Conference Agenda

In the specialized field of chemical engineering, particularly in managing batch chemical processes, the necessity for precise and reliable monitoring and control systems is critical. These processes are episodic, traversing various operational phases under fluctuating conditions, which introduce challenges such as high dimensionality, significant batch-to-batch variability, non-linearity, and dynamic behavior. Traditional monitoring systems often fall short in adapting to the unpredictability of batch operations, highlighting the urgent need for an advanced, adaptable solution. Our study introduces a novel approach integrating a deep learning framework with transfer learning to significantly enhance the accuracy and adaptability of process monitoring in batch chemical processes. This methodology leverages Temporal Convolutional Networks (TCN) for feature extraction and Multi-Layer Perceptrons (MLP) for predicting Quality-Indicative Variables (QIV), forming the core of our innovative process monitoring system. TCNs excel in analyzing temporal data, making them perfectly suited for capturing the complex temporal dependencies and patterns characteristic of batch process operational phases. This meticulous feature extraction by TCNs provides a comprehensive understanding of process dynamics, essential for the predictive modeling that follows. The extracted features are then processed by an MLP architecture, tasked with predicting QIVs. The MLP's predictive capability is crucial for preemptive process monitoring, enabling timely intervention to rectify issues before they develop into significant problems. To ensure the model's robustness and adaptability across various operational strategies and conditions—a frequent scenario in batch processing where modifications are commonly made, our approach incorporates transfer learning. This allows the model to adjust to new or altered processes with minimal retraining by leveraging previously learned features and patterns, ensuring the fault detection system's effectiveness and reliability even as the monitored process evolves. A case study using a simulation dataset from a penicillin fermentation simulation process (IndPenSim) validates our method. This simulation offers a complex, dynamic environment that closely simulates real-world batch chemical processing challenges. The successful application of our methodology to the IndPenSim dataset underscores its ability to accurately predict QIVs and detect potential process deviations, affirming the potential of our integrated TCN and MLP framework, augmented with transfer learning, to revolutionize process monitoring and control in the chemical engineering sector. Our study's integration of TCN-based feature extraction with MLP-based QIV prediction, enhanced by strategic transfer learning, marks a significant advancement in chemical engineering. This comprehensive approach addresses the complexities of monitoring and controlling batch chemical processes and offers a model of unmatched accuracy and flexibility. By providing a solution adaptable to the dynamic nature of batch operations, our study represents a significant step towards improved operational efficiency and safety in the chemical processing industry, heralding a new era of precision and reliability in batch process monitoring and control.

Accurate dynamic modeling is essential for optimizing refinery operations, such as alkylation units, where process precision dictates performance outcomes. This study investigates multi-fidelity (MF) modeling techniques, utilizing historical measurements from a comprehensive industrial dataset. The dataset, consisting of 1085 online process measurements, serves as the foundation for both static and dynamic modeling approaches. We explore the efficacy of low-fidelity data from online composition analyzers combined with high-fidelity data from infrequent laboratory sampling to improve operational decision making.

We implement a novel correction strategy based on a Gaussian process (GP) (Rasmussen, 2004) to construct a MF model based on a low-fidelity (LF) model and high-fidelity (HF) data. We train a static LF model using Principal Component Regression, Partial Least Squares, LASSO and Stepwise regression (SR). These models demonstrate notable practicality and computational efficiency. SR emerges as the most suitable method, balancing predictive accuracy and simplicity, achieving satisfactory results in terms of normalized RMSE values for training and testing, respectively, on LF data. The dynamic models, trained using the Systems Identification Package for Python (SIPPY) (Armenise et al., 2018), effectively capture time-dependent behavior, yet require more complex structure for satisfactory prediction performance. The MF models, realized through the GP-based correction, capture the residual error between the LF model and HF data.

The MF models based on dynamic LF models outperform those based on static LF models, achieving RMSE of 0.37. For comparison HF model, trained only with HF data, reached the RMSE of 0.58. This result shows a major potential for improving decision making in complex industrial processes by a deeper understanding of the process behavior and an integrated usage of different types of data.

Optimizing large-scale partial differential algebraic equation (PDAE) systems has always been a challenging task in chemical engineering. In recent years, there has been an increasing demand for multi-objective optimization of PDAE systems with coupled constraints. Therefore, it is necessary to develop an optimization framework that can be used to solve such problems. The main challenges in optimizing PDAE systems with coupled constraints include:

1. The coupled constraints with PDAEs make it difficult to obtain feasible solutions.

2. Solving PDAEs is very expensive, and satisfactory Pareto fronts need to be obtained within a limited number of solution iterations.

