Process Identification Techniques. Taylor R. Holcomb, Carl A. Rhodes, Manfred Morari. Frequency Domain Methods for Analysis and Design. M p Tuning and Synthesis. Jay H. Lee, Manfred Morari, Carlos E. Topics in Model Predictive Control. Nonlinear Moving Horizon State Estimation. Optimization in Model Predictive Control. Adaptive Model Predictive Control. Le Lann, M. The reason for this is the lack of practicable knowledge management systems 7.
A simple control loop with the related four challenges I-IV of process development and the process lifecycle. Challenge I is the generation and storage of knowledge within models. Challenge II is the process monitoring. Challenge III is the determination of optimal process conditions for different applications and IV the continuous improvement of a process by data mining tools.
In order to solve the four previously presented challenges during the process lifecycle an overview of available methods and technologies is given in the present manuscript. The focus lies on model-based methods which are characterized by the use of mathematical models. Basically, each process model can be described by an Eq. In order to show the interaction between the four separate challenges I-IV , the red line of this paper will be analogous to a simple control loop Fig. This approach allows a scientific discussion of interaction and a possible outlook with respect to the process lifecycle.
The first challenge challenge I investigated is the identification of CPPs, kPPs and the generation of process knowledge. Process development and improvement can only occur if relationships and interactions are understood.
With respect to model-based methods process relevant critical knowledge is defined as the sum of relationships and interactions, which should be considered in a process model in order to predict a target value CPP, kPP or CQA. Modelling is a tool for the identification and description of these relationships with mathematical equations verified by statistic tests.
In chapter 2. The basis of the parametrization and verification of each model are data. Especially in model development, data have a major impact on model structure and validity space. Therefore, there is a strong iteration between modelling and data collection. In the second part of chapter 2. The models and their parameters are necessary for further monitoring and control applications. Since every process is affected by certain disturbances which affect quality and productivity, monitoring is a need for biopharmaceutical production processes challenge II 2.
Monitoring is defined as the supervision of process parameters and variables, which is needed for subsequent control actions. Monitoring hereby includes the collection of information by measurements and subsequent data processing, whereas in the latter model-based methods can be applied. These methods and their application in monitoring will be discussed in chapter 2.
It will focus on methods which help to define the needed measurements, allow the combination of multiple measurements to handle process noise and measurement uncertainty and finally allow the estimation of unmeasured states. The final aim of process design is process control, discussed in chapter 2. The first topic is a clear description of the control goal within certain boundaries that are based on product, technical, physiological and economic limits. Thereby various model-based methods for open-loop and closed-loop applications will be presented.
With regard to model-based methods, methodologies for optimal and predictive control are presented. Certain disturbances that affect every process can be classified as a known but neglected and b unknown and neglected ones. Both can have a significant impact on process performance and should be continuously improved. This continuous improvement challenge IV is a key innovation motor for existing processes during their entire lifecycle. New analytical methods, measurement devices, automation, further data evaluation and others can lead to process relevant knowledge which should be taken into account.
Within chapter 2. Regarding model-based methods the focus will be on data-mining tools, which allow researchers to set up hypotheses of potential correlations. These hypotheses are a necessary input for further process model-extensions and support the overall goal of an adequate product quality and high productivity throughout the entire process lifecycle. Finally, an overall statement on further applications and perspectives of model-based methods within the biopharmaceutical process lifecycle is presented in the conclusion.
Within the process lifecycle, knowledge is defined as the ability to describe relationships between critical process parameters and critical quality or performance attributes. This knowledge needs to be documented. The trend of the last years is clearly from a transfer approach, which is based on spoken and written words, towards a model approach 8. In the context of biopharmaceutical processes, this indicates the possible usage of process models as knowledge storage systems 9.
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The setup of these process models is still challenging. Contributions presenting workflows for modeling are increasing 10 — According to good modelling practice, the single steps of modelling are always similar These steps are: i setup of a modelling project, ii setup of a model, iii analysis of the model.
In addition, the documentation of the complete modelling project should be entire and transparent. The basis of each modelling workflow is a clear definition of the model goal. This often resents a major challenge and cannot be achieved without iterations between modelers and project managers. The model goal should include the definition of target values, acceptance criteria and boundary conditions. Furthermore, the application of the model should be considered.
