Design Of Dynamic Experiments Research Articles

Efficient optimization of time-varying inputs in a fed-batch cell culture process using design of dynamic experiments.

In cell culture process development, we rely largely on an iterative, one-factor-at-a-time procedure based on experiments that explore a limited process space. Design of experiments (DoE) addresses this issue by allowing us to analyze the effects of process inputs on process responses systematically and efficiently. However, DoE cannot be applied directly to study time-varying process inputs unless an impractically large number of bioreactors is used. Here, we adopt the methodology of design of dynamic experiments (DoDE) and incorporate dynamic feeding profiles efficiently in late-stage process development of the manufacture of therapeutic monoclonal antibodies. We found that, for the specific cell line used in this article, (1) not only can we estimate the effect of nutrient feed amount on various product attributes, but we can also estimate the effect, develop a statistical model, and use the model to optimize the slope of time-trended feed rates; (2) in addition to the slope, higher-order dynamic characteristics of time-trended feed rates can be incorporated in the design but do not have any significant effect on the responses we measured. Based on the DoDE data, we developed a statistical model and used the model to optimize several process conditions. Our effort resulted in a tangible improvement in productivity-compared with the baseline process without dynamic feeding, this optimized process in a 200-L batch achieved a 27% increase in titer and > 92% viability. We anticipate our application of DoDE to be a starting point for more efficient workflows to optimize dynamic process conditions in process development.

Using the design of dynamic experiments to optimize photosynthetic cyanophycin production by Synechocystis sp.

The production of cyanophycin by photosynthetic microorganisms, as a high-value bio-based compound, is getting increasing interest. The aim of this work is to maximize the production of this compound by the cyanobacterium Synechocystis sp. in semi-batch cultivation systems, by applying a data-driven modeling approach based on the Design of Dynamic Experiments (DoDE) and Response Surface Model (RSM) methodologies. A first set of experiments, carried out inside an initially defined domain, was used to find a preliminary RSM model describing cyanophycin concentration as a function of incident light intensity profile, temperature, and phosphorus supply profile. The model was then improved, according to an evolutionary optimization approach, by carrying out additional experiments in a modified domain, exploiting information derived by the initial model. The updated model was used to identify the optimal operating conditions resulting in maximum cyanophycin concentration at the end of the batch. The cyanophycin concentration found experimentally (228.2 ± 20.0 mg/L) in these conditions fell within the confidence interval of the model prediction. Remarkably, this experimentally obtained value represents a significant (about 20 %) increase in the cyanophycin production with respect to the highest value found in the experiments before the optimization step (184.3 ± 0.8 mg/L).

Experimental Test of the Design of Dynamic Experiments and Dynamic Response Surface Methodologies: Growth of a Photosynthetic Microorganism

The design of dynamic experiments (DoDE) and dynamic response surface methodology (DRSM) have been recently applied to accurately model and optimize several types of industrial and pharmaceutical processes. In this work, we apply the above methodologies to the growth of a photosynthetic microorganism, a bioprocess characterized by a high degree of complexity. Compared to conventional bioprocesses involving heterotrophic bacteria, the high adaptability of photosynthetic microorganisms to environmental conditions and the complexity of understanding the effect of light intensity on biomass growth make the development of a thorough knowledge-driven model a difficult task. Based on a predefined experimental design taking into account the effect of light, temperature, and nutrient feeding profiles, we performed a set of dynamic biomass growth experiments, from which we estimated different DRSM models. The best one was then used to predict the behavior of a new set of experiments. We show that through such a model, valuable insights into the process can be gained and that the model is fairly reliable in predicting growth behavior under different experimental conditions.

Mass and energy balance-assisted data-driven modeling and optimization of batch processes: The case of a batch polymerization process

In this paper, we use two data-driven modeling methodologies that we have been recently developed: the design of dynamic experiments (DoDE) (Georgakis 2013) and the dynamic response surface methodology (DRSM) (Klebanov and Georgakis 2016, Wang and Georgakis 2017). DoDE allows time-varying inputs, and DRSM models time-varying process outputs. We combine the above two data-driven tools and partial process knowledge to develop an integrated data and knowledge-driven model. We use this hybrid model to improve process productivity. The material and energy balances we use here lack a quantitative description of all rate phenomena. The optimization of the process is evolutionary and thus done in cycles. After three cycles, we have increased the productivity of the process, defined as the ratio of polymer produced over the batch duration, by 39.6% compared to the base case productivity. We also show how this productivity increase could have been as high as 81%.

