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DRSM Models

Capturing the Dynamics of a Process from Data

DRSM models

Generalization of RSM Models to Capture Dynamics

In the classic DoE methodology, the data-driven model estimated from data collected at the end of a batch process is called the RSM model.  However, if data were collected at, say, ten instants during the experiment, the estimation of ten RSM models would not reveal the dynamic evolution of the process. This is achieved by developing a Dynamic Response Surface Methodology (DRSM) model, which generalizes RSM models capturing the dynamic behavior of the process.

The form of the DRSM model when two factors are considered could be either a linear, a two-factor Interaction (2FI), or a quadratic model.

DRSM model with n factors

LASSO regression

The estimation of the parametric functions β(t) is obtained using Lasso Regression.

A follow-up test of significance ensures that the DRSM model will not be overparametrized and its confidence and prediction intervals will not be overly conservative.

DRSM model vs. time-resolved biomass data

Cross Validation

The accuracy of the model is tested through cross-validation against experiments not used in the estimation of the DRSM model

The β(t) Parametric Functions Provide Unique Insight

Plotting the time dependence of the β(t) parametric functions of the DRSM model provides unique insight to the inner dynamics of the process. The figure on the left plod the function from a DRSM model for the titer measurements in a cell based process. It is apparent that the third factor (x3 = pH) has the largest effect. Since β3(t) increases with time, the implication is that pH should be increased from its base value after day 4. However, since the β33(t) function is also important and negative, big pH  increases might have the opposite effect.  An optimal increase needs to be calculated.

A forthcoming publication will demonstrate that this results in a significant increase in titer compared to an operation where pH was kept constant through all 14 days.