(542a) A Deep Learning Approach for Chord Length Distribution Modeling of Two-Dimensional Crystals

Despite significant advances in process analytical technology, online monitoring of particle size distributions (PSDs) in industrial crystallizations remains a challenge. Laser backscattering using focused beam reflectance measurement (FBRM) has been widely shown to be a promising technique for online, but indirect measurement of PSDs [1]. In fact, FBRM measures chord length distribution (CLD), which does not provide a physical meaning of crystal size (e.g., [2,3]).

Towards converting CLDs to PSDs to enhance process monitoring capabilities, in this talk, we will present a deep learning approach for automatically converting simulated PSDs to CLDs which resemble the ones measured by FBRM. Deep learning and deep learning inspired methods have been recently applied to map the relationship between CLD and PSD [2,3,4], though without fully exploring their potential and limitations. In particular, we use convolutional neural networks (CNNs) [5], which are frequently used for image classification as they excel at identifying spatial patterns and relationships within data. By discretizing the PSD into finite bins, the multi-variate PSD can be effectively treated as an “image”. As a result, each PSD is converted into an image and serves as the input to the CNN, while conveying the information about the frequency, position, and spacing of each bin within the discretized distribution. We use Bayesian optimization (BO) [6] to automatically tune hyperparameters of the CNN model. Specifically, BO is used to determine the optimal number of filters to use in each of the convolutional layers, as well as the optimal CNN training parameters.

To demonstrate the proposed deep learning approach, we first use simulation data of CLDs and PSDs for needle-like crystals to train and validate a CNN model. We show that the CNN model performs with an industrially pragmatic accuracy. We then investigate the generalizability of the CNN using transfer learning techniques [7], with the goal of obtaining better predictions for “unseen” types of crystals not included in the training data, or in cases where there is a limited amount of data. In particular, we examine the transfer learning by using a CNN that is trained for needle-like crystals, the dense layer of which is then retrained using a limited dataset of platelet-like crystals, while the convolutional layers part that performs feature extraction remains “frozen”. We demonstrate the effectiveness of the CNN model augmented with transfer learning using experimental data. The proposed deep learning approach for converting PSDs to CLDs, which relies only minimally on system specific measurements, often time-consuming and expensive, and can be particularly useful for enhancing process monitoring capabilities in industrial crystallization processes, as well as laboratory studies for elucidating crystallization kinetics.

[1] Simon, L. L., Pataki, H., Marosi, G., Meemken, F., Hungerbühler, K., Baiker, A. & Chiu, M. S. (2015). Assessment of recent process analytical technology (PAT) trends: a multiauthor review. Organic Process Research & Development, 19(1), 3-62.

[2] Szilagyi, B., & Nagy, Z. K. (2018). Aspect ratio distribution and chord length distribution driven modeling of crystallization of two-dimensional crystals for real-time model-based applications. Crystal Growth & Design, 18(9), 5311-5321.

[3] Crestani, C. E., Bernardo, A., Costa, C. B. B., & Giulietti, M. (2021). An artificial neural network model applied to convert sucrose chord length distributions into particle size distributions. Powder Technology, 384, 186-194.

[4] Irizarry R., Chen A., Crawford R., Codan L., & Jöchen S. (2017). Data-driven model and model paradigm to predict 1D and 2D particle size distribution from measured chord-length distribution. Chemical Engineering Science, 164, 202-218.

[5] Bengio, Y., Goodfellow, I., & Courville, A. (2017). Deep learning (Vol. 1), Massachusetts, USA: MIT press.

[6] Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical Bayesian optimization of machine learning algorithms, arXiv preprint arXiv:1206.2944

[7] Tan, C., Sun, F., Kong, T., Zhang, W., Yang, C., & Liu, C. (2018). A survey on deep transfer learning, “International conference on artificial neural networks” (pp. 270-279). Springer, Cham.