Data-Based Modeling of a Nonexplicit Two-Time Scale Process via Multiple Time-Scale Recurrent Neural Networks

Abstract

Modern chemical process plants are typically very complex in nature due to the various material and energy recycling streams, including the implementation of process intensification in order to improve the sustainability factor. Looking at each individual unit operation, there are inherent nonlinear properties that may often involve physical and chemical phenomena occurring on different time scales. In addition, there exist chemical processes that also inherently have dynamics that are multi time-scale in nature. However, designing the control system for those integrated and intensified processes poses significant difficulties because they naturally lead to the dynamics of the network having multiple timescale behaviors and a reduced number of degrees of freedom. The status quo approach to handle multiple time scales would be to separate the plant-wide dynamics into their fast and slow components and implement a hierarchical control structure, but the current practices would lead to computational issues when being applied to model-based controllers due to the inversion of ill-conditioned and stiff differential algebraic equation models under large time-scale separation. To address this issue, this study proposes an alternative approach to modeling multi time-scale processes based on the use of multiple time-scale recurrent neural networks (MTRNNs). The analysis is demonstrated via a benchmark multi time-scale continuous stirred tank reactor (CSTR) case study, using input−output data generated via simulation of nonlinear dynamical equations of the CSTR with large parameters (reciprocal of the singular perturbation small parameter) in the form of 1/ε as the large heat transfer coefficient. The MTRNN model is constructed with groups of neuronal nodes grouped together based on their assigned time constant (also known as decay rate), which leads to an improved prediction performance when compared to other common modeling methods. The prediction performance of the proposed MTRNN model when applied to the multi time-scale CSTR results in an R 2 value of 0.9997, in addition to an average of 75 times lower root mean square error when compared to that of the nonlinear autoregressive network with exogenous inputs (NARX) and transfer function methods, implying its higher potential efficacy in modeling complex multi timescale processes.

Control of the Multi-Timescale Process Using Multiple Timescale Recurrent Neural Network-Based Model Predictive Control

“…The MTRNN model of the nonexplicit two-timescale CSTR is developed in our previous work, 25 whereby the training of the network is done through 70,000 input−output CSTR data, sampled from MATLAB for 0.02 sampling instants. The data is generated through perturbation of inputs using a pseudorandom binary signal.…”

“…With the completion of controller optimization and the evaluation of the controller robustness in previous sections, this section attempts to compare the closed-loop response performance in terms of tracking the setpoint trajectory as per (10) between the proposed MTRNN-based NNPC and the conventional NARX-based NNPC. The comparison of prediction performance has been carried out in our previous published paper, 25 whereby the application of MTRNN to model the CSTR supersedes the performance of the NARX modeling method by producing a 75 times lower RMSE in addition to an R 2 value of 0.9997. To ensure fair comparison, the conventional NARX-based NNPC is subjected to a similar concept of controller optimization as the MTRNN-based NNPC that is discussed in Section 4.3 prior to comparing their closed-loop response.…”

“…These components of the MTRNN are grouped based on their assigned time constant, τ also known as the decay rate. This is the unique feature that allows temporal hierarchy to be represented by the MTRNN hence, giving rise to its capability in handling networked processes that have multi-timescale behaviors. , The RNN nature of the MTRNN represents temporal processing of the brain, such that similarities can be drawn whereby neural activity is determined by the past history of neural states. The outputs of the neurons in MTRNN are used as feedback inputs for other neurons.…”

“…Arguably, the ability to capture the dynamics of a multi-timescale process accurately is a prerequisite to the reliable design and operation of a well-tuned controller. In our previous work, it is demonstrated that multiple timescale recurrent neural network (MTRNN) architecture is a feasible option in modeling a multi-time scaled process, without forcing architectural hierarchy onto the system. Instead, functional hierarchy emerges through the form of self-organization of the system’s timescale that is based on two distinct types of neurons, each with different time properties .…”

Semantic Hybrid Signal Temporal Logic Learning-Based Data-Driven Anomaly Detection in the Textile Process

“…Therefore, state monitoring is a technical process that involves monitoring operation variables to determine whether abnormal changes occur in relevant production links. The monitoring process should be continuous and should be conducted online to ensure that anomalies can be detected and used to guide subsequent maintenance operations [25].…”