(149p) Hybrid Subspace-Rnn Based Approach for Modelling of Non-Linear Processes

Batch processes are commonly found in many domains including chemical, mechanical, biochemical, agriculture and pharmaceutical industries due to the requirement of producing high-value products. Since the productions amount is small in batch process, it is important to maintain consistency in obtaining products with excellent quality and this can be only achieved by deploying a suitable control strategy. In particular, model predictive controllers (MPC) are preferred since the underlying model aids the controller by precisely predicting the process trajectory. Naturally, the challenge is to arrive at a suitable model that is able to mimic the process reasonably well especially when the process has non-linear dynamics and possibly also multiple phases.

Non-linear machine learning based models like neural networks have become increasingly popular with the rise in computational resources due to their ability to capture any kind of trend [1,2]. However, a sizeable amount of process data is required to train the model since even a seemingly simple neural network might contain a significant number of parameters that need to be tuned. With increasing number of parameters, the immediate concern is the time taken for training the network and moreover there is always a risk of over-fitting. Hence it is desired to get away with a simpler network with fewer parameters to address these issues, and additionally, it could be easier to explain a simpler model rather than a highly complex model. There has been work done in reducing the higher dimensional model [3], especially to obtain a better functioning MPC [4,5]. The present work discusses the possible limitations of these techniques and hence proposes a hybrid recurrent neural network (RNN) modelling strategy which incorporates the rigor of subspace-based approaches that are known to be designed for robustly identifying linear models.

The proposed modeling strategy is as follows. Subspace identification algorithm is first utilized on all the training batches to obtain the state sequence for these batches. Then the state sequences from all the training batches and the corresponding input sequences are given as the output and the input to the RNN, respectively. This step essentially builds a non-linear state space model, albeit using the state trajectory identified by the subspace model. The output equation obtained from the above-mentioned subspace identification step along with the newly obtained non-linear state equation, is now ready to be used for predicting the output trajectory of the system. The results illustrate the difference in prediction performance of a model obtained by 1) pure subspace-based approach, 2) pure RNN-based approach, and 3) the proposed hybrid Subspace-RNN approach.

References:

1. Gopaluni, R. Bhushan, et al. "Modern machine learning tools for monitoring and control of industrial processes: A survey." IFAC-PapersOnLine 53.2 (2020): 218-229.

2. Wu, Z., Rincon, D., & Christofides, P. D. (2020). Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes. Journal of Process Control, 89, 74-84.

3. Prasad, V., & Bequette, B. W. (2003). Nonlinear system identification and model reduction using artificial neural networks. Computers & chemical engineering, 27(12), 1741-1754.

4. Narasingam, A., Son, S. H., & Kwon, J. S. I. (2022). Data-driven feedback stabilisation of nonlinear systems: Koopman-based model predictive control. International Journal of Control, 1-12.

5. Lee, K. S., Eom, Y., Chung, J. W., Choi, J., & Yang, D. (2000). A control-relevant model reduction technique for nonlinear systems. Computers & Chemical Engineering, 24(2-7), 309-315.