Data-Driven Process Modeling and Optimization Aided by Material and Energy Balances: The Case of a Batch Polymerization Process

Abstract Our group recently defined two novel data-driven modeling methodologies: The Design of Dynamic Experiments (DoDE) and the Dynamic Response Surface Methodology (DRSM). These two methods enable the quick and efficient data-driven modeling of processes with a partial understanding of their inner workings. They generalize the Design of Experiments (DoE) and the Response Surfaces Methodology (RSM). DoDE allows time-varying inputs, and DRSM models time-varying process outputs. In this paper, we combine the above data-driven tools and partial knowledge of a batch polymerization process to develop an integrated data and knowledge-driven model. The optimization objective is to minimize the process’s batch time while producing the same product quality, increasing productivity. The process knowledge incorporated into the model consists of material and energy balances in which we lack a quantitative description of the rate phenomena, such as reaction or mass/heat transfer rates. The optimization is evolutionary; initially, targeting small improvements through constrained extrapolations around the normal operating conditions. Then, we build the first models and use such models to design the next set of experiments that meet our specifications. This cycle of running experiments and updating the models is repeated until an optimum is reached. After three cycles, we succeeded in reducing the batch time by 26%, while producing acceptable product.

Dynamic Response Surface Models: A Data-Driven Approach for the Analysis of Time-Varying Process Outputs

In a recent publication (Ind. Eng. Chem. Res. 2013, 52 (35), 12369) we generalized the classic design of experiments (DoE) methodology by introducing the Design of Dynamic Experiments (DoDE), allowing for the systematic design of experiments involving time-varying inputs. Here, we expand the response surface model (RSM) methodology, used in DoE and DoDE problems, so that it describes the time-evolution of the process, not just the results at the end of the experiment. We apply this generalized type of RSM model, to be denoted by DRSM, to three example processes; a nonisothermal batch reactor with a simple reaction, an isothermal semibatch reactor with several reactions, and a semibatch penicillin fermentation process. Using a limited number of online measurements at prespecified equidistant time instants, we are able to quickly and accurately represent the time evolution of the process output through these simple interpolative data-driven models. The ever-increasing availability of time-resolved measureme...

Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes

A new methodology for the design of experiments is presented that provides a way to optimize the operation of a variety of batch and semibatch or fed-batch processes without the use of a knowledge-driven or fundamental model describing the inner workings of the process, when one or more time-varying decision variables must be selected. The types of processes that can benefit from this approach include those producing specialty chemical, pharmaceutical, or food products whose production rate is not high enough to justify the development of a knowledge-driven model. The approach generalizes the classical and widely used Design of Experiments (DoE), which considers only decision variables, or factors, which are constant with time. The new approach, called the Design of Dynamic Experiments (DoDE), systematically designs experiments that explore a considerable number of dynamic signatures, called dynamic subfactors (DSFs), in the time dependency of the unknown decision variables or factors. Two example process...

On the Performance of DoDE in a class of in silico Fermentation Processes and the Impact of the Input Domain

In a recent publication (Georgakis, 2013), it was shown that a data-driven model obtained through the proposed Design of Dynamic Experiments (DoDE) was able to accurately optimize a penicillin fermentation process without the use a knowledge-driven model. The resulting optimal operation, just after a set of experiments, is almost identical to the one obtained in (Riascos and Pinto, 2004) using the detailed model of the process by B&R (Bajpai and Reuss, 1980). Here we examine in silico whether a similar number of DoDE experiments will result in an equally accurate estimation of the optimal process operation of 32 other fermentation processes. This set of fermentation processes is defined by significantly varying the values of 10 key parameters of the initial penicillin model. Only between 3 and 7 of the 32 fermentations require additional experiments to obtain a satisfactory process optimization through a more accurate data-driven model. Furthermore, we examine two different time-evolving domains, A and B, within which the substrate in-flow is varied. One of them, domain A, forces the substrate inflow to be zero at the end of the batch. Domain B removes this constraint but requires more experiments. The obtained optimal operation in domain B is always better than that in domain A; sometimes by as much as 280%. This implies that limiting the number of experiments might also limit optimization gains