Each process related model should be as simple as possible and as accurate as necessary. From this dogma, it follows that a model should only include necessary critical states, model parameters and process parameters. Depending on the goal of the model, different model types are suitable. Frequently used is the classification between data driven, mechanistic and hybrid models In terms of applications of models, the classification between dynamic and static models is more appropriate. Dynamic models include differential equations, typically over time or location coordinates which allow prediction.
Static models are correlations which cannot provide time-dependent simulation results.
Hence, they are not applicable for prediction over time or location, which is commonly required in bioprocess development. Data driven, mechanistic as well as hybrid models can be both, static and dynamic. The set up and analysis of a model are iterative steps within each modelling workflow 13 , 17 , which are illustrated in Fig. For the setup of models, different approaches are reported in literature. To date, experts are required to set up models, as they strongly depend on prior knowledge.
This limited prior knowledge is a general gap for the application of all model-based methods. Only a few workflows for automated modelling are available. With regard to the process lifecycle, the focus of this review will be on these automated workflows for the setup of dynamic mechanistic models. A generic and strongly knowledge-driven approach is shown by the company Bayer AG 18 , 19 : Based on an extensive dynamic metabolic flux model in combination with a generic algorithm, the initial complex model is reduced to the most necessary parts.
The benefit of this top-down approach is the intense use of prior knowledge. The working group of King shows another approach, based on the detection of process events in combination with a model library 10 , 20 , The benefit of this approach is that less prior knowledge is necessary and the transferability on other bioprocesses is given. As one of the drawbacks of model-based methods is the validation of models and there parameters an automated workflow for the generation of substantial target-oriented mechanistic process models was developed in our working group This approach allows the generation and validation of process models with less prior knowledge and without model libraries.
Systematic overview of a model-development including interlinks between data, database and datamining, information and necessary experiments and knowledge. The analysis of each model follows the same order. Based on collected data and an assumed model structure a parameter fit is performed. With the use of optimization algorithms, the model parameters are adapted in a way, that the previous defined descriptor is optimized see chapter 2.
Typically, this is a minimization of a model deviation, which can be described by different characteristics such as the sum of square errors SSE , a normalized root mean square error NRMSE , a profile likelihood or other descriptors. A comparison of the achieved descriptor with a previously defined acceptance criterion is the first analysis of each model. If this fails, the model structure is not suitable for the present issue.
If the model passes, the model structure could be suitable to describe the relation. Therefore, typically, an identifiability analysis is performed which follows two aims: The first aim is the structural identifiability of model parameters, which is necessary for process models with the aim of monitoring and control.
If structural identifiability is not given, model parameters can compensate each other due to cross correlation. This results in multiple solutions and can lead to spurious results. There are several methods in order to evaluate structural identifiability 23 , If structural identifiability is given, practical identifiability should be investigated in order to fulfil the second goal, which is a statement about confidence intervals of model parameters based on existing data 24 , This is necessary in order to decide if parameters can be estimated with the data available.
If practical identifiability is given, the model parameters are significant.
Disturbance Estimation and Compensation Based on a Simple Observer
If not, two statements can be made: i the available data allows no determination of the model parameter or ii the model structure allows cross correlations between model parameters and is therefore not as simple as possible. In addition to the analysis of model and model parameter deviations, there is a variety of methods to characterize models with their focus on robustness.
The first check should be a global behavior test with the goal of ensuring the right implementation of a model: here the model is tested with extreme input values. Additionally, if possible, certain redundancy should be implemented in the model see chapter 2. Typical approaches are material balances, as they are typically used for yeast or microbial processes 13 , Another frequently used method is a sensitivity analysis with the aim of showing the impact of deviations of model parameters, process parameters and model inputs on model outputs 27 , The information obtained in this sensitivity analysis can be used to improve the model within the process lifecycle.
With respect to the further usage of models certain causes for deviations must be considered. Deviations can be mainly obtained from two sources. The first source of deviations is the model structure in itself. Based on the principle that a model is always a sum of assumptions, there is always an accepted model deviation with a predefined validity space. In addition, models can always only explain a part of the process variance.
