acid within 48 h. In conclusion, the identified mechanistic model offers a powerful tool for a cost-efficient process design.     

Structural identifiability of a model for the acetic acid fermentation process

Modelling has proved an essential tool for addressing research into biotechnological processes, particularly with a view to their optimization and control. Parameter estimation via optimization approaches is among the major steps in the development of biotechnology models. In fact, one of the first tasks in the development process is to determine whether the parameters concerned can be unambiguously determined and provide meaningful physical conclusions as a result. The analysis process is known as 'identifiability' and presents two different aspects: structural or theoretical identifiability and practical identifiability. While structural identifiability is concerned with model structure alone, practical identifiability takes into account both the quantity and quality of experimental data. In this work, we discuss the theoretical identifiability of a new model for the acetic acid fermentation process and review existing methods for this purpose.     

A hybrid neural learning algorithm using evolutionary learning and derivative free local search method

In this paper we investigate a hybrid model based on the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. Also we discuss different variants for hybrid models using the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. The Discrete Gradient method has the advantage of being able to jump over many local minima and find very deep local minima. However, earlier research has shown that a good starting point for the discrete gradient method can improve the quality of the solution point. Evolutionary algorithms are best suited for global optimisation problems. Nevertheless they are cursed with longer training times and often unsuitable for real world application. For optimisation problems such as weight optimisation for ANNs in real world applications the dimensions are large and time complexity is critical. Hence the idea of a hybrid model can be a suitable option. In this paper we propose different fusion strategies for hybrid models combining the evolutionary strategy with the discrete gradient method to obtain an optimal solution much quicker. Three different fusion strategies are discussed: a linear hybrid model, an iterative hybrid model and a restricted local search hybrid model. Comparative results on a range of standard datasets are provided for different fusion hybrid models.     

Kinetics for activated sludge process design: Experiment application to straw paper wastewater treatment

Degradation kinetics for the treatment of straw paper wastewater in an activated sludge process have been studied and a kinetic model has been derived for both batch and continuous experiments. These two methods are reasonably equivalent only when rather low concentrations of substrate are involved. In other cases batch and continuous results are quite different. Both models, however, show a dependence upon concentration corresponding to that which is typical of multicomponent substrate degradation. The kinetic model derived from continuous tests appears to be more suitable for designing industrial processes in that it avoids oversizing of the aeration unit.     

The relationship between count-location and stationary renewal models for the chiasma process

It is often convenient to define models for the process of chiasma formation at meiosis as stationary renewal models. However, count-location models are also useful, particularly to capture the biological requirement of at least one chiasma per chromosome. The Sturt model and truncated Poisson model are both count-location models with this feature. We show that the truncated Poisson model can also be expressed as a stationary renewal model, while the Sturt model cannot. More generally, we show that there is only one family of count-location models for the chiasma process that can also be expressed as stationary renewal models. The models in this family can exhibit either positive or negative interference.     

Multi-model statistical process monitoring and diagnosis of a sequencing batch reactor

Biological processes exhibit different behavior depending on the influent loads, temperature, microorganism activity, and so on. It has been shown that a combination of several models can provide a suitable approach to model such processes. In the present study, we developed a multiple statistical model approach for the monitoring of biological batch processes. The proposed method consists of four main components: (1) multiway principal component analysis (MPCA) to reduce the dimensionality of data and to remove collinearity; (2) multiple models with a posterior probability for modeling different operating regions; (3) local batch monitoring by the T(2)- and Q-statistics of the specific local model; and (4) a new discrimination measure (DM) to identify when the system has shifted to a new operating condition. Under this approach, local monitoring by multiple models divides the entire historical data set into separate regions, which are then modeled separately. Then, these local regions can be supervised separately, leading to more effective batch monitoring. The proposed method is applied to a pilot-scale 80-L sequencing batch reactor (SBR) for biological wastewater treatment. This SBR is characterized by nonstationary, batchwise, and multiple operation modes. The results obtained for the pilot-scale SBR indicate that the proposed method has the ability to model multiple operating conditions, to identify various operating regions, and also to determine whether the biosystem has shifted to a new operating condition. Our findings show that the local monitoring approach can give more reliable and higher resolution monitoring results than the global model.     

Enhanced process understanding and multivariate prediction of the relationship between cell culture process and monoclonal antibody quality

This work investigates the insights and understanding which can be deduced from predictive process models for the product quality of a monoclonal antibody based on designed high‐throughput cell culture experiments performed at milliliter (ambr‐15^®) scale. The investigated process conditions include various media supplements as well as pH and temperature shifts applied during the process. First, principal component analysis (PCA) is used to show the strong correlation characteristics among the product quality attributes including aggregates, fragments, charge variants, and glycans. Then, partial least square regression (PLS1 and PLS2) is applied to predict the product quality variables based on process information (one by one or simultaneously). The comparison of those two modeling techniques shows that a single (PLS2) model is capable of revealing the interrelationship of the process characteristics to the large set product quality variables. In order to show the dynamic evolution of the process predictability separate models are defined at different time points showing that several product quality attributes are mainly driven by the media composition and, hence, can be decently predicted from early on in the process, while others are strongly affected by process parameter changes during the process. Finally, by coupling the PLS2 models with a genetic algorithm first the model performance can be further improved and, most importantly, the interpretation of the large‐dimensioned process–product‐interrelationship can be significantly simplified. The generally applicable toolset presented in this case study provides a solid basis for decision making and process optimization throughout process development. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1368–1380, 2017     

Markovian and non-Markovian protein sequence evolution: aggregated Markov process models

Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models.     

Using partition designs to enhance purification process understanding

Characterization of purification processes by identifying significant input parameters and establishing predictive models is vital to developing robust processes. Current experimental design approaches restrict analysis to one process step at a time, which can severely limit the ability to identify interactions between process steps. This can be overcome by the use of partition designs which can model multiple, sequential process steps simultaneously. This paper presents the application of partition designs to a monoclonal antibody purification process. Three sequential purification steps were modeled using both traditional experimental designs and partition designs and the results compared as a proof of concept study. The partition and traditional design approaches identified the same input parameters within each process step that significantly affected the product quality output examined. The partition design also identified significant interactions between input parameters across process steps that could not be uncovered by the traditional approach. Biotechnol. Bioeng. 2010;107: 814–824. © 2010 Wiley Periodicals, Inc.