3. The gradient is not available, which greatly restricts the use of gradient-based algorithms.

Pressure swing adsorption (PSA) for gas separation is a typical PDAE problem and the most common research subject. The commonly used method for solving PSA problems is Nondominated Sorting Genetic Algorithm II (NSGA-II). Although this heuristic algorithm is computationally expensive, it can obtain a good Pareto front. Researchers have used Artificial Neural Networks to solve PSA problems, which can also achieve good results, but require a large number of PDAE problem solutions to obtain training samples. Recently, Hao et al. developed a hybrid optimization framework efficiently solving unconstrained PSA optimization problems using the TSEMO algorithm and DyOS, but it cannot handle PSA problems with coupled constraints. Pini et al. used penalty function method to handle coupled constraints, but the selection of penalty function parameters becomes a new issue.

To tackle this, we propose a hybrid optimization framework, which integrates three steps. In the first step, we establish surrogate models for the constraints using Gaussian processes (GPs) and employ multi-objective Bayesian optimization to search for feasible points that satisfy the constraints. In the second step, we establish surrogate models for the objective function and constraints using GPs and utilize constrained multi-objective Bayesian optimization to search for an approximate Pareto front. In the third step, we perform a local search based on the approximate Pareto front. By employing the trust region filter method, we construct quadratic models for each constraint and objective function and refine the Pareto front to achieve local optimality. This framework demonstrates the efficiency of Bayesian optimization and the local optimality of the trust region method. A comparison with the popular evolutionary algorithm, NSGA-II, showed that this framework had a higher hypervolume of the Pareto front while halving the runtime and reducing the number of simulations by a factor of 20.

Accurate and continuous monitoring of process variables are crucial for ensuring process control and safety. Interface level is a commonly occurring variable in many processes. Typically, differential pressure cells and nucleonic profilers are used to measure interface level [1]. However, these sensors may provide inaccurate measurements due to malfunctions, potentially leading to equipment downtime and complicating process control and supervision. At worst, sensor failure can lead to disasters, like the 2005 Buncefield incident, where a stuck sensor and disabled safety switch caused a petrol tank to overfill [2]. Computer vision techniques can be utilized to overcome these issues. Images can provide valuable insights into process equipment and their dynamics. Monitoring cameras can be installed at remote locations to analyze video data from the equipment's sight glass. This serves as motivation to develop robust image-based sensors for interface-level detection.

Previously, liquid level detection has been studied using techniques such as image segmentation and edge detection. Jampana et al. (2010) proposed a simple edge detection method combined with a particle filter to estimate interface level. Liu et al. (2016) proposed a Markov random field-based image segmentation method to convert raw data into binary and utilized the vertical profile of averaged pixel values for level measurement. Vicente (2019) estimated the froth-middling interface level using static and dynamic image processing. The performance of such methods degrade when variations occur in the image quality such as due to lighting variations, occlusion, and artifacts on the sight glass. We seek to a robust method that addresses these complexities.

We propose an unsupervised approach to detect interface levels using mutual information within pixels of an image. Our method utilizes extremely local pixel features and baseline rarity between two features to detect crisp and highly localized edges. Affinity is modelled using pointwise mutual information, i.e., the log ratio of the observed joint probability to the feature pair probability in an image. Low affinity is expected across object boundaries and high affinity within similar texture regions. The overall affinity function guides pixel grouping. This is followed by spectral clustering to identify boundaries in an image. After segmentation, we applied vertical profiling, averaging pixel values for each row across all columns to detect abrupt intensity changes suggesting potential level positions in the images. The methodology's effectiveness is evaluated on a lab scale unit at IIT Madras process control lab. Various noise factors were introduced, such as lighting variations, stains, artifacts, and occlusion on the sight glass. Results from the proposed level detection are evaluated against ground truth, and demonstrate that the model has high accuracy even in the presence of various noise.

References-

1. Jampana et al. 2010. Computer vision-based interface level control in a separation cell.
2. Ansaldi et al. 2016. Incidents Triggered by Failures of Level Sensors.
3. Vicente et al. 2019. Computer vision system for froth-middlings interface level detection in the primary separation vessels.

Surrogate models are widely used for improving the tractability of process optimization (Misener and Biegler, 2023). Some commonly used surrogate models are obtained via machine learning, such as multi-layer perceptrons (MLPs), gaussian processes, and decision trees. Recently, a new class of machine learning models named Kolmogorov Arnold Networks (KANs) have been proposed (Liu et al., 2024). Broadly, KANs are similar to MLPs, yet they are based on the Kolmogorov representation theorem instead of the universal approximation theorem for MLPs. Compared to MLPs, it was reported that KANs require significantly fewer parameters to approximate a given input/output relationship (Liu et al., 2024). One of the bottlenecks preventing the embedding of MLPs into optimization formulations is that MLPs with a high number of parameters (larger width or depth) are more challenging to globally optimize (Schweidtmann and Mitsos, 2019). We investigate whether the parameter efficiency of KANs relative to MLPs can be translated to computational benefits when embedding them into optimization problems and solving them to global optimality. We apply our recently proposed mixed-integer nonlinear programming formulation of a KAN. Three case studies of varying input dimensions considering both regression (1 and 2) and classification (3) tasks are chosen for investigation from the literature: (1) optimization of auto thermal reforming process (Bugosen et al., 2024), (2) optimization of methanol synthesis process (Bampou et al., 2023), and (3) designing homogeneous solvent mixtures for pharmaceutical crystallization (Karia et al., 2024). We observe that KANs offer significant computational benefits over MLPs, particularly when globally optimizing over surrogate models with less than five inputs. For surrogate models with higher input dimensions, stronger formulations must be developed to improve global optimization of models with KANs embedded.

