(674d) Development of a Hybrid First Principles – Artificial Intelligence Approach for Dynamic Modeling of Complex Systems

First-principles models can provide very good prediction even for cases when there are no data at all, or data are limited in certain range of operating conditions or for cases where data collection is infeasible. However, construction of these models can be time consuming, computationally expensive, and intractable for online adaptation. Furthermore, it can be difficult, if not impossible, to develop accurate models for some complex phenomena, that are poorly understood. On the other hand, artificial intelligence (AI) models can be simpler to develop even for complex and ill-defined dynamic systems. These models are typically computationally inexpensive, and therefore can be adapted online. However, development of AI models requires large amount of data¹ so can be infeasible where data collection is expensive or collection of certain type of data is practically impossible given the current state of the measurement technology. Furthermore, AI models may not be predictive especially when they are extrapolated and/or if the data used for developing the AI models suffer from information gap. This work develops an approach where the first-principles models can be synergistically coupled with the AI models thus exploiting their key strengths.

Various types of AI modeling techniques such as neural network (NN), deep learning, expert systems and fuzzy logic have been employed for process synthesis, design and modelling². More recently, hybrid first-principle AI approaches have been proposed³ for reactive systems by using a linear dynamic model that is obtained through linearization of a non-linear dynamic model followed by a static neural network. That approach fails to account for the nonlinearity in the first-principles model and dynamics in the nonlinear AI model. Furthermore, neither the first-principles model nor the NN model is adaptive. If both the first-principles model and AI model are dynamic, nonlinear, and adaptive, it becomes considerably challenging to optimally synthesize such hybrid models with due consideration of complexity, computational expense, and accuracy.

A hybrid first principles-AI modeling technique has been developed where not only both the first principles and AI models are dynamic and nonlinear but they also interact with each other leading to a time-varying model. Instead of a series structure, we propose a hybrid series-parallel structure where, instead of propagation of information from the first- principles model through the AI model in the series structure mentioned above, the AI model learns the residual error from the first-principles model stemming from the unmodeled and/or unknown phenomena. The AI model is desired to be dynamic, nonlinear, and adaptive. While existing adaptive NN models such as adaptive bidirectional associative memory (ABAM)⁴ and transversal/recursive filters^5,6 have found applications in signal processing and communication, they are inadequate for many chemical engineering applications where learning must be accomplished with data that may be noisy, limited, and non-informative. In this work, we propose a hybrid static-dynamic NN structure that can quickly learn to equilibrate to a minimum energy state. The developed gradient descent algorithm for learning can efficiently deal with blowing and vanishing gradients by developing a modified batch normalization approach. The algorithm also quantifies optimality gaps at every iteration reflecting the tradeoff between the computational expense and accuracy. For making the learning process computationally efficient for highly parameterized system, the algorithm down selects weights using a sensitivity-based approach.

The proposed algorithm is applied to the Van de Vusse reactor model as well as to a supercritical boiler system where complex dynamics associated with reactive-diffusive processes leading to oxide scale formation in the superheater tube banks coupled with mass and heat transfer makes it a challenging system. Our work shows the tradeoff between computational expense and accuracy. It is observed that the stability and speed of the learning algorithm are critical for success of the proposed algorithm for a real-life application.

References

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