White-box Machine learning approaches to identify governing equations for overall dynamics of manufacturing systems: A case study on distillation column

Subramanian, Renganathan; Moar, Raghav Rajesh; Singh, Shweta

doi:10.1016/j.mlwa.2020.100014

Cited by 12 publications

(12 citation statements)

References 33 publications

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“…Both the symbolic and sparse regression techniques explore the governing equations within an ample space of possibly non-linear mathematical terms. The comparisons and discussions between them can be found in a recent work [34], which identifies dynamical equations of a distillation column.…”

Section: Sparse Regressionmentioning

confidence: 99%

Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems

Zhou¹,

Pan²

2022

Preprint

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Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by designing the Mathematical Operation Network (MathONet) with a deep neural network-like hierarchical structure. Specifically, the MathONet is stacked by several layers of unary operations (e.g. sin, cos, log) and binary operations (e.g. +, −, ×), respectively. An initialized MathONet is typically regarded as a supergraph with a redundant structure, a sub-graph of which can yield the governing equation. We develop a sparse group Bayesian learning algorithm to extract the sub-graph by employing structurally constructed priors over the redundant mathematical operations. By demonstrating on the chaotic Lorenz system, Lotka-Volterra system, and Kolmogorov-Petrovsky-Piskunov system, the proposed method can discover the ordinary differential equations (ODEs) and partial differential equations (PDEs) from the observations given limited mathematical operations, without any prior knowledge on possible expressions of the ODEs and PDEs.Preprint. Under review.

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Section: Sparse Regressionmentioning

confidence: 99%

Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems

Zhou¹,

Pan²

2022

Preprint

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“…As an alternative, the reference data can be obtained from rigorous dynamic simulations based on first-principles models, which inherently have a much wider range of applicability and do not suffer from the above-mentioned limitations. The idea of using process simulators for data generation in machine learning applications has been used commonly in the literature (see refs , , and for example).…”

Section: Neural Network Modeling Of a Single Pipelinementioning

confidence: 99%

Dynamic Simulation of Natural Gas Transmission Pipeline Systems through Autoregressive Neural Networks

Fakhroleslam

Boozarjomehry

Sahlodin

et al. 2021

Ind. Eng. Chem. Res.

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Transmission of natural gas from its sources to end users in various geographical locations is carried out mostly by natural gas transmission pipeline networks (NGTNs). Effective design and operation of NGTNs requires insights into their steady-state and, particularly, dynamic behavior. This, in turn, calls for efficient computer-aided approaches furnished with accurate mathematical models. The conventional mathematical methods for the dynamic simulation of NGTNs are computationally intensive. In this paper, the use of autoregressive neural networks for cost-effective dynamic simulation of NGTNs is proposed. Considering the length, diameter, roughness, and elevation as the main characteristics of a single pipeline, a neural network pipeline (NNPL) is designed and trained based on the data from a dynamic process simulator. Arbitrary NGTNs can then be easily constructed by connecting the developed NNPLs as the building blocks. The performance of the NNPL network is demonstrated through a number of benchmark pipeline systems, where a very good agreement with the benchmark results is found.

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“…Finally, Ref. [35] aimed to identify the governing equations regarding a distillation column using a white-box machine-learning approach.…”

Section: Related Work 21 Distillation Process-related Modelsmentioning

confidence: 99%

Cyber-Physical LPG Debutanizer Distillation Columns: Machine-Learning-Based Soft Sensors for Product Quality Monitoring

Rožanec

Trajkova

et al. 2021

Applied Sciences

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Refineries execute a series of interlinked processes, where the product of one unit serves as the input to another process. Potential failures within these processes affect the quality of the end products, operational efficiency, and revenue of the entire refinery. In this context, implementation of a real-time cognitive module, referring to predictive machine learning models, enables the provision of equipment state monitoring services and the generation of decision-making for equipment operations. In this paper, we propose two machine learning models: (1) to forecast the amount of pentane (C5) content in the final product mixture; (2) to identify if C5 content exceeds the specification thresholds for the final product quality. We validate our approach using a use case from a real-world refinery. In addition, we develop a visualization to assess which features are considered most important during feature selection, and later by the machine learning models. Finally, we provide insights on the sensor values in the dataset, which help to identify the operational conditions for using such machine learning models.

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White-box Machine learning approaches to identify governing equations for overall dynamics of manufacturing systems: A case study on distillation column

Cited by 12 publications

References 33 publications

Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems

Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems

Dynamic Simulation of Natural Gas Transmission Pipeline Systems through Autoregressive Neural Networks

Cyber-Physical LPG Debutanizer Distillation Columns: Machine-Learning-Based Soft Sensors for Product Quality Monitoring

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