Data-driven, using design of dynamic experiments, versus model-driven optimization of batch crystallization processes

A new data-driven experimental design methodology, design of dynamic experiments (DoDE), is proposed as a means of developing a response surface model that can be used to effectively optimize batch crystallization processes. This data-driven approach is especially useful for complex processes for which it is difficult or impossible to develop a knowledge-driven model in a timely fashion for the optimization of an industrial process. Design of dynamic experiments [1] generalizes the formulation of time-invariant design variables from design of experiments, allowing for consideration of time-variant design variables in the experimental design. When combined with response surface modeling and an appropriate optimization algorithm, a data-driven optimization methodology is produced, which we call DoDE optimization. The method is used here to determine the optimal cooling rate profile, which integrates to give the optimum temperature profile, for a batch crystallization process. To examine the effectiveness of the DoDE optimization method, the data-driven optimum temperature profile is compared to the optimum temperature profile obtained using a model-based optimization technique for the potassium nitrate–water batch crystallization model developed by Miller and Rawlings [2]. The temperature profiles calculated using DoDE optimization yield response values within a few percent of the true model-based optimum values. A sensitivity analysis is performed on one case study to evaluate the distribution of the response variable from each method in the presence of parameter and initial seed distribution variability. It is demonstrated that there is partial overlap in the distributions when only variability in the model parameters is evaluated and there is substantial overlap when variability is included in both the model and initial seed distribution parameters. From this evidence, it can be concluded that the DoDE optimization method has the potential to be a useful data-driven optimization tool for batch crystallization processes where a first-principles model is not available or cannot be developed due to time and/or cost constraints.

Dynamic Experiment Design Regularization Approach to Adaptive Imaging with Array Radar/SAR Sensor Systems

We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the “model-free” variational analysis (VA)-based image enhancement approach and the “model-based” descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations.

Dynamic Optimization of a Batch Pharmaceutical Reaction using the Design of Dynamic Experiments (DoDE): the Case of an Asymmetric Catalytic Hydrogenation Reaction

The present research work aims to demonstrate the effectiveness of the new methodology of Design of Dynamic Experiments (DoDE) in optimizing an important pharmaceutical reaction. An easily developed response surface model (RSM) is used instead of a hard to develop knowledge-driven process model. The DoDE approach allows the experimenter to introduce dynamic factors in the design, which during the RSM optimization are treated as all the other factors, simplifying the analysis significantly, leading to the rapid optimization of batch processes with respect to time-varying decision variables. The DoDE approach enables the discovery of optimal time-variant operating conditions that are better than the optimal time-invariant conditions discovered by the classical Design of Experiments (DoE) approach. In the present case of the asymmetric catalytic hydrogenation, 24 experiments are conducted for the DoDE approach and the best run results in a 45% improvement comparing to the best run of 17 runs of the DoE approach. This is achieved by applying a decreasing temperature profile during the batch reaction. Optimization of the economic performance index of the process through the respective response surface models defines an optimum operation. The DoDE optimum operation is better than the respective one through the DoE. The DoDE advantage increases as the required quality level for the final product is higher. For the medium quality, the DoDE approach results in an improvement of 30% over the DoE one.

A Model-Free Methodology for the Optimization of Batch Processes: Design of Dynamic Experiments

The new methodology presented provides a way to optimize the operation of a variety of batch processes (chemical, pharmaceutical, food processing, etc.) especially when at least one time-varying operating decision function needs to be selected. This methodology calculates the optimal operation without the use of an a priori model that describes in some accuracy the internal process characteristics. The approach generalizes the classical and widely used Design of Experiments (DoE), which is limited in its consideration of decision variables that are constant with time. The new approach, called the Design of Dynamic Experiments (DoDE), systematically designs experiments that explore a considerable number of dynamic signatures in the time variation of the unknown decision function(s). Constrained optimization of the interpolated response surface model, calculated from the performance of the experiments, leads to the selection of the optimal operating conditions. Two examples demonstrate the powerful utility of the method. The first examines a simple reversible reaction in a batch reactor, where the time-dependant reactor temperature is the decision function. The second example examines the optimization of a penicillin fermentation process, where the feeding profile of the substrate is the decision variable. In both cases, a finite number of experiments (4 or 16, respectively) lead to the very quick and efficient optimization of the process.