Page 73 - IJAMD-2-3

International Journal of AI for
Materials and Design Optimization of membrane shrinkage and stability

experimental database from controlled electrospinning validation. Each model was trained to establish the non-
tests using thermoplastic polyurethane (TPU) solutions. linear mapping from processing parameters (applied
Shrinkage ratios in the rotational direction (RD) and voltage, TPU concentration, collector speed, electrode
transverse direction (TD) were obtained by measuring distance) to shrinkage ratios (%RD and %TD). Model
the linear dimensions of the membrane before and after performance was evaluated on the testing set using a
ethanol activation, where RD is parallel to the axis of set of complementary metrics, including mean squared
rotation of the roller collector and TD is perpendicular to error (MSE), root mean square error (RMSE), mean
it. The shrinkage ratio in each direction was calculated as absolute error (MAE), mean absolute percentage error
the percentage reduction in length relative to the initial (MAPE), coefficient of determination (R ), and Pearson
2
length, that is, the difference between the initial and final correlation coefficient (R). These metrics capture different
lengths divided by the initial length. The four input features aspects of predictive accuracy: MSE and RMSE emphasize
(solvent concentration, distance between electrodes, penalization of large errors, MAE reflects the average
collector speed, and applied voltage) were selected for magnitude of deviation, MAPE provides a relative error
their direct influence on jet formation, fiber deposition, assessment normalized to the scale of measurement, and
and solvent evaporation, which together determine the R , along with R, quantify the proportion of variance
2
internal prestrain distribution. The solution flow rate explained and the degree of linear correlation between
was maintained at a fixed constant value throughout all predicted and observed values. The optimal model was
experiments to avoid introducing additional variability selected based on a composite assessment of these metrics.
from unstable jet formation. Each parameter combination Priority was given to models achieving low error values
was tested at least five times under controlled conditions, (MSE, RMSE, and MAE) and high consistency indicators
revealing up to 10% variation in shrinkage ratios under (R , R). The selected model was then integrated into
2
identical settings. This variability was expressed as the the stability evaluation framework, providing a reliable
confidence interval width (CIW), the range between the predictive core for Monte Carlo-based optimization.
upper and lower bounds of the 95% confidence interval, Subsequently, the Shapley Additive Explanations
with a smaller CIW indicating higher stability. CIW was (SHAP) method 18,28-33 was applied to interpret the trained
used as the stability metric alongside mean shrinkage model and reveal the relationship between electrospinning
values. The dataset spans practical parameter ranges, parameters and shrinkage behavior. This analysis enabled
ensuring representativeness and reliability for model the identification of key process features that most
training. The details of the materials and experimental strongly influence shrinkage, providing a clear basis for
procedures are described in. The measured shrinkage understanding and optimizing critical factors in membrane
11
ratios (%RD and %TD) of each tested membrane are fabrication. Mathematically, SHAP values are derived
presented in Figure 1.
from the cooperative game theory framework, where each
2.2. Model development and interpretation feature is considered a “player” contributing to the model
prediction. For a model prediction f(x), the SHAP value for
In this study, predictive models were developed for the i feature is computed with Equation I,
th
both the shrinkage ratio and shrinkage stability. The
S
S !1
shrinkage stability metric was defined based on the CIW ||! M| | f x ( ) fx () (I)

of repeated measurements under identical processing i SN {} i M! S i {} S i {} S S

conditions, with lower values indicating higher process
robustness and consistency. To identify the most effective where M is the total number of features, S represents
predictive model for shrinkage behavior, several machine a subset of features excluding i; f (x ) is the model output
S
S
learning algorithms were assessed, including support when only features in S are included; ϕ quantifies the
i
vector regression (SVR), random forest (RF), extreme average marginal contribution of feature i over all possible
24
23
gradient boosting (XGBT), artificial neural networks feature combinations.
25
(ANN), and linear regression (LR). These models were In the context of this study, the trained regression
26
27
selected to cover kernel-based, ensemble, neural network, model f(x) maps the four process parameters (voltage, TPU
and linear paradigms, offering complementary strengths concentration, collector speed, and electrode distance)
for small-sample, non-linear, and high-variability to the predicted shrinkage ratios and stability. The
systems, and providing a balanced basis for robust model SHAP value ϕ for each parameter represents its average
selection. contribution to increasing or decreasing the predicted
i
The dataset was randomly partitioned into a training shrinkage outcome, aggregated over all permutations of
set (80%) and a testing set (20%) to ensure robust model feature inclusion. By summing all contributions and the
Volume 2 Issue 3 (2025) 67 doi: 10.36922/IJAMD025260022