References

M. Bampaou, S. Haag, A.-S. Kyriakides, K. Panopoulos, P. Seferlis, 2023. Optimizing methanol synthesis combining steelworks off-gases and renewable hydrogen. Renewable and Sustainable Energy Reviews 171, 113035. URL https://www.sciencedirect.com/science/article/pii/S1364032122009169

S. Bugosen, C. D. Laird, R. B. Parker, 2024. Process Flowsheet Optimization with Surrogate and Implicit Formulations of a Gibbs Reactor. Systems and Control Transactions 3, 113 – 120, The Proceedings of the 10th International Conference on Foundations of Computer Aided Process Design (FOCAPD 2024). URL https://doi.org/10.69997/sct.148498

T. Karia, G. Chaparro, B. Chachuat, C. S. Adjiman, 2024. Classifier surrogates to ensure phase stability in optimisation-based design of solvent mixtures. Available at SSRN 4898054. URL https://dx.doi.org/10.2139/ssrn.4898054

Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljačić, T. Y. Hou, M. Tegmark, 2024. KAN: Kolmogorov-Arnold Networks. URL https://arxiv.org/abs/2404.19756

R. Misener, L. Biegler, 2023. Formulating data-driven surrogate models for process optimization. Computers & Chemical Engineering 179, 108411. URL https://www.sciencedirect.com/science/article/pii/S0098135423002818

A. M. Schweidtmann, A. Mitsos, 2019. Deterministic Global Optimization with Artificial Neural Networks Embedded. Journal of Optimization Theory and Applications 180 (3), 925–948. URL https://doi.org/10.1007/s10957-018-1396-0

Data-driven models have become a valuable asset for real-time applications in chemical and process engineering. Typical examples include feed-forward neural networks, recurrent neural networks, or networks with long short-term memory. However, these networks may struggle when many dynamic inputs are required. This is typically the case for systems with large time constants where there is a significant time period between an input and its observable consequence for outputs. Within this contribution, we propose the use of convolutional neural networks (CNNs) to counteract this problem.

CNNs are currently preferably used for image processing. They reduce the dimension of the input space, before a standard neural network is trained via so-called convolutions These convolutions are averaging operations on the inputs and outputs. Of particular interest is the filter size, i.e., the number of inputs that are considered when calculating this average, and the stride, i.e., the number of inputs the filter is moved before calculating the next average. The number of filters used determines the number of feature maps. Each filter receives its own filter weights – hence, more filters result in a larger number of trainable parameters. Too many feature maps cause overfitting and poor prediction outside the training data.

To study the potential of CNNs for dynamic models in chemical engineering, training data is generated and normalized. Afterwards, the training algorithm is started and combined with hyperparameter tuning. This hyperparameter tuning determines the optimal number of past states and controls, i.e., how much data from the past is required, filter size and stride, the number of feature maps, and the activation function for the neural network. The CNN framework is applied to two case studies: the chloralkali electrolysis (CAE, a simple almost linear example) and a capillary tube, which serves as throttling device in a heat pump (more complex with hysteresis).

For the CAE, the training and validation data is generated with a rigorous dynamic process model [1]. The dynamic model receives the current density, inlet temperature, water dilution, and inlet anolyte feed as inputs. The mass fractions of sodium ions on both the anolyte and the catholyte side are predicted outputs.

The data of the capillary process was generated within a test rig in our lab. The CNN takes inlet pressure, inlet enthalpy, and mass flow as inputs, whereas outlet pressure and enthalpy are predicted. This second case study shows hysteresis in the measured data, which makes it a more challenging application of CNNs.

To analyze the computational advantages of this network type, the results are compared to those for more classical structures, i.e., a recurrent neural network. It is found that CNNs can reduce the input space for dynamic systems and that CNNs can automatically recognize at which frequency new measurements are required to accurately describe the dynamic profiles.

References

[1] J. Weigert, C. Hoffmann, E. Esche, P. Fischer, J.-U. Repke (2021): Towards demand-side management of the chlor-alkali electrolysis: Dynamic modeling and model validation. Computers & Chemical Engineering 149, 107287. DOI: 10.1016/j.compchemeng.2021.107287.