(676g) Development of Steady-State and Dynamic Mass-Energy Constrained Neural Network Models Using Noisy Temporal Data for Dynamic Optimization of Distributed Chemical Systems

First-principles models can provide very good prediction even for cases when there are no or limited data or for cases where data collection is infeasible. However, constructing accurate first-principles models for dynamic optimization of complex nonlinear dynamic systems may be computationally expensive, time consuming, and intractable for online adaptation. On the contrary, artificial intelligence (AI) or black-box models are relatively easier to develop, simulate, and adapt online¹. Although various types of AI modeling techniques have been widely employed for process synthesis, design and modeling², development of such models requires large amount of data so can be infeasible where data acquisition is prohibitive or collection of certain type of data is practically impossible given the current state of the measurement technology. Moreover, the measurement data available for training the neural networks (NNs) may not necessarily satisfy mass and energy balances and other physics of the system. If these constraints are not satisfied during machine learning and during simulation (i.e., inverse and forward problems), model predictions can violate the conservation laws and therefore optimization by using such models may not be meaningful. This work develops algorithms for NNs where mass and energy constraints are exactly satisfied during inverse and forward problems while modeling distributed process systems, even though the corresponding training data violate the same.

Recent years have seen the development of a relatively new branch of supervised data-driven modeling of nonlinear systems known as physics-informed neural networks³ (PINNs) where typically desired physics constraints are imposed by penalizing the objective function in typical NN training algorithms, thus serving as a soft constraint only during the inverse problem. But in most chemical engineering applications, it is desired that certain mathematical relationships are exactly satisfied, which cannot be guaranteed by these PINNs⁴. Moreover, most hybrid mechanistic approaches focused on exactly conserving mass and/or energy of a system require rigorous understanding of the process for formulating the physics-based differential or algebraic constraints and hence become system-specific⁵. In this work, a novel class of network models in proposed, namely the Mass-Energy Constrained Neural Networks (MECNNs), that exactly satisfies the mass and energy constraints, expressed in terms of the species molar/atom or enthalpy balance equations and posed as equality constraints in the nonlinear parameter estimation problem. The developed algorithms for both inverse and forward problems provide sufficient flexibility to model any distributed dynamic nonlinear chemical process system involving addition / removal of mass and/or heat as well as transformation of energy from one form to another. The proposed approaches can also accommodate nonlinear transformation for constraint satisfaction, even when there is no close-form equation available for the same (e.g., constraint satisfaction may require solution of an optimization problem). Efficient algorithms are developed for optimal network synthesis and parameter estimation involving the incorporation of local measurements especially while modeling distributed process systems. The proposed algorithms for solving both the inverse and forward problems are tested by using noisy steady-state and dynamic training data. Furthermore, most data-driven approaches for modeling complex nonlinear dynamic systems with respect to available measurements may not provide any information about the ‘true’ data. The optimal MECNNs developed in this work yields the system truth with minimum bias when the noise in the training data is represented by a Gaussian distribution with time-invariant as well as time-varying mean.

Unlike steady-state, developing a fully data-driven dynamic modeling approach by exactly satisfying the mass and energy balance equations can be significantly challenging, since conservation of mass/energy during transience is difficult to satisfy, in general, due to insufficient information about the holdup of a system. Efficient algorithms are also developed in this work for estimating optimal parameters for dynamic MECNNs represented by hybrid series/parallel all-nonlinear static-dynamic neural network models (developed as part of our previous work⁶), which have been shown to perform significantly superior to many existing state-of-the-art approaches in terms of both computational expense as well as predictive accuracy, while modeling many complex nonlinear dynamic chemical process systems⁶. The proposed structures and algorithms are applied to model three nonlinear dynamic chemical processes, namely a distributed superheater system, a nonisothermal continuous stirred tank reactor (CSTR) involving exothermic reaction, i.e., generation of heat within the system and an electrically heated tubular reactor where one form of energy (electric) gets transformed to another (heat). It has been observed that the outputs from the MECNN exactly satisfy mass and energy conservation, even though the data used for training the network violate the same. In addition, the model output exactly satisfy mass and energy conservation thus making them particularly attractive for dynamic optimization of chemical processes.

References

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