Disturbances that are not considered in the model cannot be explained by it. Within the concept of process lifecycle this implies a continuous model improvement see chapter 2. This can be improved by adapting the model structure or parameters. For both additional information is necessary. It can be provided by additional data or additional hypotheses from data mining methodologies see chapter 2.
With respect to real-time application, several methodologies for model adaption are shown in chapter 2. During the process development certain experiments must be performed in order to identify CPPs and an adequate design space and to verify process models. The most widely used strategy is the standard design of experiments DoE 29 , which is given as an example in the guidelines ICH Q8 R2 2. However, the applicability of standard DoEs for bioprocesses comprising a huge number of potential CPPs is not given to the full extent.
Known relationships describing physiological interactions are usually not taken into account in standard DoEs. Therefore other model-based methods are available which are based on information. In order to verify certain process models, information is necessary. The design vector includes all possible process parameters, which are considered in the model, and sampling points t k where additional data are collected. An experiment has per definition the aim to prove, refute or confirm a hypothesis. In the case of MB-DoE the hypothesis is the process model in itself.
Telen et al. In addition, drawbacks of the single criteria are discussed and a novel multi-objective approach is investigated. This implies that MB-DoE strongly depends on the chosen information criteria. This must be transparent in order to ensure systematic and sound decisions.
However, information is strongly coupled with the identifiability analysis of modelling workflows see chapter 2. As described there, available data are necessary in order to estimate identifiable parameters. MB-DoE is the model-based method solving this issue. Several publications show the application of MB-DoE in order to reduce the experimental effort with the goal of verifying process models.
Model-Based Methods in the Biopharmaceutical Process Lifecycle
An issue for MB-DoE is the handling with uncertainties based on model and experimental deviations One possibility is the real-time adaption of the experimental design, which is called continuous model-based experimental design CMB-DoE 39 , 40 or online optimal experimental re-design 41 , This is finally a control issue and strongly related to process monitoring see chapter 2.
Process monitoring is the description of the actual state of the process system in order to detect deflections of CPPs or key process parameters in time. With regard to the definition of PAT, monitoring without a feedback for process control is only measurement Process monitoring can be seen in the context of measurement, monitoring, modeling and control M 3 C Measurements are a central part of monitoring as they provide the time resolved raw information of the ongoing process.
Measurement methodologies and devices should be simple, robust and as accurate as necessary. Besides well-established measurements such as pH, dissolved oxygen and gas analysis, a vast amount of process analyzers is available nowadays; however the development of measurement techniques is still a field for extensive research in Biotechnology 53 , In order to include process analyzers into monitoring it is not important whether measurements are performed in-line, on-line, at-line or off-line, but it is important that the data are available in time to detect deflections and to perform control actions.
After data collection, the measured raw information needs to be converted into the desired monitoring outputs. This conversion is to be performed in real-time and includes data preprocessing e. For these purposes, mathematical models and model-based methods can be used. Hereby measurements provide real-time data of the ongoing process, whereas the deployed model contains prior knowledge, technical and biological relationships and boundaries of the system This combination of measurements and mathematical models is referred to as soft-sensor software sensor.
In Fig. In addition to measurements, the designed inputs u are included as time dependent variables. The software-implemented models and estimation algorithms can hereby be of any format and structure. Principle of model based monitoring with multiple measurements. Through the reconciliation of measured model outputs with current model simulations actual process states can be estimated by considering measurement and process uncertainty. Critical to the implementation of models in monitoring is the prediction and estimation ability of the model. Apart from the determination of reliable and significant model parameters see chapter 2.
An observability analysis can assess the structure of models in order to test whether the information contained in a set of measurements is sufficient for estimating model states A simple approach is the numerical determination of initial values with a subset of known state trajectories, which fails in the unobservable and succeeds in the observable case. This can also be used to define the needed measurement accuracy and frequency in order to fulfil the monitoring goal.
To guarantee observability the methodology can also be used to define suitable measurement combinations for specific model implementations, which has exemplarily been shown by our group for P. Once the measurement scenario is defined, it needs to be interlinked with the model. Therefore, several algorithms are available, which can be summarized as observers or filters The goal of the observer is to reconstruct current states of interest by real-time collected information and the given process model.
Although the appropriate observer type is strongly dependent on the monitoring goal and the process model, the underlying principle is always similar. Under the condition of observability, which means that the provided information in y is enough to reconstruct x, the current states can be estimated.
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Additionally, the measurement errors as well as process noise are considered as weightings 61 , Using this approach, multiple measurements can be combined or unmeasured states can be reconstructed. Additionally, this methodology can be used to provide a real-time estimate based on infrequent or very noisy measurements, which can exemplarily be seen in Hereby Goffaux and Wouwer implemented different observer algorithms in a cell culture process and changed measurement noise and model uncertainty. In order to cope with non-linearities and the complexity of biological systems suitable filtering algorithms need to be implemented, such as extended and unscented Kalman and particle filters Kalman filters are especially suitable when the model is well-suited and only measurement and process noise occur.
Particle filters allow a certain degree of model uncertainty and non-Gaussian noise distributions. Simple examples of successful model based monitoring are based on mass balancing 64 , 65 , Thus elemental in- and out- fluxes of the reactor are measured. Considering the law of the conservation of mass, conversion rates can be determined. By applying multiple material balances, system redundancy can hereby increase the robustness of the methodology.
Kinetic models, which are more detailed and enable the description of cell internal behavior, are also well suited as soft-sensors. The limiting factor is often the system observability of complex kinetic models. Therefore, these models have to be simplified according to the monitoring goal. Aehle et al. For this purpose, the spectral data were transformed by partial least square regression PLS into product and substrate concentrations, which were then used as observer input.
Other approaches deal with the incorporation of delayed offline measurements for real time monitoring 75 — The additional information can help to bring the observer on the right track until the next measurement is available. In order to provide reliable and robust monitoring as a basis for control, the inclusion of all available process information and knowledge is needed. With this regard the presented model based methods enable i the determination of needed measurements to guarantee system observability ii the inclusion of process knowledge in form of a model iii possible system redundancy with multiple measurements iv the evaluation of process and measurement noise, which finally leads to v most probable estimates of the current state of interest.
Industrial processes aim to find process inputs also denoted as design vector to achieve the process goal e. Additionally, those inputs have to respect physiological and technical constraints as well as product and system rationales. Optimal means getting to the best achievable results with respect to specified might counteracting objectives and conditions. If a reliable process model exists, it can be used to determine the optimal process inputs. In addition, the process should ideally be controlled to achieve an optimal process performance.
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Table III summarizes a selection of examples for model-based optimization and control from literature. In the following, typical optimization goals, variables and optimization spaces according to literature are described. Afterwards, an overview on methods and software of how to perform optimizations is presented. Finally, following a description of aspects of model based optimal control, typical challenges are presented. Mathematically, optimization problems are typically interpreted as minimization problems of an objective function. In general, three types of optimization objectives typically arising in different stages of the process lifecycle can be distinguished.
These are optimizing i information content, ii productivity and iii robustness and reproducibility: i Especially but not only during process development optimization algorithms are used to find the parameters of a process model by minimizing the model deviation from the given data see chapter 2. In this case the objective is usually a minimal deviation from identified optimal set points during the whole process.
Examples are dissolved oxygen or pH, but also variables like metabolite concentration 81 , growth rate or a process variable related to it like the oxygen consumption rate In these cases a dynamic model is needed see chapter 2. A fact to be considered during model development is that only inputs that are included in the process model can be optimized see chapter 2.
For bioprocesses those are usually feed-rates or initial values. The optimization space is frequently constrained, as shown in Fig. Because product quality is the priority aim of pharmaceutical production processes, the design space is limited by certain product rationales e. In addition to that, reducing the size of the optimization space also can speed up the computation time which is needed for time-sensitive optimization tasks.
The optimization space is strongly dependent on the process lifecycle. New models, monitoring methods, control strategies, regulatory requirements and changed costs can lead to an expansion of the optimization space and therefore to new optimal design vectors. Louis, where he teaches and does research in process control and related fields. He can be found on the Web at joseph. We're sorry! We don't recognize your username or password.
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